JP4145672B2 - Image forming apparatus - Google Patents

Description

【０１０５】
なお、本実施の形態では、フィルタ２３の異物除去能力の点から、インクエンプティ時におけるインク吸収体２２による臨界圧力Ｐ_E（以下、インク吸収体の臨界圧力と記す場合がある）及びフィルタ２３による臨界圧力Ｐｍ（以下、フィルタの臨界圧力と記す場合がある）が、Ｐｍ＞Ｐ_Eを満たすように設定されている。そして、本実施の形態では、図６に示すように上記臨界圧力Ｐ_E、Ｐｍ、並びに、インク供給経路３の圧力損失Ｐμ、タンク水頭圧Ｐｉが、Ｐｍ＞Ｐ_E＞Ｐμ＋Ｐｉを満たすように設定されている。但し、本実施の形態はこれに限定されるものではなく、インク供給系の設定の仕方によっては、上記大小関係が逆転する場合、もしくはフィルタ２３を用いない場合がある。
【０１０６】
また、後で詳細説明するが、発生負圧の実測値を流体力学理論に基づき詳細検討した結果、インク上限時安定負圧Ｐｕは、インクの粘性抵抗による、流路すなわちインク供給経路３の圧力損失Ｐμに起因し、またインク下限時安定負圧ＰＬは、インクの表面張力ηに基づくものであることが判明した。
【０１０７】
なお、上記測定においては、インクの保持力は、インクカートリッジ２０の高さ、インク吸収体２２（フォーム材）のセル２２ａのばらつき、及びインクカートリッジ２０にかかる振動を考慮して定める必要がある。これは、保持力が足りないと、特にインク上限時にインクカートリッジ２０の着脱時にインクが不用意に漏れるといった問題が生じるためである。
【０１０８】
例えば、インクカートリッジ２０の高さが３４ｍｍであれば、安全率を２とすると、インクの比重γは約１．０であるため、保持力は、水頭で６８（＝３４×２）ｍｍ、つまり０．６７ｋＰａ必要である。また、一般的に広く用いられているインクカートリッジの高さは概ね４０ｍｍ以下であり、このことから、０．８ｋＰａのインクの水頭圧に耐えることが必要とされる。
【０１０９】
インクの保持力は表面張力ηに基づく毛管圧力であり、圧縮時のセル径を、直径ｄ（ｍ）の円形状の開口部とみなすと、圧縮時のインク吸収体２２（フォーム材）の実装セル密度Ｍ（Ｍ＝Ｎ・Ｒ；但し、厳密にはＭ≒Ｎ・Ｒ）（個／ｍ）より、圧縮時のセル径ｄ（ｍ）は、以下の関係式（３）
ｄ＝１／（Ｎ・Ｒ） ・・・（３）
で表されることから、その臨界圧力Ｐ_Eと、セル密度Ｎ（個／ｍ）及び圧縮率（Ｒ）との関係は、インクの表面張力をη（Ｎ／ｍ）とすると、前記一般式（１）及び上記関係式（３）から、下記関係式（４）
Ｐ_E＝４・η・（Ｎ・Ｒ） ・・・（４）
で表される。したがって、インク下限時安定負圧ＰＬは、実装セル密度Ｍ（Ｍ＝Ｎ・Ｒ）が７．８７×１０³（個／ｍ）以上（すなわち、２００個／inch以上）であれば、水頭で０．８６ｋＰａ、８９ｍｍ以上の保持力が得られるので、インクカートリッジ２０の着脱時にインクが不用意に漏れるといった問題が生じることを防ぐことができる。
【０１１０】
また、インクを連続吐出するときに、インク供給系の負圧（インク吸収体２２もしくはフィルタ２３の臨界圧力）は、安全率を考慮すると、２．０ｋＰａ以下でなければ、インク供給系に発生する負圧にて、インクが供給不足になり、吐出ノズル１ａの先端部（ノズル先端）よりインク液面が後退しすぎて空気を吸入してしまうという問題が生じ、インクの安定供給ができなくなる。
【０１１１】
そこで、実装セル密度Ｍが１２．６×１０³（個／ｍ）以下（すなわち、３２０個／inch以下）であれば、インク供給系の負圧は１．５ｋＰａ以下となり、インクを連続吐出するときにも、マージンを持ってインクの安定供給が可能になる。
【０１１２】
また、インクカートリッジ２０内面のインク収納体積（充填インク体積）に対して実際に使用（吐出）可能となるインク容積の比を効率τ（タンク効率）とすると、図１０に示すように、効率τ（％）は、Ｒの値、言い換えればＮ・Ｒの値が増加するのに伴って低下し、図１１に示すように、実装セル密度Ｍ（Ｍ＝Ｎ・Ｒ）が１２．６×１０³（個／ｍ）（すなわち３２０個／inch）になると大きく低下し始める。したがって、インクカートリッジ２０の体積を効率よく活用する条件としては、実装セル密度Ｍ（Ｍ＝Ｎ・Ｒ）が１２．６×１０³（個／ｍ）以下となる。
【０１１３】
よって、上記インクカートリッジ２０を、実装セル密度Ｍ（個／ｍ）（Ｍ＝Ｎ・Ｒ）が、７．８７×１０³≦Ｍ≦１２．６×１０³を満足するように設計することで、インクカートリッジ２０の着脱時にインクが不用意に漏れるといった問題が生じることを防ぐことができると共に、インクを連続吐出するときにも、マージンを持ってインクの安定供給が可能になり、かつ、インクカートリッジ２０の体積を効率よく活用することができる。さらに、上記の構成によれば７．８７×１０³以上でも１２．６×１０³以下であればよいので、インク吸収体２２の設計における選択の幅を広げることができる。
【０１１４】
なお、これらは理論値であるが、実測値においても、これを満たしていることが、確認された。すなわち、前記表１において、実装セル密度Ｍ＝Ｎ・Ｒが７．８７×１０³（個／ｍ）のとき、実測安定負圧であるインク下限時安定負圧ＰＬが０．８６ｋＰａ以上となっているとともに、実装セル密度Ｍ（Ｍ＝Ｎ・Ｒ）が１２．６×１０³（個／ｍ）以下であれば、インク供給系の負圧は１．５ｋＰａ以下となっており、インクを連続吐出するときにも、マージンを持ってインクの安定供給が可能になる。なお、この実測安定負圧であるインク下限時安定負圧ＰＬは、インクのメニスカスがいかなる負圧に耐え得るかを示している。
【０１１５】
次に、インク下限時安定負圧ＰＬ及びインク上限時安定負圧Ｐｕに対して考察を加える。なお、インク上限時安定負圧Ｐｕとは、インクが流れているときの負圧を表したものである。
【０１１６】
まず、正規化するために、圧縮率Ｒ＝５．５、流量Ｑ＝８．１７ｎｍ³／ｓ（０．４９ｃｃ／ｍｉｎ）におけるインク上限時安定負圧Ｐｕ＝０．６２ｋＰａに対して、各データにおけるインク上限時安定負圧Ｐｕを正規化した値を、始点比Ｒｓとする。また、Ｒ２は、圧縮率Ｒ²について、圧縮率Ｒ＝５．５に対して正規化したものである。
【０１１７】
一方、圧縮率Ｒ＝５．５、流量Ｑ＝８．１７ｎｍ³／ｓ（０．４９ｃｃ／ｍｉｎ）におけるインク下限時安定負圧ＰＬ＝０．９９ｋＰａに対して、各データにおけるインク下限時安定負圧ＰＬを正規化した値を、終点比Ｒｅとする。また、Ｒ１は、圧縮率Ｒについて、圧縮率Ｒ＝５．５に対して正規化したものである。
【０１１８】
ここで、それぞれ、始点においてＲｓ／Ｒ２を算出し、終点においてＲｅ／Ｒ１を算出すると、表１より、それぞれ略１であることがわかる。したがって、インク上限時安定負圧Ｐｕは圧縮率Ｒの２乗に比例し、インク下限時安定負圧ＰＬは圧縮率Ｒに比例することがわかる。
【０１１９】
以上の結果から、さらに、インク及びインク吸収体２２（フォーム材）の設計指針を詳しく得るために、これらの理論付けを行い、検討を加えた。以下に、詳細に説明する。
【０１２０】
先ず、インクカートリッジ２０内のインクが上限まで充填されている時の安定負圧（インク上限時安定負圧Ｐｕ）と圧縮率Ｒとの関係について以下に考察する。
【０１２１】
インクカートリッジ２０内のインクが上限まで充填されている時、すなわち、インクカートリッジ２０にインクが満載されている時には、インク吸収体２２（フォーム材）の各セル２２ａを円形の管路とみなし、該管路の圧力差ΔＰ（管路始点の圧力Ｐ１−管路終点の圧力Ｐ２）、すなわち、粘性抵抗による管路の圧力損失Ｐμによって管路内の液（インク）が流れていると想定することができる。図１２に示すように円形の管路（各セル２２３ａを円形の管路とみなし、該管路の圧力差ΔＰ（管路始点の圧力Ｐ１−管路終点の圧力Ｐ２）、すなわち、粘性抵抗による管路の圧力損失Ｐμによって管路内の液（インク）が流れていると想定することができる。図１２に示すように円形の管路（各セル２２ａ）を流れる流量（Ｑ）の理論値、つまり、管路１本当たりを流れるインクの流量の理論値を流量Ｑｉ（ｍ³／ｓ）とすると、該流量Ｑｉ（ｍ³／ｓ）は、下記一般式（５）
Ｑｉ＝Ｐｕ・π・ｄ⁴／（１２８・μ・Ｌ） ・・・（５）
によって定義される。ここで、Ｐｕはインクの粘性抵抗による管路の圧力損失（Ｐａ）であるインク上限時安定負圧、ｄは管路直径（ｍ）、μはインクの粘度（Ｐａ・ｓ）、Ｌは管路の流路長（ｍ）である。
【０１２２】
ここで、ｄ（ｍ）を圧縮時のセル径とみなすと、圧縮時のインク吸収体２２（フォーム材）の実装セル密度Ｍ（個／ｍ）（Ｍ＝Ｎ・Ｒ）より、圧縮時のセル径ｄ（ｍ）は、前記したように、下記関係式（３）
ｄ＝１／（Ｎ・Ｒ） ・・・（３）
で表される。
【０１２３】
このとき、インク吸収体２２（フォーム材）は圧縮されてインクカートリッジ２０内に収容されているので、インク吸収体２２（フォーム材）の各セル２２ａは、図１３に示すように、最密状態であると考えられる。したがって、圧縮時のフォーム材下端におけるセル２２ａは、図１３に示すように、最密状態であると考えられる。したがって、圧縮時のフォーム材下端におけるセル２２ａの総数であるセル総数Ｎｄ（個）は、下記関係式（６）
Ｎｄ＝（２／√３）・Ｓ／（ｄ²） ・・・（６）
で表される。なお、式（６）中、Ｓは、上記インクカートリッ２０（インクタンク２１）に圧縮されて収納されたときのインク吸収体２２（フォーム材）の断面積（幅Ｗ×奥行Ｖ）を示す。
【０１２４】
したがって、上記関係式（６）で表される数のセル２２ａからなる直径一定の円柱状の流路を想定した場合、該円柱状の流路を流れるインクの全流量Ｑｔ（ｍ³／ｓ）（Ｑｔ＝Ｑｉ・Ｎｄ；理論値）は、上記一般式（５）並びに関係式（３）・（６）より、以下の関係式（７）

(但し、式中、係数Ａ＝２．８３×１０^-2を表す)
で表される。従って、上記全流量Ｑｔは圧縮時のインク吸収体２２（フォーム材）の実装セル密度Ｍ（個／ｍ）（Ｍ＝Ｎ・Ｒ）の２乗に反比例していることがわかる。
【０１２５】
上記関係式（７）により、図１４に示す円柱状の流路を想定した理論値である全流量Ｑｔを求めた結果を、表２に示す。
【０１２６】
【表２】

【０１２７】
実際のインク吸収体２２内（フォーム材内部）では、図１４に示すように、球形状又は多面体上のセル２２ａが数珠状に連通している。このため、この連珠状の流路により、実効の直径は上記理論値よりも小さな値となる。そこで、セル径を用いて求めた上記全流量Ｑｔ（理論値）の実際の流量Ｑ（実測流量）に対する平均倍率を求め、これを補正係数ｋとする。つまり、Ｑｔ／Ｑ≒ｋとすると、表２の場合、補正係数ｋは１３．７５である。
【０１２８】
ここで、図１５に示すように、直径をｄｍ、その中心位置をＸ＝０とした球状流路を積分して求めた正規化流路抵抗をＲｄ、円柱状流路の正規化流路抵抗をＲｍとした抵抗比Ｒｄ／Ｒｍを、図１６に示す。図１６に示すように、Ｘが０近傍の場合にはｒｄ／Ｒｍ≒１であるが、Ｘがｄｍ／２（図１５参照）に近づくに伴ってＲｄ／Ｒｍが上昇することがわかる。この検討より、補正係数ｋ＝１３．７５を考察すると、正規化セル径を１としたとき、Ｘ＝０．４８８の位置でＲｄ／Ｒｍ＝１３．７５となる。これは流路を、正規化直径０．２１で隣接セル２２ａ同士が連通しているモデル化することができることを意味し、この検討からも実測値より決定した補正係数ｋの値が適切であると言える。
【０１２９】
よって、上記補正係数ｋを用いて、算出流量Ｑｃ（ｍ³／ｓ）は、下記関係式（８）
Ｑｃ＝Ｑｔ／ｋ ・・・（８）
(但し、式中、係数ｋ＝１３．７５を表す)
或いは、上記関係式（８）に関係式（７）を代入して、下記関係式（９）
Ｑｃ＝（Ａ／ｋ）・Ｐｕ・Ｓ／[μ・Ｌ・（Ｎ・Ｒ）²] ・・・（９）
(但し、式中、係数（Ａ／ｋ）＝２．０６×１０^-3を表す)
として求めることができる。
【０１３０】
ここで、表２より、各データにおいて、Ｑ／Ｑｃは略１であるので、補正係数ｋを用いることにより、
Ｑ＝（Ａ／ｋ）・Ｐｕ・Ｓ・／[μ・Ｌ・（Ｎ・Ｒ）²]
により、精度よく流量Ｑを求めることができることがわかる。
【０１３１】
また、粘性抵抗による管路の圧力損失（圧力差ΔＰ）の理論値Ｐｖ（Ｐａ）、は、実測流量Ｑから、
Ｐｖ＝（１／Ａ）・[μ・Ｌ・（Ｎ・Ｒ）²／Ｓ]・Ｑ
(但し、式中、係数Ａ＝２．８３×１０^-2を表す）
で表される。
【０１３２】
さらに、関係式（８）、（９）と同様に上記の補正係数ｋ＝１３．７５を用いた、粘性抵抗による管路の圧力損失（圧力差ΔＰ）、つまり、粘性抵抗による管路の圧力損失（圧力差ΔＰ）の算出値をＰμ（算出圧力差）とすると、該Ｐμ（Ｐａ）は、

(但し、式中、（ｋ／Ａ）＝４８５を表す)
で表される。
【０１３３】
ここで、上記関係式（１０）を用いて、管路の圧力損失（圧力差ΔＰ）の理論値Ｐｖ及び算出値Ｐμを、実測流量Ｑより求めた結果を、表３に示す。なお、表３中、流量ｑは、管路１本当たりの実測流量を示す。
【０１３４】
【表３】

【０１３５】
ここで、管路の圧力損失（圧力差ΔＰ）の算出値Ｐμ（算出圧力差）とインク上限時安定負圧Ｐｕとの比をＰμ／Ｐｕとすると略１である。
【０１３６】
また、図１７に、表２と表３とをグラフ化して示す。図１７に示すように、理論値からの算出値（算出圧力差Ｐμ）による安定負圧は、実際に測定した安定負圧（インク上限時安定負圧Ｐｕ）とよく一致していることがわかる。また、インク上限時安定負圧Ｐｕはインクの粘度に基づく圧力損失に起因し、補正係数を用いて精度よくインク上限時安定負圧Ｐｕを求めることができることがわかる。
【０１３７】
次に、インクカートリッジ２０内のインクが下限までしか充填されていない時の安定負圧（インク下限時安定負圧ＰＬ）と圧縮率Ｒとの関係について以下に考察する。
【０１３８】
インクカートリッジ２０内のインクが下限までしか充填されていない時、すなわちインクカートリッジ２０内のインクが無くなる直前の状態は、インク吸収体２２（フォーム材）の下端のセル２２ａを毛管とみなすことができる。
【０１３９】
したがって、図１８（液体に正圧が印加時）及び図１９（液体に負圧が印加時）に示すように、毛管内の液面（インクのメニスカス）の臨界圧力Ｐｔ（Ｐａ）はセル２２ａを毛管とみなすことができる。
【０１４０】
したがって、図１８及び図１９に示すように、毛管内の液面（インクのメニスカス）の臨界圧力Ｐｔ（Ｐａ）、つまり、インクエンプティ時におけるインク吸収体２２による臨界圧力Ｐ_E（＝Ｐｔ）は、下記一般式（１１）
Ｐｔ＝２・η・ｃｏｓθ／（ｄ／２） ・・・（１１）
によって定義される。ここで、ηは管内の液（インク）の表面張力（Ｎ／ｍ）であり、θは毛管内の液面（インクのメニスカス）の、管との接触角であり、ｄは毛管の直径（ｍ）である。なお、インク吸収体２２はインクに対して濡れ性の良いものが選ばれるので、θは略０とみなすことができる。したがって、上記一般式（１１）は、下記一般式（１２）
Ｐｔ＝４・η／ｄ ・・・（１２）
（厳密にはＰｔ≒４・η／ｄ）として表すことができる。
【０１４１】
したがって、前記関係式（３）並びに上記一般式（１２）より、インク吸収体２２による臨界圧力Ｐ_E（＝Ｐｔ）は、前記関係式（４）
Ｐ_E＝４・η・（Ｎ・Ｒ） ・・・（４）
で表される。
【０１４２】
この関係式（４）より、インク吸収体２２の液面（インクのメニスカス）の臨界圧力Ｐｔを求めた結果を、表４に示す。
【０１４３】
【表４】

【０１４４】
上記関係式（４）より求めた理論値臨界圧力Ｐｘの、実際の圧力であるインク下限時安定負圧ＰＬに対する比Ｐｘ／ＰＬは、略１であるので、インク下限時安定負圧ＰＬはインクの表面張力に基づく毛管の臨界圧力に起因しているという理論の正しさを示すとともに、精度よくインク下限時安定負圧ＰＬを求めることができることがわかる。
【０１４５】
インクカートリッジ２０の着脱時にインクが不用意に漏れるといった問題が生じることを防ぐ条件としては、インク吸収体２２（フォーム材）の保持力、つまり、表面張力ηの液体でインクのメニスカスを形成する、圧縮時のセル２２ａの大きさ（セル径）が１／（Ｎ・Ｒ）のインク吸収体２２（フォーム材）のセル２２ａにおける臨界圧力である、インク吸収体２２（フォーム材）の下端のセル２２ａ（毛管）内の液面（インクのメニスカス）の臨界圧力Ｐ_E（Ｐａ）が、インクの水頭圧よりも大きいことが要求される。
【０１４６】
したがって、インクカートリッジ２０において、インクの比重をγ、任意の姿勢でとり得るインクタンク２１のインク供給口２４に対する鉛直方向の最大高さのインクの水頭高さをｈ（ｍ）とすると、インクの水頭圧は９．８×１０³・γ・ｈ（Ｐａ）で表されるため、上記関係式（４）における臨界圧力Ｐ_E（Ｐａ）は、以下の条件
４・η・（Ｎ・Ｒ）＞９．８×１０³・γ・ｈ
を満足することが要求される。すなわち、インクカートリッジ２０の着脱時にインクが不用意に漏れるといった問題が生じることを防ぐためには、下記関係式（１３）
η・Ｎ・Ｒ・Ｂ＞γ・ｈ ・・・（１３）
(但し、式中、係数Ｂ＝４．０８×１０^-4を表す)
を満足することが必要である。
【０１４７】
また、インクカートリッジ２０内に収納された状態でのインク吸収体２２（フォーム材）のセル密度、つまり実装セル密度Ｍ（個／ｍ）（Ｍ＝Ｎ・Ｒ）は、例えばセル密度Ｎ＝１５７５（個／ｍ）（＝４０個／inch）を圧縮率Ｒ＝５で圧縮加工して得られたインク吸収体２２（フォーム材）をインクカートリッジ２０に収納することにより該インク吸収体２２（フォーム材）がさらに１０％の圧縮を受けるとき、
Ｍ＝１５７５×５．５×１．１＝９５２８（個／ｍ） (＝２４２個／inch)
であり、上記関係式（１３）に実装セル密度Ｍ（個／ｍ）を代入すると、下記関係式（１４）
η・Ｍ・Ｂ＞γ・ｈ ・・・（１４）
(但し、式中、係数Ｂ＝４．０８×１０^-4を表す)
となる。なお、実装セル密度Ｍは、実測値を用いてもよい。
【０１４８】
インク供給口２４に対するインクの水頭高さｈ（ｍ）、つまり、任意の姿勢でとり得るインクタンク２１のインク供給口２４に対する鉛直方向の最大高さのインクの水頭高さｈ（ｍ）は、通常の姿勢においてはインク吸収体２２（フォーム材）或いはインクカートリッジ２０内壁の高さとすればよい。
【０１４９】
ハンドリングに配慮する必要がある場合は、インクカートリッジ２０を傾けた姿勢も含めてとり得るインク供給口２４に対する鉛直方向の最大高さのインクの水頭高さとする。
【０１５０】
また、セル径の分布等を考慮すると、安全率を２倍程度以上とすることが望ましく、よって、下記関係式（１５）
η・Ｎ・Ｒ・Ｂ＞２・γ・ｈ ・・・（１５）
(但し、式中、係数Ｂ＝４．０８×１０^-4を表す)
又は、下記関係式（１６）
η・Ｍ・Ｂ＞２・γ・ｈ ・・・（１６）
(但し、式中、係数Ｂ＝４．０８×１０^-4を表す)
を満足するように上記インクカートリッジ２０を設計することが望ましい。
【０１５１】
一般的に、インクカートリッジの高さは、インクレベルの変動への配慮により、前記したように概ね４０ｍｍ以下が広く実用化されている。このため、安全率を２とすると、インク吸収体（フォーム材）のセル（開口部）における具体的な臨界圧力は、前記したように０．８ｋＰａ（０．０８ｍＨ₂Ｏ）を満足することが望ましい。よって、上記インク吸収体２２（フォーム材）のセル２２ａにおける具体的な臨界圧力Ｐ_E（Ｐａ）は、Ｐ_E≧８００の関係を満足することが望ましい。
【０１５２】
よって、前記関係式（４）から、下記関係式（１７）
４・η・Ｎ・Ｒ≧８００ ・・・（１７）
又は、下記関係式（１８）
４・η・Ｍ≧８００ ・・・（１８）
の関係を満足することにより、インク吸収体２２（フォーム材）のセル２２ａにおける臨界圧力Ｐ_E（Ｐａ）、つまり、インク吸収体２２（フォーム材）の保持力を、０．８ｋＰａ（８００Ｐａ）以上に保つことができ、インクカートリッジ２０の着脱時にインクが不用意に漏れるといった問題が生じることを防ぐことができる。
【０１５３】
なお、図１７から、上記関係式（４）より求められる理論値（理論値臨界圧力Ｐｘ）による負圧が、実際に測定した負圧（インク下限時安定負圧ＰＬ）とよく一致していることがわかる。また、実装セル密度Ｍ（Ｍ＝Ｎ・Ｒ）の各設定時における負圧を表４に示す。
【０１５４】
次に、印字ヘッド１における吐出ノズル（インクノズル部）１ａのインク滴出によるオリフィスのインク後退による臨界圧力Ｐｎ（以下、ノズルの臨界圧力と記す場合がある）を求める。
【０１５５】
なお、オリフィスの形状は、図２０に示すように、円管の吐出ノズルの径を２０μｍ、長さを２０μｍとし、吐出ノズル１ａの先端部（ノズル先端）から、頂角９０度、頂部円径２０μｍの円錐台形が延出していると仮定する。
【０１５６】
印字ヘッド１における吐出ノズル１ａのインク吐出周波数を８０００ｐｐｓ、ノズル数を６４本に設定したときのインク流量ＱがＱ＝８．１７ｎｍ³／ｓ（＝０．４９ｃｃ／ｍｉｎ）であったとき、インクの１滴は、
（８.１７×１０^-9）／８０００／６４＝１．６×１０^-14（ｍ³） （＝１６ｐＬ）
となる。
【０１５７】
この場合にインクを１滴吐出したときの、オリフィス内のインクの後退による液面（インクのメニスカス）位置における円錐部の直径Ｈを表５に示す。なお、表５において、円錐部の直径Ｈ＝２０μｍとは、エキシマレーザ加工等により、ノズル先端のストレート部が充分に長い場合（図２０参照）を表している。また、表５は、インク１滴が１．６×１０^-14（ｍ³）(＝１６ｐＬ)の場合における、ノズル先端でのインクのメニスカスの過渡振動を考慮しない場合と、図２１（ａ）〜（ｈ）に示すようなノズル先端でのインクメニスカスの過渡振動等により、オリフィス内のインクが、インク吐出量に対して２倍後退した場合を示している。なお、図２１（ａ）〜（ｈ）は、インクが吐出ノズル１ａから吐出する状態を順に示す断面図である。例えば、６００ｄｐｉのインクジェットプリンタでは、１．６×１０^-14〜２．０×１０^-14（ｍ³）（＝１６〜２０ｐＬ）のインク滴が要求される。
【０１５８】
ノズル（本実施の形態においては吐出ノズル１ａ）の臨界圧力Ｐｎ（Ｐａ）は、前記一般式（１２）に上記円錐部の直径Ｈ（ｍ）を代入して下記一般式（１９）
Ｐｎ＝４・η／Ｈ ・・・（１９）
（厳密にはＰｎ≒４・η／Ｈ）
により求めることができる。
【０１５９】
インクの供給不足を起こさない必須条件は（Ｐμ）＜（Ｐｎ）であり、吐出ノズル１ａの直径をＤ_N（ｍ）とすると、インクの供給不足を起こさないためには、前記関係式（１０）並びに上記一般式（１９）より、下記関係式（２０）
（ｋ／Ａ）・[μ・Ｌ・（Ｎ・Ｒ）²／Ｓ]・Ｑ＜４・η／Ｄ_N ・・・（２０）
(但し、式中、係数（ｋ／Ａ）＝４８５を表す)
を満足している必要がある。つまり、上記関係式（２０）を整理すれば、下記関係式（２１）
Ｃ・[μ・Ｌ・Ｑ・（Ｎ・Ｒ）²／Ｓ]＜η／Ｄ_N ・・・（２１）
(但し、式中、Ｃ＝（ｋ／Ａ）／４＝１２１を表す)
を満足している必要がある。
【０１６０】
また、実装セル密度Ｍ（個／ｍ）（Ｍ＝Ｎ・Ｒ）を上記関係式（２１）に適合すると、上記の必須条件は、
Ｃ・[μ・Ｌ・Ｑ・Ｍ²／Ｓ]＜η／Ｄ_N ・・・（２２）
(但し、式中、Ｃ＝（ｋ／Ａ）／４＝１２１を表す)
となる。
【０１６１】
上記一般式（１９）を用いて算出した、各設定条件における吐出ノズル１ａの臨界圧力Ｐｎを表５に示す。
【０１６２】
【表５】

【０１６３】
表５から、インクを連続吐出するときに、インク供給系の負圧（インク吸収体２２もしくはフィルタ２３の臨界圧力）は、安全率、すなわち、過渡振動及び流量の誤差を考慮すると、約２．０ｋＰａ以下であれば、インク吐出後にノズル先端のインクのメニスカスが後退した状態でインクのメニスカスにより生じるインクを吸引する上記臨界圧力Ｐｎが、インク供給系の負圧より大きくなり、インクの連続吐出を行った場合でも、必要量のインクを安定供給することが可能となることがわかる。
【０１６４】
したがって、インク供給系の負圧が２．０ｋＰａ以下であれば、インク供給系に発生する負圧にて、インクが供給不足になり、ノズル先端よりインク液面（インクメニスカス）が後退しすぎて空気を吸入してしまうという問題が発生することを防止することができ、インクを連続吐出するときにも、インクの安定供給が可能になる。
【０１６５】
なお、インク供給系に生じる負圧が２．０ｋＰａ以下であれば、インク供給系に発生する負圧に打ち勝ってメニスカスの表面張力によりインクを吸引し、メニスカスが前進してインク補給がなされ、インク供給系の負圧とメニスカスの吸引力とが平衡した時点でインク補給が終了する。逆に、インク供給系に発生する負圧がメニスカスの臨界圧より大きいとメニスカスは後退し、印字ヘッド１内に空気を吸い込み、吐出不良となる。
【０１６６】
また、インクカートリッジ２０における充填インク体積に対する、吐出に用いることができたインク体積の比である効率τ（タンク効率）を考慮すると、実装セル密度Ｍの上限は、１２．６×１０³（個／ｍ）（＝３２０個／inch）程度であり、インクの臨界圧力、つまり、インクの表面張力ηに基づくインク吸収体２２の液面の臨界圧力Ｐ_Eによって決まるインク下限時安定負圧ＰＬ（Ｐａ）は、表１から、該セル密度において、１．５ｋＰａであり、印字ヘッド１ａの水頭及びインクタンク２１の水頭は通常４０ｍｍ程度に抑えて設定されるので、両者の合計（Ｐ_E＋Ｐi）からも約２．０ｋＰａの値が導き出される。
【０１６７】
以上の検討結果を整理すると、インク吸収体２２（フォーム材）のセル密度Ｎ及び圧縮率Ｒに要求される条件は以下の通りとなる。まず、前記関係式（１３）から、下記関係式（２３）
（Ｎ・Ｒ）＞γ・ｈ／（η・Ｂ） ・・（２３）
(但し、式中、係数Ｂ＝４．０８×１０^-4を表す)
が得られる。また、前記関係式（２１）から、
[η・Ｓ／（Ｃ・Ｄ_N・μ・Ｌ・Ｑ）]^0.5＞（Ｎ・Ｒ） ・・・(２４)
(但し、式中、係数Ｃ＝（ｋ／Ａ）／４＝１２１を表す)
が得られる。したがって、インク吸収体２２（フォーム材）のセル密度Ｎ及び圧縮率Ｒに要求される条件は、上記関係式（２３）・（２４）から、

(但し、式中、係数Ｂ＝４．０８×１０^-4、係数Ｃ＝１２１を表す)
となる。
【０１６８】
また、インク吸収体２２（フォーム材）の実装状態の実装セル密度Ｍ（Ｍ＝Ｎ・Ｒ）（個／ｍ）に要求される条件としては、上記と同様にして、前記関係式（１４）・（２２）から、
[η・Ｓ／（Ｃ・Ｄ_N・μ・Ｌ・Ｑ）]^0.5＞Ｍ＞γ・ｈ／（η・Ｂ）・・・（２６）
(但し、式中、係数Ｂ＝４．０８×１０^-4、係数Ｃ＝１２１を表す)
となる。よって、上記関係式（２５）又は（２６）を満足することにより、インクカートリッジ２０着脱時のインクの洩れを防止し、かつ、連続吐出時にインクを安定供給することが可能となる。
【０１６９】
なお、インクジェット記録装置に用いられるインクは、
・粘度μ＝０．０１５〜０.１５（Ｐａ・ｓ）
・インクの表面張力η＝０．０３〜０．０５（Ｎ／ｍ）
・インク吸収体２２（フォーム材）のセル密度Ｎ＝１．５７×１０³〜３．９４×１０³（個／ｍ） （＝４０〜１００個／inch）
が一般的である。
【０１７０】
そこで、例えば、異なる条件として、以下の条件
・粘度μ＝０．０１５（Ｐａ・ｓ）
・インクの表面張力η＝０．０４（Ｎ／ｍ）
・フォーム材のセル密度Ｎ＝３．１５×１０³（個／ｍ） (＝８０個／inch)を採用して検討を行った結果、条件を変更した場合においても上述した各式を満たすことが確認された。
【０１７１】
このように、フィルタを用いない場合、もしくは、フィルタを用いる場合でもフィルタの開口がインク吸収体２２（フォーム材）のセル２２ａよりも大きい場合には、インク吸収体２２におけるセル２２ａ（毛管）内の液面（インクのメニスカス）の臨界圧力Ｐ_E（Ｐａ）、つまり、インクエンプティ時におけるインク吸収体２２の臨界圧力Ｐ_E（Ｐａ）で、インク供給系に生じる負圧が決定される。
【０１７２】
しかしながら、フィルタの濾過性能を確保するためフィルタの開口をインク吸収体２２のセル２２ａよりも小さくした場合、あるいは、インク吸収体２２（フォーム材）を用いない場合には、フィルタによる臨界圧力Ｐｍ（Ｐａ）で、インク供給系に生じる負圧（インク吸収体２２もしくはフィルタの臨界圧力）が決定される。
【０１７３】
このため、フィルタの開口をインク吸収体２２のセル２２ａよりも小さくした場合、インク供給系に生じる負圧を２．０ｋＰａ以下とするには、下記関係式（２７）
Ｐｍ≦２０００（Ｐａ） ・・・（２７）
を満足する必要がある。
【０１７４】
また、フィルタによる臨界圧力Ｐｍ（Ｐａ）は、前記一般式（１）並びに実験式（２）に示したように、インクの表面張力η（Ｎ／ｍ）と、フィルタの開口の大きさ、つまり、フィルタの濾過精度Ｆ（ｍ）とで決まる。したがって、Ｐｍ≦２０００（Ｐａ）とするには、前記一般式（１）並びに実験式（２）より、フィルタの濾過精度をＦ（ｍ）とすると、下記関係式（２８）
Ｐｍ＝４・η／Ｆ’ ・・・（２８）
（但し、フィルタの開口が円形の場合はＦ’＝Ｆ、
その他の場合はＦ’＝√２・Ｆ）
を満足する必要がある。
【０１７５】
よって、上記関係式（２７）・（２８）から、インクタンク２１側のインク供給経路３内の一部に、下記関係式（２９）
Ｆ’＝４・η／Ｐｍ ・・・（２９）
（但し、フィルタの開口が円形の場合はＦ’＝Ｆ、
その他の場合はＦ’＝√２・Ｆ）
並びに前記関係式（２７）を満足するフィルタが設けられていることで、インク供給系に発生する負圧、つまり、この場合はインク供給時にフィルタで発生する負圧（フィルタによる臨界圧力Ｐｍ）を、印字ヘッド１の吐出ノズル１ａにて発生する吸引圧力（ノズルの臨界圧力Ｐｎ）未満（Ｐｎ＞Ｐｍ）とすることができる。
【０１７６】
したがって、インク供給経路３内に上記したフィルタを設けることで、インク供給系に発生する負圧に打ち勝ち、フィルタの開口部に形成されているメニスカスの表面張力に打ち勝ってインクを吸引し、開口部のメニスカスが後退し、この結果、空気が印字ヘッドのノズル先端より混入することなくインクの安定供給（補給）を行うことができる。なお、この場合においても、前記したようにインク供給系の負圧とメニスカスの吸引力とが平衡した時点でインク補給が終了する。なお、逆に、ノズル先端のメニスカスによる臨界圧力が、フィルタの開口部に形成されているメニスカスの臨界圧力以下（つまり、Ｐｎ≦Ｐｍ）、特に該臨界圧力（Ｐｍ）よりも小さいと、ノズル先端のメニスカスは後退し、印字ヘッド１内に空気を吸い込み、吐出不良となる。
【０１７７】
つまり、インクを印字ヘッド１に供給するとき、印字ヘッド１がインクを吸引するときに必要な圧力、つまり、印字ヘッド１の吐出ノズル１ａのメニスカスによる圧力（インク吸引圧力）が、上記インク供給経路３（フィルタ）にかかる。そして、このインク吸引圧力、すなわち、吐出ノズル１ａの臨界圧力Ｐｎが、インク供給時に上記フィルタで発生する負圧、つまり、フィルタの開口部のメニスカスによるインク負圧の臨界圧力Ｐｍ（フィルタ圧）以下、特に該臨界圧力Ｐｍ（フィルタ圧）よりも小さくなると、該フィルタの開口部に形成しているメニスカスを破る前に、空気が印字ヘッド１のノズル先端より混入してしまうことになる。
【０１７８】
このため、インクを印字ヘッド１に供給するときの吐出ノズル１ａのメニスカスによる圧力、すなわちインク吸引圧力（吐出ノズル１ａの臨界圧力Ｐｎ）を、上記フィルタ圧（フィルタによる臨界圧力Ｐｍ）よりも大きい値になるように設定しておけば、上記した問題を抑制することができる。
【０１７９】
したがって、インク供給時に上記フィルタで発生する負圧が、上記印字ヘッド１の吐出ノズル１ａによるインク吸引圧力よりも小さくなるように、上記画像形成装置、より具体的には、上記負圧の要因となる各種条件、特に、フィルタを構成（設計）することで、上記した問題を抑制することができる。
【０１８０】
つまり、上記構成を満足するために、例えばインク供給経路３内、具体的には、インクタンク２１側のインク供給経路３の一部（端部）には、インク供給時に上記フィルタで発生する負圧が、上記印字ヘッド１の吐出ノズル１ａによるインク吸引圧力よりも小さくなるフィルタ、具体的には、前記関係式（２９）並びに関係式（２７）を満足するフィルタ、つまり、下記関係式（３０）
Ｆ’≧４・η／２０００ ・・・（３０）
（但し、フィルタの開口が円形の場合はＦ’＝Ｆ、
その他の場合はＦ’＝√２・Ｆ）
を満足するフィルタが設けられていることが望ましい。
【０１８１】
なお、液体の表面張力は水の０．０７２Ｎ／ｍが最大であり、インクの表面張力η（Ｎ／ｍ）に関連する吐出エネルギーの低減、吐出ノズル１ａにおけるノズル先端からの空気の吸い込み、吐出ノズル１ａ周辺のインクによる濡れやインクの洩れ等による吐出不良、および、紙面上でのインクの滲みによる画質劣化を防止するためには、インクの表面張力η（Ｎ／ｍ）は、０．０３〜０．０６の範囲内に設定する必要があり、一般的には、０．０３〜０．０５の範囲内に設定される。
【０１８２】
したがって、本実施の形態にかかる画像形成装置において、インクの表面張力η（Ｎ／ｍ）が０．０３であるとき、上記関係式（３０）から、前記フィルタ２３に、濾過精度Ｆ（ｍ）が、４２×１０^-6（ｍ）以上、つまり４２μｍ以上のフィルタ、好適には、表面張力、濾過精度Ｆ等の変動等に対するマージンを約２０％とすると、Ｆ≧５０×１０^-6（ｍ）のフィルタを用いることで、インク供給系にかかる負圧、つまり、フィルタ２３にかかる臨界圧力Ｐｍを２０００Ｐａ以下とすることができる。なお、このことは、例えば図９において濾過精度Ｆが５０μｍ、つまり、５０×１０^-6（ｍ）の場合に、フィルタ２３（メッシュフィルタ）によるインク負圧の臨界圧力（最大負圧）Ｐｍが２．０ｋＰａ以下となることからも確認できる。
【０１８３】
一方、フィルタ２３として円形の開口を有するフィルタを用いる場合には、上記関係式（３０）から、濾過精度Ｆ（ｍ）が、６０×１０^-6（ｍ）以上、つまり６０μｍ以上のフィルタ、好適には、表面張力、濾過精度Ｆ等の変動等に対するマージンを約２０％とすると、Ｆ≧７０×１０^-6（ｍ）のフィルタを用いることで、インク供給系にかかる負圧、つまり、フィルタ２３にかかる臨界圧力Ｐｍを２０００Ｐａ以下とすることができる。
【０１８４】
以上のように、上記インクジェット記録装置のインクカートリッジ２０には、インク供給経路３におけるインクタンク２１側の端部に、インク供給時に上記インク供給経路３にかかる負圧を２．０ｋＰａ以下とするメッシュ状のフィルタ２３が設けられている。
【０１８５】
このため、印字ヘッド１がインク滴を吐出することによりに生じるインク吸引圧力、（インクの供給に必要な圧力）、つまり、インク吸収体２２にかかる圧力（インク供給圧力）は、インクタンク２１内部にかからず、インク供給圧力は、フィルタ２３の開口部２３ａ（網目）にかかるフィルタ圧よりも小さくなる。
【０１８６】
したがって、上記インクジェット記録装置によれば、フィルタ２３の開口部２３ａ（網目）に形成されているインクのメニスカスが破れるまでは、インク供給経路３内への空気の混入を防止することができ、また、メニスカスが破れ、インク供給経路３内に空気が吸入されインクエンプティを検出した際にもノズル先端におけるメニスカスが後退し過ぎてノズル先端より空気が混入することを防止できる。
【０１８７】
また、このようにインク充填時にインクタンク２１内に混入した気泡がフィルタ２３前面、つまり、フィルタ２３のインクタンク２１側端面の一部に捕獲された場合、もしくは、上記インクタンク２１が、インクエンプティ直前（近傍）の状態にあり、インク吸収体２２の一部分が空の状態でフィルタ２３に接触している場合に、フィルタ２３に接触している空気（気泡）を吸い込むことなくインク吸収体２２が保持しているインクを印字ヘッド１に有効に供給するための条件、言い換えれば、不用意にインク供給口３ａにインクタンク２１から空気を吸い込まない条件は、Ｐｍ＞Ｐ_Eである。
【０１８８】
ここで、前記したように、インクカートリッジ２０内のインクが無くなる直前の状態は、インク吸収体２２（フォーム材）の下端のセル２２ａを毛管とみなすことができることから、インクエンプティ時におけるインク吸収体２２による臨界圧力Ｐ_E（Ｐａ）、つまり、セル２２ａ内の液面（インクのメニスカス）の臨界圧力Ｐ_E（Ｐａ）は、前記関係式（４）によって与えられる。
【０１８９】
一方、濾過精度Ｆ（ｍ）のフィルタ２３を用いた場合のフィルタ２３による臨界圧力Ｐｍは、前記実験式（２）によって与えられることから、濾過精度Ｆ（ｍ）のフィルタ２３を用いた場合における上記条件、すなわち、不用意にインク供給口３ａにインクタンク２１から空気を吸い込まない条件は、前記実験式（２）並びに関係式（４）から、下記関係式（３１）
（４・η）／（√２・Ｆ）＞４・η・（Ｎ・Ｒ） ・・・（３１）
で表される。
【０１９０】
したがって、上記関係式（３１）を濾過精度Ｆについて整理すると、以下の関係式（３２）
√２・Ｆ＜１／（Ｎ・Ｒ） ・・・（３２）
が得られる。
【０１９１】
また、前記一般式（１）から、円形状の開口を有するフィルタによる臨界圧力Ｐｍ’は、該インクの表面張力η（Ｎ／ｍ）と、濾過精度Ｆ(ｍ)とを用いて、下記一般式（３３）
Ｐｍ’＝４・η／Ｆ ・・・（３３）
で表される。
【０１９２】
したがって、円形状の開口を有する濾過精度Ｆ（ｍ）のフィルタを用いた場合、不用意にインク供給口３ａにインクタンク２１から空気を吸い込まない条件は、上記したフィルタ２３を用いた場合と同様に、前記関係式（４）並びに上記一般式（３３）から、下記関係式（３４）
Ｆ＜１／（Ｎ・Ｒ） ・・・（３４）
で与えられる。
【０１９３】
したがって、インク供給経路３内に、濾過精度Ｆ（ｍ）のフィルタを用いる場合、インクタンク２１に収納する前のインク吸収体２２のセル密度をＮ（個／ｍ）、上記インクタンク２１に収納される前に対する上記インクタンク２１に圧縮されて収納されたときの上記インク吸収体２２の体積比で示される圧縮比をＲとすると、以下の関係式（３５）
Ｆ’＜１／（Ｎ・Ｒ） ・・・（３５）
（但し、フィルタの開口が円形の場合はＦ’＝Ｆ、
その他の場合はＦ’＝√２・Ｆ）
を満足するように上記インクカートリッジ２０を設計することで、インク供給圧力を、上記フィルタ２３にかかる負圧より小さく調整することができ、空気がフィルタ２３の開口部２３ａに形成されたインクのメニスカスを破り、インク供給経路３内に混入してしまうことを防止することができる。このため、上記の構成によれば、インク残量の低下以外の要因による、インク供給経路３中への空気混入を防止し、インク残量検出の誤動作を防止することができ、品位に関して信頼性の高い印刷を行うことができる。
【０１９４】
なお、上記条件は、濾過精度Ｆ（ｍ）の代わりに、セル径を用いて管理することもできる。しかしながら、上記したようにインク供給時（エンプティ時）の負圧を、バラツキの大きいセル径ではなく、バラツキの小さな濾過精度Ｆ（ｍ）、つまり、開口の最短長さ（最小空隙幅）で管理することにより、安定した負圧を得ることができる。
【０１９５】
また、上述した実施形態においては、上記インクタンク２１、つまり、インク収納部に収納する前のインク吸収体（インク吸収体２２）のセル密度をＮ（個／ｍ）、上記インク収納部に収納される前に対する上記インク収納部に圧縮されて収納されたときの上記インク吸収体の体積比で示される圧縮比をＲとして説明したが、上記インク吸収体は、上記インク収納部に収容する際に圧縮して収納してもよく、予め圧縮してから収納してもよい。
【０１９６】
上記インク吸収体としては、例えば、圧縮加工されたスポンジ等、インク吸収体に広く使われる圧縮加工されたフォーム材（圧縮した状態で加熱プレスし、永久圧縮を与えたもの）を用いることができ、この場合、上記セル密度Ｎ（個／ｍ）並びに圧縮比Ｒとしては、圧縮加工前のインク吸収体のセル密度（個／ｍ）並びに圧縮加工前に対する圧縮加工後、つまり、圧縮加工後のフォーム材をインク吸収材としてインクタンクに挿入した際のインク吸収体の体積比で示される圧縮比（圧縮率）を用いることができる。
【０１９７】
よって、圧縮加工前のインク吸収体のセル密度をＮ’（個／ｍ）、圧縮加工前に対する圧縮加工後の上記インク吸収体の体積比で示される圧縮比（圧縮率）をＲ’とすると、前記した各式は、Ｎ＝Ｎ’、Ｒ＝Ｒ’として表すことができる。
【０１９８】
例えば、前記関係式（３５）は、上記フィルタの濾過精度をＦ（ｍ）、圧縮加工前のインク吸収体のセル密度をＮ’（個／ｍ）、圧縮加工前に対する圧縮加工後の上記インク吸収体の体積比で示される圧縮比（圧縮率）をＲ’とすると、下記関係式（３６）
Ｆ’＜１／（Ｎ’・Ｒ’） ・・・（３６）
（但し、フィルタの開口が円形の場合はＦ’＝Ｆ、
その他の場合はＦ’＝√２・Ｆ）
で表される。なお、前述した各式あるいは、後述する各式についても同様にＮ＝Ｎ’、Ｒ＝Ｒ’として表すことができる。勿論、Ｎ・ＲあるいはＮ’・Ｒ’の代わりに、実装セル密度Ｍを用いることができることは言うまでもない。
【０１９９】
また、吐出ノズル１ａの直径をＤ_N（ｍ）とすると、前記関係式（１９）から、吐出ノズル１ａのメニスカスの臨界圧力Ｐｎ（Ｐａ）は、下記一般式（３７）
Ｐｎ＝４・η／Ｄ_N ・・・（３７）
で表される。
【０２００】
ここで、ノズル先端から空気を吸い込まない条件は、
Ｐｎ＞Ｐｍ
であり、前記したように、不用意にインク供給口３ａにインクタンク２１から空気を吸い込むことなくインク吸収体２２が保持しているインクを印字ヘッド１に有効に供給するための条件は
Ｐｍ＞Ｐ_E
であるため、インク残量の低下以外の要因による、インク供給経路中への空気混入をより一層防止し、インク残量検出の誤動作をより効果的に防止するためには、以下の条件、
Ｐｎ＞Ｐｍ＞Ｐ_E
を満足すること、つまり、前記関係式（３１）および上記一般式（３７）から、以下の関係式（３８）
（４・η／Ｄ_N）＞（４・η）／Ｆ’＞４・η・(Ｎ・Ｒ) ・・・（３８）
（但し、フィルタの開口が円形の場合はＦ’＝Ｆ、
その他の場合はＦ’＝√２・Ｆ）
を満足することがより望ましい。
【０２０１】
したがって、上記関係式（３８）を濾過精度Ｆ’（ｍ）について整理すると、以下の関係式（３９）
Ｄ_N＜Ｆ’＜１／（Ｎ・Ｒ） ・・・（３９）
（但し、フィルタの開口が円形の場合はＦ’＝Ｆ、
その他の場合はＦ’＝√２・Ｆ）
が得られる。
【０２０２】
次に、インクの消費に伴って変化するインクレベルの影響について考察する。図３に示すようにインク供給口２４と吐出ノズル１ａ先端（ノズル先端）との落差ｈによるヘッド水頭圧をＰｈとすると、吐出ノズル１ａにおけるインクのメニスカスによる有効保持力Ｐｎ’(Ｐａ)は、下記一般式（４０）
Ｐｎ’＝Ｐｎ−｜Ｐｈ｜ ・・・（４０）
で定義される。なお、｜Ｐｈ｜はＰｈの絶対値を示す。つまり、｜｜は絶対記号を示し、以下、｜ｘ｜はｘの絶対値を示すものとする。
【０２０３】
このとき、ノズル先端よりインクのメニスカスが後退しすぎて空気を吸い込んでしまわない条件は、インクタンク２１へのインクフル充填時で、下記関係式（４１）
Ｐｎ’＞｜Ｐμ｜−｜Ｐｉ｜ ・・・（４１）
を満たすことであり、インクエンプティ時で、下記関係式（４２）
Ｐｎ’＞Ｐｍ ・・・（４２）
を満たすことである。
【０２０４】
ヘッド水頭圧Ｐｈ（インクの水頭）を考慮しない場合にノズル先端から空気を吸い込まない条件はＰｎ＞Ｐｍであるが、ヘッド水頭圧Ｐｈを考慮することで、より実使用に則した条件となる。つまり、ヘッド水頭圧Ｐｈは、ノズル先端からのインク漏れを防ぐための負の静圧が発生するように設定され、上記インクジェット記録装置は、上記ヘッド水頭圧Ｐｈを考慮しない場合よりもノズル先端から空気を吸い込み易い条件において使用される。このため、ヘッド水頭圧Ｐｈを考慮することで、より実使用に則した条件とすることができる。
【０２０５】
ここで、前記したように異物混入を防止するためにフィルタ２３を設計すると、通常、
Ｐｍ＞｜Ｐμ｜＋｜Ｐｉ｜ ・・・（４３）
となるので、上記関係式（４２）・（４３）から、以下の関係
Ｐｎ’＞Ｐｍ＞｜Ｐμ｜＋｜Ｐｉ｜ ・・・（４４）
が導かれる。
【０２０６】
したがって、上記関係式（４１）・（４４）から、以下の関係
Ｐｎ’＞Ｐｍ＞｜Ｐμ｜＋｜Ｐｉ｜＞｜Ｐμ｜−｜Ｐｉ｜
が成り立つため、上記関係式（４４）を満足、つまり、吐出ノズル１ａの直径をＤ_N（ｍ）とすると、前記実験式（２）および一般式（３７）から、以下の関係式（４５）
４・η／Ｄ_N−｜Ｐｈ｜＞４・η／Ｆ’＞｜Ｐμ｜＋｜Ｐｉ｜・・・（４５）
（但し、フィルタの開口が円形の場合はＦ’＝Ｆ、
その他の場合はＦ’＝√２・Ｆ）
を満足することで、インク供給時、特に、インクエンプティ直前におけるインク供給時にフィルタ２３でリークする圧力を、印字ヘッド１の吐出ノズル１ａの臨界圧Ｐｎを越えることなく適宜管理でき、吐出ノズル１ａより空気の吸い込みを防止することができると共に、インク供給経路３に向かう異物を効果的に濾過し、吐出ノズル１ａによる吐出動作の信頼性を高めることができる。なお、上記した各式、例えば上記関係式（４１）並びに（４３）〜（４５）において、Ｐμは前記関係式（１０）にて与えられる。
【０２０７】
次に、本願本発明者らは、種々の物質の粘度と温度との関係について検討したので、その結果について説明する。
【０２０８】
先ず、以下の表６に、種々の物質についての温度Ｔ（℃）と粘度μ（Ｐａ・ｓ）との関係を示す。
【０２０９】
【表６】

【０２１０】
上記表６のデータに基づいて作成した温度Ｔ（℃）と粘度μ（Ｐａ・ｓ）との関係を、図２２に示す。図２２からは温度Ｔ（℃）と粘度μ（Ｐａ・ｓ）との相関関係を見出すことは困難である。
【０２１１】
さらに、以下の表７に、上記した各物質について、２５℃における粘度μ₂₅（Ｐａ・ｓ）に対する各温度Ｔ（℃）における粘度μＴ（Ｐａ・ｓ）、つまり、２５℃における粘度μ₂₅を１とした場合の各温度Ｔ（℃）における粘度μＴ／μ₂₅（正規化粘度）を示す。
【０２１２】
【表７】

【０２１３】
上記表７のデータに基づいて作成した温度Ｔ（℃）と、各温度Ｔ（℃）における粘度μＴ／μ₂₅（正規化粘度）との関係を図２３に示す。図２３からは温度Ｔ（℃）と粘度μ／μ₂₅（正規化粘度）との相関関係を見出すことは困難である。
【０２１４】
ところで、一般に、任意の温度Ｔ_Ｋ（Ｋ）の液体の粘度μ_ＴＫ（Ｐａ・ｓ）は、下記一般式（４６）
μ_ＴＫ＝α・ｅｘｐ（β／Ｔ_Ｋ） ・・・（４６）
で示されるアンドレードの式にて表される。
【０２１５】
このアンドレードの式を用いて、Ｔ_２５（Ｋ）（＝２５℃）における液体の粘度をμ_２５（Ｐａ・ｓ）、温度Ｔ_Ｋ（Ｋ）における液体の粘度をμ_ＴＫ（Ｐａ・ｓ）とすると、下記一般式（４７）
μ_ＴＫ／μ_２５＝ｅｘｐ（β／Ｔ_Ｋ）／ｅｘｐ（β／Ｔ_２５）
＝ｅｘｐ｛（１／Ｔ_Ｋ−１／Ｔ_２５）・β｝ ・・・（４７）
で表される関係が導かれる。よって、上記一般式（４７）より、
Ｌｎ（μ_ＴＫ／μ_２５）＝（１／Ｔ_Ｋ−１／Ｔ_２５）・β
となり、下記一般式（４８）
β＝Ｌｎ（μ_ＴＫ／μ_２５）／（１／Ｔ_ｋ−１／Ｔ_２５） ・・・（４８）
が得られる。
【０２１６】
そこで、次に、上記した各物質について、表７に示したデータに基づいて、粘度μ₂₅と、粘度μ／μ₂₅（正規化粘度）、ここでは、μ₀／μ₂₅，μ₅₀／μ₂₅，μ₇₅／μ₂₅との相関関係について調べた。この結果を図２４に示す。
【０２１７】
図２４に示したプロットデータから、粘度μ₀／μ₂₅に着目すると、以下の近似式
μ₀／μ₂₅＝０．４２・Ｌｎ（μ₂₅）＋４．７１ ・・・（４９）
を得ることができる。
【０２１８】
よって、２５（℃）は絶対温度で２９８（Ｋ）であるから、前記一般式（４８）
および上記近似式（４９）から、下記関係式（５０）

が得られる。
【０２１９】
また、前記一般式（４６）で示されるアンドレードの式から、２５℃における液体の粘度μ₂₅（Ｐａ・ｓ）は、
μ₂₅＝α・ｅｘｐ（β／２９８）
となり、これにより、下記一般式（５１）
α＝μ₂₅／ｅｘｐ（β／２９８） ・・・（５１）
が成り立つ。
【０２２０】
そこで、前記した種々の物質について、前記一般式（４６）・（５１）および関係式（５０）によって得られる以下の近似式（５２）

を用いて求められるμ_TK（Ｐａ・ｓ）にて表される近似式粘度μ’（Ｐａ・ｓ）を、以下の表８に示す。
【０２２１】
【表８】

【０２２２】
また、前記一般式（４６）・（５１）および関係式（５０）によって得られる上記近似式（５２）により求められる近似式粘度μ’（Ｐａ・ｓ）と、実際の粘度μ（Ｐａ・ｓ）との関係を、図２５に示す。なお、図２５中、実線は、上記近似式粘度μ’（Ｐａ・ｓ）を示し、各識別マークは実際の粘度μ（Ｐａ・ｓ）を示す。
【０２２３】
図２５に示すように、近似式粘度μ’（Ｐａ・ｓ）と、実際の粘度μ（Ｐａ・ｓ）、つまり、実測値との間にそれほどの差異はなく、上記近似式（５２）の精度が良好であることが確認された。
【０２２４】
さらに、上記近似式（５２）を、８種類のインク（インク１〜８）並びに水（Ｈ₂Ｏ）に適用した場合の温度Ｔ（℃）と粘度μ（Ｐａ・ｓ）、μ／μ₂₅、μ’／μ（近似式粘度／実測値）との関係を表９に示す。
【０２２５】
【表９】

【０２２６】
上記表９のデータに基づいて作成した近似式粘度μ’（Ｐａ・ｓ）と、実際の粘度μ（Ｐａ・ｓ）との関係を、図２６に示す。また、図２７は上記した各インク並びに水の２５℃における粘度μ₂₅と、正規化粘度μ／μ₂₅の実測値及び近似値との関係を示す。なお、図２６中、実線は、上記近似式粘度μ’（Ｐａ・ｓ）を示し、各識別マークは、実測値、つまり、実際の粘度μ（Ｐａ・ｓ）を示す。また、図２７中、破線は、正規化近似粘度μ’₅／μ₂₅、及び、μ’₄₀／μ₂₅を示し、「○」は５℃のときの正規化粘度μ／μ₂₅（すなわち、μ₅／μ₂₅）、「△」は４０℃のときの正規化粘度μ／μ₂₅（すなわち、μ₄₀／μ₂₅）、各識別マークは、実測値、つまり、実際の粘度μ（Ｐａ・ｓ）を示す。
【０２２７】
図２６に示す結果から、インクカートリッジ２０に用いるインクについて上記近似式（４８）を適用した場合であっても、近似式粘度μ’（Ｐａ・ｓ）と実際の粘度μ（Ｐａ・ｓ）との間にそれほど差が出ないことがわかった。
【０２２８】
以上の検討結果により、任意の温度Ｔ_K（Ｋ）におけるインクの粘度μ（Ｐａ・ｓ）は、μ＝μ’として算出することが可能であり、上記近似式（４８）を用いれば、任意の温度Ｔ_K（Ｋ）におけるインクの粘度μ（Ｐａ・ｓ）を精度良く算出できることが確認できた。
【０２２９】
したがって、上記実験結果に基づけば、前記関係式（１０）において、インクの粘度μ（Ｐａ・ｓ）に、上記近似式（５２）を用いて求められるμ_TK（Ｐａ・ｓ）にて表される近似式粘度μ’（Ｐａ・ｓ）を適用すれば、前記関係式（１０）は、以下の関係式（５３）
Ｐμ＝（ｋ／Ａ）・[μ_TK・Ｌ・（Ｎ・Ｒ）²／Ｓ]・Ｑ ・・・（５３）
（但し、係数（ｋ／Ａ）＝４８５）
によって表すことができる。
【０２３０】
したがって、関係式（４３）・（４５）・（５２）・（５３）および実験式（２）より、フィルタの濾過精度をＦ（ｍ）、インクタンク２１にインクがフル充填されているときに、インクを、インク供給経路３を介して印字ヘッド１に供給しようとするときに生じるインクタンク２１の水頭圧をＰｉ（Ｐａ）、上記インクタンク２１におけるインクの粘性抵抗による圧力損失をＰμ（Ｐａ）、上記インクの表面張力をη（Ｎ／ｍ）、上記インクタンク２１に収納する前のインク吸収体２２のセル密度をＮ（個／ｍ）、上記インクタンク２１に収納される前に対する上記インクタンク２１に圧縮されて収納されたときの上記インク吸収体２２の体積比で示される圧縮比をＲ、圧縮加工前の上記インク吸収体のセル密度をＮ’（個／ｍ）、圧縮加工前に対する圧縮加工後の上記インク吸収体の体積比で示される圧縮比（圧縮率）をＲ'、上記インクタンク２１に圧縮されて収納されたときのインク吸収体２２の断面積をＳ（ｍ²）、上記インクタンク２１に圧縮されて収納されたときのインク吸収体２２の高さをＬ（ｍ）、２５℃におけるインクの粘度をμ₂₅（Ｐａ・ｓ）、任意の温度Ｔ_K（Ｋ）における粘度をμ_TK（Ｐａ・ｓ）とすると、任意の温度Ｔ_K（Ｋ）において、
４・η／Ｆ’＞｜Ｐμ｜＋｜Ｐｉ｜
Ｐμ＝（ｋ／Ａ）・[μ_TK・Ｌ・（Ｎ・Ｒ）²／Ｓ]・Ｑ
（但し、係数（ｋ／Ａ）＝４８５）
μ_TK＝α・ｅｘｐ（β／Ｔ_K）、
α＝μ₂₅／ｅｘｐ（β／２９８）、
β＝Ｌｎ[０．４２・Ｌｎ(μ₂₅)＋４．７１]／(１／２７３−１／２９８)
（但し、フィルタの開口が円形の場合はＦ’＝Ｆ、
その他の場合はＦ’＝√２・Ｆ）
もしくは
４・η／Ｆ’＞｜Ｐμ｜＋｜Ｐｉ｜
Ｐμ＝（ｋ／Ａ）・[μ_TK・Ｌ・（Ｎ'・Ｒ'）²／Ｓ]・Ｑ
（但し、係数（ｋ／Ａ）＝４８５）
μ_TK＝α・ｅｘｐ（β／Ｔ_K）、
α＝μ₂₅／ｅｘｐ（β／２９８）、
β＝Ｌｎ[０．４２・Ｌｎ(μ₂₅)＋４．７１]／(１／２７３−１／２９８)
（但し、フィルタの開口が円形の場合はＦ’＝Ｆ、
その他の場合はＦ’＝√２・Ｆ）
を満足することで、フィルタの開口部におけるインクのメニスカスの負圧の臨界値よりもインク吸収体で生じる負圧を小さく調整することができ、空気がフィルタの網目に形成されたインクのメニスカスを破り、インク供給経路３内に混入してしまうことを防止することができる。このため、上記の構成によれば、インク残量の低下以外の要因による、インク供給経路３中への空気混入を防止し、インク残量検出の誤動作を防止することができ、品位に関して信頼性の高い印刷を行うことができる。
【０２３１】
また、上記の構成においても、濾過精度Ｆ（ｍ）の代わりに、セル径を用いて管理することもできるが、インク供給時（エンプティ時）の負圧を、バラツキの大きいセル径ではなく、バラツキの小さな濾過精度Ｆ（ｍ）、つまり、開口の最短長さ（最小空隙幅）で管理することにより、安定した負圧を得ることができる。
【０２３２】
また、この場合に前記関係式（４５）を満足することで、インク供給時、特に、インクエンプティ直前におけるインク供給時にフィルタでリークする圧力を、印字ヘッド１の吐出ノズル１ａの臨界圧Ｐｎを越えることなく適宜管理でき、吐出ノズル１ａより空気の吸い込みを防止することができると共に、インク供給経路３に向かう異物を効果的に濾過し、吐出ノズル１ａによる吐出動作の信頼性を高めることができる。
【０２３３】
なお、本発明は上述した実施形態に限定されるものではなく、請求項に示した範囲で種々の変更が可能であり、上述した各実施形態にそれぞれ開示された技術的手段を適宜組み合わせて得られる実施形態についても本発明の技術的範囲に含まれる。
【０２３４】
【発明の効果】
本発明にかかる画像形成装置は、以上のように、インクを保持する多孔質のインク収納体が収納されたインク収納部と、該インク収納部から印字ヘッドにインクを供給するインク供給経路とを備えた画像形成装置において、上記インク供給経路内部にフィルタを備え、上記フィルタの濾過精度をＦ（ｍ）、上記インク収納部に収納する前のインク吸収体のセル密度をＮ（個／ｍ）、上記インク収納部に収納される前に対する上記インク収納部に圧縮されて収納されたときの上記インク吸収体の体積比で示される圧縮比をＲとすると、
Ｆ’＜１／（Ｎ・Ｒ）
（但し、フィルタの開口が円形の場合はＦ’＝Ｆ、
その他の場合はＦ’＝√２・Ｆ）
を満足する構成である。
【０２３５】
インクを印字ヘッドに供給するとき、印字ヘッドがインクを吸引するのに必要な圧力、つまり、印字ヘッドのノズルのメニスカスによる圧力（インク吸引圧力）が、上記インク供給経路にかかる。このとき、上記のように設定することにより、インクタンク内で発生する負圧の臨界値はフィルタによって決まる。
【０２３６】
よって、上記の構成によれば、インクの表面張力によりインク吸収体で発生する負圧の臨界値を、該臨界値が、インクの表面張力により上記フィルタで発生する負圧、つまり、フィルタの開口部（網目）のメニスカスによる圧力（フィルタ圧）の臨界値よりも小さくなるように調整することができ、インクエンプティになる前にフィルタの網目に形成されたインクのメニスカスが破れ、空気がインク供給経路内に混入してしまうことが防止され、インクの消費に応じてインク吸収体のメニスカスが後退して安定したインク供給動作が可能となる。さらに、インク残量の低下以外の要因、例えば、キャリッジ振動、気圧もしくは周囲温度変化等によりインク収納部のインク中に生じる気泡等は、フィルタで捕獲され、インク供給経路中への空気混入を防止し、信頼性の高い印刷を行うことができるとともにインクを無駄なく消費することができる。
【０２３７】
よって、上記の構成によれば、インクの連続吐出時に、インクエンプティ以前にインク供給系に空気が混入するといった不具合の発生を防止し得るように、インク供給系の設計指針を有する画像形成装置を提供することができる。
【０２３８】
また、上記の構成によれば、上記したようにインク供給時（エンプティ時）の負圧を、バラツキの小さな濾過精度Ｆ（ｍ）で管理することができ、安定した負圧を得ることができるという効果を併せて奏する。
【０２３９】
本発明にかかる画像形成装置は、以上のように、上記印字ヘッドのノズル（インク吐出ノズル）の直径をＤ_N（ｍ）とすると、
Ｄ_N＜Ｆ’＜１／（Ｎ・Ｒ）
（但し、フィルタの開口が円形の場合はＦ’＝Ｆ、
その他の場合はＦ’＝√２・Ｆ）
を満足する構成である。
【０２４０】
上記の構成によれば、上記印字ヘッドのノズル（ノズル部）におけるインクのメニスカスによるインク吸引圧力の臨界値を、該臨界値が、フィルタの開口部でのインクのメニスカスによる圧力の臨界値よりも小さくなるように調整することができ、ノズル先端より空気を吸入してしまい、印字ヘッドが吐出不良となることを防止することができる。
【０２４１】
また、上記の構成によれば、フィルタの開口部に形成されたインクのメニスカスが破れ、インク収納部からインク供給経路内に不用意に空気を吸い込むことを防止することができ、インク吸収体が保持しているインクを、印字ヘッドに、より有効に供給することができる。したがって、上記の構成によれば、インク残量の低下以外の要因による、インク供給経路中への空気混入をより一層防止し、インク残量検出の誤動作をより効果的に防止することができるという効果を奏する。よって、上記の構成によれば、インクの連続吐出時に、インクエンプティ以前にインク供給系に空気が混入するといった不具合の発生を防止し得るように、インク供給系の設計指針を有する画像形成装置を提供することができる。
【０２４２】
本発明にかかる画像形成装置は、以上のように、インクを保持する多孔質のインク収納体が収納されたインク収納部と、該インク収納部から印字ヘッドにインクを供給するインク供給経路とを備えた画像形成装置において、上記インク供給経路内部にフィルタを備え、上記インク吸収体は、上記インク収納部に収納される前に予め圧縮加工が施されており、上記フィルタの濾過精度をＦ（ｍ）、圧縮加工前の上記インク吸収体のセル密度をＮ’（個／ｍ）、圧縮加工前に対する圧縮加工後の上記インク吸収体の体積比で示される圧縮比（圧縮率）をＲ’とすると、
Ｆ’＜１／（Ｎ’・Ｒ’）
（但し、フィルタの開口が円形の場合はＦ’＝Ｆ、
その他の場合はＦ’＝√２・Ｆ）
を満足する構成である。
【０２４３】
インクを印字ヘッドに供給するとき、印字ヘッドがインクを吸引するのに必要な圧力、つまり、印字ヘッドのノズルのメニスカスによる圧力（インク吸引圧力）が、上記インク供給経路にかかる。このとき、上記のように設定することにより、インクタンク内で発生する負圧の臨界値はフィルタによって決まる。
【０２４４】
よって、インクの表面張力によりインク吸収体で発生する負圧の臨界値を、該臨界値が、インクの表面張力により上記フィルタで発生する負圧、つまり、フィルタの開口部（網目）のメニスカスによる圧力（フィルタ圧）の臨界値よりも小さくなるように調整することができ、インクエンプティになる前にフィルタの網目に形成されたインクのメニスカスが破れ、空気がインク供給経路内に混入してしまうことが防止され、インクの消費に応じてインク吸収体のメニスカスが後退して安定したインク供給動作が可能となる。さらに、インク残量の低下以外の要因、例えば、キャリッジ振動、気圧もしくは周囲温度変化等によりインク収納部のインク中に生じる気泡等はフィルタで捕獲され、インク供給経路中への空気混入を防止し、信頼性の高い印刷を行うことができるとともにインクを無駄なく消費することができるという効果を奏する。よって、上記の構成によれば、インクの連続吐出時に、インクエンプティ以前にインク供給系に空気が混入するといった不具合の発生を防止し得るように、インク供給系の設計指針を有する画像形成装置を提供することができる。
【０２４５】
また、上記の構成によれば、上記したようにインク供給時（エンプティ時）の負圧を、バラツキの小さな濾過精度Ｆ（ｍ）で管理することができ、安定した負圧を得ることができるという効果を併せて奏する。
【０２４６】
本発明にかかる画像形成装置は、以上のように、上記印字ヘッドのノズルの直径をＤ_N（ｍ）とすると、
Ｄ_N＜Ｆ’＜１／（Ｎ’・Ｒ’）
を満足する構成である。
【０２４７】
上記の構成によれば、上記印字ヘッドのノズル先端から空気を吸い込むことを防止することができると共に、インク収納部からインク供給経路内に不用意に空気を吸い込むことを防止することができ、インク吸収体が保持しているインクを印字ヘッドにより有効に供給することができる。したがって、上記の構成によれば、インク残量の低下以外の要因による、インク供給経路中への空気混入をより一層防止し、インク残量検出の誤動作をより効果的に防止することができるという効果を奏する。よって、上記の構成によれば、インクの連続吐出時に、インクエンプティ以前にインク供給系に空気が混入するといった不具合の発生を防止し得るように、インク供給系の設計指針を有する画像形成装置を提供することができる。
【０２４８】
本発明にかかる画像形成装置は、以上のように、インクを保持する多孔質のインク収納体が収納されたインク収納部と、該インク収納部から印字ヘッドにインクを供給するインク供給経路とを備えた画像形成装置において、上記インク供給経路内部にフィルタを備え、上記フィルタの濾過精度をＦ（ｍ）、上記インク収納部にインクがフル充填されているときにインクを上記インク供給経路を介して上記印字ヘッドに供給しようとするときに生じるインク収納部の水頭圧をＰｉ（Ｐａ）、上記インク収納部におけるインクの粘性抵抗による圧力損失をＰμ（Ｐａ）、上記インクの表面張力をη（Ｎ／ｍ）、上記インク収納部に収納する前のインク吸収体のセル密度をＮ（個／ｍ）、上記インク収納部に収納される前に対する上記インク収納部に圧縮されて収納されたときの上記インク吸収体の体積比で示される圧縮比をＲ、上記インク収納部に圧縮されて収納されたときのインク吸収体の断面積をＳ（ｍ²）、上記インク収納部に圧縮されて収納されたときのインク吸収体の高さをＬ（ｍ）、２５℃におけるインクの粘度をμ₂₅（Ｐａ・ｓ）、任意の温度Ｔ_K（Ｋ）における粘度をμ_TK（Ｐａ・ｓ）とすると、任意の温度Ｔ_K（Ｋ）において、
４・η／Ｆ’＞|Ｐμ|＋|Ｐｉ|
Ｐμ＝（ｋ／Ａ）・[μ_TK・Ｌ・（Ｎ・Ｒ）²／Ｓ]・Ｑ
（但し、係数（ｋ／Ａ）＝４８５）
μ_TK＝α・ｅｘｐ（β／Ｔ_K）、
α＝μ₂₅／ｅｘｐ（β／２９８）、
β＝Ｌｎ[０．４２・Ｌｎ(μ₂₅)＋４．７１]／(１／２７３−１／２９８)
（但し、フィルタの開口が円形の場合はＦ’＝Ｆ、
その他の場合はＦ’＝√２・Ｆ）
を満足する構成である。
【０２４９】
上記の構成によれば、インク吸収体で生じる負圧を、該負圧が、フィルタの開口部におけるインクのメニスカスの負圧の臨界値よりも小さくなるように調整することができ、フィルタの開口部に形成されたインクのメニスカスが破れ、空気がインク供給経路内に混入してしまうことを防止することができる。このため、上記の構成によれば、インク残量の低下以外の要因による、インク供給経路中への空気混入を防止し、インク残量検出の誤動作を防止することができ、品位に関して信頼性の高い印刷を行うことができるという効果を奏する。よって、上記の構成によれば、インクの連続吐出時に、インクエンプティ以前にインク供給系に空気が混入するといった不具合の発生を防止し得るように、インクの特性に応じたインク供給系の設計指針を有する画像形成装置を提供することができる。
【０２５０】
また、上記の構成によれば、上記したようにインク供給時（エンプティ時）の最大負圧を、バラツキの小さな濾過精度Ｆ（ｍ）で管理することができ、安定した負圧を得ることができるという効果を奏する。
【０２５１】
本発明にかかる画像形成装置は、以上のように、上記印字ヘッドにおけるノズルの直径をＤ_N（ｍ）、該ノズルのインク吐出口と上記インク収納部のインク供給口との間の水頭圧をＰｈ（Ｐａ）とすると、
４・η／Ｄ_N−|Ｐｈ|＞４・η／Ｆ’＞|Ｐμ|＋|Ｐｉ|
（但し、フィルタの開口が円形の場合はＦ’＝Ｆ、
その他の場合はＦ’＝√２・Ｆ）
を満足する構成である。
【０２５２】
上記の構成によれば、インク供給時、フィルタの開口部におけるメニスカスによる圧力の臨界値を、上記印字ヘッドのノズルのメニスカスによるインク吸引圧力の臨界値を越えることなく適宜管理でき、上記ノズルからの空気の吸い込みを防止することができると共に、インク供給経路に向かう空気及び異物を効果的に濾過することができ、上記ノズルによる吐出動作の信頼性を高めることができるという効果を奏する。よって、上記の構成によれば、インクの連続吐出時に、インクエンプティ以前にインク供給系に空気が混入するといった不具合の発生を防止し得るように、インク供給系の設計指針を有する画像形成装置を提供することができる。
【０２５３】
本発明にかかる画像形成装置は、以上のように、インクを保持する多孔質のインク収納体が収納されたインク収納部と、該インク収納部から印字ヘッドにインクを供給するインク供給経路とを備えた画像形成装置において、上記インク供給経路内部にフィルタを備え、上記インク吸収体は、上記インク収納部に収納される前に予め圧縮加工が施されており、上記フィルタの濾過精度をＦ（ｍ）、上記インク収納部にインクがフル充填されているときにインクを上記インク供給経路を介して上記印字ヘッドに供給しようとするときに生じるインク収納部の水頭圧をＰｉ（Ｐａ）、上記インク収納部におけるインクの粘性抵抗による圧力損失をＰμ（Ｐａ）、上記インクの表面張力をη（Ｎ／ｍ）、圧縮加工前の上記インク吸収体のセル密度をＮ’（個／ｍ）、圧縮加工前に対する圧縮加工後の上記インク吸収体の体積比で示される圧縮比（圧縮率）をＲ’上記インク収納部に圧縮されて収納されたときのインク吸収体の断面積をＳ（ｍ²）、上記インク収納部に圧縮されて収納されたときのインク吸収体の高さをＬ（ｍ）、２５℃におけるインクの粘度をμ₂₅（Ｐａ・ｓ）、任意の温度Ｔ_K（Ｋ）における粘度をμ_TK（Ｐａ・ｓ）とすると、任意の温度Ｔ_K（Ｋ）において
４・η／Ｆ’＞|Ｐμ|＋|Ｐｉ|
Ｐμ＝（ｋ／Ａ）・[μ_TK・Ｌ・（Ｎ’・Ｒ’）²／Ｓ]・Ｑ
（但し、係数（ｋ／Ａ）＝４８５）
μ_TK＝α・ｅｘｐ（β／Ｔ_K）、
α＝μ₂₅／ｅｘｐ（β／２９８）、
β＝Ｌｎ[０．４２・Ｌｎ(μ₂₅)＋４．７１]／(１／２７３−１／２９８)
（但し、フィルタの開口が円形の場合はＦ’＝Ｆ、
その他の場合はＦ’＝√２・Ｆ）
を満足する構成である。
【０２５４】
上記の構成によれば、インク吸収体で生じる負圧を、該負圧が、フィルタの開口部におけるインクのメニスカスの負圧の臨界値よりも小さくなるように調整することができ、フィルタの開口部に形成されたインクのメニスカスが破れ、空気が、インク供給経路内に混入してしまうことを防止することができる。このため、上記の構成によれば、インク残量の低下以外の要因による、インク供給経路中への空気混入を防止し、インク残量検出の誤動作を防止することができ、品位に関して信頼性の高い印刷を行うことができるという効果を奏する。よって、上記の構成によれば、インクの連続吐出時に、インクエンプティ以前にインク供給系に空気が混入するといった不具合の発生を防止し得るように、インクの特性に応じたインク供給系の設計指針を有する画像形成装置を提供することができる。
【０２５５】
また、上記の構成によれば、上記したようにインク供給時（エンプティ時）の最大負圧を、バラツキの小さな濾過精度Ｆ（ｍ）で管理することができ、安定した負圧を得ることができるという効果を奏する。
【０２５６】
本発明にかかる画像形成装置は、以上のように、上記印字ヘッドにおけるノズルの直径をＤ_N（ｍ）、該ノズルのインク吐出口と上記インク収納部のインク供給口との間の水頭圧をＰｈ（Ｐａ）とすると、
４・η／Ｄ_N−|Ｐｈ|＞４・η／Ｆ’＞|Ｐμ|＋|Ｐｉ|
（但し、フィルタの開口が円形の場合はＦ’＝Ｆ、
その他の場合はＦ’＝√２・Ｆ）
を満足する構成である。
【０２５７】
上記の構成によれば、インク供給時、フィルタの開口部におけるメニスカスによる圧力の臨界値を、上記印字ヘッドのノズルのメニスカスによるインク吸引圧力の臨界値を越えることなく適宜管理でき、上記ノズルからの空気の吸い込みを防止することができると共に、インク供給経路に向かう空気及び異物を効果的に濾過することができ、上記ノズルによる吐出動作の信頼性を高めることができるという効果を奏する。よって、上記の構成によれば、インクの連続吐出時に、インクエンプティ以前にインク供給系に空気が混入するといった不具合の発生を防止し得るように、インク供給系の設計指針を有する画像形成装置を提供することができる。
【０２５８】
本発明にかかる画像形成装置は、以上のように、上記インク供給経路内のインクの有無を検出する検出器を備えている構成である。
【０２５９】
上記の構成によれば、上記インク供給経路内のインクの有無を検出することにより、インクエンプティを確実に検出することができる。したがって、上記の構成によれば、上記インク供給経路内に空気が混入してしまうことをより確実に防止することができるという効果を奏する。
【図面の簡単な説明】
【図１】（ａ）は本発明の実施の一形態にかかる要部の構成を示す断面図であり、（ｂ）は（ａ）に示すインクカートリッジからインク供給経路を抜いた状態を示す断面図であり、（ｃ）は検出電極の構成を示す断面図である。
【図２】上記インクジェット記録装置の全体構成を一部切り欠いて示す斜視図である。
【図３】上記インクジェット記録装置におけるインク供給装置の概略構成図である。
【図４】上記インク供給装置のフィルタの構成を示す正面図である。
【図５】上記インクカートリッジにインクを満たした状態からインクを継続して吐出したときの時間とインクカートリッジの負圧との関係を示すグラフである。
【図６】図５を模式的に示すグラフである。
【図７】上記インクジェット記録装置のインク供給経路にかかる負圧の測定実験に用いた測定装置の概略構成図である。
【図８】図７に示す測定装置を用いて実際に測定したフィルタの濾過精度とインク供給経路にかかる負圧との関係を示すグラフである。
【図９】フィルタの濾過精度とフィルタによるインク負圧の臨界圧力との関係を示すグラフである。
【図１０】セル密度と効率との関係を示すグラフである。
【図１１】実装セル密度と効率との関係を示すグラフである。
【図１２】インクカートリッジのフォーム材の各セルを円形管路とみなしたとき、円形管路を流れる流量と管路の圧力差とを示す模式図である。
【図１３】最密充填されているセルを示す構成図である。
【図１４】インクカートリッジにおける実際のフォーム材内では、球形状又は多面体上のセルが数珠状に連通している状態を示す断面図である。
【図１５】実際のフォーム材内ではセルは連珠状の流路となっているとしたときの、実効直径の求め方を示す説明図である。
【図１６】セルの直径をｄｍ、その中心位置をＸ＝０とした球状流路を積分して求めた正規化流路抵抗をＲｄ、円柱状流路の正規化流路抵抗をＲｍとしたときの、Ｘと抵抗比Ｒｄ／Ｒｍ及びセル直径ｄとの関係を示すグラフである。
【図１７】圧縮率と負圧との関係を示すグラフである。
【図１８】インクカートリッジ内のインクが無くなる直前の状態ではフォーム材の下端のセルを毛管とみなすことができるとしたときの、毛管内の液面（インクのメニスカス）の臨界圧力を示す模式図である。
【図１９】毛管内の液面（インクのメニスカス）の臨界圧力を示す模式図である。
【図２０】供給口の端部の構成を拡大して示す断面図である。
【図２１】（ａ）〜（ｈ）はインクがノズルから吐出する状態を順に示す断面図である。
【図２２】表６のデータに基づいて作成した温度Ｔ（℃）と粘度μ（Ｐａ・ｓ）との関係を、示すグラフである。
【図２３】表７のデータに基づいて作成した温度Ｔ（℃）と、各温度Ｔ（℃）におけるμＴ／μ₂₅との関係を示すグラフである。
【図２４】表７に示したデータに基づいて作成した、μ₂₅とμ／μ₂₅との相関関係を示すグラフである。
【図２５】近似式粘度μ’（Ｐａ・ｓ）と、実際の粘度μ（Ｐａ・ｓ）との関係を示すグラフである。
【図２６】表９のデータに基づいて作成した近似式粘度μ’（Ｐａ・ｓ）と、実際の粘度μ（Ｐａ・ｓ）との関係を示すグラフである。
【図２７】各インク並びに水の２５℃におけるμ₂₅とμ／μ₂₅との関係を示すグラフである。
【符号の説明】
１ 印字ヘッド
３ インク供給経路
３ａ インク供給経路
４ インク供給チューブ
１０ インク供給装置
２０ インクカートリッジ
２１ インクタンク（インク収納部）
２２ インク吸収体
２３ フィルタ
２４ インク供給口
２５ 検出電極（検出器）
３１ フィルタ[0001]
BACKGROUND OF THE INVENTION
The present invention relates to an image forming apparatus including an ink storage unit that stores ink, and more particularly to an ink jet recording apparatus as an image forming apparatus.
[0002]
[Prior art]
An ink jet recording apparatus is an image forming apparatus that performs printing by ejecting ink onto a sheet as a recording sheet, and generally includes an ink cartridge including an ink tank, and ink is supplied from the ink cartridge to a print head. Ink is discharged from the print head onto the sheet.
[0003]
When such an ink jet recording apparatus is used, air is mixed into the ink supply system before ink empty, which may cause ejection failure. Therefore, measures to prevent air from being mixed with an ink absorber or a filter are widely used. Yes.
[0004]
For example, Patent Document 1 discloses that a filter having an effective transmission dimension of 8 μm is provided downstream of the ink absorber to capture air, and the suction force by the recovery means is set to a pressure at which air does not pass through the filter. ing.
[0005]
In addition, when using such an ink jet recording apparatus, the user needs to replace the ink cartridge when the ink in the ink cartridge is exhausted. Therefore, the ink jet recording apparatus needs to detect the remaining amount of ink in the ink cartridge and inform the user.
[0006]
Therefore, various ink cartridges that can detect the remaining amount of ink have been proposed. In such ink cartridges, a method of informing the user of ink empty before sucking air into the ink supply system using an optical ink level sensor is widely adopted, and the optical sensor is used for cost reduction. The thing replaced with the electrode is used. For example, Patent Document 1 includes an ink absorber (foam material) that absorbs ink in an ink tank, and a filter in an ink supply path that connects the ink tank and a print head. An ink cartridge is disclosed which includes an electrode for detecting the presence or absence of ink in the ink supply path on the downstream side, that is, on the ink discharge port side.
[0007]
An ink jet recording apparatus using such an ink cartridge supplies ink from the ink cartridge to the print head by applying a negative pressure for sucking out ink through the filter from the print head side which is the ink discharge port side. It is supposed to be. The presence or absence of ink in the ink supply path is detected by the current flowing between the electrodes. That is, when the remaining amount of ink in the ink cartridge is reduced, there is no ink in the ink supply path, and no current flows between the electrodes. For this reason, the case where the current stops flowing between the electrodes is detected and the ink is empty.
[0008]
[Patent Document 1]
JP 2001-219583 A (publication date: August 14, 2001)
[0009]
[Patent Document 2]
Japanese Patent Laid-Open No. 3-288654 (Release Date: December 18, 1991)
[0010]
[Problems to be solved by the invention]
However, in Patent Document 1, no consideration is given to preventing bubbles from passing through the filter during the discharging operation.
[0011]
Moreover, in the said patent document 1, the characteristic of the ink absorbed by an ink absorber is not considered.
[0012]
In the invention described in Patent Document 2, an ink absorber having N · R exceeding 200 cannot be used, and the selection range of the ink absorber is narrowed.
[0013]
In the invention described in Patent Document 2, the characteristics of the ink absorbed by the ink absorber are not considered, as in Patent Document 1. Therefore, depending on the type of ink, in the ink jet recording apparatus, problems such as insufficient ink supply during continuous discharge or ink leakage when the ink cartridge is attached / detached have occurred.
[0014]
In addition, as described above, when a negative pressure for sucking ink from the print head side that is the ink discharge port side is applied through the filter, for example, if the negative pressure on the downstream side of the filter becomes too high, the nozzle of the print head Air may be sucked from the leading edge and the print head may cause ejection failure. In addition, if the negative pressure becomes too high, air trapped in the filter may pass through the filter, and this air may block the supply path or reach the print head, causing discharge failure. In addition, when the ink remaining amount detection unit is reached, there is a possibility that current will not flow between the electrodes due to the air that has passed through the filter, and it may be erroneously determined as ink empty. Thus, if the ink supply pressure is made larger than the negative pressure applied to the filter, air may enter the ink supply path due to factors other than a decrease in the remaining amount of ink, leading to a malfunction of the remaining ink detection. is there.
[0015]
However, Patent Documents 1 and 2 do not take into account the above problems.
[0016]
The present invention has been made in view of the above-described conventional problems, and an object thereof is to provide an image forming apparatus capable of preventing air from being mixed into the ink supply path due to factors other than a decrease in the remaining amount of ink. There is to do.
[0017]
A further object of the present invention is that, when ink is continuously ejected, air is mixed into the ink supply system before the ink is empty, ink shortage occurs, or ink leakage occurs when the ink cartridge is attached or detached. An object of the present invention is to provide an image forming apparatus having an ink supply system design guideline, preferably an ink supply system design guideline corresponding to the characteristics of the ink, so as to prevent the occurrence.
[0018]
Another object of the present invention is to provide an image forming apparatus capable of widening the selection range of the design guideline for the ink absorber.
[0019]
[Means for Solving the Problems]
  In order to solve the above problems, an image forming apparatus according to the present invention has an ink storage portion (for example, an ink tank provided in an ink cartridge) in which a porous ink storage body (for example, a foam material) that holds ink is stored. And an ink supply path for supplying ink to the print head from the ink storage section, a filter (for example, provided at an end of the ink supply path on the ink storage section side) inside the ink supply path. Filter)The negative pressure generated in the ink supply path at the time of ink supply and on the downstream side of the filter and the value when the meniscus of the ink formed at the opening of the filter is torn is defined as Pm (Pa). PE (Pa) is a value when the ink meniscus of the ink absorber breaks, and the critical pressure when the ink meniscus formed on the nozzle of the print head is broken is Pn (Pa ), And the water head pressure between the ink discharge port of the nozzle and the ink supply port of the ink container is Ph (Pa), Pn− | Ph | >Pm> PE is established,The filtration accuracy of the filter is F (m), the cell density of the ink absorber before being stored in the ink storage portion is N (cells / m), and is compressed into the ink storage portion before being stored in the ink storage portion. When the compression ratio indicated by the volume ratio of the ink absorber when stored is R,
  F ′ <1 / (N · R)
      (However, when the opening of the filter is circular, F ′ = F,
              In other cases, F ′ = √2 · F)
It is characterized by satisfying.
[0020]
When ink is supplied to the print head, a pressure necessary for the print head to suck ink, that is, a pressure by the meniscus of the nozzle of the print head (ink suction pressure) is applied to the ink supply path. At this time, by setting as described above, the critical value of the negative pressure generated in the ink tank is determined by the filter.
[0021]
Therefore, according to the above configuration, the critical value of the negative pressure generated in the ink absorber due to the surface tension of the ink is the negative value generated in the filter due to the surface tension of the ink, that is, the opening of the filter. Can be adjusted to be smaller than the critical value of the pressure (filter pressure) by the meniscus of the part (mesh), the ink meniscus formed on the filter mesh before ink emptying is broken, and air is supplied to the ink supply path The ink is prevented from being mixed in, and the meniscus of the ink absorber is retracted according to the consumption of the ink, thereby enabling a stable ink supply operation. In addition, factors other than a decrease in the remaining amount of ink, such as bubbles generated in the ink in the ink storage section due to carriage vibration, atmospheric pressure, or ambient temperature change, are captured by the filter to prevent air from entering the ink supply path. Thus, highly reliable printing can be performed and ink can be consumed without waste.
[0022]
Therefore, according to the above-described configuration, the image forming apparatus having the design guideline for the ink supply system can be prevented so as to prevent the occurrence of problems such as air mixing into the ink supply system before ink empty during continuous ink discharge. Can be provided.
[0023]
Further, according to the above configuration, as described above, the negative pressure at the time of ink supply (including the time of ink empty) can be managed with a filtration accuracy F (m) with small variation. Pressure can be obtained.
[0024]
In order to solve the above problems, an image forming apparatus according to the present invention sets the diameter of the nozzle (ink discharge nozzle) of the print head to D._N(M)
D_N<F '<1 / (NR)
(However, when the opening of the filter is circular, F ′ = F,
In other cases, F ′ = √2 · F)
It is characterized by satisfying.
[0025]
According to the above configuration, the critical value of the ink suction pressure due to the ink meniscus in the nozzle (nozzle portion) of the print head is greater than the critical value of the pressure due to the ink meniscus at the opening of the filter. It can be adjusted to be small, and air can be sucked from the nozzle tip, preventing the print head from causing ejection failure.
[0026]
Further, according to the above configuration, it is possible to prevent the ink meniscus formed in the opening of the filter from being broken and air from being mixed into the ink supply path, and from the ink storage section to the ink supply path. It is possible to prevent air from being inadvertently sucked in, and the ink held by the ink absorber can be effectively supplied from the print head. Therefore, according to the above configuration, it is possible to further prevent air from being mixed into the ink supply path due to factors other than a decrease in the remaining amount of ink, and to more effectively prevent a malfunction in detecting the remaining amount of ink.
[0027]
Therefore, according to the above-described configuration, the image forming apparatus having the design guideline for the ink supply system can be prevented so as to prevent the occurrence of problems such as air mixing into the ink supply system before ink empty during continuous ink discharge. Can be provided.
[0028]
  In order to solve the above problems, an image forming apparatus according to the present invention has an ink storage portion (for example, an ink tank provided in an ink cartridge) in which a porous ink storage body (for example, a foam material) that holds ink is stored. And an ink supply path for supplying ink to the print head from the ink storage section, a filter (for example, provided at an end of the ink supply path on the ink storage section side) inside the ink supply path. Filter)The negative pressure generated in the ink supply path at the time of ink supply and on the downstream side of the filter and the value when the meniscus of the ink formed at the opening of the filter is torn is defined as Pm (Pa). PE (Pa) is a value when the ink meniscus of the ink absorber breaks, and the critical pressure when the ink meniscus formed on the nozzle of the print head is broken is Pn (Pa ), And the water head pressure between the ink discharge port of the nozzle and the ink supply port of the ink container is Ph (Pa), Pn− | Ph | >Pm> PE is established,The ink absorber is compressed in advance before being stored in the ink storage portion, the filtering accuracy of the filter is F (m), and the cell density of the ink absorber before the compression is N ′. (Pieces / m), when R ′ is a compression ratio (compression ratio) indicated by the volume ratio of the ink absorber after compression processing before compression processing,
  F ′ <1 / (N ′ · R ′)
      (However, when the opening of the filter is circular, F ′ = F,
              In other cases, F ′ = √2 · F)
It is characterized by satisfying.
[0029]
As described above, when ink is supplied to the print head, the pressure required for the print head to suck ink, that is, the pressure (ink suction pressure) by the meniscus of the nozzle of the print head is applied to the ink supply path. . At this time, by setting as described above, the critical value of the negative pressure generated in the ink tank is determined by the filter.
[0030]
Therefore, according to the above configuration, the critical value of the negative pressure generated in the ink absorber due to the surface tension of the ink is the negative value generated in the filter due to the surface tension of the ink, that is, the opening of the filter. Can be adjusted to be smaller than the critical value of the pressure (filter pressure) by the meniscus of the part (mesh), the ink meniscus formed in the filter mesh before ink emptying is broken, and air is supplied to the ink Mixing in the path is prevented, and the meniscus of the ink absorber is retracted according to the consumption of the ink, so that a stable ink supply operation is possible. In addition, factors other than a decrease in the remaining amount of ink, such as bubbles generated in the ink in the ink storage section due to carriage vibration, atmospheric pressure, or ambient temperature change, are captured by the filter to prevent air from entering the ink supply path. Highly reliable printing can be performed and ink can be consumed without waste.
[0031]
Therefore, according to the above-described configuration, the image forming apparatus having the design guideline for the ink supply system can be prevented so as to prevent the occurrence of problems such as air mixing into the ink supply system before ink empty during continuous ink discharge. Can be provided.
[0032]
In addition, according to the above configuration, as described above, the negative pressure at the time of ink supply (including the time of empty) can be managed with a filtration accuracy F (m) with small variation, and as a result, a stable negative pressure can be obtained. Can be obtained.
[0033]
In order to solve the above problems, an image forming apparatus according to the present invention sets the diameter of the nozzle (ink discharge nozzle) of the print head to D._N(M)
D_N<F ′ <1 / (N ′ · R ′)
(However, when the opening of the filter is circular, F ′ = F,
In other cases, F ′ = √2 · F)
It is characterized by satisfying.
[0034]
According to the above configuration, the critical value of the ink suction pressure due to the ink meniscus in the nozzle (nozzle portion) of the print head is greater than the critical value of the pressure due to the ink meniscus at the opening of the filter. It can be adjusted to be small, and air can be sucked from the nozzle tip, preventing the print head from causing ejection failure.
[0035]
Further, according to the above configuration, it is possible to prevent the ink meniscus formed at the opening of the filter from being broken and air from being mixed into the ink supply path, and from the ink storage section to the ink supply path. It is possible to prevent air from being inadvertently sucked in, and the ink held by the ink absorber can be effectively supplied from the print head. Therefore, according to the above configuration, it is possible to further prevent air from being mixed into the ink supply path due to factors other than a decrease in the remaining amount of ink, and to more effectively prevent a malfunction in detecting the remaining amount of ink.
[0036]
Therefore, according to the above-described configuration, the image forming apparatus having the design guideline for the ink supply system can be prevented so as to prevent the occurrence of problems such as air mixing into the ink supply system before ink empty during continuous ink discharge. Can be provided.
[0037]
  In order to solve the above problems, an image forming apparatus according to the present invention has an ink storage portion (for example, an ink tank provided in an ink cartridge) in which a porous ink storage body (for example, a foam material) that holds ink is stored. And an ink supply path for supplying ink to the print head from the ink storage section, a filter (for example, provided at an end of the ink supply path on the ink storage section side) inside the ink supply path. Filter)The negative pressure generated in the ink supply path at the time of ink supply and on the downstream side of the filter and the value when the meniscus of the ink formed at the opening of the filter is torn is defined as Pm (Pa). PE (Pa) is a value when the ink meniscus of the ink absorber breaks, and the critical pressure when the ink meniscus formed on the nozzle of the print head is broken is Pn (Pa ), And the water head pressure between the ink discharge port of the nozzle and the ink supply port of the ink container is Ph (Pa), Pn− | Ph | >Pm> PE is established,The filtration accuracy of the filter is F (m), and the water head of the ink storage portion that is generated when ink is supplied to the print head via the ink supply path when the ink storage portion is fully filled with ink. The pressure is Pi (Pa), the pressure loss due to the viscous resistance of the ink in the ink storage part is Pμ (Pa), the surface tension of the ink is η (N / m), and the ink absorber before being stored in the ink storage part A cell density of N (cells / m), a compression ratio indicated by a volume ratio of the ink absorber when stored in the ink storage unit with respect to before being stored in the ink storage unit, R, The cross-sectional area of the ink absorber when it is compressed and stored in the ink storage portion is S (m²), The height of the ink absorber when compressed and stored in the ink storage portion is L (m), and the viscosity of the ink at 25 ° C. is μ.₂₅(Pa · s), any temperature T_KThe viscosity in (K) is μ_TK(Pa · s), any temperature T_KIn (K),
  4 • η / F ′> | Pμ | + | Pi |
  Pμ = (k / A) · {μ_TK・ L ・ (N ・ R)²/ S} ・ Q
      (However, coefficient (k / A) = 485)
  μ_TK= Α · exp (β / T_K),
  α = μ₂₅/ Exp (β / 298),
  β = Ln {0.42 · Ln (μ₂₅) +4.71} / (1 / 273−1 / 298)
      (However, when the opening of the filter is circular, F ′ = F,
              In other cases, F ′ = √2 · F)
It is characterized by satisfying.
[0038]
According to the above configuration, the negative pressure generated in the ink absorber can be adjusted so that the negative pressure is smaller than the critical value of the negative pressure of the ink meniscus in the opening of the filter. It is possible to prevent the ink meniscus formed in the portion from being broken and air from being mixed into the ink supply path. For this reason, according to the above-described configuration, it is possible to prevent air from being mixed into the ink supply path due to factors other than a decrease in the remaining amount of ink, to prevent a malfunction in detecting the remaining amount of ink. High printing can be performed.
[0039]
Therefore, according to the above configuration, the ink supply system design guideline according to the characteristics of the ink can prevent the occurrence of problems such as air mixing into the ink supply system before ink empty during continuous ink ejection. Can be provided.
[0040]
Moreover, according to said structure, the maximum negative pressure at the time of ink empty can be managed by the filtration accuracy F (m) with a small variation as mentioned above, As a result, the stable negative pressure can be obtained. .
[0041]
In order to solve the above problems, an image forming apparatus according to the present invention sets the diameter of a nozzle (ink discharge nozzle) in the print head to D._N(M) When the water head pressure between the ink discharge port of the nozzle and the ink supply port of the ink container is Ph (Pa)
4 • η / D_N− | Ph |> 4 · η / F ′> | Pμ | + | Pi |
(However, when the opening of the filter is circular, F ′ = F,
In other cases, F ′ = √2 · F)
It is characterized by satisfying.
[0042]
According to the above configuration, the pressure leaked by the filter when ink is supplied, particularly when ink is supplied immediately before ink empty, can be appropriately managed without exceeding the critical pressure of the nozzle of the print head, and air is sucked from the nozzle. In addition, it is possible to effectively filter the foreign matters going to the ink supply path, and to improve the reliability of the ejection operation by the nozzles.
[0043]
Therefore, according to the above-described configuration, the image forming apparatus having the design guideline for the ink supply system can be prevented so as to prevent the occurrence of problems such as air mixing into the ink supply system before ink empty during continuous ink discharge. Can be provided.
[0044]
  In order to solve the above problems, an image forming apparatus according to the present invention has an ink storage portion (for example, an ink tank provided in an ink cartridge) in which a porous ink storage body (for example, a foam material) that holds ink is stored. And an ink supply path for supplying ink to the print head from the ink storage section, a filter (for example, provided at an end of the ink supply path on the ink storage section side) inside the ink supply path. Filter)The negative pressure generated in the ink supply path at the time of ink supply and on the downstream side of the filter and the value when the meniscus of the ink formed at the opening of the filter is torn is defined as Pm (Pa). PE (Pa) is a value when the ink meniscus of the ink absorber breaks, and the critical pressure when the ink meniscus formed on the nozzle of the print head is broken is Pn (Pa ), And the water head pressure between the ink discharge port of the nozzle and the ink supply port of the ink container is Ph (Pa), Pn− | Ph | >Pm> PE is established,The ink absorber is pre-compressed before being stored in the ink storage portion, and the filter has a filtration accuracy of F (m), and the ink storage portion is fully filled with ink. Pi (Pa) is the water head pressure of the ink storage unit that is generated when ink is supplied to the print head via the ink supply path, and Pμ (Pa) is the pressure loss due to the viscous resistance of the ink in the ink storage unit. The surface tension of the ink is η (N / m), the cell density of the ink absorber before compression processing is N ′ (number / m), and the volume ratio of the ink absorber after compression processing to that before compression processing is shown. R ′ is a compression ratio (compression ratio) R ′ is a cross-sectional area of the ink absorber when it is compressed and stored in the ink storage portion.²), The height of the ink absorber when compressed and stored in the ink storage portion is L (m), and the viscosity of the ink at 25 ° C. is μ.₂₅(Pa · s), any temperature T_KThe viscosity in (K) is μ_TK(Pa · s), any temperature T_KIn (K),
  4 • η / F ′> | Pμ | + | Pi |
  Pμ = (k / A) · {μ_TK・ L ・ (N '・ R')²/ S} ・ Q
      (However, coefficient (k / A) = 485)
  μ_TK= Α · exp (β / T_K),
  α = μ₂₅/ Exp (β / 298),
  β = Ln {0.42 · Ln (μ₂₅) +4.71} / (1 / 273−1 / 298)
      (However, when the opening of the filter is circular, F ′ = F,
              In other cases, F ′ = √2 · F)
It is characterized by satisfying.
[0045]
According to the above configuration, when ink is supplied, the critical value of the pressure caused by the meniscus in the opening of the filter can be appropriately managed without exceeding the critical value of the ink suction pressure caused by the meniscus of the nozzle of the print head. The suction of air can be prevented, and the negative pressure generated in the ink absorber can be adjusted to be smaller than the critical value of the negative pressure of the ink meniscus in the opening of the filter. Further, it is possible to prevent the ink meniscus from being broken and air from being mixed into the ink supply path. For this reason, according to the above-described configuration, it is possible to prevent air from being mixed into the ink supply path due to factors other than a decrease in the remaining amount of ink, to prevent a malfunction in detecting the remaining amount of ink. High printing can be performed.
[0046]
Therefore, according to the above configuration, the ink supply system design guideline according to the characteristics of the ink can prevent the occurrence of problems such as air mixing into the ink supply system before ink empty during continuous ink ejection. Can be provided.
[0047]
Moreover, according to said structure, the maximum negative pressure at the time of ink empty can be managed by the filtration accuracy F (m) with a small variation as mentioned above, As a result, the stable negative pressure can be obtained. .
[0048]
In order to solve the above problems, an image forming apparatus according to the present invention sets the diameter of a nozzle (ink discharge nozzle) in the print head to D._N(M) When the water head pressure between the ink discharge port of the nozzle and the ink supply port of the ink storage unit is Ph (Pa),
4 • η / D_N− | Ph |> 4 · η / F ′> | Pμ | + | Pi |
(However, when the opening of the filter is circular, F ′ = F,
In other cases, F ′ = √2 · F)
It is characterized by satisfying.
[0049]
According to the above configuration, when ink is supplied, the critical value of the pressure caused by the meniscus in the opening of the filter can be appropriately managed without exceeding the critical value of the ink suction pressure caused by the meniscus of the nozzle of the print head. The suction of air can be prevented, and the negative pressure generated in the ink absorber can be adjusted to be smaller than the critical value of the negative pressure of the ink meniscus in the opening of the filter. Further, it is possible to prevent the ink meniscus from being broken and air from being mixed into the ink supply path. For this reason, according to the above-described configuration, it is possible to prevent air from being mixed into the ink supply path due to factors other than a decrease in the remaining amount of ink, to prevent a malfunction in detecting the remaining amount of ink. High printing can be performed.
[0050]
Therefore, according to the above-described configuration, the image forming apparatus having the design guideline for the ink supply system can be prevented so as to prevent the occurrence of problems such as air mixing into the ink supply system before ink empty during continuous ink discharge. Can be provided.
[0051]
Moreover, according to said structure, the maximum negative pressure at the time of ink empty can be managed by the filtration accuracy F (m) with a small variation as mentioned above, As a result, the stable negative pressure can be obtained. .
[0052]
In order to solve the above problems, an image forming apparatus according to the present invention is a detector that detects the presence or absence of ink in the ink supply path (for example, a detection that detects the presence or absence of ink when current does not flow between electrodes). Electrode).
[0053]
According to the above configuration, the negative pressure generated in the ink absorber can be adjusted so that the negative pressure becomes smaller than the critical value of the negative pressure of the ink meniscus at the opening of the filter. It is possible to prevent the ink meniscus formed in the portion from being broken and air from being mixed into the ink supply path. For this reason, according to the above configuration, it is possible to prevent air from being mixed into the ink supply path due to factors other than a decrease in the remaining amount of ink, that is, other than when the ink is empty, and to prevent a malfunction in detecting the remaining amount of ink. Printing with high reliability.
[0054]
DETAILED DESCRIPTION OF THE INVENTION
An embodiment of the present invention will be described with reference to FIGS. 1 to 27 as follows.
[0055]
As shown in FIG. 2, the ink jet recording apparatus as an image forming apparatus in the present embodiment includes a paper feeding unit, a separation unit, a transport unit, a printing unit, and a discharge unit.
[0056]
The paper feed unit supplies a sheet 201 as a recording paper when printing is performed, and includes a paper feed tray 101 and a pickup roller 102. When printing is not performed, the sheet 201 is stored.
[0057]
The separating unit is for supplying the sheets 201 supplied from the sheet feeding unit one by one to the printing unit, and includes a sheet feeding roller and a separating device (not shown). In the separation device, the friction between the sheet 201 and the pad portion that is a contact portion with the sheet 201 is set to be larger than the friction between the sheets 201 and 201. In the paper feed roller, the friction between the paper feed roller and the sheet 201 is set to be larger than the friction between the pad and the sheet 201 and the friction between the sheets 201 and 201. Therefore, even if the two sheets 201 are sent to the separation unit, these sheets 201 and 201 can be separated by the paper feed roller and only the upper sheet 201 can be sent to the conveyance unit.
[0058]
The conveyance unit is for conveying the sheets 201 supplied one by one from the separation unit to the printing unit, and includes a guide plate (not shown) and a roller pair such as a conveyance pressing roller 111 and a conveyance roller 112. The roller pair is a member that adjusts the conveyance of the sheet 201 so that the ink from the print head 1 is sprayed to an appropriate position of the sheet 201 when the sheet 201 is fed between the print head 1 and the platen 113. .
[0059]
The printing unit is for performing printing on the sheet 201 supplied from the roller pair of the conveying unit. The printing head 1, the carriage 2 on which the printing head 1 is mounted, and a guide for guiding the carriage 2. The ink supply path 3 includes a shaft (carriage holding shaft) 121, an ink cartridge 20 that supplies ink to the print head 1, a platen 113 that serves as a base of the sheet 201 during printing, and an ink supply tube 4. An ink supply path 3 including an ink supply tube 4 connects the print head 1 and the ink cartridge 20 and supplies ink from the ink cartridge 20 to the print head 1 as an ink flow path. Among these, the print head 1, the ink supply path 3 including the ink supply tube 4, and the ink cartridge 20 constitute an ink supply device 10 described later.
[0060]
The discharge unit is for discharging the printed sheet 201 to the outside of the ink jet recording apparatus, and includes discharge rollers 131 and 132 and a discharge tray 134.
[0061]
The ink jet recording apparatus having the above configuration performs printing by the following operation.
[0062]
First, a print request based on image information is made to an inkjet recording apparatus from a computer or the like (not shown). The ink jet recording apparatus that has received the print request carries out the sheet 201 on the paper feed tray 101 from the paper feed unit by the pickup roller 102.
[0063]
Next, the unloaded sheet 201 passes through the separation unit by the sheet feeding roller and is sent to the conveyance unit. In the transport unit, the sheet 201 is sent between the print head 1 and the platen 113 by the roller pair of the transport press roller 111 and the transport roller 112.
[0064]
In the printing unit, ink is sprayed from the discharge nozzle (ink discharge nozzle) 1a (see FIG. 20), which is the ink nozzle unit in the print head 1, to the sheet 201 on the platen 113 in accordance with the image information. At this time, the sheet 201 is temporarily stopped on the platen 113. While blowing ink, the carriage 2 is guided by the guide shaft 121 and scanned for one line in the main scanning direction.
[0065]
When this is completed, the sheet 201 is moved on the platen 113 by a certain width in the sub-scanning direction. In the printing unit, the above processing is continuously performed corresponding to the image information, whereby printing is performed on the entire surface of the sheet 201.
[0066]
The printed sheet 201 passes through the ink drying section and is discharged to the discharge tray 134 through the paper discharge port 133 by the discharge rollers 131 and 132. Thereafter, the sheet 201 is provided to the user as a printed matter.
[0067]
Here, the ink supply device 10 of the ink jet recording apparatus will be described in detail with reference to FIGS. 1, 3, and 5.
[0068]
As shown in FIG. 3, the ink supply device 10 includes the print head 1, the ink supply path 3, and the ink cartridge 20, as described above.
[0069]
As shown in FIGS. 1A and 1B, the ink cartridge 20 is usually provided with an ink tank 21 as an ink storage portion having a space for storing ink. In the ink cartridge 20 of the present embodiment, an ink absorber 22 that is a porous holder made of, for example, polyurethane resin is provided inside the ink tank 21 (space).
[0070]
An ink supply path 3 including an ink supply tube 4 for supplying ink to the print head 1 is provided on the bottom surface of the ink tank 21, for example.
[0071]
A filter 23 is provided in the ink supply path 3, specifically, a part of the ink supply path 3 on the side of the ink tank 21, preferably at the end, and the ink supply tube 4 is connected to the filter 23. The ink supply path 3 end (ink supply port 3a) on the formation side, that is, the end of the ink supply tube 4 is inserted into the ink supply port 24 provided on the bottom surface of the ink tank 21, for example. The ink tank 21 is connected. Thus, the end of the ink supply tube 4 on the filter 23 forming side, that is, the end of the ink supply path 3 where the filter 23 is formed in the ink supply tube 4 (ink supply port 3a) is placed in the ink tank 21. positioned.
[0072]
Further, as shown in FIGS. 1A to 1C, the ink supply tube 4 outside the ink tank 21 is used as an ink remaining amount detection electrode (detector) so as to sandwich the ink supply tube 4. A pair of detection electrodes (electrode portions) 25 and 25 are provided. That is, the ink supply path 3 outside the ink tank 21 is provided with a pair of detection electrodes 25 and 25 so as to sandwich the ink supply path 3.
[0073]
The ink supply device 10 supplies the ink stored in the ink tank 21 to the print head 1 by applying a negative pressure for sucking out ink through the filter 23 from the print head 1 side.
[0074]
For example, the print head 1 has a maximum of 0.49 cc per minute (0.49 × 10 10) when all channels are continuously driven.^-6m^Three) And the same amount of ink is sucked from the ink tank 21, and the pressure applied to the ink supply path 3 at that time is a pressure gauge 26 as shown in FIG. It can be measured with. The print head 1 and the ink cartridge 20 are arranged such that, for example, the print head 1 has a head (Ph; head head pressure) of 50 mm and the ink tank 21 has a head (Pi; tank head pressure) of 30 mm. Has been. Here, the head head pressure Ph indicates the head pressure between the discharge nozzle 1 a of the print head 1 and the ink supply port 24. Further, the tank head pressure Pi is the head pressure generated in the ink tank 21 when the ink is fully supplied to the print head 1 through the ink supply port 24 when the ink tank 21 is fully filled with ink. Indicates.
[0075]
As shown in FIG. 4, the filter 23 is formed by knitting a belt-like, for example, stainless steel material as a weft and warp into a net shape. In addition to the above method, for example, a plate-like member having an opening formed by etching may be used as the filter 23.
[0076]
In this ink cartridge 20, as shown in FIGS. 1A to 1C, the ink between the detection electrodes 25, 25 is caused by the air mixed in the ink supply path 3 through the filter 23. When the ink is pushed out, that is, when there is no ink between the detection electrodes 25 and 25, the remaining amount of ink, that is, the ink is utilized by utilizing the fact that no current flows between the detection electrodes 25 and 25. (Ink empty) is detected.
[0077]
Hereinafter, the relationship between the negative pressure applied to the ink supply path 3 and the time course in the process of detecting the remaining amount of ink will be described in detail with reference to FIGS. 5 and 6 are graphs showing the relationship between the elapsed time and the negative pressure applied to the ink supply path 3 when ink is continuously ejected from a state where the ink cartridge 20 is filled with ink. 6 is a graph schematically showing the relationship shown in FIG.
[0078]
First, when the print head 1 is driven, that is, when negative pressure is applied to the ink supply path 3 in order to consume ink in the ink tank 21, the amount of ink used increases as shown in FIGS. Along with this, the negative pressure applied to the ink supply path 3 also gradually increases.
[0079]
However, when the remaining amount of ink decreases, the negative pressure applied to the ink supply path 3 rapidly increases at a certain point and decreases after reaching the maximum value. This is because when a large suction force is applied to the ink supply path 3, the ink meniscus formed in the opening 23a (see FIG. 4) of the filter 23 is broken, and air is sucked to reduce the negative pressure. It is shown that.
[0080]
That is, as the remaining amount of ink decreases, the ink meniscus absorbed in the cell 22a (opening, see FIG. 13) of the ink absorber 22 moves backward, and the negative pressure applied to the ink supply path 3 by the surface tension of the ink is reduced. Increase gradually. The negative pressure applied to the ink supply path 3 is the critical pressure of the cell 22a of the ink absorber 22, that is, the critical pressure P by the ink absorber 22 when the ink is empty._EWhen the pressure exceeds the upper limit, the ink meniscus reaches the filter 23, and the opening 23 a of the filter 23 dominates the negative pressure applied to the ink supply path 3. As the ink is further consumed, the ink meniscus in the opening 23a of the filter 23 recedes as in the ink absorber 22, and the negative pressure applied to the ink supply path 3 increases due to the surface tension of the ink. The critical pressure (filter pressure) due to the opening diameter of the opening 23a, that is, the critical pressure (maximum negative pressure) Pm due to the filter 23 rapidly increases. Thereafter, when the suction pressure from the print head 1 exceeds the critical pressure Pm by the filter 23, the surface of the ink meniscus formed in the opening 23a of the filter 23 is broken, and air is sucked into the ink supply path 3. . Thereby, the negative pressure applied to the ink supply path 3 is reduced.
[0081]
In the measurement of the negative pressure applied to the ink supply path 3, as shown in FIG. 7, a mesh-like filter infiltrated with ink (same as the filter 23 in the process of detecting the remaining ink amount) ( A measuring device is used in which an ink supply tube 4 is connected to a cylinder 32 to which a mesh filter 31 is bonded so that the filter 31 becomes a lid.
[0082]
The ink supply tube 4 is used to eliminate the influence of ink that has been infiltrated into the filter 31 through the ink supply tube 4 connected to the cylinder 32 using a pump (not shown). The flow rate of ink flowing in the ink supply path 3 (ink supply amount) is 0.05 cc per minute (that is, 0.05 × 10 5).^-6m^Three), And the negative pressure applied to the filter 31 at this time was measured by the pressure gauge 26, whereby the negative pressure applied to the ink supply path 3 including the ink supply tube 4 was measured.
[0083]
Further, when the measurement of the negative pressure using this measuring apparatus was performed while changing the size of the filter 23 opening 23a (mesh) (filtration accuracy F), that is, the size of the opening of the filter 31, As shown in FIG. 8, the smaller the filtration accuracy F, the higher the negative pressure applied to the ink supply path 3, that is, the negative pressure applied to the filter 23 (the filter 31 in the above measurement).
[0084]
Therefore, next, this tendency is verified by graphing the relationship between the critical pressure (maximum negative pressure) Pm of the ink negative pressure by the filter 23 (mesh filter) and the filtration accuracy F of the filter 23 (FIG. 9). did.
[0085]
Here, the filtration accuracy F can be interpreted as the shortest length (minimum gap width) of the opening 23a of the filter 23 (mesh filter).
[0086]
The critical pressure (critical pressure due to surface tension) Pc (Pa) in a circular opening having a diameter d (m) that forms a meniscus of ink with a liquid having a surface tension η (N / m) is expressed by the following general formula (1).
Pc = 4η / d (1)
Widely known in
[0087]
Note that in this embodiment, the same symbols indicate the same physical properties in the general formulas, the empirical formulas, the relational formulas, and the like. In addition, regarding the calculation value calculation unit in each formula, the same symbol indicates the same unit.
[0088]
Therefore, the critical pressure Pm (Pa) by the filter 23 is obtained as the critical pressure Pc (Pa) by substituting the filtration accuracy F (m) of the filter 23 into the diameter d (m) of the general formula (1). The calculated value obtained by the general formula (1) with respect to the actually measured value is √2 times, and it is found that if the filtration accuracy F of the filter 23 is substituted as it is, a large flaw occurs between the calculated value and the actually measured value. .
[0089]
This is because, as shown in FIG. 4, the opening shape of the filter 23 composed of weft and warp is not circular, and the filtration accuracy F depends on the minimum gap width of the opening 23a of the filter 23, whereas It is considered that the critical pressure Pm due to the filter 23 depends on the maximum gap width of the opening 23a of the filter 23.
[0090]
Therefore, based on this consideration, the critical pressure Pm (Pa) by the filter 23 is obtained by multiplying the filtration accuracy F by √2 using the surface tension η (N / m) of the ink and the filtration accuracy F (m). The following empirical formula (2)
Pm = 4η / (√2 · F) (2)
Represented as:
[0091]
Therefore, the vertical axis is the critical pressure Pm by the filter 23, that is, the negative pressure applied to the ink supply path 3, and the horizontal axis is the filtration accuracy F of the filter 23. The measured values shown in FIG. 9 is used to obtain a graph of the relationship between the critical pressure Pm by the filter 23 and the filtration accuracy F. In FIG. 9, “Δ” indicates the actually measured value shown in FIG. 8, and the solid line indicates the calculated value by the above experimental formula (2).
[0092]
From the results shown in FIG. 9, it was found that the actually measured values and the calculated values obtained by the empirical formula (2) almost coincided with each other, and the above-described tendency is correct. That is, from the results shown in FIGS. 8 and 9, it was found that the critical pressure Pm by the filter 23 depends on the size of the opening 23 a of the filter 23.
[0093]
For this reason, in this embodiment, as shown in FIG. 6, the negative pressure applied to the ink supply path 3 becomes the critical pressure Pm by the filter 23, and the ink meniscus (ink liquid level) formed in the opening of the filter 23. ) Is broken and the air reaches the electrode portion composed of the detection electrodes 25 and 25, and when the detection resistance value by the detection electrodes 25 and 25 exceeds a predetermined value, the ink tank 21 is substantially empty, that is, The critical pressure Pm by the filter 23, which is a critical pressure at which the ink meniscus is broken, is controlled so as not to exceed a predetermined value.
[0094]
In this embodiment, as a result of various experiments on the negative pressure applied to the ink supply path 3 when the remaining ink amount is empty, the negative pressure of the ink supply system (the critical pressure of the ink absorber 22 or the filter 23) is set to 2. 0 kPa or less.
[0095]
This is because, for example, when the negative pressure of the ink supply system (the critical pressure of the ink absorber 22 or the filter 23) is not 2.0 kPa or less when ink is continuously ejected, the filter 23 is generated by the negative pressure generated in the ink supply system. As shown in FIGS. 20 and 21, before the ink meniscus formed in the opening of the ink breaks and air reaches the electrode portion and is judged empty, the tip of the discharge nozzle 1a of the print head 1 ( The problem is that the ink meniscus (ink level) retreats too much from the nozzle tip and air is sucked from the nozzle tip, and ink droplets cannot be ejected (supplied) normally and stably. It is.
[0096]
Next, design guidelines for optimizing the ink absorber 22 in the ink cartridge 20 will be described below.
[0097]
As shown in FIGS. 1A to 1C, the ink cartridge 20 includes an ink cartridge 20 including an ink tank 21 in which a foam material as an ink absorber 22 is stored. A porous body of the foam material is impregnated with ink, and the foam material is compressed and accommodated in the ink tank 21.
[0098]
The ink held in the porous body is discharged from the ink cartridge 20 to the print head 1 side by capillary force through the discharge nozzle 1a (see FIG. 20) which is the ink supply port 24 provided in the ink cartridge 20. .
[0099]
However, depending on the holding force of the ink held in the porous holder in the ink tank 21, there may be a problem such as insufficient ink supply during continuous discharge or ink leakage when the ink cartridge 20 is attached or detached.
[0100]
In order to solve this problem, a design guideline for the ink absorber 22 corresponding to the ink characteristics is required. Therefore, in the present embodiment, an experiment was conducted using the following ink and ink cartridge as the ink and ink cartridge 20, the stable negative pressure P in the ink cartridge 20 was measured, and design guidelines were examined. . The results of this experiment are shown in Table 1. The conditions used for the ink and the ink cartridge 20 used in the experiment are as follows.
[0101]
Ink surface tension η = 0.03 (N / m) (= 30 dyn / cm)
・ Ink viscosity μ = 0.07 (Pa · s) (= 7 cp)
-Ink composition: H₂O, pigment, polyethylene glycol
-Cell density N of ink absorber 22 (foam material) = 1.57 × 10^Three(Pieces / m) (= 40 pieces / inch)
-Material of ink absorber 22 (foam material): polyurethane
・ Inner size of ink cartridge 20 (width W x depth V x height L)
W x V x L = 0.015 x 0.074 x 0.030 (m)
The outer size of the ink absorber 22 when stored in the ink cartridge 20 (ink tank 21) is equal to the inner size of the ink cartridge 20.
[0102]
The evaluation items in Table 1 are as follows.
[0103]
Compression ratio R: Volume ratio of the ink absorber 22 (foam material) before being stored in the ink cartridge 20 when compressed and stored in the ink cartridge 20
Cell density N (pieces / m): Cell density of the ink absorber 22 (foam material) before being stored in the ink cartridge 20
Mounting cell density M (pieces / m) of ink absorber 22 (foam material) during compression: Mounting cell density of ink absorber 22 (foam material) when compressed and stored in ink cartridge 20
・ Flow rate Q (m^Three/ S): ink flow rate
Efficiency τ (%): Total outflow amount from ink cartridge 20 (actually usable ink volume) ÷ ink filling amount (filled ink volume)
Ink upper limit stable negative pressure Pu (Pa): The stable negative pressure in the ink cartridge 20 measured when the ink in the ink cartridge 20 is filled up to the upper limit, that is, when the ink flow is full and a predetermined ink flow rate is set. Measured value
Ink lower limit stable negative pressure PL (Pa): measured when the ink in the ink cartridge 20 is filled only to the lower limit, that is, when a predetermined ink flow rate is set immediately before the ink in the ink cartridge 20 runs out. Measured value of stable negative pressure in ink cartridge 20
[0104]
[Table 1]

[0105]
In the present embodiment, the critical pressure P by the ink absorber 22 at the time of ink empty is considered from the viewpoint of the foreign matter removing ability of the filter 23._E(Hereinafter, sometimes referred to as the critical pressure of the ink absorber) and the critical pressure Pm by the filter 23 (hereinafter, sometimes referred to as the critical pressure of the filter) are Pm> P_EIt is set to satisfy. And in this Embodiment, as shown in FIG._E, Pm, the pressure loss Pμ of the ink supply path 3, and the tank head pressure Pi are Pm> P_E> Pμ + Pi is set to be satisfied. However, the present embodiment is not limited to this, and the magnitude relationship may be reversed or the filter 23 may not be used depending on how the ink supply system is set.
[0106]
As will be described in detail later, as a result of detailed examination of the actual measurement value of the generated negative pressure based on the hydrodynamic theory, the stable negative pressure Pu at the upper limit of the ink is the pressure of the flow path, that is, the pressure of the ink supply path 3 due to the viscous resistance of the ink. It has been found that the stable negative pressure PL at the ink lower limit is based on the surface tension η of the ink due to the loss Pμ.
[0107]
In the above measurement, the ink holding force needs to be determined in consideration of the height of the ink cartridge 20, the variation of the cells 22 a of the ink absorber 22 (foam material), and the vibration applied to the ink cartridge 20. This is because if the holding force is insufficient, there is a problem that the ink leaks carelessly when the ink cartridge 20 is attached / detached particularly at the upper limit of the ink.
[0108]
For example, if the height of the ink cartridge 20 is 34 mm and the safety factor is 2, the specific gravity γ of the ink is about 1.0, so the holding force is 68 (= 34 × 2) mm at the water head. 0.67 kPa is required. In general, the height of an ink cartridge that is widely used is approximately 40 mm or less, and therefore, it is necessary to withstand a water head pressure of 0.8 kPa.
[0109]
The ink holding force is a capillary pressure based on the surface tension η. When the cell diameter during compression is regarded as a circular opening having a diameter d (m), the ink absorber 22 (foam material) during compression is mounted. From the cell density M (M = N · R; strictly speaking, M≈N · R) (pieces / m), the cell diameter d (m) during compression is expressed by the following relational expression (3)
d = 1 / (N · R) (3)
The critical pressure P_EAnd the cell density N (pieces / m) and the compression rate (R) are as follows from the general formula (1) and the relational formula (3), where the surface tension of the ink is η (N / m): The following relational expression (4)
P_E= 4 ・ η ・ (N ・ R) (4)
It is represented by Accordingly, the stable negative pressure PL at the ink lower limit has a mounting cell density M (M = N · R) of 7.87 × 10.^ThreeIf it is (pieces / m) or more (that is, 200 pieces / inch or more), a holding force of 0.86 kPa and 89 mm or more can be obtained with the water head, so that there is a problem that ink is leaked carelessly when the ink cartridge 20 is attached or detached. It can be prevented from occurring.
[0110]
In addition, when ink is continuously ejected, the negative pressure of the ink supply system (the critical pressure of the ink absorber 22 or the filter 23) is generated in the ink supply system if the safety factor is not less than 2.0 kPa. Ink supply becomes insufficient due to the negative pressure, and a problem arises that the ink liquid surface is retracted too much from the tip (nozzle tip) of the discharge nozzle 1a and air is sucked in, so that the ink cannot be stably supplied.
[0111]
Therefore, the mounting cell density M is 12.6 × 10 6.^ThreeIf (pieces / m) or less (that is, 320 pieces / inch or less), the negative pressure of the ink supply system is 1.5 kPa or less, and even when ink is continuously ejected, the ink can be stably supplied with a margin. It becomes possible.
[0112]
If the ratio of the ink volume that can actually be used (discharged) to the ink storage volume (filled ink volume) on the inner surface of the ink cartridge 20 is the efficiency τ (tank efficiency), as shown in FIG. (%) Decreases as the value of R, in other words, the value of N · R increases, and as shown in FIG. 11, the mounted cell density M (M = N · R) is 12.6 × 10 6.^ThreeWhen it reaches (pieces / m) (that is, 320 pieces / inch), it starts to decrease greatly. Therefore, as a condition for efficiently utilizing the volume of the ink cartridge 20, the mounting cell density M (M = N · R) is 12.6 × 10 6.^Three(Pieces / m) or less.
[0113]
Therefore, the ink cartridge 20 has a mounting cell density M (pieces / m) (M = N · R) of 7.87 × 10 6.^Three≦ M ≦ 12.6 × 10^ThreeBy designing so as to satisfy the above, it is possible to prevent problems such as inadvertent leakage of ink when the ink cartridge 20 is attached / detached, and to stabilize the ink with a margin even when ink is continuously ejected. Supply becomes possible and the volume of the ink cartridge 20 can be utilized efficiently. Furthermore, according to the above configuration, 7.87 × 10^ThreeEven above, 12.6 × 10^ThreeSince the following is sufficient, the range of selection in the design of the ink absorber 22 can be expanded.
[0114]
In addition, although these are theoretical values, it was confirmed that the measured values also satisfy these values. That is, in Table 1, the mounting cell density M = N · R is 7.87 × 10.^Three(Pieces / m), the lower limit stable negative pressure PL, which is an actually measured stable negative pressure, is 0.86 kPa or more, and the mounting cell density M (M = N · R) is 12.6 × 10 6.^ThreeIf it is (pieces / m) or less, the negative pressure of the ink supply system is 1.5 kPa or less, and stable ink supply with a margin is possible even when ink is continuously ejected. The measured stable negative pressure, the ink lower limit stable negative pressure PL, indicates what negative pressure the ink meniscus can withstand.
[0115]
Next, consideration is given to the stable negative pressure PL at the ink lower limit and the stable negative pressure Pu at the ink upper limit. The ink upper limit stable negative pressure Pu represents a negative pressure when ink is flowing.
[0116]
First, in order to normalize, compression rate R = 5.5, flow rate Q = 8.17 nm^ThreeA value obtained by normalizing the ink upper limit stable negative pressure Pu in each data with respect to the ink upper limit stable negative pressure Pu = 0.62 kPa at / s (0.49 cc / min) is defined as a starting point ratio Rs. R2 is the compression ratio R²Is normalized with respect to the compression ratio R = 5.5.
[0117]
On the other hand, compression ratio R = 5.5, flow rate Q = 8.17 nm^ThreeA value obtained by normalizing the ink lower limit stable negative pressure PL in each data with respect to the ink lower limit stable negative pressure PL = 0.99 kPa at / s (0.49 cc / min) is defined as an end point ratio Re. R1 is obtained by normalizing the compression rate R with respect to the compression rate R = 5.5.
[0118]
Here, when Rs / R2 is calculated at the start point and Re / R1 is calculated at the end point, Table 1 shows that each is approximately 1. Therefore, it can be seen that the ink upper limit stable negative pressure Pu is proportional to the square of the compression rate R, and the ink lower limit stable negative pressure PL is proportional to the compression rate R.
[0119]
Based on the above results, in order to obtain detailed design guidelines for the ink and the ink absorber 22 (foam material), these theories were given and studied. This will be described in detail below.
[0120]
First, the relationship between the stable negative pressure when the ink in the ink cartridge 20 is filled to the upper limit (the stable negative pressure Pu at the upper limit of the ink) and the compression ratio R will be considered below.
[0121]
When the ink in the ink cartridge 20 is filled up to the upper limit, that is, when the ink cartridge 20 is full of ink, each cell 22a of the ink absorber 22 (foam material) is regarded as a circular conduit, Assume that the liquid (ink) in the pipe is flowing due to the pressure difference ΔP of the pipe (pressure P1 at the pipe start point P1-pressure P2 at the pipe end point), that is, the pressure loss Pμ of the pipe due to viscous resistance. Can do. As shown in FIG. 12, a circular pipe line (each cell 223a is regarded as a circular pipe line, and the pressure difference ΔP (pressure P1 at the pipe start point—pressure P2 at the pipe end point), that is, due to viscous resistance It can be assumed that the liquid (ink) in the pipe is flowing due to the pressure loss Pμ of the pipe, as shown in Fig. 12. The theoretical value of the flow rate (Q) flowing through the circular pipe (each cell 22a). That is, the theoretical value of the flow rate of the ink flowing per pipe line is expressed as the flow rate Qi (m^Three/ S), the flow rate Qi (m^Three/ S) is the following general formula (5)
Qi = Pu · π · d^Four/ (128 ・ μ ・ L) (5)
Defined by Here, Pu is the pressure loss (Pa) of the pipe due to the viscous resistance of the ink, the negative negative pressure at the upper limit of the ink, d is the pipe diameter (m), μ is the viscosity of the ink (Pa · s), and L is the pipe. The flow path length (m) of the path.
[0122]
Here, when d (m) is regarded as a cell diameter at the time of compression, from the mounting cell density M (pieces / m) (M = N · R) of the ink absorber 22 (foam material) at the time of compression, As described above, the cell diameter d (m) is expressed by the following relational expression (3).
d = 1 / (N · R) (3)
It is represented by
[0123]
At this time, since the ink absorber 22 (foam material) is compressed and accommodated in the ink cartridge 20, each cell 22a of the ink absorber 22 (foam material) is in a close-packed state as shown in FIG. It is thought that. Accordingly, the cells 22a at the lower end of the foam material at the time of compression are considered to be in a close-packed state as shown in FIG. Therefore, the total cell number Nd (number), which is the total number of cells 22a at the lower end of the foam material during compression, is expressed by the following relational expression (6).
Nd = (2 / √3) · S / (d²(6)
It is represented by In Expression (6), S represents a cross-sectional area (width W × depth V) of the ink absorber 22 (foam material) when compressed and stored in the ink cartridge 20 (ink tank 21).
[0124]
Therefore, when assuming a cylindrical flow path having a constant diameter composed of the number of cells 22a represented by the relational expression (6), the total flow rate Qt (m) of ink flowing through the cylindrical flow path.^Three/ S) (Qt = Qi · Nd; theoretical value) is obtained from the following relational expression (7) based on the general formula (5) and the relational expressions (3) and (6).

      (However, in the formula, coefficient A = 2.83 × 10^-2Represents
It is represented by Therefore, it can be seen that the total flow rate Qt is inversely proportional to the square of the mounting cell density M (pieces / m) (M = N · R) of the ink absorber 22 (foam material) during compression.
[0125]
Table 2 shows the result of obtaining the total flow rate Qt, which is a theoretical value assuming the cylindrical flow path shown in FIG.
[0126]
[Table 2]

[0127]
In the actual ink absorber 22 (inside the foam material), as shown in FIG. 14, spherical or polyhedral cells 22 a communicate in a beaded manner. For this reason, an effective diameter becomes a value smaller than the said theoretical value by this continuous flow path. Therefore, an average magnification of the total flow rate Qt (theoretical value) obtained using the cell diameter with respect to the actual flow rate Q (measured flow rate) is obtained, and this is set as a correction coefficient k. That is, assuming that Qt / Q≈k, in the case of Table 2, the correction coefficient k is 13.75.
[0128]
Here, as shown in FIG. 15, the normalized flow path resistance obtained by integrating the spherical flow path with the diameter dm and the center position X = 0 is Rd, and the normalized flow path resistance of the cylindrical flow path FIG. 16 shows a resistance ratio Rd / Rm where Rm is Rm. As shown in FIG. 16, rd / Rm≈1 when X is close to 0, but it can be seen that Rd / Rm increases as X approaches dm / 2 (see FIG. 15). From this study, considering the correction coefficient k = 13.75, when the normalized cell diameter is 1, Rd / Rm = 13.75 at the position of X = 0.488. This means that the channel can be modeled with the normalized diameter of 0.21 and the adjacent cells 22a communicating with each other, and the value of the correction coefficient k determined from the actual measurement value is appropriate also from this study. It can be said.
[0129]
Therefore, the calculated flow rate Qc (m^Three/ S) is the following relational expression (8)
Qc = Qt / k (8)
(However, in the formula, the coefficient k represents 13.75)
Alternatively, by substituting the relational expression (7) into the relational expression (8), the following relational expression (9)
Qc = (A / k) · Pu · S / [μ · L · (N · R)²] (9)
(However, in the formula, coefficient (A / k) = 2.06 × 10^-3Represents
Can be obtained as
[0130]
Here, from Table 2, since Q / Qc is approximately 1 in each data, by using the correction coefficient k,
Q = (A / k) · Pu · S · / [μ · L · (N · R)²]
Thus, it is understood that the flow rate Q can be obtained with high accuracy.
[0131]
Further, the theoretical value Pv (Pa) of the pressure loss (pressure difference ΔP) in the pipe line due to viscous resistance is obtained from the measured flow rate Q,
Pv = (1 / A) · [μ · L · (N · R)²/ S] ・ Q
(However, in the formula, coefficient A = 2.83 × 10^-2Represents)
It is represented by
[0132]
Further, the pressure loss (pressure difference ΔP) of the pipeline due to the viscous resistance, that is, the pressure of the pipeline due to the viscous resistance, using the correction coefficient k = 13.75 as in the relational expressions (8) and (9). When the calculated value of the loss (pressure difference ΔP) is Pμ (calculated pressure difference), the Pμ (Pa) is

      (However, in the formula, (k / A) = 485 is represented)
It is represented by
[0133]
Here, Table 3 shows the results of calculating the theoretical value Pv and the calculated value Pμ of the pressure loss (pressure difference ΔP) of the pipe line from the measured flow rate Q using the relational expression (10). In Table 3, the flow rate q indicates the actually measured flow rate per pipe line.
[0134]
[Table 3]

[0135]
Here, when the ratio between the calculated value Pμ (calculated pressure difference) of the pressure loss (pressure difference ΔP) of the pipe and the stable negative pressure Pu at the upper limit of the ink is Pμ / Pu, it is approximately 1.
[0136]
FIG. 17 is a graph showing Table 2 and Table 3. As shown in FIG. 17, it can be seen that the stable negative pressure based on the calculated value from the theoretical value (calculated pressure difference Pμ) is in good agreement with the actually measured stable negative pressure (ink upper limit stable negative pressure Pu). . In addition, it can be seen that the stable negative pressure Pu at the upper limit of the ink is caused by the pressure loss based on the viscosity of the ink, and the stable negative pressure Pu at the upper limit of the ink can be accurately obtained using the correction coefficient.
[0137]
Next, the relationship between the compression rate R and the stable negative pressure (ink lower limit stable negative pressure PL) when the ink in the ink cartridge 20 is filled only to the lower limit will be considered below.
[0138]
When the ink in the ink cartridge 20 is filled only to the lower limit, that is, immediately before the ink in the ink cartridge 20 runs out, the cell 22a at the lower end of the ink absorber 22 (foam material) can be regarded as a capillary. .
[0139]
Accordingly, as shown in FIG. 18 (when positive pressure is applied to the liquid) and FIG. 19 (when negative pressure is applied to the liquid), the critical pressure Pt (Pa) of the liquid surface (ink meniscus) in the capillary is the cell 22a. Can be regarded as a capillary.
[0140]
Therefore, as shown in FIGS. 18 and 19, the critical pressure Pt (Pa) of the liquid surface (ink meniscus) in the capillary, that is, the critical pressure P by the ink absorber 22 at the time of ink empty._E(= Pt) is the following general formula (11)
Pt = 2 · η · cos θ / (d / 2) (11)
Defined by Here, η is the surface tension (N / m) of the liquid (ink) in the tube, θ is the contact angle of the liquid surface (ink meniscus) in the capillary with the tube, and d is the diameter of the capillary ( m). Note that since the ink absorber 22 is selected to have good wettability with respect to ink, θ can be regarded as substantially zero. Therefore, the general formula (11) is represented by the following general formula (12).
Pt = 4 · η / d (12)
(Strictly speaking, it can be expressed as Pt≈4 · η / d).
[0141]
Therefore, from the relational expression (3) and the general formula (12), the critical pressure P by the ink absorber 22 is obtained._E(= Pt) is the relational expression (4).
P_E= 4 ・ η ・ (N ・ R) (4)
It is represented by
[0142]
Table 4 shows the result of obtaining the critical pressure Pt of the liquid surface (ink meniscus) of the ink absorber 22 from this relational expression (4).
[0143]
[Table 4]

[0144]
The ratio Px / PL of the theoretical critical pressure Px obtained from the relational expression (4) to the ink lower limit stable negative pressure PL, which is the actual pressure, is approximately 1, so the ink lower limit stable negative pressure PL is the ink. This shows the correctness of the theory that it is caused by the critical pressure of the capillary based on the surface tension of the ink, and it can be seen that the stable negative pressure PL at the ink lower limit can be obtained with high accuracy.
[0145]
As a condition for preventing the problem of inadvertent leakage of ink when the ink cartridge 20 is attached / detached, a holding force of the ink absorber 22 (foam material), that is, a liquid having a surface tension η forms an ink meniscus. The cell at the lower end of the ink absorber 22 (foam material), which is the critical pressure in the cell 22a of the ink absorber 22 (foam material) having a size (cell diameter) of the cell 22a during compression of 1 / (N · R) Critical pressure P of the liquid level (ink meniscus) in 22a (capillary)_E(Pa) is required to be larger than the ink head pressure.
[0146]
Therefore, in the ink cartridge 20, when the specific gravity of the ink is γ and the head height of the ink in the vertical direction with respect to the ink supply port 24 of the ink tank 21 which can be taken in an arbitrary posture is h (m), Water head pressure is 9.8 × 10^ThreeSince it is expressed by γ · h (Pa), the critical pressure P in the above relational expression (4)_E(Pa) is the following condition
4.η · (N · R)> 9.8 × 10^Three・ Γ ・ h
It is required to satisfy. That is, in order to prevent the problem of inadvertent leakage of ink when the ink cartridge 20 is attached or detached, the following relational expression (13)
η · N · R · B> γ · h (13)
(However, in the formula, coefficient B = 4.08 × 10^-FourRepresents
It is necessary to satisfy
[0147]
Further, the cell density of the ink absorber 22 (foam material) in the state accommodated in the ink cartridge 20, that is, the mounting cell density M (pieces / m) (M = N · R) is, for example, cell density N = 1575. By storing the ink absorber 22 (foam material) obtained by compressing (pieces / m) (= 40 pieces / inch) at a compression ratio R = 5 in the ink cartridge 20, the ink absorber 22 (foam) When the material is subjected to a further 10% compression,
M = 1575 × 5.5 × 1.1 = 9528 (pieces / m) (= 242 pieces / inch)
When the mounting cell density M (pieces / m) is substituted into the relational expression (13), the following relational expression (14)
η · M · B> γ · h (14)
(However, in the formula, coefficient B = 4.08 × 10^-FourRepresents
It becomes. Note that an actual measurement value may be used as the mounting cell density M.
[0148]
The ink head height h (m) with respect to the ink supply port 24, that is, the ink head height h (m) of the maximum height in the vertical direction with respect to the ink supply port 24 of the ink tank 21 that can be taken in an arbitrary posture, In a normal posture, the height of the ink absorber 22 (foam material) or the inner wall of the ink cartridge 20 may be used.
[0149]
When handling needs to be taken into consideration, the maximum ink head height in the vertical direction with respect to the ink supply port 24 that can be taken, including the posture in which the ink cartridge 20 is tilted, is used.
[0150]
In addition, considering the cell diameter distribution and the like, it is desirable to set the safety factor to about twice or more. Therefore, the following relational expression (15)
η · N · R · B> 2 · γ · h (15)
(However, in the formula, coefficient B = 4.08 × 10^-FourRepresents
Or the following relational expression (16)
η · M · B> 2 · γ · h (16)
(However, in the formula, coefficient B = 4.08 × 10^-FourRepresents
It is desirable to design the ink cartridge 20 to satisfy the above.
[0151]
In general, the height of the ink cartridge is generally practically 40 mm or less, as described above, in consideration of fluctuations in the ink level. Therefore, when the safety factor is 2, the specific critical pressure in the cell (opening) of the ink absorber (foam material) is 0.8 kPa (0.08 mH) as described above.₂It is desirable to satisfy O). Therefore, a specific critical pressure P in the cell 22a of the ink absorber 22 (foam material)._E(Pa) is P_EIt is desirable to satisfy the relationship of ≧ 800.
[0152]
Therefore, from the relational expression (4), the following relational expression (17)
4 ・ η ・ N ・ R ≧ 800 (17)
Or the following relational expression (18)
4 ・ η ・ M ≧ 800 (18)
Is satisfied, the critical pressure P in the cell 22a of the ink absorber 22 (foam material) is satisfied._E(Pa), that is, the holding force of the ink absorber 22 (foam material) can be maintained at 0.8 kPa (800 Pa) or more, and there is a problem that ink is inadvertently leaked when the ink cartridge 20 is attached or detached. Can be prevented.
[0153]
From FIG. 17, the negative pressure based on the theoretical value (theoretical value critical pressure Px) obtained from the relational expression (4) is in good agreement with the actually measured negative pressure (stable negative pressure PL at the ink lower limit). I understand that. Table 4 shows the negative pressure at each setting of the mounting cell density M (M = N · R).
[0154]
Next, a critical pressure Pn (hereinafter sometimes referred to as a critical pressure of the nozzle) due to ink retraction of the orifice due to ink ejection from the discharge nozzle (ink nozzle portion) 1a in the print head 1 is obtained.
[0155]
As shown in FIG. 20, the shape of the orifice is such that the diameter of the discharge nozzle of the circular tube is 20 μm, the length is 20 μm, and the apex angle is 90 degrees from the tip (nozzle tip) of the discharge nozzle 1a. Assume that a 20 μm frustoconical shape extends.
[0156]
The ink flow rate Q when the ink discharge frequency of the discharge nozzle 1a in the print head 1 is set to 8000 pps and the number of nozzles to 64 is Q = 8.17 nm.^Three/ S (= 0.49cc / min), one drop of ink
(8.17 × 10^-9) /8000/64=1.6×10^-14(M^Three(= 16pL)
It becomes.
[0157]
Table 5 shows the diameter H of the conical portion at the position of the liquid surface (ink meniscus) due to the receding ink in the orifice when one drop of ink is ejected in this case. In Table 5, the diameter H = 20 μm of the conical portion represents a case where the straight portion of the nozzle tip is sufficiently long due to excimer laser processing or the like (see FIG. 20). Table 5 shows that one drop of ink is 1.6 × 10.^-14(M^Three) (= 16 pL), in the case where the transient vibration of the ink meniscus at the nozzle tip is not considered, and the transient vibration of the ink meniscus at the nozzle tip as shown in FIGS. This shows a case where the ink in the orifice has retreated twice with respect to the ink discharge amount. 21A to 21H are cross-sectional views sequentially showing the state in which ink is ejected from the ejection nozzle 1a. For example, in a 600 dpi inkjet printer, 1.6 × 10^-14~ 2.0 × 10^-14(M^Three) (= 16-20 pL) is required.
[0158]
The critical pressure Pn (Pa) of the nozzle (discharge nozzle 1a in the present embodiment) is expressed by the following general formula (19) by substituting the diameter H (m) of the cone portion into the general formula (12).
Pn = 4 · η / H (19)
(Strictly speaking, Pn ≒ 4 · η / H)
It can ask for.
[0159]
The indispensable condition for not causing insufficient ink supply is (Pμ) <(Pn), and the diameter of the discharge nozzle 1a is set to D._NAssuming that (m), in order not to cause an insufficient supply of ink, the following relational expression (20) is obtained from the relational expression (10) and the general formula (19).
(K / A) ・ [μ ・ L ・ (N ・ R)²/ S] · Q <4 · η / D_N  ... (20)
(However, in the formula, coefficient (k / A) = 485)
It is necessary to be satisfied. That is, if the relational expression (20) is arranged, the following relational expression (21)
C ・ [μ ・ L ・ Q ・ (N ・ R)²/ S] <η / D_N              (21)
(However, in the formula, C = (k / A) / 4 = 121)
It is necessary to be satisfied.
[0160]
Further, when the mounting cell density M (pieces / m) (M = N · R) is adapted to the relational expression (21), the above essential condition is
C ・ [μ ・ L ・ Q ・ M²/ S] <η / D_N                    (22)
(However, in the formula, C = (k / A) / 4 = 121)
It becomes.
[0161]
Table 5 shows the critical pressure Pn of the discharge nozzle 1a calculated using the general formula (19) under each setting condition.
[0162]
[Table 5]

[0163]
  From Table 5, when ink is continuously ejected, the negative pressure of the ink supply system (the critical pressure of the ink absorber 22 or the filter 23) is about 2. If the pressure is 0 kPa or less, the ink that is generated by the ink meniscus is sucked in a state where the ink meniscus at the tip of the nozzle is retracted after ink discharge.criticalIt can be seen that the pressure Pn is greater than the negative pressure of the ink supply system, and even when ink is continuously ejected, the required amount of ink can be stably supplied.
[0164]
Therefore, if the negative pressure of the ink supply system is 2.0 kPa or less, the ink is insufficiently supplied by the negative pressure generated in the ink supply system, and the ink liquid level (ink meniscus) is retracted too much from the nozzle tip. It is possible to prevent the problem of inhaling air and to stably supply ink even when ink is continuously ejected.
[0165]
If the negative pressure generated in the ink supply system is 2.0 kPa or less, the ink is sucked by the surface tension of the meniscus by overcoming the negative pressure generated in the ink supply system, and the meniscus is advanced to replenish the ink. Ink supply is completed when the negative pressure of the supply system and the suction force of the meniscus are balanced. On the contrary, when the negative pressure generated in the ink supply system is larger than the critical pressure of the meniscus, the meniscus moves backward, sucks air into the print head 1, and discharge becomes defective.
[0166]
In consideration of the efficiency τ (tank efficiency) that is the ratio of the ink volume that can be used for ejection to the filled ink volume in the ink cartridge 20, the upper limit of the mounting cell density M is 12.6 × 10.^ThreeThe critical pressure of the ink, that is, the critical pressure P of the liquid surface of the ink absorber 22 based on the surface tension η of the ink is about (number / m) (= 320 / inch)._EFrom Table 1, the stable negative pressure PL (Pa) at the ink lower limit determined by is 1.5 kPa at the cell density, and the water head of the print head 1a and the water head of the ink tank 21 are normally set to about 40 mm. So the sum of both (P_EA value of about 2.0 kPa is also derived from + Pi).
[0167]
To summarize the above examination results, the conditions required for the cell density N and compression rate R of the ink absorber 22 (foam material) are as follows. First, from the relational expression (13), the following relational expression (23)
(N · R)> γ · h / (η · B) (23)
(However, in the formula, coefficient B = 4.08 × 10^-FourRepresents
Is obtained. From the relational expression (21),
[η · S / (C · D_N・ Μ ・ L ・ Q)]^0.5> (N ・ R) (24)
(However, in the formula, coefficient C = (k / A) / 4 = 121 is represented)
Is obtained. Therefore, the conditions required for the cell density N and the compression ratio R of the ink absorber 22 (foam material) are as follows from the above relational expressions (23) and (24).

      (However, in the formula, coefficient B = 4.08 × 10^-FourRepresents a coefficient C = 121)
It becomes.
[0168]
In addition, as a condition required for the mounting cell density M (M = N · R) (pieces / m) in the mounting state of the ink absorber 22 (foam material), the relational expression (14) is applied in the same manner as described above.・ From (22)
[η · S / (C · D_N・ Μ ・ L ・ Q)]^0.5> M> γ · h / (η · B) (26)
(However, in the formula, coefficient B = 4.08 × 10^-FourRepresents a coefficient C = 121)
It becomes. Therefore, by satisfying the relational expression (25) or (26), it is possible to prevent ink leakage when the ink cartridge 20 is attached / detached and to stably supply ink during continuous ejection.
[0169]
The ink used in the ink jet recording apparatus is
・ Viscosity μ = 0.015 to 0.15 (Pa · s)
Ink surface tension η = 0.03 to 0.05 (N / m)
-Cell density N of ink absorber 22 (foam material) = 1.57 × 10^Three~ 3.94 × 10^Three(Pieces / m) (= 40-100 pieces / inch)
Is common.
[0170]
Therefore, for example, as a different condition, the following condition:
・ Viscosity μ = 0.015 (Pa · s)
Ink surface tension η = 0.04 (N / m)
・ Cell density of foam material N = 3.15 × 10^ThreeAs a result of study using (pieces / m) (= 80 pieces / inch), it was confirmed that the above-described equations were satisfied even when the conditions were changed.
[0171]
As described above, when the filter is not used or when the filter has an opening larger than the cell 22a of the ink absorber 22 (foam material), the inside of the cell 22a (capillary) in the ink absorber 22 is not used. Critical pressure P of the liquid surface (ink meniscus)_E(Pa), that is, the critical pressure P of the ink absorber 22 at the time of ink empty._E(Pa) determines the negative pressure generated in the ink supply system.
[0172]
However, when the opening of the filter is made smaller than the cell 22a of the ink absorber 22 in order to ensure the filtration performance of the filter, or when the ink absorber 22 (foam material) is not used, the critical pressure Pm ( Pa) determines the negative pressure (critical pressure of the ink absorber 22 or the filter) generated in the ink supply system.
[0173]
For this reason, in order to make the negative pressure generated in the ink supply system 2.0 kPa or less when the opening of the filter is made smaller than the cell 22a of the ink absorber 22, the following relational expression (27)
Pm ≦ 2000 (Pa) (27)
Need to be satisfied.
[0174]
Further, the critical pressure Pm (Pa) by the filter, as shown in the general formula (1) and the experimental formula (2), is the surface tension η (N / m) of the ink and the size of the opening of the filter, that is, , And the filtration accuracy F (m) of the filter. Therefore, in order to satisfy Pm ≦ 2000 (Pa), from the general formula (1) and the empirical formula (2), when the filtration accuracy of the filter is F (m), the following relational expression (28)
Pm = 4 · η / F ′ (28)
(However, when the opening of the filter is circular, F ′ = F,
In other cases, F ′ = √2 · F)
Need to be satisfied.
[0175]
Therefore, from the above relational expressions (27) and (28), the following relational expression (29) is applied to a part of the ink supply path 3 on the ink tank 21 side.
F ′ = 4 · η / Pm (29)
(However, when the opening of the filter is circular, F ′ = F,
In other cases, F ′ = √2 · F)
In addition, since the filter satisfying the relational expression (27) is provided, the negative pressure generated in the ink supply system, that is, in this case, the negative pressure generated in the filter during ink supply (critical pressure Pm by the filter) is generated. The suction pressure (nozzle critical pressure Pn) generated at the discharge nozzle 1a of the print head 1 can be made lower (Pn> Pm).
[0176]
Therefore, by providing the above-described filter in the ink supply path 3, the negative pressure generated in the ink supply system is overcome, the surface tension of the meniscus formed at the opening of the filter is overcome, and the ink is sucked. As a result, the ink can be stably supplied (supplemented) without air being mixed from the nozzle tip of the print head. Also in this case, as described above, the ink supply is completed when the negative pressure of the ink supply system and the suction force of the meniscus are balanced. Conversely, if the critical pressure due to the meniscus at the nozzle tip is less than or equal to the critical pressure of the meniscus formed in the opening of the filter (that is, Pn ≦ Pm), in particular, smaller than the critical pressure (Pm), the nozzle tip The meniscus retreats and sucks air into the print head 1 to cause ejection failure.
[0177]
That is, when ink is supplied to the print head 1, the pressure required when the print head 1 sucks ink, that is, the pressure (ink suction pressure) by the meniscus of the discharge nozzle 1a of the print head 1 is the ink supply path. 3 (filter). The ink suction pressure, that is, the critical pressure Pn of the discharge nozzle 1a is equal to or lower than the negative pressure generated by the filter when ink is supplied, that is, the critical pressure Pm (filter pressure) of the ink negative pressure caused by the meniscus at the opening of the filter. In particular, when the pressure is smaller than the critical pressure Pm (filter pressure), air is mixed from the nozzle tip of the print head 1 before breaking the meniscus formed in the opening of the filter.
[0178]
For this reason, the pressure by the meniscus of the discharge nozzle 1a when supplying ink to the print head 1, that is, the ink suction pressure (critical pressure Pn of the discharge nozzle 1a) is larger than the filter pressure (critical pressure Pm by the filter). If it sets so that it may become, the above-mentioned problem can be suppressed.
[0179]
Accordingly, the negative pressure generated by the filter when ink is supplied becomes smaller than the ink suction pressure by the discharge nozzle 1a of the print head 1, more specifically, the negative pressure factor. The above-described problems can be suppressed by constructing (designing) the filter under various conditions.
[0180]
In other words, in order to satisfy the above-described configuration, for example, in the ink supply path 3, specifically, in a part (end part) of the ink supply path 3 on the ink tank 21 side, a negative generated by the filter when ink is supplied. A filter whose pressure becomes smaller than the ink suction pressure by the discharge nozzle 1a of the print head 1, specifically, a filter that satisfies the relational expression (29) and the relational expression (27), that is, the following relational expression (30 )
F ′ ≧ 4 · η / 2000 (30)
(However, when the opening of the filter is circular, F ′ = F,
In other cases, F ′ = √2 · F)
It is desirable that a filter satisfying the above is provided.
[0181]
The liquid has a maximum surface tension of 0.072 N / m of water, reduces the discharge energy related to the surface tension η (N / m) of the ink, sucks air from the nozzle tip of the discharge nozzle 1 a, and discharges it. In order to prevent ejection failure due to wetting or ink leakage around the nozzle 1a and image quality deterioration due to ink bleeding on the paper surface, the surface tension η (N / m) of the ink is 0.03. It is necessary to set within the range of -0.06, and generally it is set within the range of 0.03-0.05.
[0182]
Therefore, in the image forming apparatus according to the present embodiment, when the surface tension η (N / m) of the ink is 0.03, the filtering accuracy F (m) is applied to the filter 23 from the relational expression (30). Is 42 × 10^-6(M) or more, that is, 42 μm or more, preferably F ≧ 50 × 10, assuming that the margin for fluctuations in surface tension, filtration accuracy F, etc. is about 20%.^-6By using the filter (m), the negative pressure applied to the ink supply system, that is, the critical pressure Pm applied to the filter 23 can be set to 2000 Pa or less. For example, in FIG. 9, the filtration accuracy F is 50 μm, that is, 50 × 10^-6In the case of (m), it can be confirmed that the critical pressure (maximum negative pressure) Pm of the ink negative pressure by the filter 23 (mesh filter) is 2.0 kPa or less.
[0183]
On the other hand, when a filter having a circular opening is used as the filter 23, the filtration accuracy F (m) is 60 × 10 0 from the relational expression (30).^-6(M) or more, that is, a filter of 60 μm or more, and preferably F ≧ 70 × 10 when a margin for fluctuations of surface tension, filtration accuracy F, etc. is about 20%.^-6By using the filter (m), the negative pressure applied to the ink supply system, that is, the critical pressure Pm applied to the filter 23 can be set to 2000 Pa or less.
[0184]
As described above, the ink cartridge 20 of the ink jet recording apparatus has a mesh at the end of the ink supply path 3 on the ink tank 21 side so that the negative pressure applied to the ink supply path 3 during ink supply is 2.0 kPa or less. A filter 23 is provided.
[0185]
For this reason, the ink suction pressure generated when the print head 1 ejects ink droplets (the pressure necessary for ink supply), that is, the pressure applied to the ink absorber 22 (ink supply pressure) Regardless, the ink supply pressure is smaller than the filter pressure applied to the opening 23a (mesh) of the filter 23.
[0186]
Therefore, according to the ink jet recording apparatus, air can be prevented from being mixed into the ink supply path 3 until the ink meniscus formed in the opening 23a (mesh) of the filter 23 is broken. Even when the meniscus is broken and air is sucked into the ink supply path 3 and ink empty is detected, it is possible to prevent the meniscus at the nozzle tip from retreating and air from entering the nozzle tip.
[0187]
In addition, when air bubbles mixed in the ink tank 21 during ink filling are trapped on the front surface of the filter 23, that is, a part of the end surface of the filter 23 on the ink tank 21 side, or the ink tank 21 is in an empty state. When the ink absorber 22 is in the immediately preceding (near) state and a part of the ink absorber 22 is in contact with the filter 23 in an empty state, the ink absorber 22 does not suck in air (bubbles) in contact with the filter 23. The condition for effectively supplying the retained ink to the print head 1, in other words, the condition for inadvertently sucking air from the ink tank 21 into the ink supply port 3a is Pm> P_EIt is.
[0188]
Here, as described above, in the state immediately before the ink in the ink cartridge 20 runs out, the cell 22a at the lower end of the ink absorber 22 (foam material) can be regarded as a capillary, so that the ink absorber at the time of ink empty 22 critical pressure P_E(Pa), that is, the critical pressure P of the liquid level (ink meniscus) in the cell 22a._E(Pa) is given by the relational expression (4).
[0189]
On the other hand, since the critical pressure Pm by the filter 23 when the filter 23 having the filtration accuracy F (m) is used is given by the empirical formula (2), the filter 23 having the filtration accuracy F (m) is used. The above condition, that is, the condition in which air is not inadvertently sucked into the ink supply port 3a from the empirical formula (2) and the relational expression (4), is expressed by the following relational expression (31).
(4 · η) / (√2 · F)> 4 · η · (N · R) (31)
It is represented by
[0190]
Therefore, when the above relational expression (31) is arranged for the filtration accuracy F, the following relational expression (32)
√2 · F <1 / (N · R) (32)
Is obtained.
[0191]
Further, from the general formula (1), the critical pressure Pm ′ by the filter having a circular opening is expressed by the following general formula using the surface tension η (N / m) of the ink and the filtration accuracy F (m). Formula (33)
Pm ′ = 4 · η / F (33)
It is represented by
[0192]
Therefore, when a filter having a circular opening and having a filtration accuracy F (m) is used, the conditions for not inadvertently sucking air from the ink tank 21 into the ink supply port 3a are the same as in the case of using the filter 23 described above. From the relational expression (4) and the general formula (33), the following relational expression (34)
F <1 / (N · R) (34)
Given in.
[0193]
Therefore, when a filter having a filtration accuracy F (m) is used in the ink supply path 3, the cell density of the ink absorber 22 before being stored in the ink tank 21 is N (pieces / m), and is stored in the ink tank 21. If the compression ratio indicated by the volume ratio of the ink absorber 22 when stored in the ink tank 21 before being compressed is R, the following relational expression (35)
F ′ <1 / (N · R) (35)
(However, when the opening of the filter is circular, F ′ = F,
In other cases, F ′ = √2 · F)
By designing the ink cartridge 20 to satisfy the above, the ink supply pressure can be adjusted to be smaller than the negative pressure applied to the filter 23, and the meniscus of the ink formed in the opening 23 a of the filter 23 Can be prevented from being mixed in the ink supply path 3. For this reason, according to the above configuration, it is possible to prevent air from being mixed into the ink supply path 3 due to factors other than a decrease in the remaining amount of ink, prevent malfunction of the remaining ink amount, and reliability in terms of quality. High printing can be performed.
[0194]
In addition, the said conditions can also be managed using a cell diameter instead of the filtration accuracy F (m). However, as described above, the negative pressure at the time of ink supply (empty) is managed not by the cell diameter having a large variation but by the filtration accuracy F (m) having a small variation, that is, the shortest opening length (minimum gap width). By doing so, a stable negative pressure can be obtained.
[0195]
In the embodiment described above, the cell density of the ink tank 21, that is, the ink absorber (ink absorber 22) before being stored in the ink storage portion is N (pieces / m), and is stored in the ink storage portion. Although the compression ratio indicated by the volume ratio of the ink absorber when compressed and stored in the ink storage portion before being stored is described as R, the ink absorber is stored in the ink storage portion. Or may be stored after being compressed in advance.
[0196]
As the ink absorber, for example, a compression-processed foam material widely used for the ink absorber, such as a compressed sponge (heat-pressed in a compressed state and subjected to permanent compression) can be used. In this case, the cell density N (pieces / m) and the compression ratio R are the cell density (pieces / m) of the ink absorber before the compression process and the compression process before the compression process, that is, after the compression process. A compression ratio (compression ratio) indicated by a volume ratio of the ink absorber when the foam material is inserted into the ink tank as an ink absorbing material can be used.
[0197]
Therefore, when the cell density of the ink absorber before compression processing is N ′ (pieces / m) and the compression ratio (compression ratio) indicated by the volume ratio of the ink absorber after compression processing before compression processing is R ′. The above formulas can be expressed as N = N ′ and R = R ′.
[0198]
For example, the relational expression (35) indicates that the filtration accuracy of the filter is F (m), the cell density of the ink absorber before compression processing is N ′ (pieces / m), and the ink after compression processing before compression processing. When the compression ratio (compression ratio) indicated by the volume ratio of the absorber is R ′, the following relational expression (36)
F ′ <1 / (N ′ · R ′) (36)
(However, when the opening of the filter is circular, F ′ = F,
In other cases, F ′ = √2 · F)
It is represented by It should be noted that the above-described formulas or formulas described later can be similarly expressed as N = N ′ and R = R ′. Of course, it goes without saying that the mounting cell density M can be used instead of N · R or N ′ · R ′.
[0199]
The diameter of the discharge nozzle 1a is D_N(M), from the relational expression (19), the meniscus critical pressure Pn (Pa) of the discharge nozzle 1a is expressed by the following general formula (37).
Pn = 4 · η / D_N                                      ... (37)
It is represented by
[0200]
Here, the condition for not sucking air from the nozzle tip is
Pn> Pm
As described above, the conditions for effectively supplying the ink held by the ink absorber 22 to the print head 1 without inadvertently sucking air from the ink tank 21 into the ink supply port 3a are as follows.
Pm> P_E
Therefore, in order to further prevent air from being mixed into the ink supply path due to factors other than a decrease in the remaining amount of ink and to prevent malfunction of the remaining ink amount more effectively, the following conditions are satisfied:
Pn> Pm> P_E
That is, from the relational expression (31) and the general formula (37), the following relational expression (38)
(4 · η / D_N)> (4 · η) / F ′> 4 · η · (N · R) (38)
(However, when the opening of the filter is circular, F ′ = F,
In other cases, F ′ = √2 · F)
It is more desirable to satisfy.
[0201]
Therefore, when the relational expression (38) is rearranged with respect to the filtration accuracy F ′ (m), the following relational expression (39)
D_N<F ′ <1 / (N · R) (39)
(However, when the opening of the filter is circular, F ′ = F,
In other cases, F ′ = √2 · F)
Is obtained.
[0202]
Next, the influence of the ink level that changes as the ink is consumed will be considered. As shown in FIG. 3, when the head hydraulic head pressure due to the drop h between the ink supply port 24 and the discharge nozzle 1a tip (nozzle tip) is Ph, the effective holding force Pn ′ (Pa) due to the ink meniscus in the discharge nozzle 1a is The following general formula (40)
Pn ′ = Pn− | Ph | (40)
Defined by | Ph | represents the absolute value of Ph. That is, || represents an absolute symbol, and | x | represents an absolute value of x.
[0203]
At this time, the condition that the ink meniscus does not retract too much from the nozzle tip and does not suck in the air is when the ink tank 21 is fully filled with the following relational expression (41).
Pn ′> | Pμ | − | Pi | (41)
When ink is empty, the following relational expression (42) is satisfied.
Pn ′> Pm (42)
Is to satisfy.
[0204]
When the head head pressure Ph (ink head) is not taken into consideration, the condition that air is not sucked from the nozzle tip is Pn> Pm. However, the head head pressure Ph is taken into consideration, and the condition is more in line with actual use. That is, the head hydraulic head pressure Ph is set so as to generate a negative static pressure to prevent ink leakage from the nozzle tip, and the ink jet recording apparatus starts from the nozzle tip than when the head hydraulic head pressure Ph is not taken into consideration. Used in conditions where air is easily sucked. For this reason, it can be set as the condition according to actual use more by considering the head hydraulic head pressure Ph.
[0205]
Here, as described above, when the filter 23 is designed to prevent foreign matter from being mixed,
Pm> | Pμ | + | Pi | (43)
From the above relational expressions (42) and (43),
Pn ′> Pm> | Pμ | + | Pi | (44)
Is guided.
[0206]
Therefore, from the above relational expressions (41) and (44),
Pn ′> Pm> | Pμ | + | Pi |> | Pμ | − | Pi |
Therefore, the above relational expression (44) is satisfied, that is, the diameter of the discharge nozzle 1a is D_N(M), from the empirical formula (2) and the general formula (37), the following relational formula (45)
4 • η / D_N− | Ph |> 4 · η / F ′> | Pμ | + | Pi | (45)
(However, when the opening of the filter is circular, F ′ = F,
In other cases, F ′ = √2 · F)
By satisfying the above, the pressure leaked by the filter 23 at the time of ink supply, particularly at the time of ink supply immediately before ink empty, can be appropriately managed without exceeding the critical pressure Pn of the discharge nozzle 1a of the print head 1, and from the discharge nozzle 1a. In addition to preventing air from being sucked in, it is possible to effectively filter the foreign matter toward the ink supply path 3 and to improve the reliability of the discharge operation by the discharge nozzle 1a. In each of the above formulas, for example, the above relational expressions (41) and (43) to (45), Pμ is given by the relational expression (10).
[0207]
Next, since the present inventors examined the relationship between the viscosity and temperature of various substances, the results will be described.
[0208]
First, Table 6 below shows the relationship between temperature T (° C.) and viscosity μ (Pa · s) for various substances.
[0209]
[Table 6]

[0210]
FIG. 22 shows the relationship between the temperature T (° C.) and the viscosity μ (Pa · s) created based on the data in Table 6 above. From FIG. 22, it is difficult to find the correlation between the temperature T (° C.) and the viscosity μ (Pa · s).
[0211]
Furthermore, in Table 7 below, the viscosity μ at 25 ° C._{twenty five}Viscosity μT (Pa · s) at each temperature T (° C.) with respect to (Pa · s), that is, viscosity μ at 25 ° C._{twenty five}Viscosity μT / μ at each temperature T (° C.)_{twenty five}(Normalized viscosity) is shown.
[0212]
[Table 7]

[0213]
The temperature T (° C.) created based on the data in Table 7 above, and the viscosity μT / μ at each temperature T (° C.)_{twenty five}The relationship with (normalized viscosity) is shown in FIG. From FIG. 23, temperature T (° C.) and viscosity μ / μ_{twenty five}It is difficult to find a correlation with (normalized viscosity).
[0214]
  By the way, in general, any temperature T_K(K) Liquid viscosity μ_TK(Pa · s) is represented by the following general formula (46)
  μ_TK= Α · exp (β / T_K(46)
It is expressed by the Andrade formula shown by the following.
[0215]
  Using this Andrade equation, T₂₅The viscosity of the liquid at (K) (= 25 ° C.) is μ₂₅(Pa · s), temperature T_KThe viscosity of the liquid in (K) is μ_TK(Pa · s), the following general formula (47)
  μ_TK/ Μ₂₅= Exp (β / T_K) / Exp (β / T₂₅)
              = Exp {(1 / T_K-1 / T₂₅) · Β} (47)
The relationship expressed by Therefore, from the general formula (47),
  Ln (μ_TK/ Μ₂₅) = (1 / T_K-1 / T₂₅) ・ Β
And the following general formula (48)
  β = Ln (μ_TK/ Μ₂₅) / (1 / T_k-1 / T₂₅(48)
Is obtained.
[0216]
Therefore, next, for each of the substances described above, based on the data shown in Table 7, the viscosity μ_{twenty five}And viscosity μ / μ_{twenty five}(Normalized viscosity), here μ₀/ Μ_{twenty five}, Μ₅₀/ Μ_{twenty five}, Μ₇₅/ Μ_{twenty five}The correlation with was investigated. The results are shown in FIG.
[0217]
From the plot data shown in FIG.₀/ Μ_{twenty five}, The following approximate expression
μ₀/ Μ_{twenty five}= 0.42 · Ln (μ_{twenty five}) +4.71 (49)
Can be obtained.
[0218]
Therefore, since 25 (° C.) is 298 (K) in absolute temperature, the general formula (48)
From the approximate expression (49), the following relational expression (50)

Is obtained.
[0219]
Further, from the Andrade's formula represented by the general formula (46), the viscosity of the liquid μ at 25 ° C._{twenty five}(Pa · s) is
μ_{twenty five}= Α · exp (β / 298)
Thus, the following general formula (51)
α = μ_{twenty five}/ Exp (β / 298) (51)
Holds.
[0220]
Therefore, for the various substances described above, the following approximate expression (52) obtained by the general formulas (46) and (51) and the relational expression (50):

Μ obtained using_TKThe approximate viscosity μ ′ (Pa · s) represented by (Pa · s) is shown in Table 8 below.
[0221]
[Table 8]

[0222]
Further, the approximate expression viscosity μ ′ (Pa · s) obtained by the approximate expression (52) obtained by the general formulas (46) and (51) and the relational expression (50), and the actual viscosity μ (Pa · s). The relationship with () is shown in FIG. In FIG. 25, the solid line indicates the approximate viscosity μ ′ (Pa · s), and each identification mark indicates the actual viscosity μ (Pa · s).
[0223]
As shown in FIG. 25, there is no significant difference between the approximate expression viscosity μ ′ (Pa · s) and the actual viscosity μ (Pa · s), that is, the actual measurement value. It was confirmed that the accuracy was good.
[0224]
Further, the above approximate expression (52) is converted into eight types of ink (inks 1 to 8) and water (H₂O) when applied to temperature T (° C.) and viscosity μ (Pa · s), μ / μ_{twenty five}, Μ ′ / μ (approximate viscosity / measured value) are shown in Table 9.
[0225]
[Table 9]

[0226]
FIG. 26 shows the relationship between the approximate expression viscosity μ ′ (Pa · s) created based on the data in Table 9 and the actual viscosity μ (Pa · s). FIG. 27 shows the viscosity μ of each ink and water at 25 ° C._{twenty five}And normalized viscosity μ / μ_{twenty five}The relationship between the actual measured value and the approximate value is shown. In FIG. 26, the solid line indicates the approximate expression viscosity μ ′ (Pa · s), and each identification mark indicates an actual measurement value, that is, the actual viscosity μ (Pa · s). In FIG. 27, the broken line indicates the normalized approximate viscosity μ ′._Five/ Μ_{twenty five}And μ ’₄₀/ Μ_{twenty five}“○” indicates normalized viscosity μ / μ at 5 ° C._{twenty five}(Ie μ_Five/ Μ_{twenty five}), “△” is normalized viscosity μ / μ at 40 ° C._{twenty five}(Ie μ₄₀/ Μ_{twenty five}), Each identification mark indicates an actual measurement value, that is, an actual viscosity μ (Pa · s).
[0227]
From the results shown in FIG. 26, even when the approximate expression (48) is applied to the ink used in the ink cartridge 20, the approximate expression viscosity μ ′ (Pa · s) and the actual viscosity μ (Pa · s) are obtained. It turned out that there was not much difference between.
[0228]
Based on the above examination results, an arbitrary temperature T_KThe ink viscosity μ (Pa · s) in (K) can be calculated as μ = μ ′. If the approximate expression (48) is used, an arbitrary temperature T_KIt was confirmed that the ink viscosity μ (Pa · s) in (K) can be calculated with high accuracy.
[0229]
Therefore, based on the experimental result, in the relational expression (10), the viscosity μ (Pa · s) of the ink can be obtained by using the approximate expression (52)._TKWhen the approximate expression viscosity μ ′ (Pa · s) represented by (Pa · s) is applied, the relational expression (10) is expressed by the following relational expression (53).
Pμ = (k / A) · [μ_TK・ L ・ (N ・ R)²/ S] · Q (53)
(However, coefficient (k / A) = 485)
Can be represented by
[0230]
Therefore, from the relational expressions (43), (45), (52), (53) and the experimental expression (2), when the filtration accuracy of the filter is F (m) and the ink tank 21 is fully filled with ink, , Pi (Pa) is the water head pressure of the ink tank 21 generated when the ink is supplied to the print head 1 via the ink supply path 3, and Pμ (Pa) is the pressure loss due to the viscous resistance of the ink in the ink tank 21. ), The surface tension of the ink is η (N / m), the cell density of the ink absorber 22 before being stored in the ink tank 21 is N (cells / m), The compression ratio indicated by the volume ratio of the ink absorber 22 when compressed and stored in the ink tank 21 is R, the cell density of the ink absorber before compression processing is N ′ (pieces / m), and compression processing is performed. The compression ratio (compression ratio) indicated by the volume ratio of the ink absorber after compression processing with respect to the front is R ′, and the cross-sectional area of the ink absorber 22 when stored in the ink tank 21 is S (m²), The height of the ink absorber 22 when compressed and stored in the ink tank 21 is L (m), and the viscosity of the ink at 25 ° C. is μ._{twenty five}(Pa · s), any temperature T_KThe viscosity in (K) is μ_TK(Pa · s), any temperature T_KIn (K),
4 • η / F ′> | Pμ | + | Pi |
Pμ = (k / A) · [μ_TK・ L ・ (N ・ R)²/ S] ・ Q
(However, coefficient (k / A) = 485)
μ_TK= Α · exp (β / T_K),
α = μ_{twenty five}/ Exp (β / 298),
β = Ln [0.42 · Ln (μ_{twenty five}) +4.71] / (1 / 273-1 / 298)
(However, when the opening of the filter is circular, F ′ = F,
In other cases, F ′ = √2 · F)
Or
4 • η / F ′> | Pμ | + | Pi |
Pμ = (k / A) · [μ_TK・ L ・ (N '・ R')²/ S] ・ Q
(However, coefficient (k / A) = 485)
μ_TK= Α · exp (β / T_K),
α = μ_{twenty five}/ Exp (β / 298),
β = Ln [0.42 · Ln (μ_{twenty five}) +4.71] / (1 / 273-1 / 298)
(However, when the opening of the filter is circular, F ′ = F,
In other cases, F ′ = √2 · F)
By satisfying the above, the negative pressure generated in the ink absorber can be adjusted to be smaller than the critical value of the negative pressure of the ink meniscus at the opening of the filter, and the air meniscus formed in the filter mesh can be reduced. It is possible to prevent tearing and mixing into the ink supply path 3. For this reason, according to the above configuration, it is possible to prevent air from being mixed into the ink supply path 3 due to factors other than a decrease in the remaining amount of ink, prevent malfunction of the remaining ink amount, and reliability in terms of quality. High printing can be performed.
[0231]
Also in the above configuration, the cell diameter can be managed instead of the filtration accuracy F (m), but the negative pressure at the time of ink supply (empty) is not a cell diameter having a large variation, A stable negative pressure can be obtained by managing the filtration accuracy F (m) with small variations, that is, the shortest opening length (minimum gap width).
[0232]
Further, in this case, by satisfying the relational expression (45), the pressure leaked by the filter at the time of ink supply, particularly at the time of ink supply immediately before ink empty, exceeds the critical pressure Pn of the discharge nozzle 1a of the print head 1. Therefore, the air can be prevented from being sucked in from the discharge nozzle 1a, and the foreign matter directed to the ink supply path 3 can be effectively filtered to improve the reliability of the discharge operation by the discharge nozzle 1a.
[0233]
It should be noted that the present invention is not limited to the above-described embodiments, and various modifications are possible within the scope shown in the claims, and obtained by appropriately combining the technical means disclosed in each of the above-described embodiments. Such embodiments are also included in the technical scope of the present invention.
[0234]
【The invention's effect】
As described above, the image forming apparatus according to the present invention includes an ink storage portion that stores a porous ink storage body that holds ink, and an ink supply path that supplies ink from the ink storage portion to the print head. The image forming apparatus includes a filter in the ink supply path, the filtering accuracy of the filter is F (m), and the cell density of the ink absorber before being stored in the ink storage portion is N (cells / m). When the compression ratio indicated by the volume ratio of the ink absorber when compressed and stored in the ink storage unit with respect to before being stored in the ink storage unit is R,
F ′ <1 / (N · R)
(However, when the opening of the filter is circular, F ′ = F,
In other cases, F ′ = √2 · F)
It is the structure which satisfies.
[0235]
When ink is supplied to the print head, a pressure necessary for the print head to suck ink, that is, a pressure by the meniscus of the nozzle of the print head (ink suction pressure) is applied to the ink supply path. At this time, by setting as described above, the critical value of the negative pressure generated in the ink tank is determined by the filter.
[0236]
Therefore, according to the above configuration, the critical value of the negative pressure generated in the ink absorber due to the surface tension of the ink is the negative value generated in the filter due to the surface tension of the ink, that is, the opening of the filter. Can be adjusted to be smaller than the critical value of the pressure (filter pressure) by the meniscus of the part (mesh), the ink meniscus formed in the filter mesh before ink emptying is broken, and air is supplied to the ink Mixing in the path is prevented, and the meniscus of the ink absorber is retracted according to the consumption of the ink, so that a stable ink supply operation is possible. Furthermore, factors other than a decrease in the remaining amount of ink, such as bubbles generated in the ink in the ink storage section due to carriage vibration, atmospheric pressure or ambient temperature change, etc. are captured by the filter to prevent air from entering the ink supply path In addition, highly reliable printing can be performed and ink can be consumed without waste.
[0237]
Therefore, according to the above-described configuration, the image forming apparatus having the design guideline for the ink supply system can be prevented so as to prevent the occurrence of problems such as air mixing into the ink supply system before ink empty during continuous ink discharge. Can be provided.
[0238]
Further, according to the above configuration, as described above, the negative pressure at the time of ink supply (empty) can be managed with the filtration accuracy F (m) with small variation, and a stable negative pressure can be obtained. Also has the effect of.
[0239]
In the image forming apparatus according to the present invention, the diameter of the nozzle (ink discharge nozzle) of the print head is set to D as described above._N(M)
D_N<F '<1 / (NR)
(However, when the opening of the filter is circular, F ′ = F,
In other cases, F ′ = √2 · F)
It is the structure which satisfies.
[0240]
According to the above configuration, the critical value of the ink suction pressure due to the ink meniscus in the nozzle (nozzle portion) of the print head is greater than the critical value of the pressure due to the ink meniscus at the opening of the filter. It can be adjusted to be small, and air can be sucked from the nozzle tip, preventing the print head from causing ejection failure.
[0241]
In addition, according to the above configuration, the ink meniscus formed in the opening of the filter is broken, and air can be prevented from being inadvertently sucked into the ink supply path. The retained ink can be supplied to the print head more effectively. Therefore, according to the above configuration, it is possible to further prevent air from being mixed into the ink supply path due to factors other than a decrease in the remaining amount of ink, and to more effectively prevent a malfunction in detecting the remaining amount of ink. There is an effect. Therefore, according to the above-described configuration, the image forming apparatus having the design guideline for the ink supply system can be prevented so as to prevent the occurrence of problems such as air mixing into the ink supply system before ink empty during continuous ink discharge. Can be provided.
[0242]
As described above, the image forming apparatus according to the present invention includes an ink storage portion that stores a porous ink storage body that holds ink, and an ink supply path that supplies ink from the ink storage portion to the print head. In the provided image forming apparatus, a filter is provided in the ink supply path, and the ink absorber is compressed in advance before being stored in the ink storage portion, and the filtration accuracy of the filter is F ( m), the cell density of the ink absorber before compression processing is N ′ (pieces / m), and the compression ratio (compression ratio) indicated by the volume ratio of the ink absorber after compression processing to that before compression processing is R ′. Then,
F ′ <1 / (N ′ · R ′)
(However, when the opening of the filter is circular, F ′ = F,
In other cases, F ′ = √2 · F)
It is the structure which satisfies.
[0243]
When ink is supplied to the print head, a pressure necessary for the print head to suck ink, that is, a pressure by the meniscus of the nozzle of the print head (ink suction pressure) is applied to the ink supply path. At this time, by setting as described above, the critical value of the negative pressure generated in the ink tank is determined by the filter.
[0244]
Therefore, the critical value of the negative pressure generated in the ink absorber due to the surface tension of the ink is determined by the negative pressure generated in the filter due to the surface tension of the ink, that is, the meniscus of the opening (mesh) of the filter. The pressure (filter pressure) can be adjusted to be smaller than the critical value, and the ink meniscus formed on the filter mesh before ink empty is broken, and air enters the ink supply path. This prevents the meniscus of the ink absorber from retreating as the ink is consumed, and enables a stable ink supply operation. In addition, factors other than a decrease in the remaining amount of ink, such as bubbles generated in the ink in the ink storage section due to carriage vibration, atmospheric pressure, or ambient temperature change, are captured by the filter to prevent air from entering the ink supply path. Thus, it is possible to perform highly reliable printing and to consume ink without waste. Therefore, according to the above-described configuration, the image forming apparatus having the design guideline for the ink supply system can be prevented so as to prevent the occurrence of problems such as air mixing into the ink supply system before ink empty during continuous ink discharge. Can be provided.
[0245]
Further, according to the above configuration, as described above, the negative pressure at the time of ink supply (empty) can be managed with the filtration accuracy F (m) with small variation, and a stable negative pressure can be obtained. Also has the effect of.
[0246]
As described above, the image forming apparatus according to the present invention sets the diameter of the nozzle of the print head to D._N(M)
D_N<F ′ <1 / (N ′ · R ′)
It is the structure which satisfies.
[0247]
According to the above configuration, it is possible to prevent air from being sucked from the nozzle tip of the print head, and it is possible to prevent air from being inadvertently sucked into the ink supply path from the ink storage portion. The ink held by the absorber can be effectively supplied by the print head. Therefore, according to the above configuration, it is possible to further prevent air from being mixed into the ink supply path due to factors other than a decrease in the remaining amount of ink, and to more effectively prevent a malfunction in detecting the remaining amount of ink. There is an effect. Therefore, according to the above-described configuration, the image forming apparatus having the design guideline for the ink supply system can be prevented so as to prevent the occurrence of problems such as air mixing into the ink supply system before ink empty during continuous ink discharge. Can be provided.
[0248]
As described above, the image forming apparatus according to the present invention includes an ink storage portion that stores a porous ink storage body that holds ink, and an ink supply path that supplies ink from the ink storage portion to the print head. In the image forming apparatus, a filter is provided in the ink supply path, the filtration accuracy of the filter is F (m), and the ink is filled through the ink supply path when the ink storage unit is fully filled with ink. Pi (Pa) is the water head pressure of the ink containing portion generated when trying to supply to the print head, Pμ (Pa) is the pressure loss due to the viscous resistance of the ink in the ink containing portion, and η ( N / m), the cell density of the ink absorber before being stored in the ink storage portion is N (cells / m), and the ink storage portion is stored in the ink storage portion before being stored in the ink storage portion. The compression ratio indicated by the volume ratio of the ink absorber when compressed and stored is R, and the cross-sectional area of the ink absorber when compressed and stored in the ink storage portion is S (m²), The height of the ink absorber when compressed and stored in the ink storage portion is L (m), and the viscosity of the ink at 25 ° C. is μ._{twenty five}(Pa · s), any temperature T_KThe viscosity in (K) is μ_TK(Pa · s), any temperature T_KIn (K),
4 • η / F ′> | Pμ | + | Pi |
Pμ = (k / A) · [μ_TK・ L ・ (N ・ R)²/ S] ・ Q
(However, coefficient (k / A) = 485)
μ_TK= Α · exp (β / T_K),
α = μ_{twenty five}/ Exp (β / 298),
β = Ln [0.42 · Ln (μ_{twenty five}) +4.71] / (1 / 273-1 / 298)
(However, when the opening of the filter is circular, F ′ = F,
In other cases, F ′ = √2 · F)
It is the structure which satisfies.
[0249]
According to the above configuration, the negative pressure generated in the ink absorber can be adjusted so that the negative pressure becomes smaller than the critical value of the negative pressure of the ink meniscus at the opening of the filter. It is possible to prevent the ink meniscus formed in the portion from being broken and air from being mixed into the ink supply path. For this reason, according to the above-described configuration, it is possible to prevent air from being mixed into the ink supply path due to factors other than a decrease in the remaining amount of ink, to prevent malfunction of the remaining amount of ink, and to improve reliability in terms of quality. There is an effect that high printing can be performed. Therefore, according to the above configuration, the ink supply system design guideline according to the characteristics of the ink can prevent the occurrence of problems such as air mixing into the ink supply system before ink empty during continuous ink ejection. Can be provided.
[0250]
Further, according to the above configuration, as described above, the maximum negative pressure at the time of ink supply (at the time of empty) can be managed with a filtration accuracy F (m) with small variation, and a stable negative pressure can be obtained. There is an effect that can be done.
[0251]
As described above, the image forming apparatus according to the present invention sets the nozzle diameter of the print head to D._N(M) When the water head pressure between the ink discharge port of the nozzle and the ink supply port of the ink storage unit is Ph (Pa),
4 • η / D_N− | Ph |> 4 · η / F ′> | Pμ | + | Pi |
(However, when the opening of the filter is circular, F ′ = F,
In other cases, F ′ = √2 · F)
It is the structure which satisfies.
[0252]
According to the above configuration, when ink is supplied, the critical value of the pressure caused by the meniscus in the opening of the filter can be appropriately managed without exceeding the critical value of the ink suction pressure caused by the meniscus of the nozzle of the print head. Air can be prevented from being sucked in, and air and foreign matters directed to the ink supply path can be effectively filtered, and the reliability of the ejection operation by the nozzle can be improved. Therefore, according to the above-described configuration, the image forming apparatus having the design guideline for the ink supply system can be prevented so as to prevent the occurrence of problems such as air mixing into the ink supply system before ink empty during continuous ink discharge. Can be provided.
[0253]
As described above, the image forming apparatus according to the present invention includes an ink storage portion that stores a porous ink storage body that holds ink, and an ink supply path that supplies ink from the ink storage portion to the print head. In the provided image forming apparatus, a filter is provided in the ink supply path, and the ink absorber is compressed in advance before being stored in the ink storage portion, and the filtration accuracy of the filter is F ( m) Pi (Pa), the water head pressure of the ink containing portion that is generated when the ink containing portion is fully filled with the ink and the ink is supplied to the print head via the ink supply path. The pressure loss due to the viscous resistance of the ink in the ink storage portion is Pμ (Pa), the surface tension of the ink is η (N / m), and the cell density of the ink absorber before compression processing is N ′. The compression ratio (compression ratio) indicated by the volume ratio of the ink absorber after the compression processing to the compression processing before the compression processing (R / m) is R ′ of the ink absorber when compressed and stored in the ink storage portion. The cross-sectional area is S (m²), The height of the ink absorber when compressed and stored in the ink storage portion is L (m), and the viscosity of the ink at 25 ° C. is μ._{twenty five}(Pa · s), any temperature T_KThe viscosity in (K) is μ_TK(Pa · s), any temperature T_KIn (K)
4 • η / F ′> | Pμ | + | Pi |
Pμ = (k / A) · [μ_TK・ L ・ (N '・ R')²/ S] ・ Q
(However, coefficient (k / A) = 485)
μ_TK= Α · exp (β / T_K),
α = μ_{twenty five}/ Exp (β / 298),
β = Ln [0.42 · Ln (μ_{twenty five}) +4.71] / (1 / 273-1 / 298)
(However, when the opening of the filter is circular, F ′ = F,
In other cases, F ′ = √2 · F)
It is the structure which satisfies.
[0254]
According to the above configuration, the negative pressure generated in the ink absorber can be adjusted so that the negative pressure becomes smaller than the critical value of the negative pressure of the ink meniscus at the opening of the filter. It is possible to prevent the ink meniscus formed in the portion from being broken and air from being mixed into the ink supply path. For this reason, according to the above-described configuration, it is possible to prevent air from being mixed into the ink supply path due to factors other than a decrease in the remaining amount of ink, to prevent malfunction of the remaining amount of ink, and to improve reliability in terms of quality. There is an effect that high printing can be performed. Therefore, according to the above configuration, the ink supply system design guideline according to the characteristics of the ink can prevent the occurrence of problems such as air mixing into the ink supply system before ink empty during continuous ink ejection. Can be provided.
[0255]
Further, according to the above configuration, as described above, the maximum negative pressure at the time of ink supply (at the time of empty) can be managed with a filtration accuracy F (m) with small variation, and a stable negative pressure can be obtained. There is an effect that can be done.
[0256]
As described above, the image forming apparatus according to the present invention sets the nozzle diameter of the print head to D._N(M) When the water head pressure between the ink discharge port of the nozzle and the ink supply port of the ink storage unit is Ph (Pa),
4 • η / D_N− | Ph |> 4 · η / F ′> | Pμ | + | Pi |
(However, when the opening of the filter is circular, F ′ = F,
In other cases, F ′ = √2 · F)
It is the structure which satisfies.
[0257]
According to the above configuration, when ink is supplied, the critical value of the pressure caused by the meniscus in the opening of the filter can be appropriately managed without exceeding the critical value of the ink suction pressure caused by the meniscus of the nozzle of the print head. Air can be prevented from being sucked in, and air and foreign matters directed to the ink supply path can be effectively filtered, and the reliability of the ejection operation by the nozzle can be improved. Therefore, according to the above-described configuration, the image forming apparatus having the design guideline for the ink supply system can be prevented so as to prevent the occurrence of problems such as air mixing into the ink supply system before ink empty during continuous ink discharge. Can be provided.
[0258]
As described above, the image forming apparatus according to the present invention includes a detector that detects the presence or absence of ink in the ink supply path.
[0259]
According to the above configuration, it is possible to reliably detect ink empty by detecting the presence or absence of ink in the ink supply path. Therefore, according to said structure, there exists an effect that it can prevent more reliably that air mixes in the said ink supply path | route.
[Brief description of the drawings]
1A is a cross-sectional view showing a configuration of a main part according to an embodiment of the present invention, and FIG. 1B is a cross-sectional view showing a state where an ink supply path is removed from the ink cartridge shown in FIG. It is a figure, (c) is sectional drawing which shows the structure of a detection electrode.
FIG. 2 is a perspective view showing the overall configuration of the inkjet recording apparatus with a part cut away.
FIG. 3 is a schematic configuration diagram of an ink supply device in the ink jet recording apparatus.
FIG. 4 is a front view showing a configuration of a filter of the ink supply device.
FIG. 5 is a graph showing a relationship between a time when ink is continuously ejected from a state where the ink cartridge is filled with ink and a negative pressure of the ink cartridge.
FIG. 6 is a graph schematically showing FIG. 5;
FIG. 7 is a schematic configuration diagram of a measurement apparatus used in a negative pressure measurement experiment applied to an ink supply path of the inkjet recording apparatus.
8 is a graph showing the relationship between the filtration accuracy of the filter actually measured using the measuring apparatus shown in FIG. 7 and the negative pressure applied to the ink supply path.
FIG. 9 is a graph showing the relationship between the filtration accuracy of the filter and the critical pressure of the ink negative pressure by the filter.
FIG. 10 is a graph showing the relationship between cell density and efficiency.
FIG. 11 is a graph showing the relationship between mounting cell density and efficiency.
FIG. 12 is a schematic diagram showing a flow rate through a circular pipe and a pressure difference in the pipe when each cell of the foam material of the ink cartridge is regarded as a circular pipe.
FIG. 13 is a block diagram showing a cell that is closest packed.
FIG. 14 is a cross-sectional view showing a state in which cells on a spherical shape or polyhedron are connected in a bead shape in an actual foam material in an ink cartridge.
FIG. 15 is an explanatory diagram showing how to obtain an effective diameter when the cells are formed in a continuous bead-like flow path in the actual foam material.
FIG. 16 shows normalized channel resistance Rd obtained by integrating a spherical channel having a cell diameter dm and a center position X = 0, and a normalized channel resistance Rm of a cylindrical channel. It is a graph which shows the relationship between X, resistance ratio Rd / Rm, and cell diameter d.
FIG. 17 is a graph showing the relationship between compression rate and negative pressure.
FIG. 18 is a schematic diagram showing the critical pressure of the liquid surface (ink meniscus) in the capillary when the cell at the lower end of the foam material can be regarded as a capillary in a state immediately before the ink in the ink cartridge runs out. It is.
FIG. 19 is a schematic diagram showing the critical pressure of the liquid surface (ink meniscus) in the capillary.
FIG. 20 is an enlarged cross-sectional view showing the configuration of the end portion of the supply port.
FIGS. 21A to 21H are cross-sectional views sequentially showing a state in which ink is ejected from a nozzle.
22 is a graph showing the relationship between temperature T (° C.) and viscosity μ (Pa · s) created based on the data in Table 6. FIG.
FIG. 23 shows temperature T (° C.) created based on the data in Table 7 and μT / μ at each temperature T (° C.)._{twenty five}It is a graph which shows the relationship.
FIG. 24 shows a μ created based on the data shown in Table 7._{twenty five}And μ / μ_{twenty five}It is a graph which shows correlation with.
FIG. 25 is a graph showing the relationship between the approximate viscosity μ ′ (Pa · s) and the actual viscosity μ (Pa · s).
FIG. 26 is a graph showing the relationship between the approximate viscosity μ ′ (Pa · s) created based on the data in Table 9 and the actual viscosity μ (Pa · s).
FIG. 27 shows μ for each ink and water at 25 ° C._{twenty five}And μ / μ_{twenty five}It is a graph which shows the relationship.
[Explanation of symbols]
1 Print head
3 Ink supply path
3a Ink supply path
4 Ink supply tube
10 Ink supply device
20 Ink cartridge
21 Ink tank (ink storage part)
22 Ink absorber
23 Filter
24 Ink supply port
25 Detection electrode (detector)
31 filters

Claims (9)

In an image forming apparatus comprising: an ink storage unit having a porous ink absorber that holds ink; a print head that discharges ink; and an ink supply path that supplies ink from the ink storage unit to the print head.
A filter is provided inside the ink supply path,
The negative pressure generated in the ink supply path at the time of ink supply and on the downstream side of the filter and the value when the meniscus of the ink formed at the opening of the filter is torn is defined as Pm (Pa). P _E (Pa) is the pressure when the ink meniscus of the ink absorber breaks, and the critical pressure when the ink meniscus formed on the nozzle of the print head is broken is Pn. (Pa), and the water head pressure between the ink discharge port of the nozzle and the ink supply port of the ink container is Ph (Pa) ,
Pn− | Ph | > Pm> P _E holds,
The filtration accuracy of the filter is F (m), the cell density of the ink absorber before being stored in the ink storage portion is N (cells / m), and the ink storage portion is stored in the ink storage portion before being stored in the ink storage portion. When the compression ratio indicated by the volume ratio of the ink absorber when compressed and stored is R,
F '<1 / (NR)
(However, if the filter has a circular opening, F ′ = F,
In other cases, F '= √2 · F)
An image forming apparatus satisfying the requirements. If the diameter of the nozzle of the print head is D _N (m),
D _N <F ′ <1 / (N · R)
(However, if the filter has a circular opening, F ′ = F,
In other cases, F '= √2 · F)
The image forming apparatus according to claim 1, wherein: In an image forming apparatus comprising: an ink storage unit having a porous ink absorber that holds ink; a print head that discharges ink; and an ink supply path that supplies ink from the ink storage unit to the print head.
A filter is provided inside the ink supply path,
The negative pressure generated in the ink supply path at the time of ink supply and on the downstream side of the filter and the value when the meniscus of the ink formed at the opening of the filter is torn is defined as Pm (Pa). P _E (Pa) is the pressure when the ink meniscus of the ink absorber breaks, and the critical pressure when the ink meniscus formed on the nozzle of the print head is broken is Pn. (Pa), and the water head pressure between the ink discharge port of the nozzle and the ink supply port of the ink container is Ph (Pa) ,
Pn− | Ph | > Pm> P _E holds,
The ink absorber is compressed in advance before being stored in the ink storage portion,
The filtration accuracy of the filter is F (m), the cell density of the ink absorber before compression processing is N ′ (number / m), and the compression is expressed by the volume ratio of the ink absorber after compression processing before compression processing. If the ratio is R ′,
F '<1 / (N' ・ R ')
(However, if the filter has a circular opening, F ′ = F,
In other cases, F '= √2 · F)
An image forming apparatus satisfying the requirements. If the diameter of the nozzle of the print head is D _N (m),
D _N <F ′ <1 / (N ′ · R ′)
The image forming apparatus according to claim 3, wherein: In an image forming apparatus comprising: an ink storage unit having a porous ink absorber that holds ink; a print head that discharges ink; and an ink supply path that supplies ink from the ink storage unit to the print head.
A filter is provided inside the ink supply path,
The negative pressure generated in the ink supply path at the time of ink supply and on the downstream side of the filter and the value when the meniscus of the ink formed at the opening of the filter is torn is defined as Pm (Pa). P _E (Pa) is the pressure when the ink meniscus of the ink absorber breaks, and the critical pressure when the ink meniscus formed on the nozzle of the print head is broken is Pn. (Pa), and the water head pressure between the ink discharge port of the nozzle and the ink supply port of the ink container is Ph (Pa) ,
Pn− | Ph | > Pm> P _E holds,
The filtration accuracy of the filter is F (m), and the water head of the ink storage portion that is generated when ink is supplied to the print head via the ink supply path when the ink storage portion is fully filled with ink. The pressure is Pi (Pa), the pressure loss due to the viscous resistance of the ink in the ink storage part is Pμ (Pa), the surface tension of the ink is η (N / m), and the ink absorber before being stored in the ink storage part The cell density is N (cells / m), the compression ratio indicated by the volume ratio of the ink absorber when compressed and stored in the ink storage unit with respect to before being stored in the ink storage unit is R, S (m ² ) represents the cross-sectional area of the ink absorber when compressed and stored in the ink storage unit, and L (m) represents the height of the ink absorber when stored in the ink storage unit. At 25 ° C When the viscosity of the tank is μ ₂₅ (Pa · s) and the viscosity at an arbitrary temperature T _K (K) is μ _TK (Pa · s), at an arbitrary temperature T _K (K),
4. η / F '> | Pμ | + | Pi |
Pμ = (k / A) · [ _μTK · L · (N · R) ² / S] · Q
(However, coefficient (k / A) = 485)
μ _TK = α · exp (β / T _K ),
α = μ ₂₅ / exp (β / 298),
β = Ln [0.42 · Ln (μ ₂₅ ) +4.71] / (1 / 273−1 / 298)
(However, if the filter has a circular opening, F ′ = F,
In other cases, F '= √2 · F)
An image forming apparatus satisfying the requirements. When the diameter of the nozzle in the print head is D _N (m ) ,
4 · η / D _N − | Ph |> 4 · η / F ′> | Pμ | + | Pi |
(However, if the filter has a circular opening, F ′ = F,
In other cases, F '= √2 · F)
The image forming apparatus according to claim 5, wherein: In an image forming apparatus comprising: an ink storage unit having a porous ink absorber that holds ink; a print head that discharges ink; and an ink supply path that supplies ink from the ink storage unit to the print head.
A filter is provided inside the ink supply path,
The negative pressure generated in the ink supply path at the time of ink supply and on the downstream side of the filter and the value when the meniscus of the ink formed at the opening of the filter is torn is defined as Pm (Pa). P _E (Pa) is the pressure when the ink meniscus of the ink absorber breaks, and the critical pressure when the ink meniscus formed on the nozzle of the print head is broken is Pn. (Pa), and the water head pressure between the ink discharge port of the nozzle and the ink supply port of the ink container is Ph (Pa) ,
Pn− | Ph | > Pm> P _E holds,
The ink absorber is compressed in advance before being stored in the ink storage portion,
The filtration accuracy of the filter is F (m), and the water head of the ink storage portion that is generated when ink is supplied to the print head via the ink supply path when the ink storage portion is fully filled with ink. The pressure is Pi (Pa), the pressure loss due to the viscous resistance of the ink in the ink storage portion is Pμ (Pa), the surface tension of the ink is η (N / m), and the cell density of the ink absorber before compression processing is N ′ (pieces / m), the compression ratio indicated by the volume ratio of the ink absorber after the compression processing before the compression processing, R ′, the cross-sectional area of the ink absorber when stored in the ink storage portion after being compressed S (m ² ), the height of the ink absorber when compressed and stored in the ink storage unit is L (m), the viscosity of the ink at 25 ° C. is μ ₂₅ (Pa · s), an arbitrary temperature viscosity in T _{K (K)} In the _mu TK when (Pa · s) to any temperature _T K (K),
4. η / F '> | Pμ | + | Pi |
Pμ = (k / A) · [ _μTK · L · (N ′ · R ′) ² / S] · Q
(However, coefficient (k / A) = 485)
μ _TK = α · exp (β / T _K ),
α = μ ₂₅ / exp (β / 298),
β = Ln {0.42 · Ln (μ ₂₅ ) +4.71} / (1 / 273−1 / 298)
(However, if the filter has a circular opening, F ′ = F,
In other cases, F '= √2 · F)
An image forming apparatus satisfying the requirements. When the diameter of the nozzle in the print head is D _N (m ) ,
4 · η / D _N − | Ph |> 4 · η / F ′> | Pμ | + | Pi |
(However, if the filter has a circular opening, F ′ = F,
In other cases, F '= √2 · F)
The image forming apparatus according to claim 7, wherein:   The image forming apparatus according to claim 1, further comprising a detector that detects the presence or absence of ink in the ink supply path.

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