JP2004230668A - Image forming apparatus - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide an image forming apparatus which can prevent air from being mixed into an ink supply path due to a factor except a decrease in the remaining quantity of ink. <P>SOLUTION: This image forming apparatus is equipped with an ink tank 21 wherein a porous ink storage body 22 is housed, and the ink supply path 3 for supplying the ink to a print head from the ink tank 21. A filter 23 is provided inside the path 3. The image forming apparatus satisfies the expression, F'<1/(N×R), wherein F (m) represents the filtration accuracy of the filter 23; N (number/m) represents the cell density of an ink absorber 22 before the ink absorber 22 is housed in the ink tank 21; and R represents a compression ratio which is expressed by the ratio of the volume of the ink absorber 22 housed in the ink tank 21 in a compressed state, to that of the ink absorber 22 before the ink absorber 22 is housed in the ink tank 21. However, the expression, F'=F, is satisfied when an opening of the filter 23 is circular, and the expression, F'=√2×F, is satisfied in other cases. <P>COPYRIGHT: (C)2004,JPO&NCIPI

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７．８７×１０^３（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１２．６×１０^３（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１２．６×１０^３（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１２．６×１０^３（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、７．８７×１０^３≦Ｍ≦１２．６×１０^３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７．８７×１０^３以上でも１２．６×１０^３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７．８７×１０^３（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１２．６×１０^３（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＝８．１７ｎｍ^３／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Ｒ^２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＝８．１７ｎｍ^３／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（ｍ^３／ｓ）とすると、該流量Ｑｉ（ｍ^３／ｓ）は、下記一般式（５）
Ｑｉ＝Ｐｕ・π・ｄ^４／（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／（ｄ^２） ・・・（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（ｍ^３／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（ｍ^３／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、
Ｐμ＝ｋ・Ｐｖ
＝（ｋ／Ａ）・［μ・Ｌ・（Ｎ・Ｒ）^２／Ｓ］・Ｑ ・・・・（１０）
（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９．８×１０^３・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）＞９．８×１０^３・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（０．０８ｍＨ_２Ｏ）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＝８．１７ｎｍ^３／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（ｍ^３） （＝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（ｍ^３）（＝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（ｍ^３）（＝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・Ｍ^２／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海圧力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、１２．６×１０^３（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、
［η・Ｓ／（Ｃ・Ｄ_Ｎ・μ・Ｌ・Ｑ）］^０．５＞（Ｎ・Ｒ）＞γ・ｈ／（η・Ｂ）・・・（２５）
（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＝１．５７×１０^３〜３．９４×１０^３（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＝３．１５×１０^３（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μ_２５（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μ_２５を１とした場合の各温度Ｔ（℃）における粘度μＴ／μ_２５（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／μ_２５（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／μ_２５（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（４２）
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（４３）

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μ_２５と、粘度μ／μ_２５（正規化粘度）、ここでは、μ_０／μ_２５，μ_５０／μ_２５，μ_７５／μ_２５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μ_０／μ_２５に着目すると、以下の近似式
μ_０／μ_２５＝０．４２・Ｌｎ（μ_２５）＋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）
β＝Ｌｎ［０．４２・Ｌｎ（μ_２５）＋４．７１］／（１／２７３−１／２９８）・・・（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μ_２５（Ｐａ・ｓ）は、
μ_２５＝α・ｅｘｐ（β／２９８）
となり、これにより、下記一般式（５１）
α＝μ_２５／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）
μ_ＴＫ＝α・ｅｘｐ（β／Ｔ_Ｋ）
（但し、式中、α＝μ_２５／ｅｘｐ（β／２９８）、
β＝Ｌｎ［０．４２・Ｌｎ（μ_２５）＋４．７１］／（１／２７３−１／２９８）
を示す）・・・（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（Ｈ_２Ｏ）に適用した場合の温度Ｔ（℃）と粘度μ（Ｐａ・ｓ）、μ／μ_２５、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μ_２５と、正規化粘度μ／μ_２５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／μ_２５、及び、μ’_４０／μ_２５を示し、「○」は５℃のときの正規化粘度μ／μ_２５（すなわち、μ_５／μ_２５）、「△」は４０℃のときの正規化粘度μ／μ_２５（すなわち、μ_４０／μ_２５）、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（ｍ^２）、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μ_２５（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＝μ_２５／ｅｘｐ（β／２９８）、
β＝Ｌｎ［０．４２・Ｌｎ（μ_２５）＋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＝μ_２５／ｅｘｐ（β／２９８）、
β＝Ｌｎ［０．４２・Ｌｎ（μ_２５）＋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（ｍ^２）、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μ_２５（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＝μ_２５／ｅｘｐ（β／２９８）、
β＝Ｌｎ［０．４２・Ｌｎ（μ_２５）＋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（ｍ^２）、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μ_２５（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＝μ_２５／ｅｘｐ（β／２９８）、
β＝Ｌｎ［０．４２・Ｌｎ（μ_２５）＋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／μ_２５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、μ_２５とμ／μ_２５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μ_２５とμ／μ_２５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]
TECHNICAL FIELD OF THE INVENTION
The present invention relates to an image forming apparatus having an ink storage unit for storing 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 recording paper, and generally includes an ink cartridge having an ink tank. , The ink is ejected from the print head onto the sheet.
[0003]
When such an ink jet recording apparatus is used, before air becomes empty, if air enters the ink supply system, it may cause a discharge failure. Therefore, measures to prevent air from being mixed by an ink absorber or a filter are widely used. I have.
[0004]
For example, Patent Document 1 discloses that a filter having an effective transmission dimension of 8 μm is provided downstream of an ink absorber to capture air, and the suction force of the recovery unit 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 runs out. For this reason, the ink jet recording apparatus needs to detect the remaining amount of ink in the ink cartridge and notify the user.
[0006]
Therefore, various ink cartridges capable of detecting the remaining amount of ink have been proposed. In such ink cartridges, a method of using an optical ink level sensor to notify a user of the ink empty before sucking air into an ink supply system has been widely adopted. An electrode replaced with an electrode is used. For example, Patent Document 1 discloses that an ink absorber (foam material) for absorbing ink is incorporated in an ink tank, and a filter is provided in an ink supply path connecting the ink tank and a print head. An ink cartridge having an electrode for detecting the presence or absence of ink in the ink supply path is disclosed on the downstream side of the ink supply port, that is, on the ink ejection 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 from the print head side, which is the ink discharge port side, to suck out the ink through the filter. It is supposed to. Then, the presence or absence of ink in the ink supply path is detected based on the current flowing between the electrodes. That is, when the remaining amount of the ink in the ink cartridge becomes small, the ink does not exist in the ink supply path, and the current stops flowing 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]
Japanese Patent Application Laid-Open No. 2001-219584 (Published date: August 14, 2001)
[0009]
[Patent Document 2]
JP-A-3-288654 (publication date: December 18, 1991)
[0010]
[Problems to be solved by the invention]
However, Patent Document 1 does not consider preventing bubbles from passing through the filter during the discharging operation.
[0011]
Further, in Patent Document 1, the characteristics of the ink absorbed by the ink absorber are not considered.
[0012]
In the invention described in Patent Document 2, an ink absorber having an N / R exceeding 200 cannot be used, and the range of selection of the ink absorber is narrowed.
[0013]
Also, in the invention described in Patent Document 2, similarly to Patent Document 1, characteristics of the ink absorbed by the ink absorber are not considered. Therefore, depending on the type of ink, the ink jet recording apparatus has suffered problems such as a shortage of ink supply during continuous discharge and an ink leak when attaching / detaching the ink cartridge.
[0014]
Further, as described above, when a negative pressure for sucking ink from the print head side which is the ink discharge port side through the filter is applied, 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 in from the leading end, and the print head may cause ejection failure. Further, if the negative pressure becomes too high, air trapped by the filter may pass through the filter, and this air may block the supply path or reach the print head to cause a discharge failure. In addition, when the ink reaches the ink remaining amount detection unit, the air passing through the filter stops the current from flowing between the electrodes, and there is a possibility that the ink may be erroneously determined to be empty. As described above, when the ink supply pressure is higher than the negative pressure applied to the filter, air may be mixed into the ink supply path due to a factor other than a decrease in the remaining amount of ink, and a malfunction of the remaining ink amount detection may be caused. is there.
[0015]
However, Patent Documents 1 and 2 do not consider the above problem at all.
[0016]
SUMMARY An advantage of some aspects of the invention is to provide an image forming apparatus that can prevent air from entering an ink supply path due to factors other than a decrease in the amount of remaining ink. Is to do.
[0017]
Further, a further object of the present invention is to prevent problems such as air being mixed into the ink supply system before the ink becomes empty, ink supply shortage occurring, and ink leakage occurring when the ink cartridge is attached / detached, during continuous ink ejection. 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 guide according to the characteristics of the ink, so as to prevent the occurrence.
[0018]
A further object of the present invention is to provide an image forming apparatus capable of expanding the range of selection of a design guide for an 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 unit (for example, an ink tank provided in an ink cartridge) that stores a porous ink storage body (for example, a foam material) that holds ink. And an ink supply path for supplying ink from the ink storage section to the print head, wherein a filter (for example, provided at an end of the ink supply path on the ink storage section side) is provided inside the ink supply path. Filter), the filtering accuracy of the filter is F (m), the cell density of the ink absorber before being stored in the ink storage unit is N (cells / m), When a compression ratio represented by a volume ratio of the ink absorber when compressed and stored in the ink storage unit is R,
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.
[0020]
When the ink is supplied to the print head, a pressure required for the print head to suck the ink, that is, a 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.
[0021]
Therefore, according to the above configuration, the critical value of the negative pressure generated in the ink absorber by the surface tension of the ink is determined by the negative pressure generated by the filter by the surface tension of the ink, that is, the opening of the filter. It can be adjusted to be smaller than the critical value of the pressure (filter pressure) due to the meniscus of the portion (mesh), the ink meniscus formed in the mesh of the filter is broken before the ink becomes empty, and the air is supplied to the ink supply path. The ink is prevented from being mixed into the ink absorber, and the meniscus of the ink absorber retreats in accordance with the consumption of the ink, thereby enabling a stable ink supply operation. Furthermore, factors other than a decrease in the remaining amount of ink, such as bubbles generated in the ink in the ink storage unit due to carriage vibration, atmospheric pressure, or a change in ambient temperature, 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.
[0022]
Therefore, according to the above configuration, an image forming apparatus having a design guideline for an ink supply system is provided so that it is possible to prevent occurrence of a problem that air is mixed into the ink supply system before the ink is empty during continuous ejection of ink. Can be provided.
[0023]
Further, according to the above configuration, as described above, the negative pressure at the time of ink supply (including at the time of ink empty) can be controlled with a small variation in filtration accuracy F (m). Pressure can be obtained.
[0024]
In order to solve the above-described problems, the image forming apparatus according to the present invention is configured such that the diameter of the nozzle (ink ejection nozzle) of the print head is 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 set to be larger than the critical value of the pressure due to the ink meniscus at the opening of the filter. It can be adjusted to be smaller, and it is possible to prevent the air from being sucked in from the tip of the nozzle and the printing head from becoming defective in ejection.
[0026]
Further, according to the above configuration, it is possible to prevent the meniscus of the ink formed in the opening of the filter from being broken, and to prevent air from being mixed into the ink supply path. Inadvertent inhalation of air into the inside can be prevented, and the ink held by the ink absorber can be effectively supplied by the print head. Therefore, according to the above configuration, it is possible to further prevent air from entering the ink supply path due to factors other than a decrease in the remaining amount of ink, and to more effectively prevent malfunction in detecting the remaining amount of ink.
[0027]
Therefore, according to the above configuration, an image forming apparatus having a design guideline for an ink supply system is provided so that it is possible to prevent occurrence of a problem that air is mixed into the ink supply system before the ink is empty during continuous ejection of ink. Can be provided.
[0028]
In order to solve the above problems, an image forming apparatus according to the present invention has an ink storage unit (for example, an ink tank provided in an ink cartridge) that stores a porous ink storage body (for example, a foam material) that holds ink. And an ink supply path for supplying ink from the ink storage section to the print head, wherein a filter (for example, provided at an end of the ink supply path on the ink storage section side) is provided inside the ink supply path. The ink absorber is pre-compressed before being stored in the ink storage unit, and the filtering accuracy of the filter is F (m). Assuming that the cell density is N ′ (cells / m) and the compression ratio (compression ratio) indicated by the volume ratio of the ink absorber after compression processing before compression processing 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.
[0029]
As described above, when the ink is supplied to the print head, the pressure required for the print head to suck the ink, that is, the pressure (ink suction pressure) due to 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 by the surface tension of the ink is determined by the negative pressure generated by the filter by 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) due to the meniscus in the portion (mesh), and the ink meniscus formed in the mesh of the filter is broken before the ink becomes empty, and the air is supplied to the ink. The ink is prevented from being mixed into the path, and the meniscus of the ink absorber retreats in accordance with the consumption of the ink, thereby enabling a stable ink supply operation. Furthermore, factors other than a decrease in the remaining amount of ink, such as bubbles generated in the ink in the ink storage unit due to carriage vibration, atmospheric pressure, or a change in ambient temperature, are captured by the filter to prevent air from entering the ink supply path. Reliable printing can be performed, and ink can be consumed without waste.
[0031]
Therefore, according to the above configuration, an image forming apparatus having a design guideline for an ink supply system is provided so that it is possible to prevent occurrence of a problem that air is mixed into the ink supply system before the ink is empty during continuous ejection of ink. Can be provided.
[0032]
Further, according to the above configuration, as described above, the negative pressure at the time of ink supply (including at the time of emptying) can be managed with a small variation in filtration accuracy F (m). Can be obtained.
[0033]
In order to solve the above-described problems, the image forming apparatus according to the present invention is configured such that the diameter of the nozzle (ink ejection nozzle) of the print head is 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 defined as the critical value of the pressure due to the meniscus of the ink at the opening of the filter. It can be adjusted to be smaller, and it is possible to prevent the air from being sucked in from the tip of the nozzle and the printing head from becoming defective in ejection.
[0035]
Further, according to the above configuration, it is possible to prevent the meniscus of the ink formed in the opening of the filter from being broken, and to prevent air from being mixed into the ink supply path, and also to prevent the ink supply path from passing through the ink supply path. Inadvertent inhalation of air into the inside can be prevented, and the ink held by the ink absorber can be effectively supplied by the print head. Therefore, according to the above configuration, it is possible to further prevent air from entering the ink supply path due to factors other than a decrease in the remaining amount of ink, and to more effectively prevent malfunction in detecting the remaining amount of ink.
[0036]
Therefore, according to the above configuration, an image forming apparatus having a design guideline for an ink supply system is provided so that it is possible to prevent occurrence of a problem that air is mixed into the ink supply system before the ink is empty during continuous ejection of ink. Can be provided.
[0037]
In order to solve the above problems, an image forming apparatus according to the present invention has an ink storage unit (for example, an ink tank provided in an ink cartridge) that stores a porous ink storage body (for example, a foam material) that holds ink. And an ink supply path for supplying ink from the ink storage section to the print head, wherein a filter (for example, provided at an end of the ink supply path on the ink storage section side) is provided inside the ink supply path. Filter), the filtering accuracy of the filter is F (m), and this occurs when ink is to be supplied to the print head via the ink supply path when the ink container is fully filled with ink. The head pressure of the ink storage unit is Pi (Pa), the pressure loss due to the viscous resistance of the ink in the ink storage unit is Pμ (Pa), The surface tension of the ink is η (N / m), the cell density of the ink absorber before being stored in the ink storage unit is N (cells / m), The compression ratio represented 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 unit is S (m²), The height of the ink absorber when compressed and stored in the ink storage unit is L (m), and the viscosity of the ink at 25 ° C. is μ.₂₅(Pa · s), arbitrary temperature T_KThe viscosity at (K) is μ_TK(Pa · s), an arbitrary 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= Αexp (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 can be prevented that the meniscus of the ink formed in the portion is broken and air is mixed into the ink supply path. For this reason, according to the above-described configuration, it is possible to prevent air from entering 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, and to improve reliability in terms of quality. High printing can be performed.
[0039]
Therefore, according to the above configuration, at the time of continuous ejection of ink, the design guideline of the ink supply system according to the characteristics of the ink can be prevented so that a problem such as air entering the ink supply system before the ink is empty can be prevented. An image forming apparatus having:
[0040]
Further, according to the above configuration, as described above, the maximum negative pressure at the time of ink emptying can be managed with the small filtering accuracy F (m), and as a result, a stable negative pressure can be obtained. .
[0041]
In order to solve the above-mentioned problems, the image forming apparatus according to the present invention is configured such that the diameter of a nozzle (ink ejection nozzle) in the print head is D._N(M), when the 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.
[0042]
According to the above configuration, the pressure that leaks through the filter during ink supply, particularly when ink is supplied immediately before the ink is empty, can be appropriately controlled without exceeding the critical pressure of the nozzles of the print head. Can be prevented, and foreign substances heading toward the ink supply path can be effectively filtered, and the reliability of the ejection operation by the nozzles can be improved.
[0043]
Therefore, according to the above configuration, an image forming apparatus having a design guideline for an ink supply system is provided so that it is possible to prevent occurrence of a problem that air is mixed into the ink supply system before the ink is empty during continuous ejection of ink. Can be provided.
[0044]
In order to solve the above problems, an image forming apparatus according to the present invention has an ink storage unit (for example, an ink tank provided in an ink cartridge) that stores a porous ink storage body (for example, a foam material) that holds ink. And an ink supply path for supplying ink from the ink storage section to the print head, wherein a filter (for example, provided at an end of the ink supply path on the ink storage section side) is provided inside the ink supply path. The ink absorber is pre-compressed before being stored in the ink storage unit, the filtering accuracy of the filter is F (m), and the ink storage unit is fully filled with ink. When the ink is supplied to the print head via the ink supply path while the ink is being supplied, the water head pressure of the ink storage unit is represented by Pi (Pa). The pressure loss due to the viscous resistance of the ink in the ink storage section 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 ′ (pcs / m). ), The compression ratio (compression rate) indicated by the volume ratio of the ink absorber after compression processing before compression processing is R ′, and the cross-sectional area of the ink absorber when compressed and stored in the ink storage unit is S ′. (M²), The height of the ink absorber when compressed and stored in the ink storage unit is L (m), and the viscosity of the ink at 25 ° C. is μ.₂₅(Pa · s), arbitrary temperature T_KThe viscosity at (K) is μ_TK(Pa · s), an arbitrary 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= Αexp (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, at the time of ink supply, the critical value of the pressure due to the meniscus at the opening of the filter can be appropriately managed without exceeding the critical value of the ink suction pressure due to 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. It is possible to prevent the meniscus of the broken ink 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 entering 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, and to improve reliability in terms of quality. High printing can be performed.
[0046]
Therefore, according to the above configuration, at the time of continuous ejection of ink, the design guideline of the ink supply system according to the characteristics of the ink can be prevented so that a problem such as air entering the ink supply system before the ink is empty can be prevented. An image forming apparatus having:
[0047]
Further, according to the above configuration, as described above, the maximum negative pressure at the time of ink emptying can be managed with the small filtering accuracy F (m), and as a result, a stable negative pressure can be obtained. .
[0048]
In order to solve the above-mentioned problems, the image forming apparatus according to the present invention is configured such that the diameter of a nozzle (ink ejection nozzle) in the print head is D._N(M), when the 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, at the time of ink supply, the critical value of the pressure due to the meniscus at the opening of the filter can be appropriately managed without exceeding the critical value of the ink suction pressure due to 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. It is possible to prevent the meniscus of the broken ink 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 entering 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, and to improve reliability in terms of quality. High printing can be performed.
[0050]
Therefore, according to the above configuration, an image forming apparatus having a design guideline for an ink supply system is provided so that it is possible to prevent occurrence of a problem that air is mixed into the ink supply system before the ink is empty during continuous ejection of ink. Can be provided.
[0051]
Further, according to the above configuration, as described above, the maximum negative pressure at the time of ink emptying can be managed with the small filtering accuracy F (m), and as a result, a stable negative pressure can be obtained. .
[0052]
In order to solve the above-mentioned problem, an image forming apparatus according to the present invention includes a detector for detecting the presence or absence of ink in the ink supply path (for example, a detector for detecting the presence or absence of ink by stopping the flow of current between electrodes). Electrodes).
[0053]
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 meniscus of the ink at the opening of the filter. It is possible to prevent the meniscus of the ink formed in the portion from being broken and the air from being mixed into the ink supply path. For this reason, according to the above configuration, it is possible to prevent air from entering the ink supply path due to factors other than a decrease in the remaining amount of ink, that is, a factor other than when the ink is empty, and prevent malfunction of the remaining ink amount detection. And highly reliable printing can be performed.
[0054]
BEST MODE FOR CARRYING OUT THE INVENTION
One embodiment of the present invention will be described below with reference to FIGS.
[0055]
As shown in FIG. 2, the ink jet recording apparatus as an image forming apparatus according to the present embodiment includes a sheet feeding unit, a separating unit, a conveying unit, a printing unit, and a discharging unit.
[0056]
The paper supply unit supplies a sheet 201 which is a recording paper when printing is performed, and includes a paper supply tray 101 and a pickup roller 102. When printing is not performed, the function of storing the sheet 201 is performed.
[0057]
The separation unit is for supplying sheets 201 supplied from the paper supply unit to the printing unit one by one, and includes a paper supply roller and a separation device (not shown). In the separating device, the friction between the sheet 201 and the pad portion, which is the contact portion with the sheet 201, is set to be larger than the friction between the sheets 201. Further, in the sheet feeding roller, the friction between the sheet feeding 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. Therefore, even if the two sheets 201 are sent to the separation unit, the sheets 201 can be separated by the paper feed roller and only the upper sheet 201 can be sent to the conveyance unit.
[0058]
The transport unit is for transporting the sheets 201 supplied one by one from the separation unit to the printing unit, and includes a guide plate (not shown) and a pair of rollers such as a transport press roller 111 and a transport 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 on the sheet 201 when the sheet 201 is sent between the print head 1 and the platen 113. .
[0059]
The printing unit is for printing on the sheet 201 supplied from the roller pair of the transport unit, and includes a print head 1, a carriage 2 on which the print head 1 is mounted, and a guide that is a member for guiding the carriage 2. It comprises a shaft (carriage holding shaft) 121, an ink cartridge 20 for supplying ink to the print head 1, a platen 113 serving as a base for a sheet 201 during printing, and an ink supply path 3 including an ink supply tube 4. An ink supply path 3 composed of 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 discharges the printed sheet 201 to the outside of the inkjet 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 printing request based on image information is made to the inkjet recording apparatus from a computer (not shown) or the like. The inkjet recording apparatus that has received the print request transports the sheet 201 on the paper feed tray 101 from the paper feed unit by the pickup roller 102.
[0063]
Next, the conveyed sheet 201 passes through the separation unit by the paper feed 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 a roller pair of a transport pressing roller 111 and a transport roller 112.
[0064]
In the printing unit, ink is sprayed from a discharge nozzle (ink discharge nozzle) 1a (see FIG. 20), which is an ink nozzle unit of the print head 1, onto the sheet 201 on the platen 113 in accordance with image information. At this time, the sheet 201 is temporarily stopped on the platen 113. While spraying the ink, the carriage 2 is guided by the guide shaft 121 and is scanned by 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 in accordance with the image information, so that printing is performed on the entire surface of the sheet 201.
[0066]
The printed sheet 201 is discharged to the discharge tray 134 through the paper discharge port 133 by the discharge rollers 131 and 132 via the ink drying unit. Thereafter, the sheet 201 is provided to the user as a printed matter.
[0067]
Here, the ink supply device 10 of the above-described ink jet recording apparatus will be described in detail with reference to FIGS. 1, 3, and 5. FIG.
[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 unit having a space for storing ink. In the ink cartridge 20 of the present embodiment, an ink absorber 22 which is a porous holding member made of, for example, polyurethane resin is provided inside the ink tank 21 (space portion).
[0070]
An ink supply path 3 including an ink supply tube 4 for supplying ink to the print head 1 is provided on, for example, a bottom surface of the ink tank 21.
[0071]
A filter 23 is provided in the ink supply path 3, specifically, in a part, preferably an end, of the ink supply path 3 on the ink tank 21 side. The end of the ink supply path 3 (ink supply port 3a) on the forming 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. It is connected to the ink tank 21. As a result, the end of the ink supply tube 4 on the side where the filter 23 is formed, that is, the end of the ink supply path 3 where the filter 23 is formed (the ink supply port 3 a) in the ink supply tube 4 is placed in the ink tank 21. positioned.
[0072]
As shown in FIGS. 1A to 1C, an ink remaining amount detection electrode (detector) is provided on the ink supply tube 4 outside the ink tank 21 so as to sandwich the ink supply tube 4. Are provided as a pair of detection electrodes (electrode portions) 25. That is, the ink supply path 3 outside the ink tank 21 is provided with a pair of detection electrodes 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 from the print head 1 side to suck out the ink through the filter 23.
[0074]
The print head 1 has, for example, a maximum of 0.49 cc (0.49 × 10^-6m³) Is ejected, and the same amount of ink is sucked from the ink tank 21 with the ejection, and the pressure applied to the ink supply path 3 at that time is, as shown in FIG. Can be measured at The print head 1 and the ink cartridge 20 are arranged such that, for example, the water head (Ph; head water pressure) of the print head 1 is 50 mm and the water head (Pi; tank water head pressure) of the ink tank 21 is 30 mm. Have been. Here, the head water pressure Ph indicates the water head pressure between the discharge nozzle 1a of the print head 1 and the ink supply port 24. The tank head pressure Pi is the head pressure of the ink tank 21 generated when the ink is to be supplied to the print head 1 via the ink supply port 24 when the ink tank 21 is fully filled with ink. Is shown.
[0075]
As shown in FIG. 4, the filter 23 is formed by weaving a band-like, for example, stainless steel material into a net shape using weft yarns and warp yarns. Further, the filter 23 is not limited to the above-described method, and may be a plate-like member having an opening formed by etching, for example.
[0076]
Then, in the ink cartridge 20, as shown in FIGS. 1A to 1C, the ink between the detection electrodes 25 is discharged by the air that has entered 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, 25, the current is prevented from flowing between the detection electrodes 25, 25. (Ink empty) is detected.
[0077]
Hereinafter, the relationship between the negative pressure applied to the ink supply path 3 and the time in the process of detecting the remaining amount of ink will be described in detail with reference to FIGS. FIGS. 5 and 6 are graphs showing the relationship between the elapsed time when ink is continuously ejected from the state where the ink cartridge 20 is filled with ink and the negative pressure applied to the ink supply path 3. FIG. 6 is a graph schematically showing the relationship shown in FIG.
[0078]
First, when the print head 1 is driven, that is, a negative pressure is applied to the ink supply path 3 in order to consume the ink in the ink tank 21, as shown in FIGS. Accordingly, the negative pressure applied to the ink supply path 3 also gradually increases.
[0079]
However, when the amount of remaining ink decreases, the negative pressure applied to the ink supply path 3 rapidly increases at a certain point in time, and decreases after reaching the maximum value. This is because, when a large suction force is applied to the ink supply path 3, the meniscus of the ink formed in the opening 23a of the filter 23 (see FIG. 4) is broken, air is sucked in, and the negative pressure is reduced. It is shown that.
[0080]
That is, as the remaining amount of ink decreases, the meniscus of the ink absorbed in the cells 22a (opening, see FIG. 13 and the like) of the ink absorber 22 recedes, and the negative pressure applied to the ink supply path 3 due to the surface tension of the ink is reduced. Increase gradually. The negative pressure applied to the ink supply path 3 is equal to the critical pressure of the cell 22a of the ink absorber 22, that is, the critical pressure P due to the ink absorber 22 when the ink is empty._EIs exceeded, the meniscus of the ink reaches the filter 23, and the opening 23 a of the filter 23 controls the negative pressure applied to the ink supply path 3. Then, as the ink is further consumed, the meniscus of the ink at the opening 23a of the filter 23 recedes, similarly to 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 pressure rapidly increases to a critical pressure (filter pressure) based on the diameter of the opening 23a, that is, a critical pressure (maximum negative pressure) Pm of the filter 23. Thereafter, when the suction pressure from the print head 1 exceeds the critical pressure Pm of 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 decreases.
[0081]
In order to measure the negative pressure applied to the ink supply path 3, as shown in FIG. 7, a mesh-like filter (infiltrated with ink) so as to satisfy the same condition as the filter 23 in the process of detecting the remaining amount of ink. A measuring device was used in which an ink supply tube 4 was connected to a cylinder 32 to which a mesh filter 31 was attached so that the filter 31 became a lid.
[0082]
The ink that has been infiltrated into the filter 31 is removed from the ink supply tube 4 via the ink supply tube 4 connected to the cylinder 32 by a pump (not shown). The flow rate (ink supply amount) of the ink flowing in the ink supply path 3 is 0.05 cc per minute (that is, 0.05 × 10^-6m³), And at this time, the negative pressure applied to the filter 31 was measured by the pressure gauge 26 to measure the negative pressure applied to the ink supply path 3 including the ink supply tube 4.
[0083]
The measurement of the negative pressure using this measuring device was performed by changing the size of the opening 23a (mesh) of the filter 23 (filtration accuracy F), that is, the size of the opening of the filter 31. As shown in FIG. 8, the smaller the filtering 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]
Then, next, this tendency is verified by making a graph (FIG. 9) 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. 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) at 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 represented by the following general formula (1).
Pc = 4η / d (1)
Widely known for.
[0087]
Note that, in the present embodiment, the same symbol indicates the same physical property in each of the general formula, the experimental formula, the relational formula, and the like. Also, the same symbols indicate the same units for the calculation units of the calculated values in each equation.
[0088]
Then, by substituting the filtration accuracy F (m) of the filter 23 into the diameter d (m) of the general formula (1), the critical pressure Pm (Pa) by the filter 23 was determined as the critical pressure Pc (Pa). It has been found that the calculated value obtained by the general formula (1) becomes √2 times the actually measured value, and that if the filtering accuracy F of the filter 23 is substituted as it is, a large discrepancy 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 the weft yarn and the warp yarn is not circular, and the filtering accuracy F depends on the minimum gap width of the opening 23a of the filter 23. It is considered that the critical pressure Pm by 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 times using the surface tension η (N / m) of the ink and the filtration accuracy F (m). Empirical formula (2)
Pm = 4η / (√2 · F) (2)
It is expressed as
[0091]
Thus, the vertical axis represents the critical pressure Pm of the filter 23, that is, the negative pressure applied to the ink supply path 3, and the horizontal axis represents the filtration accuracy F of the filter 23, as shown in FIG. When the relationship between the critical pressure Pm by the filter 23 and the filtration accuracy F is graphed using the calculated values according to the above, the result shown in FIG. 9 is obtained. In FIG. 9, “Δ” indicates the measured value shown in FIG. 8, and the solid line indicates the value calculated by the empirical formula (2).
[0092]
From the results shown in FIG. 9, the measured values and the calculated values according to the empirical formula (2) almost matched, and it was found that the above tendency was 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 the present 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 meniscus (ink level) of the ink formed in the opening of the filter 23 ) Is broken and the air reaches the electrode portion composed of the detection electrodes 25, 25, and when the detection resistance value of the detection electrodes 25, 25 exceeds a predetermined value, the ink tank 21 is substantially empty, The control is performed such that the critical pressure Pm by the filter 23, which is the critical pressure at which the meniscus of the ink is broken, does not exceed a predetermined value.
[0094]
In the present embodiment, as a result of performing various experiments on the negative pressure applied to the ink supply path 3 when the remaining amount of ink 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]
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 negative pressure generated in the ink supply system is Before the meniscus of the ink formed in the opening is broken and the air reaches the electrode and is judged to be empty, as shown in FIGS. 20 and 21, the tip of the discharge nozzle 1a of the print head 1 ( This causes a problem that the meniscus of the ink (ink liquid level) retreats too far from the nozzle tip and the air is sucked in from the nozzle tip, which makes it impossible to discharge (supply) ink droplets 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. The porous body of the foam material is impregnated with ink, and the foam material is compressed and stored in the ink tank 21.
[0098]
The ink held in the porous body is discharged from the inside of the ink cartridge 20 to the print head 1 side by capillary force through a discharge nozzle 1a (see FIG. 20) which is an ink supply port 24 provided in the ink cartridge 20. .
[0099]
However, depending on the holding power of the ink held by the porous holding member in the ink tank 21, problems such as insufficient ink supply during continuous discharge and ink leakage when the ink cartridge 20 is attached / detached occur.
[0100]
In order to solve this problem, it is necessary to design guidelines for the ink absorber 22 according to the characteristics of the ink. Therefore, in the present embodiment, an experiment was performed 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. . Table 1 shows the results of this experiment. The conditions of 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 x 10³(Pcs / m) (= 40 / inch)
-Material of the 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 dimensions of the ink absorber 22 when housed in the ink cartridge 20 (ink tank 21) are equal to the inner dimensions 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) when stored in the ink cartridge 20 when compressed and stored in the ink cartridge 20
Cell density N (cells / m): cell density of ink absorber 22 (foam material) before housed in ink cartridge 20
-Mounting cell density M of ink absorber 22 (foam material) at the time of compression: mounting cell density of ink absorber 22 (foam material) when compressed and stored in ink cartridge 20
・ Flow rate Q (m³/ S): Ink flow rate
Efficiency τ (%): Total outflow amount from the 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 to the upper limit, that is, when the ink flow is set to a predetermined ink flow rate in a full state. Measured value
Ink lower limit stable negative pressure PL (Pa): measured when ink in ink cartridge 20 is filled only to the lower limit, that is, when a predetermined ink flow rate is set immediately before ink in ink cartridge 20 runs out. Actual measured value of stable negative pressure in ink cartridge 20
[0104]
[Table 1]

[0105]
In the present embodiment, from the viewpoint of the ability of the filter 23 to remove foreign matter, the critical pressure P_E(Hereinafter sometimes referred to as the critical pressure of the ink absorber) and the critical pressure Pm of the filter 23 (hereinafter sometimes referred to as the critical pressure of the filter) is Pm> P_EIs set to meet. In the present 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. 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 actually measured value of the generated negative pressure based on the fluid dynamics theory, the stable negative pressure Pu at the time of the ink upper limit is determined by the viscosity of the ink due to the viscosity resistance of the ink. It has been found that the stable negative pressure PL at the time of the lower limit of the ink is based on the surface tension η of the ink.
[0107]
In the above measurement, it is necessary to determine the ink holding force in consideration of the height of the ink cartridge 20, the variation of the cells 22a 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 is inadvertently leaked when the ink cartridge 20 is attached / detached, particularly when the ink is at the upper limit.
[0108]
For example, if the height of the ink cartridge 20 is 34 mm, and if the safety factor is 2, the specific gravity γ of the ink is about 1.0, the holding power is 68 (= 34 × 2) mm at the water head, that is, 0.67 kPa is required. In addition, the height of an ink cartridge that is generally widely used is approximately 40 mm or less, and therefore, it is necessary to withstand the ink head pressure of 0.8 kPa.
[0109]
The ink holding force is a capillary pressure based on the surface tension η, and if the cell diameter at the time of compression is regarded as a circular opening having a diameter d (m), the mounting of the ink absorber 22 (foam material) at the time of compression From the cell density M (M = N · R; strictly speaking, M ≒ N · R) (cells / m), the cell diameter d (m) at the time of compression is represented by the following relational expression (3).
d = 1 / (N · R) (3)
, The critical pressure P_EAnd the cell density N (cells / m) and the compression ratio (R), assuming that the surface tension of the ink is η (N / m), from the general formula (1) and the relational expression (3), The following relational expression (4)
P_E= 4 · η · (N · R) (4)
Is represented by Accordingly, the stable negative pressure PL at the ink lower limit is such that the mounting cell density M (M = N · R) is 7.87 × 10³If it is not less than (pieces / m) (ie, not less than 200 pieces / inch), a holding force of 0.86 kPa and 89 mm or more can be obtained at the water head. Can be prevented.
[0110]
In addition, when ink is continuously discharged, a negative pressure of the ink supply system (critical pressure of the ink absorber 22 or the filter 23) is generated in the ink supply system unless the pressure is 2.0 kPa or less in consideration of a safety factor. Due to the negative pressure, the ink supply becomes insufficient, causing a problem that the ink liquid level retreats too far from the tip of the discharge nozzle 1a (nozzle tip) and air is sucked in, so that stable supply of ink cannot be performed.
[0111]
Therefore, the mounting cell density M is 12.6 × 10³(M / m) or less (that is, 320 m / inch or less), the negative pressure of the ink supply system becomes 1.5 kPa or less, and even when ink is continuously ejected, a stable supply of ink with a margin is provided. Will be possible.
[0112]
If the ratio of the ink volume that can be actually used (discharged) to the ink storage volume (filled ink volume) on the inner surface of the ink cartridge 20 is 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 mounting cell density M (M = N · R) is 12.6 × 10³(Pieces / m) (that is, 320 pieces / inch), a large decrease starts. Therefore, a condition for efficiently utilizing the volume of the ink cartridge 20 is that the mounting cell density M (M = N · R) is 12.6 × 10³(Pieces / m) or less.
[0113]
Therefore, when the mounting cell density M (cells / m) (M = N · R) of the ink cartridge 20 is 7.87 × 10³≦ M ≦ 12.6 × 10³Is satisfied, it is possible to prevent a problem that ink is inadvertently leaked when the ink cartridge 20 is attached / detached, and it is also possible to maintain a stable ink with a margin when continuously ejecting ink. Supply becomes possible, and the volume of the ink cartridge 20 can be efficiently utilized. Further, according to the above configuration, 7.87 × 10³Even above, 12.6 × 10³Since it is only necessary that the following conditions are satisfied, the range of choice in designing the ink absorber 22 can be expanded.
[0114]
Although these are theoretical values, it was confirmed that the measured values also satisfied these values. That is, in Table 1, the mounting cell density M = N · R is 7.87 × 10³(Pcs / m), the ink lower limit stable negative pressure PL, which is the actually measured stable negative pressure, is 0.86 kPa or more, and the mounting cell density M (M = N · R) is 12.6 × 10³(M / m) or less, the negative pressure of the ink supply system is 1.5 kPa or less, and a stable supply of ink with a margin becomes possible even when ink is continuously ejected. The actually measured stable negative pressure, that is, the ink lower limit stable negative pressure PL indicates what negative pressure the meniscus of the ink can withstand.
[0115]
Next, consideration is given to the stable negative pressure PL at the lower limit of the ink and the stable negative pressure Pu at the upper limit of the ink. Note that the ink upper limit stable negative pressure Pu indicates a negative pressure when ink is flowing.
[0116]
First, for normalization, a compression ratio R = 5.5 and a flow rate Q = 8.17 nm³The value obtained by normalizing the stable negative pressure Pu at the upper limit of the ink in each data with respect to the stable negative pressure Pu at the upper limit of the ink at / s (0.49 cc / min) is defined as the starting point ratio Rs. R2 is the compression ratio R²Are 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 nm³The value obtained by normalizing the stable negative pressure PL at the lower limit of the ink in each data with respect to the stable negative pressure PL at the lower limit of the ink at / s (0.49 cc / min) is defined as the end point ratio Re. R1 is a value obtained by normalizing the compression ratio R with respect to the compression ratio 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 stable negative pressure Pu at the upper limit of the ink is proportional to the square of the compression ratio R, and the stable negative pressure PL at the lower limit of the ink is proportional to the compression ratio R.
[0119]
From the above results, in order to obtain more detailed design guidelines for the ink and the ink absorber 22 (foam material), these theories were added, and studies were conducted. The details will be described below.
[0120]
First, the relationship between the stable negative pressure when the ink in the ink cartridge 20 is filled up to the upper limit (the stable negative pressure Pu at the upper limit of the ink) and the compression ratio R will be discussed 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 pipe, and It is assumed that the liquid (ink) in the pipeline flows due to the pipeline pressure difference ΔP (the pressure P1 at the pipeline start point−the pressure P2 at the pipeline end point), that is, the pressure loss Pμ of the pipeline due to viscous resistance. Can be. As shown in FIG. 12, a circular pipe (each cell 223a is regarded as a circular pipe, and the pressure difference ΔP of the pipe (pressure P1 at the start of the pipe1−pressure P2 at the end of the pipe), ie, viscous resistance It can be assumed that the liquid (ink) in the pipeline is flowing by the pressure loss Pμ in the pipeline, and the theoretical value of the flow rate (Q) flowing through the circular pipeline (each cell 22a) as shown in FIG. That is, the theoretical value of the flow rate of the ink flowing per pipe is calculated as the flow rate Qi (m³/ S), the flow rate Qi (m³/ S) is the following general formula (5)
Qi = Pu · π · d⁴/ (128 μL) (5)
Defined by Here, Pu is a pressure drop (Pa) of the pipe due to the viscous resistance of the ink, a stable 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 path length (m) of the road.
[0122]
Here, assuming that d (m) is the cell diameter at the time of compression, from the mounting cell density M (cells / 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 determined by the following relational expression (3).
d = 1 / (N · R) (3)
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 the most dense state as shown in FIG. It is considered to be. Therefore, the cells 22a at the lower end of the foam material at the time of compression are considered to be in the closest 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 at the time of compression, is expressed by the following relational expression (6).
Nd = (2 / √3) · S / (d²・ ・ ・ ・ ・ ・ (6)
Is represented by In the 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, assuming a columnar 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 the ink flowing through the columnar flow path is considered.³/ S) (Qt = Qi · Nd; theoretical value) is obtained from the following relational expression (7) from the general expression (5) and the relational expressions (3) and (6).

(However, in the formula, coefficient A = 2.83 × 10^-2Represents)
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 (cells / m) (M = N · R) of the ink absorber 22 (foam material) during compression.
[0125]
Table 2 shows the result of calculating the total flow rate Qt, which is a theoretical value, assuming the cylindrical flow path shown in FIG.
[0126]
[Table 2]

[0127]
Inside the actual ink absorber 22 (inside the foam material), spherical or polyhedral cells 22a communicate in a rosary as shown in FIG. For this reason, the effective diameter becomes smaller than the above theoretical value by the cascading 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 (actually 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 a spherical flow path whose diameter is dm and the center position is X = 0 is Rd, and the normalized flow path resistance of the cylindrical flow path is Rd. FIG. 16 shows the resistance ratio Rd / Rm where is Rm. As shown in FIG. 16, when X is near 0, rd / Rm ≒ 1, but it can be seen that Rd / Rm increases as X approaches dm / 2 (see FIG. 15). Considering the correction coefficient k = 13.75 from this study, when the normalized cell diameter is 1, Rd / Rm = 13.75 at the position of X = 0.488. This means that the flow path can be modeled such that the adjacent cells 22a communicate with each other with a normalized diameter of 0.21, and from this study, the value of the correction coefficient k determined from the actually measured value is appropriate. It can be said.
[0129]
Accordingly, the calculated flow rate Qc (m³/ S) is expressed by the following relational expression (8):
Qc = Qt / k (8)
(However, in the equation, the coefficient k represents 13.75.)
Alternatively, by substituting the relational expression (7) into the relational expression (8), the following relational expression (9) is obtained.
Qc = (A / k) · Pu · S / [μ · L · (N · R)²] ... (9)
(Where, coefficient (A / k) = 2.06 × 10^-3Represents)
Can be obtained as
[0130]
Here, from Table 2, Q / Qc is approximately 1 in each data, and therefore, by using the correction coefficient k,
Q = (A / k) · Pu · S · / [μ · L · (N · R)²]
Thus, it can be understood that the flow rate Q can be accurately obtained.
[0131]
The theoretical value Pv (Pa) of the pressure loss (pressure difference ΔP) of the pipe due to the viscous resistance is calculated from the actually measured flow rate Q as follows:
Pv = (1 / A) · [μ · L · (N · R)²/ S] ・ Q
(However, in the formula, coefficient A = 2.83 × 10^-2Represents)
Is represented by
[0132]
Further, the pressure loss (pressure difference ΔP) of the pipe due to the viscous resistance, that is, the pressure of the pipe due to the viscous resistance, using the correction coefficient k = 13.75 as in the relational expressions (8) and (9). Assuming that the calculated value of the loss (pressure difference ΔP) is Pμ (calculated pressure difference), the Pμ (Pa) is
Pμ = kPv
= (K / A) · [μ · L · (N · R)²/ S] · Q (10)
(Where, (k / A) = 485 is represented)
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 pipeline from the actually measured flow rate Q using the relational expression (10). In Table 3, the flow rate q indicates an actually measured flow rate per pipe.
[0134]
[Table 3]

[0135]
Here, when the ratio of the calculated value Pμ (calculated pressure difference) of the pressure loss (pressure difference ΔP) of the pipeline to the stable negative pressure Pu at the time of the ink upper limit is Pμ / Pu, it is approximately 1.
[0136]
FIG. 17 is a graph showing Tables 2 and 3. As shown in FIG. 17, the stable negative pressure based on the calculated value (calculated pressure difference Pμ) from the theoretical value is in good agreement with the actually measured stable negative pressure (stable negative pressure Pu at the ink upper limit). . Further, it is understood that the stable negative pressure Pu at the time of ink upper limit can be accurately obtained by using the correction coefficient because the stable negative pressure Pu at the time of ink upper limit is caused by the pressure loss based on the viscosity of the ink.
[0137]
Next, the relationship between the stable negative pressure when the ink in the ink cartridge 20 is filled up to the lower limit (the stable negative pressure PL at the lower limit of the ink) and the compression ratio R will be discussed 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]
Therefore, as shown in FIG. 18 (when a positive pressure is applied to the liquid) and FIG. 19 (when a 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 considered as capillaries.
[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 Pt by the ink absorber 22 at the time of ink emptying._E(= Pt) is represented by 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). Since the ink absorber 22 is selected to have good wettability with ink, θ can be regarded as substantially zero. Therefore, the above general formula (11) is converted into the following general formula (12)
Pt = 4 · η / d (12)
(Strictly speaking, Pt ≒ 4 · η / d).
[0141]
Therefore, from the relational expression (3) and the general expression (12), the critical pressure P by the ink absorber 22 is obtained._E(= Pt) is expressed by the above-mentioned relational expression (4).
P_E= 4 · η · (N · R) (4)
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 the relational expression (4).
[0143]
[Table 4]

[0144]
The ratio Px / PL of the theoretical critical pressure Px obtained from the above relational expression (4) to the actual negative pressure stable negative pressure PL at the lower limit of the ink is substantially 1, so that the stable negative pressure PL at the lower limit of the ink is It is shown that the theory is based on the critical pressure of the capillary based on the surface tension of the ink, and that the stable negative pressure PL at the time of the ink lower limit can be accurately obtained.
[0145]
Conditions for preventing the problem of inadvertent leakage of ink when attaching / detaching the ink cartridge 20 include the holding force of the ink absorber 22 (foam material), that is, forming a meniscus of ink with a liquid having a surface tension η. A cell at the lower end of the ink absorber 22 (foam material) which is a critical pressure in the cell 22a of the ink absorber 22 (foam material) whose size (cell diameter) at the time of compression is 1 / (N · R). Critical pressure P of liquid surface (ink meniscus) in 22a (capillary tube)_E(Pa) is required to be larger than the head pressure of the ink.
[0146]
Therefore, in the ink cartridge 20, assuming that the specific gravity of the ink is γ, and the maximum water head height of the ink in the vertical direction with respect to the ink supply port 24 of the ink tank 21 that can be taken in any posture is h (m), Head pressure is 9.8 × 10³· Since 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 × 10³・ Γ ・ h
Must be satisfied. That is, in order to prevent a problem that ink is inadvertently leaked when the ink cartridge 20 is attached or detached, the following relational expression (13) is used.
η · N · R · B> γ · h (13)
(However, in the equation, coefficient B = 4.08 × 10^-4Represents)
It is necessary to satisfy
[0147]
The cell density of the ink absorber 22 (foam material) in the state of being housed in the ink cartridge 20, that is, the mounting cell density M (cells / m) (M = NR) is, for example, the cell density N = 1575. The ink absorber 22 (foam material) obtained by compressing (ink / m) (= 40 ink / inch) at a compression ratio R = 5 is stored in the ink cartridge 20 to form the ink absorber 22 (foam). Material) undergoes an additional 10% compression,
M = 1575 × 5.5 × 1.1 = 9528 (pieces / m) (= 242 pieces / inch)
Substituting the mounting cell density M (pieces / m) into the above relational expression (13), the following relational expression (14) is obtained.
η ・ MB ・ γ ＞ h (14)
(However, in the equation, coefficient B = 4.08 × 10^-4Represents)
Becomes Note that an actual measurement value may be used as the mounting cell density M.
[0148]
The head height h (m) of the ink with respect to the ink supply port 24, that is, the head height h (m) of the ink having 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 any posture, In a normal posture, the height may be the height of the ink absorber 22 (foam material) or the inner wall of the ink cartridge 20.
[0149]
When handling needs to be considered, the head height of the ink 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 inclined is set to the head height.
[0150]
In consideration of the distribution of cell diameters and the like, it is preferable that the safety factor be about twice or more. Therefore, the following relational expression (15)
η · N · R · B> 2 · γ · h (15)
(However, in the equation, coefficient B = 4.08 × 10^-4Represents)
Or, the following relational expression (16)
η ・ M ・ B> 2 ・ γ ・ h (16)
(However, in the equation, coefficient B = 4.08 × 10^-4Represents)
It is desirable to design the ink cartridge 20 so as to satisfy the following.
[0151]
In general, the height of an ink cartridge is generally 40 mm or less, as described above, in consideration of fluctuations in the ink level. Therefore, assuming that 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.₂O) is preferably satisfied. Therefore, the 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) is obtained.
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]
In addition, from FIG. 17, the negative pressure based on the theoretical value (theoretical value critical pressure Px) obtained from the above relational expression (4) is in good agreement with the actually measured negative pressure (the stable negative pressure PL at the lower limit of the ink). You can see 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 retreat of the orifice due to ejection of ink 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 as follows: the diameter of the discharge nozzle of the circular tube is 20 μm, the length is 20 μm, the apex angle is 90 degrees, the apex diameter is Assume that a 20 μm frustoconical shape extends.
[0156]
When the ink ejection frequency of the ejection nozzles 1a in the print head 1 is set to 8000 pps and the number of nozzles is set to 64, the ink flow rate Q is 8.17 nm.³/ S (= 0.49 cc / min), one drop of ink
(8.17 × 10^-9) /8000/64=1.6×10^-14(M³) (= 16pL)
Becomes
[0157]
Table 5 shows the diameter H of the conical portion at the liquid surface (ink meniscus) position due to the receding of the ink in the orifice when one drop of ink is ejected in this case. In Table 5, the diameter H of the conical portion is 20 μm when the straight portion at the tip of the nozzle is sufficiently long by excimer laser processing or the like (see FIG. 20). Table 5 shows that one drop of ink is 1.6 × 10^-14(M³) (= 16 pL) when the transient vibration of the meniscus of the ink at the nozzle tip is not taken into consideration 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 retreats twice as much as the ink ejection amount. FIGS. 21A to 21H are cross-sectional views sequentially showing a 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(M³) (= 16 to 20 pL).
[0158]
The critical pressure Pn (Pa) of the nozzle (the discharge nozzle 1a in the present embodiment) is calculated by substituting the diameter H (m) of the conical portion into the general formula (12) and using the following general formula (19)
Pn = 4 · η / H (19)
(Strictly speaking, Pn ≒ 4 · η / H)
Can be obtained by
[0159]
An essential condition that does not cause the ink supply shortage is (Pμ) <(Pn), and the diameter of the ejection nozzle 1a is D_NAssuming that (m), in order to prevent the ink supply shortage from occurring, from the relational expression (10) and the general expression (19), the following relational expression (20)
(K / A) · [μ · L · (N · R)²/ S] · Q <4 · η / D_N  ... (20)
(However, in the equation, coefficient (k / A) = 485 is represented)
Must be satisfied. That is, if the above relational expression (20) is arranged, the following relational expression (21) is obtained.
C ・ [μ ・ L ・ Q ・ (N ・ R)²/ S] <η / D_N              ... (21)
(Where C = (k / A) / 4 = 121 in the formula)
Must be satisfied.
[0160]
When the mounting cell density M (pieces / m) (M = N · R) conforms to the above relational expression (21), the above essential condition is as follows:
C ・ [μ ・ L ・ Q ・ M²/ S] <η / D_N                    ... (22)
(Where C = (k / A) / 4 = 121 in the formula)
Becomes
[0161]
Table 5 shows the critical pressure Pn of the discharge nozzle 1a under each setting condition, calculated using the general formula (19).
[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 critical pressure Pn for sucking ink generated by the meniscus of the ink in a state where the meniscus of the ink at the nozzle tip is retracted after the ink discharge becomes larger than the negative pressure of the ink supply system. It can be seen that even when the operation is performed, a 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, ink supply becomes insufficient due to the negative pressure generated in the ink supply system, and the ink liquid surface (ink meniscus) retreats too far from the nozzle tip. It is possible to prevent the problem of inhaling air from occurring, and it is possible to supply ink stably even when ink is continuously ejected.
[0165]
If the negative pressure generated in the ink supply system is 2.0 kPa or less, ink is sucked by the surface tension of the meniscus by overcoming the negative pressure generated in the ink supply system, the meniscus advances, and ink is supplied. The ink supply ends when the negative pressure of the supply system and the meniscus suction force are balanced. Conversely, if the negative pressure generated in the ink supply system is larger than the critical pressure of the meniscus, the meniscus retreats, sucks air into the print head 1, and causes ejection failure.
[0166]
Considering the efficiency τ (tank efficiency), which is the ratio of the volume of ink used for ejection to the volume of ink filled in the ink cartridge 20, the upper limit of the mounting cell density M is 12.6 × 10³(Pcs / m) (= 320 / inch), which is the critical pressure of the ink, that is, the critical pressure P of the liquid level of the ink absorber 22 based on the surface tension η of the ink._EFrom Table 1, the stable negative pressure PL (Pa) at the lower limit of the ink is 1.5 kPa at the cell density from Table 1, and the head of the print head 1a and the head of the ink tank 21 are usually set to about 40 mm. Therefore, the sum of both (P_EA value of about 2.0 kPa is derived from + Pi).
[0167]
Summarizing the above examination results, the conditions required for the cell density N and the compression ratio 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 equation, coefficient B = 4.08 × 10^-4Represents)
Is obtained. Also, from the relational expression (21),
[Η · S / (C · D_N・ Μ ・ L ・ Q)]^0.5> (N · R) (24)
(However, in the formula, the 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 obtained from the above relational expressions (23) and (24).
[Η · S / (C · D_N・ Μ ・ L ・ Q)]^0.5> (N · R)> γ · h / (η · B) (25)
(However, in the equation, coefficient B = 4.08 × 10^-4, Coefficient C = 121)
Becomes
[0168]
The condition required for the mounting cell density M (M = N · R) (pieces / m) of the mounting state of the ink absorber 22 (foam material) is the same as that described above in the relational expression (14).・ From (22)
[Η · S / (C · D_N・ Μ ・ L ・ Q)]^0.5> M> γ · h / (η · B) (26)
(However, in the equation, coefficient B = 4.08 × 10^-4, Coefficient C = 121)
Becomes Therefore, by satisfying the relational expression (25) or (26), it is possible to prevent ink leakage when the ink cartridge 20 is attached and 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 x 10³~ 3.94 × 10³(Pcs / m) (= 40-100pcs / inch)
Is common.
[0170]
Therefore, for example, as different conditions, the following conditions
・ Viscosity μ = 0.015 (Pa · s)
・ Ink surface tension η = 0.04 (N / m)
・ Cell density N of foam material = 3.15 × 10³(Pcs / m) (= 80 / inch)
As a result, 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 even when the filter is used, when the opening of the filter is larger than the cell 22a of the ink absorber 22 (foam material), the inside of the cell 22a (capillary tube) of the ink absorber 22 is changed. Pressure P of the liquid surface (meniscus of ink)_E(Pa), that is, the critical pressure P of the ink absorber 22 when the ink is empty._EIn (Pa), the negative pressure generated in the ink supply system is determined.
[0172]
However, when the opening of the filter is made smaller than the cell 22a of the ink absorber 22 in order to secure the filtering performance of the filter, or when the ink absorber 22 (foam material) is not used, the critical pressure Pm ( Pa), the negative pressure (critical pressure of the ink absorber 22 or the filter) generated in the ink supply system is determined.
[0173]
For this reason, if the opening of the filter is made smaller than the cell 22a of the ink absorber 22, in order to reduce the negative pressure generated in the ink supply system to 2.0 kPa or less, the following relational expression (27) is used.
Pm ≦ 2000 (Pa) (27)
Needs to be satisfied.
[0174]
Further, as shown in the general formula (1) and the experimental formula (2), the critical pressure Pm (Pa) of the filter is determined by the surface tension η (N / m) of the ink and the size of the filter opening, that is, , And the filtering accuracy F (m) of the filter. Therefore, in order to satisfy Pm ≦ 2000 (Pa), from the general formula (1) and the empirical formula (2), if the filtering accuracy of the filter is F (m), the following relational expression (28) is obtained.
Pm = 4 · η / F ′ (28)
(However, when the opening of the filter is circular, F ′ = F,
In other cases, F '= √2 · F)
Needs to be satisfied.
[0175]
Therefore, from the above-mentioned relational expressions (27) and (28), the following relational expression (29) is partially added to 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, by providing a filter that satisfies the relational expression (27), the negative pressure generated in the ink supply system, that is, in this case, the negative pressure (critical pressure Pm by the filter) generated by the filter during ink supply is reduced. The suction pressure generated at the discharge nozzle 1a of the print head 1 (the critical pressure Pn of the nozzle) can be less than (Pn> Pm).
[0176]
Therefore, by providing the above-described filter in the ink supply path 3, it is possible to overcome the negative pressure generated in the ink supply system, overcome the surface tension of the meniscus formed in the opening of the filter, and suck the ink, and The meniscus recedes, and as a result, ink can be stably supplied (supplied) without air entering from the nozzle tip of the print head. In this case as well, the ink replenishment ends when the negative pressure of the ink supply system and the meniscus suction force are balanced as described above. Conversely, if the critical pressure due to the meniscus at the tip of the nozzle is lower than or equal to the critical pressure of the meniscus formed at the opening of the filter (that is, Pn ≦ Pm), and especially smaller than the critical pressure (Pm), The meniscus retreats, air is sucked into the print head 1, and ejection failure occurs.
[0177]
That is, when the ink is supplied to the print head 1, the pressure required when the print head 1 sucks the ink, that is, the pressure (ink suction pressure) due to the meniscus of the discharge nozzle 1 a of the print head 1 depends on the ink supply path. It takes 3 (filter). The ink suction pressure, that is, the critical pressure Pn of the discharge nozzle 1a is equal to or less than the negative pressure generated by the filter at the time of ink supply, that is, the critical pressure Pm (filter pressure) of the ink negative pressure due to the meniscus at the opening of the filter. In particular, when the pressure is lower than the critical pressure Pm (filter pressure), air breaks in from the nozzle tip of the print head 1 before breaking the meniscus formed in the opening of the filter.
[0178]
Therefore, the pressure due to the meniscus of the discharge nozzle 1a when supplying ink to the print head 1, that is, the ink suction pressure (the critical pressure Pn of the discharge nozzle 1a) is set to a value larger than the filter pressure (the critical pressure Pm of the filter). If the setting is made such that, the above problem can be suppressed.
[0179]
Therefore, the image forming apparatus, more specifically, the factor of the negative pressure is set so that the negative pressure generated by the filter during ink supply is smaller than the ink suction pressure by the discharge nozzle 1a of the print head 1. By configuring (designing) a filter under various conditions, in particular, the above-described problem can be suppressed.
[0180]
In other words, in order to satisfy the above-described configuration, for example, a part (end) of the ink supply path 3 on the side of the ink tank 21, in the ink supply path 3, is negatively generated by the filter during ink supply. A filter in which the pressure is smaller than the ink suction pressure by the discharge nozzle 1a of the print head 1, specifically, a filter that satisfies the relational expressions (29) and (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 following condition be provided.
[0181]
The maximum surface tension of the liquid is 0.072 N / m of water, so that the discharge energy related to the surface tension η (N / m) of the ink can be reduced, and air can be sucked and discharged from the nozzle tip of the discharge nozzle 1 a. The surface tension η (N / m) of the ink is 0.03 in order to prevent ejection failure due to ink wetting or ink leakage around the nozzle 1a and image quality deterioration due to ink bleeding on the paper surface. It is necessary to set within the range of 0.06, and generally, it is set within the range of 0.03 to 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 42 × 10^-6(M) or more, that is, a filter of 42 μm or more, preferably, a margin for fluctuation of surface tension, filtration accuracy F and the like is about 20%, F ≧ 50 × 10^-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 reduced to 2000 Pa or less. This means that, for example, in FIG. 9, the filtration accuracy F is 50 μm, that is, 50 × 10^-6In the case of (m), it can also be confirmed from the fact 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 filtering accuracy F (m) is 60 × 10^-6(M) or more, that is, a filter having a size of 60 μm or more, preferably a margin of about 20% for fluctuations in surface tension, filtration accuracy F, etc., is F ≧ 70 × 10^-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 reduced 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 where the negative pressure applied to the ink supply path 3 during ink supply is 2.0 kPa or less. Filter 23 is provided.
[0185]
For this reason, the ink suction pressure (pressure required for ink supply) generated by the print head 1 ejecting ink droplets, that is, the pressure applied to the ink absorber 22 (ink supply pressure), Regardless, the ink supply pressure becomes smaller than the filter pressure applied to the opening 23a (mesh) of the filter 23.
[0186]
Therefore, according to the ink jet recording apparatus, it is possible to prevent air from entering the ink supply path 3 until the meniscus of the ink formed in the opening 23a (mesh) of the filter 23 is broken. Even when the meniscus is torn, 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 too much and to mix air from the nozzle tip.
[0187]
Further, when the air bubbles mixed into the ink tank 21 at the time of ink filling are captured 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 In the state immediately before (near), when a part of the ink absorber 22 is in contact with the filter 23 in an empty state, the ink absorber 22 is inflated without sucking the air (bubbles) in contact with the filter 23. The condition for effectively supplying the held ink to the print head 1, that is, the condition for not 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 cells 22a at the lower end of the ink absorber 22 (foam material) can be regarded as capillaries. Critical pressure P by 22_E(Pa), that is, the critical pressure P of the liquid surface (ink meniscus) in the cell 22a_E(Pa) is given by the relational expression (4).
[0189]
On the other hand, the critical pressure Pm of the filter 23 when the filter 23 having the filtration accuracy F (m) is used is given by the empirical formula (2). The above condition, that is, the condition under which air is not inadvertently sucked from the ink tank 21 into the ink supply port 3a, is obtained from the empirical formula (2) and the relational expression (4) from the following relational expression (31)
(4 · η) / (√2 · F)> 4 · η · (N · R) (31)
Is represented by
[0190]
Therefore, when the above relational expression (31) is arranged for the filtering accuracy F, the following relational expression (32) is obtained.
√2 · F <1 / (N · R) (32)
Is obtained.
[0191]
Further, from the general formula (1), the critical pressure Pm ′ by a filter having a circular opening can be calculated by using the surface tension η (N / m) of the ink and the filtration accuracy F (m) as follows. Equation (33)
Pm ′ = 4 · η / F (33)
Is represented by
[0192]
Therefore, when a filter having a filtration accuracy of F (m) having a circular opening is used, the condition under which air is not inadvertently sucked from the ink tank 21 into the ink supply port 3a is the same as that when the filter 23 is used. From the relational expression (4) and the general formula (33), the following relational expression (34)
F <1 / (NR) (34)
Given by
[0193]
Therefore, when a filter having a filtration accuracy of 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 set to N (cells / m), and the ink absorber 22 is stored in the ink tank 21. Assuming that a compression ratio represented by a volume ratio of the ink absorber 22 when compressed and stored in the ink tank 21 before being stored is R, the following relational expression (35):
F '<1 / (NR) (35)
(However, when the opening of the filter is circular, F ′ = F,
In other cases, F '= √2 · F)
By designing the ink cartridge 20 so as to satisfy the following condition, the ink supply pressure can be adjusted to be smaller than the negative pressure applied to the filter 23, and the air is supplied to the ink meniscus formed in the opening 23 a of the filter 23. Can be prevented from being mixed into the ink supply path 3. For this reason, according to the above-described configuration, it is possible to prevent air from entering the ink supply path 3 due to factors other than a decrease in the remaining amount of ink, to prevent a malfunction in detecting the remaining amount of ink, and to improve the reliability of the quality. Printing with high quality.
[0194]
Note that the above conditions can be managed by using the cell diameter instead of the filtration accuracy F (m). However, as described above, the negative pressure at the time of ink supply (at the time of emptying) is controlled not by a cell diameter having a large variation but by a filtration accuracy F (m) having a small variation, that is, a shortest length of an opening (minimum gap width). By doing so, a stable negative pressure can be obtained.
[0195]
In the above-described embodiment, the cell density of the ink tank 21, that is, the ink absorber (ink absorber 22) before being stored in the ink storage unit is set to N (cells / m) and stored in the ink storage unit. Although the compression ratio indicated by the volume ratio of the ink absorber when compressed and stored in the ink storage unit before the storage is described as R, the ink absorber is stored in the ink storage unit when And may be stored after being compressed in advance.
[0196]
As the ink absorber, for example, a compressed foam material widely used for an ink absorber, such as a compressed sponge, which is heated and pressed in a compressed state and subjected to permanent compression can be used. In this case, the cell density N (cells / m) and the compression ratio R are the cell density (cells / m) of the ink absorber before compression processing and after compression processing before compression processing, that is, after compression processing. A compression ratio (compression ratio) indicated by the volume ratio of the ink absorber when the foam material is inserted into the ink tank as the ink absorber can be used.
[0197]
Therefore, assuming that the cell density of the ink absorber before compression processing is N ′ (cells / m), and the compression ratio (compression ratio) indicated by the volume ratio of the ink absorber after compression processing before compression processing is R ′. , Each of the above equations can be represented as N = N ′, R = R ′.
[0198]
For example, the relational expression (35) indicates that the filtering accuracy of the filter is F (m), the cell density of the ink absorber before compression is N ′ (cells / m), and the ink after compression with respect to the ink before compression. Assuming that 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)
Is represented by Note that each of the above-described equations or each of the following equations can be similarly represented as N = N ′ and R = R ′. Of course, it is needless to say that the mounting cell density M can be used instead of NR or N'R '.
[0199]
Further, the diameter of the discharge nozzle 1a is D_NAssuming that (m), from the relational expression (19), the critical pressure Pn (Pa) of the meniscus of the discharge nozzle 1a is represented by the following general formula (37)
Pn = 4 · η / D_N                                      ... (37)
Is represented by
[0200]
Here, the condition that air is not sucked in 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 more effectively prevent malfunction in detecting the remaining amount of ink, the following conditions must be satisfied.
Pn> Pm> P_E
That is, from the relational expression (31) and the general expression (37), the following relational expression (38) is satisfied.
(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 the following.
[0201]
Therefore, when the above relational expression (38) is rearranged for the filtering accuracy F ′ (m), the following relational expression (39) is obtained.
D_N<F '<1 / (NR) (39)
(However, when the opening of the filter is circular, F ′ = F,
In other cases, F '= √2 · F)
Is obtained.
[0202]
Next, the effect of the ink level that changes with the consumption of ink will be considered. As shown in FIG. 3, when the head water pressure due to the head h between the ink supply port 24 and the tip (nozzle tip) of the ejection nozzle 1a is Ph, the effective holding force Pn ′ (Pa) of the meniscus of the ink at the ejection nozzle 1a is The following general formula (40)
Pn '= Pn- | Ph | (40)
Is defined by | Ph | indicates the absolute value of Ph. That is, || indicates an absolute symbol, and | x | indicates the absolute value of x.
[0203]
At this time, the condition that the meniscus of the ink retreats too far from the nozzle tip and does not suck the air is the condition when the ink tank 21 is fully filled with the ink, by the following relational expression (41).
Pn ′> | Pμ | − | Pi | (41)
Is satisfied, and at the time of ink empty, the following relational expression (42) is satisfied.
Pn '> Pm (42)
It is to satisfy.
[0204]
The condition that air is not sucked in from the nozzle tip when the head water pressure Ph (ink head) is not taken into account is Pn> Pm. However, by taking the head water pressure Ph into consideration, the condition becomes more practical. That is, the head head pressure Ph is set so that a negative static pressure for preventing ink leakage from the nozzle tip is generated, and the ink jet recording apparatus is closer to the nozzle tip than when the head head pressure Ph is not considered. Used in conditions where air is easily sucked. For this reason, by considering the head hydraulic pressure Ph, it is possible to make the conditions more suitable for actual use.
[0205]
Here, when the filter 23 is designed to prevent foreign matter from entering as described above, usually,
Pm> | Pμ | + | Pi | (43)
From the above relational expressions (42) and (43), the following relation
Pn ′> Pm> | Pμ | + | Pi | (44)
Is led.
[0206]
Therefore, from the above relational expressions (41) and (44), the following relation
Pn ′> Pm> | Pμ | + | Pi |> | Pμ | − | Pi |
Is satisfied, the above relational expression (44) is satisfied, that is, the diameter of the discharge nozzle 1a is_N(M), the following relational expression (45) is obtained from the empirical expression (2) and the general expression (37).
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)
Is satisfied, it is possible to appropriately manage the pressure leaking from the filter 23 at the time of supplying the ink, particularly at the time of supplying the ink immediately before the empty of the ink, without exceeding the critical pressure Pn of the discharge nozzle 1a of the print head 1. It is possible to prevent air from being sucked in, and to effectively filter foreign substances heading toward the ink supply path 3, thereby improving the reliability of the discharge operation by the discharge nozzle 1a. In each of the above expressions, for example, in the above-mentioned relational expressions (41) and (43) to (45), Pμ is given by the above-mentioned relational expression (10).
[0207]
Next, the present inventors have studied the relationship between the viscosity and temperature of various substances, and the results will be described.
[0208]
First, Table 6 below shows the relationship between the temperature T (° C.) and the 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 a correlation between the temperature T (° C.) and the viscosity μ (Pa · s).
[0211]
Table 7 below shows the viscosity μ at 25 ° C. for each of the above substances.₂₅(Pa · s) to viscosity μT (Pa · s) at each temperature T (° C.), that is, viscosity μ at 25 ° C.₂₅ΜT / μ at each temperature T (° C) where₂₅(Normalized viscosity).
[0212]
[Table 7]

[0213]
Temperature T (° C.) created based on the data in Table 7 above, and viscosity μT / μ at each temperature T (° C.)₂₅(Normalized viscosity) is shown in FIG. From FIG. 23, the temperature T (° C.) and the viscosity μ / μ₂₅It is difficult to find a correlation with (normalized viscosity).
[0214]
By the way, in general, any temperature T_KViscosity μ of liquid of (K)_TK(Pa · s) is represented by the following general formula (42)
μ_TK= Αexp (β / T_K) (46)
And is represented by the Andrade equation shown below.
[0215]
Using this Andrade equation, T₂₅(K) The viscosity of the liquid at (= 25 ° C.)₂₅(Pa · s), temperature T_KThe viscosity of the liquid in (K) is μ_TK(Pa · s), the following general formula (43)

Is derived. Therefore, from the above 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]
Then, based on the data shown in Table 7, the viscosity μ₂₅And viscosity μ / μ₂₅(Normalized viscosity), where μ₀/ Μ₂₅, Μ₅₀/ Μ₂₅, Μ₇₅/ Μ₂₅The correlation with was examined. The result is shown in FIG.
[0217]
From the plot data shown in FIG.₀/ Μ₂₅Focusing on
μ₀/ Μ₂₅= 0.42 · Ln (μ₂₅) +4.71 (49)
Can be obtained.
[0218]
Therefore, since 25 (° C.) is 298 (K) in absolute temperature, the above general formula (48)
From the above approximate expression (49), the following relational expression (50)
β = Ln [0.42 · Ln (μ₂₅) +4.71] / (1 / 273-1 / 298) (50)
Is obtained.
[0219]
From the Andrade equation shown in the general formula (46), the viscosity μ of the liquid at 25 ° C.₂₅(Pa · s) is
μ₂₅= Αexp (β / 298)
By this, the following general formula (51)
α = μ₂₅/ 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_TK= Αexp (β / T_K)
(Where α = μ₂₅/ Exp (β / 298),
β = Ln [0.42 · Ln (μ₂₅) +4.71] / (1 / 273-1 / 298)
(52)
Μ using_TKThe approximate viscosity μ ′ (Pa · s) represented by (Pa · s) is shown in Table 8 below.
[0221]
[Table 8]

[0222]
Further, the approximate viscosity μ ′ (Pa · s) obtained by the above-described approximate expression (52) obtained by the general formulas (46) and (51) and the relational expression (50), and the actual viscosity μ (Pa · s) 25) are 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 viscosity μ ′ (Pa · s) and the actual viscosity μ (Pa · s), that is, the actually measured value. It was confirmed that the accuracy was good.
[0224]
Further, the above approximation formula (52) is converted to eight kinds of inks (inks 1 to 8) and water (H₂Temperature T (° C.) and viscosity μ (Pa · s), μ / μ when applied to O)₂₅, Μ ′ / μ (approximate formula viscosity / measured value) are shown in Table 9.
[0225]
[Table 9]

[0226]
FIG. 26 shows 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 the viscosity μ of each ink and water at 25 ° C.₂₅And normalized viscosity μ / μ₂₅3 shows the relationship between the measured value and the approximate value. In FIG. 26, the solid line indicates the approximate viscosity μ ′ (Pa · s), and each identification mark indicates the actually measured value, that is, the actual viscosity μ (Pa · s). In FIG. 27, the broken line indicates the normalized approximate viscosity μ ′.₅/ Μ₂₅, And μ '₄₀/ Μ₂₅Indicates the normalized viscosity μ / μ at 5 ° C.₂₅(Ie, μ₅/ Μ₂₅), “△” indicates normalized viscosity μ / μ at 40 ° C.₂₅(Ie, μ₄₀/ Μ₂₅), Each identification mark indicates an actually measured value, that is, an actual viscosity μ (Pa · s).
[0227]
From the results shown in FIG. 26, even when the above-described approximate expression (48) is applied to the ink used in the ink cartridge 20, the approximate viscosity μ ′ (Pa · s) and the actual viscosity μ (Pa · s) It turned out that there was not much difference between the two.
[0228]
From the above examination results, the arbitrary temperature T_KThe viscosity μ (Pa · s) of the ink in (K) can be calculated as μ = μ ′, and if the approximate expression (48) is used, an arbitrary temperature T_KIt was confirmed that the viscosity μ (Pa · s) of the ink in (K) can be accurately calculated.
[0229]
Therefore, based on the above experimental results, in the above-mentioned relational expression (10), the viscosity μ (Pa · s) of the ink is calculated by using the above-mentioned approximate expression (52)._TKIf the approximate expression viscosity μ ′ (Pa · s) represented by (Pa · s) is applied, the relational expression (10) becomes 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 empirical expression (2), the filtering accuracy of the filter is F (m), and when the ink tank 21 is fully filled with ink. The ink head pressure of the ink tank 21 generated when the ink is to be supplied to the print head 1 via the ink supply path 3 is Pi (Pa), and the pressure loss due to the viscous resistance of the ink in the ink tank 21 is Pμ (Pa). ), The surface tension of the ink is η (N / m), and 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 is N ′ (pieces / m), The compression ratio (compression ratio) indicated by the volume ratio of the ink absorber after the compression process is R ′, and the cross-sectional area of the ink absorber 22 when compressed and 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.₂₅(Pa · s), arbitrary temperature T_KThe viscosity at (K) is μ_TK(Pa · s), an arbitrary 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= Αexp (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)
Or
4 · η / F ′> | Pμ | + | Pi |
Pμ = (k / A) · [μ_TK・ L ・ (N ′ ・ R ′)²/ S] ・ Q
(However, coefficient (k / A) = 485)
μ_TK= Αexp (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)
By satisfying the above condition, 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, and the air reduces the ink meniscus formed in the mesh of the filter. It is possible to prevent breakage and mixing in the ink supply path 3. For this reason, according to the above-described configuration, it is possible to prevent air from entering the ink supply path 3 due to factors other than a decrease in the remaining amount of ink, to prevent a malfunction in detecting the remaining amount of ink, and to improve the reliability of the quality. Printing with high quality.
[0231]
Also, in the above configuration, it is also possible to manage using the cell diameter instead of the filtration accuracy F (m). However, the negative pressure at the time of supplying the ink (at the time of emptying) is not controlled by the cell diameter having large variation, A stable negative pressure can be obtained by controlling the filtration accuracy F (m) with small variation, that is, the shortest length of the opening (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 the ink empty, exceeds the critical pressure Pn of the discharge nozzle 1a of the print head 1. This can prevent the air from being sucked in from the discharge nozzle 1a, and can effectively filter foreign matter toward the ink supply path 3, thereby improving 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 embodiment, and various changes can be made within the scope shown in the claims, and the technical means disclosed in each of the above-described embodiments can be appropriately combined. 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 unit that stores a porous ink storage body that holds ink, and an ink supply path that supplies ink from the ink storage unit to the print head. In the image forming apparatus, a filter is provided inside 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 unit is N (number / m). When a compression ratio represented by a volume ratio of the ink absorber when compressed and stored in the ink storage unit before being stored in the ink storage unit is R,
F '<1 / (NR)
(However, when the opening of the filter is circular, F ′ = F,
In other cases, F '= √2 · F)
It is a configuration that satisfies the following.
[0235]
When the ink is supplied to the print head, a pressure required for the print head to suck the ink, that is, a 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.
[0236]
Therefore, according to the above configuration, the critical value of the negative pressure generated in the ink absorber by the surface tension of the ink is determined by the negative pressure generated by the filter by 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) due to the meniscus in the portion (mesh), and the ink meniscus formed in the mesh of the filter is broken before the ink becomes empty, and the air is supplied to the ink. The ink is prevented from being mixed into the path, and the meniscus of the ink absorber retreats in accordance with 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 unit due to carriage vibration, atmospheric pressure, or a change in ambient temperature, 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 configuration, an image forming apparatus having a design guideline for an ink supply system is provided so that it is possible to prevent occurrence of a problem that air is mixed into the ink supply system before the ink is empty during continuous ejection of ink. Can be provided.
[0238]
Further, according to the above configuration, as described above, the negative pressure at the time of supplying the ink (at the time of emptying) can be controlled with the filtering accuracy F (m) having a small variation, and a stable negative pressure can be obtained. The effect is also achieved.
[0239]
As described above, in the image forming apparatus according to the present invention, the diameter of the nozzle (ink ejection nozzle) of the print head is set 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 a configuration that satisfies the following.
[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 set to be larger than the critical value of the pressure due to the ink meniscus at the opening of the filter. It can be adjusted to be smaller, and it is possible to prevent the air from being sucked in from the tip of the nozzle and the printing head from becoming defective in ejection.
[0241]
Further, according to the above configuration, it is possible to prevent the meniscus of the ink formed in the opening of the filter from being broken, and to prevent the air from being carelessly sucked into the ink supply path from the ink storage section. The retained ink can be more effectively supplied to the print head. Therefore, according to the above configuration, it is possible to further prevent air from entering the ink supply path due to factors other than a decrease in the remaining amount of ink, and to more effectively prevent malfunction in detecting the remaining amount of ink. It works. Therefore, according to the above configuration, an image forming apparatus having a design guideline for an ink supply system is provided so that it is possible to prevent occurrence of a problem that air is mixed into the ink supply system before the ink is empty during continuous ejection of ink. Can be provided.
[0242]
As described above, the image forming apparatus according to the present invention includes an ink storage unit that stores a porous ink storage body that holds ink, and an ink supply path that supplies ink from the ink storage unit to the print head. In the image forming apparatus provided with a filter, a filter is provided inside the ink supply path, the ink absorber is subjected to compression processing before being stored in the ink storage unit, and the filtering accuracy of the filter is F ( m), the cell density of the ink absorber before compression processing is N ′ (cells / m), and the compression ratio (compression rate) represented by the volume ratio of the ink absorber after compression processing 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 a configuration that satisfies the following.
[0243]
When the ink is supplied to the print head, a pressure required for the print head to suck the ink, that is, a 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.
[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 by the filter due to the surface tension of the ink, that is, by the meniscus of the opening (mesh) of the filter. The pressure (filter pressure) can be adjusted so as to be smaller than the critical value, and the ink meniscus formed in the mesh of the filter before the ink becomes empty breaks, causing air to enter the ink supply path. Is prevented, and the meniscus of the ink absorber recedes in accordance with the consumption of the ink, thereby enabling a stable ink supply operation. Furthermore, factors other than a decrease in the remaining amount of ink, such as bubbles generated in the ink in the ink storage unit due to carriage vibration, atmospheric pressure, or a change in ambient temperature, are captured by the filter to prevent air from entering the ink supply path. In addition, it is possible to perform printing with high reliability and to consume ink without waste. Therefore, according to the above configuration, an image forming apparatus having a design guideline for an ink supply system is provided so that it is possible to prevent occurrence of a problem that air is mixed into the ink supply system before the ink is empty during continuous ejection of ink. Can be provided.
[0245]
Further, according to the above configuration, as described above, the negative pressure at the time of supplying the ink (at the time of emptying) can be controlled with the filtering accuracy F (m) having a small variation, and a stable negative pressure can be obtained. The effect is also achieved.
[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 a configuration that satisfies the following.
[0247]
According to the configuration, it is possible to prevent suction of air from the nozzle tip of the print head, and to prevent careless suction of air from the ink storage unit into the ink supply path. 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 entering the ink supply path due to factors other than a decrease in the remaining amount of ink, and to more effectively prevent malfunction in detecting the remaining amount of ink. It works. Therefore, according to the above configuration, an image forming apparatus having a design guideline for an ink supply system is provided so that it is possible to prevent occurrence of a problem that air is mixed into the ink supply system before the ink is empty during continuous ejection of ink. Can be provided.
[0248]
As described above, the image forming apparatus according to the present invention includes an ink storage unit that stores a porous ink storage body that holds ink, and an ink supply path that supplies ink from the ink storage unit to the print head. In the image forming apparatus, a filter is provided inside the ink supply path, the filtering accuracy of the filter is set to F (m), and the ink is supplied through the ink supply path when the ink container is fully filled with ink. The head pressure of the ink storage unit that occurs when the ink is to be supplied to the print head is Pi (Pa), the pressure loss due to the viscous resistance of the ink in the ink storage unit is Pμ (Pa), and the surface tension of the ink is η ( N / m), the cell density of the ink absorber before being stored in the ink storage unit is N (cells / m), The compression ratio represented 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 unit is S (m²), The height of the ink absorber when compressed and stored in the ink storage unit is L (m), and the viscosity of the ink at 25 ° C. is μ.₂₅(Pa · s), arbitrary temperature T_KThe viscosity at (K) is μ_TK(Pa · s), an arbitrary 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= Αexp (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 a configuration that satisfies the following.
[0249]
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 meniscus of the ink at the opening of the filter. It is possible to prevent the meniscus of the ink formed in the portion from being broken and the 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, to prevent a malfunction in detecting the remaining amount of ink, and to improve the reliability of the quality. This produces an effect that high printing can be performed. Therefore, according to the above configuration, at the time of continuous ejection of ink, the design guideline of the ink supply system according to the characteristics of the ink can be prevented so that a problem such as air entering the ink supply system before the ink is empty can be prevented. An image forming apparatus having:
[0250]
Further, according to the above configuration, as described above, the maximum negative pressure at the time of supplying the ink (at the time of emptying) can be controlled with the small filtering accuracy F (m), and a stable negative pressure can be obtained. It has the effect of being able to do it.
[0251]
As described above, the image forming apparatus according to the present invention sets the diameter of the nozzle in the print head to D_N(M), when the 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 a configuration that satisfies the following.
[0252]
According to the above configuration, at the time of ink supply, the critical value of the pressure due to the meniscus at the opening of the filter can be appropriately managed without exceeding the critical value of the ink suction pressure due to the meniscus of the nozzle of the print head. In addition to preventing air from being sucked in, it is possible to effectively filter air and foreign substances heading toward the ink supply path, thereby improving the reliability of the ejection operation by the nozzles. Therefore, according to the above configuration, an image forming apparatus having a design guideline for an ink supply system is provided so that it is possible to prevent occurrence of a problem that air is mixed into the ink supply system before the ink is empty during continuous ejection of ink. Can be provided.
[0253]
As described above, the image forming apparatus according to the present invention includes an ink storage unit that stores a porous ink storage body that holds ink, and an ink supply path that supplies ink from the ink storage unit to the print head. In the image forming apparatus provided with a filter, a filter is provided inside the ink supply path, the ink absorber is subjected to compression processing before being stored in the ink storage unit, and the filtering accuracy of the filter is F ( m) The water head pressure of the ink storage unit, which is generated when the ink is to be supplied to the print head via the ink supply path when the ink storage unit is fully filled with ink, is Pi (Pa); The pressure loss due to the viscous resistance of the ink in the ink storage unit 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 (compression rate) indicated by the volume ratio of the ink absorber after compression processing before compression processing is R ′ of the ink absorber when compressed and stored in the ink storage unit. The cross-sectional area is S (m²), The height of the ink absorber when compressed and stored in the ink storage unit is L (m), and the viscosity of the ink at 25 ° C. is μ.₂₅(Pa · s), arbitrary temperature T_KThe viscosity at (K) is μ_TK(Pa · s), an arbitrary 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= Αexp (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 a configuration that satisfies the following.
[0254]
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 meniscus of the ink at the opening of the filter. It is possible to prevent the meniscus of the ink formed in the portion from being broken and the 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, to prevent a malfunction in detecting the remaining amount of ink, and to improve the reliability of the quality. This produces an effect that high printing can be performed. Therefore, according to the above configuration, at the time of continuous ejection of ink, the design guideline of the ink supply system according to the characteristics of the ink can be prevented so that a problem such as air entering the ink supply system before the ink is empty can be prevented. An image forming apparatus having:
[0255]
Further, according to the above configuration, as described above, the maximum negative pressure at the time of supplying the ink (at the time of emptying) can be controlled with the small filtering accuracy F (m), and a stable negative pressure can be obtained. It has the effect of being able to do it.
[0256]
As described above, the image forming apparatus according to the present invention sets the diameter of the nozzle in the print head to D_N(M), when the 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 a configuration that satisfies the following.
[0257]
According to the above configuration, at the time of ink supply, the critical value of the pressure due to the meniscus at the opening of the filter can be appropriately managed without exceeding the critical value of the ink suction pressure due to the meniscus of the nozzle of the print head. In addition to preventing air from being sucked in, it is possible to effectively filter air and foreign substances heading toward the ink supply path, thereby improving the reliability of the ejection operation by the nozzles. Therefore, according to the above configuration, an image forming apparatus having a design guideline for an ink supply system is provided so that it is possible to prevent occurrence of a problem that air is mixed into the ink supply system before the ink is empty during continuous ejection of ink. Can be provided.
[0258]
As described above, the image forming apparatus according to the present invention is configured to include the detector that detects the presence or absence of ink in the ink supply path.
[0259]
According to the configuration, it is possible to reliably detect the ink empty by detecting the presence or absence of the ink in the ink supply path. Therefore, according to the above configuration, an effect is obtained that it is possible to more reliably prevent air from being mixed into the ink supply path.
[Brief description of the drawings]
FIG. 1A is a cross-sectional view illustrating a configuration of a main part according to an embodiment of the present invention, and FIG. 1B is a cross-sectional view illustrating a state where an ink supply path is removed from an ink cartridge illustrated in FIG. It is a figure and (c) is sectional drawing which shows the structure of a detection electrode.
FIG. 2 is a perspective view showing the entire 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 measuring device used in a measurement experiment of a negative pressure applied to an ink supply path of the ink jet recording apparatus.
8 is a graph showing the relationship between the filtration accuracy of the filter actually measured using the measuring device 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 a relationship between mounting cell density and efficiency.
FIG. 12 is a schematic diagram showing a flow rate flowing through a circular pipe and a pressure difference between the pipes when each cell of the foam material of the ink cartridge is regarded as a circular pipe.
FIG. 13 is a configuration diagram showing cells that are closest packed.
FIG. 14 is a cross-sectional view showing a state in which cells on a spherical shape or a polyhedron communicate in a bead shape in an actual foam material in the ink cartridge.
FIG. 15 is an explanatory diagram showing how to determine the effective diameter when it is assumed that cells form a continuous flow path in an actual foam material.
FIG. 16 shows a normalized flow path resistance obtained by integrating a spherical flow path where the cell diameter is dm, the center position is X = 0, and Rd is a normalized flow path resistance of a cylindrical flow path. 6 is a graph showing a relationship between X, a resistance ratio Rd / Rm, and a cell diameter d at the time.
FIG. 17 is a graph showing a relationship between a compression ratio and a negative pressure.
FIG. 18 is a schematic view showing a critical pressure of a liquid surface (ink meniscus) in a capillary when a cell at a lower end of a 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 illustrating a critical pressure of a liquid surface (ink meniscus) in a capillary.
FIG. 20 is an enlarged cross-sectional view showing the configuration of the end of the supply port.
FIGS. 21A to 21H are cross-sectional views sequentially showing states in which ink is ejected from nozzles.
FIG. 22 is a graph showing a relationship between a temperature T (° C.) and a viscosity μ (Pa · s) prepared based on data in Table 6.
FIG. 23 shows temperature T (° C.) created based on the data in Table 7 and μT / μ at each temperature T (° C.)₂₅6 is a graph showing a relationship with the graph.
FIG. 24 shows μ, which is created based on the data shown in Table 7.₂₅And μ / μ₂₅6 is a graph showing a correlation with.
FIG. 25 is a graph showing the relationship between approximate viscosity μ ′ (Pa · s) and actual viscosity μ (Pa · s).
FIG. 26 is a graph showing a relationship between an approximate viscosity μ ′ (Pa · s) created based on data in Table 9 and an actual viscosity μ (Pa · s).
FIG. 27 shows μ of each ink and water at 25 ° C.₂₅And μ / μ₂₅6 is a graph showing a relationship with the graph.
[Explanation of symbols]
1 print head
3 Ink supply route
3a Ink supply path
4 Ink supply tube
10 Ink supply device
20 ink cartridge
21 Ink tank (ink storage section)
22 Ink absorber
23 Filter
24 Ink supply port
25 Detection electrode (detector)
31 Filter

Claims (9)

An image forming apparatus comprising: an ink storage section in which a porous ink storage body that holds ink is stored; and an ink supply path that supplies ink from the ink storage section to the print head.
A filter is provided inside the ink supply path,
The filtering accuracy of the filter is F (m), the cell density of the ink absorber before being stored in the ink storage unit is N (cells / m), and the filter is compressed into the ink storage unit before being stored in the ink storage unit. When the compression ratio indicated by the volume ratio of the ink absorber when stored and stored is R,
F '<1 / (NR)
(However, if the filter opening is circular, F '= F,
In other cases, F '= √2 · F)
An image forming apparatus characterized by satisfying the following. When the diameter of the nozzle of the print head is D _N (m),
_DN <F '<1 / (NR)
(However, if the filter opening is circular, F '= F,
In other cases, F '= √2 · F)
The image forming apparatus according to claim 1, wherein the following condition is satisfied. An image forming apparatus comprising: an ink storage section in which a porous ink storage body that holds ink is stored; and an ink supply path that supplies ink from the ink storage section to the print head.
A filter is provided inside the ink supply path,
The ink absorber is pre-compressed before being stored in the ink storage unit,
The filtering accuracy of the filter is F (m), the cell density of the ink absorber before compression is N '(cells / m), and the compression is expressed by the volume ratio of the ink absorber after compression to that before compression. When the ratio (compression ratio) is R ′,
F '<1 / (N'R')
(However, if the filter opening is circular, F '= F,
In other cases, F '= √2 · F)
An image forming apparatus characterized by satisfying the following. When the diameter of the nozzle of the print head is D _N (m),
_DN <F '<1 / (N'R')
The image forming apparatus according to claim 3, wherein the following is satisfied. An image forming apparatus comprising: an ink storage section in which a porous ink storage body that holds ink is stored; and an ink supply path that supplies ink from the ink storage section to the print head.
A filter is provided inside the ink supply path,
The filtering accuracy of the filter is F (m), and the water head of the ink storage portion which is generated when the ink is to be 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 unit is Pμ (Pa), the surface tension of the ink is η (N / m), and the ink absorber before being stored in the ink storage unit Is the cell density of N (cells / m), R is the compression ratio represented by the volume ratio of the ink absorber when compressed and stored in the ink storage section before storage in the ink storage section, and R The sectional area of the ink absorber when compressed and stored in the ink storage unit is S (m ² ), and the height of the ink absorber when compressed and stored in the ink storage unit is L (m). At 25 ° C The viscosity of the ink _μ 25 (Pa · s), the viscosity at any temperature _T K (K) and _μ TK (Pa · s), at any temperature _T K (K),
4 · η / F '> | Pμ | + | Pi |
Pμ = (k / A) · [μT _KL · (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 opening is circular, F '= F,
In other cases, F '= √2 · F)
An image forming apparatus characterized by satisfying the following. When the diameter of the nozzle in the print head is D _N (m), and the 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, if the filter opening is circular, F '= F,
In other cases, F '= √2 · F)
6. The image forming apparatus according to claim 5, wherein the following condition is satisfied. An image forming apparatus comprising: an ink storage section in which a porous ink storage body that holds ink is stored; and an ink supply path that supplies ink from the ink storage section to the print head.
A filter is provided inside the ink supply path,
The ink absorber is pre-compressed before being stored in the ink storage unit,
The filtering accuracy of the filter is F (m), and the water head of the ink storage portion which is generated when the ink is to be 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 unit 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 (compression rate) indicated by the volume ratio of the ink absorber after compression processing before compression processing is R ′ the ink absorption when compressed and stored in the ink storage unit. The cross-sectional area of the body is S (m ² ), the height of the ink absorber when compressed and stored in the ink storage section is L (m), and the viscosity of the ink at 25 ° C. is μ ₂₅ (Pa · s). , any temperature _T K (K) When the definitive viscosity and _μ TK (Pa · s), at any temperature _T K (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 ₂₅ / exp (β / 298),
β = Ln ｛0.42 · Ln (μ ₂₅ ) +4.71｝ / (1 / 273-1 / 298)
(However, if the filter opening is circular, F '= F,
In other cases, F '= √2 · F)
An image forming apparatus characterized by satisfying the following. When the diameter of the nozzle in the print head is D _N (m), and the 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, if the filter opening is circular, F '= F,
In other cases, F '= √2 · F)
The image forming apparatus according to claim 7, wherein the following condition is satisfied. The image forming apparatus according to claim 1, further comprising a detector that detects presence or absence of ink in the ink supply path.

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