JP4088480B2 - Prediction of warp deformation at corners of injection molded products - Google Patents

Description

【００３１】
また、関数Ｆ１〜Ｆ３として以下の（３ａ）〜（３ｃ）式を採用してもよい。
Ｆ１（ｔ）＝ｔ^0.5 …（３ａ）
Ｆ２（θ）＝９０−θ …（３ｂ）
Ｆ３（ψ）＝（９０−ψ）／９０ …（３ｃ）
ここで、注入方向ψは、コーナ部の稜方向（コーナ部の稜が伸びる方向）と注入方向のなす角度として定義されており、順方向ではψ＝０、直交方向ではψ＝９０である。
【００３２】
なお、関数Ｆ１〜Ｆ３が（２ａ）〜（２ｃ）式で与えられるときには、（１）式は１次多項式である。
【００３３】
関数Ｆ１（ｔ）は、板厚ｔに応じて決定される板厚指標値を表している。同様に、関数Ｆ２（θ）はコーナ角度θに応じて決定されるコーナ角度指標値を表しており、関数Ｆ３（ψ）は樹脂注入方向Ｄに応じて決定される樹脂注入方向指標値を表している。これらの指標値Ｆ１〜Ｆ３としては、（２ａ）〜（２ｃ）式や（３ａ）〜（３ｃ）式以外の任意の関数やグラフで表現されたものを利用することが可能である。
【００３４】
（２ａ）〜（２ｃ）式を（１）式に代入すると、次の（４ａ），（４ｂ）式が得られる。
・樹脂注入方向が順方向の場合：
δθ＝Ｃ１×ｔ＋Ｃ２×（９０−θ）＋Ｃ３ …（４ａ）
・樹脂注入方向が直交方向の場合：
δθ＝Ｃ１×ｔ＋Ｃ２×（９０−θ） …（４ｂ）
【００３５】
なお、定数Ｃ１〜Ｃ３の値は、樹脂の組成などに応じて実験的に決定される。これらの内反り角度δθの予測式（４ａ），（４ｂ）は、頂角θが９０°以下である場合に適用することが好ましい。但し、頂角θが９０°以上の場合にも、同様に、反り角度δθ（すなわち、反り変形の量）を、板厚ｔと、頂角θと、樹脂注入方向ψとをパラメータとして予測できる。
【００３６】
図９は、（４ａ），（４ｂ）式による内反り角度の予測値と実測値との関係を示すグラフである。（４ａ），（４ｂ）式は、板厚ｔと、頂角θと、樹脂の注入方向と、の３つのパラメータ以外のパラメータを含まないので、これらの同一の複数の実験における内反り角度の予測値は同じ値となる。一方、これらの３つのパラメータが同一でも、他の実験条件によって実際の内反り角度は多少異なる。従って、図９のグラフでは、同じ内反り角度の予測値に対して、実測値が異なる多数の実験結果がプロットされている。
【００３７】
図９の実験結果から、（４ａ），（４ｂ）式による内反り角度の予測値が実測値と良く一致していることが理解できる。ちなみに、図９の場合の予測値と実測値の重相関係数は０．９５３であり、この値からも両者の相関が高いことが裏付けられる。これらの予測式による予測誤差は±１°程度であり、単純な予測式を用いた結果としては十分に有用な結果が得られる。
【００３８】
このように、内反り角度δθは、コーナ部の板厚ｔと、コーナ角度θと、コーナ部に関する樹脂注入方向ψと、をパラメータとして予測することが可能である。特に、（１）式を用いれば、３つのパラメータだけで極めて簡単に内反り角度δθを算出できるので、樹脂成形品の設計時に内反り量を容易に予測できるという利点がある。
【００３９】
なお、コーナ部の反り変形は、板厚ｔが大きいほど大きく、コーナ部の頂角θが小さいほど大きいものと予測すれば、精度の良い予測が可能である。樹脂注入方向については、上述した実験では直交方向よりも順方向の方が反り変形が大きいが、一般には、樹脂注入方向がコーナ部の稜方向に近いほど反り変形が大きくなるものと予測することが好ましい。なお、「コーナ部の稜方向」とは、コーナ部のかど部（稜）が伸びる方向であり、図２のテストピースＴＰの例では長手方向に相当する。また、「樹脂注入方向がコーナ部の稜方向に近い」とは、樹脂注入方向と、コーナ部の稜方向とのなす角度が０°に近いことを意味している。
【００４０】
Ｃ．第２の予測方法：
図１０は、内反り角度の第２の予測方法を示す説明図である。図１０（Ａ）は、コーナ部の断面の原形（すなわち金型のキャビティ形状）を示している。このコーナ部は外周線ＯＬ０と内周線ＩＬ０とで挟まれた部分であり、その形状は、コーナ部の内角φと、板厚ｔと、板厚中心の半径ｒとで規定される。なお、図１１（Ａ）に示されているように、πから内角φを引いた値（π−φ）が頂角θに相当する。
【００４１】
図１０（Ｂ）は、冷却後の外周線ＯＬ１と内周線ＩＬ１とを示している。但し、図１０（Ｂ）では、内角φが一定であり、表面方向の収縮によって元の線ＯＬ０，ＩＬ０が短くなったことと、板厚方向の収縮によって元の厚みｔが減少したことのみが反映されている。図１０（Ｃ）は、図１０（Ｂ）の外周線ＯＬ１と内周線ＩＬ１とそれぞれ同じ長さの外周線ＯＬ２と内周線ＩＬ２が、変形後の内角φ’を形成する様子を示している。図１１（Ｂ）は、このときの内角φ’と頂角θとの関係を示している。
【００４２】
このような反り変形モデルにおいて、収縮後の外周線ＯＬ２と内周線ＩＬ２の長さは、以下の（５ａ），（５ｂ）式で与えられる。
【００４３】
・外周線ＯＬ２の長さ：
（ｒ＋ｔ／２）×φ×（１−α）＝（ｒ’＋ｔ’／２）×φ’ …（５ａ）
・内周線ＩＬ２の長さ：
（ｒ−ｔ／２）×φ×（１−α）＝（ｒ’−ｔ’／２）×φ’ …（５ｂ）
ここで、ｒ’，ｔ’，φ’は変形後のコーナ部の半径と板厚と内角、αは表面方向の収縮率、βは板厚方向の収縮率である。なお、収縮率α，βは、（線膨張係数×温度変化量）である。
【００４４】
（５ａ），（５ｂ）式を解くと、以下の（６ａ），（６ｂ）式が得られる。
ｒ’＝ｒ×ｔ’／ｔ …（６ａ）
φ’＝φ×ｔ×（１−α）／ｔ’ …（６ｂ）
【００４５】
ここで、ｔ’＝（１−β）×ｔを（６ｂ）式に代入すると、次の（７）式が得られる。
φ’＝φ×（１−α）／（１−β） …（７）
【００４６】
一方、頂角θの減少量（すなわち内反り角度）δθは、以下の（８）式で与えられる。

【００４７】
（７）式を用いると、（８）式は以下の（９）式に変形できる。
δθ＝（π−θ）・（α−β）／（１−β） …（９）
【００４８】
（９）式に従えば、内反り角度δθは、元の頂角θと、表面方向の収縮率αと、板厚方向の収縮率βとから算出できる。
【００４９】
図１２は、第２の予測方法による内反り角度の計算例を示している。ケース１〜４は元の頂角θが６０°の場合であり、ケース５〜８は元の頂角θが９０°の場合である。なお、収縮時の温度変化量ΔＴは６０°一定と仮定した。また、表面方向の線膨張率α／ΔＴは0.0001／℃一定として、板厚方向の線膨張率β／ΔＴは0.0001／℃〜0.0010／℃の範囲の値とした。表面方向と板厚方向の収縮率α，βは、これらの線膨張率α／ΔＴ，β／ΔＴに温度変化量ΔＴをそれぞれ乗じた値である。
【００５０】
元の頂角θが６０°の場合には内反り角度δθの実験結果（図９）は約６．５°であった。これに対して、図１２の予測例では、板厚方向の収縮率βを表面方向の収縮率αの約１０倍の値に設定したとき（ケース４）に、内反り角度として約７°の値が得られている。
【００５１】
元の頂角θが９０°の場合には内反り角度δθの実験結果（図９）は約３°〜約５．５°であった。これに対して、図１２の予測例では、板厚方向の収縮率βを表面方向の収縮率αの約５倍〜約１０倍の値に設定したとき（ケース６〜８）に、内反り角度として約３°〜約５．５°の値が得られている。
【００５２】
これらの結果から理解できるように、表面方向の収縮率αよりも板厚方向の収縮率βを大きな値に設定することによって、内反り角度δθをかなり正確に予測することが可能である。通常の樹脂材料に関して入手できる線膨張率は表面方向の線膨張率に相当するものであり、射出成形時の板厚方向の線膨張率や収縮率の値は未知であるのが普通である。しかしながら、図９のような実験結果を基に、板厚方向の収縮率β（すなわち板厚方向の線膨張率β／ΔＴ）を、表面方向の収縮率α（すなわち表面方向の線膨張率α／ΔＴ）よりも大きな値とすることによって、内反り角度δθをかなり良い精度で予測できる。例えば、頂角θが６０°の場合には、表面方向の収縮率αの約１０倍の値を板厚方向の収縮率βとして採用することが可能である。また、頂角θが９０°の場合には、表面方向の収縮率αの約５倍〜約１０倍の値を板厚方向の収縮率βとして採用することが可能である。一般には、板厚方向の収縮率βとしては、表面方向の収縮率αの約３倍〜約２０倍の範囲の値を採用することが可能であり、特に約５倍〜約１０倍の値に設定することが好ましい。
【００５３】
このように、第２の予測方法では、表面方向の収縮率αよりも板厚方向の収縮率βを大きな値に設定することによって、内反り角度δθをかなり良い精度で予測することが可能である。また、本実施例では、図１０（Ａ）〜（Ｃ）で説明したように、反り変形の予測が、コーナ部の内周と外周の表面方向の収縮と板厚の収縮とを考慮して、収縮後の内周と外周と板厚とが形成するコーナ角度を算出することによって行われている。この結果、表面方向と板厚の収縮率を適正に設定すれば、良好な予測結果を得ることができるという利点がある。
【００５４】
Ｄ．変形例：
なお、この発明は上記の実施例や実施形態に限られるものではなく、その要旨を逸脱しない範囲において種々の態様において実施することが可能であり、例えば次のような変形も可能である。
【００５５】
Ｄ１．変形例１：
上記実施例では、断面がＬ字状で、かつ、両端が解放されている形状のテストピースＴＰに関するコーナ部の内反り角度δθを予測していたが、本発明は、これ以外の形状の射出成形品に対しても適用可能である。例えば、両端が何らかの形で拘束されている場合には、その拘束の結果、内反り角度δθが目に見える形では現れない。しかし、この場合にも、上述の予測方法で予測した内反り角度に基づいてコーナ部の回転モーメント（内部応力）を算出し、これに基づいてコーナ部の変形量を予測することが可能である。
【００５６】
この例からも理解できるように、本明細書において「コーナ部の反り変形を予測する」という文言は、内反り角度δθを求める場合に限らず、コーナ部の回転モーメントや、変形量を予測する場合を含む広い意味を有している。
【００５７】
Ｄ２．変形例２：
上記実施例では、予測値算出部１１０（図１）によって内反り変形のみを予測していたが、さらに、この内反り変形の予測値を用いて解析部１２０が成形品の構造解析（応力解析や変形解析）を行うことが可能である。
【００５８】
Ｄ３．変形例３：
上記実施例において、ハードウェアによって実現されていた構成の一部をソフトウェアに置き換えるようにしてもよく、逆に、ソフトウェアによって実現されていた構成の一部をハードウェアに置き換えるようにしてもよい。例えば、ワークステーション１００（図１）の各部の機能の一部をハードウェア回路で実行するようにすることもできる。
【図面の簡単な説明】
【図１】エンジニアリングワークステーション１００の構成を示す説明図。
【図２】本実施例の反り変形予測のために行った実験のテストピースＴＰを示す斜視図。
【図３】テストピースＴＰの成形に用いた金型３００の断面図。
【図４】順方向に樹脂を注入する際の注入ゲート位置を示す説明図。
【図５】直交方向に樹脂を注入する際の注入ゲート位置を示す説明図。
【図６】テストピースＴＰの射出成形の実験条件を示す説明図。
【図７】射出成形時のデータの時間経過の例を示すグラフ。
【図８】金型温度差と内反り角度との関係を示すグラフ。
【図９】第１の予測方法による内反り角度の予測値と実測値との関係を示すグラフ。
【図１０】内反り角度の第２の予測方法を示す説明図。
【図１１】コーナ部の内角φと頂角θとの関係を示す説明図。
【図１２】第２の予測方法による内反り角度の計算例を示す説明図。
【符号の説明】
５０…外部記憶装置
１００…ワークステーション
１１０…予測値算出部
１２０…解析部
２００…外部記憶装置
２１０…反り変形データベース
２２０…コンピュータプログラム
３００…金型
３１０…固定型
３１２，３１４…温度センサ
３２０…可動型
３２２，３２４…温度センサ
３３０…キャビティ[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a technique for predicting warp deformation of a corner portion of an injection molded product.
[0002]
[Prior art]
Generally, when a resin injection molded product is cooled after being taken out of a mold, deformation due to the temperature change occurs. In particular, it is known that when the molded product has a corner portion, “inward warping” occurs in which the apex angle of the corner portion becomes small. As a method for predicting the deformation of a resin injection molded product, for example, there is a method described in Japanese Patent Application Laid-Open No. 2002-49650. In this method, a shrinkage database is constructed, and deformation analysis of an injection molded product is performed using the shrinkage database.
[0003]
[Problems to be solved by the invention]
However, in the conventional deformation analysis, it is impossible to predict the deformation of the corner portion of the molded product with sufficiently good accuracy.
[0004]
The present invention has been made to solve the above-described conventional problems, and an object thereof is to provide a technique for predicting deformation of a corner portion of a molded product by a method different from the conventional one.
[0005]
[Means for solving the problems and their functions and effects]
In order to achieve the above object, a prediction method according to the present invention is a method for predicting warp deformation of a corner portion of a molded product due to a temperature change accompanying cooling during injection molding,
By setting the shrinkage rate in the plate thickness direction at the corner portion to a value larger than the shrinkage rate in the surface direction, predicting the warp deformation of the corner portion,
The warpage deformation is predicted by forming the inner circumference, outer circumference, and plate thickness after shrinkage in consideration of the shrinkage in the surface direction of the inner circumference and outer circumference of the corner portion and the shrinkage in the plate thickness direction of the corner portion. Done by calculating the corner angle,
Prediction of warpage deformation is based on the following equation: θ is the apex angle of the corner portion before warpage deformation, α is the shrinkage rate in the surface direction, and β is the shrinkage rate in the sheet thickness direction. The following formula:
δθ = (π−θ) · (α−β) / (1-β)
The process of calculating using is included .
[0006]
According to this method, the inner warp angle can be predicted in consideration of the difference between the shrinkage rate in the surface direction and the plate thickness direction, which is the main cause of the inner warp of the corner portion. Can be done. Further, it is possible to predict warpage deformation by simple calculation.
[0016]
The present invention can be realized in various forms, for example, a method and an apparatus for predicting warp deformation of a corner portion of an injection molded product, a method and an apparatus for analyzing a structure of a molded product using the warp deformation prediction, The present invention can be realized in the form of a computer program for realizing the functions of the method or apparatus, a recording medium recording the computer program, a data signal including the computer program and embodied in a carrier wave, and the like.
[0017]
DETAILED DESCRIPTION OF THE INVENTION
Next, embodiments of the present invention will be described in the following order based on examples.
A. Equipment configuration and experiment contents:
B. First prediction method:
C. Second prediction method:
D. Variation:
[0018]
A. Equipment configuration and experiment contents:
FIG. 1 is an explanatory diagram showing the configuration of the engineering workstation 100. The workstation 100 includes an external storage device 200 that stores various data including a warp deformation database 210 and various computer programs 220.
[0019]
The workstation 100 has two functions of a predicted value calculation unit 110 that predicts warp deformation of a corner portion of a resin molded product, and an analysis unit 120 that analyzes stress of the resin molded product. The functions of these units 110 and 120 are realized by various computer programs stored in the external storage device 50.
[0020]
The warpage deformation database 210 is constructed based on the experimental results of warpage deformation of the corner portion of the resin molded product. FIG. 2 is a perspective view showing a test piece TP of an experiment conducted for predicting warpage deformation of the present embodiment. The test piece TP is a long resin injection molded product having a substantially isosceles triangle cross section. The length W of one side of the cross section was about 50 mm, the apex angle θ was 60 ° or 90 °, and the thickness 2t was constant 2 mm or 3 mm.
[0021]
FIG. 3 shows a cross section of a mold 300 used for forming the test piece TP. In the mold 300, a cavity 330 is formed by a fixed mold 310 and a movable mold 320. The fixed mold 310 and the movable mold 320 are provided with temperature sensors 312, 314, 322, and 324, respectively. In particular, the temperature of the portion corresponding to the top of the test piece TP (FIG. 2) is considered to have a close influence on the warp deformation of the test piece TP. Therefore, the temperature sensors 312 and 322 are disposed in the vicinity of the top. Yes.
[0022]
Incidentally, it is known that the shrinkage of the resin accompanying the cooling during the injection molding has a correlation with the injection direction of the resin. In general, it is said that the shrinkage rate in the direction along the resin injection direction is relatively small, and the shrinkage rate in the direction orthogonal to the injection direction is relatively large. Therefore, it is considered that the injection direction of the resin with respect to the corner portion has an influence on the warp deformation of the corner portion. Therefore, two directions, the forward direction (longitudinal direction of the test piece TP) and the orthogonal direction (direction perpendicular to the longitudinal direction of the test piece TP), are employed as the resin injection directions during the test piece TP molding.
[0023]
4A and 4B show the injection gate position when the resin is injected in the forward direction. FIG. 4A is a front view, FIG. 4B is a bottom view, and FIG. 4C is a side view. When the resin was injected in the forward direction, the test piece TP was obtained by cutting the upper end along the one-dot chain line after molding. 5A and 5B show the injection gate position when the resin is injected in the orthogonal direction. FIG. 5A is a front view and FIG. 5B is a bottom view. When the resin was injected in the orthogonal direction, the test piece TP was obtained by cutting the side end along the one-dot chain line after molding.
[0024]
FIG. 6 shows experimental conditions for injection molding of the test piece TP. The experiment was performed on 324 combinations of each condition shown in this table. Note that polypropylene (PP) was used as the resin.
[0025]
FIG. 7 is a graph showing an example of the passage of time of measurement data during injection molding. FIG. 7A shows the injection pressure, screw displacement, and resin internal pressure (pressure in the mold). FIG. 7B shows the temperatures measured by the four temperature sensors 312, 314, 322, and 324 shown in FIG. As can be seen from FIG. 3, the temperature sensor 322 installed near the surface of the movable mold 320 corresponds to a position inside the corner portion of the test piece TP. The inner part of the corner part has a smaller contact area between the mold and the test piece TP than the outer part of the corner part (the part on the fixed mold 310 side), and therefore the temperature of the mold tends to be higher. As a result, as shown in FIG. 7B, the temperature near the surface of the movable mold 320 is the highest, and the temperature inside the movable mold 320 is also higher than the temperature of the fixed mold 310.
[0026]
As can be understood from the temperature change in FIG. 7B, generally, the temperature of the inner portion of the corner portion of the resin molded product tends to be higher than the temperature of the outer portion. That is, the high temperature portion of the resin before curing is generated at a position slightly inward of the corner portion. When the high-temperature portion in the vicinity of the inside is finally cooled, it is estimated that the inner warp (decrease in the apex angle) of the corner portion occurs due to the shrinkage accompanying the cooling.
[0027]
FIG. 8 is a graph showing the relationship between the mold temperature difference and the inward warping angle obtained from the experimental results. It can be seen that the greater the mold temperature difference, the greater the warp angle. Further, even when the apex angle is the same, the warp is larger when the plate thickness t is larger. Furthermore, even when the apex angle and the plate thickness are the same, the inward warping angle is greater in the case where the resin injection direction is the forward direction than in the orthogonal direction. Although not shown in FIG. 8, the smaller the apex angle (60 ° than 90 ° in the above experiment), the greater the internal curvature angle.
[0028]
B. First prediction method:
From the above experimental results (particularly FIG. 8), it was found that the inward warping angle δθ (the amount of decrease in the apex angle) is represented by the polynomial shown in the following equation (1).
[0029]
δθ = C1 × F1 (t) + C2 × F2 (θ) + C3 × F3 (ψ) (1)
Here, C1 to C3 are constants, F1 (t) is a function of the plate thickness t, F2 (θ) is a function of the apex angle θ (corner angle), and F3 (ψ) is a function of the resin injection direction ψ. is there.
[0030]
The functions F1 to F3 are given by the following equations (2a) to (2c), for example.

[0031]
Further, the following expressions (3a) to (3c) may be adopted as the functions F1 to F3.
F1 (t) = t ^0.5 (3a)
F2 (θ) = 90−θ (3b)
F3 (ψ) = (90−ψ) / 90 (3c)
Here, the injection direction ψ is defined as an angle formed between the ridge direction of the corner portion (the direction in which the ridge of the corner portion extends) and the injection direction, and ψ = 0 in the forward direction and ψ = 90 in the orthogonal direction.
[0032]
When the functions F1 to F3 are given by the expressions (2a) to (2c), the expression (1) is a first order polynomial.
[0033]
The function F1 (t) represents a plate thickness index value determined according to the plate thickness t. Similarly, the function F2 (θ) represents a corner angle index value determined according to the corner angle θ, and the function F3 (ψ) represents a resin injection direction index value determined according to the resin injection direction D. ing. As these index values F1 to F3, it is possible to use an expression expressed by an arbitrary function or graph other than the expressions (2a) to (2c) and the expressions (3a) to (3c).
[0034]
By substituting the equations (2a) to (2c) into the equation (1), the following equations (4a) and (4b) are obtained.
・ When the resin injection direction is forward:
δθ = C1 × t + C2 × (90−θ) + C3 (4a)
・ When resin injection direction is orthogonal:
δθ = C1 × t + C2 × (90−θ) (4b)
[0035]
The values of the constants C1 to C3 are experimentally determined according to the resin composition and the like. These prediction formulas (4a) and (4b) for the warpage angle δθ are preferably applied when the apex angle θ is 90 ° or less. However, even when the apex angle θ is 90 ° or more, the warp angle δθ (that is, the amount of warp deformation) can be similarly predicted using the plate thickness t, the apex angle θ, and the resin injection direction ψ as parameters. .
[0036]
FIG. 9 is a graph showing the relationship between the predicted value of the warpage angle and the actual measurement value according to the equations (4a) and (4b). Since the equations (4a) and (4b) do not include parameters other than the three parameters of the plate thickness t, the apex angle θ, and the resin injection direction, The predicted value is the same value. On the other hand, even if these three parameters are the same, the actual warp angle differs somewhat depending on other experimental conditions. Therefore, in the graph of FIG. 9, a large number of experimental results with different actual measurement values are plotted against the predicted values of the same warp angle.
[0037]
From the experimental results shown in FIG. 9, it can be understood that the predicted values of the warpage angle according to the equations (4a) and (4b) are in good agreement with the actually measured values. Incidentally, the multiple correlation coefficient between the predicted value and the actually measured value in the case of FIG. 9 is 0.953, and this value supports the high correlation between the two. The prediction error by these prediction formulas is about ± 1 °, and a sufficiently useful result is obtained as a result using a simple prediction formula.
[0038]
Thus, the inward warping angle δθ can be predicted using the plate thickness t of the corner portion, the corner angle θ, and the resin injection direction ψ with respect to the corner portion as parameters. In particular, if the equation (1) is used, the inner warp angle δθ can be calculated very simply by using only three parameters, so that there is an advantage that the amount of inner warp can be easily predicted at the time of designing a resin molded product.
[0039]
In addition, if it is predicted that the warp deformation of the corner portion is larger as the plate thickness t is larger and the vertex angle θ of the corner portion is smaller, it is possible to predict with high accuracy. Regarding the resin injection direction, warpage deformation is larger in the forward direction than in the orthogonal direction in the above-described experiment, but in general, it is predicted that the warpage deformation increases as the resin injection direction is closer to the corner ridge direction. Is preferred. Note that the “ridge direction of the corner portion” is a direction in which the corner portion (ridge) of the corner portion extends, and corresponds to the longitudinal direction in the example of the test piece TP in FIG. Also, “the resin injection direction is close to the corner ridge direction” means that the angle formed between the resin injection direction and the corner ridge direction is close to 0 °.
[0040]
C. Second prediction method:
FIG. 10 is an explanatory diagram showing a second method of predicting the inward curvature angle. FIG. 10A shows the original shape of the cross section of the corner portion (that is, the cavity shape of the mold). This corner portion is a portion sandwiched between the outer peripheral line OL0 and the inner peripheral line IL0, and its shape is defined by the inner angle φ of the corner portion, the plate thickness t, and the radius r of the plate thickness center. As shown in FIG. 11A, a value (π−φ) obtained by subtracting the inner angle φ from π corresponds to the apex angle θ.
[0041]
FIG. 10B shows the outer peripheral line OL1 and the inner peripheral line IL1 after cooling. However, in FIG. 10B, the inner angle φ is constant, the original lines OL0 and IL0 are shortened by the shrinkage in the surface direction, and the original thickness t is reduced by the shrinkage in the plate thickness direction. It is reflected. FIG. 10C shows a state in which the outer circumferential line OL2 and the inner circumferential line IL2 having the same length as the outer circumferential line OL1 and the inner circumferential line IL1 in FIG. 10B form the deformed inner angle φ ′, respectively. Yes. FIG. 11B shows the relationship between the inner angle φ ′ and the apex angle θ at this time.
[0042]
In such a warp deformation model, the lengths of the outer peripheral line OL2 and the inner peripheral line IL2 after contraction are given by the following equations (5a) and (5b).
[0043]
-Length of outer circumference line OL2:
(R + t / 2) × φ × (1−α) = (r ′ + t ′ / 2) × φ ′ (5a)
-Length of inner circumference line IL2:
(R−t / 2) × φ × (1−α) = (r′−t ′ / 2) × φ ′ (5b)
Here, r ′, t ′, and φ ′ are the radius, plate thickness, and internal angle of the corner after deformation, α is the shrinkage rate in the surface direction, and β is the shrinkage rate in the plate thickness direction. The shrinkage rates α and β are (linear expansion coefficient × temperature change amount).
[0044]
When the equations (5a) and (5b) are solved, the following equations (6a) and (6b) are obtained.
r ′ = r × t ′ / t (6a)
φ ′ = φ × t × (1−α) / t ′ (6b)
[0045]
Here, when t ′ = (1−β) × t is substituted into the equation (6b), the following equation (7) is obtained.
φ ′ = φ × (1-α) / (1-β) (7)
[0046]
On the other hand, the amount of decrease in the apex angle θ (that is, the inward warping angle) δθ is given by the following equation (8).

[0047]
Using equation (7), equation (8) can be transformed into the following equation (9).
δθ = (π−θ) · (α−β) / (1-β) (9)
[0048]
According to the equation (9), the warpage angle δθ can be calculated from the original apex angle θ, the shrinkage rate α in the surface direction, and the shrinkage rate β in the plate thickness direction.
[0049]
FIG. 12 shows an example of calculation of the inward curvature angle by the second prediction method. Cases 1 to 4 are cases where the original apex angle θ is 60 °, and cases 5 to 8 are cases where the original apex angle θ is 90 °. Note that the temperature change ΔT during shrinkage was assumed to be constant at 60 °. Further, the linear expansion coefficient α / ΔT in the surface direction was constant at 0.0001 / ° C., and the linear expansion coefficient β / ΔT in the thickness direction was set to a value in the range of 0.0001 / ° C. to 0.0010 / ° C. The shrinkage rates α and β in the surface direction and the plate thickness direction are values obtained by multiplying the linear expansion rates α / ΔT and β / ΔT by the temperature change amount ΔT, respectively.
[0050]
When the original apex angle θ was 60 °, the experimental result (FIG. 9) of the inward warping angle δθ was about 6.5 °. On the other hand, in the prediction example of FIG. 12, when the contraction rate β in the thickness direction is set to a value about 10 times the contraction rate α in the surface direction (case 4), the inward warping angle is about 7 °. The value is obtained.
[0051]
When the original apex angle θ was 90 °, the experimental result (FIG. 9) of the inward warping angle δθ was about 3 ° to about 5.5 °. On the other hand, in the prediction example of FIG. 12, when the shrinkage rate β in the plate thickness direction is set to a value of about 5 to 10 times the shrinkage rate α in the surface direction (cases 6 to 8), the inward warping occurs. A value of about 3 ° to about 5.5 ° is obtained as the angle.
[0052]
As can be understood from these results, it is possible to predict the inward warping angle δθ fairly accurately by setting the contraction rate β in the sheet thickness direction to a larger value than the contraction rate α in the surface direction. The linear expansion coefficient available for ordinary resin materials corresponds to the linear expansion coefficient in the surface direction, and the values of the linear expansion coefficient and shrinkage ratio in the plate thickness direction during injection molding are generally unknown. However, based on the experimental results as shown in FIG. 9, the contraction rate β in the plate thickness direction (that is, the linear expansion rate β / ΔT in the plate thickness direction) is changed to the contraction rate α in the surface direction (that is, the linear expansion rate α in the surface direction). By setting the value larger than / ΔT), the inner curvature angle δθ can be predicted with considerably good accuracy. For example, when the apex angle θ is 60 °, a value about ten times the shrinkage rate α in the surface direction can be adopted as the shrinkage rate β in the plate thickness direction. When the apex angle θ is 90 °, a value about 5 to about 10 times the shrinkage rate α in the surface direction can be adopted as the shrinkage rate β in the plate thickness direction. In general, a value in the range of about 3 times to about 20 times the shrinkage rate α in the surface direction can be adopted as the shrinkage rate β in the plate thickness direction, particularly about 5 times to about 10 times. It is preferable to set to.
[0053]
As described above, in the second prediction method, the inner warp angle δθ can be predicted with considerably good accuracy by setting the contraction rate β in the plate thickness direction to a larger value than the contraction rate α in the surface direction. is there. Further, in this embodiment, as described with reference to FIGS. 10A to 10C, the warpage deformation is predicted in consideration of the shrinkage in the surface direction of the inner and outer circumferences of the corner portion and the shrinkage of the plate thickness. This is done by calculating the corner angle formed by the inner circumference, outer circumference and plate thickness after shrinkage. As a result, there is an advantage that a good prediction result can be obtained by appropriately setting the shrinkage ratio of the surface direction and the plate thickness.
[0054]
D. Variation:
The present invention is not limited to the above-described examples and embodiments, and can be implemented in various modes without departing from the gist thereof. For example, the following modifications are possible.
[0055]
D1. Modification 1:
In the above-described embodiment, the inward warping angle δθ of the corner portion with respect to the test piece TP having a L-shaped cross section and a shape in which both ends are released is predicted. The present invention can also be applied to molded products. For example, when both ends are constrained in some form, the warping angle δθ does not appear in a visible form as a result of the constraining. However, also in this case, it is possible to calculate the rotational moment (internal stress) of the corner portion based on the inward warping angle predicted by the above-described prediction method, and to predict the deformation amount of the corner portion based on this. .
[0056]
As can be understood from this example, in the present specification, the phrase “predicting the warp deformation of the corner portion” is not limited to obtaining the inner warp angle δθ, but predicts the rotational moment and the deformation amount of the corner portion. It has a broad meaning including cases.
[0057]
D2. Modification 2:
In the above-described embodiment, only the inward warpage deformation is predicted by the predicted value calculation unit 110 (FIG. 1). Further, the analysis unit 120 uses the predicted value of the inward warpage deformation to analyze the structure of the molded product (stress analysis). Or deformation analysis).
[0058]
D3. Modification 3:
In the above embodiment, a part of the configuration realized by hardware may be replaced with software, and conversely, a part of the configuration realized by software may be replaced by hardware. For example, a part of the function of each part of the workstation 100 (FIG. 1) can be executed by a hardware circuit.
[Brief description of the drawings]
FIG. 1 is an explanatory diagram showing a configuration of an engineering workstation 100. FIG.
FIG. 2 is a perspective view showing a test piece TP of an experiment performed for warpage deformation prediction according to the present embodiment.
FIG. 3 is a cross-sectional view of a mold 300 used for forming a test piece TP.
FIG. 4 is an explanatory diagram showing an injection gate position when resin is injected in the forward direction.
FIG. 5 is an explanatory view showing an injection gate position when injecting resin in an orthogonal direction.
FIG. 6 is an explanatory diagram showing experimental conditions for injection molding of a test piece TP.
FIG. 7 is a graph showing an example of time passage of data at the time of injection molding.
FIG. 8 is a graph showing the relationship between mold temperature difference and inward warping angle.
FIG. 9 is a graph showing the relationship between the predicted value of the warpage angle and the actual measurement value according to the first prediction method;
FIG. 10 is an explanatory diagram showing a second prediction method of the inward curvature angle.
FIG. 11 is an explanatory diagram showing a relationship between an inner angle φ and a vertex angle θ of a corner portion.
FIG. 12 is an explanatory diagram showing an example of calculation of an internal warp angle by a second prediction method.
[Explanation of symbols]
DESCRIPTION OF SYMBOLS 50 ... External storage apparatus 100 ... Workstation 110 ... Predicted value calculation part 120 ... Analysis part 200 ... External storage apparatus 210 ... Warp deformation database 220 ... Computer program 300 ... Mold 310 ... Fixed mold 312,314 ... Temperature sensor 320 ... Movable Molds 322, 324 ... temperature sensor 330 ... cavity

Claims (1)

A method for predicting warpage deformation of a corner portion of a molded product due to a temperature change accompanying cooling during injection molding,
By setting the shrinkage rate in the plate thickness direction at the corner portion to a value larger than the shrinkage rate in the surface direction , predicting the warp deformation of the corner portion ,
The warpage deformation is predicted by forming the inner circumference, outer circumference, and plate thickness after shrinkage in consideration of the shrinkage in the surface direction of the inner circumference and outer circumference of the corner portion and the shrinkage in the plate thickness direction of the corner portion. Done by calculating the corner angle,
Prediction of warpage deformation is based on the following equation: θ is the apex angle of the corner portion before warpage deformation, α is the shrinkage rate in the surface direction, and β is the shrinkage rate in the sheet thickness direction. The following formula:
δθ = (π−θ) · (α−β) / (1-β)
A method comprising the step of calculating using

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