JPH08230008A - Method and device for estimating warping deformation of injection molded article - Google Patents

Abstract

PURPOSE: To make it possible to exactly estimate warping deformation even in the case of a thin-wall molded article by a method wherein in-plane shrinkage factor is calculated by introducing specified formulae for calculating. CONSTITUTION: In a thin-wall molded article, in which the anisotropic behavior of plastic resin is remarkable, in-plane shrinkage factor is calculated by introducing the equations on the basis of the formulae I (the formulae representing shrinkage anisotropy) or the formulae II (the formulae representing the shrinkage anisotropy of fiber-filled material) so as to estimate warpage in order to realize more accurate warp estimate. An analyzing device consists of a resin data base comprizing a data inputting device such as a key board and the like, a built-in hard disk device and the like, a molding condition inputting parts, inputted data part for temporarily storing, an analytical calculating device for performing analytical calculation and a result outputting device comprizing displaying or printing device. In the formulae, εz, εp and ev are shrinkage factors in the direction of the thickness, in in-plane direction and in volume, A and B are coefficients of shrinkage, εL and εT are shrinkage factors in in-plane flow direction and in the direction normal to in-plane flow direction and αL and αT are coefficients of thermal expansion in flow direction and in the direction normal to flow direction.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for predicting warpage deformation of an injection-molded article and an apparatus therefor, for example, in the injection-molding method of a plastic, from the behavior of the resin of the plastic in the mold, the plastic-molded article after being taken out. It is particularly suitable for a simulation program for predicting the occurrence of warpage.

[0002]

2. Description of the Related Art Conventionally, in a simulation program for predicting the behavior of a plastic resin by injection molding and the warp deformation of a plastic molded product, in the process of filling the mold cavity with the plastic resin, a motion equation and energy conservation Formulas of continuous and continuous equations are formulated to the finite element method to predict the behavior of the plastic resin in the molten state, while the compressibility of the resin is further increased in the pressure holding / cooling process after the resin is filled in the cavity. In order to take into account the change of pressure (P) and temperature (T),
In consideration of the relational expression of the specific volume (V), the volume contraction rate is calculated, and the contraction rate is equally calculated in each of the three directions of plate thickness and in-plane.

Then, the in-plane shrinkage distribution finally obtained is set as an initial strain to predict the warp deformation of a plastic molded product obtained by injection molding. Here, in calculating the resin behavior and warpage prediction, a model shape of a plastic molded product is created, mesh division is performed so that calculation by the finite element method can be performed, and molding conditions as boundary conditions are given. I am trying to give the physical property data.

[0004]

However, an important feature of the plastic resin molded product is the anisotropy of the shrinkage ratio. That is, when the molded product is thin,
It is known that the shrinkage behavior differs between the thickness direction and the in-plane direction. Furthermore, it is known that in an injection-molded product of a fiber-reinforced resin, each shrinkage behavior differs in the in-plane flow direction of the resin and the direction perpendicular to this flow.

Further, in the conventional warpage prediction method, such an anisotropic behavior of shrinkage has not been clarified,
Simply divide the volume contraction rate into three equal parts and distribute to the respective directions of plate thickness and in-plane, then calculate the contraction rate, and use the contraction rate in the in-plane direction as the initial strain to predict warpage deformation of the injection molded product. are doing. Therefore, there is a problem in that accurate warpage cannot be predicted when the molded product is thin.

Accordingly, the present invention has been made in view of the above-mentioned problems, and a method and apparatus for predicting warpage deformation of an injection-molded product capable of accurately predicting warpage even when the molded product is thin. For the purpose of providing.

[0007]

[Means for Solving the Problems] and

In order to solve the above-mentioned problems and achieve the object,
In the present invention, the relational expression based on the following (formula of contraction anisotropy) (formula of contraction anisotropy in the case of a material containing fibers) is calculated in the case where the anisotropic behavior of the plastic resin is a thin-walled molded product. Introduced into, the in-plane shrinkage ratio is calculated and the warp deformation is predicted, thereby achieving more accurate warp prediction.

[0008]

(Equation 5)

(Expression of shrinkage anisotropy) εz = A + B · ev εp = (ev−εz) / 2 εz: Shrinkage ratio in the plate thickness direction, εp: Shrinkage ratio in the in-plane direction ev: Volume shrinkage ratio, A, B: Shrinkage coefficient

[0010]

[Equation 6]

(Formula of shrinkage anisotropy in the case of a material containing fibers) εL = (ev−εz) · αL / (αL + αT) εT = (ev−εz) · αT / (αL + αT) εL: in-plane flow Shrinkage, εT Shrinkage in the direction perpendicular to the in-plane flow αL: Thermal expansion coefficient in the flow direction αT: Thermal expansion coefficient in the direction perpendicular to the flow

Preferred embodiments of the present invention will be described below with reference to the accompanying drawings. First, FIG. 1 is a schematic configuration diagram showing the overall configuration of an analysis apparatus, and shows one configuration example of an analysis calculation system operating in this system configuration.

In the figure, what is shown surrounded by the one-dot chain line in the figure is the part of the analysis device composed of a personal computer or the like. This analysis device includes a data input device 1 such as a keyboard and a resin database 2 including a built-in hard disk device, a molding condition input unit 3, an input data unit 4 for temporarily storing input data, and an analysis based on the input data. It is composed of an analysis calculation device 5 that performs calculation and a result output device 6 that is a display or printer device. First, using the analysis apparatus having the above-described configuration, a shape is created and modeled as input data so that the analysis calculation of the plastic molded product that is the target of the analysis calculation can be performed.

In order to create and model this shape, the CAD 11 is a local area network LAN in the analysis device.
Connected via the two-dimensional shape created by the CAD 11, the input data is created by the data input device 1 or the input data is created by the data input device 1 from the beginning. I am trying to do it. When the two-dimensional shape created by the CAD 11 is used as it is, the shape is transferred to the analysis device, and then the three-dimensional shape is created and then further element division is performed, or a magneto-optical disk, a magnetic tape, or the like is used. Data is transferred to the analysis device via the external input device 12 consisting of
Subsequently, shape data is created.

On the other hand, in the data input device 1, elements are created for all locations to be modeled according to the shape and element creation tool software. The resin database 2 for the shape for which the element is created in this way
After selecting and reading the resin to be analyzed symmetrically from, the resin data as the input data is set.

Further, for each process of calculation, the necessary conditions are input by reading from the molding condition input 3.

FIG. 2 is a flow chart showing the contents of processing executed in the analyzing apparatus of FIG. In the figure, in addition to the resin conditions and the molding conditions 3 from the resin database 2 described above, the data input device 1 has shape data 101
The load applied to the molded product and the constraint condition 102 are input. Further, in the analysis calculation device 5, a flow analysis process 501 for predicting the filling behavior of the molten plastic resin into the mold.
And a holding pressure analysis process 502 in which a certain pressure is applied to the resin in the mold after the resin is filled in the mold, and a cooling analysis process for predicting the cooling process in the mold until the molded product is taken out from the mold. 503, and if the target plastic resin contains glass fibers, an orientation analysis process 504 for predicting the orientation of the fibers when flowing and holding pressure (the orientation of the fibers, etc.); After the mold is opened, five processes of the deformation analysis process 505 for predicting how much the molded product taken out to the outside will be deformed while being cooled to room temperature are considered and calculated.

As described above, the input data for the analytical calculation is created by inputting the shape and the conditions in the data input device 1 and the analytical calculation device 5. In addition, the calculation performed by the analysis calculation device 5 of FIG. 1 is such that, as shown in FIG. 2, the process of flowing the plastic resin into the mold in the flow analysis 5 is performed according to the time history specified by the condition. The position where the resin has flown up to, the velocity distribution at that time, the pressure distribution at each position of the resin, and the temperature distribution are calculated.

Next, on the basis of the result of the flow analysis, the behavior of the resin in the pressure-holding process in consideration of the compressibility of the resin is calculated in the pressure-holding analysis 502, and the resin behavior in the subsequent cooling stage is further measured in the cooling analysis 503. calculate. In the prediction of resin behavior during these pressure-holding / cooling processes, the results obtained in the same way as in the flow analysis are the same as those for pressure distribution, temperature distribution, etc., but in order to understand the density changes that occur during the pressure-holding process. The contraction rate distribution of is also obtained.

In order to consider the compressibility of the pressure holding / cooling process, the following P-V-T relational expression is introduced.

[0020]

(Equation 7)

(P + W) (V-V0) = R.T P: Pressure, T: Temperature, V: Specific volume, W, V0, R: Constant This equation is a change in pressure (P) and temperature (T). At the same time, the specific volume (V) also changes. By introducing the above equation, the volumetric shrinkage rate at each position of the molded product is obtained from the obtained specific volume V, room temperature T, and specific volume at atmospheric pressure according to the following equation for calculating volumetric shrinkage rate.

[0022]

(Equation 8)

Volume contraction rate ev = (V0-V) / VV: Specific volume at the start of contraction, V0: Specific volume at room temperature and atmospheric pressure. Following this calculation, there is a relational expression of anisotropic contraction. The shrinkage rate in the plate thickness direction and the shrinkage rate in the in-plane direction are calculated by the following equations.

[0024]

[Equation 9]

(Expression of shrinkage anisotropy) εz = A + B · ev εp = (ev−εz) / 2 εz: Shrinkage ratio in the plate thickness direction, εp: Shrinkage ratio in the in-plane direction ev: Volume shrinkage ratio, A, B: Shrinkage coefficient When a fiber-reinforced resin is used, the shrinkage rates in the in-plane flow direction and the direction perpendicular to the flow are calculated by the following equation.

[0026]

[Equation 10]

(Formula of shrinkage anisotropy in the case of a material containing fibers) εL = (ev−εz) · αL / (αL + αT) εT = (ev−εz) · αT / (αL + αT) εL: in-plane flow Shrinkage in the direction, εT Shrinkage in the direction perpendicular to the in-plane flow αL: Thermal expansion coefficient in the flow direction αT: Thermal expansion coefficient in the direction perpendicular to the flow As a result of the above, the fiber-reinforced resin was If used, orientation analysis 504 is performed to predict the orientation of the fibers in the resin in the molded article. And finally, based on the predicted behavior of the resin in the mold above,
A deformation analysis 505 for determining the warp deformation of the molded product after being taken out from the mold is performed.

In calculating the warp deformation in this way, the balance equation shown in FIG.
The calculation is performed based on the FEM formulation under the given boundary conditions, with the stress-strain relational expression of 1 and the displacement-strain relational expression of FIG. 5 as basic expressions.

Then, in the relational expression shown in FIG. 6, the in-plane shrinkage rate obtained by each of the above calculations is obtained as a shrinkage strain for each divided element, and given as the initial strain, the calculation is performed. To do. By performing the above calculation, warp deformation, stress, etc. of each part of the molded product are calculated.

The calculation results, pressure distributions, temperature distributions, shrinkage ratio distributions, warp deformation graphs, etc., obtained in the above respective calculation processes are displayed by the result output device 6 in FIG.

Next, the contraction anisotropy formula and the method for deriving the contraction anisotropy formula containing fibers will be described in detail. FIG. 7 shows a plan view and a side view of a flat plate-shaped test piece, respectively. That is, the dimension between the pin marks at each of the measurement points P1 to P9 shown in FIG. 7 is sampled after a sample obtained under the molding conditions shown in the molding condition table of FIG. 8 is obtained. Therefore, the actual pin positions of P1 to P9 of the mold are measured in advance.

In general, the plastic molded product is in a state where the temperature is still high at the time of taking it out of the mold, and then shrinkage occurs in most cases while it is cooled to room temperature. Therefore, the shrinkage ratio in the in-plane direction can be calculated by measuring the distance between the pin positions of the actual mold and the sampled molded product. So, for example, P6-P
If the distance in the mold at the position 5 is M65 and the distance of the sampled molded product is S65, the shrinkage ratio obtained is (M65-S65) / M65, and the P6-P5 direction is located in the resin flow direction. The obtained shrinkage ratio is the shrinkage ratio in the flow direction.

Similarly, when the contraction rate at each position is obtained,
By measuring P3-P2, P9-P8, and P5-P4 points, the shrinkage rate in the resin flow direction is also P6-P3, P6-P.
9, the shrinkage ratio in the direction perpendicular to the resin flow can be obtained by measuring each point P5-P8.

Next, the plate thickness at the positions H1 to H4 shown in FIG. 7 is measured. Since the mold size is known in advance when the cavity is manufactured, the shrinkage ratios in the plate thickness direction from H1 to H4 can be calculated by the same method. Therefore, the contraction ratios between positions H1 to H4 are used as the contraction ratios between the pin positions that have already been obtained, and the in-plane contraction ratios at the positions H1 to H4 are used.

For example, since H1 is surrounded by P2-P5-P4-P1, the average value of the contraction rates of P2-P1 and P5-P4 is taken as the contraction rate in the flow direction at the position of H1, and P5- The average value of the shrinkage rates of P2 and P4-P1 is taken as the in-plane shrinkage rate at the H1 position. Other points H2, H3,
Similarly, at the H4 position, the shrinkage rate in each of the three directions at each position is obtained. Therefore, the volume shrinkage rate at each of the positions H1 to H4 is obtained from the formula in FIG. 6 and the measured values and the analysis shown in FIG. 9 are analyzed. A shrinkage rate comparison table of values is obtained. The shrinkage rates are compared at positions H1 to H4 in Table 3, and the results are shown in Table 3. In the table of FIG. 9, the contraction rates in the three directions of the plate thickness, the flow, and the right angle at the positions H1 to H4 are shown in the upper row, and the actual values of the contraction rates at the respective positions are shown in the middle row. Shows the result of the shrinkage ratio when the relational expression of anisotropic shrinkage was used, and the lower part shows the result of the shrinkage ratio when the isotropic shrinkage was used. From this table, it is understood that the accuracy of the in-plane shrinkage rate (flow direction, right-angle direction) is improved as compared with the result of the shrinkage rate obtained in consideration of isotropic shrinkage.
Here, it is particularly important to improve the accuracy of the shrinkage ratio in the in-plane direction,
As described above, the warpage analysis after the cooling analysis is performed using the shrinkage ratio in the in-plane direction.

As described above, the volumetric shrinkage at each position of the sampled test piece and the shrinkage in three directions are obtained, and the relationship between the volumetric shrinkage and the shrinkage in each direction is plotted on a graph. Graphs of the shrinkage ratio of the resin of PC are shown in FIGS. 10 to 14, respectively.

First, looking at the graph of the relationship between the volume contraction rate and the contraction rate in the plate thickness direction of FIG. 10, it is confirmed that the relationship between the two is shown on a substantially linear line. The dashed line in FIG. 10 is a line obtained by simply connecting the volume contraction rate to 1/3 of the volume contraction rate with a straight line. This line is the contraction rate in the plate thickness direction. Is 1/3 of the volumetric shrinkage, that is, it shrinks equally in 3 directions (in the case of isotropic shrinkage)
Indicates the value of. In contrast to this line, the actual contraction line shown by the solid line in the figure has a larger gradient. This indicates that the ratio of the shrinkage ratio in the plate thickness direction to the volume shrinkage ratio is very large.

From the above, it can be seen that the volume shrinkage ratio and the shrinkage ratio in the plate thickness direction are expressed by linear expressions as shown by εz = A + B · ev (expression of shrinkage anisotropy). Further, in the equation of shrinkage anisotropy, A and B are physical property values that differ depending on the type of resin, and are calculated by the least square method using the respective numerical data plotted in FIG. Each physical property value obtained is the resin D / B of FIG.
Registered in 2.

Next, in FIGS. 11 and 12, it can be confirmed that the contraction rate in the flow direction and the contraction rate in the direction perpendicular to the flow are on the first-order straight line having substantially the same gradient with respect to the volume contraction rate. As a result, the volume shrinkage rate and the in-plane shrinkage rate are εp = (ev
It is shown by the relational expression of −εz) / 2.

This tendency has been confirmed not only in PC but also in other resins.

From the above, the relational expression of anisotropic shrinkage is derived.

Further, the results of the resin containing 30% of PC glass fiber are shown in FIGS. The contraction rate in the plate thickness direction with respect to the volume contraction rate in FIG. 13 has a relationship as shown by εz = A + B · ev, but the contraction rate in the in-plane direction in FIG. 14 is in the direction perpendicular to the flow direction and the flow direction. Anisotropy is seen. Therefore, using the linear expansion coefficients in both directions, εL =
(Ev-εz) · αL / (αL + αT), εT = (ev-εz)
-By drawing the straight lines shown in each equation of αT / (αL + αT) on the graph, it can be confirmed that the contraction rates in both directions are almost on the respective straight lines. From the above phenomenon, the relational expression of anisotropic contraction is derived.

Next, a comparison between the result of the shrinkage ratio of the actual molded product measured by using the flat plate-shaped test piece as shown in FIG. 15 and the result of the analysis is shown. First, create a model shape and divide it into meshes so that the flat plate test piece can be analyzed. For molding conditions, set the same conditions as the actual molding conditions,
Further, the resin is selected from the database 2 and the physical property data of the plastic resin is input. Here, the resin is a material containing PC fibers. Regarding the physical property data, the value of the shrinkage coefficient considering the anisotropy of the shrinkage rate is also included.

After setting the above conditions, the calculation is performed from the flow to the pressure holding / cooling stage in accordance with the analysis flow of FIG. In the pressure holding / cooling stage, the shrinkage rate at each position of the molded product is obtained by performing the calculation in consideration of anisotropic shrinkage.

In this design example, since a material containing fibers is used, the shrinkage ratio is calculated using the above-mentioned relational expressions of anisotropic shrinkage.

FIG. 16 shows the measurement position 2 shown in FIG.
It shows a comparison between the measured value of the deformation amount and the analysis result. FIG.
6, it can be seen that the deformation amount at the measurement position 2 is approximated and predicted with considerably high accuracy in comparison between the actual measurement value (broken line in FIG. 16) and the analysis result (solid line in FIG. 16).

Next, an example of applying this simulation system to the molded product of the camera body shown in FIGS. 17 and 18 and feeding back to the design is shown.

The model of FIG. 18 (model name: F12) is a model in which ribs are added to the back surface of the model shape of FIG. 17 (model name: F1). The simulation is applied to both of them, and which one has less warp deformation after forming, the shape is determined, and feedback is given to the design. Further, FIG. 19 shows the molding conditions, and from the formation of the shape to the warp deformation, the respective results are obtained in accordance with the series of flow as shown in FIG.

20 and 21 show the results of deformation of the rail surface of each model. Comparing the results of both, Fig. 2
It is confirmed that the model 1 has a small amount of deformation. Based on the above results, the shape of the molded product is determined and fed back to the design. The feedback to this design assisted in determining whether the addition of rib shape is effective for warpage deformation.In addition to this, parameters to be applied and fed back to the actual design and molding using this analysis system Examples are strengthening ribs, adding ribs, changing the thickness (effect of uneven thickness, etc.),
There are comparison materials, search for optimum molding conditions, addition and modification of water pipe positions, etc., and as a result, development into product design, mold design, molding, etc. will be done, and the optimum product shape in the overall configuration of FIG. While the condition 8 is fed back, the optimum molding condition 9 for molding is determined and the molding machine 10 is set so as to be useful for molding a desired molded product. In particular, it is a suitable analysis tool for obtaining a molded product such as a camera body that requires a flatness of the photosensitive surface.

[0050]

As described above, according to the present invention, it is possible to provide a warp deformation prediction method for injection molded products and an apparatus therefor, which can accurately predict warpage even when the molded product is thin.

[0051]

[Brief description of drawings]

FIG. 1 is a schematic configuration diagram of an overall configuration of an analysis apparatus according to an embodiment.

FIG. 2 is a flowchart of the analysis device of FIG.

FIG. 3 is a balance equation (kinetic method formula).

FIG. 4 is a constitutive equation (stress-strain relational expression).

FIG. 5 is a displacement-strain relational expression.

FIG. 6 is a volume contraction rate calculation formula.

FIG. 7 is a plan view and a side view of a test piece.

FIG. 8 is a molding condition table.

FIG. 9 is a contraction rate comparison table.

FIG. 10 is a relationship diagram of the shrinkage rate in the plate thickness direction and the volumetric shrinkage rate.

FIG. 11 is a relationship diagram of a shrinkage rate in the resin flow direction and a volumetric shrinkage rate.

FIG. 12 is a relationship diagram of the shrinkage ratio and the volumetric shrinkage ratio in the direction perpendicular to the resin flow.

FIG. 13 is a diagram showing the relationship between the shrinkage ratio and the volume shrinkage ratio of the glass fiber-containing resin in the plate thickness direction.

FIG. 14 is a diagram showing the relationship between the in-plane shrinkage rate and the volumetric shrinkage strain of resin containing glass fiber.

FIG. 15 is an external perspective view of a sample (sheet feed guide).

FIG. 16 is a relationship diagram of the amount of deformation for each position in FIG. 15.

FIG. 17 is a model diagram of a sample (camera body).

FIG. 18 is a model diagram of a sample (camera body).

FIG. 19 is an analysis condition table for the samples (camera bodies) of FIGS.

20 is an analysis result diagram of the sample (camera body) in FIG.

FIG. 21 is an analysis result diagram of the sample (camera body) of FIG. 18.

[Explanation of symbols]

 1 data input device 2 resin database 3 molding condition input 5 analysis calculation device

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[Procedure amendment]

[Submission date] June 1, 1995

[Procedure Amendment 1]

[Document name to be amended] Statement

[Name of item to be corrected] Brief description of the drawing

[Correction method] Change

[Correction content]

[Brief description of drawings]

FIG. 1 is a schematic configuration diagram of an overall configuration of an analysis apparatus according to an embodiment.

FIG. 2 is a flowchart of the analysis device of FIG.

FIG. 3 is a balance equation (kinetic method formula).

FIG. 4 is a constitutive equation (stress-strain relational expression).

FIG. 5 is a displacement-strain relational expression.

FIG. 6 is a volume contraction rate calculation formula.

FIG. 7 is a plan view and a side view of a test piece.

FIG. 8 is a table of molding conditions.

FIG. 9 is a chart for comparison of shrinkage rates.

FIG. 10 is a relationship diagram of the shrinkage rate in the plate thickness direction and the volumetric shrinkage rate.

FIG. 11 is a relationship diagram of a shrinkage rate in the resin flow direction and a volumetric shrinkage rate.

FIG. 12 is a relationship diagram of the shrinkage ratio and the volumetric shrinkage ratio in the direction perpendicular to the resin flow.

FIG. 13 is a diagram showing the relationship between the shrinkage ratio and the volume shrinkage ratio of the glass fiber-containing resin in the plate thickness direction.

FIG. 14 is a diagram showing the relationship between the in-plane shrinkage rate and the volumetric shrinkage strain of resin containing glass fiber.

FIG. 15 is an external perspective view of a sample (sheet feed guide).

FIG. 16 is a relationship diagram of the amount of deformation for each position in FIG. 15.

FIG. 17 is a model diagram of a sample (camera body).

FIG. 18 is a model diagram of a sample (camera body).

FIG. 19 is a chart of analysis conditions of the samples (camera bodies) of FIGS.

20 is an analysis result diagram of the sample (camera body) in FIG.

FIG. 21 is an analysis result diagram of the sample (camera body) of FIG. 18.

[Explanation of symbols] 1 data input device 2 resin database 3 molding condition input 5 analysis calculation device

Claims (2)

[Claims] 1. Injection molding for predicting the behavior of plastic resin in a mold during a filling, holding, and cooling process by a basic formula formulated by the finite element method, and for predicting subsequent warpage deformation of the plastic molded product. A method for predicting warpage deformation of a product, particularly for a thin-walled molded product having a remarkable anisotropic behavior, ## EQU1 ## (Expression of shrinkage anisotropy) εz = A + B · ev εp = (ev−εz) / 2 εz: Shrinkage in the plate thickness direction, εp: Shrinkage in the in-plane direction, ev: Volume shrinkage, A, B: Shrinkage coefficient [Equation 2] (Expression of shrinkage anisotropy in the case of a material containing fibers) εL = (Ev−εz) ・ αL / (αL + αT) εT = (ev−εz) ・ αT / (αL + αT) εL: Shrinkage in the in-plane flow direction, εT Shrinkage in the direction perpendicular to the in-plane flow αL: Flow direction Thermal expansion coefficient, αT: Introducing the relational expression of thermal expansion coefficient in the direction perpendicular to the flow into the calculation to obtain the in-plane shrinkage ratio Warpage prediction method of an injection molded article and performing prediction. 2. Injection molding for predicting the behavior of the plastic resin in the mold during the filling, holding and cooling processes by the basic formula formulated by the finite element method, and for predicting the subsequent warpage deformation of the plastic molded product. An apparatus for predicting warpage deformation of a product, particularly in a thin-walled molded product with remarkable anisotropic behavior, ## EQU3 ## (equation of shrinkage anisotropy) εz = A + B · ev εp = (ev−εz) / 2 εz: Shrinkage ratio in the thickness direction, εp: Shrinkage ratio in the in-plane direction, ev: Volume shrinkage ratio, A, B: Shrinkage coefficient [Equation 4] (Formula of shrinkage anisotropy in the case of a material containing fibers) εL = (Ev−εz) ・ αL / (αL + αT) εT = (ev−εz) ・ αT / (αL + αT) εL: Shrinkage in the in-plane flow direction, εT Shrinkage in the direction perpendicular to the in-plane flow αL: Flow direction Thermal expansion coefficient, αT: equipped with analytical calculation means for introducing the relational expression of the thermal expansion coefficient in the direction perpendicular to the flow into the calculation, Determined shrinkage of the inner, injection-molded articles of warpage deformation prediction apparatus and performing prediction of warpage.