Int J Adv Manuf Technol DOI 10.1007/s00170-006-0435-4
O R I G I N A L A RT I C L E
Cheng-Hsien Wu . Yu-Jen Huang
The influence of cavity deformation on the shrinkage and warpage
of an injection-molded part
Received: 10 May 2005 / Accepted: 28 November 2005 / Published online: 4 April 2006
# Springer-Verlag London Limited 2006
Abstract As soon as the gate solidifies or the nozzle is closed, the amount of melt inside a cavity remains constant. At this moment, the cavity deformation affects the final product shape and size. A set of simulation procedures has been developed in this study to estimate the cavity deformation which arises during an injection-molding process. A mold-filling program was applied to calculate the molding variables. The estimated cavity pressure, temperature distribution, and clamping force were em-ployed as the boundary conditions in the mold-deformation analysis. A structural analysis program was developed to predict the cavity deformation. Molding experiments were carried out for polymethyl methacrylate (PMMA) wedge-shaped parts. To verify the structural analysis, a strain gauge was installed on the sidewall of the mold. The measured strains agreed with the simulated results. A commercial simulation software package was also used to predict the shrinkage and warpage of injection-molded parts. Numerical results showed the improvement in predicting the shape and size of a final product by taking the cavity deformation into account. The influences of the packing pressure, mold temperature, or melt temperature on shrinkage and warpage were also investigated.
Keywords Injection molding . Shrinkage . Warpage . Deformation
1 Introduction
The injection-molding process involves the injection of a polymer melt into a mold, where the melt cools and solidifies to form a plastic product. The process comprises filling, packing, and cooling phases. During these
processes, the residual stress is produced due to high pressure, temperature change, and the relaxation of poly-mer chains, resulting in shrinkage and warpage of the part. In order to yield a product with high precision, the optimum mold geometry and processing parameters must be found. To reduce the cost and time required at the design stage, it is important to simulate shrinkage and warpage of the injection-molded part considering residual stress [1].
Shrinkage and warpage are two important factors determining the quality of injection-molded parts. The packing pressure, melt temperature, mold temperature, and packing time affect the shrinkage and warpage behavior [2]. Injection-molding processes can be simulated with some commercial software. The shrinkage and warpage of injection-molded parts can also be predicted. However, a significant discrepancy was found between the simulated and experimental results [3]. One reason for this is that the shrinkage of injection-molded parts could be anisotropic. The complicated dimensional change is caused by uneven cooling, non-uniform planar volumetric shrinkage, and differential thermal strain due to geometric effects. This effect increases the difficulty in molding simulation. Another possible reason is that commercial software does not consider the mold deformation. If the cavity is distorted, the shape or size of the molding is affected.
The industry continuously requires more accurate and precise results from simulation software. Simulations have to consider more detailed aspects of the process, the material, and the mold. Therefore, the obtained results can be closer to reality and contain all of the information required to describe product properties accurately and completely [4].
As the injected melt solidifies because of the cold mold walls, the screw presses additional melt into the mold under a holding pressure to compensate for the shrinkage of the polymer. The result is that air bubbles and sink marks in the molding may be eliminated, and shrinkage and warpage can be minimized.
Pressure gradients during the packing phase depend on the process and design parameters, and are also affected by the mold elasticity. Mold elastic deformation can play a C.-H. Wu (*) . Y.-J. Huang
Department of Mechanical and Automation Engineering, Da-Yeh University,
Changhua, Taiwan, 51505, Republic of China e-mail: chengwu@mail.dyu.edu.tw
Tel.: +886-4-8511888 Fax: +886-4-8511227
32:
significant role in the cavity pressure–time history. To assess the importance of mold deformability, Leo and Cuvelliez [5] added a strain gauge to the setup and monitored the flexural strain of the mold backplate. The deflection and cavity pressure observations have been found to agree with a simple model of the holding phase, including an elastic volumetric expansion of the cavity under pressure.
Tests were performed by Pantani et al. [4] with different holding programs up to pressures high enough to give evidence of the effect of mold deformation. Molding tests were simulated by means of a software code with the aim of understanding the role and relevance of mold deformation, and of some options for thermal boundary conditions to the modeling and simulation of the post-filling steps. Com-parison between the simulation results and the experi-mental data shows that considering a rigid mold can lead to predicted values of post-filling pressure profiles much different from experimental profiles.
The pressure in the melt can reach very large values during the packing process. Because of such internal pressures, molds are exposed to a high mechanical loading that induces a deformation. The main cavity deformation is concentrated along the direction perpendicular to the largest surface, i.e., along the thickness direction.
To prevent the mold from being opened, an appropriate clamping force is applied by the clamping unit. The mold is compressed along the thickness direction. The clamping force compresses the mold and which also results in a deformation.
The original mold size is measured at 25°C. The mold is conditioned by cooling channels to a specified mold temperature. The cavity wall is also heated when it comes in contact with the injected melt. Thermal loading leads to the thermal expansion of the mold.
The purpose of this paper is to assess the influence of mold deformation on the product accuracy. A numerical approach was developed to estimate mold deformation. First, mold-filling analysis was conducted to obtain the molding information. Then, the predicted cavity pressure and temperature, along with the applied clamping force, were applied as the boundary conditions in the mold deformation analysis. The predicted strains were compared with the strains measured by installing a strain gauge on the sidewall of the mold. After verifying the strain data, the mold deformation analysis can be applied. The shrinkage and warpage of injection-molded parts were calculated based on the mold-filling program by taking cavity deformation into account. To check the accuracy of the numerical approach, the predicted product shape and size were compared with the measured results. The influence of the packing pressure, mold temperature, or melt temper-ature on shrinkage and warpage were also studied.
Table 1 Values of the 7-constant Cross-WLF (Williams-Landell-Ferry) model for the polymethyl methacrylate (PMMA) used in the numerical simulation Symbol Value n 0.2136 τ* 1.37×105Pa D1 1.9×1013Pa s D2 377.1°K D3 0 A1 33.05 eA2 51.6°K
Table 2 Values of the double-domain Tait model for the PMMA used in the numerical simulation
Symbol Value b1,m 8.629×10−4m3/kg b2,m 5.55×10−7m3/kg°K b3,m 1.838×108Pa b4,m 0.003879°K−1 b1,s 0.0008629 m3/kg b2,s 1.71×10−7m3/kg°K b3,s 3.282×108Pa b4,s 0.00432°K−1 b5 378.6°K b6 3.8×10−7°K/Pa b7 0 b8 0 b9 0 65.5mm 86mm 1mm 4mm
Fig. 1 Designed geometry and dimensions of the cavity
Movable plates
Movable insert
Fixed plates
Fixed insert
2 Experimental analysis 2.1 Material
The material used in this study is a commercially available injection-molding grade of polymethyl methacrylate (PMMA). The material was pre-conditioned at 120°C for 4 h using a dehumidifying drier before molding. The relevant properties of the material are summarized below.
Viscosity curves of the polymer are well described in the whole pressure, temperature, and shear rate ranges of interest by a 7-constant Cross-WLF (Williams-Landell-Ferry) model [6–8]: η ¼ η0 1þ η0γ : τ 1n (1) η0 ¼ D1exp A1 T T ð Þ A2þ T Tð Þ (2) T¼ D2þ D3p (3) A2¼ eA2þ D3p (4)
The values of the constants are listed in Table1.
A double-domain Tait model [1, 8] was applied to represent the PMMA used in this study:
v Tð ; pÞ ¼ v0ð Þ 1 C ln 1 þT p B Tð Þ þ vtðT; pÞ (5) where C=0.0894. The double-domain representation is then given as:
v0ð Þ ¼ bT 1;mþ b2;mT b1;sþ b2;sT if T> Tg T< Tg (6) B Tð Þ ¼ b3;mexp b4;mT b3;sexp b 4;sT if T> Tg T< Tg (7) vtðT; pÞ ¼ b 0 7exp b 8T b9p if T > Tg T< Tg (8) where T T b5. In addition, the transition temperature is assumed to be a linear function of pressure:
Tgð Þ ¼ bp 5þ b6p: (9)
The values of the constants are listed in Table2.
2.2 Part geometry and mold design
The product is an 86-mm×65.5-mm rectangular wedge-shaped plate. The thickness varies from 4 mm at one end to
Fig. 3 A molded part
a
b Mid-surface= LS plane
LS plane
Mid-surface
Fig. 4 a, b Schematic illustrations of (a) an undeformed part and (b) a deformed part
1 mm at the other end. The designed geometry and dimensions of the test part are shown in Fig.1.
A special mold, as shown in Fig. 2, was designed for injection-molding processes. The mold has a cold round runner system of diameter 5 mm and a sprue of diameter 5 mm. The film gate has dimensions 6 mm×20 mm×2 mm.
The mold plates and the inserts are made of S55C(1055) steel and STAVAX steel. The Young’s modulus and the thermal expansion coefficient of each part are similar and are around 210 GPa and 11.4μm/m°C, respectively. 2.3 Molding
Molding operations were conducted with an injection-molding machine. The machine can offer a clamping force up to 220 tons. The screw diameter is 50 mm and the shot capacity is 490 cm3. The stroke of the injection system was increased from 1 mm to 13 mm for the injection-molding experiments. From the measured weights of the products, 12 mm was found to be an appropriate stroke.
Under each set of process conditions, 10 shots were made to ensure that the process was stable before the samples were collected. If no significant variation was observed during these first 10 runs, the molded parts from the next 5 runs were collected as the samples for product characterization. A molded part is shown in Fig.3.
2.4 Measurements
The measurement along the diagonal was taken for each molded part using a digital caliper with a minimum reading of 1μm. The in-plane shrinkage was calculated based on the following equation:
In plane shrinkage ¼ Lcavity Lpart
; (10)
whereLcavityis the diagonal length of the cavity andLpartis the diagonal length of the part.
The warpage measurement system consists of two digital dial gauges positioned head-to-head to measure the warpage across the width of the part. The dial gauges were fixed on the spindle of a CNC machine center. To measure different points of the product, the working table was moved by operating the controller. Sixty-three points (9 points×7 points) are specified as the measured points. At each measured location, the point equi-spaced between the upper and lower surfaces is called the point. A mid-surface can be formed by grouping these mid-points together. Because the upper and lower surfaces may not be parallel, deformation of the mid-surface is implemented to define the warpage of the product. Curve fitting is applied to this mid-surface and a least square plane (LS plane) can be obtained. A schematic notation for the definitions of these planes is illustrated in Fig.4. Along the perpendicular direction of the LS plane, the transverse distance between the highest point and the lowest point is defined as the product warpage.
3 Procedures for estimating cavity deformation The temperature decrease results in the shrinkage and warpage of the product. The effects of cavity deformation and melt deformation can be added together. The total value is equal to the final product deformation.
A mold-filling program is developed and applied to carry out the injection-molding simulation. The filling of thin cavities of arbitrary planar geometry may be described in terms of a generalized Hele-Shaw flow. According to the previous investigations [9–11], the governing equations for the flow field can be written as:
@ρ @tþ @@xð Þ þ @ρu @yð Þ þ @ρv @zð Þ ¼ 0;ρw (11) 0 ¼ @ @z η @u @z @ρ @x; (12) 0 ¼ @ @z η @v @z @ρ @y; (13)
where x, y are the planar coordinates, z the gap-wise direction coordinate, (u, v, w) the flow velocity in local (x, y, z) directions, ρ the density, t the time, η the shear velocity, andp is the pressure.
Because most injection-molded parts are thin plate geometries, thermal energy is transferred mostly in the in-plane direction. Neglecting thermal diffusion along the plane direction, the energy equation can be expressed by:
ρcplð Þ @T T @t þ u @ T @xþ v @ T @y ¼ @ @z klð Þ @T T @z þ ηγ: 2; (14) Fig. 6 Finite element division of the mold
ρcpsð Þ @T T @t ¼ @@z ksð Þ @T T @z ; (15)
whereT is the temperature, cpthe specific heat, andk is the thermal conductivity of the material, with subscriptsl and s denoting the liquid and solid phases, respectively. Further, the shear rateγ: is defined by:
γ: ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi @u @z 2 þ @v @z 2 s (16) In addition, the following boundary conditions should be applied: u¼ 0 ¼ v ¼ w; T ¼ Tw at z¼ h; (17) @u @z¼ 0 ¼ @v @z¼ @ T @z; w ¼ 0 at z¼ 0; (18) ksð Þ @T Ts @z ¼ klð Þ @T Tl @z at z¼ δ; (19)
whereh is the thickness of the cavity and δ is the half-thickness of the liquid zone. During the packing and cooling stages, the pressure over most of the regions in the cavity becomes equal to the packing pressure. A hybrid numerical scheme is employed in which the planar coordinates are described in terms of finite elements, and the gapwise and time derivatives are expressed in terms of finite differences.
A wedge-shaped plate with a runner system was modeled and meshed as shown in Fig.5. The total number of nodes is 638, the total number of triangular elements is 1,088, and the number of one-dimensional elements is 51. The mold-filling program was executed after specifying the process conditions. The simulation results includes the
a
b Calculated pressure and
temperature distribution on the sprue and the runner
Initial temperature 25ºC Coupled with movable plate Fixed in 6 degrees of freedom Mold temperature Calculated temperature and pressure distribution Constrained by fixed plate Mold temperature Initial temperature 25ºC Fig. 7 a, b Specified loads and
boundary conditions of (a) the fixed plate and (b) the insert of the fixed mold half
related processing conditions during the molding pro-cesses, such as flow front advancement, temperature distribution, melt velocity, pressure distribution, etc.
Part of the cavity deformation is caused by the cavity pressure, which can be influenced by the cavity
deforma-tion. To increase the accuracy of the mold deformation analysis, the molding analysis and structural analysis should be run simultaneously to describe the real physics of the phenomenon. The coupling of the molding analysis and structural analysis complicates the simulation. From some
a
b Calculated pressure and
temperature distribution on the runner Clamping force Initial temperature 25ºC Mold temperature Coupled with fixed plate Calculated temperature and pressure distribution Mold temperature Coupled with movable plate Initial temperature 25ºC Fig. 8 a, b Specified loads and
boundary conditions of (a) the movable plate and (b) the insert of the mobile mold half
Fig. 9 Location of strain gauge on the side wall of the mobile mold half
initial tests, the cavity deformation is small compared to the cavity size. Therefore, the cavity deformation has little effect on the cavity pressure. The cavity pressure predicted by the molding analysis does not need to be modified after carrying out structural analysis. The molding analysis and structural analysis can be decoupled and independently executed.
To calculate the mold deformation just before the gate solidifies or the nozzle is closed, a three-dimensional thermo-elastic analysis has been developed. The potential energy of an elastic bodyπpis defined as [12]:
πp ¼ π Wp (20)
whereπ is the strain energy and Wpis the work done on the body by the external forces.
The strain energy of a linear elastic body is defined as:
π ¼12 Z V " f gT D ½ "f gdV Z V " f gT D ½ "f gdV0 (21) where {ɛ}, {ɛ0}, and [D] represent the strain vector, initial strain vector, and the matrix of material property, respectively.V is the volume of the body.
The work done by the external forces can be expressed as:
Wp¼ Z V δ f gT F ½ dV þ Z S δ f gTf gdS þ QΦ f gT Pc f g (22) where {F}, {Φ}, and {Pc} denote the known body force vector, vector of prescribed surface forces (tractions), and concentrated forces and/or moments applied to the body, respectively. {δ} is a displacement vector and {Q} presents the displacement and/or rotation vector.
The displacement vector {δ} within an element can be described as:
δ
f g ¼ N½ Qf g (23)
where [N] is the matrix of the shape function and {Q} is the vector of nodal displacement degrees of freedom.
The strain vector {ɛ} appearing in Eq. 21 can be expressed in terms of the vector of nodal displacement degrees of freedom {Q} as:
"
f g ¼ B½ Qf g (24)
where [B] is the geometric differentiation of the shape function [N]. a 0 0.05 0.1 0.15 0.2 0.25 0.3 4 5 6 7 8
Packing pressure (MPa)
Product shrinkage (mm) b 0.022 0.0222 0.0224 0.0226 0.0228 0.023 0.0232 4 6 8
Packing pressure (MPa)
Cavity expansion (mm)
Fig. 10 a Product shrinkage (molding simulation). b Cavity expansion vs. packing pressure
a 0.037 0.0375 0.038 0.0385 0.039 0.0395 0.04 0.0405 20 25 30 35 40 45 Mold temperature ( ºC) Product shrinkage (mm) b 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 20 25 30 35 40 45 Mold temperature (ºC ) Cavity expansion (mm)
Fig. 11 a Product shrinkage (molding simulation). b Cavity expansion vs. mold temperature
Substituting Eqs. 23 and 24 into Eq. 20 yields the potential energy of the element as:
πp¼12 R V Q f gT B ½ T D ½ B½ Qf gdV R V Q f gT B ½ T D ½ "½ dV0 R V Q f gT N ½ T F f gdV R S Q f gT N ½ Tf gdS QΦ f gT Pc f g (25) Minimizing the potential energy of the element yields: Z V B ½ T D ½ B½ dV Qf g ¼ Z V B ½ T D ½ "f gdV þ0 Z V N ½ T F f gdV þ Z S N ½ T Φ f gdS þ Pf gc (26)
which can also be expressed as: K
½ Qf g ¼ Pf g þ Pi f g þ Pb f g þ Ps f g ¼ Pc f g (27) where [K] is the stiffness matrix and {Pi}, {Pb}, and {Ps} denote load vectors due to initial strains, body forces, and surface forces, respectively. Thus, the nodal deflection {Q}
can be obtained by solving Eq.27. It is worth mentioning that the free expansion of an isotropic material with principal axesxyz produces the initial strains:
"0
f g ¼ "xx0; "yy0; "zz0; γxy0; γyz0; γzx0
n oT
¼ αT; αT; αT; 0; 0; 0f gT (28) whereα is the coefficient of thermal expansion and T is the temperature change. The cavity pressure and clamping force can be expressed in {Ps}, the load vectors due to surface forces.
Four-node tetrahedral elements are chosen in this study. Each node has three translational degrees of freedom in the nodal x, y, and z directions, as well as rotations about the nodalx, y, and z directions. Finite element division of the mold is shown in Fig.6.
As previously stated, three sources which cause mold deformation are the cavity pressure, clamping force, and temperature increase. Mold deformation changes the cavity dimensions and affects the melt quantity inside the cavity. As the gate solidifies, no more polymer flow can be generated through the gate. In some cases, the gate may not be completely frozen when packing stops. While packing ends, the nozzle is closed and no more polymer flows through the gate. At this moment, deformation relative to the original cavity affects the final product dimension. An expanded cavity contains more melt and the product size increases, while a shrunk cavity contains less melt and the
a b 0.0116 0.0118 0.012 0.0122 0.0124 0.0126 4 5 6 7 8
Packing pressure (MPa)
Product warpage (mm) 0.00776 0.0078 0.00784 0.00788 0.00792 4 5 6 7 8
Packing pressure (MPa)
Cavity warpage (mm)
Fig. 12 a Product warpage (molding simulation). b Cavity warpage vs. packing pressure a b 0.01 0.011 0.012 0.013 0.014 0.015 200 210 220 230 240 250 260 Melt temperature (ºC ) Product warpage (mm) 0.0074 0.0076 0.0078 0.008 0.0082 0.0084 0.0086 0.0088 200 210 220 230 240 250 260 Melt temperature (ºC ) Cavity warpage (mm)
Fig. 13 a Product warpage (molding simulation). b Cavity warpage vs. melt temperature
product size decreases. During the cooling stage, the melt quantity stays constant, while the pressure or the volume reduces due to thermal shrinkage.
The effects of cavity deformation and melt deformation can be superimposed. The total value is equal to the thermal error of the final product. Both the temperature field and the pressure distribution of the cavity are obtained from the mold-filling simulation. Three sets of boundary conditions are applied to calculate the thermal deformation of the cavity. The cavity temperature field, along with the mold temperature, is applied to calculate the thermal deformation of the mold. The other two sets, the cavity pressure distribution and the clamping force, are employed to predict the compressive deformation of the mold. The thermal deformation is predicted by conducting the struc-tural analysis.
The specified loads and boundary conditions are shown in Figs.7and 8. The fixed mold half is composed of a fixed plate and a mold insert. The fixed plate contains a sprue, a runner, and a gate, as shown in Fig.7a. Each node on the outside surface is fixed with six degrees of freedom because the plate is clamped to the injection-molding machine. The initial temperature of the mold is room temperature (25°C). During the molding process, the temperature of the mold is equal to the specified mold temperature, i.e., the prescribed temperature of the cooling channels. The inside surface of the fixed mold half is coupled with the inside surface of the mobile mold half. Figure 7b illustrates the specified loads and boundary conditions of the insert. The initial temper-ature is set at room tempertemper-ature (25°C). When the gate is closed or frozen, the cavity temperature and pressure distribution can be obtained by conducting the mold-filling analysis. The simulated temperature and pressure distribu-tion of the cavity wall are specified on the inside surface of the insert. The other portion of the fixed mold half is specified at the mold temperature. The outside surface of the insert is coupled with the fixed plate.
The specified loads and boundary conditions of the mobile mold half are similar to those of the fixed mold half. The only difference is that the outside surface of the movable plate is loaded with a clamping force instead of being fixed. The detailed boundary conditions are shown in Fig.8.
The mold deforms in three-dimensional directions. The in-plane cavity expansion is defined based on the following equation:
in plane cavity expansion ¼ L0cavity Lcavity
; (29)
where L0cavity is the diagonal length of the deformed cavity andLcavityis the diagonal length of the original cavity.
In addition to the in-plane cavity expansion, the cavity warpage is also investigated. The results of the structural analysis are applied to calculate the cavity warpage. Similar to the warpage measurement, the cavity warpage is calculated based on the mid-surface of the planar cavity walls. The transverse distance between the highest node and the lowest node is defined as the cavity warpage.
4 Verification of strain analysis
To verify the simulated strain of the mold, the strain induced by mold deformation was also measured in this study. A one-dimensional strain gauge (KFG-10-120-C1-11, KYOWA) was stuck on the mold wall. The specified processing conditions are as follows: a melt temperature of 230°C, a mold temperature of 33°C, an injection speed of 11.4 cm/s, a packing pressure of 4.5 MPa, a packing period of 10 s, and a cooling time of 30 s. The processing conditions are applied to the mold filling and the structure analysis programs. The preliminary result shows that the maximum strain exists at the insert of the movable mold half. However, it is difficult to stick the strain gauge on to the insert. The strain gauge was installed on the edge corner of the mobile mold half, as shown in Fig.9. The strain at this point was also calculated by executing the structure analysis program. The predicted strain was compared with the measured strain to check the accuracy of the numerical model.
Table 3 Three investigated process conditions Case no. Mold temperature (°C) Melt temperature (°C) Injection velocity (cm/s) Packing pressure (MPa) Packing time (s) Cooling time (s) A 33 240 10.2 4.5 8 35 B 33 230 10.2 4.5 8 30 C 33 230 11.4 7.5 10 35
Table 4 Measured and simulated shrinkages vs. cavity deformation Case no. Measured
shrinkage Simulated shrinkage (mold-filling simulation) Deviation Cavity deformation (structural analysis) A 0.23 mm 0.2608 mm −0.0308 mm 0.0254 mm B 0.25 mm 0.2752 mm −0.0252 mm 0.0246 mm C 0.075 mm 0.105 mm −0.0300 mm 0.0230 mm
Table 5 Measured and simulated warpages vs. cavity expansion Case no. Measured warpage Simulated warpage (mold-filling simulation) Deviation Cavity expansion (structural analysis) A 0.0256mm 0.0130 mm 0.0126mm 0.0089 mm B 0.0278mm 0.0138 mm 0.0140mm 0.0085 mm C 0.0210mm 0.0123 mm 0.0087mm 0.0080 mm
Three sets of experiments were carried out to verify the numerical method. The three packing pressures are 4.5 MPa, 6 MPa, and 7.5 MPa. The measured strains are 93×10−6, 88×107−6, and 85×10−6, respectively. The simulated strains are 128×10−6, 127.43×10−6, and 115.1×10−6. The discrepancies between the simulated and the experimental results are 25∼1/430%. Both the simula-tion and experimental results reveal that the strain decreases with packing pressure. To explain this tendency, further verifications were carried out.
As previously stated, the three loading conditions are temperature increase, packing pressure, and clamping force. Assuming that these three loading conditions are independent, each condition is separately discussed. Firstly, only the temperature increase is applied to calculate the strain. The strain is about −15×10−6 for packing pressures of 4.5 MPa, 6 MPa, and 7.5 MPa. Secondly, only the clamping force is applied to calculate the strain. The strain is about 143×10−6 for different packing pressures. Lastly, only the packing pressure is applied to calculate the strain. The strains are 0, −1.6×10−6, −13.6×10−6 for the different packing pressures.
The packing pressure compresses the mold and produces a compressive strain on the sidewall of the mold. The compressive strain increases with the packing pressure. The strain resulting from the temperature increase and the clamping force does not change with the packing pressure. If these three effects are added together, the strain decreases with the packing pressure. This verification explains why both the measured strain and the simulated strain decrease with the packing pressure.
5 Parametric study 5.1 Shrinkage
The optimum processing conditions that generate the lowest shrinkage are a packing pressure of 7.5 MPa, a packing period of 10 s, a mold temperature of 33°C, an injection velocity of 11.4 cm/s, a melt temperature of 230°C, and a cooling time of 30 s [3]. By applying the Taguchi method, the packing pressure and mold temper-ature are found to be the most important factors. Numerical analysis is applied to study the effects of these two factors on mold deformation.
Three packing pressures were applied to calculate mold deformation and product shrinkage. The molding-filling simulation predicts product shrinkage, and the structural analysis program predicts mold deformation. Because the packing procedure helps to compensate for insufficient melt, the shrinkage of the product decreases with the packing pressure as shown in Fig.10a. However, the in-plane cavity expansion is found to be almost constant with the packing pressure, as shown in Fig.10b. Combining these two effects, the in-plane shrinkage of the product is smaller than the value predicted by the mold-filling simulation. Expansion enables the cavity to contain more polymeric melt and reduces the in-plane shrinkage of the product.
With similar procedures, three different mold tempera-tures were applied to calculate the mold deformation and product shrinkage. The mold-filling simulation gives the product shrinkage (Fig. 11a) and the structural analysis program predicts the mold deformation (Fig. 12b). The cooling rate is smaller with a higher mold temperature. It reduces the frozen layer and more melt can be packed into the cavity. Therefore, the predicted shrinkage of the product with the mold-filling simulation slightly decreases with the mold temperature. However, the cavity also expands with the mold temperature. About half of the product shrinkage is compensated by cavity expansion. Therefore, cavity expansion helps to control product size.
5.2 Warpage
The optimum processing conditions that generate the lowest warpage are a packing pressure of 7.5 MPa, a packing period of 10 s, a mold temperature of 33°C, an injection velocity of 11.4 cm/s, a melt temperature of 230°C, and a cooling time of 35 s [3]. By applying the Taguchi method, the packing pressure and melt tempera-ture are found to be the most important factors. Numerical analysis is applied to study the effects of these two factors on mold deformation.
Three packing pressures of 4.5 MPa, 6.0 MPa, and 7.5 MPa were applied to calculate mold deformation and product warpage. The mold-filling simulation program was used to predict the product warpage and the structural analysis program was applied to predict the in-plane cavity deformation, as shown in Fig.12. Because the plastic part has a wedge shape, the temperature distribution is not uniform over the cavity. Higher packing pressure produces larger residual stress and creates larger product warpage. Figure 12a reveals that the induced product warpage increases with the packing pressure. However, the cavity warpage is almost constant with the packing pressure, as shown in Fig.12b. Combining these two effects, the final warpage of the product is expected to be less than the value predicted by the mold-filling simulation.
With similar procedures, three different melt tempera-tures were applied to calculate the mold warpage and the product warpage. The mold-filling simulation gives the product warpage and structural analysis predicts mold deformation. The predicted warpage of the product with the mold-filling program increases with the melt temperature, as shown in Fig.13a. The cavity expands and warps with the melt temperature. Figure13b reveals that the predicted cavity warpage also increases with the melt temperature.
6 Case study
Table 3 summarizes the three investigated processing conditions. As seen, the mold temperature and melt temperature are constant, while the other processing variables are changed in these cases. Part shrinkage and warpage were measured. The values are listed in Tables4
and 5. The mold-filling simulation was conducted. Shrinkage and warpage are also shown in Tables4and5. It is found that the measured shrinkage is smaller than the simulated shrinkage. The deviation is considered to result from mold deformation. The mold was simulated by using the structural analysis program and the cavity expansion was close to the deviation. Similarly, the measured warpage is smaller than the simulated warpage. The deviation is considered to result from mold deformation. The cavity warpage was obtained by executing the structural analysis and it was found be close to be the deviation.
The predicted cavity deformation occupies only 10∼31% of the measured product shrinkage in these three cases. The predicted cavity expansion occupies 31∼38% of the measured product warpage in these three cases.
7 Conclusions
An injection-molded part shrinks during the cooling stage. The cavity may also deform because of temperature, clamping force, and cavity pressure increases. Both of these two phenomena affect the final size of the product. A mold-filling program can be used to predict the thermal shrinkage of a plastic part. A structure analysis program can be applied to simulate cavity deformation. Adding these two effects together, the results are in good agreement with the measured size of the product.
In the present study, a physical modeling and a corresponding numerical analysis system has been devel-oped to accurately predict the actual product size by taking mold deformation into account. To prove the validity of the program, two verification tests are carried out. The strain of the mold at certain locations was measured and it was compared with the simulated strain. Three sets of processing conditions were applied to simulate the actual product sizes and they were compared with the measured sizes. The compared results are shown to be in good agreement.
Some conclusions can be drawn from the numerical analyses:
1. The two most important factors for the shrinkage of an injection-molded part are the packing pressure and mold temperature. The packing pressure is the most important of these two factors.
2. Mold-filling simulation does not take account of mold deformation. It can only simulate the shrinkage of the
plastic part without considering the effect of cavity size change. For the processing conditions discussed in this study, the cavity expands and it allows more melt to flow into the cavity. This effect reduces the actual shrinkage of an injection-molded part.
3. An injection-molded part has a larger measured size than the predicted size. There are two error sources resulting in this deviation. One is inaccurate modeling of the commercial software. The other is cavity deformation. In this study, cavity deformation occupies 10∼38% of the product shrinkage and warpage. If the effect of cavity deformation is taken into account, the simulation accuracy can be improved.
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