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b3;s exp b4;sT ifT > TgT < Tg(7)vt T; p0b7 exp b8T b9p ifT > TgT < Tg(8)where T T b5 . In addition, the transition temperatureis assumed to be a linear function of pressure:Tg p b5 b6p: (9)The values of the constants are listed in Table
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2.2.2 Part geometry and mold designThe product is an 86-mm×65.5-mm rectangular wedge-shaped plate. The thickness varies from 4 mm at one end tobMid-surface= LS planeLS 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 anddimensions of the test part are shown in Fig. 1.A special mold, as shown in Fig. 2, was designed forinjection-molding processes. The mold has a cold roundrunner system of diameter 5 mm and a sprue of diameter5 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 thethermal expansion coefficient of each part are similar andare around 210 GPa and 11.4 μm/m°C, respectively.2.3 MoldingMolding operations were conducted with an injection-molding machine. The machine can offer a clamping forceup to 220 tons. The screw diameter is 50 mm and the shotcapacity is 490 cm3. The stroke of the injection system wasincreased from 1 mm to 13 mm for the injection-moldingexperiments. From the measured weights of the products,12 mm was found to be an appropriate stroke.Under each set of process conditions, 10 shots weremade to ensure that the process was stable before thesamples were collected. If no significant variation wasobserved during these first 10 runs, the molded parts fromthe next 5 runs were collected as the samples for productcharacterization.
A molded part is shown in Fig. 3.2.4 MeasurementsThe measurement along the diagonal was taken for eachmolded part using a digital caliper with a minimum readingof 1 μm. The in-plane shrinkage was calculated based onthe following equation:In plane shrinkage Lcavity Lpart ; (10)where Lcavity is the diagonal length of the cavity and Lpart isthe diagonal length of the part.The warpage measurement system consists of two digitaldial gauges positioned head-to-head to measure thewarpage across the width of the part. The dial gaugeswere fixed on the spindle of a CNC machine center. Tomeasure different points of the product, the working tablewas moved by operating the controller. Sixty-three points(9 points×7 points) are specified as the measured points. Ateach measured location, the point equi-spaced between theupper and lower surfaces is called the mid-point. A mid-surface can be formed by grouping these mid-pointstogether. Because the upper and lower surfaces may not beparallel, deformation of the mid-surface is implemented todefine the warpage of the product. Curve fitting is appliedto this mid-surface and a least square plane (LS plane) canbe obtained. A schematic notation for the definitions ofthese planes is illustrated in Fig. 4. Along the perpendiculardirection of the LS plane, the transverse distance betweenthe highest point and the lowest point is defined as theproduct warpage.3 Procedures for estimating cavity deformationThe temperature decrease results in the shrinkage andwarpage of the product. The effects of cavity deformationand melt deformation can be added together. The totalvalue is equal to the final product deformation.A mold-filling program is developed and applied tocarry out the injection-molding simulation. The filling ofthin cavities of arbitrary planar geometry may be describedin terms of a generalized Hele-Shaw flow. According to theprevious investigations [9–11], the governing equations forthe flow field can be written as:@ρ@t@@xρu@@yρv@@zρw 0; (11)0@@zη@u@z @ρ@x; (12)0@@zη@v@z @ρ@y; (13)where x, y are the planar coordinates, z the gap-wisedirection coordinate, (u, v, w) the flow velocity in local (x,y, z) directions, ρ the density, t the time, η the shear velocity,and p is the pressure.Because most injection-molded parts are thin plategeometries, thermal energy is transferred mostly in the in-plane direction. Neglecting thermal diffusion along theplane direction, the energy equation can be expressed by:ρcpl T@T@tu@T@xv@T@y @@zkl T@T@z ηγ: 2;(14)Fig. 6 Finite element pision of the mold1147 where h is the half-thickness of the cavity and δ is the half-thickness of the liquid zone. During the packing andcooling stages, the pressure over most of the regions in thecavity becomes equal to the packing pressure. A hybridnumerical scheme is employed in which the planarcoordinates are described in terms of finite elements, andthe gapwise and time derivatives are expressed in terms offinite differences.A wedge-shaped plate with a runner system wasmodeled and meshed as shown in Fig. 5. The total numberof nodes is 638, the total number of triangular elements is1,088, and the number of one-dimensional elements is 51.The mold-filling program was executed after specifying theprocess conditions. The simulation results includes the