Modeling and simulation of MIM(11.1-11.2)

Table of Contents

• 11.1 Modeling and simulation of the mixing process

• 11.1.1 Modeling

• 11.1.2 Numerical methods

• 11.1.3 Applications

• 11.2 Modeling and simulation of the injection molding process

• 11.2.1 Theoretical background and governing equations

• 11.2.2 Numerical simulation

• 11.2.3 Experimental-Material properties and verification

• 11.2.4 Applications

11.1 Modeling and simulation of the mixing process

In analysis of the mixing process as relevant to powder injection molding (PIM), we are mostly concerned with distributive mixing without molecular diffusion, governed by the flow kinematics of specific mixer geometry for given material properties and operating conditions. This is the case for flows with an infinite Peclet number. The flow problem in this mixer can be solved using the finite element method (FEM). As for mixing analysis with the kinematics of fluid-particle interactions like the PIM process, a particle-tracking method can be employed . A distribution of particles at a downchannel location is used to characterize the progress of mixing both qualitatively and quantitatively. A measure of mixing, called the information entropy, based on the particle distribution, can be introduced to quantify a degree of mixing.

11.1.1 Modeling

It is assumed that materials to be mixed are homogeneous generalized Newtonian fluids and the flow is governed by viscous force only, neglecting inertia force, which is a reasonable assumption in the mixing analysis of highly viscous PIM feedstock. In the creeping flow regime, continuity and momentum balance equations are given as follows:

where h is the viscosity, D is the rate-of-deformation tensor, p is the pressure, and u is the velocity. The viscosity of a feedstock is generally represented by a function of the shear rate γ , temperature T, and pressure p. The Cross-Williams-Ladel-Ferry (WLF) model, one of viscosity models for the feedstock in PIM, is defined as follows:

where h0 is the zero-shear-rate viscosity described by the WLF model, given by

where A2 ¼ Ae2 + D3p and T*¼D2+D3P and the materials parameters, A1, A2, D1, D2, and D3, are determined by curve fitting using the experimental viscosity data. Although PIM feedstock has a more involved rheological response, the corrections are not significant.

11.1.2 Numerical methods

Finite element formulation

To obtain the velocity field and pressure distribution, the set of governing equations, Eq. (11.1), together with proper boundary conditions, are solved using the Galerkin FEM. The weak formulation for the incompressible Stokes equations is given by

where W is the computational domain, G is the boundary, w is the weighting function for the velocity u, q is the weighting function for the pressure p, and t is the traction force defined by

In three-dimensional (3D) flow simulations, the resulting matrix equation after numerical integration is a huge sparse symmetric matrix. Thus, one needs an efficient method to solve the resulting matrix equation. A parallel direct solver, such as PARDISO (Schenk & G€artner, 2004), can be used to solve the resulting sparse matrix on a parallel computer with multiple CPUs.

Particle-tracking method

Mixing analysis based on a particle-tracking scheme consists of three steps:

1. flow analysis to obtain a velocity field of a mixing device;

2. Particle-tracking step to obtain a distribution of particles at the end of the mixer;

3. quantification of mixing from the obtained particle distribution.

To track the position of particles, the problem to be solved is an ordinary differential equation

where x is the particle position vector, u is the particle velocity, and t is the time. A fourth-order Runge-Kutta method is widely used to integrate the set of ordinary differential equations, Eq. (11.6), with respect to time. However, in some cases, the problem can be simplified such that a 2D problem may be solved instead of a 3D one. By changing the original equation, one can reduce the dimensions of the system and integration can be performed using a fixed spatial increment along the downchannel direction. This approach has several advantages such as faster solution and ease of representing the dynamics at any cross-sectional area in terms of the downchannel direction. This scheme is restricted to problems where all the axial components of the velocity field are positive in the whole domain, i.e., no backflow. The resulting 2D problem is represented as follows:

where u, v, and w denote the velocity components along the x, y, and z coordinates, respectively. Thus, the particles are tracked along the axial position rather than time.

11.1.3 Applications

Mixer and mixing materials

A static mixer, called the Kenics mixer as a mixing device for PIM feedstock preparation, operates in the Stokes flow regime where inertia is negligible. Fig. 11.1 depicts a representative geometry of a six-element static mixer (Fig. 11.1A), with mixing elements twisted by 180 degrees in alternating directions (Fig. 11.1B), that is used in simulations.

The viscosity of the PIM feedstock of carbonyl iron at 63 vol% solids loading is measured by means of a capillary rheometer, following ASTM 3835-96 for three temperatures versus a range of shear rates. From these data, we determined the seven coefficients of the Cross-WLF model by curve fitting: n¼0.4999, τ*¼0.0005734 Pa, D1 ¼1.501011Pa s, D2¼373.15 K, D3¼0 K/Pa, A1¼6.30 K, and Ae2 ¼ 51:6K.

Fig. 11.1 Kenics static mixer. (A) Shaded image of a mixer with six helical elements. (B) two mixing elements twisted by 180 degrees in alternating directions, called LR-180 elements.

Working principle of the Kenics mixer based on flow characteristics

First, the flow problems are solved using the FEM. The mixer geometry is divided into 344 510 ten-node tetrahedral elements with 519 155 nodes. A quadratic interpolation for the velocity and a linear interpolation for the pressure are used, which satisfy the compatibility condition of the interpolation functions for the velocity and pressure. The mixing principle of the Kenics mixer is also based on the baker's transformation consisting of repeated stretching, cutting, stacking, which is realized in a pipe flow with blades twisted by a fixed angle in alternating directions. Fig. 11.2 illustrates the progress of mixing in the first half period, with the blade rotating 180 degrees in a counterclockwise direction. The two fluids are split horizontally by the mixing element (blade) and the split materials are deformed by the helical motion leading to an increase in the number of striations at the end of the operation. At the beginning of the next half-period, the materials are split vertically and similar operations (stretching and stacking) are repeated. The same operations are repeated to the number of mixing elements inserted in the circular channel.

Mixing analysis

A particle-tracking method is used to analyze mixing. Given velocity field, the particles initially located at the interface between the two fluids with different power-law index n are tracked to the end of the mixer geometry. The more uniform the distribution at a cross-sectional area, the better the mixing. The final result of the particle tracking is evident in the distribution of tracer particles. Evaluation of the mixing uniformity is made from the information on the distribution of the particles. A proper measure of mixing is the uniformity of the particle distribution, for example, the information entropy of the particles at any cross section (Kang & Kwon, 2004; Shannon, 1948). Along these lines, characterization of the mixing progress requires first the division of the mixer cross section into a number of cells. Then, for a certain particle configuration, the mixing entropy S is defined as a sum of the information entropy of individual cells constituting the cross-sectional area, defined by

Fig. 11.2 Working principle of the Kenics mixer by the two gray tints representing fluid-particles mixtures.

where N is the number of cells and ni is the particle number density at the ith cell.Instead of direct use of the information entropy in the mixing analysis, we employ a normalized entropy increase S* as a measure of mixing, given by

where S0 is the entropy at the inlet and Smax is the maximum possible entropy, defined by log N, which is the ideal case with a uniform distribution of the particles, i.e., ni¼1/N. Fig. 11.3 shows the progress of mixing characterized by the normalized entropy increase defined in Eq.(11.9). In this plot, the influence of the index n on the progress of mixing is not significant, but this is an example of the parameter study and design process.

11.2 Modeling and simulation of the injection molding process

Models and simulations used for plastics have been applied to PIM, but the high solid content often makes for differences that are ignored in the plastic simulations. Several situations demonstrate the problems, such as powder-binder separation at weld lines, high inertial effects such as in molding tungsten alloys, and rapid heat loss such as in molding copper and aluminum nitride. Also, powder-binder mixtures are very sensitive to shear rate. Thus, the computer simulations, to support molding build from the success demonstrated in plastics, and adapt those concepts in new customized PIM simulations for filling, packing, and cooling.

Fig. 11.3 The progress of mixing characterized by the normalized entropy increase S* along the axial direction z depending on the index n in the viscosity model.

11.2.1 Theoretical background and governing equations

A typical injection molded component has a thickness much smaller than the overall largest dimension (German, 2003). In molding such components, the molten powder-binder feedstock mixture is highly viscous. As a result, the Reynolds number (a dimensionless number characterizing the ratio of inertia force to viscous force) is much smaller than 1 and the flow is modeled as a creeping flow with lubrication, as treated with the Hele-Shaw formulation. With the Hele-Shaw model, the continuity and momentum equations for the melt flow in the injection molding cavity are merged into a single Poisson equationin terms ofthe pressure and fluidity.Computer simulation is usually based on a 2.5-dimensional approach because of the thin wall and axial symmetry. But the Hele-Shaw model has its limitations and cannot accurately describe 3D flow behavior inthe melt front, whichis called fountain flow, and special problems arise with thick parts with sudden thickness changes, which cause race-track flow. Nowadays, several 3D computer-aided engineering (CAE) simulations exist that successfully predict conventional plastic advancement and pressure variation with changes in component design and forming parameters (Kim & Turng, 2004). In this section, we will focus on the 2.5-dimensional approach rather than a full 3D approach, because the 2.5-dimensional approach is more robust and commonly accepted by industry.

Filling stage

PIM involves a cycle that repeats every few seconds. At the start of the cycle, the molding machine screw rotates in the barrel and moves backward to prepare molten feedstock for the next injection cycle while the mold closes. The mold cavity fills as the reciprocating screw moves forward, acting as a plunger, which is called the filling stage. During the filling stage, a continuum approach is used to establish the system of governing equations as follows.

• Mass and momentum conservation: with the assumption of incompressible flow, the mass conservation, also called continuity equation, is expressed as

where x, y, and z are Cartesian coordinates and u, v, and w are corresponding orthogonal velocity components. As for the momentum conservation, with lubrication and the Hele-Shaw approximation, the Navier-Stokes equation is modified for molten feedstock during filling stage as follows (Chiang, Hieber, & Wang, 1991; Hieber & Shen, 1980):

where P is the pressure, z is the thickness, and h is the viscosity of PIM feedstock. Combining Eqs.(11.10), (11.11) with integration in the z-direction (thickness direction) gives

where

Eq. (11.12) is the flow-governing equation for the filling stage. This is exactly the same form as the steady-state heat conduction equation obtained by substituting temperature T into P and thermal conductivity k into S. In this analogy, S is the flow conductivity or fluidity. As a simple interpretation of this flow-governing equation, molten PIM feedstock flows from the high-pressure region to the low-pressure region, and the speed of flow depends on the fluidity S.

• Energy equation: in accordance with the lubrication and Hele-Shaw approximations during the filling stage, the energy equation is simplified as follows:

where ρ is the molten PIM feedstock's density, CP is the molten PIM feedstock's specific heat,  γ=√(∂u/∂z)^2+(∂u/∂z)^2the generalized shear rate, and k is the thermal conductivity of the feedstock.

In addition, we need a constitutive relation to describe the molten PIM feedstock's response to its flow environment during cavity filling, which requires a viscosity model. Several viscosity models for polymers containing high concentrations of particles are available. Generally, they include temperature, pressure, solids loading, and shear rate, and selected models will be introduced later in this chapter. The selection of a viscosity model depends on the desired simulation accuracy over the range of processing conditions, such as temperature and shear rate, as well as access to the experimental procedures used to obtain the material parameters.

Once we have the system of differential equations from continuum-based conservation laws and the constitutive relations for analysis of the filling stage, then we need boundary conditions. Typical boundary conditions during the filling stage are as follows:

• boundary conditions for flow equation: flow rate at injection point, free surface at melt-front, no slip condition at cavity wall;

• boundary conditions for energy equation: injection temperature at injection point, free surface at melt-front, mold-wall temperature condition at cavity wall.

Note that the only required initial condition is the flow rate and injection temperature at the injection node, which is one of the required boundary conditions.

Packing stage

When mold filling is nearly completed, the packing stage starts. This precipitates a change inthe ram control strategy fortheinjection molding machine, from velocity control to pressure control, which is called the switchover point. As the cavity nears filling, the pressure control ensures fulfilling and pressurization of the filled cavity prior to freezing of the gate. It is important to realize the packing pressure is used to compensate for the anticipated shrinkage in the following cooling stage. Feedstock volume shrinkage results fromthe highthermal expansion coefficient ofthe binder, so on coolingthere is a measurable contraction. Too low a packing pressure before the gate freezes results in sink marks due to the component shrinkage, while too high a packing pressure results in difficulty with ejection. Therefore appropriate pressurization prior to cooling is critical for component quality. Forthe analysis of the packing stage,it is essential to include the effect of melt compressibility. Consideration is given to the melt compressibility using a dependency of the specific volume on pressure and temperature, leading to a feedstock-specific pressure-volume-temperature (pvT) relationship, or the equation of state. Several models are availableto describethe pvTrelation of PIM feedstock, such as the two-domain modified Tait model and IKV model. These models predict an abrupt volumetric change for both semi-crystalline polymers used in the binder and the less abrupt volume change for amorphous polymers used in the binder.

With the proper viscosity and pvT models, the system of governing equation for the packing stage based on the continuum approach is as follows.

• Mass conservation: the continuity equation of compressible PIM feedstock is expressed as

with the assumption that pressure convection terms may be ignored in the packing stage this becomes

where κ is the isothermal compressibility coefficient of the material (∂ρ/ρ∂p) and β measures the volumetric expansivity of the material (∂ρ/ρ∂T). Those are easily calculated from the equation of state. Note that the same momentum conservation is used as Eq. (11.12) regardless of the material to be considered as compressible or not.

• Energy equation: the energy equation is derived as

That is, the shear rate for the compressible case in packing is for practical purposes the same as for the filling phase.

Typical initial and boundary conditions during packing stage are as follows:

• initial conditions: pressure, velocity, temperature, and density from the results of the filling stage analysis;

• boundary conditions for equations of mass and momentum conservations: prescribed pressure at injection point, free surface at melt-front, no slip condition at cavity wall;

• boundary conditions for energy equation: injection temperature at injection point, free surface at melt-front, and mold-wall temperature condition at the cavity wall, which is interfaced with the cooling stage analysis.

Cooling stage

Of the three stages in the injection molding process, the cooling stage significantly affects the productivity and the quality of the final component. Cooling starts immediately upontheinjection ofthe feedstock melt, but formallythe coolingtimeis referredto as the time after the gate freezes and no more feedstock melt enters the cavity. It lasts up to the point of component ejection, when the temperature is low enough to withstand the ejection stress. In the cooling stage, the feedstock volumetric shrinkage is counteracted by the pressure decay until the local pressure drops to atmospheric pressure. Thereafter, the material shrinks with any further cooling, possibly resulting in residual stresses due to nonuniform shrinkage or mold constraints (which might not be detected until sintering). In this stage, the convection and dissipation terms in the energy equation are neglected since the velocity of a feedstock melt in the cooling stage is almost zero. Therefore, the objective of the mold-cooling analysis is to solve only the temperature profile at the cavity surface to be used as boundary conditions of feedstock melt during the filling and packing analysis.When the injection molding process is in steady state, the mold temperature will fluctuate periodically over time during the process due to the interaction between the hot melt and the cold mold and circulating coolant. To reduce the computation time for this transient process, a 3D cycle-average approach is adopted for the thermal analysis to determine the cycleaveraged temperature field and its effects on the PIM component. Although the mold temperatureis assumed invariant overtimethere is still atransient forthe PIM feedstock, leading to the following features.

• Mold cooling analysis: under this cycle-average concept, the governing equation of the heat transfer for injection mold cooling system is written as

where T is the cycle-averaged temperature of the mold.

• PIM component cooling analysis: without invoking a flow field, the energy equation is simplified as

Typical initial and boundary conditions applied during the cooling stage are as

follows:

• initial conditions: temperature as calculated from the packing stage analysis;

• boundary conditions for the mold: interface input from the PIM feedstock cooling analysis, convection heat transfer associated with the coolant, natural convection heat transfer with air, and thermal resistance condition from the mold platen;

• boundary conditions for the component: interface input from the mold cooling analysis.

Note that the boundary conditions for the mold and PIM feedstock cooling are coupled to each other. More details on this are given in Section 11.2.2 on numerical simulation later.

11.2.2 Numerical simulation

As far as the numerical analysis of injection molding is concerned, several numerical packages are already available for conventional thermoplastics, and one may try to apply the same numerical analysis techniques to PIM. However, the rheological behavior of a powder-binder feedstock mixture is significantly different from that of a thermoplastic. Hence, the direct application of methods developed for thermoplastics to PIM requires caution. Commercial software packages, including Moldflow, Moldex 3D, PIMsolver, and SIMUFLOW are available for PIM simulation. These commercial software packages have been developed and are developing based on their own technical and historical backgrounds, which results in their own pros and cons. Further, several research groups have written customized codes, but generally these are not released for public use.

Filling and packing analysis

For numerical analysis of the filling and packing stages of PIM, both the pressure and energy equations must be solved during the entire filling and packing cycle. This is achieved using the FEM for Eq. (11.11) while a finite difference method (FDM) is used in the z-direction (thickness), making use of the same finite elements in the xy plane for solving Eq. (11.12).

The FDM is a relatively efficient and simple numerical method for solving differential equations. In this method, the physical domain is discretized in the form of finite-difference grids. A set of algebraic equations is generated as the derivatives of the partial differential equations and these are expressed by finite differences of the variable values at the grid points. The resulting algebraic equation array, which usually forms a banned matrix, is solved numerically. Generally, the solution accuracy is improved by reducing the grid spacing. However, since the FDM is difficult to apply to a highly irregular boundary or a complicated domain typical of injection molding, the use of this method has to be restricted to regular and simple domains, or used with the FEM as a FDM-FEM hybrid scheme.

For the numerical analysis of the filling process of PIM, one has to solve both the pressure equation and energy equation during the entire filling cycle until the injection mold cavity is filled. A FEM method is employed to solve Eqs. (11.11), (11.12) while FDM is used in the thickness-wise or z-direction, making use of the same finite elements in the x-y plane.

Cooling analysis

For the numerical analysis of the cooling process in PIM, the boundary element method (BEM) is widely used due to its advantage in reduction of the dimensionality of the solution. The BEM discretizes the domain boundary rather than the interior of the physical domain. As a result, the volume integrals become surface integrals, then the number of unknowns, computation effort, and mesh generation are significantly reduced (Kim & Turng, 2004). A standard BEM formulation for Eq. (11.18) based on Green's second identity leads to the following:

Here, x and z relate to the positional vector in the mold, r=丨z-x丨，and a denotes a solid angle formed by the boundary surface. Eq. (11.18) for two closed surfaces, such as defined by the component shape, leads to a redundancy in the final system of linear algebraic equations, so a modified procedure is used. For a circular hole, a special formulation is created based on the line-sink approximation. This approach avoids discretization of the circular channels along the circumference and significantly saves computer memory and time. For the thermal analysis of a PIM component, the FDM is used with the Crack-Nicholson algorithm for time advancement. The mold and PIM component analyses are coupled with each other in boundary conditions so iteration is required until the solution converges.

Coupled analysis between filling, packing, and cooling stages

The filling, packing, and cooling analyses are coupled to each other. When we analyze the filling and packing stages, we have the cavity wall temperature as a boundary condition for the energy equation. This cavity wall temperature is obtained from the cooling analysis. On the other hand, when we analyze the cooling stage, we have the temperature distribution of the powder-binder feedstock mixture in the thickness direction at the end of filling and packing as an initial condition for the heat transfer of powder-binder feedstock. This initial temperature distribution is obtained from the filling and packing analysis. Therefore, the coupled analysis among the filling, packing, and cooling stages might be made for accurate numerical simulation results.

Typical procedure for computer simulation of a PIM process consists of three components: input data, analysis, and output data. The quality of the input data is essential to success. The preprocessor is a software tool used to prepare a geometric model and mesh for the component and mold; it includes material data for feedstock, mold, and coolant, and processing conditions for filling, packing, and cooling processes. Fig. 11.4 shows one example of geometry modeling and mesh generation for a U-shape component, including the delivery system and cooling channels.

Fig. 11.4 Geometry modeling and mesh generation for U-shape part including delivery system and cooling channels (pressure measurements at A, B, and C) (Ahn et al., 2008).

11.2.3 Experimental-Material properties and verification

Material properties for the filling stage

Successful simulation of the filling stage during PIM depends on measuring the material properties, including density, viscosity, and thermal behavior. Among these, the viscosity of the PIM feedstock and its variation with temperature, shear rate, and solid volume fraction are special concerns. The following procedure is an example of the method used to obtain these material properties. For this illustration, assume a spherical stainless steel powder in a wax-polymer binder.

• First, melt densities, heat capacities, and thermal conductivities of the feedstock are required. These are obtained using a helium pycnometer, differential scanning calorimeter, and laser flash thermal conductivity device.

• Second, the transition temperature for the feedstock is measured, again using differential scanning calorimetry.

• Third, the feedstock viscosity is measured in relation to key parameters. The rheological behavior of the feedstock is measured by capillary rheometry. By using high length-to-diameter ratio capillaries, the pressure loss correction, called Bagley's correction, is avoided. Rabinowitch's correction is extracted to obtain the true shear rate from the apparent shear rate for a non-Newtonian fluid, characteristic of the feedstock (Kwon & Ahn, 1995). The variation of viscosity with temperature is determined by testing the feedstock at different temperature above the transition temperature. Then, the feedstock viscosity data are modeled using standard loaded polymer concepts based on Eqs. (11.2), (11.3).

Material properties for the packing stage

To simulate the packing stage, the Hele-Shaw flow of a compressible viscous melt of PIM feedstock under nonisothermal conditions is assumed. For this, the two-domain modified Tait model is adopted to describe the phase behavior of the feedstock. A dilatometer is used to measure dimensional changes as a function of temperature and other variables and the results are extracted by curve fitting.

Fig. 11.5 gives one example of pvT material properties based on the following twodomain modified Tait model for the packing stage simulation for a stainless steel feedstock. For the solid-liquid phase,

with

Material properties for the cooling stage

For the cooling stage simulation, material properties of mold material and coolant need to be measured.

Verification

Verification of the simulation is a critical step prior to any effort to optimize a design based on simulations. This verification usually includes the validation of the model used in developing the software. To demonstrate the verification of the simulation tool through experiment, we selected the U-shaped test mold shown in Fig. 11.4 with the stainless steel PIM feedstock reported earlier and an H13 mold. Three pressure transducers were used to compare the simulation results with the experimental data. The cavity thickness is 3 mm and the gate diameter is 1mm. The coolant inlet temperature is 20℃, the inlet flow rate is 50 cm3 /s, and the cooling time is 10 s.

Fig. 11.5 Pressure-volumetemperature (pvT) data of the feedstock

Fig. 11.6 describes some of the simulation results obtained using PIMsolver. Plate 11.1A shows the filling pattern, indicating how the mold cavity fills as a function of time. The filling time is 1.28 s. Plate 11.1B shows the average mold-temperature distributions in K on the upper and lower surfaces of the cavity from the cooling analysis results. The highest average temperature is 51℃ and occurs at the base of the U and the lowest temperature is 34℃ at the runner inlet. The mold wall temperature is not uniform and the difference between maximum and minimum values is 18℃. This variation is large enough to cause a significant difference in the solidification layer development during the packing stage. Therefore, one might expect the simulation to have a significant error in pressure prediction during the packing stage without consideration of the cooling effect.

Fig. 11.6 Pressure-time plot at three points indicated in Fig. 11.4

（A）                                                                    （B）

To examine the validation, the pressure traces are compared between simulation and experiment, as shown in Fig. 11.6 using the three positions indicated in Fig. 11.4. Fig. 11.6 gives the pressure-time plot obtained from the experiment and simulation. The simulation results are obtained from the filling and packing analyses at a constant cavity wall temperature of 30℃. The results with the distributed mold wall temperature interfaced with the results from cooling analysis, as shown in Fig. 11.6, explain this deviation. If we consider the cavity wall temperature distributions from the cooling analysis (coupled analysis), then that temperature enables the best agreement to the experimental results.

11.2.4 Applications

This section presents simulation results from some of the 2.5D examples to demonstrate the usefulness of the CAE analysis and optimization capability of the PIM process. We will demonstrate how to use this basic information from the simulation tool to predict injection molding related defects and will present the systematic way of using the CAE tool to develop an optimal injection molding process.

Basic capability-Short shot, flash, weld line, air vent, and other features

This section will demonstrate use of the simulation results to predict typical molding defects. There are many kinds of molding defects and we can identify them mainly as basic defects, dimensional defects, and other defects. The basic defects are traced to the molding parameters.

For the basic defects, simulations use the pressure field analysis to predict short shots and flashing, as well as the filling pattern to identify trapped air and weld line location. A short shot occurs when the molded part is filled incompletely because insufficient material is injected into the mold. Flash is a defect where excessive material is found at locations where the mold separates, notably the parting surface, moveable core, vents, or venting ejector pins. The causes of flash are low clamping force, gap within the mold, molding conditions, and improper venting.

Weld line and the resulting mark or knit line is another flaw that is also a potential weakness in a molded plastic part. Weld lines are formed by the union of two or more streams of feedstock flowing together, such as when flow passes around a hole,insert, or in the case of multiple gates or variable thickness in the component. Consequently, a weld line reduces the strength of the green component and leaves an undesirable surface appearance, and should be avoided when possible. The results from the computer analysis are used to predict the weld line location. An air trap or air vent is a defect by air that is caught inside the mold cavity. The air trap locations are usually in areas that fill last. The air trap is predicted from the filling pattern analysis and can be avoided by reducing the injection speed, and enlarging or properly placing vents. Other defects, such as burn marks, flow marks, meld lines, jetting, surface ripples, sink marks, and suchlike are also accessible using computer simulation tools in the design process stage. Especially important in production is the control of factors related to dimensional uniformity. These are analyzed by checking all three main stages of the injection molding. Plate 11.2 shows some predicted defects from injection molded PIM components.

Plate 11.2 Some molding defects predicted by using a CAE tool for PIM process. (A) Plate (B) Dental scaler tip (C) Geometry evaluation of micro features

Optimization of filling time

Filling time is an important variable that is optimized to reduce the required injection pressure. From the CAE filling analysis, by varying the filling time the injection pressure is calculated. When plotting the required injection pressure versus various filling times, the optimal filling time ranges are determined for the lowest injection pressure. The curve is U-shaped because, on the one hand, a short fill time involves a high melt velocity and thus requires a higher injection pressure to fill the mold. On the other hand, the injected feedstock cools more with a prolonged fill time. This results in a higher melt viscosity and thus requires a higher injection pressure to fill the mold. The shape of the curve of injection pressure versus fill time depends very much on the material used, as well as on the cavity geometry and mold design. If the required injection pressure exceeds the maximum machine capacity, the process conditions or runner system must be modified.