Prediction of Core Shift Effects

FLOW ANALYSIS OF INJECTION MOLDING WITH RETRACTABLE PINS SUPPORT OF INSERTS OR CORES Alexander Bakharev and David Astbury Autodesk Australia 259 Colchester Rd. Kilsyth 3137 Australia Abstract Some injection molds utilize retractable pin supports of inserts. In this process the inserts are initially supported by the pins that are retracted before the melt touches them. This method is commonly used for manufacturing golf balls and similar moldings. Retractable pins can also be used for injection molds with slender cores to minimize the core shift effect. The article presents algorithms and results of mold filling simulations that take into account movement of the inserts and cores supported by those retractable pins. The simulation is implemented as a new feature of the core shift analysis for mold filling simulation.

Introduction Injection molds with retractable pin supporting inserts similar to shown on Figure 1 are used for moldings that completely enclose inserts. Common examples of such moldings are golf balls where injection molded plastic enclose rubber inserts (124,126). The pins (130136 support the inserts during the beginning of filling the cavities. The pins are retracted at some time ( and afterwards the inserts are supported only by the hydrodynamic forces from the polymer melt. Polymer pressure on the rubber insert causes its deformation while even slightest unbalance in the melt flow originated from different flow paths towards the gates (20..30) causes shift of the center of the inserts that in turn causes stronger unbalance, causing higher shift etc. The progressively increasing misbalance of flow may cause a significant shift of the rubber inserts, warpage of the balls, variations of the plastic thickness, etc. Those factors are critically important for quality of the balls, thus, prediction of the deformation and shift of the inserts is an important part of the mold filling analysis. The retractable supports are also quite usable for limiting the effect of the core shift if elastic slender cores are used. Since limiting the core shift effects is the main motivation for putting the retractable pins the prediction of the core shift effects is very important for such molding processes. The core shift analysis is used to predict deformation of the inserts and cores supported by the retractable pins.

Figure 1 A typical setup for molding golf balls. Retractable pins 130-136 support rubber inserts 124 and 126. For other features of the design refer to [1]. Core shift can be defined as the spatial deviation of the position of the mold cores and inserts caused by the imbalance of polymer pressure during injection molding. The resulting change of the boundary conditions in turn affects filling pattern and packing pressure distribution and may create residual pressure at the end of cooling (over-packing) and deviations of the molding thickness. The final result may be an inferior quality of the molded parts. It is a pervasive problem in the manufacturing of thin-walled containers [2-8]. Work [9] described an algorithm for predicting the core shift effects that uses a combination of mold filling simulation and a structural analysis. The same algorithm is applied for the retractable pin supports using two approaches:





”Retractable constraints” applied to the inserts or cores as shown on Figure 2. The retractable constraints (A) are excluded from the analysis after some retraction time. ”Retractable bodies” connected to the inserts or cores as shown on Figure 3. The retractable bodies (A) representing the pins themself are excluded from the analysis after some retraction time.

The first approach does not require users to model the geometry of the support pins, while the second approach is more accurate, allowing to account for the deformation of the retractable pins themselves.

( v) 

  S t

/4/

where: τ  shear stress; p – pressure, γ    v  (  v)T  shear rate, T – temperature, t – time, v – melt velocity,   thermal diffusivity, τ : γ Wshear _ heat   shear heating C T Dp  compression heating, Wcompr _ heat  C Dt    (T , p) - polymer density and S  is an additional polymer velocity source term for the nodes on the mold core – polymer melt interface, that describes movement of the mold core:

S   Figure 2 Retractable constraints (A) applied to an insert (B)

 un, t

where u is the deformation of the interface and n is the direction of the normal to this surface. This additional term is quite important for the retractable supports as it provides the only resistance to a free body movement of the inserts. Hele-Shaw approximation using triangular elements is used to solve fluid dynamics equations 1-4 [10]. For chunky moldings equations 1-4 are solved in true 3D formulation using 4-node tetrahedral elements [11].

Figure 3 Retractable bodies (A) supported by constraints (C) are connected with an insert (B)

Theory Following the convention for the core-shift analysis below we would refer to the deforming solid parts supported by the retractable pins as the cores whether the parts are inserts, cores or the retractable pins themselves. Melt pressure through the cavity and runners is predicted by using numerical solution of low-Reynolds number momentum-equation:   (τ  pI)  0 /1/ together with a rheological equation: τ   (, T )γ /2/ energy equation: T  v  T   2T  Wshear _ heat  Wcompress _ heat /3/ t and mass-conservation equation:

The melt pressure p creates additional surface forces f acting on the boundary of the insert: /5/ f  pn these forces would cause deformation of the core u that can be found using momentum equations inside the core: /6/ σ  0 together with Hook’s law:

ε

(   u)  (   u) T  Cσ 2

/7/

and boundary conditions: /8/ f  σn In the equations 5-8 σ is stress, ε is strain, n is a normal vector for polymer-core interface and C is the mold material compliance. The supports for the cores are implemented as springs there an additional nodal force freaction is proportional to the deflection of the node u :

f reaction  K(u  u0 )

/9/

In the equation /9/ K is the spring elasticity and u 0 is the equilibrium position of the node. If the support fixes a deflection component ui we select the corresponding component of the spring elasticity tensor K ii to be a large value (much higher than the elasticity of the core itself), if the support leaves the deflection component ui to be free we chose the elasticity K ii to be zero. For elastic support the appropriate values of the spring elasticity K allow to accurately take into account movement of the support. For one-sided supports the effective spring elasticity K and equilibrium position become dependent upon the deformation of the constrained node u as described in [12]: [

;

[

Figure 4 Case study: thermoplastic polyurethane ball

/10/

Finally, for the retractable support, the spring elasticity becomes a function of time. [

/11/

A similar approach is taken for the “retractable bodies” representing the retractable pins. For those bodies the material elastic modulus E is set to zero after the retraction time : [

/12/

Figure 5 Case study: rubber insert (red) is supported by two retractable steel pins (grey). The simulation shows that due to progressively increasing pressure misbalance (see Figure 6) displacements of the rubber insert approach 0.55 mm prior to retraction of the supports (see Figure 7).

As described in our work [9] the elasticity equations 6-8 are discretized using 3-dimensional models for mold cores represented by 4 and 10 node tetrahedral elements, assembled together with equations describing support 911. The system is solved simultaneously with flow equations 1-5. The resulting software allows prediction of core shift with retractable constraints during injection molding of thermoplastics.

Case Study As a case study we would consider a thermoplastic polyurethane ball (shown on Figure 4) filled from multiple gates in equatorial plane. The spherical rubber insert is supported by two steel retractable pins at the poles as shown on Figure 5. The pins are retracted at 0.6 seconds while the filling time is 0.664 seconds.

Figure 6 Melt pressure prior to retraction of the supports After retraction of the support displacements of the insert redistribute to a more uniform shift of approximately 0.45mm as shown on Figure 8. The displacements of the insert do not change much during packing and are fixed at the end of cool by frozen polyurethane (see Figure 9) leaving significantly unbalanced wall thickness. Those golf balls would

probably be not acceptable, so a change in design of the mold or molding conditions is required.

Conclusions A working algorithm for considering retractable supports of cores and inserts during mold filling analysis is presented. Retractable supports significantly affect predictions of core shift and their proper consideration is paramount for prediction quality of the parts.

Acknowledgements Authors thank Callaway Golf Company for their discussions on the retractable supports in the injection molds and providing finite element models used in the study.

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Figure 7 Displacements of the rubber insert prior to retraction of supports. Magnification factor x10

Figure 8 Displacements of the rubber insert after retraction of support. Magnification factor x10

Figure 9 Final displacements of the rubber insert at the end of cooling. Magnification factor x10