Optimization of Runner Balance for a Family Product of Injection Molding Process

A family mold is used in the injection molding process to produce components of different sizes that would normally be assembled into a single product assembly. The uniform quality of each injection molded part is strongly influenced by the filling balance of the mold cavity. The filling balance can be controlled by optimizing the dimensions of runners that are directed towards each cavity. In this paper, an optimization method is proposed that aims at balancing the filling time that maximizes the quality of a family mold cavity. There are two steps proposed in this research, namely theoretical calculations and simulation of runner balanced design using the software. The results of this study can be used as a practical reference in designing a mold for family products to avoid design errors as early as possible. The result obtained from an industrial case study highlighted the effectiveness of the proposed approach in finding the optimal runner dimension by a restricted number of simulations.


Introduction
The family mold structure is one type of multi-cavity system in the injection molding process to make a series of assembled components that can increase efficiency and reduce costs.Family mold involves making products of different sizes in one mold [1].Some of the family mold products include automotive components, smartphone lenses, and children's toys [2].Along with its development, family mold products are inseparable from weaknesses because there are complex component features, and the assembly process is quite sensitive to design and processing during injection molding [2].One of the problems in the family mold is that the plastic melt filling time is not uniform for the formation of its products and there is residual stress in certain areas [2].Filling imbalance can lead to a pressure spike at the end of fill that can lead to non-uniform shrinkage of components that can cause alignment issues, flashing or sink mark development and a narrower process window.All these issues can increase the cost of the component by increasing the scrap rate or requiring the use of an operator to remove the flash or visually inspect the parts.This problem can be solved by several approaches that have been used by previous researchers, including Leo and Cuvelliez [3] modified the dimensions of the gate section and process parameters, the results showed predictions of overpacking and permanent deformation effects according to semi-quantitative measurements of mold deformation with simple analytical estimates.Then, Yen et al. [4] changed the diameter and length of the runner to minimize warpage in the injected part and optimize the runner system parameters, the research results obtained an abductive network that can predict the maximum warp according to different control parameters and correlates warp performance with runner system parameters.M Zhai et al., [5] analyzed a balanced flow through modification of size, runner volume, and part quality in terms of warpage, the results show runner volume and injection pressure can reduce production costs of plastic products.Wang and Sun [6] analyzed the runner imbalance in the top cover cavity and brought the product box with the Moldflow Insight 5.0 analysis, the results showed that through optimization, the imbalance of plastic fluid flow in the cavity decreased from 28.6% to 0.7%, the pressure imbalance rate injection can be decreased from 42.0% to 4.2%, and the pressure distribution in the cavity is more uniform throughout the injection-process.Raz et al., [7] modified the runner angle and balanced the injection of plastic material in the three products, the results showed that the 90º angle configuration for the runner was proven to be able to uniform the filling time of the plastic material to the three products.Azaman et al., [8] examined the process of filling plastic material in the cavity for analysis of residual stress and warpage in both types of thin parts of the cavity with Moldflow software.The results of the research showed that the shallow part of the cavity, having a stiffer structure, had lower residual stresses (surface center 15-23 MPa) and warpage (0.02-0.42 mm).Azaman et al., [9] performed a residual stress analysis using numerical methods for thin-walled parts produced after the filling stage using Moldflow software.The results showed that the residual stress in the entire thickness experienced high tensile stress on the surface, then changed to a peak value of low tensile stress in the surface area and experienced a parabolic tensile stress peak.The optimum parameter ranges are mold temperature of 40-45 C, cooling time of 20-30 seconds, packing pressure of 0.85 of injection pressure, and packing time of 15-20 seconds.Research by Tsai et al [10] focuses on minimizing the imbalance of plastic liquid filling into multi-cavity for PVC injection molding with Moldflow software and the Taguchi method.The result is that the optimization of the injection rate at filling time has been verified to reduce the imbalance and the fitting temperature in filling and packing is lower than the PVC degradation temperature.
Another study that discusses warpage analysis with Moldflow software [11] designs and manufactures transmission parts for micro-winged air vehicles (FW-MAV), which are made by injection molding, and analyzes the warpage phenomenon with Moldflow, the results show that the cause of warpage in the transmission factor of the mold temperature, injection pressure, packing time, and injection temperature.According to Wilczyński et al. [12], several experiments showed that the injection rate, molding, and melting temperature substantially affect the filling imbalance.Experimental and theoretical studies were carried out to analyze the filling imbalance in a geometrically balanced injection molding.The result proved that the charging imbalance problem is still not solved.There is no universal solution that can be successfully applied to mold design and will be accepted by all engineers and researchers.The proper design of the runner system is dependent on the material characteristics and process parameters.If the design parameters do not match, then imbalance still occurs, simulation/optimization is one way to deal with this phenomenon effectively.Wang et al., [13] analyzed the filling imbalance on the top and bottom lids of a plastic soap box produced by injection molding at one time, the filling imbalance appeared due to the different dimensions of the two products.The results showed that the optimized runner cross section can reduce the filling balance ratio from 3.38% to 0.73%, and the filling time can meet operational requirements.
From the literature above, it is known that to balance the filling time and minimize stress concentration, several methods of modification approaches to runner, gate, gate angle, and process parameters can be used.This study uses the theoretical calculation method and runner balance simulation with Autodesk Moldflow Plastic Insight software which aims to balance the filling time and maximize the quality of the family mold product.

Material and Product Dimension
As mentioned in the introduction, there have been many approaches to balancing filling time in plastic products.This study uses two problem-solving methods, namely theoretical calculations and runner balance analysis with Autodesk Moldflow Plastic Insight.Both methods can be a practical reference in designing family molds to avoid design errors.The plastic products are shown in Figure 1, and the dimensions and weight of the products are in Table 1.The material used for plastic products is Polypropylene (PP) under the name BP Amaco 1046 produced by the BP Chemicals industry.In the theoretical calculation method, the researcher uses equation 1 which aims to get the pressure drop value.The pressure drop for each runner is obtained by calculating the runner radius using equation 2. Microsoft Excel was used to obtain theoretical calculations, which were then the results entered the Moldflow Simulation.
The case of the family mold product is shown in Figure 1, there are 3 products of different sizes and weights and will be made in one mold.The three products are made of the same material and will be assembled after molding.To achieve an equal service life of the three components, it is necessary to achieve uniform quality by ensuring uniform filling times in the injection molding process.The dimensions and weight of the three components are shown in Table 1.For molds that utilize a cold runner the control of the flow to the different cavities is often achieved by either varying the size of the runner channel or by varying the flow length the polymer needs to take to reach the cavity.Since injection molding is a pressure-driven process, it is possible either to reduce the size of the runner or increase the length of the runner to the smaller cavities so the material will preferentially fill the larger cavities first.Thus, equilibrium flow through the runner system can be affected by runner layout, runner, and gate sizes.A simple approach based on the calculation of the pressure drop can help to determine the proportional dimensions of the runner system so that the filling time in the three cavities can be balanced.The pressure drop can be calculated using Eq. 1 [14].As Equation 1 highlights, a change in runner radius (diameter), R, has a much more significant effect on our flow resistance as compared to a change in the runner length, L. Because of this sensitivity, it is preferred to balance the filling pattern of the runners rather than the gates.The use of the gate size alone to address any fill imbalance will minimize the amount of time to influence the molten material and increase the sensitivity to any dimensional inconsistencies in the gate.Therefore, it is more likely to have a narrow process window and a less robust solution over time.
Where: ∆P = pressure drop (MPa) R = channel radius (mm) L = channel length (mm) k = polymer melt viscosity (Pa s) n = power law index at a melt temperature = volumetric flow rate (cc/s) Then, the power law model can be used to calculate the radius of the runner: Based on the mold design layout in Figure 2, the runner balance calculation is carried out with Eq. (1) and Eq. ( 2).The calculation with equation (1) produces a pressure drop on the runner that flows the plastic to part 1.Based on the equilibrium pressure drop for all parts, these results are used to calculate the diameters of runner 2 and runner 3 by equation ( 2).The length and diameter of the runner were applied in the Moldflow Plastic Insight simulation with Sequence Flow analysis.Nine variations of runner length and diameter were simulated to get the most balanced value of filling time, minimum incavity residual stress, and minimum volumetric shrinkage.
The first pressure drop calculation is carried out on the sprue as the entrance of the plastic melt into the mold.The analysis assumes that the product made of Polypropylene (PP) is molded with a volumetric flow rate at the inlet of 125 cm 3 /s.To avoid calculating the shear rate in each portion of the runner, the power law model is used with k equal to 2006.4 Pa s and n equal to 0.35.The bore of the sprue bushing is 90 mm in length and has an average radius of 3 mm, then the pressure drop through the sprue is calculated using equation 3.
As can be seen in Figure 3, the initial simulation of part 1 resulted in a filling time of 2 seconds, this value is used as the initial assumption of filling time.Table 2 is the process parameters for injection molding simulation, these parameters follow the recommendations from Moldflow which generally refers to the type of plastic material being processed.

Result and Discussion
From Run 1 to Run 4, the runner diameter for Part 1 (D1) is varied to calculate D2 and D3 while the length of all runners is constant.In Run 5 to Run 7 the runner length is extended by 15 mm.Moldflow simulation can help to optimize the runner system automatically by using a Runner Balance Analysis.This type of analysis allows the computer to resize the runners through an automatic algorithm that will yield a more balanced filling pattern for the mold.From the Runner Balance Analysis, the software will guide the designer to appropriate sizes to help optimize the filling balance between the cavities and attempt to stay below a target pressure for the mold.From this analysis, the computer can automatically update the runner sizes for each part and get an initial mold filling study performed so it can be confirmed that all parts can be filled and packed uniformly.Therefore, in Run 8 and Run 9, all runner diameters were generated automatically by setting the runner balance sequence in the Moldflow simulation.Table 3 shows the calculation and simulation results.Automatic runner diameter balancing by Moldflow simulation in Run 8 and Run 9 can result in uniform filling times for all three parts.The uniformity of filling time is proven to minimize the difference in residual stress and shrinkage of the three parts to ensure balanced product quality [4][6] [15].The simulation results of Run 8 are shown in Figure 4.
The simulation in Run 6 produces the largest gap for filling time, residual stress, and volumetric shrinkage, as shown in Figure 5.The large volumetric shrinkage gap will increase the difficulty of assembling parts from the mold family product, [16] while the large residual stress difference will influence the difference in product resistance when loading so that the lifetime of each family mold product will also be different [17] [18].The existence of in-cavity residual stresses will directly affect the mechanical properties of the part, and in severe cases will cause warping and cracking.Therefore, it is necessary to minimize residual stresses in the injection molding process for high-quality molding.Although Run 8 and Run 9 were able to produce a balanced product quality, the diameter of the runner suggested by the Moldflow simulation was too small, resulting in a high-pressure drop (5.3 MPa) and high clamping tonnage (267 tons).Clamping tonnage is the basis of the selection of injection machines, the greater the clamping tonnage the greater the capacity of the machine energy required.In economic considerations for mass production, this is not profitable [19].As an alternative recommendation, Run 4 can provide a solution to this problem.Figure 6 shows the simulation results from Run 4. Gap filling time, residual stress, and volumetric shrinkage are considerably low and more importantly, the low clamping tonnage (110 tons) gives the possibility of selecting injection machines with lower capacities and more economical.In real production cases, the clamping force always is an important consideration, a smaller clamping force can increase the possibility of selecting the machine which may significantly reduce the production cost [20].

Figure 6 .
Figure 6.Simulation results of Run 4: (a) Filling time; (b) Residual stress; (c) Volumetric Shrinkage; (d) Clamping tonnage 4. Conclusions Runner balance calculation and simulation is an effective method to ensure the quality balance of the mold family product.The balance of product quality is influenced by several factors including residual

Table 1 .
Dimensions and weight of plastic products.

Table 3 .
Experimental design and results