The purpose of mold flow analysis is to solidify the feasibility of design for manufacture (DFM)

There are myriad design schemes for plastic products, but not every one of them can be smoothly molded. Mold flow analysis facilitates the rapid integration of material properties such as rheology, thermal characteristics, and mechanical properties. This allows design and development personnel to conduct qualitative and quantitative analyses and diagnostics for mold design or existing molds and operational conditions. The goal is to ensure the feasibility of these products or molds during the design phase, enhancing production capacity.

Figure 1: Flow path - Gate - Mold cavity system schematic.

The development of mold flow analysis originated in the 1970s at McGill University in Canada under Prof Kamal. In 1978, Colin Austin developed the first commercial software, using the layflat method to flatten three-dimensional thin-walled structures into planes for flow path analysis.

Figure 2: The evolution of grid technology

The evolution of grid technology started with the layflat method in the 1970s and progressed to 2.5D or midplane flow, shell technology in the 1980s, dual-domain quasi-three-dimensional flow in the 1990s, and the development of true three-dimensional solid grid methods in the 2000s. As computational efficiency improved, the number of manageable grids increased, theoretically making three-dimensional solid grids more accurate.

Figure 3: Midplane/2.5D/Shell

After the layflat method, Cornell University developed 2.5D shell grid technology using the Cornell Injection Molding Program (CIMP). This method simplifies a three-dimensional model into a 2.5D model, taking the middle face of the geometry as the computational element. The theoretical basis for this 2.5D midplane flow method is the Hele-Shaw equation, which utilizes the narrow features of the injection mold cavity in the thickness direction, neglecting pressure gradients in the thickness direction. This assumption simplifies the two-dimensional pressure equation used for mass conservation and momentum conservation.

Figure 4: 2.5D method limitation: heat conduction

For the energy conservation aspect, although thermal convection effects in the thickness direction and heat conduction within the flow plane can be ignored, the three-dimensional temperature changes in the system still need to be considered. Thus, this is summarized as solving the coupled 2.5D problem of the two-dimensional pressure field and the three-dimensional temperature field, commonly known as the "2.5D" problem.

Figure 5: 2.5D method limitation: areas with varying wall thickness

For the 2.5D problem, the applicable numerical method is the finite element method, which can be used to solve the pressure equation and the finite difference method to solve the temperature field in the thickness direction. However, in certain flow areas, this method has limitations, such as in the fountain flow area at the flow front, T-shaped regions (e.g., reinforced ribs), or places with sudden thickness changes, where the assumption of neglecting pressure gradients in the thickness direction made by Hele-Shaw does not hold, leading to some degree of error.

Figure 6: 2.5D method limitation: Fiber orientation behavior driven by flow field

These errors significantly impact the prediction of fiber plastics because fiber movement requires consideration of movements and rotations in three-dimensional space. The 2.5D model cannot accurately predict the orientation of fibers in these thickness-changing areas. Additionally, due to the simplifying assumption of Hele-Shaw, the heat transfer mechanism neglects thermal convection in the thickness direction and heat conduction within the flow plane. For some components with embedded parts or hole structures, the 2.5D model becomes distorted.

To address the limitations of the 2.5D method, the dual-domain flow model emerged. This model establishes surface grids for the product on both the core and cavity sides, then uses additional linking coefficients to correct the model's two-sided flow behavior. The advantage of this approach is that it is closer to three-dimensional results and does not require extracting a middle plane. However, it is limited to products with high geometric consistency on both sides.

Figure 7 : The Dual-Domain Flow Model

Although the dual-domain flow method is simple, there is still a risk when dealing with areas where thickness is not clearly defined. For simple circular-external-square-internal geometries, errors in thickness judgment can occur in rectangular corners. If the dual-domain flow method is used for simulation, erroneous results such as discontinuous glue, as shown in the example of Figure 8, may occur.

Figure 8: Thickness determination issue in the dual-domain flow model

In contrast, true three-dimensional solid grids remain the most accurate method to date because they do not make any simplifying assumptions about geometry, as shown in Figure 9.

Figure 9: true three-dimensional solid grids

Moreover, governing equations precisely describe the three-dimensional spatial phenomena of the system. Constructing the product and runner with a solid grid method, as shown in Figure 10, can yield simulation results closer to real situations. The key to using this grid method lies in the stability and efficiency of the solver.

Figure 10: the product and runner with a solid grid method

The application of three-dimensional solid grids goes beyond simulating melt behavior within the cavity. It can also be arranged in the entire mold to obtain accurate mold temperature distribution information, as shown on the left in Figure 11. Considering the layout of the cooling system is an indispensable and important technology.

Figure 11: Complex conformal cooling layout with the associated three-dimensional solid boundary layer mesh.

As shown on the right in Figure 11, the BLM grid can accurately capture the drastic changes in temperature and velocity near the mold wall during the filling process. It can precisely detect issues such as viscous heating and warping. In other words, BLM is a powerful pre-processing tool for complex geometric shapes.