With rapid development of China's industrialization process, demand for plastic products has increased significantly. Since production capacity and quality of plastic products are related to performance of injection molding machines, more and more injection molding machine manufacturers are paying attention to research in the field of injection molding machines. Mold clamping mechanism is one of important components of injection molding machine (see Figure 1), stiffness and strength of fixed mold fixing plate are main factors affecting quality of plastic products.

 

Figure 1 Mold clamping mechanism
1. Fixed mold fixing plate 2. Tie rod 3. Moving mold fixing plate 4. Toggle lever 5. Cross head 6. Rear mold plate 7. Mold clamping hydraulic cylinder
Movable and fixed mold fixing plates of mold closing mechanism are affected by clamping force and mold expansion force under actual working conditions. Mold clamping force and mold expansion force have characteristics of large force and concentration. In order to ensure production safety and reduce deformation of parts during design and manufacturing, fixed plates of movable and fixed molds are generally thicker, which increases the overall quality of equipment and is not conducive to handling of parts during processing and assembly process and transportation and installation of the entire equipment. In addition, heavy mold plate design leads to an increase in amount of mechanical processing of parts and increases processing costs. Therefore, in order to solve above problems, various injection molding machine manufacturers and university researchers have carried out lightening and optimization design and research on fixed mold fixed plates while ensuring that deformation of movable and fixed mold fixed plates is within allowable range and force is good, reasonably change structure and design parameters of moving and fixed mold plates to alleviate and reduce processing volume, reduce manufacturing costs, and improve economic benefits of enterprise, thereby improving market competitiveness of enterprise.
Taking fixed mold fixing plate of mold closing mechanism of a certain model of injection molding machine as a research example, difficulty of common optimization forms such as topology optimization, shape optimization and size optimization is comparatively analyzed, ensure safety of lightweight design and optimization of fixed mold fixed plate to avoid accidents such as fracture of fixed mold fixed plate, a topology optimization method that is easy to operate and suitable for widespread application in enterprises is selected as optimization method of fixed mold fixed plate of mold closing mechanism of injection molding machine. Topology optimization establishes a structure of finite elements in design space, determines whether to retain elements in design space according to algorithms such as structural optimization method, variable density method, and uniformization method. Retained elements are final topology solution to achieve topology optimization. This optimization is based on principle of variable density method to achieve a lightweight design of fixed mold plate and reduce amount of mechanical processing.

As can be seen from Figure 1, mold clamping mechanism used by injection molding machine is a crank-connection rod structure. Main components include fixed mold fixed plate 1, tie rod 2, movable mold fixed plate 3, toggle lever 4, cross head 5, rear mold plate 6, and mold clamping hydraulic cylinder 7. When injection molding machine is working, piston rod of hydraulic cylinder drives crosshead to move forward, which in turn drives toggle rod to push movable mold fixed plate to move forward along tie rod to complete mold closing process; when opening mold, piston rod of hydraulic cylinder drives crosshead to move backward, drives toggle lever to rotate and retract, and pulls fixed plate of movable mold to move backward along tie rod to complete mold opening process.
Simplified force analysis diagram of fixed mold and fixed plate is shown in Figure 2. Fixed mold and fixed plate mainly bears two parts of force, which are clamping force P transmitted by mold clamping mechanism to fixed mold fixed plate through mold, and pulling force of tie rod acting on four connecting holes on fixed mold fixed plate, which are T1, T2, T3 and T4 respectively. Under ideal conditions, default T1=T2=T3=T4=T, then following relationship is established: P=4T. Among them, under full load condition, P=680 kN; T represents pulling force of tie rod acting on connection hole on fixed plate.

 

Figure 2 Simplified diagram of stress analysis of fixed plate of fixed mold

Based on structural characteristics of mold clamping mechanism, software UG12.0 was used to establish a partial assembly model of fixed mold fixing plate in mold clamping mechanism, and following modeling process was performed.
(1) Simplifying fixed plate mold, such as simplifying screws, bosses, fillets and other structures, can reduce capacity and shorten calculation time.
(2) Model mainly analyzes stress and deformation of fixed plate. Tie rod model can be ignored. When conducting finite element analysis of fixed plate, it only needs to be constrained at threaded holes of mold base.
(3) Based on design of conventional die fixing plate, material is QT500-7A ductile iron. Material properties edited in Workbench software are as shown in Table 1.

Table 1 QT500-7A ductile iron material properties

Fixed mold fixed plate is imported for mesh division. In order to facilitate observation and judgment of stress points and deformation points, mesh of stressed area of fixed mold fixed plate is refined. Divided mesh is shown in Figure 3.

 

Figure 3 Mesh division

According to actual working conditions of injection molding machine, loads and constraints are added to topology optimization model of fixed mold fixed plate. Load and constraints are shown in Figure 4.

 

Figure 4 Loads and constraints of fixed plate of fixed mold base
(1) Positioning constraints. Fixed mold fixing plate forms positioning constraints with the four tie rods of mold closing mechanism and injection molding machine base respectively. They form spatial position constraints at tie rod mounting holes on fixed mold fixing plate and at the center of connecting screw holes between fixed mold fixing plate and injection molding machine base.
(2) Add load. Hydraulic force of mold clamping mechanism will pass through movable mold fixed plate, mold, fixed mold fixed plate, tie rod, and rear template to form a force circulation effect on mold clamping mechanism. Therefore, fixed support force between fixed mold fixed plate and injection molding machine base has a small deformation and influence on fixed mold fixed plate, can be ignored; force causing deformation of fixed mold fixed plate comes from clamping force P transmitted by mold clamping mechanism to fixed plate through mold, and pulling force T of tie rod acting on four connection holes on fixed plate.

Based on Shape Optimization analysis of Workbench, a lightweight design is carried out for fixed mold plate. As shown in Figure 5, injection holes, mounting holes, tie rod holes, etc. of fixed mold fixing plate are functional areas for equipment installation and assembly, and are non-designable areas. Surrounding area outside non-designable area is designable area, and topology optimization design is carried out around designable area to achieve lightweight design.

 

Figure 5 Fixed mold fixed plate optimization area

Essence of variable density method is to divide design structure into finite cells, set divided finite cells as independent optimization variables, and change change domain from discrete [0, 1] form to continuous [0, 1] form, establish a corresponding empirical formula to penalize unit materials so as to gradually converge to both ends of 0/1. Final topology optimization result is a model approaching discrete [0, 1].
Combined with experiments, static load conditions of continuum structure are considered, and topology optimization problem of maximizing structural stiffness (minimizing flexibility value) under limited mass (volume) is discussed. Taking maximum stiffness of fixed plate as target and constraining its mass retention percentage, topology optimization mathematical model is:
 
 
 
 
In formula: p1 - relative density of i-th unit, g/cm3; c1 - total strain energy of fixed mold fixed plate; p0 - original density of unit, g/cm3; p - total number of working conditions; Voi - Volume of i-th unit, cm3; m0 - initial weight of fixed mold plate, g; ∝ - weight retention percentage.
According to topology optimization mathematical model and using iterative convergence analysis, topology optimization is feasible.

Based on topology optimization area determination, response is set to material density, response type is selected for compliance, maximum number of iterations is 500, minimum normalized density is 0.001, and weight is used as response. Quality retention percentage is selected as 90%, and topology optimization iteration is shown in Figure 6. As number of optimization iterations increases, combined target convergence curve shows a downward trend. After 10 iterations, combined target convergence curve intersects with combined target convergence standard curve. Iteration is stopped after 12th time, and target retention percentage error is 3.49%, which satisfied convergence results and achieved optimization goal. Combined target convergence curve has no rising process during iteration process, indicating that optimization process is in line with expected results of experiment and proves that experiment is feasible.

 

Figure 6 Fixed mold fixed plate optimization iteration curve

When designing mold plate, in order to enhance rigidity of fixed mold fixed plate, structure of middle area, base and connecting rod contact area remains unchanged. In order to ensure that fixed mold fixed plate meets installation dimensions of injection molding machine, dimensions of four sides remain unchanged, and other areas are optimized. Based on optimization design cloud chart shown in Figure 7, results show that fixed mold fixed plate forms a cross-shaped figure, remaining part is non-optimizable design area that must be retained. Deleted part represents optimizable design area, in which processing such as resection can be performed. Marginal part represents transition area between designable and undesignable areas, can be appropriately optimized and designed. In order to ensure normal installation of mold between moving and fixed mold fixed plates, safety and stability of mold clamping mechanism, default processing is adopted for non-optimizable design areas and transition areas, only optimized design areas are optimized, forming two types of optimized designs. Scheme is shown in Figure 8.

 

Figure 7 Fixed mold fixing plate design area

 

Figure 8 Design of fixed mold and fixed plate before and after optimization
Optimization plan 1 is shown in Figure 8(b). A trapezoidal hollow is made around fixed mold fixed plate. Upper bottom edge closer to center of fixed mold fixed plate is changed to an arc of R200 mm, and length of lower bottom edge is 200 mm, distance between lower bottom edge and center of upper bottom arc is 40 mm, hollow thickness is thickness of the entire template, four hollow center positions are all located 220 mm from center of fixed mold fixed plate, and are all in positive z-axis direction. Based on actual situation, corners of hollow part were chamfered to make fixed mold fixed plate easier to cast. At the same time, in order to meet structural strength, hollow part was connected to four sides, which improved the overall strength of fixed mold fixed plate.
Optimization Plan 2 is shown in Figure 8(c). Based on Optimization Design Plan 1, two hollow quadrilaterals are designed on four sides of fixed mold fixing plate. Dimensions of quadrilateral are 60 mm * 20 mm * 20 mm, hollow center is 60 mm above and below center of four sides to further optimize quality of fixed mold plate.
Comparing weight and processing area of unoptimized mold plate and optimized plan mold plates 1 and 2, as shown in Table 2, model weight of optimized plan 1 and 2 is reduced by 16.06 and 18.07 respectively compared with unoptimized version (167.95 kg). kg, reduced by 9.56% and 10.75%; processing area of optimization schemes 1 and 2 also decreased from 5 092.26 cm2 to 4 547.86 cm2, a decrease of 10.69%. Analysis results before and after optimization show that: under conditions of deformation and stress when injection molding machine is working, fixed mold fixing plate can achieve lightweight design, achieve effect of reducing weight, and effectively save costs.

Table 2 Comparison of quality and processing area before and after optimization

For optimized design, it is necessary to ensure that strength and deformation under production conditions are met without affecting molding quality of product. Based on this, finite element simulation analysis was conducted on fixed mold fixed plate before and after optimization. Results are shown in Figure 9. Maximum total deformation of fixed mold fixed plate before optimization was 0.055 768 mm in actual working conditions. Maximum total deformation of mold fixed plate is 0.053 962 and 0.054 041 mm respectively. Compared with deformation of fixed mold fixed plate before optimization, deformation is reduced, maximum total deformation position before and after optimization is same, both at the edge of injection port. position, as injection port position extends to four sides, the total deformation gradually decreases, and the total displacement of constraint position is zero.

 

Figure 9 Strain cloud diagram of fixed mold and fixed plate before and after optimization
Results show that under actual working conditions, deformation of fixed mold fixed plate before optimization is small, and deformation of fixed mold fixed plate after optimization is further reduced. Although amplitude is not large, it is enough to show that optimized design schemes 1 and 2 can meet production needs, make improvements; optimized design changes structure of fixed mold plate, reduces weight, reduces processing area and other optimization indicators can be achieved, and stiffness of fixed plate is also guaranteed.
For optimized design scheme, finite element analysis results of strength of fixed mold fixed plate are shown in Figure 10. Maximum stress before optimization is 65.282 MPa. Maximum stress of fixed mold fixed plate of optimization schemes 1 and 2 is 95.819 and 99.395 MPa respectively. Compared with original fixed mold fixed plate, optimized design schemes 1 and 2 have stress increases of 30.537 and 34.113 MPa respectively, maximum stress positions before and after optimization are same, both at contact point between connecting rod and offset injection port of fixed mold fixed plate. Although maximum stress of optimized design options 1 and 2 is higher than that of unoptimized mold plate, maximum equivalent stress does not exceed 100 MPa, both of which are within allowable range of project that is, optimization schemes 1 and 2 are reasonably designed and can be realized.

 

Figure 10 Stress cloud diagram of fixed mold plate before and after optimization
Comparing optimization options 1 and 2, mass reduction effect of option 2 is obviously better than that of option 1. When processing area reduction is same and equivalent stress changes not significantly, option 2 should be the first choice for design.