A 3D model of a rotary blow molding machine frame was established using SolidWorks 3D design software, and imported into ANSYS Workbench for topology optimization and multi-objective optimization. Compared with the initial model, the quality of the rack model after topology optimization has decreased by 8.1%, and its static and dynamic characteristics have decreased slightly, but it is still within a safe range. On the basis of topology optimization, multi-objective optimization of the rack is carried out. Compared with the topology optimization model, the static and dynamic characteristics of the optimized model are improved to a certain extent. Research shows that topology optimization and multi-objective optimization can be combined to be used in similar rack structure optimization, and have certain engineering application value

01.

## Introduction

In recent years, with the continuous development of beverage, food, and medical industries, the demand for PET bottles with many excellent properties has also increased year by year, which requires that the efficiency of the blow molding machine for producing PET bottles can be improved…. At present, the standard blow molding machines on the market mainly adopt a two-step production process (bottle damage preparation and stretch blow molding are completed by two pieces of equipment, respectively), mainly including linear blow molding machines and rotary blow molding machines2. Compared with the linear blow molding machine, the rotary blow molding machine has the advantages of many mold cavities, quick mold replacement, high output and strong stability, and has become the choice of most food and beverage enterprises. Since the domestic PET bottle forming equipment started relatively late, although it has developed rapidly in recent years, there is still a particular gap in the technical level and performance of the equipment compared with those foreign PET bottle forming equipment research and development companies with a long history [3].

As one of the most critical parts of the rotary blow molding machine, the frame supports the weight of the entire rotary stretch blow molding part. The rigidity, strength and stability of its structure play a crucial role in operating the whole equipment. Therefore, how to improve the static and dynamic performance of the frame has become one of the critical issues in designing a high-speed rotary blow molding machine. In recent years, with the rapid development of computer technology. Structural optimization methods and computer technology have gradually been perfectly integrated, and structural optimization modules have appeared in many large-scale general-purpose CAE analysis software, which significantly improves the efficiency and accuracy of structural optimization analysis! 4 The rotary blowing bottle studied in this paper The frame of the machine is welded by four parts, which are the upper panel, the middle panel layer, the lower panel and the foot. The central panel layer is directly welded by many whole steel plates, which increases the quality of the frame itself. Expanding the manufacturing cost of the enterprise. To reduce the rate of the rack and improve its static and dynamic performance, this paper firstly reduces the weight of the rack based on the topology optimization module of the ANSYS Workbench platform. It then uses the response surface optimization module of the ANSYS Workbench platform to perform multi-objective optimization of the rack. Optimization to ensure that the static and dynamic performance of the frame is improved under the condition of reduced mass.

02.

## Analysis of the initial static and dynamic characteristics of the rack

## Establishment of the frame finite element model

The geometric dimensions of the frame are: 4150mmx3750mmx547 mm, the upper and lower panels are made of low-alloy high-strength steel, and the yield limit is about 400MPa. The three-dimensional model of the rack is reasonably simplified according to Saint-Venant’s principle5. Through the seamless connection between SolidWorks and ANSYS Workbench, the 3D model of the rack is imported into the Workbench, and the mesh is divided. In this paper, tetrahedral mesh is used to separate the rack. The unit size of the upper and lower panels and the middle panel layer is set as 40mm, the unit size of the foot is set to 25mm, the Transition is set to Slow, and the Span Angle Center is set to Fine.

## Static analysis of the frame

**1.2.1 Contact and constraint settings**

Because the rack is welded by multiple steel plates of different sizes, it can be regarded as a welded structural part, no need to set contact, just import the 3D model of the rack into Workbench, enter the DesignModeler environment, and then select all aspects Right-click From New Part, so that all parts can be grouped into one part, the standard interface shares the mesh, and the nodes are coupled. The constraints of the rack are set so that the bottom surface of the four feet is a fixed constraint.

**1.2.2 Load settings**

The load on the rack mainly includes 9 parts, which are the weight of the rotating moving parts, the weight of the mold opening and closing guide rails, the weight of the opening and closing guide rails, the weight of the blank star wheel, and the weight of the bottle star wheel. Geared motor The weight of the transition pulley set 1, and the transition pulley set 2. The weight of the transition pulley set 3, of which 1.25 times the safety factor should be set for the rotating moving parts. The specific load parameters are shown in Table 1. The load distribution is shown in picture 2.

**1.2.3 Static analysis results**

The rack’s total deformation and equivalent stress program are obtained by calculation, as shown in Figure 3 and Figure 4. The maximum deformation of the frame is 0111 mm, which appears in the middle and lower parts of the upper panel of the structure, which is related to the load distribution. The maximum stress of the frame is 82.358MPa, which appears at the sharp corner of the contact surface between a foot and the lower panel. From the knowledge of elastic mechanics, it can be seen that the stress at the sharp corner is infinite. The performance in the CAE software is that the stress value at the short corner does not converge. The stress value will continue to increase with the refinement of the mesh, so This value is not advisable. It cannot be used as an accurate value for the maximum stress of the frame. Looking at the equivalent stress cloud map of the rack, we can see that the blue and light blue areas cover the entire rack; that is, the stress value of the rack is generally as small as 36.604 MPa, which is far less than the yield limit of the material used. Through the static analysis of the rack, it can be seen that the original design of the rack was too conservative, resulting in a waste of materials, so the rack structure needs to be further optimized to reduce the quality of the rack.

## Modal analysis of the rack

Modal analysis is the basis of dynamic analysis. Its main work is to solve the living characteristics of the structure, including resident frequency, mode shape and so on. Because the inherent characteristics are only related to the structure itself, the external loads on the structure do not need to be considered when solving, so only the bottom surface of the four feet of the rack is fixedly constrained. Through software calculation, the natural frequencies of the first six modes of the rack are obtained, as shown in Table 2. In practical engineering, the low-order modes of the structure usually affect the structure because the high-order modes are often not quickly excited, so the first three modes of the frame are extracted according to the above method [7-8]. The natural frequency of the first-order mode is 76.673 Hz. Its mode shape is the frame’s vibration along the y-axis, as shown in Figure 5; the natural frequency of the second-order method is 94.906 Hz, and its mode shape is the frame winding. The first-order bending vibration of the z-axis is shown in Figure 6. The natural frequency of the third-order mode is 101.680 Hz, and its mode shape is the first-order bending vibration of the frame around the x-axis, as shown in Figure 7. Because the rotating speed of a specific type of rotary blow molding machine studied in this paper is 45r.pm and the number of mold cavities is 20. Therefore, the working frequency of the blow molding machine is about 15 Hz, which is far lower than the first three modes of the frame. Natural frequency, so there is ample room for structural optimization.

03.

## rack topology optimization

## Rack topology optimization based on ANSYS Workbench

Topology optimization is a kind of structure optimization, which optimizes the structure’s internal layout, so it is also called layout optimization. It is mainly used in the conceptual design stage of the product, especially for those without the optimal structure reference; the topology optimization can roughly determine the optimal shape of the structure. The structure topology optimization combined with the finite element method is essentially a question of whether there are elements. Through the iterative calculation of topology optimization, the components with better force transmission performance are retained, and the factors that have little effect on the structure force transmission performance are removed. Finally, Get an optimal structure that satisfies the requirements. The rack topology optimization studied in this paper is based on static analysis. The element material density as the design variable, the minimum structural compliance (maximum structural static stiffness) as the goal, and the volume reduction percentage as the constraint. The static topology optimization of the middle panel layer of the rack can be obtained through 12 generation selection calculations to get the density program of the unit of the central panel layer of the rack. As shown in Figure 8, the redfish area represents the area that can be deleted. The grey area represents the reserved area.

## Analysis of topology optimization results

Re-model the middle panel layer of the rack based on the unit pseudo-density program, and import the 3D model of the frame after topology optimization into ANSYS Workbench for static analysis and modal analysis. The settings of meshes and constraints are the same as before. . Compared with the original frame, the maximum static stress deformation of the rack after topology optimization increased by 2.7%; the mass decreased by 944kg, a decrease of 8.1%; the natural frequency of the first-order mode increased by 1.9%; the natural frequency of the second-order mode decreased 8.1%: The natural frequency of the 3rd order mode drops by 2.7%. Although the maximum static stress deformation and the natural frequencies of the 2nd and 3rd order modes of the rack after topology optimization are not improved, they are still within the safe range, so the topology optimization of the rack is effective.

04.

## Multi-objective optimization of racks

## Introduction to Response Surface Method

The response surface method is to use experimental design theory to conduct experiments on a specified set of design points. After calculating the data of all design points, the relationship between the objective function and the constraint function is fitted by a multivariate quadratic equation, which is used to predict the response of the non-experimental points. Value method [1. For the case of n variables, the quadratic polynomial response surface model is:

In the formula, X=(x,x2,…,x), x(i=1,2,…,n) is the design variable, BBBB is the unknown variable, and the number L=(n+1)(n+2) /2, so the unknown coefficient B=(B, B2,…B), when determined by the least square method, the number of test points P must be greater than L.

## Multi-objective optimization based on ANSYS Workbench

The middle panel layer of the rack is welded by steel plates of different lengths. By observing the first three-order modes and the total deformation cloud map of the middle panel layer of the rack after topology optimization, select 6, which have a greater impact on the static and dynamic characteristics of the rack. The size parameters are used as design variables for multi-objective optimization, as shown in Figure 9, and the value range is determined for them, as shown in Table 3.

The selection of experimental points in this paper adopts the method of Central Composite Design. Using this method can select appropriate data sample points for the response surface model and has the advantages of good predictability, simple design, and fewer experiments. Because the quality of the rack after topology optimization has been greatly reduced, it is not the goal of this optimization. This optimization selects the maximum deformation of static stress, the first-order natural frequency, the second-order natural frequency, and the third-order natural frequency. The natural frequency is used as the optimization target, and the specific mathematical model is as follows:

## Multi-objective optimization based on ANSYS Workbench

In the formula, d–the static stress maximum deformation of the machine base;

f–the ith order natural frequency of the frame;

f–the lower limit constraint value of the i-th order natural frequency of the frame.

The lower limit constraint values of the first, second and third-order natural frequencies are 79, 88, and 100 Hz respectively: t–the ith design variable;

t–the lower limit constraint value of the ith design variable: t–the upper limit constraint value of the ith design variable.

Because there are 4 optimization objectives at the same time, the MOGA algorithm is used for multi-objective optimization. As a multi-objective genetic algorithm, the MOGA algorithm is usually used to solve two or more objectives that need to be optimized at the same time, and a compromise solution between multiple objectives can be obtained by calculating the solution. 3 groups of candidate optimal design points are obtained through 10 iterations of calculation.

Through comparative analysis, the second group of candidate points is selected as the final optimal design point, and the values of the design variables of this group of candidate points are rounded. The rounded plates 7891418 and 45 are available in thicknesses of 22, 18, 12, 12, 25 and 12 mm.

## Analysis of multi-objective optimization results

Based on the results of the multi-objective optimization of the response surface, the three-dimensional model of the frame is improved, and the modified model is imported into ANSYS Workbench for static analysis and modal analysis. At this time, the mass of the frame is 10722kg, the maximum deformation of static stress is 0.112 mm, and the first three natural frequencies are 79.160 Hz, 88.264 Hz and 100.820 Hz, respectively. Compared with the frame model after topology optimization, the maximum deformation of static stress decreases. Up 1.8%. 1st order natural frequency increased by 1.3% 2nd order natural frequency increased by 1.2%. The 3rd order natural frequency is increased by 1.9%.

05.

## Conclusion

(1) A parametric model of a rotary blow moulding machine frame was established, and its initial static and dynamic characteristics were analyzed by finite elements to provide a reference for the subsequent frame structure optimization.

(2) Adopt the method of multi-level optimization (topology optimization and multi-objective optimization) to optimize the structure of the rack. Compared with the original frame, the optimized frame has greatly improved the quality and the first-order natural frequency, in which the mass is reduced by 939kg, a decrease of 8.1%, and the first-order natural frequency is increased by 2.487 Hz, an increase of 3.2%. The goal of improves the static and dynamic characteristics of the rack while reducing the mass of the rack.