Topology is an important branch of mathematics, which mainly studies the related characteristics that geometric figures can remain unchanged when they change shape continuously, that is, the invariance and invariance of topological space under topological transformation. Optimization is a branch of applied mathematics, and it is a method to select a scheme to achieve the optimal goal under certain constraints, which has been widely used in many fields such as engineering design and project management. At present, Japanese automobile researchers are combining topology method, optimization and computer aided engineering (CAE) perfectly, and successfully applying them to the optimization process of engine cylinder block and control arm under suspension. This paper introduces the basic principle and optimization results of applying topology method to optimize automobile parts, and shows the optimization examples of applying topology optimization analysis program to spot welding position and binder position.
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In order to protect the environment and improve fuel consumption, major car companies are rapidly promoting the lightweight of car bodies. In order to realize light weight, high-strength steel plate is preferred for automobile white body. With the application of high-strength steel plate, the thickness of the plate is reduced accordingly, and the stiffness of the whole car body is also reduced. As a relevant countermeasure, it is essential to use the lightest material to make up for the reduced stiffness. At present, it can be improved by topological optimization method. Topology optimization method is to keep the necessary units under the premise of giving certain design space. Through topology optimization design, complex and unique shapes can be applied to parts. At present, this method has been applied in the optimization process of engine cylinder block and control arm under suspension. As far as the car body composed of thin plates is concerned, it is difficult to design specific parts shapes by topological optimization method because the unit size and calculation load must be considered emphatically in the process of topological optimization, and the unit size cannot be excessively reduced. Based on the preliminary design guide, the researchers realized the topological optimization of the thin shell element for the part with high sensitivity in the current car body structure.
in this paper, the design space composed of solid elements is introduced into the automobile body structure composed of thin shell elements, and the topology optimization method is used to improve the shape of parts. In addition, the application of topological optimization analysis program in spot welding and an example of the optimization process of adhesive coating position are introduced.
1? Shape optimization of parts based on static stiffness of white body
1.1? Analysis method
fig. 1 shows the whole vehicle model used in the optimization process of body in white. The whole vehicle model was published by NCAC, and the car body is composed of thin shell units. Fig. 2 shows four constraints of the car body carrying load. Restraining the front suspension mounting parts and the rear coil spring mounting parts * * * accounts for three of the four conditions, and the remaining load condition is to load 1? ? N? Load. At the same time, the researchers set four conditions for changing the load position, and used the body-in-white shown in Figure 1 to verify the rationality of the spatial design method adopted in the car body composed of thin shell units. The target part is set as the joint part of the side member and the cross member used to constitute the rear floor in sensitivity analysis. Fig. 3 shows an optimized target component. In the process of introducing the design space, the researchers removed the terminal parts of the transverse members, thus arranging the design space composed of solid units. Considering the load transfer requirements, the design space composed of solid units is connected with the end of the transverse member, the rear side member and the floor composed of thin shell units. The objective condition of optimization is to minimize the sum of ride comfort of the four load conditions shown in Figure 2. Constraints should also take into account the shape of parts generated by thin plates in the design space, and set its volume percentage as 2%. In addition, the researchers make full use of the reserved results based on topology optimization method to optimize the shape of the part and ensure its stiffness.
1.2? Optimization result
Figure 4 shows the remaining part of the car body after topology optimization. The reserved part is composed of rear side members and cross members, and the floor side plane of the design space is mainly reserved. It is generally believed that the load should be transferred from the loading point to the floor through side members and cross members.
1.3? Shape research based on optimization results
Figure 5 shows the shape comparison between the new parts generated by topology-based optimization method and the original parts. The optimized parts are connected with the side members, transverse members and floor by spot welding as the original parts. Based on the original parts, the torsional stiffness of the optimized parts is improved by about 4.3% and the mass is increased by .1kg. Under normal circumstances, it is difficult to improve the torsional stiffness of the car body. From the point of view of quality efficiency, researchers believe that the torsional stiffness can be optimized by this method (that is, the stiffness of parts can be strengthened at the expense of minimum mass increase).
figure 6 illustrates the effect of the optimized parts by comparing the strain energy distribution. In this optimization example, the sum of ride comfort of parts can be minimized. In the original part, the edge of the transverse member and the corner position of the floor have produced great strain energy. Therefore, it is confirmed that the strain energy of the edge line and corner position of the transverse member has been greatly reduced after optimization.
2? Part shape optimization of eigenvalue of white body
2.1? Analysis method
Figure 7 shows the bending deformation state of the front part of the car body obtained by using the eigenvalue analysis of computer aided engineering (CAE). As the object of this study, the front bending mode that only moves in the width direction of the car body is selected. The total length of the car body is 4? 178? Mm, and its deformation is represented by 25 times. As can be seen from fig. 7, the car body will only face the state of front bending. From the characteristic value of this bending mode, the original car body bending characteristic value is 31? Hz, the front bending characteristic value of the car body with better handling safety will be 4? Above Hz Therefore, researchers will be more than 4? The higher value of Hz is taken as the goal to carry out research.
for the body-in-white shown in fig. 1, the optimization model is established by introducing the method of space design into the body composed of thin shell units. The target part of the optimization process is set as the front part from the radiator bracket to the upper part of the engine in the front lateral bending area. Fig. 8(a) shows the state of the original vehicle body; Fig. 8(b) shows the state after the parts are removed from the original car body; Fig. 8(c) shows the state after the design space composed of solid units is introduced into the whole vehicle model. For the car body with the radiator fixing frame and fender bracket removed and the front member retained, the design space composed of solid units is configured. In addition, considering the load transfer demand, the design space and the car body are connected, and the optimization target conditions are set to maximize the front bending characteristic value, and the volume percentage of the front bending characteristic value is set to be below 2%. As a verification of performance, models with different cross-section shapes are generated by using the reserved results after topology optimization, and their shapes and plate thicknesses are adjusted at the same time, thus verifying the eigenvalues. In addition, as a technical comparison, the tower-shaped support rod used to fix the bumper is verified, and the parts designed based on sensitivity analysis are taken as the optimization target, and the situation that the characteristic value is improved by increasing the plate thickness is verified.
2.2? Optimization result
fig. 9 shows the state that remains after topology optimization using the car body model. The result of retaining the features is that the front part presents an X-shape. First, the radiator fixing frame is shrunk once, and then it is connected with the left and right mounting parts of the bumper, and then it is shrunk at the lower part of the car body again, thus obtaining the state result after reservation. From the results, it can be seen that in order to improve the characteristic value of the front bending, the scheme of supporting the front suspension and bumper through connecting parts is effective.
2.3? Research on the shape of parts based on optimization process
The parts designed after optimization are assembled on the car body, and as a comparison with the optimized parts, a tower-shaped support rod connecting the left and right suspensions is adopted. Fig. 1 shows a part with increased plate thickness after sensitivity analysis. The thickness of these parts is also set at 1.2 times, 1.4 times and 2. times respectively, and the eigenvalue analysis is carried out. Fig. 11 also shows the front bending characteristic value of the part after using the tower-shaped support rod, increasing the plate thickness and optimizing the shape. The front bending characteristic value of the optimized parts is 55? Hz, this kind of value is greatly improved. Increase the characteristic value of tower-shaped support bar by .2? Hz, for the front bending parts, the increase of eigenvalue can not play a significant role. In addition, even if only the thickness of high-sensitivity parts is increased, for example, by 25? Kg, for example, the characteristic value can only be increased to 35? Hz, its effect can not be compared with the optimization process.
3? Optimization of spot welding position of body-in-white
3.1? Analysis method
fig. 12 shows a schematic diagram of the spot welding optimization program. The figure simulates the flange part of the part, and it is pressed 2? mm? Example of adding welding points by interval setting. The original welding point is 4? mm? Spacing arrangement, after optimization, according to the minimum 2? mm? The spacing is set as the target welding point of the optimization process. According to the topological optimization method, only the welding points which have a great effect on improving the stiffness are reserved.
in the vehicle model, according to 1? mm、2? mm、3? mm? The minimum welding point spacing is adjusted respectively, and its influence on stiffness is studied. The vehicle model uses the car body shown in Figure 1, and the load condition uses the torsional stiffness load constraint condition shown in Figure 2, and the welding points are described by solid elements. Compared with the original setting of 3 on the car body? 96 solder joints, according to the minimum of 2? mm? The welding point spacing; Set the optimized target number of welding points as 3? 168; Press the minimum 1? mm? The optimized target number of welding points is set at 1? 932; Press the minimum 3? mm? Set the optimal target number of solder joints as 1? 679. The above-mentioned welding points are set as the target conditions for the subsequent topological optimization process, so as to minimize the sum of the ride comfort of the four load conditions and make them the constraint conditions with the maximum stiffness, thus retaining the ratio of the number of welding points to the number of optimized welding points. The number of welding points reserved after optimization is set to 2, 4 and 6 respectively according to the minimum welding point interval. In addition, the reserved results based on topology optimization process are used to generate the vehicle model, and its stiffness is verified by CAE.
in addition, other welding points are added near the welding points with high strain characteristics, and the results are compared with the optimized ones. Fig. 13 shows a schematic diagram of supplementing welding points by a conventional method. The method adopted is that the distance between the two sides of the welding point with large strain energy is 2? mm? Two welding points are added to the position of. The welding points under the above four load conditions are sorted according to the sum of strain energy, and the target number of welding points is set to 1. On both sides of the 1 target welding points, press a minimum of 2? mm? 2 welding points have been added to the distance between the joints.
3.2? Results of optimization analysis of welding point positions
Figure 14 shows the welding points remaining after topology-based optimization under the conditions of minimum welding point spacing of the whole vehicle model. This is the result of adding 2 welding points under various welding point spacing conditions. The reserved welding points are mainly distributed in the rear cross member (rear cross member), the upper and lower parts of the B-pillar of the car body, and a? Perimeter of column and tower support of shock absorber. In addition, when the distance between welding points is small, it can be seen that the reserved welding points are densely distributed; When the interval between welding points is large, it can be seen that the reserved welding points are scattered.
figure 15 shows the effect of improving the rigidity of the car body by supplementing the welding points by using the topological optimization process. Under the condition of all minimum welding point spacing (i.e. welding point spacing is divided into 1? mm、2? mm、3? Mm), with the continuous supplement of welding points, the stiffness is improved. But when the distance between welding points is 3? mm? With the increase of welding points, the effect of stiffness improvement gradually tends to saturation. In addition, under the condition of the same supplementary welding points, the smaller the spacing of welding points, the more obvious the effect of stiffness improvement. This kind of phenomenon is due to 1? mm? The interval between welding points is small, so the position of welding points which are beneficial to improving stiffness can be set reliably; The interval between welding points is 3? mm? Under the condition of, due to the restriction of welding point spacing, it is usually impossible to directly improve the stiffness of components.
fig. 16 shows the comparison of the effects after 2 welding points are supplemented by the traditional method and the topological optimization method respectively. The welding points supplemented by traditional methods are concentrated in the upper and lower parts of the rear cross member and the B-pillar of the car body, while the welding points supplemented by topological optimization methods are basically distributed in the whole car body. Fig. 17 shows the effect of improving stiffness by supplementing spot welding points by using traditional methods and topological optimization methods. The stiffness improvement effect of topological method is 3 times higher than that of traditional method. It can be considered that the position of the subsequent welding points was determined by traditional methods in the early stage, but it could not adapt to the strain state in the process of supplementing welding points. On the other hand, in the application of topological method, it is considered that the position of supplementary welding points has been optimized in order to maximize the stiffness when 2 welding points are supplemented.
4? Optimization of adhesive coating position for biw structure
4.1? Analysis method
As for the optimization of adhesive coating position, the body-in-white model shown in Figure 1 is used, and the load condition is the same as the optimization process of welding point position. In the whole vehicle model, according to the state of coating adhesive on the flange surface, the topological optimization method is used to adjust the retention and study its influence on stiffness. The adhesive is usually set as a solid unit, and the total coating length is set to 13? m? Adhesive for structure. Because the front and rear bumper parts, the roof of the car, the sub-frame and other parts are not the main application parts of the adhesive, they are usually not included in the research objectives.
The researchers set the location where the binder is applied as the target condition in the topology optimization process, so as to minimize the sum of the ride comfort of the four load conditions. In order to maximize the stiffness, the proportional parameter of the amount of binder retained/the amount of binder aimed at optimization is used as the constraint condition. After the optimization process, the proportion of binder retained is set to 8%, 6%, 4% and 2% * * * respectively. In addition, using the reserved results based on topology optimization process, the whole vehicle model is constructed, the coating length of adhesive in the flange length direction is measured, and the stiffness is verified. According to the characteristics of the binder, the elastic modulus used in the research process is 3.? GPa, Poisson's ratio is .45, and specific gravity is 1., and its stiffness is verified by CAE.
The researchers used CAE to accurately construct the structural model. However, in the case of using adhesive, the process is highly dependent on manual operation, thus consuming more man-hours. Therefore, aiming at the optimization process of welding point position, the method of improving the stiffness by adjusting the adhesive coating position is emphatically studied. Because of the automatic supplementary welding points, the working hours can be reduced to less than 5%. Using the optimization program of welding points shown in Figure 12, a 1? mm? The welding points are spaced, and the joint unit is matched.