Kai-de WANG, Kai-kai HAN

(1Xuzhou Vocational College of Bioengineering, Xuzhou 221006, China) (2College of Mechanical Engineering, Donghua University, Shanghai 201620, China)

Abstract: The bed as an important support is the basis of the entire machine tool. The rigidity and stability of the bed will directly affect the size and surface accuracy of the workpiece. The natural frequency of the bed is an important parameter for evaluating the dynamic performance of the grinding machine. Increasing the natural frequency of the bed can effectively increase the structural rigidity of the bed. After the modal analysis of the bed, it visually shows the weak links in the design stage of the structure. The natural frequency of the bed could be increased by improving its structure. The optimal improvement results of grinder bed body was obtained by comparing different improvement schemes, which provide a theoretical basis and engineering reference for the subsequent structure design of the grinder bed.

Key words: Grinder bed, Natural frequency, Modal analysis, Structure optimization

The main function of the grinder bed is to bear the load, the dynamic characteristics of the bed structure have a very close relationship with the performance of the whole machine. It is of great significance to improve the dynamic characteristics of the bed of the grinding machine to ensure the machining accuracy of the machine [1]. The modal characteristics of the bed as an important indicator to evaluate the dynamic performance of the whole grinding machine play an extremely important role in the bed design stage. In the modal analysis of the bed structure of the grinding machine, the low-order frequency band can be easily coupled with the relevant external excitation conditions, and the influence of the low-order vibration mode of the structure is much higher than that of the high-order vibration mode of the structure [2]. Therefore, in the modal analysis, the entire dynamic performance of the bed structure depends on the dynamic characteristics of the lower-order modes of the bed structure.

In this paper, the structure of the grinder’s bed is optimized, the low-order natural frequency of the bed is used as the target of the dynamic optimization of the bed structure, and the low-order natural frequencies of the bed structure are improved by adopting different structural optimization forms and finally the optimal design scheme of grinding bed structure could be obtained.

1 Finite element analysis of bed structure

1.1 Bed structure establishment and model simplification

The establishment of a complete and effective bed model is the basis for finite element analysis and optimization. Because there are many ribs inside the bed of grinding machine and the structure is more complicated, and the software SolidWorks has the advantages of convenience and easy modification, SolidWorks is adopted in this paper to carry out solid modeling of the bed. In order to prevent errors when importing files and reduce the amount of calculation in finite element analysis, the model of the bed was simplified during the modeling process, and some small grooves and slender step surfaces were eliminated. Partial chamfering and other details make the simplified model similar to the original one [3].

Simplifying the model can effectively reduce the number of units in the bed model, reduce software calculation time, improve the efficiency of software analysis, reduce the cost of analysis, speed up the implementation of the project, and win more benefits for the enterprise. The simplified bed model in this paper is shown in Fig.1.

Fig.1 The structure of grinder bed

1.2 Material properties and grid division and the application of boundary conditions

1.2.1 Definition of material properties

The bed material of the grinder is HT250, the elastic modulusE=1.1×105MPa of the bed material, Poisson’s ratioγ=0.28, densityρ=7.2×103kg/m3.

1.2.2 Partitioning of finite element meshes

According to the solid model characteristics of the bed and the structural features of the bed, a three-dimensional hexahedral eight-node solid element is used in the mesh division unit, and because the line and surface in the bed are numerous and difficult to control, therefore, it is advisable to use the method of intelligent grid division for grid division. The mesh structure of the bed is shown in Fig.2.

Fig.2 FEM mesh model of machine tool bed

1.2.3 Application of boundary conditions

The bed of the grinding machine is fixedly connected to the ground through 22 anchor bolts, which impose full restraint on the bed and limit the six degrees of freedom on the bed bottom. In other words, the moving pair and rotating pair along x axis, y axis and z axis are all constrained, The constraint boundary conditions of the bed are shown in Fig.3.

Fig.3 Constraint boundary conditions of machine tool bed

1.3 Bed modal analysis results

The bed of the grinding machine must be designed to ensure that it has a certain resistance to external loads and changes, and to ensure that the dynamic mechanical properties during the machining process are good, which requires the bed to have sufficient ability of rigidity and resistance to vibration [4]. Modal analysis is an effective method to analyze, predict and optimize the dynamic performance of a system by means of a series of modal parameters of the vibration system [5].

The bed part is a continuous entity, and its mass and elasticity are presented as continuous distribution. Therefore, the bed structure has infinitely many modes. In modal analysis, the entire dynamic performance of the structure depends on the low-order modes of the structure. Dynamic characteristics, therefore, in the actual engineering applications, is very important and we only need to analyze the first six order modal of the structure[6]. Fig.4 shows the mode shape diagram of the first to sixth order grinding machine bed analyzed in this paper. Table 1 is the description of the first 6 natural frequencies of the bed and the corresponding mode shape characteristics.

From Fig.4 and Table 1, it can be seen that the first natural frequency of the grinding machine bed is relatively low, which is close to the working frequency of the electric spindle of the grinding machine (214 Hz). When the electric spindle is working, it is high likely that resonance occurs with the bed, and the bed The torsional vibration is exhibited, which causes corresponding vibration of the guide rail, which greatly interferes with the machining accuracy of the machine tool. Therefore, it is necessary to properly improve the frame structure and layout of the grinder bed to further improve the rigidity and stability of the machine bed structure.

2 Bed structure optimization design

In order to further improve the rigidity and stability of the bed structure, under the premise of basically unchanged dimensions, this paper optimized the bed and rib thickness, rib size and ribs distribution, and analyzed the influence of various structural parameters on the dynamic characteristics of the bed, which provides a necessary engineering basis for the optimal design of the bed [7-8].

In the modal analysis, the entire dynamic performance of the structure depends on the low-order modal dynamic characteristics of the structure [9-10]. Therefore, the first two natural frequencies of the structure are selected as targets for bed optimization and the structural optimization scheme is as follows:

(1) Change the wall thickness and rib thickness of the bed

Changing the thickness of the bed and the thickness of the ribs will cause the weight of the bed to be changed. Casting cracks are likely to occur during the bed casting process. At the same time, the increase in the weight of the bed will also bring great difficulties to the bed casting process. On the other hand, excessively increasing the weight of the bed will further reduce the dynamic stiffness of the bed, which is not conducive to the optimization of the bed structure. Therefore, in order to reduce the effect on the bed structure caused by the increase in the wall thickness of the bed and the thickness of the ribs, this paper controlled the variation of the thickness of the bed and the thickness of the ribs within a reasonable range. The following will give six aspects of improvement to alter the wall thickness and rib thickness of the bed: (a) increase the wall thickness of the bed by 2 mm; (b) increase the thickness of all ribs of the bed by 2 mm; (c) all wall thickness and rib thickness get increased by 2 mm; (d) all wall thicknesses of the bed get increased by 2 mm, and all ribs of the bed get increased by 5 mm; (e) all wall thicknesses of the bed get increased by 5 mm and all ribs thickness get increased by 2 mm; (f) all wall thicknesses and ribs get increased by 5 mm.

The corresponding modal analysis was performed on the improved models. The analysis results showed that the improved grinder bed was completely consistent with the original grinder bed, and the bed’s natural frequency got changed as well. The vibration characteristics of the improved grinder bed are shown in Table 2.

Table 2 Comparison table of vibration characteristics of grinding bed

From Table 2, we can see that the increase in thickness can generally increase the strength of the structure. Similarly, increasing the thickness of the machine bed and ribs can also increase the natural frequency of the bed, and in the above table we can find that: in terms of natural frequency, it is better to increase the wall thickness of the bed than to increase the wall thickness of the ribs. Therefore, in increasing the natural frequency of the bed, increasing the wall thickness of the bed should be the preferred method.

(2) Change the shape and size of the openings in the wall and inner ribs

A lot of holes are opened in the wall of the bed of the grinding machine and the inner ribs. These holes can reduce the weight of the bed on the one hand, and on the other hand, they are also convenient for sand cleaning when the bed is cast. In this paper, the following five kinds of improvement schemes to change the shape and size of the openings of the bed ribs are given for the existing process conditions and the actual production conditions of the company: (a) all openings in the wall of the machine bed are closed; (b) the size of the opening in all the ribs inside the bed is reduced by 1/5; (c) the size of all the rib openings in the bed is reduced by 1/5, and then all opening shapes are replaced with the same area. (d) reduce the size of the opening on all ribs in the machine tool bed by 1/3; (e) reduce the size of all ribs in the bed by 1/3, and then open all the openings. The shape of hole is changed to an equal area of a circular hole. The comparison of the low-order vibration characteristics of the improved grinder bed is shown in Table 3.

Table 3 Comparison of low order vibration characteristics of grinding bed

It can be seen from Table 3 that all the openings in the machine bed wall are closed in the modification (a), however, because the number of holes in the bed wall of the machine is few, the rigidity of the bed body is almost unaffected after closing all holes in the bed wall of the machine, so there is no obvious change in the natural frequency of machine bed; the comparison of the improvement scheme (b) and improvement scheme (d) could be obtained after reducing the size of the hole in the rib plate. It can further enhance the bed’s internal ribs’ load carrying capacity, and the bending resistance of the bed can be further enhanced, so that the natural frequency of the bed can be further improved. And the smaller the size of the steel plate, the higher the natural frequency of machine bed. By comparing the improvement schemes of (b), (c), (d) and (e), it can be seen that changing the square hole of the reinforcement plate into a circular hole of the same area will further improve the natural frequency of the machine bed. Therefore, in terms of increasing the natural frequency of the bed, reducing the size of the square holes in the inner ribs or changing the square holes in the inner ribs to circular holes of the same area could significantly improve the natural frequency of the machine bed.

(3) Change the layout of the ribs inside the bed

Increasing the number of ribs in the bed of the grinding machine can increase the load-bearing capacity and bending resistance of the bed, which in turn can increase the natural frequency of the bed. Based on the original bed, this paper further analyzed the change of bed natural frequency by increasing the number of bed ribs and changing the arrangement of ribs. In the scheme of changing the layout of bed ribs, this paper specifically proposed the following three improvement schemes:

(a) A longitudinal rib is added to the longitudinal “X”-shaped ribs of the bed, so that the improved longitudinal ribs are in the “*” shape. The improved bed is shown in Fig.5.

Fig.5 Improved * - type bed plan

(b) Two additional rows of oblique ribs are added to the horizontal “well” ribs of the bed so that the increased transverse ribs are “W” shaped. The improved bed is shown in Fig.6.

Fig.6 Improved W - type bed plan

(c) After the merger of improvement scheme (a) and improvement scheme (b) as comprehensive scheme (c), the improved bed scheme is shown in Fig.7.

Fig.7 Improved integrated bed and body plan

Table 4 shows the comparison of low-order vibration characteristics of the grinder bed after the above three improvement schemes.

Table 4 Comparison of low order vibration characteristics of grinding bed From Table 4, it can be seen that in the improvement scheme (a), a longitudinal rib is added to the longitudinal “X” rib of the bed, which not only does not improve the natural frequency of the bed, but also reduces the bed Natural frequency; improvement scheme (b) and improvement scheme (c) increase the natural frequency of the bed but the increase is small. In changing the layout of the bed ribs, these three improvement schemes have adopted a method of increasing the number of ribs, which has greatly increased the quality of the bed, but the overall improvement of the natural frequency of the bed is not ideal. This shows that, in increasing the natural frequency of the bed, simply increasing the number of ribs does not necessarily increase the natural frequency of the bed. Therefore, changing the layout of the bed ribs should be considered from the aspect of the dynamic characteristics of the structure, and the natural frequency of the bed can be further improved by changing the overall structural layout.

3 Analysis of bed structure analysis and actual test after optimized design

Based on the above results of various analysis and optimization, this paper finally selected the optimal form of improvement of each scheme to optimize the design of the grinder bed. The final optimized design scheme is to increase the wall thickness and rib thickness of the grinder bed by 5 mm. The shape of the opening of the internal ribs is changed to the same area of the circle, the layout of the ribs, the number of ribs, the position of the ribs does not change. The analysis values of the natural frequency of the new bed and the test values measured by the hammer method are shown in Table 5. The measured physical spectrum of the new bed is shown in Fig.8.

Table 5 Comparison between the analytical value of the new bed and the test value measured by the hammering method

Fig.8 The physical spectrum of the new bed

According to Table 5, in the first natural frequency, the new bed is increased by 14.95 Hz compared with the original bed, and the optimized goal is basically achieved. In Table 5, it can be seen that the natural bed has a natural frequency analysis value. The test values measured by the hammer method are basically consistent, and the change values are all within 10%, indicating that the optimization scheme is feasible.

4 Conclusion

In this paper, the modal analysis of the structure of the grinder bed is performed. By extracting the first six natural frequencies of the bed and describing the mode shape, the deformation characteristics of the bed are found, and then the weak link of the bed structure rigidity is defined. Through the comparison of various optimization schemes, the optimal form of the grinder bed is finally determined, and the feasibility of the optimization scheme is confirmed by the test method, which provides a theoretical basis and engineering reference for the design of the subsequent grinder bed structure.