Design and finite element optimization analyses of accessory ultrasonic vibration working table
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摘要:
超声振动辅助加工为合金材料、硬脆材料和复合材料等难加工材料提供了有效的机械制造解决方案，超声振动辅助加工装置结构复杂、专业化程度高、使用可靠性差等因素制约了超声加工技术的推广及民用化历程。为了推广超声振动辅助加工的应用范围，基于超声能量传播原理，设计了一种机床附件化的超声振动工作台，能够方便地安装于加工中心上为工件提供超声振动辅助加工。首先，选用2种材料对工作台进行整体结构设计，通过模态分析确定工作台的工作频率及振动形式，使用谐响应分析揭示工作台工作时的稳定情况。其次，采用多目标优化方法对工作台进行结构优化，在保证总模态变形量不变的情况下降低振动台的质量，以减小超声能量损耗的同时提高振动状态的可靠性。最后，对比优化前后的有限元分析结果确定工作台材料并进行尺寸调整，使其更加符合实际加工需要。分析结果表明，45#钢工作台在工作时的振动稳定性要好于Cr12Mov钢工作台，但Cr12Mov钢工作台具有较大振幅。通过多目标优化使得振动台的总体质量降低27%，其工作频率同时降低11%，优化后2种工作台的共振频率带宽相差较小。
Abstract:Ultrasonic vibration assisted machining provides effective manufacturing solutions for difficult-to-machine materials such as alloy materials, brittle materials and composite materials, which is widely used in aerospace, defense, electronics and other high-technology fields. The complex structure, high degree of specialization and poor reliability of ultrasonic vibration assisted machining device restrict the promotion of ultrasonic processing technology. In order to popularize the application scope of ultrasonic vibration assisted machining, an accessory ultrasonic vibration working table is designed based on the principle of ultrasonic energy transmission, which can be conveniently installed in the machining center to provide ultrasonic vibration assisted machining for the workpiece. First, two types of materials were applied to structural design of the table, the working frequency and vibration form were determined through the modal analysis, and the working stability was presented by harmonic response analysis. Second, the working table structure optimization was carried out by the method of multi-objective optimization. The quality of the working table was reduced under the condition of guaranteeing invariable total deformation, in order to reduce the loss of ultrasonic energy and improve the working reliability. Finally, in order to make the working table more suitable for the actual machining needs, the material of the working table was selected and the table size was adjusted by comparing the results of finite element analysis before and after optimization. The results of analysis indicate that 45 # steel vibration working table has better vibration stability and smaller vibration amplitude. The overall mass of the vibration table was reduced by 27%, the working frequency was reduced by 11% through multi-objective optimization. The bandwidth difference of resonance frequency between the two workbenches is quite small.
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图 1 工作台与振动子的连接示意图
Figure 1. Schematic diagram of connection between working table and vibrator
图 4 Cr12Mov钢工作台部分模态振型
Figure 4. Partial modal vibration shape of Cr12Mov steel working table
图 6 优化后Cr12Mov钢工作台部分模态振型
Figure 6. Partial modal vibration shape of Cr12Mov steel working table after optimization
图 7 优化后两种工作台谐响应分析
Figure 7. Harmonic response analysis of two types of working tables after optimization
图 8 优化后Cr12Mov钢工作台带工件部分模态振型
Figure 8. Partial modal vibration shape of Cr12Mov steel working table with workpiece after optimization
表 1 材料性能参数
Table 1. Material performance parameters
材料 弹性模量/(N·m-2) 泊松比 材料密度/(kg·m-3) 45#钢 2.09×1011 0.269 7 890 Cr12Mov钢 2.18×1011 0.28 7 850 
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表 2 45#钢工作台前8阶模态频率
Table 2. The first eighth-order modal frequency of 45# steel working table
阶数和模态 频率/Hz 1 17 381 2 18 423 3 19 196 4 19 668 5 20 694 6 21 199 7 21 693 8 21 782
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表 3 Cr12Mov钢工作台前8阶模态频率
Table 3. The first eighth-order modal frequency of Cr12Mov steel working table
阶数和模态 频率/Hz 1 17 787 2 18 845 3 19 640 4 20 126 5 21 165 6 21 690 7 22 182 8 22 268
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表 4 优化候选点
Table 4. Optimization candidate points
参数 候选点1 候选点2 候选点3 P1-DS-D1/mm 162.9 170.1 164.7 P2-DS-D1/mm 221.73 227.85 246.23 P3-DS-Exturde1.FD1/mm 36.2 39.756 38.867 P4-Solid Mass/kg ★★★8.742 4 ★10.472 ★10.724 P5-总变形量最大值/mm 0 0 0
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表 5 优化后Cr12Mov钢工作台前8阶模态频率
Table 5. The first eighth-order modal frequency of Cr12Mov steel working table after optimization
阶数和模态 频率/Hz 1 17 077 2 17 138 3 17 159 4 18 049 5 18 063 6 19 796 7 21 193 8 22 468
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