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工程设计学报
Chin J Eng Design  2023, Vol. 30 Issue (1): 117-126    DOI: 10.3785/j.issn.1006-754X.2023.00.013
General Parts Design     
Design and experimental study of wheel amplitude transformer for rotary ultrasonic internal grinding
Biao MA1(),Hui-bin QIN1(),Yi FENG1,Xu-ri BAI1,Jia-yi XIN2
1.Shanxi Key Laboratory of Advanced Manufacturing Technology, North University of China, Taiyuan 030051, China
2.Taiyuan Tools Factory Co. , Ltd. , Taiyuan 030008, China
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Abstract  

The wheel amplitude transformer is the key component of the rotary ultrasonic internal grinding resonant system, and its design quality directly affects the process effect of ultrasonic grinding. However, at present, the wheel amplitude transformer for internal grinding lacks a relatively complete theoretical analysis model. In order to improve the generality of the theoretical analysis model of wheel amplitude transformers, a theoretical analysis model of the longitudinal resonant wheel amplitude transformer was established based on the non-resonant design theory, and the frequency equation was derived by using the force and displacement continuity conditions and boundary conditions between the vibration elements of the wheel amplitude transformer. Then, the frequency equation was solved by programming and verified by ANSYS finite element simulation analysis. Finally, the longitudinal resonant wheel amplitude transformer was manufactured, and the impedance characteristic analysis test, ultrasonic resonance test and vibration displacement measurement test were carried out to analyze its resonance characteristics. The test results showed that the resonant test frequency of the developed wheel amplitude transformer was consistent with the theoretical design frequency, and the relative error between the test value and the simulation value of the vibration displacement at its output end was 7.83%, which met the requirements of rotary ultrasonic internal grinding and verified the correctness of the theoretical analysis model. The research results provide a convenient and effective method for the design of wheel amplitude transformer in rotary ultrasonic internal grinding.

Key words： rotary ultrasonic internal grinding      wheel amplitude transformer      theoretical analysis model      frequency equation      resonance characteristic analysis     
Received: 23 June 2022      Published: 06 March 2023
CLC:  TH 113.1  
Corresponding Authors: Hui-bin QIN     E-mail: mabiao_nuc@163.com;qhbsss@163.com
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Biao MA
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Cite this article:

Biao MA,Hui-bin QIN,Yi FENG,Xu-ri BAI,Jia-yi XIN. Design and experimental study of wheel amplitude transformer for rotary ultrasonic internal grinding. Chin J Eng Design, 2023, 30(1): 117-126.

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https://www.zjujournals.com/gcsjxb/10.3785/j.issn.1006-754X.2023.00.013     OR     https://www.zjujournals.com/gcsjxb/Y2023/V30/I1/117


旋转超声内圆磨削砂轮变幅器的设计与试验研究

砂轮变幅器是旋转超声内圆磨削谐振系统的关键部件，其设计质量直接影响超声磨削的工艺效果。但目前内圆磨削砂轮变幅器缺乏较为完善的理论分析模型。为提高砂轮变幅器理论分析模型的通用性，基于非谐振设计理论建立了纵向谐振砂轮变幅器的理论分析模型，并利用砂轮变幅器各振动单元间的力、位移连续条件与边界条件推导了其频率方程。然后，针对频率方程进行编程求解，并通过ANSYS有限元仿真分析进行验证。最后，加工制作了纵向谐振砂轮变幅器，并开展阻抗特性分析试验、超声谐振试验和振动位移测量试验，分析了其谐振特性。试验结果表明，所研制的砂轮变幅器的谐振试验频率与理论设计频率一致，其输出端振动位移的试验值与仿真值的相对误差为7.83%，符合旋转超声内圆磨削的要求，验证了理论分析模型求解的正确性。研究结果为旋转超声内圆磨削砂轮变幅器的设计提供了便捷且有效的方法。


关键词： 旋转超声内圆磨削,  砂轮变幅器,  理论分析模型,  频率方程,  谐振特性分析 
Fig.1 Schematic diagram of rotary ultrasonic internal grinding
Fig.2 Theoretical analysis model of longitudinal resonant wheel amplitude transformer
尺寸参数圆锥过渡阶梯形砂轮变幅器圆锥圆柱形砂轮变幅器阶梯形砂轮变幅器
l132034
l240421
l3待求待求待求
l4202020
d1585858
d2282828
d3404040
Table 1 Dimensional parameters of longitudinal resonant wheel amplitude transformer
材料弹性模量E/Pa密度ρ/（kg/m3）泊松比μ
45钢2.10×10117 8900.30
40Cr2.06×10117 8200.28
Table 2 Material performance parameters of longitudinal resonant wheel amplitude transformer
砂轮变幅器类型

理论设计

频率f1/Hz

有限元仿真

频率f2/Hz

相对误差δ①/%
圆锥过渡阶梯形20 00018 6396.81
圆锥圆柱形20 00018 5147.43
阶梯形20 00017 83710.81
Table 3 Frequency comparison of longitudinal resonant wheel amplitude transformer
砂轮变幅器类型尺寸l3/mm谐振频率f/Hz
圆锥过渡阶梯形13.020 098
圆锥圆柱形26.520 076
阶梯形34.520 046
Table 4 Dimension adjustment result and frequency of longitudinal resonant wheel amplitude transformer
Fig.3 Vibration displacement curve of longitudinal resonant wheel amplitude transformer
Fig.4 Comparison of vibration displacement curves of longitudinal resonant wheel amplitude transformer
Fig.5 Mode shape of longitudinal resonant wheel amplitude transformer
Fig.6 Tapered transition stepped deformation amplitude pole
Fig.7 Longitudinal resonant wheel amplitude transformer tool system
Fig.8 Impedance characteristic analysis test device
Fig.9 Impedance characteristic analysis test results
Fig.10 Ultrasonic resonance test device
Fig.11 Vibration displacement measurement test device
采样点序号谐振频率f3/Hz振动位移a/μm
119 63314.86
219 64715.98
319 60515.12
419 60615.32
519 58316.25
619 56516.61
719 58916.54
819 57016.70
919 56116.45
1019 56216.35
Table 5 Measurement results of frequency and vibration displacement of longitudinal resonant wheel amplitude transformer
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