基于多尺度理论的栓接结合部动力学建模

doi:10.13229/j.cnki.jdxbgxb20180200

摘要/Abstract

摘要：

建立准确的栓接结合部接触刚度模型对预测数控机床的动态特性至关重要。本文提出了一种基于多尺度理论的栓接结合部刚度模型，首先使用一系列叠加的三维正弦波来描述粗糙接触表面多尺度特性，每个正弦波被认为是一层频率级，推导出接触面积比与频率级的函数关系，则整体刚度可以看作不同频率级串联的弹簧模型。然后,通过数值仿真分析了结合面法向接触载荷、材料特性参数以及多尺度参数对接触刚度模型的影响。最后,设计分段梁结构进行试验验证本文模型的准确性，通过力锤敲击试验获得栓接结合部在等同预紧力下的固有频率和振型，并与仿真结果对比，结果表明本文多尺度模型固有频率与试验频率之间的相对误差小于9.94%，表明多尺度模型可以有效地预测数控机床的动态特性。

关键词: 机械设计, 动态特性, 栓接结合部, 多尺度理论, 刚度模型

Abstract:

Accurate modeling of the contact stiffness of bolted joints is therefore crucial to predict the dynamic performance of CNC machine tools. This paper presents a contact stiffness model of a bolted joint based on multi-scale theory. The model uses a series of stacked three-dimensional sine waves to describe the multiple scales of roughness of the contact surface, and each frequency level is considered a layer of asperities, stacked iteratively on top of each other. The relationship between the contact area ratio and frequency level can be deduced. Moreover, the contact stiffness at each frequency level can be regarded as a spring in series in the model, therefore, the total stiffness can be obtained by summing the contact stiffness at each frequency level. The influences of contact load, material characteristic parameters and multi-scale parameters on the contact stiffness model are analyzed by mathematical simulation. An experimental setup consisting of the section beam specimen was used to validate the numerical model of the bolted joint for the case of equal pre-tightening forces. The relative error between the multi-scale natural frequencies and experimental frequencies was less than 9.94%, suggesting the multi-scale model can be effectively used in predicting the dynamic characteristics of CNC machine tools.

Key words: mechanical design, dynamic performance, bolted joint, multi?scale theory, stiffness model

中图分类号:

TH128

杨成,赵永胜,刘志峰,蔡力钢. 基于多尺度理论的栓接结合部动力学建模[J]. 吉林大学学报(工学版), 2019, 49(4): 1212-1220.

Cheng YANG,Yong⁃sheng ZHAO,Zhi⁃feng LIU,Li⁃gang CAI. Stiffness model of bolted joint based on multi⁃scale theory[J]. Journal of Jilin University(Engineering and Technology Edition), 2019, 49(4): 1212-1220.

图/表 10

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参数	数值
材料密度/（kg?m^-3）	7200
弹性模量/GPa	174
泊松比	0.275
尺寸/m	(X,Y,Z)=(1.50,0.178,0.31)
体积/m3 质量/kg	2.0462
体积/m3 质量/kg	160.62

预紧力/kN		f₁/Hz	f₂/Hz	f₃/Hz	f₄/Hz	f₅/Hz	f₆/Hz
10	测试结果	197.73	308.75	397.21	415.22	791.67	810.20
	仿真结果	209.92	303.30	381.63	431.14	747.58	824.09
	误差/%	6.16	-1.77	-3.92	3.83	-5.57	1.71
20	测试结果	211.06	312.63	411.25	445.85	793.76	814.98
	仿真结果	214.15	306.61	419.21	458.32	756.39	831.21
	误差/%	1.46	-1.93	1.94	2.80	-4.71	1.99
30	测试结果	214.26	313.96	420.39	453.79	796.05	818.07
	仿真结果	220.10	309.08	434.47	477.75	766.89	836.98
	误差/%	2.73	-1.55	3.35	5.28	-3.66	2.31
40	测试结果	215.67	314.40	421.97	457.79	800.05	821.66
	仿真结果	225.61	323.51	439.22	490.22	789.52	840.12
	误差/%	4.61	2.90	4.09	7.08	-1.32	2.25
50	测试结果	217.19	314.88	428.35	464.46	802.55	827.33
	仿真结果	237.63	308.89	448.296	510.63	805.19	861.19
	误差/%	9.41	-1.87	4.66	9.94	0.33	4.09