Dynamic Modeling and Characteristic Analyses of Multi-Fault Coupling in Mechanical Meta-action Unit

doi:10.3969/j.issn.1004-132X.2026.09.007

Abstract

Abstract:

To address the problem that feature ambiguity caused by concurrent multiple faults in mechanical meta-action units leads to difficulties in diagnosis and control， a method based on multi-fault coupling modeling was proposed to analyze fault characteristics. First， taking the worm rotation meta-action unit as an example， key faults were extracted. Looseness of the support was simulated based on a piecewise linear spring-damper model. The coupling misalignment fault was simulated based on an additional combined misalignment excitation force. Second， integrating a rolling bearing dynamic model， the worm dynamic model was established. The above fault models were integrated to establish a multi-fault coupling dynamic model for the worm rotation meta-action unit. Then， the acceleration responses of the worm under normal conditions， single looseness fault， single misalignment fault， and the coupled fault state were solved using numerical analysis method. Spectral analyses were performed on these responses. Finally， based on the existing experimental platform， actual acceleration time-domain signals under the above four states were collected and analyzed. Spectral analyses were also performed on the actual signals. A comparison between simulation and experimental results verifies the accuracy of the established multi-fault coupling model.

Key words: meta-action unit, multi-fault coupling, numerical analysis, fault feature extraction

摘要：

针对机械元动作单元多故障并发时特征模糊导致诊断控制困难的问题，提出了一种基于多故障耦合建模分析故障特性的方法。以蜗杆转动元动作单元为例，提取关键故障，基于分段线性弹簧阻尼模型模拟支座松动，基于附加综合不对中激励力模拟联轴器不对中故障。融合滚动轴承动力学模型建立蜗杆动力学模型，集成上述故障模型，建立蜗杆转动元动作单元多故障耦合动力学模型。采用数值分析法求解蜗杆在正常、单一松动故障、单一不对中故障及耦合故障状态下的加速度响应并进行频谱分析。根据现有实验平台，采集并分析上述4种状态的实际加速度时域信号并进行频谱分析。仿真与实验结果对比验证了所建多故障耦合模型的准确性。

关键词: 元动作单元, 多故障耦合, 数值分析, 故障特征提取

CLC Number:

TH17

GE Hongyu, SUN Jiarui, LI Yi, YANG Manzhi, GAO Yang. Dynamic Modeling and Characteristic Analyses of Multi-Fault Coupling in Mechanical Meta-action Unit[J]. China Mechanical Engineering, 2026, 37(9): 2141-2152.

葛红玉, 孙佳瑞, 李艺, 杨满芝, 高扬. 机械元动作单元多故障耦合的动力学建模与特性分析[J]. 中国机械工程, 2026, 37(9): 2141-2152.

Figures/Tables 21

Fig.1 Structural diagram of worm rotation meta-action unit

Fig.2 Worm rotation meta-action unit test bench

Tab.1 Fault frequency statistics table

故障事件	年度发生频次	发生频率/%	主要伴随事件（发生频次）	并发频率/%
滚动轴承支座松动故障	20	28.60	联轴器不对中（14次）	70.00
联轴器不对中故障	18	25.70	滚动轴承支座松动（14次）	77.80
蜗杆出现裂纹	6	8.60	联轴器不对中（2次）	33.30
滚动轴承滚道划伤	6	8.60	滚动轴承支座松动（4次）	66.70
电机调速失灵	4	5.70	联轴器梅花键弹性形变（3次）	75.00
联轴器梅花键弹性形变	4	5.70	电机调速失灵（3次）	75.00
滚动轴承滚动体破损	4	5.70	滚动轴承滚道划伤（1次）	25.00
轴承装配间隙过大	4	5.70	滚动轴承滚道划伤（1次）	25.00
平键定位孔磨损	3	4.30	联轴器梅花键弹性形变（2次）	66.70
蜗杆腐蚀	1	1.40

Fig.3 Schematic diagram of fault principle in worm rotation meta-action unit

Fig.4 Simplified diagram of rolling bearing Hertz contact model

Tab.2 Simulation parameters

参数	数值
蜗杆密度ρ/（kg·m $- 3$ ）	7850
弹性模量E/GPa	200
滚动轴承等效质量m_bl1，m_bl2/kg	0.045
基础支撑等效质量m_s/kg	20
联轴器质量m_c/kg	2
基础支撑等效刚度k₃/（N·m $- 1$ ）	$1 × 105$
轴承赫兹接触刚度k_cb/（N·m $- 1.5$ ）	$2 × 108$
轴承间隙r₀/m	$0.015$
轴承外径D/mm	35
轴承内径d/mm	15
滚子数目	8
松动螺栓等效刚度k₁/（N·m $- 1$ ）	$1 × 104$
未松动螺栓等效刚度k₂/（N·m $- 1$ ）	$5 × 104$
松动螺栓等效阻尼c₁/（N·s·m $- 1$ ）	$10$
未松动螺栓等效阻尼c₂/（N·s·m $- 1$ ）	$100$
基础等效阻尼c₃/（N·s·m $- 1$ ）	$500$
支座松动间隙δ/m	0.005

Tab.2 Simulation parameters

参数	数值
蜗杆密度ρ/（kg·m $- 3$ ）	7850
弹性模量E/GPa	200
滚动轴承等效质量m_bl1，m_bl2/kg	0.045
基础支撑等效质量m_s/kg	20
联轴器质量m_c/kg	2
基础支撑等效刚度k₃/（N·m $- 1$ ）	$1 × 105$
轴承赫兹接触刚度k_cb/（N·m $- 1.5$ ）	$2 × 108$
轴承间隙r₀/m	$0.015$
轴承外径D/mm	35
轴承内径d/mm	15
滚子数目	8
松动螺栓等效刚度k₁/（N·m $- 1$ ）	$1 × 104$
未松动螺栓等效刚度k₂/（N·m $- 1$ ）	$5 × 104$
松动螺栓等效阻尼c₁/（N·s·m $- 1$ ）	$10$
未松动螺栓等效阻尼c₂/（N·s·m $- 1$ ）	$100$
基础等效阻尼c₃/（N·s·m $- 1$ ）	$500$
支座松动间隙δ/m	0.005

Tab.3 Beam element parameters

编号	1	2	3	4	5	6	7
长度/mm	65	20	15	15	15	15	15
直径/mm	40	20	25	20	20	20	20
编号	8	9	10	11	12	13	14
长度/mm	15	15	15	15	15	15	15
直径/mm	20	20	20	20	20	20	25

Fig.5 Critical speed Campbell diagram

Fig.6 Acceleration response amplitudes of key nodes at different speeds

Fig.7 Time domain and frequency domain diagrams under normal conditions

Fig.8 Time domain and frequency domain diagrams under misalignment fault

Fig.9 Time domain and frequency domain diagrams under looseness fault

Fig.10 Time domain and frequency domain diagrams under coupled fault （misalignment + looseness）

Tab.4 Characteristic frequencies of node P1 simulation acceleration response under different faults

故障类型	Y方向加速度基频幅值/（m·s $- 2$ ）	Z方向加速度2倍频幅值/（m·s $- 2$ ）	Y方向加速度基频幅值/（m·s $- 2$ ）	Z方向加速度2倍频幅值/（m·s $- 2$ ）	主要频率/Hz
仅不对中	0.83	0.37	0.80	0.35	27.3，54.7
仅松动	0.64	0.01	0.64	0.01	27.3
不对中+松动	0.42	1.21	0.46	1.23	27.3，54.7，110.3，137.7
正常状况	0.60	0	0.61	0	27.3

Tab.4 Characteristic frequencies of node P1 simulation acceleration response under different faults

故障类型	Y方向加速度基频幅值/（m·s $- 2$ ）	Z方向加速度2倍频幅值/（m·s $- 2$ ）	Y方向加速度基频幅值/（m·s $- 2$ ）	Z方向加速度2倍频幅值/（m·s $- 2$ ）	主要频率/Hz
仅不对中	0.83	0.37	0.80	0.35	27.3，54.7
仅松动	0.64	0.01	0.64	0.01	27.3
不对中+松动	0.42	1.21	0.46	1.23	27.3，54.7，110.3，137.7
正常状况	0.60	0	0.61	0	27.3

Fig.11 Misalignment fault experiment of coupling

Fig.12 Looseness fault experiment

Fig.13 Experimental time domain and frequency domain diagrams under normal conditions

Fig.14 Experimental time domain and frequency domain diagrams under misalignment fault

Fig.15 Experimental time domain and frequency domain diagrams under looseness fault

Fig.16 Experimental time domain and frequency domain diagrams under coupled fault （misalignment + looseness）

Tab.5 Characteristic frequencies of experimental acceleration response under different faults

故障类型	Y方向加速度基频幅值/（m·s $- 2$ ）	Z方向加速度2倍频幅值/（m·s $- 2$ ）	Y方向加速度基频幅值/（m·s $- 2$ ）	Z方向加速度2倍频幅值/（m·s $- 2$ ）	主要频率/Hz
仅不对中	0.80	0.28	0.80	0.33	27，55，110
仅松动	0.59	0.01	0.58	0.01	28
不对中+ 松动	0.33	1.37	0.34	1.40	28，54，110，137
正常状态	0.53	0	0.54	0	28

Tab.5 Characteristic frequencies of experimental acceleration response under different faults

故障类型	Y方向加速度基频幅值/（m·s $- 2$ ）	Z方向加速度2倍频幅值/（m·s $- 2$ ）	Y方向加速度基频幅值/（m·s $- 2$ ）	Z方向加速度2倍频幅值/（m·s $- 2$ ）	主要频率/Hz
仅不对中	0.80	0.28	0.80	0.33	27，55，110
仅松动	0.59	0.01	0.58	0.01	28
不对中+ 松动	0.33	1.37	0.34	1.40	28，54，110，137
正常状态	0.53	0	0.54	0	28

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