螺旋锥齿轮模态试验与模型修正

何宏图; 曹雪梅; 许浩; 侯圣文

doi:10.13224/j.cnki.jasp.20220978

螺旋锥齿轮模态试验与模型修正

doi: 10.13224/j.cnki.jasp.20220978

何宏图^1,,
曹雪梅^1,*, ,,
许浩²,
侯圣文³

1.
河南科技大学机电工程学院，河南洛阳 471003
2.
中国航发中传机械有限公司，长沙 410200
3.
陕西法士特齿轮有限责任公司陕西省齿轮传动重点试验室，西安 710119

基金项目: 国家自然科学基金（51675161）；陕西省重点研发计划项目（2021ZDLGY10-06）；陕西省重点研发计划项目（2021ZDLGY12-03）；龙门实验室前沿探索课题（LMQYTSKT026）

详细信息

作者简介:
何宏图（1995-），男，硕士生，研究方向为齿轮传动及振动噪声控制。E-mail：hongtuhe@126.com

通讯作者:
曹雪梅（1970-），女，教授、硕士生导师，博士，主要从事齿轮设计与性能检测研究。E-mail： caoxuemei-2002@163.com

中图分类号: V232.8；TH113.1
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出版历程
- 收稿日期: 2022-12-25
- 网络出版日期: 2024-04-01

Modal test and model modification of spiral bevel gears

HE Hongtu^1
,,
CAO Xuemei^{1,*
, ,},
XU Hao²,
HOU Shengwen³

1.
School of Mechanical Engineering，Henan University of Science and Technology，Luoyang Henan 471003，China
2.
Zhongchuan Transmission Machinery Company Limited，Aero Engine Corporation of China，Changsha 410200，China
3.
Shaanxi Key Laboratory of Gear Transmission，Shaanxi Fast Gear Company Limited，Xi’an 710119，China

摘要

摘要:
为准确提取螺旋锥齿轮模态参数，构建精确动力学模型，通过试验与仿真相结合的方法，采用移动力锤法进行模态试验，提取模态参数；基于实测数据建立精确仿真模型并进行模态分析；采用初等旋转变换法修正仿真模态振型，得到准确的试验和仿真模态置信度，提高分析精度；以试验模态频率为目标，采用响应面法修正模型材料参数。修正后固有频率最大相对误差由0.83%下降到0.353%，提高了仿真模型精度。试验与仿真频响分析结果表明：由仿真模型不准确导致的移频现象和加速度幅值误差得到有效控制，验证了动力学模型的准确性。研究方法为螺旋锥齿轮进一步的结构优化和减振避振奠定基础。
- 模态参数 /
- 螺旋锥齿轮 /
- 模态试验 /
- 模型修正 /
- 响应面法
Abstract:
To accurately extract spiral bevel gears’ modal parameters and construct an accurate dynamic model, a combination of experimental and simulation methods were used to conduct modal tests using the moving force hammer method to extract modal parameters; an accurate simulation model was established based on measured data and modal analysis was conducted; the elementary rotation transformation method was used to correct the simulation mode shapes, and the accurate confidence of the test and simulation modes was obtained to improve the analysis accuracy; taking the experimental modal frequency as the target, the response surface method was used to correct the material parameters of the model. After the correction, the maximum relative error of natural frequency was reduced from 0.83% to 0.353%, which improved the accuracy of the simulation model. The experimental and simulation frequency response analysis results showed that the frequency shift phenomenon and acceleration amplitude error caused by inaccurate simulation models were effectively controlled, verifying the accuracy of the dynamic model. The research method lays the foundation for further structural optimization and vibration reduction and avoidance of spiral bevel gears.
- modal parameter /
- spiral bevel gear /
- modal test /
- model modified /
- response surface method

HTML

图 1 试验测试的螺旋锥齿轮

Figure 1. Spiral bevel gear for experiment test

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图 2 模态测试悬挂方式及模态试验几何模型

Figure 2. Suspension mode of modal test and geometric model of modal test

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图 3 稳态图

Figure 3. Stability diagram

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图 4 试验模态振型

Figure 4. Experimental modal shapes

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图 5 试验模态的C_MAC,auto矩阵图

Figure 5. C_MAC,auto matrix of the test mode

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图 6 实测齿面点坐标

Figure 6. Measured coordinates of tooth surface points

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图 7 仿真模态振型

Figure 7. Simulated modal shape

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图 8 初始C_MAC,cross矩阵图

Figure 8. Initial C_MAC,cross matrix

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图 9 修正后的C_{MAC, cross}矩阵图

Figure 9. Corrected C_{MAC, cross} matrix

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图 10 优化后的满意度响应曲面

Figure 10. Optimized satisfaction response surface

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图 11 加速度频响曲线对比图

Figure 11. Comparison diagram of acceleration frequency response curve

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表 1 螺旋锥齿轮的几何参数

Table 1. Geometric parameters of spiral bevel gears

参数	数值及说明
齿数	26
模数/mm	8.4848
中点螺旋角/（°）	35
法向压力角/（°）	20
齿宽/mm	46
旋转方向	左旋
节锥角/（°）	38.2333
面锥角/（°）	41.415
根锥角/（°）	35.807
齿根高/mm	7.452
齿顶高/mm	8.442

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表 2 试验与仿真频率对比

Table 2. Comparison of test and simulation frequencies

阶次	频率/Hz		频率相对误差/%	阻尼比/ %	节圆- 节径
阶次	试验	仿真	频率相对误差/%	阻尼比/ %	节圆- 节径
1	3430.451	3431.706	0.037	0.060	0-2
2	3443.252	3447.495	0.123	0.078	0-2
3	5726.575	5774.115	0.830	0.035	1-0
4	7503.108	7476.442	0.355	0.029	0-3
5	7507.427	7482.220	0.336	0.022	0-3
6	10251.236	10314.870	0.621	0.050	1-1
7	10523.404	10580.790	0.545	0.041	1-1
8	11502.827	11430.140	0.632	0.035	0-4
9	11508.263	11430.430	0.676	0.026	0-4

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表 3 修正参数取值范围

Table 3. Range of modified parameters

参数	水平值
参数	−2	−1	0	1	2
弹性模量E/MPa	176364.000	19000.000	210000.000	230000.000	243636.000
泊松比U	0.132	0.200	0.300	0.400	0.468
密度ρ/（kg/m³）	7563.642	7700.000	7900.000	8100.000	8236.358

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表 4 中心复合设计试验表

Table 4. Test table of center composite design

参数编号	水平值
参数编号	弹性模量	泊松比	密度
1	−1	−1	−1
2	1	−1	−1
3	−1	1	−1
4	1	1	−1
5	−1	−1	1
6	1	−1	1
7	−1	1	1
8	1	1	1
9	−2	0	0
10	2	0	0
11	0	−2	0
12	0	2	0
13	0	0	−2
14	0	0	2
15	0	0	0

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表 5 修正后的材料参数

Table 5. Modified material parameters

材料参数	原始值	修正后值
弹性模量E/MPa	210000.000	208232.169
泊松比U	0.300	0.274
材料密度ρ/（kg/m³）	7900.000	7890.797

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表 6 模型修正后误差值

Table 6. Error value after model modification

模态阶数	试验频率/Hz	修正后
模态阶数	试验频率/Hz	仿真频率/Hz	相对误差/%
1	3430.451	3439.541	0.265
2	3443.252	3455.394	0.353
3	5726.575	5715.837	0.188
4	7503.108	7501.398	0.023
5	7507.427	7507.295	0.002
6	10251.236	10263.110	0.116
7	10523.404	10523.440	0.000
8	11502.827	11470.170	0.284
9	11508.263	11470.470	0.328

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