不对中多浮动花键接触刚度识别及动力学应用

王永亮; 赵广; 徐永强; 郝长琦; 娄馨月; 叶志旋

doi:10.13224/j.cnki.jasp.20240738

不对中多浮动花键接触刚度识别及动力学应用

doi: 10.13224/j.cnki.jasp.20240738

1.
大连海事大学船舶与海洋工程学院，辽宁大连 116026
2.
大连理工大学能源与动力学院，辽宁大连 116024
3.
中国航发四川燃气涡轮研究院，成都 610500

基金项目: 国家自然科学基金（12172073）；高性能精密制造全国重点实验室开放课题（ZY202410）；中国核动力研究设计院核反应堆技术全国重点实验室开放课题

详细信息

作者简介:
王永亮（1983-），男，副教授，博士，主要从事转子动力学方面的研究。E-mail：wangyl@dlmu.edu.cn

通讯作者:
赵广（1981-），男，教授，博士，主要从事航空动力与传动系统转子动力学方面的研究。E-mail：zhaoguang@dlut.edu.cn

中图分类号: V233.1
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出版历程
- 收稿日期: 2024-10-28
- 网络出版日期: 2025-01-22

Contact stiffness identification of misaligned multiple floating splines and its dynamic application

1.
Naval Architecture and Ocean Engineering College，Dalian Maritime University，Dalian Liaoning 116026，China
2.
School of Energy and Power Engineering，Dalian University of Technology，Dalian Liaoning 116024，China
3.
Sichuan Gas Turbine Establishment，Aero Engine Corporation of China，Chengdu 610500，China

摘要

摘要:
针对多浮动花键在不对中状态下接触刚度识别困难的问题，提出一种基于试验和薄层单元仿真的接触刚度识别方法。建立以薄层单元为基础的传动杆固有特性仿真模型，结合传动杆固有频率试验数据构建多浮动花键刚度识别函数，进而准确识别多浮动花键接触刚度，获得浮动花键接触刚度随扭矩和不对中的变化规律。结果表明：扭矩增加会增强浮动花键副的整体接触刚度，不对中角度增加会减小花键接触刚度。在低扭矩时，不对中对花键刚度的削弱作用明显；在高扭矩时，扭矩对花键刚度的增强作用明显。用薄层单元代替花键接触面接触刚度，可以比较准确地计算花键在不同接触状态下的模态频率。研究结果为对浮动花键接触刚度的准确识别提供一定参考，可直接应用到系统动力学分析中。
- 接触刚度识别 /
- 浮动花键 /
- 传动杆 /
- 薄层单元 /
- 固有特性 /
- 转子动力学
Abstract:
Considering the difficulty of contact stiffness identification of multiple floating splines in complex misalignment, a contact stiffness identification method based on test and thin-layer element simulation was proposed. Based on thin-layer elements, the finite element model of the radial transmission rod with multiple floating splines was established, the natural characteristics of the radial transmission rod with multiple floating splines were simulated, and the stiffness recognition function of the multiple floating splines was constructed by combining the natural frequency test data of the radial transmission rod, so as to accurately identify the contact stiffness of the multiple floating splines. The variation law of floating spline contact stiffness with torque and misalignment was obtained. The results showed that the contact stiffness of floating spline pair was enhanced with the increase of torque, while the contact stiffness of spline was reduced with the increase of misalignment angle. At low torque, misalignment weakened the spline stiffness obviously. At high torque, the effect of torque on spline stiffness was obvious. By replacing the contact stiffness of spline contact surface with thin layer element, the modal frequency of spline in different contact states can be calculated more accurately. The research results can provide some reference for the accurate identification of the contact stiffness of floating spline, and can be directly applied to system dynamics analysis.
- contact stiffness identification /
- floating spline /
- transmission rod /
- thin layer element method /
- inherent characteristic /
- rotor dynamics

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图 1 带多浮动花键的传动杆示意图

Figure 1. Transmission rod with multiple floating splines

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图 2 花键刚度示意图

Figure 2. Schematic diagram of spline stiffness

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图 3 基于薄层单元法的接触刚度识别思路

Figure 3. Contact stiffness recognition thought based on thin layer element method

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图 4 传动杆固有特性试验台

Figure 4. Natural characteristic test bench of central transmission rod

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图 5 传感器布置方案

Figure 5. Sensor layout scheme

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图 6 不对中施加和测量示意图

Figure 6. Schematic diagram of misalignment application and measurement

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图 7 对中状态下扭矩对传动杆固有频率影响

Figure 7. Influence of torque on natural frequencies of the transmission rod under aligned condition in the centering state

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图 8 不对中对传动杆固有频率影响（T=120 N·m）

Figure 8. Influence of misalignment on natural frequencies of the drive rod （T=120 N·m）

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图 9 花键副的薄层单元等效

Figure 9. Thin layer element equivalence of spline pair

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图 10 简化后传动杆仿真模型

Figure 10. Simplified simulation model of transmission rod

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图 11 第1阶模态振型

Figure 11. First-order mode shape

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图 12 第2阶模态振型

Figure 12. Second-order mode shape

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图 13 第3阶模态振型

Figure 13. Third-order mode shape

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图 14 第4阶模态振型

Figure 14. Forth-order mode shape

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图 15 花键单位面积接触刚度随扭矩变化曲线

Figure 15. Contact stiffness per unit area of the spline varies with torque

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图 16 传动杆前4阶固有频率仿真与试验结果对比

Figure 16. Comparison of the first four natural frequencies of the transmission rod from simulation and test

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图 17 单位面积接触刚度随不对中角度变化规律

Figure 17. Contact stiffness per unit area varies with misalignment angle

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图 18 不对中状态下单位面积接触刚度随扭矩变化规律

Figure 18. Contact stiffness per unit area varies with torque under misalignment conditions

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表 1 传动杆花键参数

Table 1. Radial transmission rod spline parameters

花键位置	齿数
内传动杆外花键（图示①）	27
内传动杆内花键（图示②）	36
外传动杆外花键（图示③）	36
外传动杆内花键（图示④）	38

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表 2 传动杆花键材料力学性能参数

Table 2. Transmission rod spline material mechanical properties parameters

材料	温度 t/℃	弹性模量 E/GPa	泊松比 μ	密度ρ/ （kg/m³）
18Cr2Ni4WA	20	202	0.273	7910
18Cr2Ni4WA	150	197	0.296	7910

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表 3 各扭矩下传动杆前4阶固有频率随不对中变化范围

Table 3. Variation ranges of the first four natural frequencies of the drive rod with misalignment under various torque

扭矩/ （N·m）	固有频率变化范围/%
扭矩/ （N·m）	1阶	2阶	3阶	4阶
60	−7.0～+2.0	−16.5～0	−7.0～+2.0	0
120	−4.1～0	−11.8～0	−4.1～0	0
180	0～+2.5	0～+2.5	−10.5～+0	0～+2.5
240	0～+2.6	−8.1～0	0～+2.6	0
270	0～+2.8	−7.7～0	0～+2.8	−2～+0.5

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表 4 传动杆模态频率随弹性模量变化结果

Table 4. Results of the modal frequency of the transmission rod changing with the elastic modulus

E/MPa	模态频率/Hz
E/MPa	1阶	2阶	3阶	4阶
1	54.0	102.5	130.8	280.1
2	70.7	112.1	134.6	324.4
3	76.1	116.2	137.8	347.7
4	78.2	118.5	140.7	362.3
5	83.2	120.2	143.4	372.4
6	87.0	121.5	145.9	379.9
7	90.1	122.5	148.2	385.7
8	92.5	123.4	150.3	390.3
9	94.6	124.2	152.1	394.2
10	96.3	124.9	153.8	397.4

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参考文献(18)

[1]	MARMOL R A,SMALLEY A J,TECZA J A. Spline coupling induced nonsynchronous rotor vibrations[J]. Journal of Mechanical Design,1980,102(1): 168-176. doi: 10.1115/1.3254709
[2]	ROGER KU C P,WALTON J F Jr,LUND J W. Dynamic coefficients of axial spline couplings in high-speed rotating machinery[J]. Journal of Vibration and Acoustics,1994,116(3): 250-256. doi: 10.1115/1.2930421
[3]	ROBINS R R. Tooth engagement evaluation of involute spline couplings[D]. Provo,US: Brigham Young University,2008.
[4]	CURÀ F,MURA A,GRAVINA M. Load distribution in spline coupling teeth with parallel offset misalignment[J]. Proceedings of the Institution of Mechanical Engineers: Part C Journal of Mechanical Engineering Science,2013,227(10): 2195-2205. doi: 10.1177/0954406212471916
[5]	CURÀ F,MURA A. Experimental procedure for the evaluation of tooth stiffness in spline coupling including angular misalignment[J]. Mechanical Systems and Signal Processing,2013,40(2): 545-555. doi: 10.1016/j.ymssp.2013.06.033
[6]	BARROT A,PAREDES M,SARTOR M. Determining both radial pressure distribution and torsional stiffness of involute spline couplings[J]. Proceedings of the Institution of Mechanical Engineers: Part C Journal of Mechanical Engineering Science,2006,220(12): 1727-1738. doi: 10.1243/0954406JMES285
[7]	BARROT A,SARTOR M,PAREDES M. Investigation of torsional teeth stiffness and second moment of area calculations for an analytical model of spline coupling behaviour[J]. Proceedings of the Institution of Mechanical Engineers: Part C Journal of Mechanical Engineering Science,2008,222(6): 891-902. doi: 10.1243/09544062JMES828
[8]	BARROT A,PAREDES M,SARTOR M. Extended equations of load distribution in the axial direction in a spline coupling[J]. Engineering Failure Analysis,2009,16(1): 200-211. doi: 10.1016/j.engfailanal.2008.03.001
[9]	HONG J,TALBOT D,KAHRAMAN A. A semi-analytical load distribution model for side-fit involute splines[J]. Mechanism and Machine Theory,2014,76: 39-55. doi: 10.1016/j.mechmachtheory.2014.02.002
[10]	YAO Y F,ZHU P H. Optimal design for non-backlash involute spline joint: 19941112-14[R]. Beijing: China Machine Press,1994.
[11]	彭和平,李志明. 扭力杆弹簧过渡部分应力集中的理论探讨及有限元分析[J]. 机械制造与自动化,2004,33(4): 15-18. PENG Heping,LI Zhiming. The theoretical research and finite element method analysis of the stress intensity in variation diameter parts of the torsion bar spring[J]. Machine Building & Automation,2004,33(4): 15-18. (in Chinese doi: 10.3969/j.issn.1671-5276.2004.04.005 PENG Heping, LI Zhiming. The theoretical research and finite element method analysis of the stress intensity in variation diameter parts of the torsion bar spring[J]. Machine Building & Automation, 2004, 33(4): 15-18. (in Chinese) doi: 10.3969/j.issn.1671-5276.2004.04.005
[12]	苏钧聪. 涡扇发动机低压转子系统振动特性研究[D]. 辽宁大连: 大连理工大学,2016. SU Juncong. Study on vibration characteristics of low pressure rotor system of turbofan engine[D]. Dalian Liaoning: Dalian University of Technology,2016. (in Chinese SU Juncong. Study on vibration characteristics of low pressure rotor system of turbofan engine[D]. Dalian Liaoning: Dalian University of Technology, 2016. (in Chinese)
[13]	赵广,苏钧聪,韩清凯,等. 圆柱面接触刚度建模与仿真[J]. 华中科技大学学报(自然科学版),2015,43(12): 21-26. ZHAO Guang,SU Juncong,HAN Qingkai,et al. Modeling and simulation of cylindrical surface contact stiffness[J]. Journal of Huazhong University of Science and Technology (Natural Science Edition),2015,43(12): 21-26. (in Chinese ZHAO Guang, SU Juncong, HAN Qingkai, et al. Modeling and simulation of cylindrical surface contact stiffness[J]. Journal of Huazhong University of Science and Technology (Natural Science Edition), 2015, 43(12): 21-26. (in Chinese)
[14]	朱彬,杨诚,刘烨辉,等. 套齿连接结构力学模型及其刚度影响因素[J]. 机械设计与制造,2019(增刊1): 86-90,94. ZHU Bin,YANG Cheng,LIU Yehui,et al. Mechanical modeling for the spline Joint and the influence factors investigation for its stiffness[J]. Mechanical Design and Manufacturing,2019(Suppl.1): 86-90,94. (in Chinese ZHU Bin, YANG Cheng, LIU Yehui, et al. Mechanical modeling for the spline Joint and the influence factors investigation for its stiffness[J]. Mechanical Design and Manufacturing, 2019(Suppl.1): 86-90, 94. (in Chinese)
[15]	霍启新. 考虑不对中的航空渐开线花键副非线性动态啮合力研究[D]. 西安: 陕西科技大学,2021. HUO Qixin. Study on nonlinear dynamic meshing force of involute spline couplings in aero-engine with misalignment[D]. Xian: Shanxi University of Science and Technology,2021. (in Chinese HUO Qixin. Study on nonlinear dynamic meshing force of involute spline couplings in aero-engine with misalignment[D]. Xian: Shanxi University of Science and Technology, 2021. (in Chinese)
[16]	杨默晗. 含套齿联轴器的柔性转子不对中故障机理研究[D]. 南京: 南京航空航天大学,2021. YANG Mohan. Study on misalignment fault mechanism of flexible rotor with sleeve gear coupling[D]. Nanjing: Nanjing University of Aeronautics and Astronautics,2021. (in Chinese YANG Mohan. Study on misalignment fault mechanism of flexible rotor with sleeve gear coupling[D]. Nanjing: Nanjing University of Aeronautics and Astronautics, 2021. (in Chinese)
[17]	LI Yingjie,ZHAO Guang,QIAN Liting,et al. Effect of time-varying friction coefficient on self-excited vibration of floating spline-rotor system[J]. Tribology International,2024,195: 109613. doi: 10.1016/j.triboint.2024.109613
[18]	李英杰,赵广,袁运博,等. 航空花键接触刚度仿真与试验[J]. 航空动力学报,2024,39(12): 20230070. LI Yingjie,ZHAO Guang,YUAN Yunbo,et al. Simulation and experiment on contact stiffness of aviation splines[J]. Journal of Aerospace Power,2024,39(12): 20230070. (in Chinese LI Yingjie, ZHAO Guang, YUAN Yunbo, et al. Simulation and experiment on contact stiffness of aviation splines[J]. Journal of Aerospace Power, 2024, 39(12): 20230070. (in Chinese)