| Citation: | YU Pingchao, JIANG Ke, TAO Xuanjun, et al. Research on analytical modeling of spline coupling based on three-dimensional contact friction unit[J]. Journal of Aerospace Power, 2026, 41（6）：20240764 doi: 10.13224/j.cnki.jasp.20240764
|
Taking the flexible spline coupling as the object, a three-dimensional contact finite unit model was used to simulate the deformation characteristics and contact state changes of the spline. Guided by the simulation results, an analytical model for predicting the hysteresis behavior of tooth coupling was proposed by introducing three-dimensional contact friction unit at the meshing points of each tooth surface and using the force balance relationship and numerical iteration method. The proposed model was verified, and the hysteresis behavior and contact characteristics of the coupling structure were analyzed by using the proposed model. The results showed that the proposed model can fully consider the contact-separation, viscous-slip and their axial distribution characteristics. Compared with the finite element model, the proposed model can accurately predict the hysteresis characteristics of the structure and improve the computational efficiency by 3 orders of magnitude. The reduction of structural stiffness was attirbutable to the reduction of contact area of meshing tooth under shear load. And, the sliding of contact surface led to the internal damping, of which axial sliding had the most significant contribution. The hysteresis characteristic of spline coupling was more sensitive to the change of tooth width and torque, and was less affected by the friction coefficient.
| [1] |
ZHAO Guang, ZHAO Xiangyang, QIAN Liting, et al. A review of aviation spline research[J]. Lubricants, 2023, 11(1): 6.
|
| [2] |
李英杰, 赵广, 吴学深, 等. 航空花键-转子系统自激振动研究综述[J]. 航空学报, 2022, 43(8): 625532. LI Yingjie, ZHAO Guang, WU Xueshen, et al. Review of research on self-excited vibration of aviation spline-rotor system[J]. Acta Aeronautica et Astronautica Sinica, 2022, 43(8): 625532. (in Chinese
LI Yingjie, ZHAO Guang, WU Xueshen, et al. Review of research on self-excited vibration of aviation spline-rotor system[J]. Acta Aeronautica et Astronautica Sinica, 2022, 43(8): 625532. (in Chinese)
|
| [3] |
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
|
| [4] |
廖仲坤, 陈果, 王海飞. 套齿联轴器对航空发动机振动特性的影响[J]. 中国机械工程, 2015, 26(10): 1312-1319. LIAO Zhongkun, CHEN Guo, WANG Haifei. Effects of gear coupling on aero-engine vibration characteristics[J]. China Mechanical Engineering, 2015, 26(10): 1312-1319. (in Chinese doi: 10.3969/j.issn.1004-132X.2015.10.007
LIAO Zhongkun, CHEN Guo, WANG Haifei. Effects of gear coupling on aero-engine vibration characteristics[J]. China Mechanical Engineering, 2015, 26(10): 1312-1319. (in Chinese) doi: 10.3969/j.issn.1004-132X.2015.10.007
|
| [5] |
YU Pingchao, WANG Cun, LIU Yunlong, et al. Analytical modeling of the lateral stiffness of a spline coupling considering teeth engagement and influence on rotor dynamics[J]. European Journal of Mechanics-A/Solids, 2022, 92: 104468. doi: 10.1016/j.euromechsol.2021.104468
|
| [6] |
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
|
| [7] |
HUANG Wenkang, TIAN Hongxu, MA Hui, et al. An improved method for calculating the lateral and angular stiffness of spline couplings considering parallel misalignment[J]. Mechanism and Machine Theory, 2023, 189: 105436. doi: 10.1016/j.mechmachtheory.2023.105436
|
| [8] |
ZHANG Chao, ZHU Rupeng, CHEN Weifang, et al. An improved dynamic model of the spline coupling with misalignment and its load distribution analysis[J]. International Journal of Mechanics and Materials in Design, 2024, 20(2): 393-408. doi: 10.1007/s10999-023-09681-6
|
| [9] |
XUE Xiangzhen, HUO Qixin, LIU Jian. Nonlinear vibration characteristics of the involute spline coupling in aeroengine with the parallel misalignment[J]. International Journal of Aerospace Engineering, 2021, 2021(1): 6689442.
|
| [10] |
XUE Xiangzhen, HUO Qixin, LIU Jian, et al. Nonlinear dynamic load analysis of aviation spline coupling with mass eccentricity and misalignment[J]. Advances in Mechanical Engineering, 2021, 13(2): 1687814021996511.
|
| [11] |
MIAO Xueyang, JIANG Dong, AI Xing, et al. Dynamic characteristics of rotor system with parallel and angular misaligned involute spline coupling[J]. Meccanica, 2024, 59(7): 1061-1085. doi: 10.1007/s11012-024-01842-x
|
| [12] |
ZHU Haimin, ZHANG Li, CHEN Qingzhang, et al. Theoretical and experimental study on the self-excited vibration of a flexible rotor system with floating spline[J]. Chinese Journal of Aeronautics, 2023, 36(12): 247-267. doi: 10.1016/j.cja.2023.03.030
|
| [13] |
ZHU Haimin, HU Shunan, ZHANG Li, et al. Dynamic characteristics of a supercritical helicopter tail transmission system with self-excited vibration and rubbing impact[J]. International Journal of Structural Stability and Dynamics, 2024, 24(17): 2450188. doi: 10.1142/S0219455424501888
|
| [14] |
高腾, 荆建平, 梅庆, 等. 花键连接转子系统稳定性研究[J]. 噪声与振动控制, 2016, 36(2): 40-45. GAO Teng, JING Jianping, MEI Qing, et al. Stability analysis of spline connected rotor system[J]. Noise and Vibration Control, 2016, 36(2): 40-45. (in Chinese doi: 10.3969/j.issn.1006-1335.2016.02.009
GAO Teng, JING Jianping, MEI Qing, et al. Stability analysis of spline connected rotor system[J]. Noise and Vibration Control, 2016, 36(2): 40-45. (in Chinese) doi: 10.3969/j.issn.1006-1335.2016.02.009
|
| [15] |
高腾. 花键连接转子系统稳定性研究[D]. 上海: 上海交通大学, 2016. GAO Teng. Research on the stability of spline connected rotor system[D]. Shanghai: Shanghai Jiao Tong University, 2016. (in Chinese
GAO Teng. Research on the stability of spline connected rotor system[D]. Shanghai: Shanghai Jiao Tong University, 2016. (in Chinese)
|
| [16] |
ZHANG Zhenguo, MA Xinxing. Friction-induced nonlinear dynamics in a spline-rotor system: Numerical and experimental studies[J]. International Journal of Mechanical Sciences, 2024, 278: 109427. doi: 10.1016/j.ijmecsci.2024.109427
|
| [17] |
王庆国, 陈大兵, 魏静, 等. 基于有限元法的渐开线花键联接接触分析[J]. 机械传动, 2014, 38(1): 134-137. WANG Qingguo, CHEN Dabing, WEI Jing, et al. Contact analysis of involute spline joint based on FEM[J]. Journal of Mechanical Transmission, 2014, 38(1): 134-137. (in Chinese
WANG Qingguo, CHEN Dabing, WEI Jing, et al. Contact analysis of involute spline joint based on FEM[J]. Journal of Mechanical Transmission, 2014, 38(1): 134-137. (in Chinese)
|
| [18] |
CURÀ F, MURA A, ADAMO F. Fatigue damage in spline couplings: numerical simulations and experimental validation[J]. Procedia Structural Integrity, 2017, 5: 1326-1333. doi: 10.1016/j.prostr.2017.07.141
|
| [19] |
李伦绪, 陈果, 杨默晗. 航空发动机套齿连接结构刚度特性仿真分析及试验研究[J]. 中国机械工程, 2022, 33(18): 2249-2257. LI Lunxu, CHEN Guo, YANG Mohan. Simulation analysis and experimental study of stiffness characteristics of aero-engine spline couplings[J]. China Mechanical Engineering, 2022, 33(18): 2249-2257. (in Chinese doi: 10.3969/j.issn.1004-132X.2022.18.012
LI Lunxu, CHEN Guo, YANG Mohan. Simulation analysis and experimental study of stiffness characteristics of aero-engine spline couplings[J]. China Mechanical Engineering, 2022, 33(18): 2249-2257. (in Chinese) doi: 10.3969/j.issn.1004-132X.2022.18.012
|
| [20] |
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 doi: 10.13224/j.cnki.jasp.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) doi: 10.13224/j.cnki.jasp.20230070
|
| [21] |
邓旺群, 王桢, 周扬, 等. 涡轴发动机动力涡轮转子平衡状态影响因素试验研究[J]. 航空发动机, 2012, 38(6): 48-52. DENG Wangqun, WANG Zhen, ZHOU Yang, et al. Experiment research of balance state influence factors of power turbine rotor of turboshaft engine[J]. Aeroengine, 2012, 38(6): 48-52. (in Chinese
DENG Wangqun, WANG Zhen, ZHOU Yang, et al. Experiment research of balance state influence factors of power turbine rotor of turboshaft engine[J]. Aeroengine, 2012, 38(6): 48-52. (in Chinese)
|
| [22] |
黄江博, 廖明夫, 刘巧英, 等. 带套齿连接结构的转子系统振动稳定性实验研究[J]. 推进技术, 2022, 43(2): 210552. HUANG Jiangbo, LIAO Mingfu, LIU Qiaoying, et al. Experimental study on vibration stability of rotor system with spline connection structure[J]. Journal of Propulsion Technology, 2022, 43(2): 210552. (in Chinese doi: 10.13675/j.cnki.tjjs.210552
HUANG Jiangbo, LIAO Mingfu, LIU Qiaoying, et al. Experimental study on vibration stability of rotor system with spline connection structure[J]. Journal of Propulsion Technology, 2022, 43(2): 210552. (in Chinese) doi: 10.13675/j.cnki.tjjs.210552
|
| [23] |
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]. Machinery Design & Manufacture, 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]. Machinery Design & Manufacture, 2019(Suppl. 1): 86-90, 94. (in Chinese)
|
| [24] |
赵广, 郭嘉楠, 王晓放, 等. 转子-齿式联轴器-轴承系统不对中动力学特性[J]. 大连理工大学学报, 2011, 51(3): 338-345. ZHAO Guang, GUO Jianan, WANG Xiaofang, et al. Dynamics of rotor-gear coupling-bearing system with misalignment[J]. Journal of Dalian University of Technology, 2011, 51(3): 338-345. (in Chinese
ZHAO Guang, GUO Jianan, WANG Xiaofang, et al. Dynamics of rotor-gear coupling-bearing system with misalignment[J]. Journal of Dalian University of Technology, 2011, 51(3): 338-345. (in Chinese)
|
| [25] |
侯志强. 航空花键连接结构刚度仿真、试验、识别及应用[D]. 大连: 大连理工大学, 2022. HOU Zhiqiang. Spline connection structural stiffness simulation, test, identification and application of aviation[D]. Dalian: Dalian University of Technology, 2022. (in Chinese
HOU Zhiqiang. Spline connection structural stiffness simulation, test, identification and application of aviation[D]. Dalian: Dalian University of Technology, 2022. (in Chinese)
|
| [26] |
ZHANG Chao, ZHU Rupeng, CHEN Weifang, et al. Dynamic modeling and analysis of the supercritical tail drive system of a helicopter considering the mounting platform deformation[J]. Nonlinear Dynamics, 2024, 112(11): 9063-9094. doi: 10.1007/s11071-024-09553-4
|
| [27] |
WANG Lei, LIU Haitao, ZHANG Jun, et al. Analysis and modeling for flexible joint interfaces under micro and macro scale[J]. Precision Engineering, 2013, 37(4): 817-824. doi: 10.1016/j.precisioneng.2013.03.008
|
| [28] |
李琳, 刘久周, 李超. 干摩擦阻尼器对宽频多阶次激励减振效果分析[J]. 航空动力学报, 2016, 31(9): 2171-2180. LI Lin, LIU Jiuzhou, LI Chao. Analysis on damping effect of dry friction damper under wideband multi-harmonic excitation[J]. Journal of Aerospace Power, 2016, 31(9): 2171-2180. (in Chinese doi: 10.13224/j.cnki.jasp.2016.09.016
LI Lin, LIU Jiuzhou, LI Chao. Analysis on damping effect of dry friction damper under wideband multi-harmonic excitation[J]. Journal of Aerospace Power, 2016, 31(9): 2171-2180. (in Chinese) doi: 10.13224/j.cnki.jasp.2016.09.016
|
| [29] |
马伍, 王艾伦, 王海, 等. 考虑齿面粗糙度的端齿连接结构接触刚度求解方法研究[J]. 机械强度, 2020, 42(6): 1389-1395. MA Wu, WANG Ailun, WANG Hai, et al. Research on solution method of contact stiffness of curvic couplings considering tooth surface roughness[J]. Journal of Mechanical Strength, 2020, 42(6): 1389-1395. (in Chinese doi: 10.16579/j.issn.1001.9669.2020.06.017
MA Wu, WANG Ailun, WANG Hai, et al. Research on solution method of contact stiffness of curvic couplings considering tooth surface roughness[J]. Journal of Mechanical Strength, 2020, 42(6): 1389-1395. (in Chinese) doi: 10.16579/j.issn.1001.9669.2020.06.017
|
DownLoad:
