Simulation and experiment on contact stiffness of aviation splines
-
摘要:
针对航空花键接触刚度数量级高导致的直接试验测量难度高、误差大的现状,以某型号航空发动机花键连接结构为研究对象,经过合理的简化与缩尺设计,建立相应的花键结构模型。仿真得到花键接触刚度及其随传递扭矩、横向力的变化规律,并搭建与仿真模型一致的试验台进行刚度测试。结果表明:当横向力不变时,花键的接触刚度随传递扭矩的增大而非线性增大,并逐渐趋于稳定;当花键处于相同的扭矩和横向力作用时,处于加载和卸载过程中的花键接触刚度值不同,并出现迟滞现象;试验测得在所有扭矩下的花键平均刚度值为20.48 MN/m,仿真结果与试验结果的平均误差为8.54%,试验与仿真结果取得了较好的一致性。该研究为航空花键接触刚度的研究提供了参考。
Abstract:The high magnitude of the contact stiffness of aviation splines leads to the difficulty in direct measurement and notable test error. A spline structure model was established through reasonable simplification and scale design according to the actual spline connection structure of an aero-engine. Simulations were made to determine the spline contact stiffness and its variation with transmission torque and lateral force. A test bench consistent with the simulation model was built to test the contact stiffness. The results showed that when the transverse force was constant, the contact stiffness of the spline increased nonlinearly with the increase of transmission torque, and was inclined to be unchanged gradually. When the spline was under the same torque and lateral force, the contact stiffness of the spline was different during loading and unloading, and the hysteresis phenomenon occurred. The average contact stiffness of splines measured under all torques was 20.48 MN/m. The test and simulation results were in good agreement, with an average error of 8.54%. This study provides a reference for studying the contact stiffness of aviation splines.
-
Key words:
- aviation spline /
- contact stiffness /
- scale model /
- finite element analysis /
- stiffness measurement
-
表 1 花键结构参数
Table 1. Structure parameters of spline
参数 模化前 模化后 齿数Z 64 24 模数m/mm 1.5 1.25 压力角Α/(°) 30 30 接触长度l/mm 139 40 基圆直径Db/mm 83.1 26.0 分度圆直径D/mm 96 30 表 2 不同网格建模的变形对照表
Table 2. Deformation comparison table for different mesh modeling
模型 节点数 单元数 变形/μm 占运行
内存/G相对
误差/%1 307658 182867 10.62 2 −24.9 2 476134 273112 14.06 3 −0.16 3 1827756 945861 14.13 9.3 −0.05 4 1866676 963731 14.14 10.2 0 表 3 花键结构接触变形试验内容矩阵规划
Table 3. Matrix planning of contact deformation test content of spline structure
序号 扭矩/(N·m) 横向载荷/N 试验内容 1 250 500~ 3000 花键刚度测试及
扭矩、载荷影响2 500 500~ 3000 3 750 500~ 3000 表 4 花键单侧加载下测点Y12的刚度仿真结果与试验结果对比
Table 4. Comparison of spline stiffness at point Y12 between test and simulation results under unilateral loading
参数 扭矩/(N·m) 刚度
平均值250 500 750 刚度仿真值/(MN/m) 21.51 22.33 22.84 22.23 刚度试验值/(MN/m) 17.74 21.48 22.21 20.48 误差/% 21.25 3.96 2.84 8.54 -
[1] 《航空发动机设计手册》总编委会. 航空发动机设计手册: 第19册 转子动力学及整机振动[M]. 北京: 航空工业出版社,2001. [2] ZHAO Guang,ZHAO Xiangyang,QIAN Liting,et al. A review of aviation spline research[J]. Lubricants,2023,11(1): 1-19. [3] 王永亮,赵广,孙绪聪,等. 航空花键研究综述[J]. 航空制造技术,2017,60(3): 91-100. WANG Yongliang,ZHAO Guang,SUN Xucong,et al. Review on research of aviation spline[J]. Aeronautical Manufacturing Technology,2017,60(3): 91-100. (in ChineseWANG Yongliang, ZHAO Guang, SUN Xucong, et al. Review on research of aviation spline[J]. Aeronautical Manufacturing Technology, 2017, 60(3): 91-100. (in Chinese) [4] 赵广,李盛翔,郭梅,等. 航空花键振动磨损预测与实验[J]. 航空动力学报,2018,33(12): 2958-2964. ZHAO Guang,LI Shengxiang,GUO Mei,et al. Prediction and experiment of vibration wear of aviation spline[J]. Journal of Aero-space Power,2018,33(12): 2958-2964. (in ChineseZHAO Guang, LI Shengxiang, GUO Mei, et al. Prediction and experiment of vibration wear of aviation spline[J]. Journal of Aero-space Power, 2018, 33(12): 2958-2964. (in Chinese) [5] CURÀ F,MURA A. Evaluation of the fretting wear damage on crowned splined couplings[J]. Procedia Structural Integrity,2017,5: 1393-1400. doi: 10.1016/j.prostr.2017.07.203 [6] 肖立,徐颖强,陈智勇,等. 直升机浮动渐开线花键微动磨损影响因素分析[J]. 航空动力学报,2021,36(4): 751-766. XIAO Li,XU Yingqiang,CHEN Zhiyong,et al. Analysis of influencing factors of fretting wear with helicopter floating involute spline[J]. Journal of Aerospace Power,2021,36(4): 751-766. (in ChineseXIAO Li, XU Yingqiang, CHEN Zhiyong, et al. Analysis of influencing factors of fretting wear with helicopter floating involute spline[J]. Journal of Aerospace Power, 2021, 36(4): 751-766. (in Chinese) [7] 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 [8] ZHAO Guang,LIU Zhansheng,CHEN Feng. Meshing force of misaligned spline coupling and the influence on rotor system[J]. International Journal of Rotating Machinery,2008,2008(1): 1-8. [9] 赵广. 转子-联轴器-轴承—隔振器系统耦合动力学特性研究[D]. 哈尔滨: 哈尔滨工业大学,2009. ZHAO Guang. Study on coupled dynamics of rotor-coupling-bearing-isolator system[D]. Harbin: Harbin Institute of Technology,2009. (in ChineseZHAO Guang. Study on coupled dynamics of rotor-coupling-bearing-isolator system[D]. Harbin: Harbin Institute of Technology, 2009. (in Chinese) [10] SILVERS J E,SORENSEN C,CHASE K. A new statistical model for predicting tooth engagement and load sharing in involute splines[C]//American Gear Manufactures Association Fall Technical Meeting 2010. Alexandria,US: American Gear Manufacturers Association,2010: 1-17. [11] 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 [12] HONG J,TALBOT D,KAHRAMAN A. A stiffness formulation for spline joints[J]. Journal of Mechanical Design,2016,138(4): 043301. doi: 10.1115/1.4032631 [13] 陈曦,廖明夫,李全坤. 带套齿联轴器的转子系统动力学特性研究[J]. 推进技术,2015,36(7): 1069-1077. CHEN Xi,LIAO Mingfu,LI Quankun. Dynamic characteristics of a rotor system with a spline coupling[J]. Journal of Propulsion Technology,2015,36(7): 1069-1077. (in ChineseCHEN Xi, LIAO Mingfu, LI Quankun. Dynamic characteristics of a rotor system with a spline coupling[J]. Journal of Propulsion Technology, 2015, 36(7): 1069-1077. (in Chinese) [14] 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 [15] XUE Xiangzhen,HUO Qixin,DEARN K D,et al. Involute spline couplings in aero-engine: predicting nonlinear dynamic response with mass eccentricity[J]. Proceedings of the Institution of Mechanical Engineers,Part K: Journal of Multi-Body Dynamics,2021,235(1): 75-92. [16] 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):168781402199651. [17] 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. [18] 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 [19] SUM W S,LEEN S B,WILLIAMS E J,et al. Efficient finite element modelling for complex shaft couplings under non-symmetric loading[J]. The Journal of Strain Analysis for Engineering Design,2005,40(7): 655-673. doi: 10.1243/030932405X30858 [20] LIU Shuguo,MA Yanhong,ZHANG Dayi,et al. Studies on dynamic characteristics of the joint in the aero-engine rotor system[J]. Mechanical Systems and Signal Processing,2012,29: 120-136. doi: 10.1016/j.ymssp.2011.12.001 [21] LIU Shuguo,WANG Jun,HONG Jie,et al. Dynamics design of the aero-engine rotor joint structures based on experimental and numerical study[C]//Proceedings of the ASME Turbo Expo 2010: Power for Land,Sea and Air. Glasgow,US: ASME,2010: 1-12. [22] MEDINA S,OLVER A V. Regimes of contact in spline couplings[J]. Journal of Tribology,2002,124(2): 351-357. doi: 10.1115/1.1403456 [23] KU C P R,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 [24] ROBINS R R. Tooth engagement evaluation of involute spline couplings[D]. Provo,US: Brigham Young University,2008. [25] 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 ChineseLIAO 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) [26] 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 [27] O’DONNELL W J. The additional deflection of a cantilever due to the elasticity of the support[J]. Journal of Applied Mechanics,1960,27(3): 461. doi: 10.1115/1.3644025 -