Dynamic characteristics of spline couplings considering the influence of tooth surface topography
-
摘要:
为提高航空发动机花键连接转子动力学建模的准确性，研究齿面粗糙度对结构动力学特性的影响机制。建立含粗糙表面的花键单对齿啮合仿真模型，揭示法向与切向啮合刚度随位移载荷的变化规律；提出基于虚拟材料法的花键连接结构动力学建模方法，构建考虑表面形貌的整体有限元模型。结果表明：齿面粗糙度降低可提升接触应力分布的均匀性与接触刚度，高粗糙度则导致接触面积损失并引发齿根滑移损伤；粗糙度通过刚度软化效应降低系统固有频率并增大振动响应，其中一阶固有频率对表面状态最为敏感，具体影响程度分别约为7%与11.8%；扭矩载荷通过改善接触状态可部分抵消粗糙度的负面效应。构建的跨尺度分析框架阐明了微观形貌对局部接触行为与整体动力学响应的影响规律，为花键连接转子性能预测与制造工艺优化提供理论依据。
Abstract:To improve the accuracy of dynamic modeling for aeroengine spline connected rotors, the influence mechanism of tooth surface roughness on structural dynamic characteristics was investigated. A simulation model of single-tooth-pair engagement with rough surfaces was established to reveal the evolution of normal and tangential meshing stiffness with displacement loads. A dynamic modeling method based on the virtual material method was proposed, and a finite element model of the overall structure considering surface topography was constructed. Results showed that lower roughness improved the uniformity of contact stress distribution and contact stiffness, whereas higher roughness caused contact area loss and induced tooth root slip damage. Roughness reduced the natural frequency and increased the vibration response through stiffness softening, with the first natural frequency being the most sensitive to surface conditions. The specific influence was about 7% on the first natural frequency and 11.8% on the radial vibration amplitude. In contrast, torque loading partially offset the negative effect of roughness by improving the contact state. The established cross-scale analysis framework clarified the influence of micro-topography on local contact behavior and global dynamic response, providing theoretical support for performance prediction and manufacturing process optimization of aeroengine spline connected rotors.
-
Key words:
- aeroengine /
- spline /
- rough surface /
- contact mechanics /
- dynamics /
- finite element analysis
-
图 2 外花键齿面形貌测量与重构
Figure 2. Measurement and reconstruction of the surface topography of external Splines
图 3 周期和振幅谱指数对表面形貌的影响
Figure 3. The influence of period and amplitude spectrum index on surface topography
图 6 法向啮合刚度理论值与仿真值
Figure 6. Theoretical value and simulation value of normal meshing stiffness
图 7 花键连接结构的虚拟材料等效模型
Figure 7. Virtual material equivalent model of the spline connection structure
图 12 三种不同粗糙度的统计粗糙齿面
Figure 12. Statistical roughened tooth surfaces with three different roughness levels
图 13 单对齿结合面的法向啮合刚度与切向啮合刚度
Figure 13. Normal and tangential meshing stiffness of the single tooth contact surface
图 17 不同粗糙度下振动响应的频域特性
Figure 17. Frequency domain characteristics of vibration responses under different roughness levels
表 1 花键的结构参数和材料参数
Table 1. The structural parameters and material parameters of the spline
参数 数值 内花键 外花键 模数/mm 1 1 齿数 18 18 压力角/（°） 30 30 齿宽/mm 2 2 大径（mm） 19.5 19 小径/mm 17 16.5 泊松比 0.3 弹性模量/GPa 205 
下载: 导出CSV
表 2 虚拟材料层的材料属性
Table 2. Material properties of the virtual material layer
参数 Ra=1 μm Ra=3 μm Ra=6 μm 弹性模量$ E' $/MPa 419 386 330 切变模量$ G' $/MPa 154 135 113 泊松比$ \nu ' $ 0.357 0.432 0.46 密度$ {\rho }{'} $/（kg/m−3） 1570 厚度δ/μm 5 15 30
下载: 导出CSV
-
[1] SONG J P, SHE G L, HE Y J. Nonlinear forced vibration of axially moving functionally graded cylindrical shells under hygro-thermal loads[J]. Geomechanics and Engineering, 2024, 36(2): 99-109. [2] 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 Aerospace Power, 2018, 33(12): 2958-2964. (in Chinese doi: 10.13224/j.cnki.jasp.2018.12.016ZHAO Guang, LI Shengxiang, GUO Mei, et al. Prediction and experiment of vibration wear of aviation spline[J]. Journal of Aerospace Power, 2018, 33(12): 2958-2964. (in Chinese) doi: 10.13224/j.cnki.jasp.2018.12.016 [3] 陈志英, 刘宏蕾, 周平. 航空发动机套齿结构动态装配关系稳健性优化设计[J]. 推进技术, 2018, 39(1): 160-168. CHEN Zhiying, LIU Honglei, ZHOU Ping. Robustness optimization of dynamic assembly parameters for aero-engine spline structure[J]. Journal of Propulsion Technology, 2018, 39(1): 160-168. (in Chinese doi: 10.13675/j.cnki.tjjs.2018.01.018CHEN Zhiying, LIU Honglei, ZHOU Ping. Robustness optimization of dynamic assembly parameters for aero-engine spline structure[J]. Journal of Propulsion Technology, 2018, 39(1): 160-168. (in Chinese) doi: 10.13675/j.cnki.tjjs.2018.01.018 [4] 王迪, 高洁, 胡柏安, 等. 含浮动花键的直升机超临界轴系自激振动实验研究[J]. 推进技术, 2024, 45(2): 151-160. WANG Di, GAO Jie, HU Boan, et al. Experimental study on self-excited vibration of helicopter supercritical shafting with floating splines[J]. Journal of Propulsion Technology, 2024, 45(2): 151-160. (in Chinese doi: 10.13675/j.cnki.tjjs.2209075WANG Di, GAO Jie, HU Boan, et al. Experimental study on self-excited vibration of helicopter supercritical shafting with floating splines[J]. Journal of Propulsion Technology, 2024, 45(2): 151-160. (in Chinese) doi: 10.13675/j.cnki.tjjs.2209075 [5] WILLIAMS R, TRENT R. The Effects of Nonlinear Asymmetric Supports on Turbine Engine Rotor Stability [Z]. SAE International. 1970. https://doi.org/10.4271/700320 [6] 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 [7] HONG J, TALBOT D, KAHRAMAN A. Load distribution analysis of clearance-fit spline joints using finite elements[J]. Mechanism and Machine Theory, 2014, 74: 42-57. doi: 10.1016/j.mechmachtheory.2013.11.007 [8] 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 [9] YU Pingchao, JIANG Ke, JIN Yize, et al. Modeling hysteresis behavior of spline coupling and its application in rotodynamic prediction[J]. Mechanical Systems and Signal Processing, 2025, 230: 112598. doi: 10.1016/j.ymssp.2025.112598 [10] 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 [11] 蒋科, 于平超, 郑华强, 等. 航空发动机套齿连接结构刚度/阻尼特性仿真及机理研究[J]. 推进技术, 2025, 46(9): 273-287. JIANG Ke, YU Pingchao, ZHENG Huaqiang, et al. Simulation and mechanism study on stiffness/damping characteristics of aero-engine spline coupling structure[J]. Journal of Propulsion Technology, 2025, 46(9): 273-287. (in Chinese doi: 10.3724/1001-4055.202410008JIANG Ke, YU Pingchao, ZHENG Huaqiang, et al. Simulation and mechanism study on stiffness/damping characteristics of aero-engine spline coupling structure[J]. Journal of Propulsion Technology, 2025, 46(9): 273-287. (in Chinese) doi: 10.3724/1001-4055.202410008 [12] XIE Wenzhen, LIU Chao, HUANG Gancai, et al. Trans-scale rough surface contact model based on molecular dynamics method: Simulation, modeling and experimental verification[J]. European Journal of Mechanics - A/Solids, 2023, 100: 105021. doi: 10.1016/j.euromechsol.2023.105021 [13] SUN Zhou, CHEN Siyu, TANG Jinyuan, et al. New deterministic model for calculating mesh stiffness and damping of rough-surface gears considering elastic–plastic contact and energy-dissipation mechanism[J]. Mechanical Systems and Signal Processing, 2024, 216: 111502. doi: 10.1016/j.ymssp.2024.111502 [14] CUFFARO V, CURÀ F, MURA A. Damage identification on spline coupling teeth by means of roughness parameters[J]. Theoretical and Applied Fracture Mechanics, 2016, 82: 9-16. doi: 10.1016/j.tafmec.2015.09.008 [15] QURESHI W, CURA F, MURA A. Experimental characterization of roughness parameters for fretting wear in spline couplings[J]. Meccanica, 2017, 52(8): 1975-1984. doi: 10.1007/s11012-016-0535-7 [16] XUE Xiangzhen, LIN Kuan, YU Wei, et al. Fractal theory-based contact analysis of surface microtextured involute spline coupling[J]. Tribology International, 2024, 200: 110055. doi: 10.1016/j.triboint.2024.110055 [17] 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 [18] WU F Y, LIANG Z C, MA Y H, et al. Bending stiffness and dynamic characteristics of a rotor with spline joints[C]// ASME 2013 International Mechanical Engineering Congress and Exposition, 2014 [19] ZHANG Q C, LI W X, LIANG Z C, et al. Study on the stiffness loss and its affecting factors of the spline joint used in rotor systems[C]// ASME Turbo Expo 2014: Turbine Technical Conference and Exposition, 2014 [20] 蒋科, 于平超, 严循金, 等. 考虑接触面摩擦的柔性套齿连接结构刚度数值建模与非线性机理分析 [J]. 中国机械工程, 2025: 1-12. JIANG Ke, YU Pingchao, YAN Xunjin, et al. Numerical modeling and nonlinear mechanism analysis of stiffness for flexible curvic coupling structures considering contact surface friction [J]. China Mechanical Engineering, 2025: 1-12. (in ChineseJIANG Ke, YU Pingchao, YAN Xunjin, et al. Numerical modeling and nonlinear mechanism analysis of stiffness for flexible curvic coupling structures considering contact surface friction [J]. China Mechanical Engineering, 2025: 1-12. (in Chinese) [21] HUANG Gancai, LIU Chao, JIANG Dongxiang. Dynamic modeling and experimental modal analysis for the central rod-fastened rotor with hirth couplings based on fractal contact theory[J]. Journal of Engineering for Gas Turbines and Power, 2024, 146(10): 101015. doi: 10.1115/1.4065672 [22] WANG Xingjie, GONG Hao, LIU Jianhua, et al. Equivalent modeling method of virtual material for flange connection structure based on contact mechanics experiment[J]. Journal of Computational Design and Engineering, 2025, 12(3): 226-240. doi: 10.1093/jcde/qwaf027 [23] LI Yonghan, LI Liting, TANG Yihu, et al. Fretting wear modeling of bolted joint interface with microscopic roughness using the 1D microslip friction model and equivalent thin layer[J]. Mechanics Based Design of Structures and Machines, 2025, 53(6): 4786-4811. doi: 10.1080/15397734.2025.2456000 [24] 王永亮, 赵广, 徐永强, 等. 不对中多浮动花键接触刚度识别及动力学应用[J]. 航空动力学报, 2025, 40(4): 110-118. WANG Yongliang, ZHAO Guang, XU Yongqiang, et al. Contact stiffness identification of misaligned multiple floating splines and its dynamic application[J]. Journal of Aerospace Power, 2025, 40(4): 110-118. (in Chinese doi: 10.13224/j.cnki.jasp.20240738WANG Yongliang, ZHAO Guang, XU Yongqiang, et al. Contact stiffness identification of misaligned multiple floating splines and its dynamic application[J]. Journal of Aerospace Power, 2025, 40(4): 110-118. (in Chinese) doi: 10.13224/j.cnki.jasp.20240738 [25] GREENWOOD J A, WILLIAMSON J B P. Contact of nominally flat surfaces[J]. Proceedings of the Royal Society of London Series A Mathematical and Physical Sciences, 1966, 295(1442): 300-319. doi: 10.1016/0043-1648(67)90287-6 [26] LIANG Yufei, ZHOU Shengqiang, LI Huafeng, et al. A contact model based on multi-scale rough surface of ultrasonic motor[J]. Measurement, 2025, 249: 117025. doi: 10.1016/j.measurement.2025.117025 [27] LI Xinxin, LI Zhimin, JIN Sun, et al. A multi-scale model of real contact area for linear guideway based on the fractal theory[J]. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2021, 235(21): 5796-5813. doi: 10.1177/0954406220983367 [28] WANG Qiaoyi, ZHANG Lukuan, ZHANG Zhen, et al. Characteristics of rolling interface lubrication considering contact surface textures in mixed lubrication[J]. Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology, 2025, 239(7): 886-897. doi: 10.1177/13506501241302380 [29] 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 [30] ZHANG Chao, CAO Peng, ZHU Rupeng, et al. Dynamic modeling and analysis of the spline joint-flexible coupling-rotor system with misalignment[J]. Journal of Sound and Vibration, 2023, 554: 117696. doi: 10.1016/j.jsv.2023.117696 [31] GOOD I J. The science of fractal images (heinz-otto peitgen and dietmar saupe, eds. )[J]. SIAM Review, 1991, 33(3): 496-499. doi: 10.1137/1033121 [32] 付才高. 航空发动机设计手册: 第19册 转子动力学及整机振动 [M]. , 2000. FU Caigao. Aero-engine design manual : Vol. 19 rotor dynamics and whole engine vibration [M]. , 2000. (in ChineseFU Caigao. Aero-engine design manual : Vol. 19 rotor dynamics and whole engine vibration [M]. , 2000. (in Chinese) [33] CHANG Yu, DING Jianguo, FAN Hui, et al. Interfacial micromechanics modeling for bolted joints in ultra-precision machine tools[J]. Journal of Mechanical Science and Technology, 2023, 37(8): 4179-4191. doi: 10.1007/s12206-023-0734-9 [34] 吕东晓, 陈雪骑, 王东, 等. 转子螺栓连接结构界面滑移损伤机理及影响因素研究[J]. 航空动力学报, 2025, 40(1): 370-380. LÜ/LV/LU/LYU) Dongxiao, CHEN (Xue)(Ji| Qi), WANG Dong, et al. Mechanism and influential factors research of slip damage in rotor bolted joint structures[J]. Journal of Aerospace Power, 2025, 40(1): 370-380. (in ChineseLÜ/LV/LU/LYU) Dongxiao, CHEN (Xue)(Ji| Qi), WANG Dong, et al. Mechanism and influential factors research of slip damage in rotor bolted joint structures[J]. Journal of Aerospace Power, 2025, 40(1): 370-380. (in Chinese [35] 杨光, 程凯博, 赵朔, 等. 激光选区熔化成形316L不锈钢下倾斜面粗糙度的预测与模型建立[J]. 中国激光, 2023, 50(20): 2002301. YANG Guang, CHENG Kaibo, ZHAO Shuo, et al. Prediction and model establishment of inclined surface roughness of laser selective melting formed 316L stainless steel[J]. Chinese Journal of Lasers, 2023, 50(20): 2002301. (in Chinese doi: 10.3788/CJL230607YANG Guang, CHENG Kaibo, ZHAO Shuo, et al. Prediction and model establishment of inclined surface roughness of laser selective melting formed 316L stainless steel[J]. Chinese Journal of Lasers, 2023, 50(20): 2002301. (in Chinese) doi: 10.3788/CJL230607 [36] 王泽坤, 陈力, 曹铭津, 等. UHMWPE层合板抗侵蚀性能的一种等效数值分析方法[J]. 含能材料, 2024, 32(9): 952-963. WANG Zekun, CHEN Li, CAO Mingjin, et al. Equivalent numerical simulation method for penetration resistance of UHMWPE laminate[J]. Chinese Journal of Energetic Materials, 2024, 32(9): 952-963. (in ChineseWANG Zekun, CHEN Li, CAO Mingjin, et al. Equivalent numerical simulation method for penetration resistance of UHMWPE laminate[J]. Chinese Journal of Energetic Materials, 2024, 32(9): 952-963. (in Chinese) -
点击查看大图
计量
- 文章访问数: 154
- HTML浏览量: 118
- PDF量: 4
- 被引次数: 0