Research on the Nonlinear Dynamics of Micro-segment Gear System with Time-Varying Friction Coefficient

doi:10.3901/JME.2021.19.011

Abstract

Abstract: A systematic dynamic analysis of a micro-segment gear system with time-varying friction coefficient, time-varying base circle, and time-varying stiffness is made. A six-degree-of freedom nonlinear dynamic model of a micro-segment gear is established by discretizing the meshing process. The numerical integration method is used to study the dynamic response of the micro-segment gear and involute gear under different operating conditions. The effects of different parameters on radial vibration are investigated from the amplitude–frequency response and bifurcation diagram. Through the experiment, the micro-segment gear and the involute gear are compared during the actual operation. The results reveal that compared with involute gear, micro-segment gear has smaller vibration and better system stability, especially in the case of medium-high speed and heavy load. The common amplitude value can be effectively reduced by increasing the support stiffness and the support damping, but the change in the support stiffness changes the position of the resonance region. The friction coefficient has little effect on the amplitude of the micro-segment gear, but increasing the friction coefficient causes the system to end the chaotic response ahead of time. The error and vibration of the micro-segment gearbox during actual operation are smaller and the performance is better.

Key words: nonlinear dynamics, microsegment gear, time-varying friction coefficient, time-varying base circle, vibration

CLC Number:

TH113

XIONG Yangshou, HAN Guangzhi, HUANG Kang, ZHAO Han. Research on the Nonlinear Dynamics of Micro-segment Gear System with Time-Varying Friction Coefficient[J]. Journal of Mechanical Engineering, 2021, 57(19): 113-127.

References

[1] 赵韩,梁锦华,刘红雨,等.微线段齿廓的形成原理及特性[J].机械工程学报,1997,33(5):7-11. ZHAO Han,LIANG Jinhua,LIU Hongyu,et al. Constructing principle and features of tooth profiles with micro-segments[J]. Chinese Journal of Mechanical Engineering,1997,33(5):7-11.
[2] LI Sheng,ANISETTI A. A tribo-dynamic contact fatigue model for spur gear pairs[J]. International Journal of Fatigue,2017,98:81-91.
[3] MORADI H,SALARIEH H. Analysis of nonlinear oscillations in spur gear pairs with approximated modelling of backlash nonlinearity[J]. Mechanism&Machine Theory,2012,51(5):14-31.
[4] 尹桩,苟向锋,朱凌云.考虑齿面冲击及摩擦的单级齿轮系统动力学建模及分析[J].振动工程学报,2018,31(6):974-983. YIN Zhu,GUO Xiangfeng,ZHU Lingyun. Dynamic modeling and analysis of single-stage gear system considering tooth surface impact and friction[J]. Journal of Vibration Engineering,2018,31(6):974-983.
[5] KANG Boqiang,GOU Xiangfeng. Modeling and dynamics characteristic analysis of helical gear system with considering tooth surface friction[J]. Journal of Mechanical Transmission,2015,39(7):136-140.
[6] LU Fengxia,WANG Haofei,ZHU Rupeng,et al. Dynamics characteristic analysis of spur gear pairs based on tooth surface friction[J]. Journal of Mechanical Transmission,2015,39(11):27-32.
[7] FANG Yining,LIANG Xihui,ZUO M J. Effects of friction and stochastic load on transient characteristics of a spur gear pair[J]. Nonlinear Dynamics,2018,93(2):599-609.
[8] HAN Lin,QI Houjun. Dynamic response analysis of helical gear pair considering the interaction between friction and mesh stiffness[J]. Meccanica,2019,54:2325-2337.
[9] 邹玉静,庞峰,樊智敏.渐开线斜齿轮传动摩擦动力学耦合研究[J].机械工程学报,2019,55(3):122-132. ZOU Yujing,PANG Feng,FAN Zhimin. Research on friction dynamics coupling of involute helical gear transmission[J]. Chinese Journal of Mechanical Engineerin,2019,55(3):122-132.
[10] 欧阳天成,黎朔宇,周峰,等.高速直齿轮摩擦动力学特性分析[J].振动,测试与诊断,2020,40(2):255-263. OUYANG Tiancheng,LI Shuoyu,ZHOU Feng, et al. Friction dynamic characteristics analysis of high speed sspur gear[J]. Journal of Vibration,Measurement&Diagnosis,2020,40(2):255-263.
[11] DONG Hao,ZHANG Jianwen,WANG Libang. Study on bifurcation characteristics of multi-clearance bending torsional coupling gear transmission based on EHL[J]. Advances in Mechanical Engineering,2020,12(6):1-19.
[12] 李直,陈剑,沈锦龙,等.基于双盘试验的齿面时变摩擦特性研究[J].机械工程学报, 2018, 54(2):73-81. LI Zhi,CHEN Jian,SHEN Jinlong,et al. Study on the time-varying friction characteristics of tooth surface based on double disc test[J]. Journal of Mechanical Engineering,2018,54(2):73-81.
[13] HOUSER D R,VAISHYA M,SORENSON J D. Vibro-acoustic effects of friction in gears:An experimental investigation[R]. SAE Technical Paper,2001.
[14] ZHAO Yulai,LIU Yang,XIN Xicheng,et al. Dynamic modelling considering nonlinear factors of coupled spur gear system and its experimental research[J]. IEEE Access,2020,8:84971-84980.
[15] WANG Cheng. Dynamic model of a helical gear pair considering tooth surface friction[J]. Journal of Vibration and Control,2020,26(15-16):107754631989612.
[16] 张靖,陈兵奎,康传章,等.计及齿面摩擦的直齿轮动力学分析[J].振动与冲击,2012,31(21):126-132. ZHANG Jing,CHEN Bingkui,KANG Chuanzhang,et al. Dynamic analysis on spur gears considering friction effect[J]. Journal of Vibration and Shock,2012,31(21):126-132.
[17] 石建飞,苟向锋,朱凌云.计及摩擦的多状态啮合渐开线直齿轮系统动力学建模分析[J].西北工业大学学报,2020,38(2):401-410. SHI Jianfei,GOU Xiangfeng,ZHU Lingyun. Dynamic modeling and analysis of involute spur gear system with multi-state meshing including friction[J]. Journal of Northwestern Polytechnical University,2020,38(2):401-410.
[18] 盛冬平,朱如鹏,靳广虎,等.考虑摩擦的多间隙直齿弯扭振动建模和分岔特性[J].航空动力学报,2015,30(2):498-506. SHENG Dongping,ZHU Rupeng,JIN Guanghu,et al. Bifurcation characteristic and modeling of transverse-torsional spur gear vibration considering friction and multiple clearances[J]. Journal of Aerospace Power,2015,30(2):498-506.
[19] BLAGOJEVIĆ M,NIKOLIĆ V,MARJANOVIĆ N,et al. Analysis of cycloid drive dynamic behavior[J]. Scientific Technical Review,2009,59(1):52-56.
[20] 董长斌,刘永平,魏永峭,等.椭圆齿轮传动系统非线性动态特性分析[J].吉林大学学报(工学版),2020,50(2):100-110. DONG Changbin,LIU Yongping,WEI Yongqiao,et al. Analysis of nonlinear dynamic characteristics of elliptic gear transmission system[J]. Journal of Jilin University (Engineering Science),2020,50(2):100-110.
[21] HUANG Kang,SANG Meng,XIONG Yangshou,et al. Bifurcation analysis and chaotic behaviors of a spur microsegment gear pair with time-varying pressure angle[J]. Journal of Computational and Nonlinear Dynamics,2019,14(12):1008.
[22] HUANG Kang,XU Fengwei,XIONG Yangshou,et al. Nonlinear dynamic analysis of micro-segment gear system with time-varying base circle[J]. Transactions-Canadian Society for Mechanical Engineering,2020,44(02):279-293.
[23] HADDAR F M. Analytical modelling of spur gear tooth crack and influence on gearmesh stiffness[J]. European Journal of Mechanics-A/Solids,2009,28(3):461-468.
[24] SAINSOT P,VELEX P,DUVERGER O. Contribution of gear body to tooth deflections-a new bidimensional analytical formula[J]. Journal of Mechanical Design,2004,126(4):748-752.
[25] YANG D C H,SUN Z S. A rotary model of spur gear dynamics[J]. Journal of Mechanisms Transmissions&Automation in Design,1985,107(4):529-535.
[26] XU Hai. Development of a generalized mechanical efficiency prediction methodology for gear pairs[D]. The Ohio State University,2005.