多因素条件下单级齿轮系统的非线性特性

摘要/Abstract

摘要： 考虑啮合刚度、齿侧间隙和轴承支撑间隙等因素，运用集中质量法建立了三自由度直齿圆柱齿轮副弯扭耦合非线性振动模型，并据此研究了各参数对齿轮系统非线性振动特性的影响。结果表明：齿侧间隙一定时，随着频率的升高，系统由周期运动通过激变直接进入混沌，然后又由混沌通过激变变为周期运动；在周期运动中，系统经过倍周期分岔,由双周期运动变为四周期运动，然后又通过逆倍周期分岔,由四周期运动变为双周期运动，之后又由双周期运动变为单周期运动；不同的输入转频条件下，间隙变化使系统表现出不同分岔特性，在某些特定频率下，间隙变化只增加系统响应能量变化，并不改变其动力学特性。

关键词: 间隙, 非线性, 分岔, 混沌

Abstract: A nonlinear vibration model of three-degree-of-freedom spur gears coupled with transverse and torsion was established by mass centralized method, considering meshing stiffness, gear backlashes and bearing clearances. Parameter influences on the nonlinear vibration characteristics of the gear system were studied. The results show that, with the increase of frequency, the system enters chaos from periodic motion through a catastrophic way, then from the chaos to periodic motions. In periodic motions, the system changes from period 2 to period 4 through a period-doubling bifurcation, then from period 4 to period 2, and then from period 2 to period 1 through a inverse period-doubling bifurcation. For the different input frequencies, the changes of backlash make the system show different bifurcation characteristics. For some specific frequencies, the changes of the backlash only increase the amplitudes of the system response and do not change its dynamic characteristics.

Key words: clearance, nonlinear, bifurcation, chaos

中图分类号:

TH132

彭毓敏;马超;栾忠权;徐小力. 多因素条件下单级齿轮系统的非线性特性[J]. 中国机械工程.

PENG Yumin;MA Chao;LUAN Zhongquan;XU Xiaoli. Nonlinear Characteristic of Single Stage Gear System under Condition of Multiple Factors[J]. China Mechanical Engineering.

参考文献

[1]NEVZAT O H, HOUSER D R. Mathematical Models Used in Gear Dynamics—a Review [J]. Journal of Sound and Vibration,1988,121 (3) :383-411.
[2]KAHRAMAN A, SINGH R. Non-linear Dynamics of a Spur Gear Pair [J]. Journal of Sound and Vibration, 1990, 142（1）:49-75.
[3]KAHRAMAN A, SINGH R. Nonlinear Dynamics of a Geared Rotor-bearing System with Multiple Clearances [J]. Journal of Sound and Vibration ,1991,144（3）:469-506.
[4]KAHRAMAN A, SINGH R. Interactions between Time-varying Mesh Stiffness and Clearance Non-linearities in a Geared System [J]. Journal of Sound and Vibration, 1991,146（1）:135-156.
[5]HOWARD I, JIA S, WANG J. The Dynamic Modeling of a Spur Gear in Mesh including Friction and a Crack [J]. Mech. Syst. Signal Process, 2001,15（5）:831-853.
[6]THEODOSSIADES S. Non-linear Dynamics of Gear-pair Systems with Periodic Stiffness and Backlash [J]. Journal of Sound and Vibration, 2000,229（2）:287-310.
[7]AL-SHYYAB A, KAHRAMAN A. Non-linear Dynamic Analysis of a Multi-mesh Gear Train Using Multi-term Harmonic Balance Method: Sub-harmonic Motions [J]. Journal of Sound and Vibration,2005,279 (1) :417-451.
[8]苏程，黄志丹.单自由度齿轮系统的周期运动和混沌运动[J].甘肃农业大学学报，2012，47(3):134-137.
SU Cheng, HUANG Zhidan. Periodic Motions and Chaotic Motion in Single Degree of Freedom Spur Gear Pair System[J]. Journal of Gansu Agricultural University, 2012，47(3):134-137.
[9]李英明，陈卫东，陈奇，等.齿侧间隙对齿轮副非线性振动特性的影响研究[J].机械传动，2013,37（5）：1-5.
LI Yingming, CHEN Weidong, CHEN Qi, et al. Research of the Influence of Gear Backlash on Gear Pair Nonlinear Vibration Characteristic[J]. Journal of Mechanical Transmission, 2013,37（5）：1-5.
[10]何航红.齿侧间隙对齿轮系统动力学行为的影响[J].机械设计与制造，2012（7）：281-283.
HE Hanghong. Effect of Backlash on Dynamics Behavior of Gear System [J]. Machinery Design ＆ Manufacture, 2012（7）：281-283.
[11]陈思雨，唐进元. 间隙对含摩擦和时变刚度的齿轮系统动力学响应的影响[J].机械工程学报，2009,45（8）：119-124.
CHEN Siyu, TANG Jinyuan. Effect of Backlash on Dynamics of Spur Gear Pair System with Friction and Time-varying Stiffness[J]. Journal of Mechanical Engineering, 2009,45（8）：119-124.
[12]王帅宝，莫云辉，张黎明. 含间隙和时变啮合刚度齿轮传动系统的分岔和混沌[J].设计与研究，2009，36（5）：25-28.
WANG Shuaibao, MO Yunhui, ZHANG Liming. Bifurcation and Chaos of the Gear System with Backlash and Time-varying Mesh Stiffness[J]. Design and Research, 2009，36（5）：25-28.
[13]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）：498-505.
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）：498-505.
[14]李润方,王建军.齿轮系统动力学——振动、冲击、噪声[M].北京:科学出版社,1997.
LI Runfang, WANG Jianjun. Dynamics of Gear System: Vibration, Shock and Noise[M]. Beijing: Science Press,1997.

[1]	商泽进, 王忠民. 形状记忆合金弹簧振子强迫振动的分岔与混沌 [J]. J4, 201016, 21(16): 1986-1991.
[2]	张家旭, 赵健, 施正堂, 杨雄. 基于耗散性理论的汽车底盘集成非线性鲁棒约束优化控制[J]. 中国机械工程, 2021, 32(08): 883-889.
[3]	江志农1;王子嘉1;张进杰2;黄翼飞3;茆志伟2. 基于能量算子梯度邻域特征提取的核电应急柴油发电机组故障诊断方法[J]. 中国机械工程, 2021, 32(05): 617-623.
[4]	杨帆, 李经伟, 李益国, 毕涛. [车辆工程与测控]磁浮列车悬浮状态数据采集系统设计与实现[J]. 中国机械工程, 2021, 32(04): 467-474.
[5]	陈冠峰1;陈松平1;蔡思捷2. 基于离散像素法的双螺杆压缩机螺杆转子间隙布置方法[J]. 中国机械工程, 2020, 31(24): 2937-2942，3023.
[6]	张宁;李田;殷国栋;吴建华;赵子乾. 转向系参数对汽车拖车组合系统稳定性的影响[J]. 中国机械工程, 2020, 31(21): 2521-2528.
[7]	王薪宇；秦伟；孙晓军；胡小亮. 3-PPR并联伺服平台非线性同步鲁棒控制[J]. 中国机械工程, 2020, 31(19): 2269-2275.
[8]	何飞1,2;杜学飞1,2;王朝俊1,2. 基于对比格兰杰因果关系的热轧带钢头部拉窄根因诊断[J]. 中国机械工程, 2020, 31(19): 2340-2346.
[9]	吴石；朱美文；张添源；刘献礼；李传东. 覆盖件模具拼接特征对球头刀铣削振动的影响 [J]. 中国机械工程, 2020, 31(18): 2143-2152.
[10]	王冠1；张骞2；寇琳媛1；刘志文3；李世康3. 基于混合元胞自动机算法的连续体结构非线性拓扑优化[J]. 中国机械工程, 2020, 31(18): 2161-2173.
[11]	杨登峰, 潘俞舟, 王贵召, 老大中, HU Leon. 分体滑动导叶可调涡轮激波与载荷波动机制[J]. 中国机械工程, 2020, 31(15): 1778-1786.
[12]	徐亭亭, 罗敏, 蒋佳骏, 王晶, 张佳贺. 管内可控铰接柔性结构双层接触非线性力学分析[J]. 中国机械工程, 2020, 31(15): 1798-1807,1814.
[13]	白国星1;孟宇1,2;刘立1;顾青1;罗维东1;甘鑫1. 基于可变预测时域及速度的车辆路径跟踪控制[J]. 中国机械工程, 2020, 31(11): 1277-1284.
[14]	孔骏成;李菊;沈惠平. 2-RPaRSS并联操作手运动副间隙误差分析及补偿[J]. 中国机械工程, 2020, 31(06): 706-713.
[15]	刘光辉1;洪军1;孙岩辉1;吴文武2. 考虑滚子位置变化的圆柱滚子轴承非线性刚度特性分析[J]. 中国机械工程, 2020, 31(05): 505-512.