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计及短周期误差的直齿轮副近周期运动及其辨识

刘鹏飞 朱凌云 苟向锋 石建飞 金国光

刘鹏飞, 朱凌云, 苟向锋, 石建飞, 金国光. 计及短周期误差的直齿轮副近周期运动及其辨识. 力学学报, 2022, 54(3): 787-800 doi: 10.6052/0459-1879-21-556
引用本文: 刘鹏飞, 朱凌云, 苟向锋, 石建飞, 金国光. 计及短周期误差的直齿轮副近周期运动及其辨识. 力学学报, 2022, 54(3): 787-800 doi: 10.6052/0459-1879-21-556
Liu Pengfei, Zhu Lingyun, Gou Xiangfeng, Shi Jianfei, Jin Guoguang. Neighboring periodic motion and its identification for spur gear pair with short-period errors. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(3): 787-800 doi: 10.6052/0459-1879-21-556
Citation: Liu Pengfei, Zhu Lingyun, Gou Xiangfeng, Shi Jianfei, Jin Guoguang. Neighboring periodic motion and its identification for spur gear pair with short-period errors. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(3): 787-800 doi: 10.6052/0459-1879-21-556

计及短周期误差的直齿轮副近周期运动及其辨识

doi: 10.6052/0459-1879-21-556
基金项目: 国家自然科学基金(51365025), 天津市自然科学基金(18JCYBJC88800, 19JCZDJC38700)和天津市研究生科研创新项目(2020YJSB067)资助项目
详细信息
    作者简介:

    苟向锋, 教授, 主要研究方向: 机械系统动力学. E-mail: 20150022@tiangong.edu.cn

  • 中图分类号: TH132, O322

NEIGHBORING PERIODIC MOTION AND ITS IDENTIFICATION FOR SPUR GEAR PAIR WITH SHORT-PERIOD ERRORS

  • 摘要: 齿轮副中的齿距偏差等短周期误差使系统出现复杂的周期运动, 影响齿轮传动的平稳性. 将该类复杂周期运动定义为近周期运动, 采用多时间尺度Poincaré映射截面对其进行辨识. 为研究齿轮副的近周期运动, 引入含齿距偏差的直齿轮副非线性动力学模型, 并计入齿侧间隙与时变重合度等参数. 采用变步长4阶Runge-Kutta法数值求解动力学方程, 由所提出的辨识方法分析不同参数影响下系统的近周期运动. 根据改进胞映射法计算系统的吸引域, 结合多初值分岔图、吸引域图与分岔树状图等研究了系统随扭矩与啮合频率变化的多稳态近周期运动. 研究结果表明, 齿轮副中的短周期误差导致系统的周期运动变复杂, 在微观时间尺度内, 系统的Poincaré映射点数呈现为点簇形式, 系统的点簇数与实际运动周期数为宏观时间尺度的Poincaré映射点数. 短周期误差导致系统在微观时间尺度内的吸引子数量增多, 使系统运动转迁过程变复杂. 合理的参数范围及初值范围可提高齿轮传动的平稳性. 该辨识与分析方法可为非线性系统中的近周期运动研究奠定理论基础.

     

  • 图  1  含短周期误差的齿轮系统的复杂周期运动[23]

    Figure  1.  Complex periodic motions of gear systems with short-period errors [23]

    图  2  随刚度波动幅值变化的直齿轮副动力学特性[10]

    Figure  2.  Dynamics characteristics of spur gear pair via stiffness fluctuation amplitude [10]

    图  3  齿轮副简化物理模型

    Figure  3.  Simplified physical model of gear pair

    图  4  随刚度波动幅值变化的直齿轮副多时间尺度分岔图

    Figure  4.  Bifurcation diagrams of the spur gear pair with different time scales via stiffness fluctuation amplitude

    图  5  随扭矩变化的直齿轮副多时间尺度分岔图

    Figure  5.  Bifurcation diagrams of the spur gear pair with different time scales via torque

    图  6  随啮合频率变化的直齿轮副多时间尺度分岔图

    Figure  6.  Bifurcation diagrams of the spur gear pair with different time scales via meshing frequency

    图  7  系统随扭矩变化的多初值分岔图及TLE谱

    Figure  7.  Multi-initial values bifurcation diagrams and TLE spectrums of system via F

    图  8  系统随扭矩变化的吸引域

    Figure  8.  Basin of attraction of system via F

    图  9  系统随扭矩变化的分岔树状图

    Figure  9.  Bifurcation dendrogram of system via F

    图  10  系统随啮合频率变化的多初值分岔图及TLE谱

    Figure  10.  Multi-initial values bifurcation diagrams and TLE spectrums of system via ω

    图  13  系统随啮合频率变化的分岔树状图

    Figure  13.  Bifurcation dendrogram of system via ω

    图  11  系统随啮合频率变化的吸引域

    Figure  11.  Basin of attraction of system via ω

    图  12  系统随啮合频率变化的相图与Poincaré映射图

    Figure  12.  Phase portraits and Poincaré maps of system via ω

    表  1  齿轮参数

    Table  1.   Parameters of a spur gear pair

    ParametersPinionGear
    precision grade6 GM6 GM
    module/mm55
    number of teeth2126
    下载: 导出CSV

    表  2  主动轮齿距偏差值(Np =21)

    Table  2.   Pitch deviation values of the pinion (Np =21)

    a1234567
    ΔFpt1(a)
    /μm
    01.943.75.095.96.35.9
    a891011121314
    ΔFpt1(a)
    /μm
    5.093.71.940−1.94−3.7−5.09
    a15161718192021
    ΔFpt1(a)
    /μm
    −5.9−6.3−5.9−5.09−3.7−1.940
    下载: 导出CSV

    表  3  从动轮齿距偏差值(Ng =26)

    Table  3.   Pitch deviation values of the gear (Ng =26)

    b1234567
    ΔFpt2(b)
    /μm
    01.743.374.75.96.66.9
    b891011121314
    ΔFpt2(b)
    /μm
    6.86.35.394.112.570.87−0.87
    b15161718192021
    ΔFpt2(b)
    /μm
    −2.57−4.11−5.39−6.3−6.8−6.9−6.6
    b2223242526
    ΔFpt2(b)
    /μm
    −5.9−4.79−3.37−1.740
    下载: 导出CSV

    表  4  从动轮齿距偏差值(Ng =13)

    Table  4.   Pitch deviation values of the gear (Ng =13)

    b1234567
    ΔFpt2(b)
    /μm
    03.56.0676.063.50
    b8910111213
    ΔFpt2(b)
    /μm
    −3.5−6.06−7−6.06−3.50
    下载: 导出CSV
  • [1] 朱孝录. 齿轮传动设计手册. 北京: 化学工业出版社, 2004

    Zhu Xiaolu. Handbook of Gear Design. Beijing: Chemical Industry Press, 2004 (in Chinese)
    [2] Kahraman A, Singh R. Non-linear dynamics of a spur gear pair. Journal of Sound and Vibration, 1990, 142(1): 49-75 doi: 10.1016/0022-460X(90)90582-K
    [3] Ma H, Zeng J, Feng RJ, et al. Review on dynamics of cracked gear systems. Engineering Failure Analysis, 2015, 55: 224-245 doi: 10.1016/j.engfailanal.2015.06.004
    [4] Xu B, Shimizu Y, Ito S, et al. Pitch deviation measurement of an involute spur gear by a rotary profiling system. Precision Engineering, 2015, 39: 152-160 doi: 10.1016/j.precisioneng.2014.08.003
    [5] Yu WN, Mechefske CK. Analytical modeling of spur gear corner contact effects. Mechanism and Machine Theory, 2016, 96: 146-164 doi: 10.1016/j.mechmachtheory.2015.10.001
    [6] 周长江, 唐进元, 钟志华. 齿轮传动的线外啮合与冲击摩擦. 机械工程学报, 2008, 44(3): 75-81 (Zhou Changjiang, Tang Jinyuan, Zhong Zhihua. Corner contact and impact friction of gear drive. Journal of Mechanical Engineering, 2008, 44(3): 75-81 (in Chinese) doi: 10.3901/JME.2008.03.075
    [7] Zhou CJ, Chen SY. Modeling and calculation of impact friction caused by corner contact in gear transmission. Chinese Journal of Mechanical Engineering, 2014, 27(5): 958-964 doi: 10.3901/CJME.2014.0616.110
    [8] 石照耀, 康焱, 林家春. 基于齿轮副整体误差的齿轮动力学模型及其动态特性. 机械工程学报, 2010, 46(17): 55-61 (Shi Zhaoyao, Tang Yan, Lin Jiachun. Comprehensive dynamics model and dynamic response analysis of a spur gear pair based on gear pair integrated error. Journal of Mechanical Engineering, 2010, 46(17): 55-61 (in Chinese) doi: 10.3901/JME.2010.17.055
    [9] 王奇斌, 张义民. 考虑齿距偏差的直齿轮转子系统振动特性分析. 机械工程学报, 2016, 52(13): 131-140 (Wang Qibin, Zhang Yimin. Vibration characteristics analysis of a spur gear rotor system with the pitch deviation. Journal of Mechanical Engineering, 2016, 52(13): 131-140 (in Chinese) doi: 10.3901/JME.2016.13.131
    [10] Liu PF, Zhu LY, Gou XF, et al. Dynamics modeling and analyzing of spur gear pair with pitch deviation considering time-varying contact ratio under multi-state meshing. Journal of Sound and Vibration, 2021, 513: 116411 doi: 10.1016/j.jsv.2021.116411
    [11] Yi Y, Huang K, Xiong YS, et al. Nonlinear dynamic modelling and analysis for a spur gear system with time-varying pressure angle and gear backlash. Mechanical Systems and Signal Processing, 2019, 132: 18-34 doi: 10.1016/j.ymssp.2019.06.013
    [12] Chen ZG, Ning JY, Wang KY, et al. An improved dynamic model of spur gear transmission considering coupling effect between gear neighbouring teeth. Nonlinear Dynamics, 2021, 106: 339-357 doi: 10.1007/s11071-021-06852-y
    [13] Moradi H, Salarieh H. Analysis of nonlinear oscillations in spur gear pairs with approximated modelling of backlash nonlinearity. Mechanism and Machine Theory, 2012, 51: 14-31 doi: 10.1016/j.mechmachtheory.2011.12.005
    [14] Shi JF, Gou XF, Zhu LY. Modeling and analysis of a spur gear pair considering multi-state mesh with time-varying parameters and backlash. Mechanism and Machine Theory, 2019, 134: 582-603 doi: 10.1016/j.mechmachtheory.2019.01.018
    [15] 吕小红, 罗冠炜. 冲击渐进振动系统相邻基本振动的转迁规律. 力学学报, 2017, 49(5): 1091-1102 (Lü Xiaohong, Luo Guanwei. Transition law of adjacent fundamental motions in vibro-impact system eith progression. Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(5): 1091-1102 (in Chinese)
    [16] 顾伟, 张博, 丁虎等. 2: 1内共振条件下变转速预变形叶片的非线性动力学响应. 力学学报, 2020, 52(4): 1131-1142 (Gu Wei, Zhang Bo, Ding Hu, et al. Nonlinear dynamic response of pre-deformed blade with variable rotational speed under 2: 1 internal resonance. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(4): 1131-1142 (in Chinese)
    [17] Cao Z, Chen ZG, Jiang HJ. Nonlinear dynamics of a spur gear pair with force-dependent mesh stiffness. Nonlinear Dynamics, 2020, 99: 1227-1241 doi: 10.1007/s11071-019-05348-0
    [18] Park CIL. Dynamic behavior of the spur gear system with time varying stiffness by gear positions in the backlash. Journal of Mechanical Science and Technology, 2020, 34: 565-572 doi: 10.1007/s12206-020-0104-9
    [19] Bonori G, Pellicano F. Non-smooth dynamics of spur gears with manufacturing errors. Journal of Sound and Vibration, 2007, 306: 271-283 doi: 10.1016/j.jsv.2007.05.013
    [20] 马锐, 陈予恕. 含裂纹故障齿轮系统的非线性动力学研究. 机械工程学报, 2011, 47(21): 84-90 (Ma Rui, Chen Yushu. Nonlinear dynamic research on gear system with cracked failure. Journal of Mechanical Engineering, 2011, 47(21): 84-90 (in Chinese) doi: 10.3901/JME.2011.21.084
    [21] 郜志英, 沈允文, 董海军等. 齿轮系统倍周期分岔和混沌层次结构的研究. 机械工程学报, 2005, 41(4): 44-48 (Gao Zhiying, Shen Yunwen, Dong Haijun, et al. Research on period-doubling bifurcation and chaos hiberarchy in gear system. Journal of Mechanical Engineering, 2005, 41(4): 44-48 (in Chinese) doi: 10.3901/JME.2005.04.044
    [22] Farshidianfar A, Saghafi A. Bifurcation and chaos prediction in nonlinear gear systems. Shock and Vibration, 2014, 2014: 809739
    [23] Xiang L, An CH, Zhang Y, et al. Failure dynamic modelling and analysis of planetary gearbox considering gear tooth spalling. Engineering Failure Analysis, 2021, 125: 105444 doi: 10.1016/j.engfailanal.2021.105444
    [24] Geng ZB, Xiao K, Li JY, et al. Bifurcation and chaos of a spur gear transmission system with non-uniform wear. Journal of Vibration and Acoustics-Transactions of the ASME, 2021, 143(3): 031004 doi: 10.1115/1.4048269
    [25] 高雪, 陈前, 刘先斌. 一类分段光滑隔振系统的非线性动力学设计方法. 力学学报, 2016, 48(1): 192-200 (Gao Xue, Chen Qian, Liu Xianbin. Nonlinear dynamics design for piecewise smooth vibration isolation system. Chinese Journal of Theoretical and Applied Mechanics, 2016, 48(1): 192-200 (in Chinese)
    [26] 邱海, 方虹斌, 徐鉴. 多稳态串联折纸结构的非线性动力学特性. 力学学报, 2019, 51(4): 1110-1121 (Qiu Hai, Fang Hongbin, Xu Jian. Nonlinear dynamical characteristics of a multi-stable series origami structure. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(4): 1110-1121 (in Chinese)
    [27] Shi JF, Gou XF, Zhu LY. Bifurcation of multi-stable behaviors in a two-parameter plane for a non-smooth nonlinear system with time-varying parameters. Nonlinear Dynamics, 2020, 100: 3347-3365 doi: 10.1007/s11071-020-05510-z
    [28] 石建飞, 苟向锋, 朱凌云. 两空间耦合下齿轮传动系统多稳态特性研究. 力学学报, 2019, 51(5): 1489-1499 (Shi Jianfei, Gou Xiangfeng, Zhu Lingyun. Research on multi-stability characteristics of gear transmission system with two-space coupling. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(5): 1489-1499 (in Chinese)
    [29] Souza D, Caldas I. Basins of attraction and transient chaos in a gear-rattling model. Journal of Vibration and Control, 2001, 7(6): 849-862 doi: 10.1177/107754630100700605
    [30] de Souza SLT, Caldas IL, Viana, RL, et al. Sudden changes in chaotic attractors and transient basins in a model for rattling in gearboxes. Chaos Solitons and Fractals, 2004, 21(3): 763-772 doi: 10.1016/j.chaos.2003.12.096
    [31] Mason JF, Piiroinen PT, Wilson RE, et al. Basins of attraction in nonsmooth models of gear rattle. International Journal of Bifurcation and Chaos, 2009, 19(1): 203-224 doi: 10.1142/S021812740902283X
    [32] Zhu LY, Li ZF, Gou XF, et al. Analysis of safety characteristics by nonlinear dynamics and safety basin methods for the spur gear pair in the established teeth contact safety domain. Mechanical Systems and Signal Processing, 2021, 158: 107718 doi: 10.1016/j.ymssp.2021.107718
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出版历程
  • 收稿日期:  2021-10-29
  • 录用日期:  2022-01-22
  • 网络出版日期:  2022-01-23
  • 刊出日期:  2022-03-18

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