Nonlinear Dynamics Characteristics of Non-circular Planetary Gear Systems

doi:10.3969/j.issn.1004-132X.2026.02.010

Abstract

Abstract:

To investigate the nonlinear dynamics behavior of non-circular planetary gear systems， a non-circular planetary gear transmission system was first developed based on the relative motion relationships among system components. Subsequently， a nonlinear dynamics model was established by incorporating critical nonlinear factors including time-varying mesh stiffness， backlash， meshing damping， and excitation frequency. The dynamics characteristics were quantitatively analyzed through bifurcation diagrams， phase portraits， and time-domain waveforms to elucidate the influence mechanism of various parameters on system vibration response. The results show that the system exhibits complex dynamics behaviors under variations in eccentricity， meshing damping， and excitation frequency. Higher damping coefficients and elevated excitation frequencies are found to enhance system stability， while eccentricity is identified as an effective parameter for sun gear performance modulation.

Key words: non-circular gear, planetary gear transmission system, nonlinear dynamics, bifurcation and chaos

摘要：

为研究非圆行星齿轮系统非线性动力学特性，基于非圆行星齿轮各构件运动关系建立非圆行星齿轮传动系统；考虑时变啮合刚度、齿侧间隙、啮合阻尼、激励频率等关键非线性因素，构建非圆行星齿轮非线性动力学模型；运用分岔图、相图和时域图等表征方法定量研究系统动态行为，揭示了不同参数条件下对系统振动响应的影响机制。结果表明，偏心率、啮合阻尼和激励频率变化的情况下系统表现出丰富的动力学行为；大阻尼和高激励频率有利于非圆行星齿轮系统的运行稳定；偏心率可调控太阳轮性能。

关键词: 非圆齿轮, 行星齿轮传动系统, 非线性动力学, 分岔与混沌

CLC Number:

TH132.424

MO Shuai, LI Yaxin, WU Shengyang, ZHAO Xinhao, CHEN Sujiao, PENG Nanjiang, ZHANG Wei. Nonlinear Dynamics Characteristics of Non-circular Planetary Gear Systems[J]. China Mechanical Engineering, 2026, 37(2): 353-360.

莫帅, 李亚鑫, 吴生阳, 赵新浩, 陈素姣, 彭南江, 张伟. 非圆行星齿轮传动系统非线性动力学特性[J]. 中国机械工程, 2026, 37(2): 353-360.

Figures/Tables 21

Fig.1 Physical and configuration model of 3-5 non-circular planetary gear

Fig.2 Non-circular planetary gear motion relationship

Fig.3 Non-circular planetary gear pitch curve

Fig.4 Non-circular planetary gear configuration

Fig.5 Dynamic model of non-circular planetary gear

Tab.1 Structural parameters of non-circular planetary gear

零件	质量/kg	模数/mm	齿数	齿宽/mm	偏心率
太阳轮	5.25	2	30	35
内齿圈	8.23	2	50	35	0.03
行星轮	0.84	2	10	35

Tab.2 Dynamic parameters of non-circular planetary gear

参数	内齿圈	太阳轮	行星轮
综合误差/μm	10	10	10
平均啮合刚度/（GN·m $- 1$ ）	1.8	2.3
阻尼	0.1	0.1	0.1
转速/（r·min $- 1$ ）		700

Tab.2 Dynamic parameters of non-circular planetary gear

参数	内齿圈	太阳轮	行星轮
综合误差/μm	10	10	10
平均啮合刚度/（GN·m $- 1$ ）	1.8	2.3
阻尼	0.1	0.1	0.1
转速/（r·min $- 1$ ）		700

Fig.6 Damped vibration response on s-p1 meshing line under the influence of eccentricity

Fig.7 The excitation vibration response on the s-p1 meshing line under the change of eccentricity

Fig.8 Damped vibration response on r-p1 meshing line under the influence of eccentricity

Fig.9 The excitation vibration response on the r-p1 meshing line under the change of eccentricity

Fig.10 The displacement bifurcation diagram on the s-p1 meshing line under the change of meshing damping

Fig.11 The spatial phase diagram on the s-p1 meshing line under the change of meshing damping

Fig.12 The displacement bifurcation diagram on the r-p1 meshing line under the influence of meshing damping

Fig.13 The spatial phase diagram on the r-p1 meshing line under the change of meshing damping

Fig.14 The displacement bifurcation diagram on the s-p1 meshing line under the influence of excitation frequency

Fig.15 The Lyapunov exponent on the s-p1 meshing line under the influence of excitation frequency

Fig.16 The vibration response on the s-p1 meshing line

Fig.17 The displacement bifurcation diagram on the r-p1 meshing line under the influence of excitation frequency

Fig.18 The Lyapunov exponent on the r-p1 meshing line under the influence of excitation frequency

Fig.19 The Vibration response on the r-p1 meshing line

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