The investigation of nonlinear dynamic characteristics of spur gear with angular misalignment error based on an improved dynamic model

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2024-11-19 DOI:10.1016/j.cnsns.2024.108476

Xiaoyu Che, Chao Zhang, Hu Yu, Rupeng Zhu

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引用次数: 0

Abstract

Angular misalignment error is a prevalent occurrence in gear systems, mainly caused by manufacturing and installation errors in gearbox components. This significantly impacts the meshing characteristics of the system, making it necessary to carry out the nonlinear dynamic analysis of spur gear pairs with angular misalignment errors. In this study, a meshing stiffness model for a spur gear pair with angular misalignment error is established based on the Load Teeth Contact Analysis (LTCA) method. The effect of misalignment errors on the distribution of tooth surface stiffness are analyzed. Additionally, an improved dynamic model considering angular misalignment errors and variable backlash along the tooth width direction was proposed based on the lumped mass method and the slicing method. The effects of angular misalignment errors parallel and perpendicular to the meshing plane on the nonlinear dynamics of the system were studied. Frequency domain diagrams, Poincaré diagrams, and bifurcation diagrams were employed to comprehensively analyze the nonlinear characteristics of the system. The results indicate that with light loads, the system experiences a sequence of periodic and chaotic motions as θ_a increases, eventually returning to periodic motion. Conversely, θ_v shows minimal influence on the gear backlash, with the system exhibiting periodic motion when θ_v is small. As θ_v increases, the system transitions to chaotic motion before ultimately returning to periodic motion. Under heavy load conditions, as θ_a increases, the system transitions gradually from chaotic to periodic motion. However, regardless of the variations in θ_v, the system consistently remains in periodic motion.

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基于改进动态模型的具有角度偏差误差的正齿轮非线性动态特性研究

齿轮系统中普遍存在角度不对中误差，这主要是由齿轮箱部件的制造和安装误差造成的。这严重影响了系统的啮合特性，因此有必要对存在角度不对中误差的正齿轮对进行非线性动态分析。在本研究中，基于载荷齿接触分析（LTCA）方法，建立了具有角度偏差的正齿轮副的啮合刚度模型。分析了不对中误差对齿面刚度分布的影响。此外，基于集合质量法和切片法，提出了一种考虑了角度不对中误差和沿齿宽方向的可变齿隙的改进动态模型。研究了平行于啮合平面和垂直于啮合平面的角度偏差对系统非线性动力学的影响。采用频域图、Poincaré 图和分岔图全面分析了系统的非线性特性。结果表明，在轻载情况下，随着 θa 的增大，系统会经历一连串的周期运动和混沌运动，最终回到周期运动。相反，θv 对齿轮反向间隙的影响很小，当θv 较小时，系统表现出周期性运动。随着θv 的增大，系统过渡到混沌运动，最终又回到周期运动。在重载条件下，随着 θa 的增大，系统逐渐从混沌运动过渡到周期运动。然而，无论 θv 如何变化，系统始终保持周期运动。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Communications in Nonlinear Science and Numerical Simulation MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

6.80

自引率

7.70%

发文量

378

审稿时长

78 days

期刊介绍： The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity. The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged. Topics of interest: Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity. No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.