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 θa increases, eventually returning to periodic motion. Conversely, θv shows minimal influence on the gear backlash, with the system exhibiting periodic motion when θv is small. As θv increases, the system transitions to chaotic motion before ultimately returning to periodic motion. Under heavy load conditions, as θa increases, the system transitions gradually from chaotic to periodic motion. However, regardless of the variations in θv, the system consistently remains in periodic motion.

中文翻译：

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基于改进动力学模型的带角度不对中误差的正齿轮非线性动力学特性研究


角度不对中误差在齿轮系统中普遍存在，主要是由变速箱部件的制造和安装错误引起的。这显著影响了系统的啮合特性，因此必须对具有角度不对中误差的正齿轮副进行非线性动态分析。本研究基于载荷齿接触分析 （LTCA） 方法建立了具有角度不对中误差的正齿轮副的啮合刚度模型。分析了错位误差对齿表面刚度分布的影响。此外，基于集总质量法和切片法，提出了一种考虑沿齿宽方向的角度错位误差和可变齿隙的改进动力学模型。研究了平行于和垂直于网格划分平面的角度不对中误差对系统非线性动力学的影响。采用频域图、Poincaré 图和分叉图全面分析系统的非线性特性。结果表明，在轻负载下，随着 θa 的增加，系统会经历一系列周期性和混沌的运动，最终返回周期性运动。相反，θv 对齿轮齿隙的影响最小，当 θv 较小时，系统表现出周期性运动。随着 θv 的增加，系统在最终返回周期性运动之前转变为混沌运动。在重负载条件下，随着 θa 的增加，系统逐渐从混沌运动转变为周期性运动。然而，无论 θv 的变化如何，系统始终保持周期性运动。