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修正变双曲线齿迹圆柱齿轮的非线性动力学特性

Nonlinear dynamic characteristics of modified variable hyperbolic circular arc tooth trace cylindrical gears.

作者信息

Ma Dengqiu, Ye Zhenhuan

机构信息

School of Engineering and Technology, Zunyi Normal University, Zunyi, 563006, China.

出版信息

Sci Rep. 2025 Apr 29;15(1):15108. doi: 10.1038/s41598-025-97254-2.

DOI:10.1038/s41598-025-97254-2
PMID:40301463
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC12041552/
Abstract

Nonlinear dynamic characteristics is one of the important performance indexes for the variable hyperbolic circular arc tooth trace (VH-CATT) cylindrical gear system. And accurate analysis of the nonlinear dynamic characteristics is of great significance to investigate service life of the VH-CATT cylindrical gear system. Therefore, the nonlinear dynamics study of the VH-CATT cylindrical gear is proposed. Firstly, the calculation methods or formulas of the time-varying stiffness, transmission error and meshing impact were given. Next, the mathematical model of the modified VH-CATT cylindrical gear was deduced based on the forming theory. Then, the controllable design model and tooth surface optimization design model were developed to calculate the best values of the modified parameters. Finally, a bending-torsion coupling dynamic model of the VH-CATT cylindrical gear pair was developed to investigate influence of the modification design on the nonlinear dynamic characteristics of the modified VH-CATT cylindrical gear, and the research conclusion was verified by the transmission experiments. Research shows that the tooth surface load reduces, the stiffness increases, the LTE and fluctuation range of the LTE decrease after modification. Modification makes the bifurcation diagram shift to the right and the complex motion of the unmodified VH-CATT cylindrical gear pair with the dimensionless frequency between 0.72 and 1.11 become a periodic motion. The vibration displacement of the modified VH-CATT cylindrical gear pair less than that of the unmodified VH-CATT cylindrical gear pair. The experiment also shows that the transmission error of the modified gear pair is less than that of the unmodified gear pair and the tooth surface modification design of the VH-CATT cylindrical gear improves the transmission efficiency. The tooth surface modification is beneficial to reduce the vibration and noise of the VH-CATT cylindrical gear pair. The research results provide a basis for improving the bearing capacity of the VH-CATT cylindrical gear.

摘要

非线性动力学特性是变双曲线圆弧齿线（VH-CATT）圆柱齿轮系统的重要性能指标之一。准确分析其非线性动力学特性对于研究VH-CATT圆柱齿轮系统的使用寿命具有重要意义。因此，开展了VH-CATT圆柱齿轮的非线性动力学研究。首先，给出了时变刚度、传动误差和啮合冲击的计算方法或公式。其次，基于成形理论推导了修形VH-CATT圆柱齿轮的数学模型。然后，建立了可控设计模型和齿面优化设计模型来计算修形参数的最佳值。最后，建立了VH-CATT圆柱齿轮副的弯扭耦合动力学模型，研究修形设计对修形VH-CATT圆柱齿轮非线性动力学特性的影响，并通过传动实验验证了研究结论。研究表明，修形后齿面载荷减小，刚度增大，传动误差及其波动范围减小。修形使分岔图右移，使无量纲频率在0.72至1.11之间的未修形VH-CATT圆柱齿轮副的复杂运动变为周期运动。修形VH-CATT圆柱齿轮副的振动位移小于未修形的VH-CATT圆柱齿轮副。实验还表明，修形齿轮副的传动误差小于未修形齿轮副，VH-CATT圆柱齿轮的齿面修形设计提高了传动效率。齿面修形有利于降低VH-CATT圆柱齿轮副的振动和噪声。研究结果为提高VH-CATT圆柱齿轮的承载能力提供了依据。

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