Parametric Solution Domain Structures for Bifurcation and Non-Meshing Dynamic Characteristics of Straight Bevel Gear Systems

Q4 Mathematics

应用数学和力学 Pub Date : 2023-01-01 DOI:10.21656/1000-0887.430330

TIAN Yaping, YANG Jianghui, WANG Ruibang

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引用次数: 0

Abstract

Aimed at the coupling transition relationship between the periodic motion, the tooth surface impact, the non-meshing state and the dynamic load of straight bevel gear systems with backlash, the 2-parameter plane with respect to the time-varying meshing stiffness and the frequency ratio was built based on the cell mapping principle. Besides, the improved CPNF (continuous-Poincaré-Newton-Floquet) method was applied to solve the solution domain structure of the periodicity, impact, non-meshing and dynamic load characteristics of the system cells. The simulation results show that, there are plentiful bifurcation modes with 3 kinds of tooth surface impacts coexisting in the 2-parameter solution domain structure, including the saddle node bifurcation, the Hopf bifurcation, the period-doubling bifurcation, the catastrophe bifurcation and the period-3 bifurcation. The tooth surface impact and chaos will intensify due to increase of the time-varying meshing stiffness coefficient. The tooth surface non-meshing, the tooth back meshing and the dynamic load coefficient will exhibit mutations under the influences of the tooth impact and the periodic motion. Meanwhile, in the same domain, the tooth surface non-meshing and the tooth back meshing will weaken with the frequency ratio but heighten with the stiffness coefficient.

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直齿锥齿轮系统分岔与非啮合动态特性的参数化解域结构

针对带间隙直齿锥齿轮系统的周期运动、齿面冲击、非啮合状态和动载荷之间的耦合过渡关系，基于单元映射原理建立了时变啮合刚度和频率比的二参数平面。此外，采用改进的CPNF (continuous- poincar - newton - floquet)方法求解了系统单元的周期性、冲击性、非啮合性和动载荷特性的解域结构。仿真结果表明，在2参数解域结构中存在丰富的3种齿面冲击共存的分岔模式，包括鞍节点分岔、Hopf分岔、倍周期分岔、突变分岔和3周期分岔。时变啮合刚度系数的增大会加剧齿面冲击和混沌。齿面不啮合、齿背啮合和动载荷系数在齿面碰撞和周期运动的影响下会发生突变。同时，在同一域内，齿面非啮合和齿背啮合随频率比的增大而减弱，随刚度系数的增大而增大。

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来源期刊

应用数学和力学 Mathematics-Applied Mathematics

CiteScore

1.20

自引率

0.00%

发文量

6042

期刊介绍： Applied Mathematics and Mechanics was founded in 1980 by CHIEN Wei-zang, a celebrated Chinese scientist in mechanics and mathematics. The current editor in chief is Professor LU Tianjian from Nanjing University of Aeronautics and Astronautics. The Journal was a quarterly in the beginning, a bimonthly the next year, and then a monthly ever since 1985. It carries original research papers on mechanics, mathematical methods in mechanics and interdisciplinary mechanics based on artificial intelligence mathematics. It also strengthens attention to mechanical issues in interdisciplinary fields such as mechanics and information networks, system control, life sciences, ecological sciences, new energy, and new materials, making due contributions to promoting the development of new productive forces.