Dynamic Modeling and Analysis of Involute Spur Gear Transmission System Considering Friction and Multi-State Meshing Conditions

计及摩擦的多状态啮合渐开线直齿轮系统动力学建模分析

¹ School of Mechanical Engineering, Tiangong University, Tianjin 300387, China
² Tianjin Key Laboratory of Modern Mechatronics Equipment Technology, Tiangong University, Tianjin 300387, China

Received: 6 May 2019

Abstract

A dynamic model for an involute spur gear system involving multi-state mesh and friction is formulated to analyze the dynamic response and meshing state property under different lubrication conditions, such as an elastohydrodynamic and mixed lubrications as well as dry friction. The dynamic equations of the system under teeth separation, drive-side and back-side tooth meshes are derived respectively based on the meshing principle of the gear transmission and the force analysis acting on teeth. The effects of the different lubrication schemes on the dynamic meshing force and motion orbit of the system are studied. Results show that the lubrication scheme greatly affects the amplitude of dynamic meshing force. However, the influence of the lubrication scheme on the motion orbit depends mainly on the meshing state. It means that the system motion orbit is largely affected by the lubrication scheme without drive-side and back-side tooth impacts, while the orbit is slightly affected by the lubrication scheme when drive-side and back-side impacts occur. Additionally, the dynamic response and meshing property are investigated with the decrease in load by defining three different Poincaré mappings. The system performs a drive-side meshing state as the load is large. The teeth separation is observed periodically with the decrease in load. While, both teeth separation and back-side mesh are observed under small load, which strengthens the impact vibration between the meshing teeth.

摘要

建立计及摩擦影响的多状态啮合渐开线直齿轮传动系统动力学模型。考虑弹流润滑、混合润滑及干摩擦的摩擦模型，基于渐开线直齿轮传动的啮合原理和轮齿受力情况，分段处理齿轮传动系统的啮合状态，并推导系统在齿面啮合、轮齿脱啮以及齿背啮合工作状态下的动力学方程。数值研究不同摩擦模型对系统动态啮合力和运动轨迹的影响规律。发现不同的摩擦模型对动态啮合力振动幅值的影响程度不同，而对运动轨迹的影响与齿面、齿背冲击有关，无齿面、齿背冲击时其对运动轨迹的影响较大，发生齿面、齿背冲击时其对运动轨迹的影响较小。通过定义3种不同的Poincaré映射，分析了载荷变化对系统啮合状态的影响规律。发现载荷较大时系统为齿面啮合状态；随着载荷减小，周期性的轮齿脱啮现象被发现；当载荷较小时，系统出现了周期性的轮齿脱啮和齿背啮合现象，引起轮齿间的冲击振动。