基于Johnson接触模型的内啮合直齿轮系统多状态啮合动力学建模与分析

Multi-state meshing dynamics modeling and analysis of an internal meshing spur gear system based on the Johnson contact model

准确解释齿侧间隙诱发的轮齿脱啮或齿背啮合可为齿轮结构优化设计提供理论指导。基于Johnson接触力模型,构建及时变齿侧间隙和啮合过程中能量耗散的渐开线内啮合直齿轮传动系统动态啮合力计算模型;根据内啮合直齿轮啮合原理和轮齿受力情况,对其啮合过程进行动作分解,建立时变齿侧间隙下具有5种啮合状态的渐开线内啮合直齿轮系统非线性动力学模型;构造5种不同的Poincaré映射,明晰5状态啮合行为特征;通过相图与动态啮合力时间历程图揭示系统多状态啮合行为的产生机理。结果表明,随着啮合频率逐渐增大,系统出现单双齿齿面啮合,动态啮合力在方向上的突变导致轮齿脱离与单双齿齿背啮合,引起轮齿间的冲击振动行为,当啮合频率较大时,系统即使表现出稳定的啮合状态,但仍然发生单双齿脱啮。以往的内啮合齿轮系统动力学模型无法揭示其多状态啮合特性,该文针对多状态啮合行为对内啮合齿轮传动周期内非线性振动特性进行分析。

The accurate explanation of the tooth deregulation or back meshing induced by the backlash can provide theoretical guidance for the optimal design of the gear structure.Based on the Johnson contact force model,the dynamic meshing force calculation model of an involute internal meshing spur gear transmission system was constructed,taking into account the time-varying backlash and energy dissipation in the meshing process.According to the meshing principle of internal meshing spur gear and the force condition of gear teeth,the meshing process was decomposed,and the nonlinear dynamic model of the involute internal meshing spur gear system with five meshing states under time-varying backlash was established.Five different Poincarémaps were constructed to clarify the characteristics of five-state meshing behaviors,and the generation mechanism of multi-state meshing behaviors of the system was revealed by the phase diagram and dynamic meshing force time history diagram.The results show that with the gradual increase of the meshing frequency,the single-tooth and double-tooth surface meshing occurs in the system,and the sudden directional change of the dynamic meshing force leads to the meshing between the gear teeth and the back of the single-tooth and double-tooth,resulting in the impact vibration behavior between the gear teeth.Even if the system shows a stable meshing state,the single and double teeth dismeshing still occurs.The previous dynamic models of internal meshing gear systems can not reveal the multi-state meshing characteristics,so that,aiming at the multi-state meshing behavior,the paper analyzes the nonlinear vibration characteristics in the internal meshing gear transmission cycle.