薄辐板齿轮柔性化动力学模型与行波共振表征

Dynamics Model of Thin-walled Gears Considering Elasticity and Its Traveling Wave Vibration Characterization

薄辐板齿轮是广泛应用于航空齿轮传动系统的轻量化高功率密度构型,但行波共振问题突出,而动力学理论模型对前、后行波及其响应特性表征仍需进一步明晰。为此,提出一种啮合激励下薄辐板齿轮动力学模型,用以表征行波共振特性,并称之为移动载荷下柔性齿轮(Elastic gear with moving loads,EGML)模型:采用虚拟轴段法退化轮齿复杂特征,进而构建等效规则结构,并分别采用混合壳单元、Timoshenko梁单元网格化轮缘、辐板以及齿轮轴;解耦齿轮副以暴露出啮合力,其为相对齿轮转动的时变激励,故建立移动载荷数学表征以反映其时空变化特征;将啮合激励作用于全柔性化齿轮模型,并构建系统运动控制方程。设计高速齿轮传动试验以验证模型。结果表明,EGML模型能准确有效表征前、后行波共振激发工况。激励源与齿轮相对转动以及计入辐板柔性是动力学模型具有行波共振表征能力必要条件。行波共振发生时位移场呈与节径振型契合的瓣式分布,并沿周向快速迁移。研究成果能高效准确地获取薄辐板齿轮受迫响应,为评估行波共振影响提供理论依据,可用于指导薄辐板齿轮设计以规避安全运行所受共振威胁。

The thin-walled gear is a lightweight type with high power density,which is widely used in the aviation geared drivetrain.But the safety risk induced by the traveling wave vibration is prominent,and the dynamic theoretical model still needs to further clarify the response characteristics of forward and backward wave types.Therefore,a dynamic model for the thin-walled gear under meshing excitation is proposed to describe vibration characteristics of traveling waves,called elastic gear with moving loads(EGML)model:the virtual shaft equivalent method is used to degrade the complex gear tooth features,so as to obtain the equivalent regular structure;the gear rim,web and shaft are meshed by hybrid shell elements and Timoshenko beams;the gear pair is decoupled to expose the meshing force,which is a time-varying excitation relative to the gear rotation,and thus to establish a mathematical representation of the moving load to reflect its time-space variation characteristics;the meshing excitation acts on the flexible gear model,and the motion governing equation can be developed.Besides,the high-speed gear transmission experiment is conducted to verify the proposed method.Results show that the EGML model can accurately characterize the forward and backward wave type.It has this characterization ability after considering the web elasticity and the relative rotation between the excitation and gear.When the traveling wave vibration occurs,the displacement field is a petal distribution that fits the nodal diameter modal shape,and moves rapidly along the circumferential direction.This research provides a dynamic model that balances accuracy and efficiency to obtain the dynamic response of thin-walled gears,and is a theoretical basis for evaluating the impact of the traveling wave resonance,and can be used to guide the thin-walled gear design to avoid the resonance threat for its safe operation.