【作者】 赵亮；

【导师】 马琮淦；

【作者基本信息】 哈尔滨工业大学 ， 机械工程， 2025， 硕士

【摘要】 高速化是电驱动系统重要的发展方向之一,高速可有效降低转矩需求,从而减小电机的体积和重量,进而提高电驱动系统的功率密度,但是在高速低转矩下,离心力对电驱动系统中减速器齿轮的影响不可忽略。减速器齿轮在生产过程中不可避免的会存在很多加工误差,偏心就是其中之一,偏心的影响在高速下会更加明显,此外新能源汽车动力需求变化剧烈,容易产生裂纹故障,因此研究偏心与裂纹复合故障下高速电驱动系统用减速器的振动特性具有重要意义。主要研究内容分为以下三部分:(1)高速斜齿圆柱齿轮综合啮合刚度的解析计算。减速器齿轮的啮合刚度激励是减速器振动最重要的内部激励。本文根据弹性力学理论计算了离心变硬刚度;根据势能法计算了横向轮齿刚度,轴向轮齿刚度和轴向圆角基础刚度;根据弹性力学计算了考虑相邻齿啮合的横向圆角基础刚度;考虑刚度的载荷相关性,根据最小势能原理,解析计算了轮齿的载荷分担比;提出了高速斜齿圆柱齿轮综合啮合刚度解析计算模型;最后建立了高速斜齿圆柱齿轮综合啮合刚度有限元模型,验证了解析计算模型的准确性,所提出的解析计算模型最大误差仅在3.21%。结果表明:离心力会增大斜齿圆柱齿轮的综合啮合刚度,转矩越小增加的效果越明显;螺旋角,力矩,轮毂孔半径均会对斜齿圆柱齿轮综合啮合刚度造成影响。(2)偏心与裂纹复合故障高速斜齿圆柱齿轮综合啮合刚度解析建模。本文考虑从动轮的时变转速,使用切分法计算了双偏心故障下齿轮的瞬时节点轨迹,计算得到了齿轮的时变中心距和时变啮合角;获得了双偏心故障下斜齿轮时变的啮合状态判定公式;考虑几何中心与旋转中心不重合的问题,转化了啮合刚度的计算基准;针对裂纹故障引起的部分承载区域失效的问题,根据势能法计算了裂纹下的横向轮齿刚度,轴向轮齿刚度和轴向圆角基础刚度;根据弹性力学理论推导了更加复杂的当裂纹轮齿存在时的横向圆角基础刚度;推导了高速离心力下裂纹轮齿部分承载区域因为失效无法对齿轮体产生牵引力时齿轮体的应力分布,根据弹性圆环理论进而获得了裂纹故障下的离心变硬刚度;最后提出了偏心与裂纹复合故障下高速斜齿圆柱齿轮综合啮合刚度解析计算模型;建立了复合故障下啮合刚度有限元计算模型,验证了解析模型的准确性。结果表明:双偏心故障会导致斜齿轮综合啮合刚度出现复杂的频率调制和幅值调制现象;裂纹故障的存在会降低裂纹轮齿的综合啮合刚度;复合故障下的高速斜齿圆柱齿轮综合啮合刚度同时出现了以上特征。(3)复合故障下高速电驱动系统用减速器动力学建模及振动特性分析。根据集中参数法建立了电机-齿轮-负载的15自由度弯-扭-轴耦合动力学模型;将复合故障下的高速斜齿圆柱齿轮综合啮合刚度作为输入,得到了复合故障下的动力学振动响应;最后搭建了减速器振动实验平台,验证了动力学模型得到的振动响应特征。结果表明:高速下减速器因啮合刚度的增加而振动加剧;裂纹故障的存在因为导致啮合刚度的降低会引起振动响应出现一个周期性的冲击特征,冲击的周期为裂纹故障所在齿轮的转动周期;双偏心故障的存在会增加减速器的振动,而且在啮合频率的周围出现明显的转频的边带成分;复合故障下的减速器振动同时出现了以上特征。更多还原

【Abstract】 High-speed capability is one of the critical development directions for electric drive systems.High-speed operation can effectively reduce torque requirements,thereby decreasing motor’s volume and weight while enhancing the system’s power density.However,under high-speed and low-torque conditions,the influence of centrifugal forces on reducer gears within electric drive systems cannot be overlooked.During production,reducer gears inevitably exhibit various manufacturing errors,with eccentricity being a prominent example.The impact of eccentricity becomes more pronounced at high speeds.Furthermore,the drastic power demand fluctuations in new energy vehicles make them susceptible to crack failures.Consequently,investigating the vibration characteristics of reducer in high-speed electric drive systems under combined eccentricity and crack faults holds significant importance.The main research content is structured into the following three components:(1)Analytical calculation of comprehensive meshing stiffness for high-speed helical gears.The meshing stiffness excitation of gearbox gears constitutes the most critical internal excitation source for gearbox vibration.Based on elastic mechanics theory,the centrifugal hardening stiffness was calculated.Following the potential energy method,the lateral tooth stiffness,axial tooth stiffness,and axial fillet foundation stiffness were determined.Using elastic mechanics principles,the fillet foundation stiffness considering adjacent tooth engagement was computed.Accounting for load-dependent stiffness characteristics,the load sharing ratio of gear teeth was analytically derived through minimum potential energy principle.A analytical model for comprehensive meshing stiffness of high-speed helical cylindrical gears was established.A finite element model of the comprehensive meshing stiffness was developed to validate the analytical approach,demonstrating maximum modeling error of 3.21%.The results indicate:Centrifugal force enhances comprehensive meshing stiffness of helical gears,with more pronounced enhancement at lower torque levels;Helix angle,torque magnitude,and hub bore radius all exhibit significant influence on comprehensive meshing stiffness.(2)Analytical modeling of comprehensive meshing stiffness for high-speed helical cylindrical gears with combined eccentricity and crack faults.Considering the time-varying rotational velocity of the driven gear,the instantaneous pitch point trajectory under dual eccentricity faults was calculated using a segmentation method,from which time-varying center distances and meshing angles were derived.A time-dependent meshing state criterion for helical gears under dual eccentricity conditions was established.To address the misalignment between geometric and rotational centers,the reference frame for meshing stiffness calculation was transformed.For crack-induced partial load-bearing zone degradation,lateral tooth stiffness,axial tooth stiffness,and axial fillet foundation stiffness under crack faults were quantified via the potential energy method.An advanced formulation of lateral fillet foundation stiffness incorporating cracked tooth engagement was developed using elastic mechanics theory.The stress distribution in gear bodies under high-speed centrifugal loading was analytically derived for scenarios where cracked teeth fail to generate traction in partial zones,enabling the determination of centrifugal hardening stiffness through elastic ring theory.A analytical model for comprehensive meshing stiffness of high-speed helical gears with combined eccentricity-crack faults was proposed.A finite element computational model of meshing stiffness under compound faults was established,validating the accuracy of the analytical model.Results demonstrate:Dual eccentricity faults induce complex frequency and amplitude modulation phenomena in comprehensive meshing stiffness;The presence of crack faults reduces the comprehensive meshing stiffness of cracked teeth.The comprehensive meshing stiffness of high-speed helical cylindrical gears under compound fault conditions exhibit both these characteristics simultaneously.(3)Dynamic modeling and vibration characteristics analysis of reducer in high-speed electric drive systems under compound faults.A 15-degree-of-freedom coupled bending-torsional-axial dynamic model for the motor-gear-load system was established using the lumped parameter method.By inputting the comprehensive meshing stiffness of high-speed helical gears under compound faults,dynamic vibration responses under compound fault conditions were obtained.A reducer vibration experimental test rig was developed to validate the vibration response characteristics derived from the dynamic model.The results indicate that at high speeds,the vibration of the reducer is exacerbated due to the increased meshing stiffness.The presence of crack faults leads to a reduction in meshing stiffness,resulting in a periodic impact characteristic in the vibration response,with the impact period matching the rotational cycle of the gear where the crack is located;The existence of dual eccentric faults intensifies the vibration of the reducer,accompanied by prominent rotational frequency sideband components around the meshing frequency;The vibration of reducers under compound faults exhibits all the aforementioned characteristics simultaneously.更多还原