不同自由度耦合斜齿轮转子系统的振动特性

以一个两对斜齿轮耦合的三平行轴转子系统为研究对象,考虑静态传递误差和齿轮几何偏心等因素的影响,建立了全自由度通用齿轮啮合动力学模型。将其与转子系统有限元模型进行耦合,建立了平行轴系齿轮转子系统有限元模型。转子系统采用梁单元模拟,齿轮之间的啮合通过啮合刚度矩阵和阻尼矩阵模拟,并分析了不同自由度耦合下系统的固有特性和振动响应特性。研究结果表明,考虑弯扭耦合和弯扭轴摆耦合会产生较多的弯扭耦合频率,响应计算结果出现的峰值点均对应系统的固有频率,而考虑弯扭轴摆耦合可以更好地表征系统的不同自由度的耦合振动情况。此研究结果可为齿轮耦合转子系统设计提供参考。     

斜齿轮副动态特性对支承结构参数的灵敏度

针对斜齿轮副动特性的灵敏度问题 ,考虑轴和轴承的柔性以及由于轮齿啮合而产生的横向运动、扭转运动、轴向运动与旋转 (摆动 )运动间的动态耦合的影响 ,建立了斜齿轮传动系统的动力学模型 ,推导了固有频率及动态啮合挠度相对于斜齿轮副支承结构参数的灵敏度计算公式 ,并给出了实例。这一方法可用于斜齿轮传动系统的动态优化设计及改进设计     

齿轮传动转子系统弯扭耦合振动研究

为分析齿轮传动复杂轴系的振动问题,根据有限元法和拉格朗日法,考虑陀螺效应、油膜支承等因素,得到了转子-轴承系统的弯扭耦合振动模型;在此基础上,根据齿轮副运动过程中啮合刚度和啮合阻尼的变化,得到了齿轮副系统的弯扭耦合振动模型。然后,根据齿轮副的实际排列方式,引入方位角,使得转子模型与齿轮副模型坐标统一化,并将其耦合到一起,得到了更加接近实际的齿轮转子模型,并且计算了其临界转速和振型。研究结果表明,耦合后转子的临界转速低于单转子的临界转速,齿轮传动对转子轴系振动有着明显影响。     

Effects of dynamic transmission errors and vibration stability in helical gears

Transmission error is an important reason for instability in helical gears. A six-degree-of-freedom dynamic model coupled flexional, torsional and axial motion of a helical gear transmission system, which includes time varying mesh stiffness, bearing supporting stiffness, mesh damping and backlash, is developed, after taking into account the dynamic characteristics and vibration responses of helical gear in three dimensions. Influences of involute contact ratio, bearing supporting stiffness, mesh damping and backlash on the dynamic transmission errors and vibration stability of the helical gear system are investigated using numerical simulation technique. The effects on dynamic transmission errors and stabilities by contact ratio, supporting stiffness and mesh damping as well as gear backlash are analyzed. The intrinsic relationship between above parameters and dynamic transmission errors and stabilities for helical gear system are presented. The stable and unstable regions under different parameters are given. The results in this paper can be helpful to the dynamic and stable design of a helical gear transmission system.     

Effects of different coupling models of a helical gear system on vibration characteristics

Time-varying mesh stiffness (TVMS) and the dynamic coupling between the helical gears have a great influence on the vibration characteristics of a helical gear rotor system. Considering the effects of TVMS and adopting two coupling models (lateral-torsional coupling model and lateral-torsional-axial-swing coupling model), the dynamic behavior of a helical gear system was studied. First, an analytical model was used to analyze TVMS of a helical gear pair where the helical tooth is simulated by many spur tooth slices along the direction of the tooth width and the mesh stiffness of each slice is calculated using the energy method. Then, considering the effects of the TVMS excitation, the finite element model of a helical gear rotor system was established. Gear mesh was simulated by the above-mentioned two coupling models to investigate the effects of coupling forms on the system vibration characteristics. The strain energy was used to distinguish the dominant mode and dominant shaft of a gear system in natural characteristics analysis. The results show that the full coupling model can analyze accurately the vibration characteristics of the system and the axial and swing motions cannot be ignored in vibration analysis. Finally, the effects of helix angle on TVMS and vibration responses of a helical gear system were also studied.     

齿轮—转子耦合系统的动态响应及齿侧间隙对振幅跳跃特性的影响

为了模拟工程应用中齿轮-转子系统的动态响应,考虑齿侧间隙、时变啮合刚度、静态传动误差、不平衡质量和弹性转轴的影响,建立齿轮一转子耦合系统的动力学模型.对动力学方程进行数值仿真,研究转速对动态响应的影响、齿侧间隙的变化对振幅跳跃现象的影响规律和转速与动态啮合力之间的关系.研究结果表明,随着齿侧间隙的增大,齿轮-转子系统的振幅跳跃现象变得更明显.振动加速度的频谱图主要包括啮合频率及其高次谐波.随着转速的逐渐升高,1倍频的振幅也逐渐增大,并且在啮合频率及其高次谐波附近还会出现边频带.动态啮合力的频谱图与动态响应的频谱图类似.对一个齿轮-转子试验台进行理论计算和试验测试,试验数据基本上验证对试验台的理论计算结果,试验测量结果和数值仿真之间的差别主要来源于建模误差和测量误差.     

Effect of manufacturing and assembly defects on two-stage gear systems vibration

The modeling of the dynamic behavior of a two-stage gear system is made for a general configuration of wheels location. The excitation is induced by the periodic variation of the mesh stiffness. This case describes the real working of the gearings. The variation of the mesh phasing is related to the number of teeth and also to the wheels location. We developed a plane model of a two-stage gear system. The modal analysis of the system was then treated. The calculation of the dynamic response was done by a step-by-step time integration method (Newmark algorithm). Three cases of wheels location are treated. The solutions are presented both in the frequency domain and in the time domain. Three types of geometric defects of the toothed wheels are introduced in the model: defect of eccentricity, profile error and assembly defect. An analysis of the effects of these defects on the gear system dynamic behavior is then treated.     

齿轮刚度及制造误差对多平行轴转子系统动力学性能的影响

分析了具有斜齿圆柱齿轮传动的多平行轴转子系统，在统一的坐标系下，建立了系统的动力学模型，考虑了系统的弯扭耦合、陀螺力矩及滑动轴承的支承刚度和阻尼。计算了系统的固有频率、动态响应及幅频特性，重点分析了齿轮的刚度、阻尼和制造误差对多平行轴转子系统动力学性能的影响     

多平行轴齿轮耦合转子系统的振动响应

以一个两对斜齿轮耦合的三平行轴转子系统膨胀机子系统为研究对象,建立了斜齿轮啮合副动力学模型和转子系统有限元模型,考虑了齿轮啮合刚度、方位角、啮合角、螺旋角以及主动轴转动方向的影响,推导出齿轮啮合刚度矩阵。基于模态叠加法,对弯-扭耦合转子系统膨胀机子系统进行了固有特性分析和瞬态方式的不平衡响应分析,得到齿轮啮合前、后系统加载处的不平衡响应变化曲线。研究表明,齿轮间的耦合使系统之间的振动强烈,系统可能会在某个非固有频率处不平衡响应进行积累叠加,出现最大振动的现象,同时识别出共振峰的产生机理。齿轮耦合对转子系统动力学特性产生了很大的影响,使系统振型表现为耦合振型,必须以耦合的方式分析系统的振动特性,为防止系统发生大的振动提供依据,对齿轮系统的设计和故障分析具有指导意义。     

含柔性转子的齿轮-轴承系统动态特性分析

为了分析齿轮系统动力学中的全耦合振动,提出采用虚拟样机建模的方法,将柔性转子引入到啮合耦合系统中,考虑齿轮时变啮合刚度、齿侧间隙和轴承间隙的影响,建立齿轮-柔性转子-轴承系统虚拟样机模型,通过求解模型的动力学方程得到系统的非线性动力学响应。仿真结果表明:考虑柔性转子的耦合系统,啮合冲击峰值下降明显;转子柔性增加,齿轮低频扭转振动出现"拍"现象;高速轻载时啮合振动非线性特性增强;轴承间隙增大使啮合力振动幅值显著增大。