【作者】 张凯；

【导师】 董惠敏；

【作者基本信息】 大连理工大学 ， 机械制造及其自动化（专业学位）， 2015， 硕士

【摘要】 齿轮传动是应用广泛的机械传动机构,随着机械传动装备向高精密方向发展,齿轮传动系统误差及其特性成为重要的性能标志。由于齿轮传动系统误差与各个零件的形状、误差、弹性变形与负载存在着密切的联系。因此,研究其传动系统误差需要建立各个零件形状、误差、弹性变形与负载的有效等效机制,构建齿轮传动系统精度等效模型。课题来源于国家自然科学基金“精密齿轮传动系统精度特性的多重共轭复合模型”项目,以直齿轮传动系统为研究对象,对其建立了直齿轮传动系统弹性误差运动模型,揭示了齿轮传动系统误差与各个零件的几何误差及弹性变形、负载之间的内在联系,为齿轮传动系统设计的零件精度分配与设计提供新的理论基础。论文的主要研究内容如下：介绍了关于标架及其特性等微分几何学知识,建立了直齿轮渐开线齿廓Frenet标架与对应的Frenet结构方程,为后续的研究做理论基础。基于实际的直齿轮传动系统的零件组成、弹性与误差分析,将轴系上的轴承组件的几何误差等效映射为刚性盘形凸轮轮廓,其弹性约束等效映射为多个弹簧约束的凸轮直动从动件支承；根据相对运动原理,两根浮动轴系的相对运动转化为一根浮动轴系相对另一根刚性支撑轴系,通过齿轮啮合副传递运动,计及齿轮的弹性变形、传动轴弹性变形,建立了直齿轮传动系统弹性误差运动模型。并确立了等效凸轮机构参数以及轴、齿轮弹性与刚度等效参数计算方法。定义了各个构件相应坐标系,用坐标系之间的运动变换表达构件的相对运动关系；以运动模型各机构为研究对象,分别建立位移方程和静力力平衡方程,通过传动系统的准静态的瞬时平衡关系,确立了以齿轮啮合时的时变中心距函数体现的运动模型的基本方程。引用微分几何学方法,在齿轮啮合齿廓面上建立Frenet标架,结合时变中心距误差函数与轮齿弹性变形的作用,基于齿面的接触与相切条件,建立了单齿弹性与误差啮合方程,补充了双齿啮合变形协调方程,形成了齿轮传动精度模型。建立了直齿轮传动系统的精度分析流程,以一个直齿轮传动系统为例,分别研究了输入转矩、轴承内圈滚道误差大小与相位对时变中心距误差函数影响；在此基础上研究了轴承组件弹性与误差、轴的弹性变形、齿轮变形与负载对齿轮啮合特性的影响。本文的研究工作为后续的深入研究直齿轮传动与斜齿轮传动的弹性啮合精度分析与设计研究奠定了理论基础。更多还原

【Abstract】 The gear drive mechanism is widely used in mechanical transmission gear mechanism. With mechanical transmission equipment to high-precision direction, the accuracy and its characteristics are important signs. Gear transmission error is linked to parts geometry error, the elastic deformation and the load. Consequently, it needs to establish effective equivalent mechanism including the shape and geometry error of various parts, elastic deformation and load. This paper is supported by the National Natural Science Foundation Program "A multiple mesh compound model for the system accuracy and its characteristics of precision gear drives". The elastic and error motion model of spur gear transmission is built. It reveals the link between gear transmission error and the geometric error and elastic deformation of the parts. It provides precision distribution of parts and new theoretical foundation for the design of spur gear transmission. The main contents are as follows:The frame and characteristics of differential geometry knowledge is simple introduced. The solving method of Frenet frame in volute gear profile is established. The structural equation of Frenet frame is established. It provides theoretical preparation for following research. Parts, the elastic and error of the actual spur gear transmission system are analyzed. Under no-load conditions, the rigid cam profiles are specified to represent the geometrical errors of bearing assembly, and the elastic deformations are simulated by springs of straight followers. According to the principle of relative motion, the deformation of both two elastic floating shaft are represented by the input one and output shaft is an ideal shaft. Considering gear elastic deformation and gear shaft elastic deformation, elastic and error motion model of spur gear transmission system is proposed. And the equivalent parameters method of cam mechanism equivalent parameters, shafts, gear elasticity and stiffness are established.It defines the coordinates of each model component. And the relative motions between the components are expressed by converting coordinate system. Respectively every component as the research object, the displacement equation and force balance equations are derived. According to instantaneous quasi-static balance, the basic equations evaluated by the time-varying center distance error are built. According to differential geometry knowledge, Frenet frame in gear tooth mesh profile surface is established. Considering the time-varying center distance error and teeth elastic deformation, single tooth elastic and error mesh equations are established based on the contact and tangency conditions. And double meshing deformation compatibility equations are added. Finally the transmission precision analysis model of spur gear transmission is established.The solving process of precision analysis is also established. The influence on time-varying center of the input torque, the bearing inner ring raceway error magnitude and phase error function are studied for a kind of spur gear reducer. The influence on meshing characteristics of geometry errors and elasticity of bearing assembly, shaft and load is conducted.The thesis laid theoretical foundation for subsequent research of precision analysis deeply and design of wide tooth spur and helical gears gear transmission subsequently.更多还原