| 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. |
PDF Full Text Request