Study On Accuracy Evaluation And Measuring Method Of Non-circular Gear

Non-circular gear can realize variable transmission ratio according to actual demand design movement,which have the advantages of stable transmission,compact structure and easy implementation of dynamic balance that compared with cylindrical gear and cam.Non-circular gear can achieve nonlinear transmission accurately and efficiently,so that it is widely used in instrument industry,light industry,hydraulic motor,agricultural machinery,textile industry,printing industry,etc.With the development of computer technology,NC machining technology and CAD/CAM technology,the better solutions to the problems in design and manufacture of non-circular gear have been proposed,meanwhile the demands of nonlinear transmission mechanism are continuously increased.These factors provide the extensive research and application prospects for non-circular gear.At present,the domestic and international research on the measurement of geometric accuracy(detection of profile error,analysis of machining error,etc.)of non-circular gear is less,the measuring technique and instrument of non-circular gear are still in the early stage of research.There is no complete accuracy evaluation system,no effective measuring method,no appropriative detection equipment,which is the current research status of accuracy measurement of non-circular gear.The subject comes from the National Natural Science Fund Project “Research on Manufacturing and Adaptive Design of Free Pitch Curve Non-circular Gear by Highorder Multi-segment Deformed Elliptical Gear”(ID: 51275147).Combined with the project research,the paper makes a comprehensive and systematic research on the related issues of machining theory,accuracy evaluation and deviation measurement of noncircular gear,therefore the main research work is as follows:(1)According to the forming principle of non-circular gear profile,the mathematical model and the motion model of non-circular gear machining are established.Based on the analysis of the principle of non-circular gear hobbing,the mathematical models of spur non-circular cylindrical gear hobbing and helical non-circular cylindrical gear hobbing are established respectively,then the corresponding motion models are established and the dynamic simulations are carried out.Based on the analysis the principle of non-circular gear shaping,the mathematical models of spur non-circular cylindrical gear shaping,helical non-circular cylindrical gear shaping and non-circular bevel gear shaping are established,then the corresponding motion models are established and the dynamic simulations are carried out.Combined with the technology of electronic gearbox,the motion models are applied to the gear cutting machines,and the CNC machining of non-circular gear is realized.(2)A method of obtaining high precision tooth profile curve of non-circular gear is proposed,and the characteristic of tooth profile is analyzed.The mathematical model of tooth profile of non-circular gear is established by using the conjugate surface theory.The method of fast obtaining high precision tooth profile curve of non-circular gear by virtual machining and spline interpolation is proposed: in accordance with the mathematical model of non-circular gear hobbing and non-circular gear shaping,the virtual machining is conducted and the 3D model of non-circular gear is obtained,the tooth profile points obtained from the 3D model are used to generate the tooth profile curve by spline interpolation method,and the interpolation accuracy are analyzed by the truncation error.The base curve of the non-circular gear is solved,on this basis,the involute characteristic of the tooth profile is analyzed.(3)The deviation items of non-circular gear are determined,the accuracy evaluation system is established,and the accuracy standard is drawn up.Based on the analysis of the origin cause of the machining error of non-circular gear,the deviation items of noncircular gear are determined.The 2D accuracy evaluation system and the 3D accuracy evaluation system of non-circular gear are established respectively,the methods of accuracy evaluation and error solution are proposed.The accuracy evaluation standard of non-circular gear is drawn up,the basic parameters are set,the tolerance group and the accuracy grade are divided.(4)According to the analysis of non-circular gear tooth profile characteristic,the measuring methods of non-circular gear deviations are established.The initial angle deviation is defined,and the measuring method is proposed.The measuring methods of the comprehensive deviations of non-circular gear are summarized,the measurement models of single-flank meshing and double-flank meshing are designed,on this basis,a full meshing measurement model is established.The feasibility of traditional measuring methods of single deviations of non-circular gear are analyzed,and then the measuring methods of tooth profile deviation,tooth direction deviation and tooth pitch deviation are put forward respectively.(5)Aiming at the key problems in non-circular gear measuring process,include measuring path planning,probe radius compensation and analysis of uncertainty in measurement,the implementation methods are proposed respectively.The extracted tooth profile points are processed by densifying and normal offsetting,on this basis the measuring path of the probe is obtained.The working principle of one-dimensional probe and three-dimensional probe are analyzed,then the corresponding radius compensation method are given respectively.The feasibility of the measuring methods are verified on the existing platform.The evaluation and classification of uncertainty in measurement are summarized,and the solutions of the uncertainty in measurement of comprehensive deviations and single deviations of non-circular gear are proposed.