The Research Of Non-circular Gear Error Measurement Method Based On Surface Measurement Theory

Since the non-circular gear can realize the variable speed transmission,in practical applications,it has the unparalleled advantages of the variable speed transmission mechanism such as the connecting rod and the cam,and thus is widely used.Although domestic and foreign scholars have carried out a lot of research on the design,manufacture and application of non-circular gears,and formed a relatively complete theoretical system,but the non-circular gear accuracy grade evaluation system and effective measurement methods have not been formed at home and abroad.To a certain extent,it has affected the promotion and use of non-circular gears.Therefore,a reasonable non-circular gear measurement method and a set of accuracy grade standards for non-circular gears are proposed,which play an important role in the manufacturing and popularization of non-circular gears.Based on the theory of cylindrical gear measurement and surface measurement,this paper proposes a method for obtaining the actual model by using a 3D scanner,and then comparing it with the theoretical model to measure the non-circular gear error.This measurement method can realize fast measurement of non-circular gears error.Finally,based on the numerical calculation of the non-circular gear error,the error values of the non-circular gears are obtained,and the accuracy grade evaluation of the non-circular gears is realized.Firstly,according to the meshing theory of non-circular gear,the tooth profile of the non-circular gear is divided into two parts: the upper pitch curve and the lower pitch curve.The tooth profile equation of the non-circular gear is established,and then the tooth surface equation of the non-circular gear is established.Different tooth profile modeling methods were used for comparative analysis.According to the non-circular gear tooth surface equation,a three-dimensional theoretical model of the non-circular gear is established in the two-dimensional and three-dimensional software,and the actual model of the non-circular gear is obtained by using the three-dimensional scanner,and the data points obtained by the scanning are processed,and then in Geomagic Qualify software aligns the theoretical model with the actual model.Through multiple experiments,it is found that the best fitting alignment method is used to obtain the highest alignment accuracy,which is suitable for non-circular gear measurement.Secondly,according to the non-circular gear processing method and the similarities and differences between the cylindrical gear,the errors of non-circulargear are compared and analyzed.The error measurement items of the cylindrical gear and the surface measurement theory are used to summarize the error measurement items of the non-circular gear.Calculation method for various errors measurement items of the non-circular gear are built.Analogous to the accuracy grade standard of cylindrical gears,a method for evaluating the accuracy grade of non-circular gears is proposed by means of equivalent circle.Based on the allowable value of the gear deviation of the spur gear,the 5-level precision gear deviation of the non-circular gear is derived.Finally,the error of the non-circular gear is measured and calculated.In the measurement of the tooth surface error,the meshing theory is used to reflect the error characteristic information of the tooth surface more realistically,and the tooth surface error is decomposed.In the measurement of the tooth profile error,compared with the coordinate measuring machine,it is found that the three-dimensional scanner can meet the accuracy requirements and the measurement efficiency is high.In the measurement of the pitch error,multiple sections are used for measurement,which reduces the randomness of the pitch error.The gear pitch error of elliptical gear is taken as an example to evaluate the accuracy level of non-circular gears.After the research of this subject,the results show that the method of measuring the non-circular gear by using the 3D scanner based on the surface measurement theory is feasible,improves the measurement efficiency,ensures the measurement accuracy,and provides a reference for the measurement technology of the non-circular gear.