The Research Of Non-circular Gear Error Measurement Method Based On Digital Scanning

Non-circular gears are a kind of transmission parts with special geometrical structure,which have unique transmission functions that other transmission parts do not have,so they are widely used in industrial production.Due to the research and application of non-circular gears are later than other gear transmission mechanism,and the geometrical structure is complicated,the machining is difficult,the measurement technology and theory are not perfect,and there is no systematic precision grade evaluation system,the popularization of its application is limited in a certain extent.In view of the above problems,on the basis of researching and summarizing the achievements of other scholars,this paper proposes a new method for measuring and calculating the machining error of non-circular gears based on the existing experimental conditions,the content is as follows.First,the equation of pitch curve is derived by the meshing theory of non-circular gears,the closure conditions need to be satisfied and the concavity and convexity of pitch curve are verified.Then the tooth profile equation is established according to the formation theory of tooth profile and verified by an example.And the machining errors of the non-circular gears are classified according to its manifestation,and the error terms are established according to the transmission requirement.Secondly,according to the non-contact active laser ranging theory,the 3D point cloud of the non-circular gear is collected by the Creaform MetraScan scanner,and the point cloud preprocessing is completed in the reverse engineering software.Then the 3D point cloud and the established 3D model are imported into reverse engineering software for 3D digital detection.Intersection point coordinates(between the tooth profile and the pitch curve)of three different plane are obtained by the annotation command.Finally,in the aspect of machining error calculation of non-circular gears.For the pitch curve error,the pitch curve error model is established by the double-sided meshing detection theory and the data points are fitted into the pitch curve by the piecewise cubic spline function,and the pitch curve error is calculated and analyzed;For the tooth profile error,the tooth profile error is calculated by the data obtained from three different planes;For the tooth surface error,the tooth surface error is calculated by the transformation matrix and the error evaluation function;For the tooth thickness error and the pitch error,the tangent function and the complex Gauss-Legendre quadrature formula are used to calculate the tooth thickness and pitch.The error model is used to obtain the tooth thickness error and the pitch error.The tooth thickness error and the pitch error calculated in three different planes are compared and analyzed.Through the research of this subject,a new measurement method and theory is used to calculate the machining error of the non-circular gear,and the validity of the verification method is calculated by an example,which provides reference value for the related research of non-circular gears in the future.