Study On Errors Analyse Of CNC Hobbing Non-Circular Gears

Noncircular gear with the advantages of cam and circular gear has been widely usded on diversified situation. The frequent noncircular gears are elliptical gears, pascal gears and so on, which precision manufacturing is always the research hotspot. As we know, CNC hobbing is the most widely used as a processing gears method, with the increase of gears machining precision, it is very important to analysis the errors of CNC hobbing non-circular gears. Thus, this thesis presents the relationship between the machine motion axis and the errors source according to the derived motion models of CNC hobbing non-circular gears. Based on the above, the influence of process errors on part precision indices (pitch curve, tooth pitch and undercut) of non-circular gears are analysed; and the effects of interpolation algorithms on hobbing noncircular gear are studied. Taking the elliptic gear as a case, the influence regularities of dynamical characteristics of one order, second order and high order servo system on the noncircular gear pitch curves contour error are analyzed. The main research contents and conclusions are as follows:(l)The relationship between the machine motion axis and the errors source is obtained form the derived motion models of CNC hobbing non-circular.(2)According to the mathematical model for hobbing noncircular gear, the expression of the noncircular gear tooth pitch deviation and tooth pitch accumulated error caused by the workbench rotary angle errors and the rack horizontal movement amount errors are presented. And the vector expression of the noncircular gear pitch curve errors caused by the stage rotary angle error and the centre space error are derived, respectively.Based on the known relative velocity and meshing equation between hobbing cutter and the gear blank, the noncircular gear tooth profile undercut limit function is proposed and deduced. Then, the change regularity of undercut limit functions with the polar angle of elliptic and the design parameters are analyzed through the numerical method. The polar angle position of noncircular gear undercut can been confirmed.(3)According to the derived mathematical model for hobbing noncircular gear, interpolation algorithms of hobbing noncircular gear are obtained. Developing regularity of different interpolation algorithms arc length of segment and machine motion axis were compared, the concept of the arc length of segment uniformity degree is proposed, thereby the uniformity of the arc length of segment can be judged.(4)Taking elliptic gear as a case, influence regularities of dynamical characteristics of one order, second order and high order servo system on noncircular gear pitch curves contour error is analyzed based on the CNC servo system model. Also the change laws of noncircular gear pitch curves contour error is obtained by using of mathematical derivation. In order to reduce the contour error, PID cross-coupled control (CCC) is proposed, the simulation results show that CCC can improve noncircular gear pitch curves contour accuracy.