| Large-sized gears whose diameters are longer than 3 meters are the key components of high-end equipment,such as large-sized ships,high-power wind turbines,and heavy-load engineering machines.The precision of the large-sized gears affects the performance and the core competence of our high-end equipment significantly.Currently,the precision of the domestic large-sized CNC gear hobbing machine is far from meeting the demands of our important equipment and projects.Therefore,most of the large-sized CNC gear hobbing machines in our country rely on import up to now,and are monopolized by the foreign companies,such as Gleason,Liebherr,and Niles,severely restricting the development of our high-end equipment and even threatens our national security.Compared with the middle-sized or small-sized CNC gear hobbing machines,the geometric-error transfer of the large-sized CNC gear hobbing machine is more complicated due to the larger size and longer transmission chain.The mechanism of the generation of the gear machining errors from the machine errors is not completely clear,making it difficult to improve the precision of the large-sized CNC gear hobbing machine.Therefore,in terms of the geometric-error mapping,tracing,and compensation of the large-sized CNC gear hobbing machine,the following research is carried out in this thesis.(1)The analytic model of the tooth-flank error generated in gear hobbing.The hobbing errors are divided into the hob error and the hob-workpiece pose errors.The hob-workpiece pose error are divided into the pose errors of the actual hob,the actual axis of the hob rotation,and the actual axis of the workpiece rotation,and is composed of total 18 pose error elements.Based on the hypothesis that the surface parameters of the contacting points between the hob and workpiece are unchanged when the hobbing errors exist,the analytic expressions of the flank errors induced by the hobbing errors are derived.The effectiveness of the analytic model is validated by simulation in MATLAB environment.The simulation results of the analytic model are compared with those of the cutting-simulation model,indicating that the prediction precision of the analytic model can meet the demands of engineering practice and that the calculation speed of the analytic model is far faster.The analytic model lays a good foundation for constructing the quantitative mapping between the geometric errors of the large-sized gear hobbing machine and the tooth-flank errors of the machined gears.(2)The comprehensive error model of the hob with multiple threads.In order to relieve the bulge phenomenon arising in the machining of the helical rake face of the hob with multiple threads and to improve the precision of the rake angle and the cutting edges,a new approach to rake face machining using a grinding wheel with a parabola profile is presented.Based on the analysis of the sources of the hob errors,the comprehensive error model is constructed by combining the approximation error,the profile error,and the cutting-tooth lead error.These errors are transformed into the normal error of the involute helicoid of the hob,and then the tooth-flank errors of the gear machined by the hob with errors are calculated by inputting the normal error into the analytic model of the tooth-flank error.Given the hob errors,by using this comprehensive error model the gear’s tooth-flank errors can be predicted,providing some references for the hob grade selection.(3)The mapping model of the geometric errors of the large-sized CNC gear hobbing machine.Total 57 geometric errors,of the 6 CNC axes(X,Y,Z,A,B,and C),the hob setting errors,and the workpiece setting errors,are analyzed.By using homogeneous coordinate transformation,the 57 geometric errors are transformed into the 18 hob-workpiece pose errors.Then according to the analytic model of the tooth-flank error,the analytic expressions of the tooth-flank errors induced by the 57 geometric errors are derived.These analytic expressions uncover the effects of the geometric errors on the tooth-flank errors,and lay a theoretical foundation for the tooth-flank error tracing and compensation in the large-sized gear hobbing.(4)Source tracing of the profile and pitch errors of large-sized gears.The frequency characteristics of the tooth-flank errors induced by the geometric errors of the large-sized gear hobbing machine are analyzed.The curve of the tooth-flank error is reconstructed by measuring the profile and pitch errors of the hobbed spur gears.The sources of the profile and pitch errors are found out by using spectral analysis.In order to eliminate the effects of the hob/workpiece setting errors on the source tracing results: the equivalent workpiece setting error is calculated from the tooth-flank error according to its mathematical property,and then the tooth-flank error induced by the workpiece setting error is separated;the hob setting error is identified by measuring the radial runout of the proof flanges of the hob,and then the tooth-flank error induced by the hob setting error is separated.An experiment is conducted on a CNC gear hobbing machine to trace the error source,in which the tracing results are compared with the measurement results obtained from the encoder and the laser interferometer.It is indicated that the source tracing method can trace not only the transmission error but also the rotation errors of the hob and workpiece spindles of the hobbing machine.This method can provide a guidance for adjusting the hobbing machine and improving the precision.(5)Compensation method for the geometric errors of the large-sized CNC gear hobbing machine.Based on the mapping relationships between the geometric errors and the tooth-flank errors,a new method is proposed to compensate the 57 geometric errors of the large-sized CNC gear hobbing machine by controlling the X and C axes.With regard to the large mass and inertia of the column of the hobbing machine,the motion curves for compensation of the X and C axes are optimized,providing the calculation method for the compensation motion of the C axis for single-flank compensation and for double-flank compensation.The experiment for single-flank compensation is conducted on a CNC gear hobbing machine.It is indicated that the precision grades of the profile and pitch of the hobbed gear are both improved one level,validating the effectiveness of the compensation method. |
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