Overcutting Research On Varying-coefficient-shift-modification Of Non-circular Gear Of Automobile Steering Gear

In order to obtain the drum tooth surface,the non-circular tooth fan of rocker arm shaft of automobile steering gear is usually modified by piecewise linear function(also known as the varying-coefficient-shift-modification),so as to improve the steering performance of automobile.However,due to overcutting in the modification process,the tooth profile of the non-circular fan is not smooth and the amount of drum is reduced.For this reason,starting from the principle and method of varying-coefficient-shiftmodification,this paper deeply studies the cause of the overcut caused by the varyingcoefficient-shift-modification.By designing the modification function and combining with the experimental measurement,the modification of the non-circular tooth fan of the rocker arm shaft is quantitatively described,which provides theoretical guidance for the design and manufacture of the automobile steering gear.The main work is as follows:The meshing motion of non-circular fan rack with varying-coefficient-shiftmodification is studied.The varying-coefficient-shift-modification method is analyzed.Based on the meshing principle of non-circular gear with fixed shaft transmission,the theoretical tooth profile equation of varying-coefficient-shift-modification non-circular tooth fan is derived.The modified motion was superimposed to the developed motion of the fan rack pair,and the actual tooth profile of the non-circular fan was obtained through motion simulation in MATLAB.By comparison,it is found that in the modified range,the actual varying-coefficient-shift-modification tooth profile does not coincide with the theoretical tooth profile,that is,the tooth profile of the non-circular fan is overcut.The cause of overcutting caused by the varying-coefficient-shift-modification of non-circular tooth fan is studied.The modification motion of piecewise linear function is analyzed.It was found that the process rack and the tooth profile of non-circular tooth fan did not satisfy the meshing condition equation at the contact point.The instantaneous center of the tooth profile modification of the non-circular tooth fan was solved by the velocity synthesis method.It was found that the instantaneous center line did not pass through the rotation center of the tooth fan in the whole modification movement,and the trajectory of the instantaneous center appeared jump and discontinuous,which was the root cause of the tooth profile overcutting.Combined with the theoretical and practical methods to solve the tooth profile,the calculation formula of overcutting amount is derived.A method to reduce and eliminate overcut caused by varying-coefficient-shiftmodification is proposed.A piecewise modified curve based on cosine function was designed according to the requirements of steering positivity.The trajectory of the instantaneous center point of the rack pair of non-circular fan during the modification was calculated.It was found that the trajectory was continuous and the amount of overcut was significantly reduced.In order to eliminate overcutting completely,the pre-modified parameters were superimposed along the normal tooth profile to construct a new tooth profile.The tool tooth profile was obtained by using the motion simulation method in reverse,and then the non-circular tooth profile was obtained by using the inverse envelope of the cutter tooth profile.The obtained non-circular tooth profile was found to be completely coincidence with the theoretical tooth profile by comparing the obtained non-circular tooth profile with the theoretical tooth profile,and the overcutting was completely eliminated.A method for measuring tooth surface error of non-circular fan is presented and verified by an example.Based on the Klingelnberg P26 gear detection center,the crosssection of the non-circular tooth fan was discretized from the big end to the small end,and the profile of each cross-section was continuously scanned to measure the tooth surface error of the non-circular tooth fan.Combined with the measurement of the noncircular tooth fan sample of the rocker arm of the steering gear,the correctness of the calculation method of the tooth profile of the non-circular tooth fan and the overcutting amount and the real existence of the overcutting phenomenon are verified.