Finishing of Tooth Flanks of Pinion Cutter With Profiled Grinding Wheel in Consideration of Accuracy of Cutting Edge After Regrinding

Two kinds of relief grinding methods for pinion cutters with profiled grinding wheels are proposed. One method finishes an involute pinion cutter with almost no regrinding error by giving the helical motion smaller or larger than that corresponding to the helix angle of the pinion cutter. Another is for a pinion cutter with an arbitrary profile, including the involute pinion cutter with a modified profile or protuberance. The tooth flank is finished by giving the three motions, i.e., the helical and approaching motions between the grinding wheel and work pinion cutter and the shifting motion of the grinding wheel. The profile calculation was conducted by using the element removal method. It was shown that the regrinding errors of the pinion cutters being finished by the proposed methods become smaller than that of pinion cutters finished by giving only the approaching motion (conventional method). The finishing tests of the involute helical pinion cutters were carried out on the CNC gear form-grinding machine with the four controlled axes. The profiles of cutting edges of the finished pinion cutters almost agreed with the calculated ones.

ELEMENT REMOVAL METHOD FOR SINGULAR MINIMIZERS IN PROBLEMS OF HYPERELASTICITY

A numerical method called element removal method is applied to calculate singular minimizers in problems of hyperelasticity. The method overcomes the difficulty in finite element approximations caused by restrictions, such as det (I+∇u)>0, on admissible functions and can avoid Lavrentiev phenomenon if it does occur in the problem. The convergence of the method is proved.

Element removal method for singular minimizers in variational problems involving Lavrentiev phenomenon

A numerical method called element removal method is designed to calculate singular minimizers which cannot be approximated by simple applications of standard numerical methods because of the so-called Lavrentiev phenomenon. The convergence of the method is proved. The results of numerical experiments show that the method is effective.