Boundary integral equation method applied to the strength design of gear (3rd report, Corner problems and efficient evaluation of integrals)

In this paper, in order to develop a more efficient and more convenient procedure for the strength design of a spur gear, substantial effort is devoted to improving the accuracy in the boundary integral equation analyses. First, corner problems associated with a gear tip are mathematically avoided by adopting Priwalow's formulae. Next, a systematic technique using higher-order shape functions is proposed for the numerical evaluation of singular integrals. Then, a Stieltjes integral is used to deal with a discontinuous change of the boundary direction a corners. The accuracy is investigated using some numerical examples and comparison is made with the results in previous reports.