document: Direct gear tooth contact analysis for hypoid bevel gears A new methodology for tooth contact analysis based on a very general mathematical model of the generating process is proposed . Considering the line of action as a first order singularity of a certain operator equation we develop first and second order conditions for a pair of generated gear tooth flanks to be in contact . The constructive approach allows the direct computation of the paths of contact as the solution of a nonlinear equation system including the exact determination of the bounds of the paths of contact . The transmission error as well as curvature properties in the contact points are obtained in a convenient way . The resulting contact ellipses approximate the bearing area . Through the use of automatic differentiation all the geometric quantities are calculable within the machine accuracy of the computer
doc_bio_tags: B I I I I O B I I O O O O O O O O O O O O B I O O B I O O O O O O O O O O B I I O O O B I O O O O B I I O O O O B I I I O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O B I O O O B I O O O O O O O O O O O O O B I O O B I O O O O O B I O O B I O O O O B I O O B
extractive_keyphrases: direct gear tooth contact analysis hypoid bevel gears mathematical model generating process first order singularity operator equation second order conditions generated gear tooth flanks nonlinear equation system transmission error curvature properties contact ellipses bearing area automatic differentiation geometric quantities machine accuracy computer
abstractive_keyphrases: first order conditions contact paths exact bound determination