This paper studies the prescribed contact angle boundary value problem of a certain type of mean curvature equation.Applying the maximum principle and the moving frame method and based on the location of the maximum p...This paper studies the prescribed contact angle boundary value problem of a certain type of mean curvature equation.Applying the maximum principle and the moving frame method and based on the location of the maximum point,the boundary gradient estimation of the solutions to the equation is obtained.展开更多
Setting up a pair of moving frames on the two pitch circles, the instantaneous contact point being considered the attendant point of the frames, the equation of the trace of the contact points in the frame being p = p...Setting up a pair of moving frames on the two pitch circles, the instantaneous contact point being considered the attendant point of the frames, the equation of the trace of the contact points in the frame being p = p(t~), we can deduce that the basic rule for the gear profiles is dp / ds = - csos 0 where s is the are length of the pitch circles. Giving a known function of p = p (0), we can obtain the equations of the two conjugate gear profiles and the curvatures and inductive curvature of the profiles. The second order contact phenomenon that a given gear profile can contact with the mating gear at two points simultaneously is discussed by the method of moving frames.展开更多
基金supported by the National Natural Science Foundation of China (No.12061078)。
文摘This paper studies the prescribed contact angle boundary value problem of a certain type of mean curvature equation.Applying the maximum principle and the moving frame method and based on the location of the maximum point,the boundary gradient estimation of the solutions to the equation is obtained.
文摘Setting up a pair of moving frames on the two pitch circles, the instantaneous contact point being considered the attendant point of the frames, the equation of the trace of the contact points in the frame being p = p(t~), we can deduce that the basic rule for the gear profiles is dp / ds = - csos 0 where s is the are length of the pitch circles. Giving a known function of p = p (0), we can obtain the equations of the two conjugate gear profiles and the curvatures and inductive curvature of the profiles. The second order contact phenomenon that a given gear profile can contact with the mating gear at two points simultaneously is discussed by the method of moving frames.
