Tooth profile designing method for strain wave gearing
According to a tooth profile designing method for a strain wave gear device, a first curve from a point A (φ=0) to a point B (φ=π/2) in a moving locus of external teeth with respect to internal teeth is extracted. A similarity curve is obtained by multiplying the first curve by (1−λ) using the point B as a center of similarity, and a second curve is obtained by rotating the similarity curve by 180° about a midpoint C between the point A and the point B as a center of similarity. A third curve is obtained by multiplying only the x-coordinate of the second curve by α (α<1), or a fourth curve is obtained by multiplying only the y-coordinate of the second curve by β (β>1). An addendum tooth profile of the external teeth is defined using the third curve or the fourth curve.
1. A tooth profile designing method for a strain wave gearing comprising a rigid internally toothed gear, a flexible externally toothed gear, and a wave generator that causes the externally toothed gear to flex into an ellipsoidal shape and mesh with the internally toothed gear at locations including positions on a major axis of the ellipsoidal shape, and causes positions where the externally toothed gear meshes with the internally toothed gear to move in a circumferential direction, said tooth profile designing method comprising:
designating a rotation angle of the wave generator as φ and focusing on internal teeth of the internally toothed gear and external teeth of the externally toothed gear positioned on the major axis when φ=0, a locus over which the external teeth move with respect to the internal teeth, obtained while the wave generator is rotating from φ=0 to φ=φ1 (0<φ1≤π/2), is determined as a first curve;
designating an endpoint of the first curve when φ=0 as point A, an endpoint when φ=φ1 as point B, a midpoint between point A and point B as point C, and λ as a positive value less than 1, a similarity curve for which the first curve is multiplied by (1−λ) using point B as a center of similarity is determined, and a second curve for which the similarity curve is rotated 180 degrees about the point C is determined;
designating a as a positive value less than 1 and β as a positive value greater than 1, and also designating a curve obtained by multiplying only the x coordinate of the second curve by α as a third curve and a curve obtained by multiplying only the y coordinate of the second curve by β as a fourth curve, either one of the third curve and the fourth curve is determined and an addendum profile of the external teeth is defined using the determined curve;
an addendum profile of the internally toothed gear is defined by a curve enveloping the addendum profile of the external teeth; and
a dedendum profile of the external teeth and a dedendum profile of the internal teeth are each set to a shape that does not interfere with a counterpart addendum profile.
2. The tooth profile designing method according to claim 1 , wherein designating a as a positive value less than 1 and β as a positive value greater than 1, and also designating a curve obtained by multiplying only the x coordinate of the second curve by α as a third curve and a curve obtained by multiplying only the y coordinate of the second curve by β as a fourth curve, the third curve is determined and an addendum profile of the external teeth is defined using the determined curve.
3. The tooth profile designing method according to claim 1 , wherein designating a as a positive value less than 1 and β as a positive value greater than 1, and also designating a curve obtained by multiplying only the x coordinate of the second curve by α as a third curve and a curve obtained by multiplying only the y coordinate of the second curve by β as a fourth curve, the fourth curve is determined and an addendum profile of the external teeth is defined using the determined curve.