A wave gear device, comprising
- an annular rigid internally toothed gear;
- a flexible externally toothed gear, arranged coaxially on an inside of the rigid internally toothed gear;
- and
- a wave generator, fitted on an inside of the flexible externally toothed gear;
- wherein
- the flexible externally toothed gear is provided with a flexible cylindrical barrel part, a diaphragm extending in a radial direction from a rear end of the cylindrical barrel part, and external teeth formed on an outer circumferential surface portion on a side towards a front-end opening of the cylindrical barrel part,
- the external teeth of the flexible externally toothed gear deflected into an ellipse-like shape by the wave generator are meshed with inner teeth of the rigid internally toothed gear at both end parts in a direction of a major axis of an ellipse-like curve;
- an amount of deflection of the external teeth of the flexible externally toothed gear deflected into the ellipse-like shape increases from a side towards the diaphragm to a side towards the front-end opening along a direction of a tooth trace of the external teeth, the amount of deflection being substantially proportional with respect to a distance from the diaphragm;
- each of the external teeth of the flexible externally toothed gear and each of the internal teeth of the rigid internally toothed gear are configured as on a spur gear having a module m;
- a number of teeth of the flexible externally toothed gear is set to a number that is 2n less than a number of teeth of the rigid internally toothed gear, where n is a positive integer;
- in an axially perpendicular cross-section of the external teeth at an arbitrary position in a tooth trace direction, the amount of deflection in a radial direction at a major axis position on an ellipse-like rim neutral line of the external teeth, relative to a rim neutral circle before the externally toothed gear are deflected into the ellipse-like shape, is 2 κmn, where κ is a deflection factor;
- if, in relation to the tooth trace direction of the external teeth of the flexible externally toothed gear, an axially perpendicular cross-section of an end nearer the front-end opening is an opening-end cross-section;
- an axially perpendicular cross-section of an end nearer the diaphragm is an inner-end cross-section;
- and an axially perpendicular cross-section designated at an arbitrary position between the opening-end cross-section and the inner-end cross-section is a main cross-section,
- the deflection factor of the main cross-section is κ=1, the deflection factor of the opening-end cross-section is κ=κo>1, and the deflection factor of the inner-end cross-section is κ=κi<1;
- an opening-end tooth profile shape on the opening-end cross-section of each of the external teeth is defined by a convex-curve-shaped external-tooth tooth-face tooth profile portion, an external-tooth straight-line tooth profile portion continuing from the external-tooth tooth-face tooth profile portion, a concave-curve-shaped external-tooth tooth-flank tooth profile portion continuing from the external-tooth straight-line tooth profile portion, and an external-tooth root portion continuing from the external-tooth tooth-flank tooth profile portion;
- the tooth profile shape of a portion extending from the opening-end cross-section to the inner-end cross-section is a profile-shifted tooth profile shape, in which the opening-end tooth profile shape has been subjected to a negative profile shift;
- a tooth profile shape on an axially perpendicular cross-section of each of the internal teeth is defined by a convex-curve-shaped internal-tooth tooth-face tooth profile portion;
- an internal-tooth straight-line tooth profile portion continuing from the internal-tooth tooth-face tooth profile portion, a concave-curve-shaped internal-tooth tooth-flank tooth profile portion continuing from the internal-tooth straight-line tooth profile portion, and an internal-tooth root portion continuing from the internal-tooth tooth-flank tooth profile portion;
- meshing between the external teeth and the internal teeth is approximated as rack meshing, and a movement trajectory of each of the external teeth of the flexible externally toothed gear relative to the internal teeth of the rigid internally toothed gear that accompanies rotation of the wave generator is determined for individual axially perpendicular cross-sections in the tooth trace direction of each of the external teeth;
- a curve portion AB extending from a point A at a peak of the movement trajectory M1 obtained at the main cross-section to a point B at a next bottom part is subjected to a λ-fold similarity transformation using a similarity ratio of λ<1 and using point B as a center of similarity transformation, to thereby a first similarity curve BC is determined, and the first similarity curve BC is moved in the direction of the tooth face of the rigid internally toothed gear by (κo−1)mn, to thereby a curve B1C1 is determined;
- a curve obtained by rotating the first similarity curve BC by 180 degrees about an end point C of the first similarity curve BC is subjected to an (1−λ)/λ-fold similarity transformation, using the end point C as a center of similarity transformation, to thereby a second similarity curve CA is determined, and the second similarity curve CA is moved in the direction of the tooth face of the flexible externally toothed gear by (κo−1)mn, to thereby a curve C2A2 is determined;
- a straight line L1 that intersects the C2A2 at a pressure angle α is drawn, and a curve portion A2D of the curve C2A2 between an end point A2 and an intersection point D with respect to the straight line L1 is determined;
- the external-tooth tooth-face tooth profile portion is defined by the curve portion A2D;
- the external-tooth straight-line tooth profile portion is defined by the straight line L1 extending from the intersection point D;
- the external-tooth tooth-flank tooth profile portion is defined by a concave curve, which links the external-tooth straight-line tooth profile portion and the external-tooth root portion defined by a predetermined external-tooth root curve, so that a predetermined top clearance is obtained for the external-tooth straight-line tooth profile portion in relation to the internal teeth;
- a position at which the external teeth having the external-tooth straight-line tooth profile portion cut in towards the internal teeth by the greatest amount after passing a peak of the movement trajectory Mo obtained at the opening-end cross-section in an instance in which the external tooth has moved along the movement trajectory Mo is determined, and the external-tooth straight-line tooth profile portion at the corresponding position is used to define the internal-tooth straight-line tooth profile portion;
- an intersection point G between the internal-tooth straight-line tooth profile portion and the curve B1C1 is determined, and a curve portion B1G of the curve B1C1 extending from an end point B1 to the intersection point G is used to define the internal-tooth tooth-face tooth profile portion;
- the internal-tooth tooth-flank tooth profile portion is defined by a concave curve, which links the internal-tooth straight-line tooth profile portion and the internal-tooth root portion defined by a predetermined root curve, so that a predetermined top clearance is obtained for the internal-tooth straight-line tooth profile portion in relation to an external tooth;
- and
- the tooth profile shape of a portion of each of the external teeth extending from the opening-end cross-section to the inner-end cross-section is a profile-shifted tooth profile shape in which the opening-end tooth profile shape has been subjected to negative profile shifting so that the movement trajectory obtained for individual axially perpendicular cross-sections from the inner-end cross-section to the opening-end cross-section is tangent, at a corresponding bottom part B thereof, to the movement trajectory Mo obtained at the opening-end cross-section.