Strain wave gearing with compound meshing that involves congruity of tooth surfaces

Patent metadata

Field	Value
Publication number	US-10871213-B2
Application number	US-201515576088-A
Country	US
Kind code	B2
Filing date	Jun 23, 2015
Priority date	Jun 2, 2015
Publication date	Dec 22, 2020
Grant date	Dec 22, 2020

Abstract

The dedendum tooth profiles of the internal teeth and external teeth of a strain wave gearing are prescribed by a first homothetic curve BC and a second homothetic curve AC obtained from a curve segment from a point A, at which the angle formed by the tangent to a movement locus Mc when meshing is approximated by rack meshing and the major axis is ΘA, to a low point B. The dedendum tooth profile of the internal teeth is prescribed by a curve formed on the internal teeth in the course of the addendum tooth profile of the external teeth moving from an apex of the movement locus to point A. The dedendum tooth profile of the external teeth is prescribed by a curve formed on the external teeth when the addendum tooth profile of the internal teeth moves from the apex to arrive at point A.

First claim

The invention claimed is:

1. A strain wave gearing with compound meshing that involves congruity of tooth surfaces, the strain wave gearing comprising: a rigid internally toothed gear; a flexible externally toothed gear disposed coaxially within the rigid internally toothed gear; and a wave generator fitted within the flexible externally toothed gear;
wherein the flexible externally toothed gear is made to flex into an ellipsoidal shape by the wave generator, and external teeth of the flexible externally toothed gear mesh with internal teeth of the rigid internally toothed gear at both ends of the ellipsoidal shape along a major axis direction;
a number of teeth of the flexible externally toothed gear is 2 n less than a number of teeth of the rigid internally toothed gear, where n is a positive integer;
the rigid internally toothed gear and the flexible externally toothed gear before being flexed are spur gears of modulus m;
an amount of flexure, relative to a pre-flexure rim-neutral circle on a major axis in an ellipsoidal rim-neutral curve of the flexible externally toothed gear in an axially perpendicular cross-section at an arbitrary position in a tooth trace direction of the external teeth, is 2 κmn, where κ is a deflection coefficient; and
the deflection coefficient in a principal cross-section is set to 1, the principal cross-section being an axially perpendicular cross-section at a position on the external teeth midway in the tooth trace direction; and,
wherein an addendum tooth profile of the internal teeth is prescribed by a first homothetic curve, and a dedendum tooth profile of the internal teeth is prescribed by a first tooth profile curve;
an addendum tooth profile of the external teeth is prescribed by a second homothetic curve, and a dedendum tooth profile of the external teeth is prescribed by a second tooth profile curve;
the first and second homothetic curves are obtained based on a movement locus through which the external teeth move relative to the internal teeth as the wave generator rotates at each position of the external teeth in the tooth trace direction, when the meshing of the external teeth and the internal teeth is approximated by rack meshing;
the first homothetic curve is obtained by taking a curve segment of the movement locus from one apex to a next bottom point, and scaling down a first curve segment in this curve segment by λ (0<λ<1) using a second point as a homothetic center, the first curve segment extending from a first point to the second point, the first point being a point of an angle θ A from 0 to π formed by a tangent of the curve segment and a major axis of the rim-neutral curve, and the second point being the bottom point of the curve segment;
the second homothetic curve is obtained by multiplying a curve by (1−λ)/λ using a third point as a homothetic center, the third point being an end point on a side opposite from the second point in the first homothetic curve, and the curve being obtained by rotating the first homothetic curve 180 degrees about the third point;
the first tooth profile curve is formed on the internal teeth in the course by which the addendum tooth profile of the external teeth, prescribed by the second homothetic curve, moves from the apex of the movement locus to arrive at the first point; and
the second tooth profile curve is formed on the external teeth when the addendum tooth profile of the internal teeth, prescribed by the first homothetic curve, moves from the apex of the movement locus to arrive at the first point.

2. The strain wave gearing according to claim 1 ,
wherein the flexible externally toothed gear comprises a flexible cylindrical barrel part, and a diaphragm extending radially from a rear end of the cylindrical barrel part, the external teeth being formed in an external peripheral surface portion of a front-end-opening side of the cylindrical barrel part;
an amount of flexure of the external teeth increases along the tooth trace direction of the external teeth from an external teeth inner end part on a side of the diaphragm toward an external teeth open end part on a side of the front-end opening, in proportion to a distance from the diaphragm;
a state of flexure in the external teeth in an axially perpendicular cross-section from the principal cross-section to the external teeth open end part on the side of the front-end opening is positive deflection flexure having the deflection coefficient κ greater than 1, and a state of flexure in an axially perpendicular cross-section from the principal cross-section along the tooth trace direction to the external teeth inner end part on the side of the diaphragm is negative deflection flexure having the deflection coefficient κ less than 1;
the tooth profile shape of the external teeth in a position other than the principal cross-section along the tooth trace direction is a profile-shifted tooth profile achieved by making a profile shift corresponding to the amount of flexure to a basic external tooth profile prescribed by the second homothetic curve and the second tooth profile curve in the principal cross-section;
the tooth profile shape of the external teeth at each position in an axially perpendicular cross-section along the tooth trace direction from the principal cross-section to the external teeth open end part is obtained by making a profile shift to the basic external teeth profile, so that a vicinity of the apex of the movement locus described by the basic external teeth profile at the position is tangent to the vicinity of the apex of the movement locus described by the basic external teeth profile in the principal cross-section; and
the tooth profile shape of the external teeth at each position in an axially perpendicular cross-section along the tooth trace direction from the principal cross-section to the external teeth inner end part is obtained by making a profile shift to the basic external teeth profile, so that the bottom part of the movement locus described by the basic external teeth profile at the position is tangent to the bottom part of the movement locus described by the basic external teeth profile in the principal cross-section.

3. The strain wave gearing according to claim 1 ,
wherein a modification that slightly lowers tooth tips is made to teeth depths in both the addendum tooth profile of the internal teeth and the addendum tooth profile of the external teeth, so that a required clearance with the dedendum tooth profile of the other gear is ensured.

4. The strain wave gearing according to claim 1 ,
wherein the movement locus is given by the following formula 1 when θ is a rotational angle of the wave generator on plane coordinates in which an x axis is a translation direction of a rack and a y axis is a direction perpendicular thereto, when the modulus m is 1 and the difference in the number of teeth is 2:
x =0.5(θ−κ sin θ)

y =κ cos θ;  (Formula 1)

the addendum tooth profile of the internal teeth in the principal cross-section is given by the following formula 2:
x (θ)=0.5{(1−λ)π+λ(θ−sinθ)}

y (θ)=λ(1+cos θ)−1  (Formula 2)

where θ A ≤θ≤π;

the addendum tooth profile of the external teeth in the principal cross-section is given by the following formula 3:
x (θ)=0.5{(1−λ)(π−θ+sin θ)+θ A -sin θ A }

y (θ)=cos θ A −(1−λ)(1+cos θ)  (Formula 3)

where θ A ≤θ≤π;

a main part of the dedendum tooth profile of the internal teeth is congruous with the addendum tooth profile of the external teeth in the bottom part of the internal teeth, and is given by the following formula 4 derived from formula 3:
x (θ)=0.5(1−λ)(π−θ+sin θ)

y (θ)=λ−(1−λ)cos θ  (Formula 4)

where θA≤θ≤π,

a curve of transition from the end point of the principal part of the dedendum tooth profile given by formula 4, to the addendum tooth profile of the in

Assignees

• Harmonic Drive Systems

Inventors

• Ishikawa Shoichi

Classifications

• F16H55/08

  Profiling · CPC title

• F16H2049/003

  Features of the flexsplines therefor · CPC title

• F16H49/001 Primary

  Wave gearings, e.g. harmonic drive transmissions · CPC title

• F16H55/0833

  Flexible toothed member, e.g. harmonic drive · CPC title

• F16H55/088

  with corrections on tip or foot of the teeth, e.g. addendum relief for better approach contact · CPC title