JP4877837B2 - Tooth profile setting method for the same number of teeth side gear of flat type wave gear device - Google Patents

Description

  The present invention relates to a flat wave gear device, and more particularly, to a tooth shape setting method for a flexible external gear and a rigid internal gear on the same number of teeth side that achieves accurate zero backlash meshing and has a high ratcheting torque.

  The wave gear device includes a rigid internal gear, a flexible external gear, and a wave generator. The wave generator generally has an elliptical outline, and the flexible external gear is bent into an oval shape by the wave generator. Thus, both end portions of the elliptical long shaft mesh with the rigid internal gear. The number of teeth of the flexible external gear is 2n less (n is a positive integer) than the number of teeth of the rigid internal gear. When the wave generator is rotated by a motor or the like, the meshing position of both gears moves in the circumferential direction, and relative rotation corresponding to the difference in the number of teeth of both gears is generated between the two gears. As a wave gear device, a so-called flat wave gear device is known.

  In the flat type wave gear device, in order to output the relative rotation of the rigid internal gear and the flexible external gear, two rigid internal gears are arranged in parallel in a coaxial state, and the number of teeth of one rigid internal gear is flexible. The number of teeth of the other rigid internal gear is 2n more than that of the flexible external gear. One rigid internal gear is fixed so as not to rotate, and rotation is output from the other rigid internal gear.

  The wave gear device is based on the founder C.I. W. Since the invention of Musser (Patent Document 1: US Pat. No. 2,906,143), various inventions have been devised by many researchers including the present inventor, including the present inventor. The present invention relates to a tooth profile when there is a difference in the number of teeth between the flexible external gear and the rigid internal gear.

There are very few proposals for the tooth shapes of the flexible external gear and the rigid internal gear with no difference in the number of teeth in the flat wave gear device, and only the proposals in Patent Document 2 and Patent Document 3 are proposed.
U.S. Pat. No. 2,906,143 Japanese Examined Patent Publication No. 38-9157 Japanese Patent No. 2503027

  Currently, in order to achieve complete zero backlash with a flat wave gear device, it is necessary to achieve zero backlash on both the flexible external gear side and the rigid internal gear side with and without the number of teeth difference. There is. Especially in the latter case, the tooth profile itself considering the actual number of teeth has not been sufficiently studied.

  The main problem of the present invention is that a flexible external gear and a rigid internal gear with the same number of teeth used in a flat wave gear device are flexible in relation to the shape of the rim neutral line of the flexible external gear. It is to clarify the movement trajectory of the teeth of the elastic external gear relative to the teeth of the rigid internal gear, and to obtain an accurate tooth profile of the rigid internal gear when the tooth profile of the flexible external gear is an arc.

In order to achieve the above object, in the flat wave gear device of the present invention, an arc tooth shape is given to the flexible external gear, and the arc center of the tooth shape of the flexible external gear and the number of actual teeth are considered. From the instantaneous center of relative motion of the flexible external gear and the rigid internal gear, the contact point of the tooth profile of both gears is obtained, and the created tooth profile of the rigid internal gear is calculated based on the contact point.

That is, the present invention relates to a D-side rigid internal gear and an S-side rigid internal gear arranged in parallel in a coaxial state, and a ring-shaped flexible outer gear arranged in a coaxial state inside these D-side and S-side rigid internal gears. A gear generator and a wave generator for rotating the shape of the flexible external gear in a shape perpendicular to the axis of the flexible external gear. The number of teeth of the D-side rigid internal gear is equal to the number of teeth of the flexible external gear. The tooth shape setting method of the flat wave gear device is the same, and the number of teeth of the S-side rigid internal gear is 2n more (n is a positive integer) than the number of teeth of the flexible external gear,
Both the flexible external gear and the D-side rigid internal gear are module m spur gears,
The amount of radial deflection of the long axis of the rim neutral line passing through the center of the thickness of the root rim when the cross section perpendicular to the axis of the flexible external gear is bent elliptically is κmn (κ: deflection coefficient),
The main part of the tooth profile of the flexible external gear is a convex arc tooth profile composed of a convex arc of radius r centered on point A,
Determining an instantaneous center S of relative movement of the flexible external gear and the D-side rigid internal gear that are generated in accordance with the rotation of the wave generator;
A point where a line segment connecting the arc center of the convex arc and the instantaneous center intersects the convex arc is defined as a contact point C between the convex arc tooth profile of the flexible external gear and the tooth profile of the D-side rigid internal gear,
The movement trajectory of the contact point on the convex arc tooth profile of the flexible external gear accompanying the rotation of the wave generator is employed as the tooth profile of the main part of the D-side rigid internal gear.

  Here, a stationary rectangular coordinate system (Ox, y) is defined with the center O of the D-side rigid internal gear as the origin, the radius of the neutral circle, which is the neutral curve before deformation, is rn, w is the amount of deflection, and θ is The angle between the tangent to the neutral curve at the point P defined on the neutral curve and the x-axis, p is the length of the perpendicular to the tangent from the origin O, and p is given by the tangent polar coordinates as

A rotation rectangular coordinate system (O) that shares the origin O and rotates the Y axis clockwise by φ with respect to the y axis so as to pass through a point Q on a virtual neutral circle corresponding to the point P on the neutral curve. -X, Y)
A rectangular coordinate system (Px _F , y _F ) is defined with the tangent drawn to the neutral curve at the point P on the neutral curve as the x _F axis and the straight line perpendicular to it as the y _F axis,
The coordinates (x _S , y _S ) on the stationary rectangular coordinate system (Ox, y) of the instantaneous center S are given by the following equation as a function of θ:

The coordinates of the center A of the convex arc are (x _a , y _a ) in the rectangular coordinate system (Px _F , y _F ), and the coordinates of the center A in the stationary rectangular coordinate system (Ox, y) ( x _A , y _A ) is given by

The stationary coordinates (x _C , y _C ) of the contact point C are given by

Rotation Cartesian coordinate system (O−) in which the above-mentioned θ is variable and the static coordinates (x _C , y _C ) obtained from the above equation are fixed to the D-side rigid internal gear from the stationary rectangular coordinate system (Ox, y). (X, Y), and the tooth profile of the main part of the D-side rigid internal gear with the Y axis as the center of the tooth gap can be obtained by the following equation.

  The deflection coefficient κ can be in the range of 0.6 <κ <1.4.

  Next, the flat wave gear device of the present invention is characterized in that the main part of the tooth profile of the flexible external gear and the main part of the tooth profile of the D-side rigid internal gear are set by the above-described tooth profile setting method. .

  According to the present invention, since the tooth profile of the rigid internal gear (D-side rigid internal gear) having the same number of teeth as that of the flexible external gear in the flat wave gear device can be accurately designed, zero backlash in meshing between both gears can be realized. it can. Further, the ratcheting torque can be increased, and continuous engagement can be realized over a wide range of the movement trajectories of the tooth shapes of both gears. Therefore, according to the present invention, the load capability of the flat wave gear device can be increased.

  A method for setting a tooth profile of a flat wave gear device to which the present invention is applied will be described below with reference to the drawings.

(Configuration of flat wave gear device)
FIG. 1 is a cross-sectional view showing a flat wave gear device to which the present invention can be applied. The flat-type wave gear device 1 includes two rigid internal gears 2 and 3 arranged in parallel in a coaxial state, a ring-shaped flexible external gear 4 arranged in a coaxial state inside these, and an inner side thereof And a wave generator 5 having an elliptical profile fitted to. The number of teeth of one rigid internal gear 2 is the same as the number of teeth of the flexible external gear 4, but the number of teeth of the other rigid internal gear 3 is 2n (n is a positive integer). When the wave generator 5 having an elliptical profile is rotated, relative rotation is generated between the flexible external gear 4 and the rigid internal gear 3 having different numbers of teeth. For example, when the rigid internal gear 2 is fixed so as not to rotate and the other rigid internal gear 3 is supported in a rotatable state, reduced rotation is output from the rigid internal gear 3 side. In the following description, the rigid internal gear 2 having the same number of teeth as the flexible external gear 4 is called a D-side rigid internal gear, and the other rigid internal gear 3 is called an S-side rigid internal gear.

  The rigid internal gears 2 and 3 and the flexible external gear 4 are both spur gears of the module m. The amount of bending in the radial direction of the flexible external gear 4 is κmn. Let κmn be the amount of bending in the radial direction of the long axis of the rim neutral line, which is a line passing through the center of the thickness of the root rim when the cross section perpendicular to the axis of the flexible external gear is bent in an elliptical shape. κ is a bending coefficient, and the amount of bending mn in the radial direction when κ = 1 is a value obtained by dividing the pitch circle diameter of the flexible external gear by the reduction ratio when the rigid internal gear is fixed. The deflection coefficient is in a range of 0.6 <κ <1.4, which is in practical use.

(Neutral curve of flexible external gear)
FIG. 2 is an explanatory diagram for explaining a tooth profile setting method. This figure shows a neutral curve of the root rim of the flexible external gear 4 in a cross section perpendicular to the axis. A stationary rectangular coordinate system (Ox, y) having the origin O as the center O of the D-side rigid internal gear 2 (which coincides with the center of the flexible external gear 4 before deformation) is set, and the flexible external gear 4 The long axis of the neutral curve of the initial position of the approximate elliptical shape assumed at the center of the rim thickness is made to coincide with the y axis, and the short axis is made to coincide with the x axis. The neutral curve before deformation, that is, the radius of the neutral circle is r _n , w is the amount of radial deflection, θ is the angle formed by the tangent to the neutral curve at the point P on the neutral curve and the x axis, and p is the origin The tangent polar coordinates are used as the length of the perpendicular drawn from, and p is given by equation (1).

This equation gives an approximate curve to an ellipse, and all the analyzes of the present invention are based on this equation. When the shape of this neutral curve is expressed by normal rectangular coordinates (x, y), the static coordinates (x _P , y _P ) of the point P are expressed by the following equation (2) (the derivation of the equation is shown at the end of this specification). ).

(Motor motion analysis of flexible external gear)
In order to analyze the movement of the flexible external gear 4 with respect to the D-side rigid internal gear 2 of the flat type wave gear device 1, as shown in FIG. 2, the D-side rigid internal gear is concentric with the D-side rigid internal gear 2. Assume a neutral circle of a flexible external gear that moves in unison with 2 and before virtual deformation.

  Let Q be the point on the virtual neutral circle of the flexible external gear 4 corresponding to the point P on the neutral curve. The correspondence between the points P and Q is that when the point P is on the long axis of the approximate ellipse, the point Q is also on the radius in the same direction, and when the point P moves on the neutral curve at a constant speed, the point Q Is also moved at the same constant speed on the neutral circle, and when the point P goes around the neutral curve, the point Q goes around the neutral circle.

The coordinates (x _Q , y _Q ) of this point Q in the stationary coordinate system are given by the expression (3), where the declination from the major axis is φ in polar coordinate display.

  Here, φ is equal to the length from the long axis of the neutral curve to the point P and the corresponding arc length s on the virtual neutral circle, and θ is expressed as (4b) using the relationship of the equation (4a). It becomes an expression relationship.

  Next, the origin O is shared, and a rotating rectangular coordinate system (X, Y) is provided in which the Y axis is rotated clockwise by φ with respect to the y axis so as to pass through the point Q described above. The conversion formula from the coordinates (x, y) to the coordinates (X, Y) is the formula (5).

Tangent to x _F axis drawn in the neutral curve point P on the neutral curve, it a line perpendicular to the y _F axis, paste tooth profile of the flexible external gear 4 in this coordinate system. The coordinate conversion formula from this coordinate system to the stationary coordinate system (x, y) is the following formula (6) with reference to formula (2).

By substituting this equation into equation (5), the coordinates (x _F , y _F ) fixed to the teeth of the flexible external gear are converted into values (X, Y) of the rotating coordinate system that moves on the virtual neutral circle. Is obtained as follows (derivation of the formula is given at the end of this specification):

Here coordinate system _{(P-x F, y F} ) is obtained in advance a moving track seen from the virtual neutral circle of origin P of. That is, the following equation (8) is obtained by using equation (4) with x _F = 0 and y _F = 0 in equation (6).

(Relative motion of flexible external gear relative to rigid internal gear)
The radius of curvature ρ at the point P of the neutral curve of the rim of the flexible external gear 4 is given by equation (9) from the tangential polar coordinate formula.

Therefore, the static coordinates (x _R , y _R ) of the curve center R of the neutral curve are changed from the equation (6) to the following equation (10).

Here, the y _F axis of the coordinate system (P-x _F , y _F ) is taken as the tooth center line of one tooth of the flexible external gear.
At the position of θ = 0, the y _F axis overlaps the y axis. Consider a tooth at a point P defined by θ. The movement of one tooth of the flexible external gear 4 is instantaneously seen as a rotation with a virtual angular velocity ω _Fν = ν / ρ about the center of curvature R of the neutral curve. Here [nu is at a peripheral speed of the rim neutral line, when the angular velocity of the virtual neutral circle of the flexible external gear 4 and omega _F, good looking implicated in ν = r _n ω _F. On the other hand, the corresponding rotational speed of the D-side rigid internal gear 2 is ω _F because the number of teeth of the flexible external gear 4 and the D-side rigid internal gear 2 is equal.

Here, when the number of teeth z _Fν of the virtual flexible external gear at the point P is _introduced as z _Fν = z _F (ω _F / ω _Fν ), z _Fν can be _expressed by the following (11) with reference to the equation (9): It is given by the formula.

On the other hand, the D-side rigid internal gear 2 also rotates at an angular velocity ω _F around the point O. Point O and center of curvature R
Is the instantaneous center line of the flexible external gear 4 and the D-side rigid internal gear 2 in this case, and ζ is the angle formed by the instantaneous center line with the −x axis, the following (12) ) Formula holds.

In this case, the virtual center distance a _v is expressed by equation (13).

Accordingly, the relative instantaneous center S of both is a point (pitch point) that _divides a _v into the ratio of z _Fν and z _F , and the coordinates (x _S , y _S ) are given by the equation (14).

  In the above equation, the following relationship based on equation (12) is used.

The imaginary pitch radii r _C and r _F of one tooth of the D-side rigid internal gear 2 and the flexible external gear 4 are obtained by equation (16) as line segments OQ and CQ, respectively.

From this, the coordinates (x _S , y _S ) can be expressed as a function of θ as shown in equation (17).

  Here, the contact condition of the tooth profile is that the normal line at the contact point C of the tooth profile passes through the point S. Therefore, if one tooth profile is given to the flexible external gear 4, the contact point is determined on the condition that the tooth profile normal passes through the point S at the moment center according to the position of the point P, and the corresponding D-side rigidity is obtained. The tooth profile of the internal gear 2 is required.

(Give convex arc tooth profile to flexible external gear)
In the present invention, a convex arc is adopted for the main tooth shape (portion including the end surface) of the flexible external gear 4. The coordinates of the arc center A of the convex arc are (x _a , y _a ) in the coordinate system (P−x _F , y _F ), and the radius is r. At this time, the contact C with the tooth profile of the D-side rigid internal gear on the arc tooth profile of the flexible external gear 4 is the instantaneous center R (the center of curvature of the neutral curve) of the coordinate system of the flexible external gear. The point S and the arc center relative to the instantaneous center S of the relative instantaneous motion of the instantaneous rotational motion around and the rotational motion of the coordinate system (O-X, Y) around the origin O of the D-side rigid internal gear 2 The straight line connecting A is obtained as the point where the arc intersects. The static coordinates (x _A , y _A ) of point _A are given by equations (7) to (18).

  From the above, the coordinates of point C are given by equation (19).

(Tooth profile of D-side rigid internal gear)
Here, when θ is variable, the coordinates (x _C , y _C ) are obtained by the equation (19), and converted from the stationary coordinate system to the coordinate system fixed to the D-side rigid internal gear 2, the equation (4) is used. The tooth profile of the main part of the D-side rigid internal gear 2 with the Y axis as the tooth gap center line is obtained by the equation (20). The actual tooth profile of the D-side rigid internal gear 2 is completed by supplementing the fillet curve.

  FIG. 4 shows the tooth profile of the D-side rigid internal gear 2 created by the teeth of the flexible external gear 4 in a cross section perpendicular to the axis. In this figure, both gears have 100 teeth and a deflection coefficient of 0.805.

  FIG. 5 is an example of meshing of both gears 2 and 4 in a cross section perpendicular to the axis on the side of the D-side rigid internal gear 2 in the flat wave gear device employing the tooth profile of FIG.

(Induction of (2) and (7) )
Derivation of equation (2) from equation (1)

  Derivation of equation (7) from equations (5) and (6)

It is sectional drawing of the flat type wave gear apparatus used as the object of this invention. It is explanatory drawing which shows the tooth profile setting procedure by this invention. It is explanatory drawing which expands and shows a part of FIG. It is explanatory drawing which shows the example of the tooth profile of the D side rigid internal gear created with the circular arc tooth profile of a flexible external gear. It is explanatory drawing which shows the meshing example of both the gears of the flat type wave gear apparatus which employ | adopted the tooth profile of FIG.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Flat type wave gear apparatus 2 D side rigid internal gear 3 S side rigid internal gear 4 Flexible external gear 5 Wave generator SD Instantaneous center of relative movement of tooth profile of D side rigid internal gear and flexible external gear A Possible Center of the arc tooth profile of the flexible external gear C Contact point with the tooth profile of the D-side rigid internal gear on the arc tooth profile of the flexible external gear

Claims (4)

A D-side rigid internal gear and an S-side rigid internal gear arranged in parallel in a coaxial state; a ring-shaped flexible external gear arranged in a coaxial state inside the D-side and S-side rigid internal gears; And a wave generator that rotates the shape of the external gear perpendicular to the axis to be elliptical, and the number of teeth of the D-side rigid internal gear is the same as the number of teeth of the flexible external gear. The number of teeth of the rigid internal gear is 2n (n is a positive integer) more than the number of teeth of the flexible external gear, and is a tooth shape setting method for a flat wave gear device,
Both the flexible external gear and the D-side rigid internal gear are module m spur gears,
The amount of radial deflection of the long axis of the rim neutral line passing through the center of the thickness of the root rim when the cross section perpendicular to the axis of the flexible external gear is bent elliptically is κmn (κ: deflection coefficient),
The main part of the tooth profile of the flexible external gear is a convex arc tooth profile composed of a convex arc of radius r centered on point A,
Determining an instantaneous center S of relative movement of the flexible external gear and the D-side rigid internal gear that are generated in accordance with the rotation of the wave generator;
A point where a line segment connecting the arc center of the convex arc and the instantaneous center intersects the convex arc is defined as a contact point C between the convex arc tooth profile of the flexible external gear and the tooth profile of the D-side rigid internal gear,
A flat type wave gear device characterized in that the movement locus of the contact point on the convex arc tooth profile of the flexible external gear accompanying the rotation of the wave generator is adopted as the tooth profile of the main part of the D-side rigid internal gear. Tooth profile setting method. In the tooth profile setting method of the flat type wave gear device according to claim 1,
A stationary rectangular coordinate system (Ox, y) with the center O of the D-side rigid internal gear as the origin is defined,
The radius of the neutral circle that is the neutral curve before deformation is rn, w is the amount of deflection, θ is the angle that the tangent to the neutral curve at the point P defined on the neutral curve is the x axis, and p is the origin O The length of the perpendicular line drawn from, and p is given by the tangent polar coordinates as

A rotation rectangular coordinate system (O) that shares the origin O and rotates the Y axis clockwise by φ with respect to the y axis so as to pass through a point Q on a virtual neutral circle corresponding to the point P on the neutral curve. -X, Y)
A rectangular coordinate system (Px _F , y _F ) is defined with the tangent drawn to the neutral curve at the point P on the neutral curve as the x _F axis and the straight line perpendicular to it as the y _F axis,
The coordinates (x _S , y _S ) on the stationary rectangular coordinate system (Ox, y) of the instantaneous center S are given by the following equation as a function of θ:

The coordinates of the center A of the convex arc are (x _a , y _a ) in the rectangular coordinate system (Px _F , y _F ), and the coordinates of the center A in the stationary rectangular coordinate system (Ox, y) ( x _A , y _A ) is given by

The stationary coordinates (x _C , y _C ) of the contact point C are given by

Rotation Cartesian coordinate system (O−) in which the above-mentioned θ is variable and the static coordinates (x _C , y _C ) obtained from the above equation are fixed to the D-side rigid internal gear from the stationary rectangular coordinate system (Ox, y). A method for setting a tooth profile of a flat wave gear device, wherein the tooth profile of the main part of the D-side rigid internal gear having the Y axis as the center of the tooth gap is obtained by the following equation after coordinate conversion to X, Y).

In the tooth profile setting method of the flat type wave gear device according to claim 2,
A tooth profile setting method for a flat wave gear device, wherein the deflection coefficient κ is in a range of 0.6 <κ <1.4.   The main part of the tooth profile of the flexible external gear and the main part of the tooth profile of the D-side rigid internal gear are set by the tooth profile setting method according to any one of claims 1 to 3. Flat type wave gear device.

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