JP3230596B2 - Method of forming three-dimensional non-displacement tooth profile of flexible meshing gear device - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a flexible meshing gear device having a rigid internal gear having a tooth difference of 4n (n is a positive integer) and a cup-shaped flexible external gear. The present invention relates to a tooth profile of a flexible external gear and a rigid internal gear.

[0002]

2. Description of the Prior Art A typical flexible meshing gear system is a circular rigid internal gear, a flexible external gear disposed inside the internal gear, and an elliptical wave generator mounted inside the internal gear. It is basically composed of The flexible external gear is bent into an elliptical shape by the elliptical wave generator, and meshes with the rigid internal gear at both ends of the elliptical major axis direction. The flexible external gear has 2n fewer teeth (n is a positive integer) than the rigid internal gear. When the wave generator is rotated, the two meshing positions of the two gears also move in the circumferential direction in accordance with the rotation, and as a result, relative rotation occurs between the two gears according to the difference in the number of teeth. This flexible meshing gear device includes a so-called flat or pancake-type flexible meshing gear device in which a flexible external gear has a flat cylindrical shape, and a cup-shaped flexible meshing gear in which a flexible external gear has a cup shape. They are roughly divided into devices.

[0003] The basic tooth profile employed for both gears in a flexion gear system is a straight line. Such a tooth profile is disclosed, for example, in U.S. Pat. No. 2,906,143. The adoption of an involute tooth profile as the tooth profile of both gears has been disclosed by the present inventors in Japanese Patent Publication No.
No. 4,171,171.

Further, the present inventors have disclosed in
In Japanese Patent No. 15943, in order to increase the load capacity of a flexion gear device, the tooth profile of the tooth flank of both gears is moved by a rack approximation of the teeth of the external gear with respect to the internal gear determined by the shape of the wave generator. A method has been proposed in which a required range of the locus is converted into a curve by similarity conversion at a contraction ratio of 1/2 from a limit point of meshing on the locus. According to this method, both gears can continuously mesh with the tooth profile of the tooth tip during the entire meshing process.

[0005]

However, Japanese Patent Application Laid-Open No.
The method disclosed in Japanese Patent No. 115943 is based on a flexible meshing gear device called a flat type or a pancake type equipped with a cylindrical flexible external gear. For this reason, if this type is employed as it is in a cup-shaped flexing meshing gear device in which the flexible external gear has a cup shape, continuous meshing cannot be guaranteed.

That is, the amount of bending of the cup-shaped flexible external gear changes in the axial direction due to the coning. However, the above method is intended for a cylindrical flexible external gear in which no coning occurs. Therefore, even if the tooth profile of both gears in the cup-shaped flexible meshing gear device is formed by this method, a continuous meshing state is formed at a certain cross section in the tooth trace direction of both gears, but other cross sections are formed. Then, problems such as interference occur. Thus, the above method is effective for a cylindrical flexible external gear, but is not suitable for a cup-shaped flexible external gear as it is.

Japanese Patent Application Laid-Open Nos. 62-75153 and 2-62461 do not disclose forming a tooth profile in consideration of the coning of such a cup-shaped flexible external gear. However, all of them require special additional processing such as crowning and releasing teeth.

An object of the present invention is to provide a flexible meshing gear device having a rigid internal gear having a tooth difference of 4n (n is a positive integer) and a cup-shaped flexible external gear, such as crowning and relief. It is an object of the present invention to propose a tooth profile that can form a wider range of meshing with the rigid internal gear without interference over all tooth traces of the cup-shaped flexible external gear without additional processing.

[0009]

According to the present invention, in a cup-shaped flexible meshing gear device, the locus of movement of each tooth in each section of the cup-shaped flexible external gear in the tooth trace direction is along the tooth trace. It has been newly found that they gradually change with a gradual decrease in the amount of bending, and that they form one envelope when their motion trajectories are superimposed on one plane. In the present invention, a method of rack approximation is introduced to simplify the analysis, and an equation representing this envelope is calculated.

Further, the present inventor has newly added that this envelope is a similar curve obtained by reducing the curve representing the movement trajectory of a cross section perpendicular to the teeth of the opening of the cup-shaped flexible external gear by half. I found it.

In the present invention, on the premise of these two newly discovered matters, a rigid internal gear and a cup-shaped flexible gear having a tooth difference of 4n (n is a positive integer) are as follows. The tooth profile of both gears is determined in a cup-shaped flexible meshing gear device having an external gear. First, the above envelope is obtained. Next, on this envelope, a required portion of the envelope is subjected to similarity conversion at a contraction ratio of 1/2 from a limit point of meshing selected in consideration of the teeth used, thereby obtaining a similarity curve. Then, this similar curve is defined as the convex tooth shape of the addendum in the cup-shaped flexible external gear and the rigid internal gear having a difference in the number of teeth of 4n. Further, the roots of both gears are concave teeth having a shape along a point symmetry curve of the addendum tooth at each pitch point.

[0012]

Embodiments of the present invention will be described below with reference to the drawings.

FIGS. 1 and 2 are a perspective view and a front view, respectively, of a known cup-shaped flexible meshing gear device. The flexible meshing gear device 1 includes an annular rigid internal gear 2, a cup-shaped flexible external gear 3 arranged inside the ring-shaped internal gear 2, and an elliptical wave generator 4 mounted inside the ring-shaped flexible external gear 3. .
The cup-shaped flexible external gear 3 is in an elliptical shape by an elliptical wave generator 4.

FIGS. 3, 4 and 5 show the bending state of the cup-shaped flexible external gear 3 due to the coning in the cross section including the shaft. FIG. 3 shows a state before being bent by the wave generator 4. FIG. 4 is an axial cross section including a major axis in a state where the wave generator 4 is bent into an elliptical shape. FIG. 5 is an axial section including a short axis in a state of being bent into an elliptical shape. As can be seen from these figures, the cup-shaped flexible external gear 3 has the largest amount of bending at the opening 3a due to the coning, and the amount of bending gradually decreases toward the diaphragm 3b. Here, the amount of deflection means an increase in the length of the major axis of the elliptical neutral line from the diameter of the neutral line when the circle is a perfect circle.

FIGS. 6, 7 and 8 show the trajectory in which one tooth of the cup-shaped flexible external gear 3 moves with respect to the tooth groove of the rigid internal gear 2 in the bending and meshing gear device 1. This is shown as a rack approximation when the number of teeth of two or three becomes infinite. Here, the motion trajectory shown in FIG. 6 is a cross section perpendicular to the tooth at the position 31 of the opening 3 a in the tooth 30 of the cup-shaped flexible external gear 3 (non-deflection cross section having a normal deflection amount).
The motion trajectory shown in FIG. 7 is obtained in a section perpendicular to the tooth at the position 32 at the center of the tooth muscle, and the motion trajectory shown in FIG. 8 is the diaphragm 3b of the tooth muscle.
This is obtained in a section perpendicular to the tooth at the position 33 of the side end.

Here, the normal amount of deflection means that the amount of deflection is the reference pitch circle diameter of the flexible external gear and the reduction ratio R (the number of teeth of the flexible external gear is the number of teeth of the rigid internal gear and the number of teeth of the flexible external gear. (The value divided by the difference), and this state is called non-deflection. Negative deviation refers to a state in which the amount of deflection is smaller than the amount of normal deflection. FIGS. 7 and 8 show the case of this negative deviation.

The tooth profile shown in FIG.
It is a curved tooth profile of irregularities determined by the method disclosed in Japanese Patent No. 15943. As can be seen from these figures, a section perpendicular to the teeth of the opening 3a shown in FIG. 6 (non-deflection section).
, A continuous meshing state is formed, but at other positions in the tooth trace direction shown in FIGS. 7 and 8, tooth interference occurs.

When this motion trajectory is expressed by a mathematical formula for an arbitrary section perpendicular to the teeth, the following equation (1) is obtained.

[0019]

(Equation 1)

Where x: coordinates in the direction of the pitch line of the rack y: coordinates in the direction of gear teeth in the rack m: module n: 1/2 of the difference in the number of teeth between the rigid internal gear and the flexible external gear η: angle parameter κ: Deflection coefficient (Value obtained by dividing the amount of deflection of an arbitrary section perpendicular to the axis of the tooth trace of the flexible external gear by the normal amount of deflection)

Here, a method of deriving the equation (1) will be described.

First, the radius of the perfect circle before deformation of the rim neutral line of the external gear 3 is rn, the deformation amount (bending amount) of the radius on the long axis and short axis of the approximated ellipse after deformation is w, Is given by the following equation using tangential polar coordinates (see FIG. 15).

P = r _n + w cos (2θ) (6) where: p: length of a perpendicular line from the coordinate origin to the tangent of the curve θ: angle between the tangent of the curve and the minor axis of the approximate ellipse

Using polar coordinates (r, ζ) with the angle of deviation from the major axis of the approximate ellipse as ζ, this curve is expressed by the following equation.

[0025] _{r = {r n + w cos} (2θ)} / cosμ ζ = θ-μ (0 ≦ θ <2π) (7) Here ^{μ = tan -1 [2wsin (2θ} ) / {r n + w cos ( 2θ)｝]

Μ is the angle formed by the normal of the neutral line and the radius line.

Assuming that the wave generator is fixed and the flexible external gear is driven from the rigid internal gear, the equation of motion of the teeth of the flexible external gear relative to the teeth of the rigid internal gear is shown in FIG. Then, it is derived as follows.

In the stationary coordinate system O-x ₀ , y ₀ , the rotation angle of the rigid internal gear is φ, the inclination angle of the target tooth of the flexible external gear is θ, the rigid internal gear and the flexible external gear are the number of teeth of each z _C of the z _F, flexible coordinate system with the teeth of the external gear O _F -x _F, y _F
The origin O _{when F} is fixed so as to coincide with the rim center line, the coordinate system O _F -x _C fixed to the rigid internal gear, the coordinates of the origin O _F flexible external gear coordinate system as viewed from the y _C Is given by the following equation.

[0029] _{x c = r n sin (θ} -φ) -0.5w {sin (3θ-φ) + 3sin (θ + φ)} y c = r n cos (θ-φ) -0.5w {cos (3θ-φ) −3cos (θ + φ)｝ (8)

The angular velocities of the rigid internal gear and the flexible external gear are denoted by ω _C and ω _F , respectively, the peripheral speed along the rim neutral line of the teeth of the flexible external gear is denoted by v, θ = 0 at time t = 0, that shall point O _F matches the point on the approximate ellipse long axis, the inclination of the teeth of the flexible external gear at time t theta, the moving distance is s along therebetween rim neutral line.

S is given by r _n θ− (3/2) w sin (2θ), where φ = ω _C , t = ω _C , s / v = ω _C , and s / (ω _F r
_From the relationship _n ), the following expression indicating the relationship between θ and φ is established as j = ω _F / ω _C = z _C / z _F.

Φ = {θ−1.5w sin (2θ) / r _n } / j (9)

[0033] (8) Using equation in expression (9), the angle θ was set to parametric, relative motion trajectory is obtained rigid internal gear of the coordinate origin O _F of the teeth of the flexible external gear.

A flexible external gear of a flexible meshing gear device,
Many of the rigid internal gears have a large number of teeth exceeding 160, and are close to the shape of a rack, so that the meshing of teeth is close to the meshing of racks. Therefore, consider the limit shift to make the number of teeth infinite in the above equations.

The reference pitch circle radius of the rigid internal gear is defined as r _C, and the origin O is defined as the pitch point O from the coordinate system Ox _C , y _C.
Transfer _{and C,} the coordinate system was further reversing the direction of the y _C coordinate O _C -
Move to x, y (see FIG. 16).

A module having both teeth is assumed to be m, and a tooth number difference coefficient n = (z _C −z _F ) / 2 and a deflection coefficient κ for defining the deflection of the flexible external gear are introduced, and the deformation amount w is defined as w. = Κmn. Here, while a constant r _C -r _n, r _n →
Assuming that →, j → l, the above equation (1) representing the relative movement of the teeth approximated by the rack is obtained from the equations (8) and (9).

When η is eliminated from equation (1), the following equation (2) is obtained.
Is obtained.

[0038]

(Equation 2)

Here, considering κ as a variable and partially differentiating equation (2) with κ and solving for κ, the following equation (3) is obtained.

[0040]

(Equation 3)

By eliminating κ from equations (2) and (3),
The envelope of the desired motion trajectory is obtained. This is given by equation (4)
It is listed below.

[0042]

(Equation 4)

The following can be understood from the definition of the envelope. When one value of the bending coefficient κ is determined, this corresponds to selecting a tooth perpendicular section having a bending amount corresponding to the determined value of the coefficient κ in the tooth trace direction of the cup-shaped flexible external gear.
In the section perpendicular to the tooth, the envelope and the motion locus of the tooth are in contact at the value of y obtained by substituting the value of the coefficient κ into the equation (3). In other words, the envelope plays the role of the locus of tooth movement in the vicinity corresponding to the value of y.

FIG. 9 shows this envelope E. In this figure, for reference, five movement trajectories L
1, L2, L3, L4, L5 are also drawn. FIG.
0 has five movement trajectories L of the teeth in a section perpendicular to each tooth in the tooth trace direction of the flexible external gear used for obtaining the envelope E.
1, L2, L3, L4, L5 are depicted with one tooth of the cup-shaped flexible external gear and the tooth space of the rigid internal gear.

Here, the present inventor has found that this envelope E is nothing but a similar curve obtained by reducing the locus curve where κ = 1 in equation (2) by 縮小. This means
This can be confirmed by setting κ = 1 in equation (2), setting y to 2y, and using the relation of equation (5) described below.

[0046]

(Equation 5)

FIG. 11 is an explanatory diagram for deriving the tooth profile of the present invention from the envelope E. Now, as a required portion of the envelope E, a curve portion E (A, B) from the vertex A to the point B is obtained.
(In general, it is not necessary to include the vertex A as a required portion, and a required portion located below the vertex A with reference to a point slightly below the vertex A). In this case, the interval between the curved portions E (A, B) in the height direction is set to be twice as long as the tooth addendum of the rigid internal gear and the cup-shaped flexible external gear. A similarity curve E1 (M, B) obtained by performing similarity conversion of the curve portion E (A, B) from one end point B at a contraction ratio of 1/2 is defined as a convex tooth profile at the end of the rigid internal gear. In the example shown in FIG.
A point-symmetric curve E2 (M, A) with respect to a point M of (M, B) (this point is a pitch point) is defined as a convex tooth profile at the end of the cup-shaped flexible external gear. Similarly, these curve portions E2
By using (M, A) and E1 (M, B), a concave tooth profile at the root of the rigid internal gear and a concave tooth profile at the root of the cup-shaped flexible external gear are obtained.

The tooth profiles of the tooth flank thus formed elapse when the teeth of the external gear move in the tooth space of the internal gear.
It is ensured that the contact is almost correctly made at the cross section corresponding to κ corresponding to each value of. This is because, when viewed in the rack approximation, for example, the tooth profiles of the tooth tips that are in contact with each other at the point Q in FIG. 11 are symmetric with respect to the point Q. As shown in the figure, the tip point P of the flexible external gear coincides with the point obtained by extending the straight line BQ twice beyond the point Q, and the inclination of the tangent line of both tooth shapes becomes equal at the point Q. It is based on.

Therefore, the tooth profile obtained in this way is
If these gears are used in a flexible meshing gear device provided with a rigid internal gear and a cup-shaped flexible external gear having a difference in the number of teeth of 4n, there is no interference over the entire tooth trace direction. Thus, a wider range of engagement between the two gears can be realized.

FIGS. 12, 13 and 14 show examples of meshing of the tooth profiles thus formed. FIG.
2 is a section perpendicular to the tooth at the position 31 of the opening (non-deflection section),
FIG. 13 shows the meshing of the tooth trace at a position 32 at the center of the tooth trace, and FIG. 14 shows the meshing of the tooth trace at the position 33 at the end of the tooth side on the diaphragm side (for each position, see FIG. 3). . As can be seen from these figures, the tooth of the present invention realizes a part of continuous contact according to the degree of contact between the envelope and the motion trajectory of this cross section in each tooth perpendicular cross section in the tooth trace direction. I have.

As can be seen by comparing these figures with FIGS. 6, 7 and 8, which show the movement trajectory of the conventional tooth at the same position in the tooth trace direction, if the tooth profile of the present invention is adopted, It can be seen that a continuous meshing state is formed in any of the cross sections perpendicular to the teeth in any direction, and no trouble such as interference has occurred.

[0052]

As described above, according to the present invention,
A flexible meshing gear device having a cup-shaped flexible external gear, wherein the cup-shaped flexible external gear is crowned,
Smooth continuous between the internal gear over the entire tooth trace from the opening to the end of the tooth trace on the tire flam side, while maintaining the root thickness constant without additional processing such as releasing. Engagement can be realized. Therefore, according to the present invention, it is possible to obtain a cup-shaped flexible meshing gear device capable of realizing three-dimensional meshing with high strength, high rigidity and high accuracy.

[Brief description of the drawings]

FIG. 1 is a perspective view of a cup-shaped flexible meshing gear device.

FIG. 2 is a schematic front view of the cup-shaped flexible meshing gear device of FIG.

FIG. 3 is a cross-sectional view of a cup-shaped flexible external gear before deformation for explaining a state of bending of the cup-shaped flexible external gear due to coning in the flexible meshing gear device of FIG. 1;

FIG. 4 is a view for explaining a bending state of the cup-shaped flexible external gear caused by the coning in the flexible meshing gear device shown in FIG. 1; FIG.

FIG. 5 is a view showing a short axis of the cup-shaped flexible external gear after being deformed into an elliptical shape for describing a state of bending of the cup-shaped flexible external gear due to the coning in the flexible meshing gear device of FIG. 1; FIG.

FIG. 6 is a view for explaining a trajectory in which one tooth of the cup-shaped flexible external gear moves with respect to the tooth space of the rigid internal gear, and illustrates a tooth at an opening position of the cup-shaped flexible external gear; It is a figure showing a locus of movement of a tooth in a perpendicular section (non-deflection section).

FIG. 7 is a diagram for explaining a trajectory in which one tooth of the cup-shaped flexible external gear moves with respect to the tooth space of the rigid internal gear, and illustrates a center of the cup-shaped flexible external gear in a tooth trace direction. FIG. 6 is a diagram illustrating a motion locus of a tooth in a section perpendicular to the tooth at the position.

FIG. 8 is a view for explaining a trajectory in which one tooth of the cup-shaped flexible external gear moves with respect to the tooth space of the rigid internal gear, and illustrates the tooth side of the cup-shaped flexible external gear on the diaphragm side. It is a figure showing a locus of movement of a tooth of a section perpendicular to a tooth at an end part position.

FIG. 9 is a diagram showing an envelope serving as a base for guiding the tooth profile of the present invention.

FIG. 10 is a diagram showing a movement trajectory of a rigid internal gear of one tooth of a cup-shaped flexible external gear for guiding the envelope of FIG. 9 with respect to a tooth space.

FIG. 11 is an explanatory diagram for deriving the tooth profile of the present invention based on the envelope of FIG. 9;

FIG. 12 is a view for explaining a trajectory in which one tooth of the cup-shaped flexible external gear whose tooth profile is determined according to the present invention moves with respect to the tooth space of the rigid internal gear; It is a figure showing a locus of movement of a tooth of a section perpendicular to a tooth (non-deflection section) of an opening position of an external gear.

FIG. 13 is a view for explaining a trajectory in which one tooth of the cup-shaped flexible external gear whose tooth profile is determined according to the present invention moves with respect to the tooth space of the rigid internal gear; It is a figure showing a locus of movement of a tooth of a section perpendicular to a tooth at a center position of an external gear in a tooth trace direction.

FIG. 14 is a view for explaining a trajectory in which one tooth of the cup-shaped flexible external gear whose tooth profile is determined according to the present invention moves with respect to the tooth space of the rigid internal gear; FIG. 7 is a diagram illustrating a locus of movement of a tooth in a cross section perpendicular to the tooth at the end of the tooth trace of the external gear on the diaphragm side.

FIG. 15 is an explanatory diagram for obtaining a deformed curve of a flexible external gear using tangential polar coordinates.

FIG. 16 is an explanatory diagram for deriving a motion equation of teeth of a flexible external gear with respect to a rigid internal gear.

[Explanation of symbols]

DESCRIPTION OF SYMBOLS 1 ... Cup-shaped flexible meshing gear device 2 ... Rigid internal gear 3 ... Cup-shaped flexible external gear 3a ... Opening of cup-shaped flexible external gear 3b ... Cup-shaped possible Diaphragm of flexible external gear 30: Teeth of cup-shaped flexible external gear 31: Opening position in the tooth trace direction of teeth of cup-shaped flexible external gear 32: Cup-shaped flexible outside Central position 33 in the tooth trace direction of the gear teeth 33... End position on the diaphragm side in the tooth trace direction of the cup-shaped flexible external gear 4. Wave generator E. Envelope E (A, M ) ... Part of the envelope E1 (M, B) ... Similar curve obtained by reducing a part of the envelope to 1/2

Claims (2)

(57) [Claims] 1. A and the rigid internal gear, which is arranged inside U
A flexible external gear having a stepped shape, and a wave that flexes the flexible external gear in the radial direction to partially mesh with the rigid internal gear and to move the meshing position in the circumferential direction.
A flexible external gear having 4n (n is a positive integer) less teeth than the rigid internal gear;
From the diaphragm side forming the cup-shaped bottom of the car
Due to the coning over the opening, the flexible
The amount of deflection of the external gear in the radial direction is
Gears that increase gradually in proportion to their distance
Flexible external gear and rigid internal gear in an arrangement
A method of forming a tooth profile according to claim 1, wherein a plurality of cross sections perpendicular to the tooth trace direction of the flexible external gear are provided.
At the position, the outer flexible portion relative to the rigid internal gear.
By calculating the motion trajectories of gear teeth by rack approximation and superimposing these motion trajectories on one tooth perpendicular plane,
The envelope of these motion trajectories is determined, and from this envelope, the distance between both ends in the height direction is determined by the rigid internal gear.
And a curved part that is twice as large as the length of the end of the flexible external gear
Cut out the minute, and of the points at both ends of the
With the point on the side far from the vertex of the envelope as the origin,
The similarity curve is obtained by performing similarity conversion on the line part at a contraction ratio of 1/2.
Is formed, and this similar curve is converted to a rigid internal gear having 4n teeth difference and a flexible
It employed as convex tooth profile of the end teeth of sexual outer gears, the tooth of the gears, to a concave tooth shape along the point-symmetric curve of addendum tooth profile for each pitch point Thus, the three-dimensional dislocation tooth The method for forming a three-dimensional non-shifting tooth profile of a flexible meshing gear device, characterized in that: Wherein a rigid internal gear, which is arranged inside U
A flexible external gear in the form of a tip, and a wave generation for bending the flexible external gear in the radial direction to partially mesh with the rigid internal gear and to move the meshing position in the circumferential direction. and a vessel, the flexible external gear is 4n Like than the number of teeth of the rigid internal gear (n is a positive integer) fewer in which flexible meshing type gear device equipped with a number of teeth, the flexible and the rigid internal gear A toothed gear device according to claim 1, wherein each tooth profile of the external gear is a three-dimensional non-displacement tooth profile formed by the tooth profile forming method according to claim 1.