JP3132777B2 - Flexible mesh gear - 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 cup-shaped flexible external gear.
More specifically, the present invention relates to a tooth shape determining technique in which the cup-shaped flexible external gear and the rigid internal gear can form an appropriate meshing state at any position in the axial direction of the device in such a flexible meshing gear device. It is.

[0002]

2. Description of the Related Art A typical example of a flexible meshing gear device is a harmonic reducer called a harmonic drive. As this harmonic reduction gear, a cup-shaped harmonic reduction gear shown in FIGS. 1 to 3 is known. As shown in these figures, the harmonic reduction gear 1 basically includes an annular rigid internal gear 2, a cup-shaped flexible external gear 3 disposed inside the internal gear 2, and a wave generator 4 mounted further inside the internal gear 2. Elements. A wave generator generally has an elliptical shape. With this wave generator, a cup-shaped flexible external gear is bent into an elliptical shape, and becomes a rigid internal gear at two places at both ends of its long axis. Are engaged. When the wave generator is rotated at high speed by a high-speed rotation output source such as a motor, these meshing positions also move in the circumferential direction. Since the cup-shaped flexible external gear is set to have 2n fewer teeth (n is a positive integer) than the rigid internal gear, there is a gap between the external gear and the internal gear as the meshing position moves. Relative rotation occurs. Normally, since the rigid internal gear is set in a fixed state, a reduced rotation output is obtained from the cup-shaped flexible external gear. An involute tooth profile is generally used as the tooth profile of the rigid internal gear and the cup-shaped flexible external gear in the flexible meshing gear device of this type.

A flex-meshing gear system is the invention of Sea Walton Masser (US Pat. No. 2,906,143).
, And seeing subsequent improvements and developments. For example,
The present inventor, in Japanese Patent Publication No. 45-41 I71,
It proposes the possibility of a so-called eccentric meshing and the possibility of a displaced involute tooth profile of such a gear train. The invention disclosed in this publication is based on the premise that the cup-shaped flexible external gear has the same amount of bending in any cross section perpendicular to the axis. That is, without considering the change in the amount of deflection of the cup-shaped flexible external gear in the axial direction, assuming that the cross section perpendicular to the axis of the cup-shaped flexible external gear takes the same shape at any position, A two-dimensional meshing tooth profile has been proposed in which a cup-shaped flexible external gear and a rigid internal gear are in an appropriate meshing state.

FIG. 3 shows a cross section of the cup-shaped flexible external gear that is bent into an elliptical shape, including the elliptical long axis 4a. As can be seen from this figure, the cup-shaped flexible external gear 3 bent into an elliptical shape has an open end 32.
The maximum amount of radial outward deflection on the side of
The amount of flexure gradually decreases along the apparatus axis 1a toward the boss 33 forming the cup bottom surface. Therefore, in order to set the meshing between the rigid internal gear and the cup-shaped flexible external gear in an appropriate state at any position in the tooth streak direction, the device axis of such a cup-shaped flexible external gear is required. It is necessary to consider the change in the amount of deflection in the direction 1a.

[0005]

In determining the tooth profile of a cup-shaped flexible external gear, a flexible meshing gear device which takes into account the fact that the amount of deflection of each cross section in the axial direction thereof is continuously changed is disclosed in Japanese Patent Application Laid-Open No. H10-163,873. 62-75153.

As disclosed in FIG. 4 of this publication, the contents disclosed in this publication are such that the teeth of the cup-shaped flexible external gear are replaced with the teeth of the rigid internal gear in the axial section including the major axis of the ellipse. Are arranged in parallel with the first. It is described that if the teeth are formed in this manner, a good tooth contact state is formed along the tooth streaks. However, as is clear from the analysis of the movement of the teeth of the flexible external gear with respect to the tooth groove of the rigid internal gear, at the cross-sectional position on the cup bottom side where the amount of bending is small, at the position deviated from the major axis position of the ellipse Interference of the teeth occurs, and a proper meshing state is not formed. Even if the gear cutting of the flexible external gear is described in
There is no guarantee that an effective tooth profile will be created even if the devices shown in FIGS. In addition, no specific description of how to determine the tooth profile is disclosed.

Next, Japanese Utility Model Laid-Open Publication No. Sho 62-96148 discloses that teeth of a flexible external gear are crowned. Further, Japanese Patent Application Laid-Open No. 2-62461 discloses that end relief processing is performed on the end of the tooth in order to prevent interference of the tooth at the end of the tooth streak. In any of these publications, it is not possible to form a proper meshing state at all cross-sectional positions in the direction of the tooth line.

On the other hand, Japanese Patent Application Laid-Open No. 63-115943 proposes a tooth profile in which a rigid internal gear and a flexible external gear of a flexible meshing gear device are continuously meshed. However, the invention disclosed in this publication also only considers the continuous meshing of the teeth in a certain section perpendicular to the axis in the direction of the tooth streaks. Therefore, there is no guarantee that an appropriate meshing state will be formed in a section that is separated in the tooth streak direction from the specific section under consideration.

As described above, most of the tooth profiles proposed so far in a flexible meshing gear device having a cup-shaped flexible external gear have a so-called two-dimensional meshing which considers only meshing at a cross section perpendicular to a certain axis. It is about. In addition, although tooth shapes that take into account so-called three-dimensional meshing in consideration of the change in the amount of deflection of the cup-shaped flexible external gear in the tooth band direction have been proposed as described above, they are not meshed in the tooth band direction. It is not based on an accurate analysis of the state and does not guarantee that a proper meshing state is formed at all cross-sectional positions. Therefore, it cannot be said that any tooth profile can form a good meshing, and there is still room for improvement in further improving the load capacity of this type of power transmission device.

SUMMARY OF THE INVENTION An object of the present invention is to provide a cup-shaped flexible meshing gear device which uses a popular involute tooth profile regardless of a special tooth profile, forms a good three-dimensional meshing, and thereby has a higher load. An object of the present invention is to realize a tooth profile having capability.

[0011]

According to the present invention, there is provided a flexible meshing gear device having a cup-shaped flexible external gear in a rigid internal gear and a cup-shaped flexible external gear. gears, and an involute tooth profile with the same reference pressure angle, also the tooth profile of the rigid internal gear and dislocation tooth profile of the addendum modification coefficient x _c, further, the tooth profile of the flexible external gear along its axis follows It is a continuously transposed allowed dislocation tooth according addendum modification coefficient x _f determined according to x _c by three expressions.

[0012] _{x f = 0.5z c χcotα 0 -x} c (1)

Χ = [0.5 (1 + kR) sin (2φ) ｛1−4j / (nR) + 4tan ² (α ₀ )} / (1 + R) −φ] / R (2)

Sin (2φ) tan {α ₀ −φ / R−1.5 sin (2φ) (1 + kR) / R / (1 + R)} + 0.5cos (2φ) −0.5 (1 + R) / (1 + kR) = 0 (3 )

Here, the contents of the symbols in the above equations are as follows. x _f: addendum modification coefficient x _c of the flexible external gear: shift coefficient of the rigid internal gear z _c: number of teeth k of the rigid internal gear: coefficient showing the deflection of any cross section perpendicular to the shaft of the flexible external gear n: stiffness 1/2 of the difference between the number of teeth of the internal gear and the number of teeth of the flexible external gear R: reduction ratio of the flexion gear type α ₀ : reference pressure angle χ: auxiliary angle indicating the influence of deviation on tooth thickness φ: tooth shape Auxiliary angle relating to the position of the contact point j: The value obtained by dividing the sum of 1/2 of the root rim thickness of the flexible external gear and the root of the tooth by the module.

[0016] Here, generally, as a rearrangement tooth profile of constant dislocation rigid internal gear (x _c = constant), addendum modification coefficient x _f of the flexible external gear by 3 expression described above is set.

[0017]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Referring to FIGS. 4 to 6, a method of deriving the above-described equations (1), (2) and (3) will be described for each embodiment, and the gist of the present invention will be described. The present embodiment is an example in which the present invention is applied to the tooth profile of the cup-shaped flexible external gear of the cup-shaped harmonic reduction gear shown in FIG. In the following description, the same parts as those in FIGS. 1 to 3 are denoted by the same reference numerals, and detailed description thereof will be omitted.

FIG. 4 shows a cross section of the cup-shaped flexible external gear 3 of this embodiment cut along a plane including a shaft. The cross section shown in this figure is a cross section position including the major axis of the ellipse in a state where the ellipse is bent by the wave generator.

External teeth 31 of the cup-shaped flexible external gear 3 of this embodiment
Are determined in accordance with the following three equations, and are obtained by continuously displacing from the open end 32 of the cup-shaped flexible external gear 3 toward the boss 33 which is the output side. Things. FIG. 5 shows this tooth profile in an enlarged manner.

The addendum modification coefficient x _f of the teeth of the external gear 31 is given by the following three equations described above.

[0021] _{x f = 0.5z c χcotα 0 -x} c (1)

Χ = [0.5 (1 + kR) sin (2φ) ｛1−4j / (nR) + 4tan ² (α ₀ )} / (1 + R) −φ] / R (2)

Sin (2φ) tan {α ₀ −φ / R−1.5 sin (2φ) (1 + kR) / R / (1 + R)} + 0.5cos (2φ) −0.5 (1 + R) / (1 + kR) = 0 (3 )

Here, the contents of the symbols in the above equations are as follows. x _f: addendum modification coefficient x _c of the flexible external gear: shift coefficient of the rigid internal gear z _c: number of teeth k of the rigid internal gear: coefficient showing the deflection of any cross section perpendicular to the shaft of the flexible external gear n: stiffness 1/2 of the difference between the number of teeth of the internal gear and the number of teeth of the flexible external gear R: reduction ratio of the flexion gear type α ₀ : reference pressure angle χ: auxiliary angle indicating the influence of deviation on tooth thickness φ: tooth shape Auxiliary angle relating to the position of the contact point j: The value obtained by dividing the sum of 1/2 of the root rim thickness of the flexible external gear and the root of the tooth by the module.

The reason why the teeth of the cup-shaped flexible external gear can achieve three-dimensional continuous meshing by adopting the tooth shapes determined as described above will be described together with how to derive the above three equations.

First, the present inventor has previously described Japanese Patent Publication No. 45-41.
No. 171 discloses that an involute curve can be used for the tooth profile of a deflected flexion gear system. However, as described above, the invention described in this publication is based on the premise that all the cross sections of the teeth of the cup-shaped flexible external gear have the same amount of deflection, that is, the same deviation coefficient. No consideration has been given to the fact that the cup-shaped flexible external gear has a variable amount of deflection in the axial direction as in the present application. That is, it is based on the premise that when the wave generator is inserted into the flexible external gear, the flexible external gear follows the cylindrical shape of the wave generator as it is. This premise applies to a flexible meshing gear device called a flat type or a pancake type in which the flexible external gear has a flat ring shape. However, the cup-shaped flexible external gear has a three-dimensional shape in the axial direction, that is, so-called coning. In this application,
The concept of continuous dislocation, in which the dislocation amount is variable in the axial direction of the gear, is applied to the tooth profile of the three-dimensional flexible external gear so as to ensure good tooth contact over the entire tooth streak.

The sum of the shift coefficients x _c and x _f of the rigid internal gear and the flexible external gear when the involute tooth profile having the same reference pressure angle is employed is the above-mentioned Japanese Patent Publication No. Sho 45-4.
This is given by the following equation (4) which makes the actual value equal to the equation (21) of Japanese Patent No. 1171.

X _c + x _f = 0.5z _c cotα _0c (4)

Here, α _0c : reference pressure angle of the rigid internal gear (= reference pressure angle of the flexible external gear) χ: auxiliary angle indicating the influence of deviation on tooth thickness

The present invention is an extension of the above equation (4) to three-dimensional meshing.

In addition, in the invention disclosed in Japanese Patent Publication No. 45-41171, the pitch circle of the flexible external gear is approximately regarded as a neutral line at the time of deformation.
In the present invention, the neutral line is set as follows. That is,
By setting a plane passing through the center of the bottom (rim) of the flexible external gear as a neutral plane, and setting an intersection of the plane and a cross section perpendicular to the axis of the flexible external gear as a neutral line for deformation. , Enables more accurate setting of the dislocation coefficient. For this reason, the auxiliary coefficient χ shown in the above equation (2) is calculated as follows:
This is a new proposal different from the first invention. Also, (2)
J in the equation is a coefficient indicating that the center of the rim is a neutral line. The coefficient jm represents the distance between the rim neutral line and the pitch circle. Φ in the expression (2) is an auxiliary angle corresponding to the movement of the teeth of the flexible external gear, and serves as a parameter for specifying the position where the teeth contact each other on the movement trajectory of the teeth. is there. The value of φ can be obtained by solving the above equation (3).

The basis of the three basic formulas (1), (2) and (3) for determining the transposition coefficient of the cup-shaped flexible external gear according to the present invention and the basis of the formula (4) will be described below.

First, equation (1) is derived from equation (4). The expression (4) has the same form as the expression (21) described in Japanese Patent Publication No. 45-41171, but in the present invention, the auxiliary angle χ is a variable considering three dimensions. The details of the derivation of equation (4) are described in the publication, but will be briefly described below with reference to FIG.

FIG. 6 is a detailed view for analyzing the meshing of the tooth profile of the deflected flexible meshing gear device. This figure is for the case of a negative deviation.

To reduce the backlash to zero, a value obtained by subtracting the reference pitch mπ (m: module) from the sum of the tooth thicknesses on the reference pitch circles of both gears is approximately d _c0 χ (= mz _c χ). It indicates that there should be anything.

When there is no deviation and the reference pitch circle of the rigid internal gear and the pitch curve of the flexible external gear (elliptic curve formed by bending the reference pitch circle) are in contact with each other on the major axis of the elliptic curve,
When the sum of the tooth thicknesses on the reference pitch circle of both gears is equal to the reference pitch mπ, the backlash is zero, but as in the present invention,
When given a deviation in the case of negative excursions of Figure 6, for example, when larger than the reference pitch mπ the sum of tooth thickness just corresponding to the length of the arc QP _0c, because the backlash becomes zero It is. The tooth thickness on the reference pitch circle of the cup-shaped flexible external gear and the rigid internal gear as the dislocation gear is respectively

[0037]

(Equation 1) Therefore, the following equation holds.

[0038]

(Equation 2) From this, equation (1) is obtained.

Next, the expression (2) is expressed by JP-B-45-41171.
This corresponds to the expression (22) in the publication. This (2
The derivation of equation 2) is given to the publication. The formula (2) of the present invention is based on the formula (22) in the above publication, but is derived as follows. Equation (16) of the publication

[0040]

(Equation 3) The effect of the distance jm from the rim neutral line of the teeth of the flexible external gear (here, the pitch point on the tooth profile is taken as a representative point)

[0041]

(Equation 4) And

This equation is derived as follows. First, the minute angle β + ξ in FIG.
From both equations (16) and (17) in

[0043]

(Equation 5) Ask like.

In Japanese Patent Publication No. 45-41171, when the reference pitch circle before deformation of the flexible external gear is regarded as a neutral circle, the degree of approximation is increased, and the center of the root rim is again regarded as a neutral circle. , Its radius r _n , half of the root rim thickness and the sum of the root height t are introduced, and the abscissa u and ordinate v of the point P in FIG. 6 are expressed as follows, respectively. I think.

[0045]

(Equation 6)

In Japanese Patent Publication No. 45-41171, (1)
Equation 3) represents the amount of deflection of the diameter. When this is expressed by the amount of deflection in the radial direction, it is r ₀ (ε + μ), which is on the deflection curve in the y direction (v direction in this description) from the axis. When the coordinates of are obtained, from the movement of the coordinate origin, r ₀ + r ₀ (ε + μ) −
[R ₀ (ε + μ) {1-cos (2φ)}] = r ₀ {1+ (ε +
μ) cos (2φ)｝, and by replacing r ₀ in this equation with r _n , the equation for v is obtained.

Next, the angle β formed by the radial radius of the point P with the vertical axis in this case is obtained as follows by further approximating the deformation of the expression using the approximate expression β = u / v.

[0048]

(Equation 7)

[0049] Here, compare the difference in the number of teeth between the flexible external gear and the rigid internal gear 2n, t / r _n 1, since a small amount, and r _n ≒ 0.5z _F m, the reduction ratio of the device the R z _F / (2n)
And represents, jm the _{t / r n / (0.5z F} m) = j / (z F /
2) Approximate by = j / (nR), ε = 1 / R and ε + μ =
Taking the relationship of (1 + Rk) / R / (1 + R) into account, the above-described expression of β is obtained as follows.

[0050]

(Equation 8)

The amount of deflection d of the cup-shaped flexible external gear, which is an increase from the true circle diameter of the elliptical major axis of an arbitrary section perpendicular to the axis shown in FIG. Introducing the deflection coefficient k = d / d _e divided by _e yields ε and ε + μ in the above publication,

Ε = 1 / R

Ε + μ = (1 + Rk) / R / (1 + R), and the relationship between the reference pressure angle α _0c of the rigid internal gear and the engagement pressure angle α _bc is expressed by the reference pressure angle α of the flexible external gear in the present invention.
_{Since f} is made equal to the reference pressure angle α _0c of the rigid internal gear, α _0c = α _f = α _bc + ξ with reference to FIG.
Is a very small angle, and from the description of item (c) on page 8 of JP-B-45-41171, approximately ξ = 2 (ε + μ) sin (2
φ), and for ε + μ,
According to equation (12) on page 4 of JP 1171, ε + μ = i
+ Λ−2, the following notation using the reduction ratio R between i and λ

[0054]

(Equation 9) By using, the above notation of ε = 1 / R ε + μ = (1 + Rk) / R / (1 + R) is obtained, from which ξ is expressed as follows. ξ = 2 (1 + Rk) / R / (1 + R) sin (2φ)

Β is expressed as follows.

[0056]

(Equation 10)

Further, regarding (invα _0c −invα _bc ),

[0058]

[Equation 11] And can be transformed. Referring to FIG. 6, χ = invα _0c −invα
_bc− β, and using the above equation of invα _0c −invα _bc and β to express the reference pressure angle α _0c of the rigid internal gear as a reference pressure angle α ₀ common to both gears, the following equation (2) is obtained. Is obtained.

The formula (3) of the basic formula represents the reduction ratio R and the reference pressure angle α ₀ of the flexible meshing gear device (JP-B-45-411).
When the coefficient k deflection indicating the deflection of any cross section perpendicular to the shaft 71 No. those that have been expressed as alpha _0c in Japanese) and the flexible external gear is given, determining the auxiliary angle φ about the position of the contact point of the tooth It is an expression. The tangent of the inclination angle α _c of the tangent to the trajectory c at the point P in FIG.

[0060]

(Equation 12) On the other hand, in relation to α _f ,
As shown in column 17 (f) on page 9 of JP-A-71, αf is the reference pressure angle α ₀ (in Japanese Patent Publication No. 45-41171, α _f is indicated as α _0c , but since it is an amount common to both gears, α _f Considering that it is α ₀ ),

[0061]

(Equation 13) It is expressed as Eliminating α _c from both equations, and then ε =
By substituting 1 / R, ε + μ = (1 + Rk) / R / (1 + R), equation (3) is obtained.

The above is the basis of the formulas of the present invention. These formulas (1), (2), tooth profile of the cup-shaped flexible external gear determined defines the specifications of the gear according to (3), when the dislocation coefficient x _c of the rigid internal gear is constant, The shape is as shown in FIG. As shown in this figure, the curve is a multi-order convex curve in which the amount of dislocation gradually increases toward the output side in the tooth streak direction. It has been confirmed by computer simulation that a good meshing state is formed in the entire tooth streak direction by employing the continuously displaced tooth profile defined in this way. In the figure, for comparison,
A tooth profile defined by the above-mentioned Japanese Patent Application Laid-Open No. 62-75153 is indicated by a broken line.

[0063]

As described above, according to the present invention,
The dislocation coefficient of the rigid internal gear is selected in advance, and the dislocation coefficient of the cup-shaped flexible external gear is obtained as a function of the deflection coefficient from the above equations (1), (2) and (3). Accordingly, the rigid internal gear is processed as a constant or variable shift gear, and the cup-shaped flexible external gear is processed as a continuous shift gear. Therefore, according to the present invention, it is possible for the first time to realize good three-dimensional meshing in which troubles such as interference do not occur over the entire gears in the tooth streak direction.

[Brief description of the drawings]

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

FIG. 2 is a front view of the apparatus of FIG.

FIG. 3 is a longitudinal sectional view showing a bent state of a cup-shaped flexible external gear in the apparatus of FIG. 1;

FIG. 4 is a longitudinal sectional view showing a cup-shaped flexible external gear having a continuously shifted tooth profile according to the present invention.

FIG. 5 is a partially enlarged sectional view showing the tooth profile of the cup-shaped flexible external gear of FIG. 4 in an enlarged manner.

FIG. 6 is an explanatory diagram for analyzing details of a tooth profile according to the present invention.

[Explanation of symbols]

 DESCRIPTION OF SYMBOLS 1 ... Cup type harmonic reduction gear 1a ... Device axis line 2 ... Rigid internal gear 3 ... Cup-shaped flexible external gear 31 ... External teeth 32 ... Open end 33 ... Boss 4 Wave generator 4a Long axis of ellipse

Claims (2)

(57) [Claims] 1. A rigid internal gear, a cup-shaped flexible external gear disposed inside the rigid internal gear, and radially bending the external gear to partially mesh with the rigid internal gear. A flexible meshing gear device comprising: a wave generator that generates a relative rotation between the rigid internal gear and the flexible external gear by moving a meshing position in a circumferential direction; tooth profile of fLEXIBLE outer gear is an involute tooth profile with the same reference pressure angle, the tooth profile of the rigid internal gear is a dislocation tooth having a dislocation coefficients x _c, the tooth profile of the flexible external gear, the axial flexible meshing type gear device, characterized in that along the heart is a dislocation tooth profile was continuously rearrangement according addendum modification coefficient x _f determined according to the addendum modification coefficient x _c by the following formula 3. x _f = 0.5z _c χcotα ₀ -x _c (1) χ = [0.5 (1 + kR) sin (2φ) ｛1-4j / (nR) + 4tan ² (α ₀ ) 1 / (1 + R) -φ] / R (2) sin (2φ) tan {α ₀ -φ / R−1.5 sin (2φ) (1 + kR) / R / (1 + R)} + 0.5cos (2φ) −0.5 (1 + R) / (1 + kR) = 0 (3) where, x _f: flexible external gear shift coefficient x _c: shift coefficient of the rigid internal gear z _c: the number of teeth of the rigid internal gear k: the deflection of any cross section perpendicular to the shaft of the flexible external gear Coefficient n: 1/2 of the difference in the number of teeth between the rigid internal gear and the flexible external gear R: Reduction ratio of the flexible meshing gear α ₀ : Reference pressure angle χ: Auxiliary indicating the effect of deviation on tooth thickness Angle φ: Auxiliary angle related to the position of the contact point of the tooth profile j: Value obtained by dividing the sum of 1/2 of the root rim thickness of the flexible external gear and the root of the tooth by the module 2. The flexible meshing gear device according to claim 1, wherein the tooth profile of the rigid internal gear is a dislocation tooth profile of a constant dislocation.