JPH05209655A - Deflection engagement type gear device - Google Patents

Abstract

PURPOSE:To provide a high load capability by forming the tooth forms of gears at a specific addendum modification coefficient in a gear device moving the engaging position of a rigid internal gear and a cup-shaped flexible external gear in the peripheral direction to generate relative rotation between both gears. CONSTITUTION:Harmonic reduction gears 1 called as a harmonic drive are constituted of a circular rigid internal gear 2 and a wave motion generator 4 fitted on its inside, a cup-shaped flexible external gear 3 having the number of teeth less than that of the rigid internal gear 2 by 2n is deflected into an elliptical shape by the wave motion generator 4, and the flexible external gear 3 is engaged with the rigid internal gear 2 at two positions on both ends of the long axis. The tooth shapes of the gears 2, 3 are made the involute tooth shape having the same reference pressure angle, and the tooth shape of the internal gear 2 is made the transitional tooth shape having the addendum modification coefficient xc. The tooth shape of the external gear 3 is made the transitional tooth shape continuously transited according to the addendum modification coefficient xf determined in response to the above addendum modification coefficient xc from the equation I along the axis.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a flexible mesh type gear device having a cup-shaped flexible external gear.
More specifically, the present invention relates to a tooth profile determining technique in which a cup-shaped flexible external gear and a rigid internal gear can form a proper meshing state at any position in the device axial direction in such a flex meshing type gear device. Is.

[0002]

2. Description of the Related Art A typical example of a flexible mesh type gear device is a harmonic speed reducer called a harmonic drive. As this harmonic reducer, the cup-shaped harmonic reducer shown in FIGS. 1 to 3 is known. As shown in these figures, the harmonic speed reducer 1 has a basic structure including an annular rigid internal gear 2, a cup-shaped flexible external gear 3 arranged inside thereof, and a wave generator 4 mounted inside thereof. As an element. The wave generator is generally in the shape of an ellipse, and the wave generator bends the cup-shaped flexible external gear into an elliptical shape so that it becomes a rigid internal gear at two locations at both ends of its long axis. It is meshed. When the wave generator is rotated at a high speed by a high-speed rotation output source such as a motor, the meshing position of these is also moved 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 decelerated rotation output can be 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 flexural mesh type gear device of this type.

The flexible mesh type gear device is the invention of Mr. Sea Walton Masser (US Pat. No. 2,906,143).
Beginning with, we are looking at improvements and developments thereafter. For example,
The present inventor has disclosed in Japanese Patent Publication No. 45-41I71.
It proposes the possibility of so-called offset meshing and the possibility of dislocation involute tooth profile of such a gear device. The invention disclosed in this publication is premised on that the cup-shaped flexible external gear has the same amount of flexure in any cross section perpendicular to the axis. That is, without considering the change in the bending amount 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 has the same shape at any position, A two-dimensional meshing tooth profile is proposed in which the cup-shaped flexible external gear and the rigid internal gear are brought into an appropriate meshing state.

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

[0005]

In determining the tooth profile of a cup-shaped flexible external gear, a flexural mesh type gear device which takes into account the fact that the flexural amount of each cross section in the axial direction thereof continuously changes is disclosed in Japanese Patent Application Laid-Open No. Sho-AO. No. 62-75153.

As can be seen from FIG. 4 of this publication, the content disclosed in this publication is such that the teeth of a cup-shaped flexible external gear are the teeth of a rigid internal gear in an axial section including the major axis of an ellipse. It is arranged to be parallel to. It is described that when the teeth are formed in this manner, a good tooth contact state is formed along the tooth streaks. However, as is clear from an analysis of the motion 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 bottom side of the cup with a small amount of deflection, the position deviates from the long axis position of the ellipse. Interference between the teeth occurs, and a proper meshing state is not formed. Even if the gear cutting of the flexible external gear is as described in
Even if the device shown in FIG. 2 and FIG. 2 is devised, there is no guarantee that an effective tooth profile will be created. In addition to this, regarding the tooth profile, no specific description of how to determine it is disclosed.

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

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

As described above, in the flexural meshing type gear device having the cup-shaped flexible external gear, most of the tooth profiles proposed so far are so-called two-dimensional meshing considering only meshing in a cross section perpendicular to a certain axis. It is about. Further, although the tooth profile in consideration of so-called three-dimensional meshing in consideration of the change in the bending amount of the cup-shaped flexible external gear in the tooth stripe direction has been proposed as described above, these are meshed in the tooth stripe 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-section positions. Therefore, it cannot be said that any tooth profile can form a good mesh, 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 type gear device with an involute tooth profile which is widely used regardless of a special tooth profile and forms a favorable three-dimensional meshing, thereby providing a higher load. It is to realize a tooth profile with the ability.

[0011]

In order to solve the above-mentioned problems, in the present invention, in a flexible mesh type gear device having a cup-shaped flexible external gear, a rigid internal gear and a cup-shaped flexible external gear are provided. The gear has an involute tooth profile having the same reference pressure angle, the tooth profile of the rigid internal gear has a dislocation tooth profile with a dislocation coefficient x _c , and the tooth profile of the flexible external gear has the following profile along its axis. It is a continuously transposed allowed dislocation tooth according addendum modification coefficient x _f determined according to x _c by three expressions.

[0012]

[0013]

[0014]

The contents of the symbols in the above equations are as follows. x _f : Dislocation coefficient of flexible external gear x _c : Dislocation coefficient of rigid internal gear z _c : Number of teeth of rigid internal gear k: Coefficient indicating flexure of arbitrary cross section of flexible external gear at right angles to axis n: Stiffness 1/2 of the difference in the number of teeth between the internal gear and the flexible external gear R: Reduction ratio of the flexible mesh type gear device α _o : Reference pressure angle χ: Auxiliary angle expressing the tooth gap when there is no dislocation φ: Tooth profile Auxiliary angle j with respect to the position of the contact point: 1/2 of the root rim thickness of the flexible external gear and the sum of the tooth roots

Here, usually, the rigid internal gear is set as a dislocation tooth profile of constant dislocation (x _c = constant), and the dislocation coefficient x _f of the flexible external gear is set by the above three equations.

[0017]

Embodiments of the present invention will be described below with reference to FIGS. This example 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 reducer shown in FIG. In the following description, the same parts as those in FIGS. 1 to 3 are designated 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 example taken along the plane containing the axis. The cross section shown in this figure is the cross-sectional position including the major axis of the ellipse when it is bent into an elliptical shape by the wave generator.

External teeth 31 of the cup-shaped flexible external gear 3 of this example
The tooth profile of is determined according to the following three formulas, and is obtained by continuously shifting from the open end 32 side of the cup-shaped flexible external gear 3 toward the output side boss 33 side. It is a thing. FIG. 5 shows this tooth profile in an enlarged manner.

The tooth transfer coefficient x _f of the external tooth 31 is given by the following equation.

[0021]

[0022]

[0023]

The contents of the symbols in the above equations are as follows. x _f : Dislocation coefficient of flexible external gear x _c : Dislocation coefficient of rigid internal gear z _c : Number of teeth of rigid internal gear k: Coefficient indicating flexure of arbitrary cross section of flexible external gear at right angles to axis n: Stiffness 1/2 of the difference in the number of teeth between the internal gear and the flexible external gear R: Reduction ratio of the flexible mesh type gear device α _o : Reference pressure angle χ: Auxiliary angle expressing the tooth gap when there is no dislocation φ: Tooth profile Auxiliary angle j with respect to the position of the contact point: 1/2 of the root rim thickness of the flexible external gear and the sum of the tooth roots

The reason why the teeth of the cup-shaped flexible external gear can realize three-dimensional continuous meshing by adopting the tooth shape determined above is shown below.

First, the present inventor firstly found that Japanese Patent Publication No. 45-41.
In U.S. Pat. No. 171, it is shown that an involute curve can be used for the tooth profile of a deflected meshing gear device. However, as described above, in the invention described in this publication, it is premised that each cross section of the tooth portion of the cup-shaped flexible external gear has the same amount of deflection, that is, the same deviation coefficient. Therefore, no consideration has been given to the fact that the cup-shaped flexible external gear has a variable amount of bending 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 surface shape of the wave generator as it is. Such a premise is applicable to a flex meshing type gear device called a flat type or a pancake type in which a flexible external gear has a flat annular shape. However, the cup-shaped flexible external gear has a three-dimensional shape in the axial direction, so-called Corning. In this application,
The idea of continuous dislocation in which the dislocation amount is variable in the axial direction of the gear is applied to the tooth profile of this three-dimensional flexible external gear to ensure good tooth contact over the entire tooth streak.

As disclosed in Japanese Patent Publication No. 45-41171, the dislocation coefficient x _c of both the rigid internal gear and the flexible external gear when the involute tooth profile having the same reference pressure angle is adopted, The sum of x _f is given by the following equation (4).

[0028]

Where z _{f is the} number of teeth of the flexible external gear ε is the (number of teeth ratio) −1 (= z _c / z _f −1) α _oc is the reference pressure angle of the rigid internal gear (= flexible) Reference pressure angle of the external gear) χ: Auxiliary angle that represents the tooth gap when there is no dislocation

The present invention develops the relationship of the above expression (4) into three-dimensional meshing.

In addition to this, in the invention disclosed in Japanese Examined Patent Publication No. 45-41171, the pitch circle of the flexible external gear is approximately regarded as the neutral line during deformation.
In the present invention, the neutral line is set as follows. That is,
By setting the plane passing through the center of the bottom (rim) of the flexible external gear as the neutral plane, and setting the line of intersection between the plane and the cross section perpendicular to the axis of the flexible external gear as the neutral line of deformation. This enables more accurate setting of the dislocation coefficient. Therefore, the auxiliary coefficient χ shown in the above equation (2) can be calculated as follows.
This is a new proposal different from the first invention. Also, (2)
In the equation, j is a coefficient indicating that the center of the rim is the neutral line. This coefficient j represents the distance between the rim neutral line and the pitch circle. Further, φ in the equation (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 locus of the teeth. is there. The value of φ can be obtained by solving the above equation (3).

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

First, the equation (1) is obtained by introducing the coefficient k considering three dimensions into the equation (4). Details of the derivation of the equation (4) are described in JP-B-45-41171. A brief description will be given with reference to FIG. FIG. 6 is a detailed view for analyzing the meshing of the tooth profile of the deflected flexural mesh type gear device. This figure is for negative excursion. To reduce the backlash to zero, the reference pitch mπ
It indicates that the value obtained by subtracting the sum of the tooth thicknesses on the reference pitch circle of both gears from (m: module) may be approximately d _co χ (= mz _c χ). The tooth thickness on the reference pitch circle of the cup-shaped flexible external gear and the rigid internal gear as the dislocation gears is
Each

[0034] Therefore, the following equation holds.

[0035]

Here,

[0037]

Using the relationship of, the equation (4) is derived from the above equation. Here, the deflection amount d of an arbitrary cross section perpendicular to the axis of the tooth portion of the cup-shaped flexible external gear shown in FIG. 6 is a standard cross section which is a non-biased cross section (here, it is an open end for simplicity). Introducing a value k divided by the amount of deflection of d _o .

K = d / d _o

This value k will be called a deflection coefficient. Considering FIG. 6 as a cross section with a deflection coefficient k,

[0041]

From this, equation (1) is obtained.

Next, the formula (2) is expressed in Japanese Patent Publication No. 45-41171.
This corresponds to the equation (22) of the publication. This (2
Derivation of equation (2) is given in the publication. The expression (2) of the present invention is based on the expression (22) of the above publication, but is derived as follows. It is the formula (16) of the publication.

[0044]

The distance j of the teeth of the flexible external gear (here, the representative points are the pitch points on the tooth profile) from the rim neutral line.
The influence of

[0046]

It is assumed that

Ε and ε + μ in the above publication are respectively

Ε = 1 / R

Ε + μ = (1 + Rk) / R / (I + R)

Considering that α _oc = α _bc + β, and β is a minute angle, (invα _oc −in
vα _bc ) is

2 (1 + kR) / R / (1 + R) Sin
(2φ) tan ² α _oc

It can be modified as follows. As a result, the equation (2) is obtained. When j / R is small, (j / R
The term R) ² can be omitted.

Finally, the expression (3) is an expression for obtaining the auxiliary angle φ concerning the position of the contact point of the tooth profile when the reduction gear ratio R and the reference pressure angle α _o of the flexible mesh type gear device are given. This equation is the equation (15) in the above publication.

Tan α _c = {-ε + (ε + μ) cos
(2φ)} / {2 (ε + μ) sin (2φ)}

And the equation (18) in the same publication.

Α _c = α _f + εφ + 1.5 (ε + μ) sin (2φ)

From the above, ε and μ are set to k as in the case of the equation (2).
It is introduced by erasing α _c by substituting with R and. Note that the relationship of α _f = α _o is also used.

The above is the basis of the formulas of the present invention. The tooth profile of the cup-shaped flexible external gear determined by determining the specifications of the gear according to these equations (1), (2), and (3) has a constant dislocation coefficient x _c of the rigid internal gear, The shape is as shown in FIG. As shown in this figure, it is a multi-order convex curve in which the dislocation amount gradually increases toward the output side in the tooth streak direction. It was confirmed by computer simulation that by adopting the continuously dislocated tooth profile defined in this way, a good meshing state was formed in the entire tooth stripe direction. In the figure, for comparison,
The broken line shows the tooth profile defined by the above-mentioned JP-A-62-75153.

[0060]

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 from the above equations (1), (2), and (3) as a function of the deflection coefficient. Accordingly, the rigid internal gear is processed as a constant or variable dislocation gear, and the cup-shaped flexible external gear is processed as a continuous dislocation gear. Therefore, according to the present invention, it is possible for the first time to realize good three-dimensional meshing over the entire tooth streak direction of both gears without causing problems such as interference.

[Brief description of drawings]

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

2 is a front view of the device of FIG. 1. FIG.

FIG. 3 is a vertical cross-sectional view showing a flexed state of a cup-shaped flexible external gear in the apparatus of FIG.

FIG. 4 is a vertical cross-sectional view showing a cup-shaped flexible external gear having a continuous dislocation tooth profile according to the present invention.

5 is a partially enlarged sectional view showing a 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 reducer 1a ... Device axis 2 ... Rigid internal gear 3 ... Cup-shaped flexible external gear 31 ... External teeth 32 ... Open end 33 ... Boss 4 ... Wave generator 4a ... Elliptical long axis

Claims (2)

[Claims] 1. A rigid internal gear, a cup-shaped flexible external gear arranged inside the rigid internal gear, and the external gear is bent in the radial direction to partially engage with the rigid internal gear. In a flexible meshing gear device having a wave generator that causes relative rotation between the rigid internal gear and the flexible external gear by moving the meshing position in the circumferential direction, the rigid internal gear and the flexible internal gear are provided. The tooth profile of the flexible external gear is an involute tooth profile having the same reference pressure angle, the tooth profile of the rigid internal gear is a transition tooth profile having a transition coefficient x _c , and the tooth profile of the flexible external gear is its axis. 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. However, 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 : 1/2 the number of teeth difference between the rigid internal gear and the flexible external gear R: Reduction ratio of the flexible meshing gear device α _o : Reference pressure angle χ: Auxiliary angle φ representing the tooth gap when there is no dislocation Auxiliary angle regarding the position of the contact point of the tooth profile j: 1/2 of the root rim thickness of the flexible external gear and the sum of the tooth roots 2. The flexible mesh type gear device according to claim 1, wherein the tooth profile of the rigid internal gear is a dislocation tooth profile with a constant dislocation.