JPH02102948A - Gears for increasing/decelerating drive machines - Google Patents

Abstract

PURPOSE:To facilitate fabrication by forming a rigid gear as an internal gear consisting of a member equipped with a circular arc shaped recess at the inner surface by a pin or a member equipped with projections and recesses in the form of circular arcs at the inner surface. CONSTITUTION:A rigid gear 1 is formed as an internal gear provided with an internal gear by a plurality of pins 4, which are arranged at a constant spacing so that their axes are parallel with one another and that the center of each pin 4 lies on a circle with any arbitrary radius. The dia. of each pin 4 and the dia. of the circle, on which the centers of these pins are located, are selected any desired, and when they are selected and the tooth shape of the rigid gear 1 is decided, the tooth shape of a soft gear 2 is obtainable by means of analysis. The pin can be processed easily and precisely with genuine roundness, and shape error is lesser. It is also practicable to grind the surface to suppress the surface roughness.

Description

DETAILED DESCRIPTION OF THE INVENTION [Field of Industrial Application] The present invention relates to a gear for an increasing/decelerating drive using a wave gear device.

[Conventional technology]

Conventionally, linear tooth profiles or involute tooth profiles have been used as tooth profiles for gears used in wave gear devices.
These tooth profiles were not determined based on gear meshing theory, but were based on approximate analysis results when the reduction ratio is large.

For this reason, if the tooth profile is inappropriate, meshing becomes difficult, which causes a reduction in the efficiency of the wave gear device.

In order to make the mesh smooth and solve this problem,
It is necessary to perform a geometric analysis of the wave motion of the gear and the meshing of the teeth, and thereby determine an appropriate tooth profile.

For this reason, the applicant of the present application provided a geometric analysis method and a gear having a tooth profile obtained thereby in Japanese Patent Publication No. 14216/1983.

However, the gears are merely theoretically determined using a geometrical analysis method, and the difficulty of actually machining and forming the gears is not taken into account.

Generally 1. Among the gears used in wave gear devices, internal gears are particularly difficult to machine. However, if the internal gear has a linear tooth profile or an involute tooth profile, it is possible to accurately process and form the tooth profile determined by the above-mentioned geometric analysis method. It is more difficult to do so, and even if processing and forming is possible, it is disadvantageous in terms of cost.

[Problem to be solved by the invention]

Therefore, the present invention provides a gear of a wave gear device used in an accelerating/decelerating drive machine, which has an appropriate tooth profile determined by a geometrical analysis method, and which facilitates processing and formation, thereby reducing cost. The aim is to provide the same advantageous results.

[Means to solve the problem]

In order to achieve this object, the wave gear device of the present invention basically uses an arc shape for the tooth profile, and applies a convex or concave arc shape to the internal gear of the external gear and the internal gear.

According to the above-mentioned geometrical analysis method, arc shapes can theoretically be applied to both internal gears and external gears. However, in general, it is more difficult to process and form an internal gear than an external gear in terms of forming technology, so it is more advantageous to apply an arc shape to the internal gear, and it is more consistent with the purpose of the present invention.

Based on this premise, the gear of the present invention has one rigid gear made of a rigid body that does not deform, and the other a flexible flexible gear that moves in a wave-like manner, and a wave generator that generates wave motion in the flexible gear. The rigid gear and flexible gear are meshed with their multiple wavy convex portions, and at this time, the movement of the meshing portion is achieved by creating a difference in the number of teeth between the rigid gear and the flexible gear between adjacent convex portions. In a strain wave gear device that enables relative movement between a rigid gear and a flexible gear due to A virtual contact plate (hereinafter referred to as a "rolling contact plate") is formed as an internal gear made of a member with an arc-shaped uneven surface, and the flexible gear makes the same relative movement as each of a pair of teeth of a rigid gear and a flexible gear that mesh with each other. '') is set as a trajectory drawn by the instantaneous center of the relative movement of the teeth on a plane fixed to each tooth, and the common normal of both tooth profiles at the meshing point of the teeth is the contact point of the rolling contact plate. It is characterized by being formed as an external gear having a tooth profile set under the condition that the gear passes through the gear.

〔Example〕

Examples of the present invention will be described below along with the analysis process.

FIG. 1 shows an example of a wave gear device. The device consists of a highly rigid gear, that is, a rigid gear 11, a gear that makes a wave motion, that is, a flexible gear 2, and a mechanism that generates a wave motion in the flexible gear 2, that is, a wave generator 3. The rigid gear and the flexible gear are meshed with their plurality of wavy convex parts, and by providing a difference in the number of teeth between the rigid gear and the flexible gear between adjacent meshing parts, the rigid gear and the flexible gear are meshed with each other. Relative movement between the gear and the soft gear is possible.

Below, the trajectory of the motion of the flexible gear will be analyzed. By clarifying this, if the tooth profile of the rigid gear is arbitrarily set, the tooth profile of the soft gear that meshes with it can be set to an appropriate tooth profile.

■Basic conditions Considering the case where the flexible gear is made of thin flexible material,
The plate thickness at the bottom of the tooth is extremely thin compared to that at the tooth, so it is thought that deformation occurs mostly at the bottom of the tooth. That is, during deformation, different teeth move relative to each other, but
- A stroke tooth can be thought of as a rigid body. This means that the movement of a flexible gear is exactly the same as that of an O-Lar chain, with the teeth serving as links and the tooth bottoms serving as hinges. Furthermore, when a thin plate undergoes bending deformation, there is a neutral line that maintains the same length as before deformation, and this line can be thought of as the same line that smoothly connects the centers of the hinges of a roller chain.

As shown in Figure 2, in a coordinate system fixed to each tooth of a flexible gear, the tangent u1 at point Mi on the neutral line is the abscissa, and the normal '/l (this passes through the center of the tooth). Consider a Cartesian coordinate system (M1u1+vi) whose ordinate is (or tooth number). At this time, we make the following assumptions.

(1) When the flexible gear moves, the coordinates fixed to the teeth (
When the tooth is observed from Mt-ut, Vt), the tooth profile does not change.

(2) The pitch MiM of each tooth is constant on the neutral line.

If each tooth is considered to be a rigid body, the tooth movement can be investigated and the tooth profile can be determined using the two-pronged tooth profile analysis method.

That is, as shown in FIG. 3, if the tooth profile C1 and the rolling contact plate P1 are integrated, and the tooth profile C2 and the rolling contact plate P2 are integrated, the common normal T of the tooth profiles at the meshing point C of the teeth is , a rolling contact plate P that performs the same relative motion.

The tooth profiles C1 and C2 can be determined by giving the mechanical requirement that they pass through the rolling contact point of and P2, that is, the instantaneous center P.

(2) Analysis of Motion Here, we will consider as an example a general wave gear device consisting of a flexible gear with the number of teeth ZF, a rigid gear with the number of teeth Z11, and an elliptical wave generator. It is assumed that no frictional force acts between the wave generator and the flexible gear.

The diameter of the neutral line before deformation is d. If F, then even after the neutral line of the flexible gear is deformed into an elliptical shape, the pitch πdoF/ZF of the teeth on the neutral line remains constant based on assumption (2).

Hereinafter, the neutral line after deformation will be referred to as a soft standard pitch curve.

In addition, in a rigid gear, there is a pitch circle having the same pitch as the soft reference pitch curve, and this will hereinafter be referred to as the relative reference pitch circle of the rigid gear. If its diameter is dell, then doi= (ZR/ZF) X day...
...(1).

Also, rigid gears, flexible gears, and wave generators can rotate around the same fixed center, but if we consider the wave generator to be fixed, the rigid gear rotates by an angle φ during time t at a constant angular velocity Ω. Suppose we did. At this time, in the flexible gear, during the same time t, the tooth part moves in the same direction as the rigid gear, along the flexible reference pitch curve 5=(ZR/ZF)X (dat/2)Xφ
...It moves at a constant speed over the distance (2), but the angular velocity of the part from which rotational motion is extracted is ΩX (Za/ZF).

Next, in order to investigate the relative motion of the flexible gear with respect to the rigid gear, we will consider the rigid gear to be fixed and analyze the motion of the flexible gear when the wave generator is rotated.

In FIG. 4, (Ox, y) are orthogonal coordinates fixed to the rigid gear whose origin is the rotation center O of the shaft, and the y-axis passes through the center of the tooth space of the rigid gear. In addition, (M-u, v) is a rectangular coordinate fixed to the tooth of the soft gear with the origin at point M on the soft standard pitch curve, the U axis is the tangent to the soft standard pitch curve, and the V axis is the coordinate system of this coordinate system. It shall pass through the center of the fixed tooth.

(0-X, Y) are orthogonal coordinates fixed to the wave generator, and the Y axis coincides with the long axis of the ellipse.

When the Y axis coincides with the y axis, the coordinate (Mu.

The origin of V) is the vertex M of the convex part of the soft reference pitch curve. Located in
It is assumed that the V-axis is on the y-axis. From this point on, when the wave generator is rotated by an angle φ, the convex apex of the soft standard pitch curve moves from Mo to Q, and the origin of the teeth of the soft gear is Me.
Move from to M. At this time, the origin of the teeth of the soft gear moves from Q to M relative to the wave generator, and the shape of the soft reference pitch curve r where the silkworm moves is such that 0 is the pole and the major axis is Y. It is assumed that it is expressed by the following polar coordinates, where is the starting line, r is the radius, and θ is the argument.

r=f(θ) ・・・・・・・・・ (3) If the length of this curve from angle 0 to θ is S, then by setting this equal to S in equation (2), the wave generator can be calculated. The relationship between the rotation angle φ and the argument angle θ of point M can be determined from the following equation.

・ ・ ・ ・ ・ ・ ・ ・ ・ (4) (4)
From the formula, the relationship between angle φ and angle θ cannot be expressed by a simple elementary function, but it can always be determined by numerical integration.

Next, the (x, y) coordinates of point M are (XM, y,
4) Then x, = -rsin (θ - φ) y = rcos (θ - φ) ... (5) Also, if the angle between the y axis and the V axis is ψ, then ψ = θ - φ 10μ ...
(6) However, μ is the angle formed by the V-axis and the radius vector OM.

In the end, the conversion formula is u= (x-Xx)cosψ+(Vyx)si
nψV= ＜'l Yx ) cosψ−(X X)
I) sin ψ...(8) These are the coordinates of (0-X, Y) and (Mu, v).

Here, the coordinates 〈M-u,
Let the (x, y) coordinates of the instantaneous center P of the motion of
p, yp), then dy, + ・ ・ ・ (9).

By changing φ, point P has coordinates (0-x, y) and coordinates (M
If the trajectories drawn in -u and v) are found, they will be in the shape of rolling contact plates that move integrally with the teeth of the rigid gear and flexible gear, respectively.

(2) Calculation of the shape of the rolling contact plate A specific calculation is performed for the case where the shape of the side beam reference pitch curve is expressed by the following polar coordinates, where r is the radius vector, θ is the cockfight, and d and δ are constants.

r= (d/2) + (δ/2) cos2θ Since the circumferential length of this soft standard pitch curve is four times the length in the first quadrant, . . . . . 01).

Further, the maximum diameter d+δ of the soft reference pitch curve and the diameter dolk of the relative reference pitch circle of the rigid gear have the following relationship with λ as the deviation coefficient.

d+δ=λaoi ・・・・・・・・・Q2) When d and δ are determined from equations (1), α1), and (12) and the shape of the soft standard pitch curve is determined, the shape of the rolling contact plate is determined. Seek.

Figures 5 (a) and (b) show the tooth number ratio Z* / ZF = 1
．． 1. This shows the rolling contact plates and their trajectories of rigid gears and flexible gears when λ=1.0.
Same as the figure.

In Fig. 5(a), the rigid gear is fixed, and the rolling contact plate PF, which is integrated with the teeth of the flexible gear and located at the apex of the convex portion of the flexible reference pitch curve, rotates as the wave generator rotates. Assuming that the contact plate PR rolls without slipping, the rotation angle φ of the wave generator is φ=20°.
When , point P becomes the contact point.

As the wave generator rotates further, the rolling contact point advances along the asymptote, and when dψ/dφ-0 is reached, the rolling contact point returns from the opposite side of the asymptote.

After that, as shown in FIG. 5(b), the rolling contact plate P
, ' and PF5 make rolling contact, and when φ=70'', point P' becomes the contact point.

Here, Lll is the coordinate (M-u,
v) is the locus of the origin M, and L12 is the coordinate (M-u
, v) at coordinate position 0'. When the flexible gear is circular, 0' coincides with the rotation center 0 of the gear. Naturally, point M
The normal of L8 at and the line at point O'. The normals of both pass through the rolling contact point P or P'. Furthermore, the rolling contact plates PF and PF5 are symmetrical with respect to the straight line MO' connecting two points M and O', and the rolling contact plates p
, / and P,'(pm' is shown by a dashed line) are symmetric about the y-axis.

The above is the analysis of the locus of motion of the flexible gear. Next, an example will be described in which the rigid gear has a tooth profile using an arc shape.

[Embodiment 1] Fig. 6 shows a rigid gear 1 in which internal teeth are formed by a plurality of pins 4, and the pins 4 are arranged so that their axes are parallel to each other and the center of the pins 4 has an arbitrary radius. 1 shows an example of a strain wave gearing device formed as internal gears arranged at equal intervals on the circumference of a circle.

The diameters of the bins 4 and the diameters of the circles in which the centers of these bins are located can be arbitrarily selected, and once the tooth profile of the rigid gear 1 is determined, the tooth profile of the flexible gear 2 can be determined by the analytical method described above. FIG. 6 shows an example of the tooth profile of a flexible gear 2 having 20 teeth that meshes with a rigid gear 1 consisting of 22 pins 4.

The bottle 4 is supported by a bottle support member 5 as shown in FIG. 6, for example.

Although the figure shows an example in which the bottle is fixed, the bottle may also have a structure in which it is rotatably supported.

[Embodiment 2] Fig. 7 shows a wave gear in which the rigid gear 1 is formed as an internal gear made of a member in which a plurality of arc-shaped recesses are provided at equal intervals along the circumferential direction on the circular inner peripheral surface. An example of a device is shown.

The radius of the circular arc forming the recess and the radius of the circle connecting the centers of the circular arcs can be arbitrarily selected, and when these are selected and the tooth profile of the rigid gear 1 is determined, the tooth profile of the flexible gear 2 is determined by the above analysis method. Figure 7 shows 22 arc-shaped recesses,
That is, this is an example of the tooth profile of a flexible gear 2 having 20 teeth that meshes with a rigid gear 1 having 22 teeth.

[Embodiment 3] FIG. 8 shows an example of a wave gear device in which the rigid gear 1 is formed as an internal gear made of a member whose inner peripheral surface is continuously provided with an arc-shaped uneven surface.

This example corresponds to a combination of the convex portion of the pin of Example 1 and the arc-shaped concave portion of Example 20.

A convex arc radius d1 of the rigid gear 1 and a radius D10 of a circle connecting the centers of the convex arc, or a concave arc radius d of the rigid gear 1
2 and the radius D2 of the circle connecting the centers of the concave arcs can be arbitrarily selected, and once they are selected, the set of d2 and D2 or d and , are selected. Once the tooth profile of the rigid gear 1 is determined in this way, the tooth profile of the flexible gear 2 can be determined by the above analysis method. FIG. 8 is an example of a tooth profile of a flexible gear 2 having 20 teeth that meshes with a rigid gear 1 having 22 teeth.

(Effects of the invention) By forming the rigid gear as an internal gear with a tooth profile applying an arcuate shape, machining becomes easier than using a linear tooth profile or an involute tooth profile for the internal gear, and various usefulness can be achieved. You can expect it.

In particular, the one using the pin shown in Example 1 is an optimal practical example.

In other words, pins are easier to machine than commonly used tooth profiles such as linear tooth profiles, and can be machined with high precision, making it possible to form pins into perfect circles and reducing shape errors. Furthermore, since surface grinding becomes possible, surface roughness is also reduced.

Furthermore, if the pin is rotatably supported, the external teeth and internal teeth engage in rolling contact, reducing frictional force and improving wear resistance and torque transmission efficiency.

In the member provided with the arcuate recess shown in Example 2, the recess can be ground with a grindstone, making machining easier and reducing costs.

The tooth profile shown in Example 3 can significantly improve torque transmission efficiency.

[Brief explanation of drawings]

Figure 1 is a sectional view showing a part of the wave gear device, Figure 2 is an explanatory diagram showing the coordinates of the flexible gear, Figure 3 is an explanatory diagram showing the relationship between the tooth profile and the rolling contact plate, and Figure 4 is the flexible gear. An explanatory diagram showing the movement of one tooth of a gear, Figures 5 (a) and (b) are explanatory diagrams showing an example of rolling contact plates for rigid gears and flexible gears, and Figure 6 is an example of implementation using a pin. FIG. 7 is a side view of an example using a member provided with an arc-shaped concave portion, and FIG. 8 is a side view of an example using a member provided with an arc-shaped uneven surface. (Explanation of symbols) 1...Rigid gear 2...Flexible gear 3...Wave generator 4...Pin 5...Pin support member (Figure CG) Figure Figure Figure ( b) Diagram diagram

Claims (3)

[Claims] (1) One is a rigid gear made of a rigid body that does not deform, and the other is a flexible gear that moves in a wave-like manner.The rigid gear and the flexible gear are connected by a wave generator that generates wave motion in the flexible gear. The plurality of wavy convex portions mesh together, and at this time, by providing a difference in the number of teeth between the rigid gear and the flexible gear between adjacent convex portions, the rigid gear and the flexible gear are In a strain wave gearing device, a rigid gear has internal teeth formed by a plurality of pins, and the pins are arranged so that their axes are parallel to each other and the centers of the pins have an arbitrary radius. The virtual contact plate is formed as internal gears arranged at equal intervals on the circumference of a circle, and the flexible gears perform the same relative motion as each of the teeth of a pair of mutually meshing rigid and flexible gears. The shape is set as a trajectory drawn by the instantaneous center of the relative movement of the teeth on a plane fixed to each tooth, and the condition is that the common normal of both tooth profiles at the meshing point of the teeth passes through the contact point of the virtual contact plate. A gear for an increasing/decelerating drive machine, characterized in that it is formed as an external gear having a tooth profile set to. (2) One is a rigid gear made of a rigid body that does not deform, and the other is a flexible gear that moves in a wave-like manner, and the rigid gear and the flexible gear are connected by a wave generator that generates wave motion in the flexible gear. The plurality of wavy convex portions mesh together, and at this time, by providing a difference in the number of teeth between the rigid gear and the flexible gear between adjacent convex portions, the rigid gear and the flexible gear are In the strain wave gear device, the rigid gear is a member having a circular inner circumferential surface, and the circular inner circumferential surface has a plurality of arc-shaped recesses arranged equally along the circumferential direction. The virtual contact plate is formed as an internal gear consisting of members provided at intervals, and the flexible gear makes the same relative movement as each of a pair of teeth of a rigid gear and a flexible gear that mesh with each other. The tooth profile is set as a locus whose instantaneous center is drawn on a plane fixed to each tooth, and the common normal of both tooth profiles at the meshing point of the teeth passes through the contact point of the virtual contact plate. A gear for an increasing/decelerating drive machine, characterized in that it is formed as an external gear. (3) One is a rigid gear made of a rigid body that does not deform, and the other is a flexible gear that moves in a wave-like manner, and the rigid gear and the flexible gear are connected by a wave generator that generates wave motion in the flexible gear. The plurality of wavy convex portions mesh together, and at this time, by providing a difference in the number of teeth between the rigid gear and the flexible gear between adjacent convex portions, the rigid gear and the flexible gear are In a wave gear device that enables relative movement between the two, the rigid gear is formed as an internal gear made of a member whose inner peripheral surface is continuously provided with an arc-shaped uneven surface, and the flexible gears mesh with each other. The shape of a virtual contact plate that makes the same relative movement as each of a pair of teeth of a rigid gear and a soft gear is set as a locus drawn on a plane where the instantaneous center of the relative movement of the teeth is fixed to each tooth, and the meshing of the teeth is determined. A gear for an accelerating/decelerating drive machine, characterized in that it is formed as an external gear having a tooth profile set under the condition that a common normal line of both tooth profiles at a point passes through a contact point of the virtual contact plate.