JP6777404B2 - Deceleration or acceleration device - Google Patents

Description

In the present invention, the first crown gear and the second crown gear having different numbers of teeth are opposed to each other, and the first crown gear is tilted with respect to the second crown gear so that the first crown gear meshes with the second crown gear. The present invention relates to a deceleration or speed increase device that makes the first crown gear wave motion so that the meshing portion moves.

As a conventional deceleration or speed increase device, a device in which two spur gears having an involute tooth profile are meshed with each other is known. Spur gears with involute tooth profiles are often used in deceleration or speed increase devices because they are easy to manufacture and efficient. However, since there is a limit to the difference in the number of teeth of the two spur gears, there is a problem that the reduction ratio or the speed increase ratio cannot be increased.

In order to increase the reduction ratio or acceleration ratio, the first crown gear and the second crown gear having different numbers of teeth face each other, and the first crown gear is second so that the first crown gear meshes with the second crown gear. A deceleration or speed-increasing device has been developed in which the first crown gear is wave-moved so as to be tilted with respect to the crown gear and the meshing portion moves. When the first crown gear is wave-moved, the second crown gear rotates relative to the first crown gear by the difference in the number of teeth each time the meshing portion makes one revolution. A large reduction ratio can be obtained by outputting the rotation corresponding to the difference in the number of teeth between the two. On the contrary, by rotating the second crown gear, a large speed increase ratio can be obtained.

As a speed reduction device of this type, for example, Patent Document 1 discloses a speed reduction device including a first crown gear, a second crown gear, and an inclined cam. The first crown gear and the second crown gear have different numbers of teeth and face each other. The first crown gear is tilted by a tilt cam integrated with the input shaft. When the first crown gear is tilted, the first crown gear and the second crown gear mesh at one place. The second crown gear is fixed to the housing. The first crown gear is wave-movably supported by a spherical spline joint located inside its radial direction.

When the input shaft is rotated, the tilt cam integrated with the input shaft causes the first crown gear to make a wave motion while moving the meshing point with the second crown gear. Due to the wave motion of the first crown gear, the first crown gear rotates with respect to the second crown gear by the difference in the number of teeth. The rotation of the first crown gear is transmitted to the output shaft via a spherical spline joint.

Japanese Unexamined Patent Publication No. 51-126467

However, in the conventional reduction gear, the tooth shape of the first crown gear and the second crown gear is formed in a triangular shape or a trapezoidal shape. Then, at the meshing portion between the first crown gear and the second crown gear, the teeth of the first crown gear are fitted into the grooves between the teeth of the second crown gear without any gap. Therefore, if the teeth of the first crown gear and the second crown gear have a pitch error and / or a tooth profile error, the teeth of the first crown gear cannot be smoothly fitted into the groove of the second crown gear. Moreover, since most of the meshing between the first crown gear and the second crown gear is not rolling but sliding, there is a problem that the efficiency of the gear is poor.

Therefore, an object of the present invention is to provide a highly efficient deceleration or speed increase device capable of smoothly fitting the teeth of the first crown gear into the groove of the second crown gear.

In order to solve the above problems, one aspect of the present invention includes a first crown gear, a second crown gear having a different number of teeth from the first crown gear, and facing the first crown gear, and the first crown. A cam portion that inclines the first crown gear with respect to the second crown gear so that the gear meshes with the second crown gear, and causes the first crown gear to wave motion so that the meshing portion moves. In the speed reduction or speed increasing device provided, the first crown gear and the second crown gear have tooth tip portions and tooth bottom portions alternately in the circumferential direction, and the first crown gear and the second crown gear The tooth tip portion has a convex shape formed of a part of the side surface of the conical shape, and the curve on the reference circle of the tooth tip portion of the first crown gear and the second crown gear is an arc, and the first in deceleration or speed increasing device for crown gear and said tooth bottom of the tooth tip portion is drawn curve of tooth bottom the curve first crown gear and the second crown gear on the reference circle of the second crown gear is there.

According to the present invention, most of the meshing between the tooth tip of the first crown gear and the tooth bottom of the second crown gear and the tooth tip of the second crown gear and the tooth bottom of the first crown gear is rolling. The efficiency of gears can be improved.

It is an input shaft side external perspective view of the reduction gear of the 1st Embodiment of this invention. It is an output part side external perspective view of the speed reduction device of the 1st Embodiment of this invention. It is sectional drawing of the reduction gear of the 1st Embodiment of this invention. It is an exploded perspective view of the speed reduction device of the 1st Embodiment of this invention. It is a perspective view which shows the 1st crown gear and the 2nd crown gear (FIG. 5 (a) shows the 2nd gear and the 1st crown gear which tilts and meshes with a 2nd crown gear, and FIG. 5 (b) is a 1st The double crown gear is shown, and FIG. 5 (c) shows the first crown gear). It is a development view of the tooth of the 1st crown gear and the 2nd crown gear. It is a perspective view which added a cone to the tooth of the 1st crown gear and the 2nd crown gear (FIG. 7A shows the 1st crown gear and the 2nd crown gear, and FIG. 7B shows the 2nd crown gear. Show). It is a development view of the tooth of the 1st crown gear and the 2nd crown gear. Is a perspective view showing a tooth profile on the reference circle r _c of the first crown gear and the second crown gear. FIG. 10A is a perspective view showing a state in which the apex of the moving cone (the base of the first crown gear) and the constant cone (the base of the second crown gear) are in contact with each other, and FIG. 10B is a moving cone. It is a perspective view which shows the precession movement of. It is a figure which shows the relationship between a point on a moving cone and a vector. It is a graph which shows the relationship between θ and ψ. It is a perspective view showing a trochoid curve vector p ₂ draws. Is a perspective view showing a formation process of a tooth bottom curved p _3. It is a graph showing how to determine the tooth bottom curve p _3. FIG. 16A shows the tooth bottom curve of the first crown gear, and FIG. 16B shows the tooth bottom curve of the second crown gear. It is a figure which shows the meshing of the 1st crown gear and the 2nd crown gear on the tooth profile curve. It is a perspective view of the 2nd crown gear when the tooth streak is helical. It is a perspective view which shows the logarithmic helix. It is sectional drawing of the reduction gear of the 2nd Embodiment of this invention. It is an exploded perspective view of the reduction gear of the 2nd Embodiment of this invention. It is sectional drawing of the reduction gear of the 3rd Embodiment of this invention. FIG. 23 (a) shows a side view of the second crown gear and the third crown gear, and FIG. 23 (b) shows a side view of the first crown gear. FIG. 24 (a) is a perspective view showing a state in which the apex of the moving cone (the base of the third crown gear) and the constant cone (the base of the first crown gear) are in contact with each other, and FIG. 24 (b) is a moving cone. It is a perspective view which shows the precession movement of. It is a perspective view showing a trochoid curve vector p ₂ draws.

Hereinafter, embodiments of the speed reducer of the present invention will be described in detail with reference to the accompanying drawings. However, the speed reducer of the present invention can be embodied in various forms, and is not limited to the embodiments described in the present specification. This embodiment is provided with the intent of allowing one of ordinary skill in the art to fully understand the scope of the invention by adequately disclosing the specification.
<Overall configuration of the reduction gear of the first embodiment>

FIG. 1 shows an external perspective view of the speed reducer according to the first embodiment of the present invention on the input shaft side, and FIG. 2 shows an external perspective view of the speed reducer on the output unit side. In addition, the same reference numerals are given to the same configurations through the attached drawings and the following specifications.

The input shaft 2 and the output unit 3 are rotatably housed in the housing 1. The axis 2a of the input shaft 2 and the axis 3a1 of the output unit 3 coincide with each other. When the input shaft 2 is rotated around the axis 2a, the output unit 3 is decelerated and rotates around the axis 3a1. The reduction ratio of the output unit 3 with respect to the input shaft 2 is determined by the number of teeth of the first crown gear 11 and the second crown gear 12 (see FIG. 3) housed in the housing 1.

The housing 1 includes a tubular housing body 1a having a flange 1a1 and disk-shaped lid members 1b and 1c attached to both ends of the housing body 1a in the axial direction. The flange 1a1 of the housing body 1a is provided with a through hole for attaching to a mating component. The lid members 1b and 1c are fixed to the housing body 1a by fastening members such as bolts.

FIG. 3 shows a cross-sectional perspective view of the speed reducer of the present embodiment, and FIG. 4 shows an exploded perspective view of the speed reducer of the present embodiment. As shown in FIG. 3, the speed reduction device enables wave motion of the housing 1, the cam portion 5 in which the inclined cam 4 is integrally provided on the input shaft 2, the first crown gear 11, and the first crown gear 11. A support portion 14 that non-rotatably supports, a second crown gear 12, and an output portion 3 connected to the second crown gear 12 are provided. In the following, for convenience of explanation, the configuration of the reduction gear will be described using the directions when the axis lines 2a of the input shaft 2 and the output unit 3 are arranged in the X direction, that is, the X, Y, and Z directions shown in FIG. To do.

As shown in FIG. 4, the first crown gear 11 and the second crown gear 12 have a disk shape. A plurality of teeth are radially formed on the facing surface 11a of the first crown gear 11 and the facing surface 12a of the second crown gear 12. The number of teeth of the first crown gear 11 and the second crown gear 12 is not particularly limited. For example, the number of teeth of the first crown gear 11 is 49, and the number of teeth of the second crown gear 12 is 50. The number of teeth of the first crown gear 11 and the number of teeth of the second crown gear 12 are different. Since the number of teeth is different, the axis of the first crown gear 11 and the axis of the second crown gear 12 cannot be meshed with each other in the same state. Therefore, the first crown gear 11 is tilted with respect to the second crown gear 12, and a part of the first crown gear 11 meshes with a part of the second crown gear 12. The facing surface 12a of the second crown gear 12 is arranged in the YZ plane of FIG. The facing surface 11a of the first crown gear 11 is tilted about the Z axis by an angle α with respect to the YZ plane of FIG.

As shown in FIG. 3, the cam portion 5 includes an input shaft 2 rotatably supported by the housing 1 around an axis, a disk-shaped inclined cam 4 integrally provided on the input shaft 2, and an inclined cam 4. It is provided with a ball 6 as a rolling element that is interposed between the first crown gear 11 (to be exact, an inner ring portion integrally fixed to the first crown gear 11) so as to be able to roll and move (see also FIG. 4). ). The tilt cam 4 is provided to tilt the first crown gear 11. The cam surface 4a of the inclined cam 4 is inclined by an angle α around the Z axis with respect to the YZ plane, similarly to the first crown gear 11. A circular ball rolling groove 4b is formed on the cam surface 4a of the inclined cam 4. The inner ring portion 7 of the support portion 14 is also formed with a circular ball rolling groove 7b facing the ball rolling groove 4b of the inclined cam 4. A plurality of balls 6 are arranged between the ball rolling groove 4b and the ball rolling groove 7b so that they can roll and move in the circumferential direction. A preload is applied to the ball 6 in order to press the first crown gear 11 against the second crown gear 12 and eliminate backlash between them. The gap between the ball rolling groove 4b and the ball rolling groove 7b is smaller than the diameter of the ball 6, and the ball 6 is compressed between them. The ball 6 is held by the ring-shaped cage 16.

The input shaft 2 penetrates the first crown gear 11 and the second crown gear 12. The input shaft 2 is hollow. Both ends of the input shaft 2 in the axial direction are rotatably supported by bearings 21 and 22. The bearings 21 and 22 are arranged outside the first crown gear 11 and the second crown gear 12 in the axial direction.

As shown in FIG. 3, the support portion 14 is arranged outside the first crown gear 11 in the radial direction so that the first crown gear 11 can wave motion with respect to the housing 1 (in other words, as shown in FIG. 3). In addition, the axis 11b of the first crown gear 11 is rotatable so as to draw a trajectory of a cone with the point P1 as the apex) and non-rotatably supports around the axis. The wave motion of the first crown gear 11 is also called a precession motion.

As shown in FIG. 3, the support portion 14 is arranged inside the outer ring portion 10 having the outer ring spline groove 10a (see FIG. 4) on the spherical inner peripheral surface, and the outer ring spline on the spherical outer peripheral surface. Rolling intervening between the inner ring portion 7 having the inner ring spline groove 7a (see FIG. 4) facing the groove 10a and the outer ring spline groove 10a and the inner ring spline groove 7a along the trajectory of an axial arc so as to be movable. It includes a ball 9 as a moving body. The outer ring portion 10 is integrated with the housing 1. The inner ring portion 7 is fixed to the first crown gear 11 by a fastening member such as a bolt. The ball 9 is held by the cage 8. The support portion 14 allows the first crown gear 11 to swing around the Z-axis and around the Y-axis around the point P1 on the axis 2a. The rotational movement of the first crown gear 11 around the axis 2a is limited by the spline mechanism of the support portion 14.

The inner ring 3a of the output unit 3 is fixed to the second crown gear 12 by a fastening member such as a bolt. The output unit 3 is rotatably supported by the housing 1 by the cross roller 23. The cross roller 23 is a roller row in which the axes of rollers adjacent to each other in the circumferential direction are orthogonal to each other when viewed from the circumferential direction (see FIG. 4). The second crown gear 12 is rotatably supported by the housing 1 via the output unit 3. A circular raceway 1c1 is formed on the inner peripheral surface of the lid member 1c of the housing 1. A circular raceway 3b facing the raceway 1c1 is formed on the outer peripheral surface of the inner ring 3a of the output unit 3. A cross roller 23 is arranged as a rolling element between the raceway 1c1 and the raceway 3b. A moment caused by the reaction force of the meshing portion between the first crown gear 11 and the second crown gear 12 acts on the output unit 3. By using the cross roller 23, the moment rigidity of the output unit 3 can be improved. The bearing 22 that rotatably supports one end of the input shaft 2 is arranged between the output unit 3 and the input shaft 2.

When the cam portion 5 is rotated around the axis using a drive source such as a motor (not shown), the first crown gear 11 moves the meshing portion with the second crown gear 12 by the inclined cam 4 of the cam portion 5. Wave motion. Along with the wave motion of the first crown gear 11, the second crown gear 12 rotates relative to the first crown gear 11 by the difference in the number of teeth. In this embodiment, for example, the number of teeth of the first crown gear 11 is 49, and the number of teeth of the second crown gear 12 is 50. The rotation of the first crown gear 11 with respect to the housing 1 is restricted by the support portion 14, and the rotation of the output portion 3 with respect to the housing 1 is allowed. Therefore, the output unit 3 decelerates and rotates by one tooth, and a reduction ratio of 1/50 can be obtained. Here, the number of teeth of the first crown gear 11 and the second crown gear 12 is not limited.
<Tooth shape of the first crown gear and the second crown gear (example in which the tip and bottom are composed of conical side surfaces)>

The tooth shapes of the first crown gear 11 and the second crown gear 12 are as follows. FIG. 5A shows a second crown gear 12 and a first crown gear 11 that is inclined and meshes with the second crown gear 12. As shown in FIG. 5A, the first crown gear 11 and the second crown gear 12 mesh with each other at one position (position A at the left end of FIG. 5A). However, since preload is applied to the first crown gear 11 from the cam portion 5, the contact points between the first crown gear 11 and the second crown gear 12 spread to a plurality of teeth in the circumferential direction around the meshing points. Since the first crown gear 11 is inclined, the gap δ between the first crown gear 11 and the second crown gear 12 gradually increases toward the right side in FIG. 5A.

As shown in FIG. 5A, the diameter of the first crown gear 11 and the diameter of the second crown gear 12 are equal to each other. Since the number of teeth of the first crown gear 11 and the number of teeth of the second crown gear 12 are different, the pitch of the teeth of the first crown gear 11 and the pitch of the teeth of the first crown gear 11 are different.

FIG. 5B shows the second crown gear 12. The second crown gear 12 has a bevel gear shape and has a conical base body. Corrugated teeth 30 are continuously formed on the surface of the second crown gear 12 in the circumferential direction. The second crown gear 12 has a plurality of tooth tip portions 31 arranged radially and a plurality of tooth bottom portions 32 arranged radially alternately in the circumferential direction. The tooth tip portion 31 of the second crown gear 12 has a convex shape formed from the side surface of the cone. The tooth bottom portion 32 of the second crown gear 12 has a concave shape formed from the side surface of the cone.

FIG. 5C shows the first crown gear 11. The first crown gear 11 is also bevel gear-shaped and has a conical base body. Corrugated teeth 35 are continuously formed on the surface of the first crown gear 11 in the circumferential direction. The first crown gear 11 also has a plurality of tooth tip portions 33 arranged radially and a plurality of tooth bottom portions 34 arranged radially alternately in the circumferential direction. The tooth tip portion 33 of the first crown gear 11 has a convex shape formed from the side surface of the cone. The tooth bottom portion 34 of the first crown gear 11 has a concave shape formed from the side surface of the cone.

As shown in the developed view of FIG. 6, the radius of the tooth bottom portion 32 of the second crown gear 12 is larger than the radius of the tooth tip portion 33 of the first crown gear 11, and the tooth tip portion 33 of the first crown gear 11 It fits into the tooth bottom 32 of the second crown gear 12. Then, the apex of the tooth tip portion 33 of the first crown gear 11 and the tooth bottom portion 32 of the second crown gear 12 come into contact with each other at the meshing position A. The radius of the tooth bottom portion 34 of the first crown gear 11 is larger than the radius of the tooth tip portion 31 of the second crown gear 12, and the tooth tip portion 31 of the second crown gear 12 becomes the tooth bottom portion 34 of the first crown gear 11. It fits. With the wave motion of the first crown gear 11, the meshing position A moves, and the apex of the tooth tip portion 31 of the second crown gear 12 and the tooth bottom portion 34 of the first crown gear 11 come into contact with each other.

7 (a) and 7 (b) show perspective views in which cones are added to the teeth of the second crown gear 12 and the first crown gear 11. Here, a cone is added to make it easier to understand the shape of the tooth. As shown in FIG. 7B, the tooth tip portion 31 of the second crown gear 12 is composed of a part of the side surface of the cone C1. The tooth bottom portion 32 of the second crown gear 12 is also composed of a part of the side surface of the cone C2. On the same circumference, the radius of the cone C2 of the tooth bottom 32 is larger than the radius of the cone C1 of the tooth tip 31. The vertices of the cones C1 of the plurality of tooth tips 31 intersect at the meshing center P2. The vertices of the cones C2 of the plurality of tooth bottoms 32 also intersect at the meshing center P2. As shown in FIG. 3, the meshing center P2 is located on the axis 2a of the input shaft 2 and coincides with the center P1 of the wave motion of the first crown gear 11.

As shown in FIG. 7A, the tooth tip portion 33 of the first crown gear 11 is composed of a part of the side surface of the cone C3. The tooth bottom portion 34 of the first crown gear 11 is composed of a part of the side surface of the cone C4. The radius of the cone C4 of the tooth bottom portion 34 is larger than the radius of the cone C3 of the tooth tip portion 33. In order to make the pitch of the teeth of the first crown gear 11 and the pitch of the teeth of the second crown gear 12 different, the radius of the cone C3 of the tooth tip portion 33 of the first crown gear 11 is the tooth tip of the second crown gear 12. Equal to the radius of the cone C1 of the portion 31, the radius of the cone C4 of the tooth bottom 34 of the first crown gear 11 is smaller than the radius of the cone C2 of the tooth bottom 32 of the second crown gear 12. The apex of the cone C3 of the plurality of tooth tips 33 of the first crown gear 11 coincides with the meshing center P2, and the apex of the cone C4 of the plurality of tooth bottom portions 34 of the first crown gear 11 coincides with the meshing center P2. ..

As shown in the developed view of FIG. 6, the tooth tip portion 33 of the first crown gear 11 is formed in an arc, and the tooth bottom portion 34 is also formed in an arc. The tooth tip portion 31 of the second crown gear 12 is formed in an arc, and the tooth bottom portion 32 is also formed in an arc. Strictly speaking, when the teeth 30 and 35 of the conical first crown gear 11 and the second crown gear 12 are expanded, it becomes an ellipse, but it is regarded as an arc. As described above, the radius of the arc of the tooth tip 33 of the first crown gear 11 is equal to the radius of the arc of the tooth tip 31 of the second crown gear 12. In order to make the pitch of the teeth 35 of the first crown gear 11 and the pitch of the teeth 30 of the second crown gear 12 different, the radius of the tooth bottom portion 34 of the first crown gear 11 is set to the tooth bottom portion 32 of the second crown gear 12. Less than the radius.

When no preload is applied to the first crown gear 11, the tooth tip 33 of the first crown gear 11 comes into contact with the second crown gear 12 only at one place A. When preload is applied to the first crown gear 11, the plurality of teeth 35 of the first crown gear 11 and the plurality of teeth 30 of the second crown gear 12 come into contact with each other. When the first crown gear 11 is wave-moved, the meshing position A moves in the circumferential direction of the first crown gear 11 and the second crown gear 12, and the second crown gear 12 has the number of teeth with respect to the first crown gear 11. It rotates relatively by the difference.
<Other examples of tooth shapes of the first and second crown gears (an example in which the tooth tip is composed of the side surface of a cone and the tooth bottom is generated using a trochoidal curve)>

When the tooth tip portions 33, 31 and the tooth bottom portions 34, 32 of the first crown gear 11 and the second crown gear 12 have a shape composed of the side surfaces of the cone, the first crown gear 11 and the second crown gear 12 are manufactured. Is easy. However, as shown in the development view of the teeth of the first crown gear 11 and the second crown gear 12 in FIG. 8, when the locus of the tooth tip portion 33 (indicated by a circle) of the first crown gear 11 is drawn, the first crown is drawn. There is a slight gap g between the gear 11 and the second crown gear 12. This gap g may cause an angle transmission error and an increase in driving noise. In this example, the gap g is filled so that the tooth tip portion 33 and the tooth bottom portion 32 roll completely, and the angle transmission accuracy and the quietness are improved. However, this gap g is extremely small, and the angle transmission accuracy equivalent to that of the involute tooth profile can be obtained without filling the gap g.
(Outline of design)

Tooth profile curved design of the first crown gear 11 and the second crown gear 12, as shown in FIG. 9, first, creating a tooth profile on the reference circle r _c of the first crown gear 11 and the second crown gear 12 It starts with that. The created tooth profile curve is a single curve, not a surface. To obtain the tooth profile curved surface of the first crown gear 11 and the second crown gear 12, a tooth profile obtained by changing the radius r _c of the reference circle of the conical first crown gear 11 and the second crown gear 12 base Line up along. As a result, the tooth profile curved surfaces of the first crown gear 11 and the second crown gear 12 can be obtained.
(Tooth curve design guideline)

The first crown gear 11 and the second crown tooth top portion 33, 31 of the gear 12 is to be composed of the side surface of the cone, the reference circle r first crown on _c gear 11 and the tooth portion 33 of the second crown gear 12 Let the curve of, 31 be a single R arc. At this time, in order for the tooth tip portions 33, 31 and the tooth bottom portions 34, 32 to perform rolling motions with each other, the tooth bottom curve of the tooth bottom portions 34, 32 becomes a trajectory drawn by the tooth tip portions 33, 31. By smoothly connecting the single R arc of the tooth tip portions 33 and 31 and the tooth bottom curve of the tooth bottom portions 34 and 32, as shown in FIG. 9, the reference of the first crown gear 11 and the second crown gear 12 tooth profile curve on the circle r _c can be obtained. The tooth profile curve is created in the following order.

(I) The curve (trochoid curve) that the tooth tips 33 and 31 should pass through is obtained by wave motion (hereinafter referred to as precession motion).
(Ii) Assuming the radius of the tooth tips 33 and 31, the curve drawn when the tooth tips 33 and 31 pass on the trochoid curve obtained in (i) is obtained, and this is the tooth of the tooth bottoms 34 and 32. Let it be a bottom curve.
(Iii) The radius of the tooth tip portions 33 and 31 is determined so as to smoothly connect the tooth tip curves (arc) of the tooth tip portions 33 and 31 and the tooth bottom curves of the tooth bottom portions 34 and 32 to each other.
(Calculation of the trochoid curve that the tip of the tooth should pass through)

The first crown gear 11 meshes with the second crown gear 12 while precessing. The first crown gear 11 and the second crown gear 12 have a conical base body, and their tooth surfaces are on the conical base body. Therefore, congruent tooth profile curves are lined up in the circumferential direction, but tooth profile curves are similar but not congruent in the radial direction. Therefore, defining a certain reference circle r _c, determining the tooth profile curve on the reference circle r _c.

First, there are two cones with the reference circle r _c to the bottom, assuming a state in which the mutual vertices and bus as shown in FIG. 10 (a) are in contact, moving the cone precess cone , Let the fixed cone be a constant cone. Here, the apex of the cone is the origin O, the contact point between the bottom surfaces is the point P ₁ , the fixed point on the bottom surface of the moving cone is the point P ₂ , the foot of the perpendicular line drawn from the apex of the fixed cone to the bottom surface is H ₁ , and the moving cone. Let H ₂ be the foot of the perpendicular line drawn from the apex to the bottom. At this time, the locus drawn by the point P ₂ at the time of the dynamic cone is precession a curve should pass through the teeth (trochoid curve). Now, as shown in FIG. 10B, consider a case where the moving cone performs a precession without leaving the constant cone. If this precession is such that the moving cone rotates -ψ around its own axis OH ₂ and θ rotates around the constant cone, then point P ₁ is θ around OH ₁ and point P ₂ is It can be regarded as a -ψ rotation around OH ₂ . Here, as shown in FIG. 11, the vector normalized parallel to the line segment OH ₂ is n, the vector from the point O to the point P ₁ is p ₁ , and the vector from the point O to the point P ₂ is p ₂ . Then, p ₂ can be regarded as a vector obtained by rotating p ₁ around n by ψ.

と表すことができる。ここで、動円錐と定円錐がともに底面半径ｒ_ｃ、底角Φ_ｃであれば、ｎとｐ_１はそれぞれ、

It can be expressed as. Here, if both the moving cone and the constant cone have a bottom radius r _c and a base angle Φ _c , n and p ₁ are respectively.

と表すことができる。

It can be expressed as.

By changing the value of ψ, p ₂ obtained so far can represent a vector representing a curve through which the centers of the tooth tips 33 and 31 of the first crown gear 11 and the second crown gear 12 should pass. First, the curve that the center of the tooth tip portion 33 of the first crown gear 11 should pass is obtained. The moving cone is regarded as the first crown gear 11 and the constant cone is regarded as the second crown gear 12, and the number of teeth is z _i and z ₀ , respectively. The parameters of the precession of the moving cone are θ = θ _i and ψ = ψ _i . At this time, in the case of a forward gear, ψ rotates one tooth more in the opposite direction while θ makes one rotation, as shown in FIG. 12, and in the case of a reverse gear, ψ occurs while θ makes one rotation. Rotates in the opposite direction by one tooth less, so that equation 3 holds.

これを整理して、

Organize this

When finding the curve that the center of the tooth tip 31 of the second crown gear 12 should pass through, the moving cone is regarded as the second crown gear 12, the constant cone is regarded as the first crown gear 11, and the parameter of precession is θ = θ _o. , Ψ = ψ _o , then the equation 5 holds in the same way.

In this way, by selecting equations 4 and 5 and substituting equation 1 for ψ according to the characteristics of the gears to be combined, a curve through which the center of the tooth tip should pass can be obtained. At this time, an example of the obtained curve is shown in FIG. 13, the locus vector p ₂ draws is trochoidal curve. The rotation angles and directions of p1 and p2 are the same as those in FIG.
(Calculation of tooth bottom curve)

Next, the tooth bottom curve is obtained. Locus addendum portion 33 of the mating gear depicted as shown in FIG. 14 is tooth root curve p _3. That is, the locus obtained when the trochoid curve p ₂ through which the center of the tooth tip 33 of the mating gear should pass is obtained and the circle having the radius of the tooth tip 33 of the mating gear is moved on this trochoid curve p _2. Should be calculated. Here, the tooth tip radius of the mating gear is h _k , and this circle is C. At this time, as shown in FIG. 15, a vector p ₃ representing the tooth bottom curve, among the points when a circle C on p _2, also orthogonal to both p ₂ and p ₂ of the direction vector Delta] p ₂ a vector of up to P ₃ points to. Therefore, the relationship between the equation 6 and the equation 7 holds.

以上の結果から、

From the above results,

が成り立つ。なお、式中の正負は、方向ベクトルの向きによって決定される。
（歯先曲線と歯底曲線の接続）

Is established. The positive or negative in the equation is determined by the direction of the direction vector.
(Connection of tooth tip curve and tooth bottom curve)

FIG. 16A shows the tooth profile curve (tooth tip curve and tooth bottom curve) of the first crown gear 11 calculated according to the above, and FIG. 16 (b) shows the tooth profile curve of the second crown gear 12 calculated according to the above. (Tooth tip curve and tooth bottom curve) are shown. Here, the radius of the tooth tip curve is determined so that the tooth tip curve and the tooth bottom curve are smoothly connected. The radius of the tooth tip curve is determined on the condition that "when the tooth tip curve and the tooth bottom curve have only one contact point". (Equation of tooth tip curve) = (equation of tooth bottom curve) should be formulated, and the value of tooth tip radius when this has a multiple solution should be searched. From the above, the tooth profile curves of the first crown gear 11 and the second crown gear 12 can be generated.

FIG. 17 shows the tooth profile curves of the first crown gear 11 and the second crown gear 12 obtained according to the above. Black circles in the figure indicate contact points. From the start of contact in (S1) to the end of contact in (S5), it can be seen that the first crown gear 11 and the second crown gear 12 are in constant contact with each other and the contact point moves. Since the contact point moves, it can be seen that the first crown gear 11 and the second crown gear 12 roll with each other.

The tooth bottoms 34 and 32 of the first crown gear 11 and the second crown gear 12 are formed from the side surfaces of the cone, and the tooth tips 33 and 31 of the first crown gear 11 and the second crown gear 12 are formed by using a trochoid curve. Can also be generated. In this case, the curve of the tooth bottom portion 34, 32 of the reference circle first crown gear 11 and the second crown gear 12 on the r _c an arc of a single R, addendum of the tooth tip 33 and 31 using a trochoidal curve You just have to calculate the curve.
<Another example of the tooth shape of the first crown gear and the second crown gear (an example in which the tooth streaks are helical)>

As shown in FIG. 18, the tooth streaks can be made helical by shifting the phase of the tooth profile curve on the reference circle of the second crown gear 12 in the circumferential direction each time the radius of the reference circle is changed. .. As shown in FIG. 18, the phases of the tooth profile curves are different between the outside and the inside of the second crown gear 12. Similarly, the tooth streaks of the first crown gear 11 can be similarly helical.

The logarithmic spiral shown in FIG. 19 can be adopted for the helical tooth streaks. The logarithmic helix has a constant angle β with the generatrix of the conical body, and can be represented by the equation 9.

ここで、ａ，ｂはらせんの巻き方のパラメータである。
＜本実施形態の減速装置の効果＞

Here, a and b are parameters of how to wind the spiral.
<Effect of reduction gear of this embodiment>

According to the speed reducer of the present embodiment, the following effects are obtained. The tooth tips 33 and 31 of the first crown gear 11 and the second crown gear 12 have a convex shape based on the side surface of the cone, and the tooth bottom portions 34 and 32 of the first crown gear 11 and the second crown gear 12 are conical. Since the concave shape is based on the side surface of the above, one of the first crown gear 11 and the second crown gear 12 can be smoothly fitted to the tooth tip portions 33 and 31 of the other tooth bottom portions 34 and 32. Further, since most of the meshing between the tooth tip portions 33 and 31 on one side and the tooth bottom portions 34 and 32 on the other side is rolling, the efficiency of the gear can be improved.

Since the apex P2 of the cones of the tooth tips 33, 31 and the tooth bottoms 34, 32 of the first crown gear 11 and the second crown gear 12 coincide with the center P1 of the precession of the first crown gear 11, the tooth tips The portions 33 and 31 and the tooth bottom portions 34 and 32 can be brought into line contact with each other. Since the tooth contact area can be increased and the meshing ratio can be increased, high rigidity, high efficiency, and quietness can be realized.

The tooth tips 33 and 31 of the first crown gear 11 and the second crown gear 12 have a shape formed from the side surface of a cone, and the tooth bottom portions 34 and 32 of the first crown gear 11 and the second crown gear 12 have a shape. Since the shape is generated by using the trochoid curve drawn when the conical base of the first crown gear 11 is rolled along the conical base of the second crown gear 12, the tooth tips 33 and 31 and The meshing with the tooth bottoms 34 and 32 can be made into perfect rolling, and further high rigidity, high efficiency, and quietness can be realized.

Since the radius R of the cone of the tooth tip 33 of the first crown gear 11 and the radius R of the cone of the tooth tip 31 of the second crown gear 12 match, it is easy to manufacture both tooth tips 33 and 31. Yes, the strength can be matched.

Since the tooth streaks of the tooth tip portions 33, 31 and the tooth bottom portions 34, 32 of the first crown gear 11 and the second crown gear 12 are helical, the tooth contact area can be increased and the meshing ratio can be increased. Further high rigidity, high efficiency, and quietness can be realized.
<Overall configuration of the reduction gear of the second embodiment>

20 and 21 show a speed reducer according to a second embodiment of the present invention. FIG. 20 shows a cross-sectional perspective view of the speed reducer, and FIG. 21 shows an exploded perspective view of the speed reducer. In the reduction gear of the first embodiment, the wave motion and the rotary motion are shared between the first crown gear 11 and the second crown gear 12, the first crown gear 11 is wave-moved, and the second crown gear 12 is rotated. Exercise. In the speed reducer of the second embodiment, the second crown gear 42 is fixed to the housing 50. Then, only the first crown gear 41 is made to perform wave motion and rotational motion. The rotational movement of the first crown gear 41 is transmitted to the output unit 62 via a spherical spline joint 44 arranged inside the first crown gear 41.

The reduction gear of this embodiment includes a housing 50, a cam portion 64 in which an inclined cam 63 is integrally provided on an input shaft 61, a first crown gear 41, and a second crown gear 42 facing the first crown gear 41. A spline joint 44 that supports the first crown gear 41 so as to be wave-movable, and an output unit 62 that is non-rotatably connected to the spline shaft 45 of the spline joint 44 are provided. When the input shaft 61 is rotated around the axis 61a, the output unit 62 is decelerated and rotates around the axis 61a. In the following, for convenience of explanation, the configuration of the speed reducer will be described using the directions when the axes of the input shaft 61 and the output unit 62 are arranged in the X direction, that is, the X, Y, and Z directions shown in FIG. ..

As shown in FIG. 21, the first crown gear 41 and the second crown gear 42 face each other. A plurality of teeth are radially formed on the facing surfaces of the first crown gear 41 and the second crown gear 42. The tooth shapes of the first crown gear 41 and the second crown gear 42 are the same as the tooth shapes of the first crown gear 11 and the second crown gear 12 of the first embodiment. The number of teeth of the first crown gear 41 and the number of teeth of the second crown gear 42 are not particularly limited. For example, the number of teeth of the first crown gear 41 is set to 51, and the number of teeth of the second crown gear 42 is set to 50. The first crown gear 41 is inclined with respect to the second crown gear 42 and meshes with the second crown gear 42. As shown in FIG. 20, the second crown gear 42 is arranged in the YZ plane. The facing surface of the first crown gear 41 is tilted by an angle α around the Z axis with respect to the YZ plane.

As shown in FIG. 20, the first crown gear 41 is supported by a spherical spline joint 44 as a support portion so as to be wave-movable and non-rotatable around the axis 61a. The spline joint 44 is integrally provided with the first crown gear 41, and is arranged inside the outer ring portion 46 and the outer ring portion 46 having the outer ring spline groove 46a on the spherical inner peripheral surface, and the outer ring spline groove on the spherical outer peripheral surface. An inner ring portion 47 having an inner ring spline groove 47a facing 46a, and a ball 48 as a rolling element intervening between the outer ring spline groove 46a and the inner ring spline groove 47a so as to roll and move along an arc trajectory in the axial direction. , Equipped with. The spline shaft 45 of the inner ring portion 47 is non-rotatably connected to the output portion 62 by using a key or the like. The ball 48 is held in the cage 49. The rotational movement of the first crown gear 41 around the axis 61a is transmitted to the output unit 62 via the spline joint 44. The output unit 62 is rotatably supported by the housing 50 by the cross roller 69.

The cam portion 64 includes an input shaft 61 rotatably supported by the housing 50 around the axis 61a, a disk-shaped inclined cam 63 integrally provided with the input shaft 61, an inclined cam 63, and a first crown gear 41. A ball 65 as a rolling element intervening so as to be able to roll and move is provided between the two. The input shaft 61 is rotatably supported by the housing 50 by two bearings 67 and 68.

When the cam portion 64 is rotated around the axis 61a using a drive source such as a motor (not shown), the tilted cam 63 of the cam portion 64 moves the first crown gear 41 to the meshing portion with the second crown gear 42. While waving. Along with the wave motion of the first crown gear 41, the first crown gear 41 rotates relative to the second crown gear 42 by the difference in the number of teeth. Since the second crown gear 42 is fixed to the housing 50, the first crown gear 41 rotates. The rotating wave motion of the first crown gear 41 is also called a precession motion. The rotational movement of the first crown gear 41 is transmitted to the output unit 62 via the spline joint 44. In this embodiment, since the second crown gear 42 is fixed, a reduction ratio of 1/50 can be obtained.
<Overall configuration of the reduction gear of the third embodiment>

FIG. 22 shows a cross-sectional perspective view of the speed reducer according to the third embodiment of the present invention. In the reduction gear of this embodiment, the second crown gear 72, the third crown gear 73, the facing teeth 71a facing the second crown gear 72, and the facing teeth 71b facing the third crown gear 73 are back-to-back. It is provided with a first crown gear 71 to be held. In the cam portions 74a and 74b, the first crown gear 71 is engaged with the second crown gear 72 and the second crown gear 72 so that the first crown gear 71 meshes with the second crown gear 72 and the first crown gear 71 meshes with the third crown gear 73. The first crown gear 71 is wave-moved so as to be tilted with respect to the triple crown gear 73 and the meshing portion moves in the circumferential direction.

When the input shaft 75 is rotated, the first crown gear 71 undulates. The rotation speed of the input shaft 75 is decelerated and transmitted to the output unit 76. The reduction ratio is determined by the number of teeth of the first crown gear 71, the second crown gear 72, and the third crown gear 73. The tooth shapes of the first crown gear 71 and the second crown gear 72 are the same as those of the first crown gear 11 and the second crown gear 12 of the first embodiment, and the first crown gear 71 and the third crown gear 73 The shape of the teeth is the same as that of the first crown gear 11 and the second crown gear 12 of the first embodiment.

FIG. 23 (a) shows a side view of the second crown gear 72 and the third crown gear 73, and FIG. 23 (b) shows a side view of the first crown gear 71. The facing teeth 72a of the second crown gear 72 are formed with a tooth bottom portion 72a1 formed from the side surface of the conical Co1. The vertices of the cone Co1 of the tooth bottom 72a1 intersect at the center P of the wave motion of the first crown gear 71. The tooth tip portion 72a2 of the second crown gear 72 is also formed on a part of the side surface of the cone (not shown). The vertices of the cone of the tooth tip 72a2 also intersect at P. Similarly, the tooth bottom portion 73a1 and the tooth tip portion 73a2 of the third crown gear 73 are also composed of the side surfaces of the cone (indicating only the cone Co2 of the tooth bottom portion 73a1), and the vertices of the cones intersect at P.

As shown in FIG. 23B, the first crown gear 71 is provided with facing teeth 71a facing the second crown gear 72 and facing teeth 71b facing the third crown gear 73 so as to face each other. The tooth bottom portion 71a1 and the tooth tip portion 71a2 of the opposing teeth 71a are formed from the side surfaces of a cone (showing only the cone Co3 of the tooth bottom portion 71a1), and the vertices of the cones intersect at P. The tooth bottom portion 71b1 and the tooth tip portion 71b2 of the opposing teeth 71b are formed from the side surfaces of a cone (showing only the cone Co4 of the tooth bottom portion 71b1), and the vertices of the cones intersect at P.

As shown in FIG. 22, when the input shaft 75 is rotated by using a drive source such as a motor (not shown), the first crown gear 71 undulates. With the wave motion of the first crown gear 71, the meshing portion between the first crown gear 71 and the second crown gear 72 and the meshing portion between the first crown gear 71 and the third crown gear 73 move in the circumferential direction. Then, with the wave motion of the first crown gear 71, the first crown gear 71 rotates relative to the second crown gear 72 by the difference in the number of teeth between them. Further, the third crown gear 73 rotates relative to the first crown gear 71 by the difference in the number of teeth between them. The rotation speed of the third crown gear 73 is the sum of the relative rotation speed of the first crown gear 71 with respect to the second crown gear 72 and the relative rotation speed of the third crown gear 73 with respect to the first crown gear 71. Become a thing. If the two sets of gears are rotated in directions that cancel each other out, a large reduction ratio can be obtained, and if they are rotated in a direction that promotes each other, a small reduction ratio can be obtained.
<Design of teeth of reduction gear according to the third embodiment>

The design of the teeth of the speed reducer of the third embodiment is substantially the same as the design of the teeth of the speed reducer of the first embodiment. However, the first crown gear 71 has a conical base that is convex toward the third crown gear 73, and the third crown gear 73 has a mortar-shaped base that is convex toward the first crown gear 71. .. Therefore, as shown in FIG. 24A, the first crown gear 71, which is a constant cone, is covered with the third crown gear 73, which is a moving cone. In finding the trochoid curve, the above number 2 is used.

に変更する必要がある。ここで、動円錐の底面半径がｒ_ｃr、底角がΦ_ｃｒ、定円錐の底面半径がｒ_ｃｆ、底角がΦ_ｃｆである。他の数３〜数７は、変更する必要がない。

Need to be changed to. Here, the bottom radius of the moving cone is r _cr , the base angle is Φ _cr , the bottom radius of the constant cone is r _cf , and the base angle is Φ _cf. The other numbers 3 to 7 do not need to be changed.

FIG. 25 shows the obtained trochoidal curve. In Figure 25, the locus vector p ₂ draws is trochoidal curve.

The present invention is not limited to the above embodiment, and can be embodied in various embodiments without changing the gist of the present invention.

In the above embodiment, the speed reducer has been mainly described, but by reversing the input side and the output side, it can also be used as a speed increaser that is compact in the axial direction. For example, by using the present invention as a speed increaser for a generator having a large power on the input side such as a hydroelectric generator, it is possible to reduce the size in the axial direction.

11, 41, 71 ... 1st crown gear, 12, 42, 72 ... 2nd crown gear, 73 ... 3rd crown gear, 31 ... 2nd crown gear tooth tip, 32 ... 2nd crown gear bottom, 33 ... the tip of the first crown gear, 34 ... the bottom of the first crown gear, 71a1, 71b1 ... the bottom of the first crown gear, 71a2, 71b2 ... the tip of the first crown gear, 72a1 ... the second Crown gear tooth bottom, 72a2 ... Second crown gear tooth bottom, 73a1 ... Third crown gear tooth bottom, 73a2 ... Third crown gear tooth tip, C1 ... Conical (second crown gear tooth tip) Cone), C2 ... Cone (cone at the bottom of the second crown gear), C3 ... Cone (cone at the tip of the first crown gear), C4 ... Cone (cone at the bottom of the first crown gear), Co1 ... Cone (cone at the bottom of the second crown gear), Co2 ... Cone (cone at the bottom of the third crown gear), Co3, Co4 ... Cone (cone at the bottom of the first crown gear), P2, P ... apex of the cone, P1, P ... center of the wave motion, p 2 _... trochoid curve

Claims (4)

With the first crown gear
The second crown gear, which has a different number of teeth from the first crown gear and faces the first crown gear,
A cam that tilts the first crown gear with respect to the second crown gear so that the first crown gear meshes with the second crown gear, and waves the first crown gear so that the meshing portion moves. In a deceleration or speed-increasing device including
The first crown gear and the second crown gear have tooth tips and tooth bottoms alternately in the circumferential direction.
The first crown gear and the tooth tip portion of the second crown gear have a convex shape formed of a part of the side surface of the cone.
The curve on the reference circle of the tooth tip portion of the first crown gear and the second crown gear is an arc.
Deceleration or increasing to the first crown gear and the tooth bottom of the tooth tip portion is drawn curve of tooth bottom the curve first crown gear and the second crown gear on the reference circle of the second crown gear Speed device. The deceleration or acceleration device according to claim 1, wherein the apex of the cone coincides with the center of the wave motion of the first crown gear. Deceleration of claim 1 or 2 and the radius of the cone of the tooth tip portion and said conical radius of the addendum portion of the first crown gear the second crown gear and said one Itasu Rukoto Or a speed increasing device. The deceleration or speed-increasing device according to any one of claims 1 to 3 , wherein the tooth streaks of the tooth tip portion and the tooth bottom portion are helical.

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