JP2612591B2 - Deflection gears - Google Patents

Description

Description: TECHNICAL FIELD The present invention relates to a flexural gear device. More specifically, the present invention relates to an improvement in the shape of teeth of an internal gear and an external gear used in a flexion gear device.

(Prior Art) A typical flexible meshing gear device is provided with a rigid internal gear, and is provided on the internal gear, and is deformed into an elliptical shape so as to mesh with the internal gear at, for example, two places. A flexible external gear having 2n less teeth (n is a positive integer) than the number of teeth;
A wave generator having an input end that fits inside the external gear and deflects the external gear into an elliptical shape. When the wave generator is rotated through an input shaft, the elliptical shape of the external gear is changed. When the two gears are rotated relative to each other according to the difference in the number of teeth by the rotation of the ellipse, and the output shaft is provided on the internal gear or the external gear, the output shaft has a large reduction ratio with respect to the input shaft. Rotate.

Normally, involute tooth profile is used as the tooth profile used in the conventional flexible meshing gear device. However, various ideas have been tried to further improve the meshing property and to enhance the driving performance and load capacity. I have. For example, one of the present inventors has proposed a method in which the meshing of an internal gear and an external gear is approximately treated as the meshing of the teeth of a rack (JP-A-63-1159).
43). In this method, the motion trajectory of the teeth of the flexible external gear relative to the tooth space of the rigid internal gear generated by the wave generator used is expressed by the contraction ratio 1 / By adopting the mapping curve analogous to 2 as the tooth profile curve of the tooth flank of both gears, continuous contact of the teeth is possible.

(Problems to be Solved by the Invention) However, the tooth profile curve adopted in this method is a relatively complicated one in which the radius of curvature along the curve changes asymmetrically across the maximum value. For this reason, in order to implement such a curve in a tool and to cut an external gear or an internal gear accurately, more advanced technology is required as compared with the conventional involute tooth profile, which leads to an increase in cost. There was a problem.

In view of this point, an object of the present invention is to provide a flexible meshing gear device in which an internal gear and an external gear can make continuous contact in a meshing region of teeth, at the same time at low cost and in production. It is an object of the present invention to realize a tooth profile that is highly susceptible and enables more accurate machining.

(Means for Solving the Problems) In order to achieve the above-mentioned object, in the flexion meshing gear device of the present invention, each tooth profile of the internal gear and the external gear is connected to a circular arc portion and a straight line smoothly connected thereto. It is created by a reference rack consisting of a tooth profile with a toothed end with a portion. This arc portion adopts an arc shape having a radius of about 1/2 or near 1/2 of the maximum radius of curvature in the motion trajectory of the external gear determined by the shape of the wave generator with respect to the tooth groove of the internal gear. It is.

(Example) Hereinafter, an example of a method of determining an arc shape of a tooth tip portion in a tooth shape of a reference rack of the present invention will be described with reference to the drawings.

First, FIG. 1 shows the entire configuration of the flexion-meshing gear device in the present embodiment.

This flexible meshing gear device 1 includes a rigid internal gear 2, a flexible ring-shaped external gear 3 provided inside the internal gear, and a fitting inside the external gear. And a wave generator 4 that deflects the ellipse into an elliptical shape. The wave generator 4 further comprises an inner elliptical cam plate 5 and a ball bearing 6 fitted on the outer periphery of the cam plate 5 and bent into an elliptical shape. The cam plate 5 is connected to an input shaft (not shown) through a hole provided in the cam plate 5. By rotating the cam plate from the input shaft, the elliptical shape of the wave generator is rotated. The two long ends A and B of the wave generator
In the region, the teeth of the internal gear and the external gear mesh with each other. That is, if the wave generator makes exactly one rotation, relative rotation occurs between the two gears by the number of teeth.

Tooth profile curve that can be continuously contacted Here, the tooth shape conventionally used in this device is a straight tooth shape or an involute tooth shape, but in these cases, the tooth engagement is compared with the long axis end of the wave generator. It is limited to a narrow area. The tooth profile proposed by one of the present inventors mentioned earlier is not limited to the meshing of the teeth in the narrow range of both long shaft ends of the wave generator, but in the range where the teeth of both gears are engaged. It creates a tooth profile that allows all teeth to touch (this is the meaning of continuous contact). To describe this method, the meshing of the internal gear and the external gear is approximated by the meshing of the teeth of the rack, and the rigid internal gear generated by the wave generator used is used. A mapping curve obtained by converting a required range of the movement trajectory of the tooth of the flexible external gear with respect to the tooth groove into a similarity at a contraction ratio of 1/2 is adopted as the tooth profile curve of the end face of the reference rack of both gear teeth. ing.

This method will be described in more detail. For the sake of simplicity, the elliptical formula of the pitch line of the flexible external gear deflected by the wave generator is given in polar coordinates (r, θ) as shown in FIG.

Here, r _o is the flexible external undeformed reference pitch circle radius of the gear, kd _O deformation amount of the reference pitch diameter, d _o is the number of teeth of the rigid internal gear z _c, of the flexible external gear when the number of teeth and z _F And k is a deviation coefficient that gives an actual deformation amount. According to k <1, k = 1, k> 1, they are referred to as negative deviation, no deviation, and positive deviation, respectively. At this time,
The motion trajectory of the teeth of the flexible external gear with respect to the tooth space of the rigid internal gear is represented by a rack approximation (z _c , z _F → ∞ while keeping z _c −z _F constant).
) Can be given by the following equation.

FIG. 3 shows an outline of the motion trajectory. A, b, and c in the figure correspond to k = 1, k <1, and k> 1, respectively.

For simplicity, the case of k = 1 will be described. FIG. 4 shows such a case. In the same figure, curve 9 is the motion trajectory, and point 8
Indicates the point of the addendum of the flexible external gear, and point 10 indicates the limit position where the teeth of the two gears contact each other farthest. Here, in FIG. 4, curve 11 shows the tooth profile of the flank surface of the rigid internal gear, and curve 13 shows the tooth profile of the flank surface of the flexible external gear. Tooth profile, curved
11 is a similarity transformation of the motion trajectory 9 at the contraction ratio 1/2 with the point 10 as the origin, and the curve 13 rotates the curve 11 by 180 ° about the point 12 which is the midpoint between the points 8 and 10. It was obtained.

If the tooth flank surfaces of both gears are configured in this way, the tooth profile 13 of the tooth flank surface of the flexible external gear will have a rigid internal gear while the tip point 8 moves along the locus 9 to the point 10. The contact can be continuously maintained with the end surface 11 of the tooth.

Method of Setting Tooth Profile Curve According to the Present Invention Regarding the tooth profile curve 11, a change in the radius of curvature ρ along the curve will be examined. Since this ρ is equal to 1/2 of the radius of curvature of the movement locus 9 from equation (3), according to the official differential geometry, as eta = 2 [Theta] _W, the following expression is obtained.

Next, this equation is differentiated with η to see the change in the radius of curvature. That is The extreme value of the radius of curvature ρ is obtained from dρ / dη = 0.

That is, −3 cos ² η + 4 cos η−1 = (3 cos η−1) (− cos η + 1) = 0 − (6) The following results are obtained by setting θ _W to a significant value of η that satisfies this expression and θ _Wo .

^{_{θ Wo = 1 / 2cos -1 (}} 1/3) = 35.26 ° - (7) Figure 5 shows the change of the radius of curvature ρ for theta _W. This shows that θ _Wo gives the maximum value ρ _max of ρ. That is, the following result is obtained from equation (4).

FIG. 6 shows the relationship between the motion trajectory and the continuous contact tooth shape again. In the figure, a point on the motion trajectory with respect to θ _Wo giving the maximum radius of curvature ρ _max is defined as P. A point on the tooth profile 11 corresponding to this point P is defined as Q. At this point Q, the curvature circle C
(Radius ρ _max ), the curve 11 fits the curve 11 very well near the point Q.
It can be seen that it may be replaced by Therefore, in the present invention, the curvature circle C is adopted as the curved shape of the tooth tip portion.

FIG. 7 shows tooth flank faces of the reference racks of the two gears according to the present invention, in which the main part of the tooth flank is formed by the above-mentioned curvature circle C and the datum of the reference rack is shown. The point M is formed as a straight line of the pressure angle α. At this time, the connection between the curvature circle and the straight line is made smoothly. That is, the pressure angles at the contact points are matched. In the same figure, MC is the linear portion of the end of the flexible external gear, Is also the arcuate part of the addendum, MA is the linear part of the addendum of the rigid internal gear, Is the arc portion of the addendum, and shows a state in which the teeth of the flexible external gear are deepest and have entered the tooth spaces of the rigid internal gear. Considering the process in which the rigid internal gear is fixed and the teeth of the flexible external gear move along the motion trajectory l from the position, the linear portion MC and the linear portion MA gradually increase in distance and increase in the interval. When point C reaches point C ′, the maximum clearance δ (= A
C ').

After that, the arc Through the position of the arc Reaches the limit position C "D" while maintaining a constant clearance δ. That is, the tooth scale according to the present invention geometrically contacts the linear portion at the deepest engagement (as described later, the tooth profile of the present invention also has a linear portion as an extension of the linear portion of the tooth end at the root of the tooth. ), There is always an engagement with a clearance between the tooth surfaces. At first glance, this seems to be a drawback of the tooth profile of the present invention, but is rather an advantage in terms of the function of forming a lubricating oil film between the tooth surfaces, and the teeth and teeth of the flexible external gear due to the load. Considering the deformation of the bottom rim, since the clearance can be made to be the same as these deformation amounts as will be seen later, an effect similar to tooth profile modification from a true involute curve in an involute gear can be expected. This is a feature that can be regarded as an advantage of the tooth profile of the present invention. That is, the tooth profile of the present invention can be said to be a substantially continuous contact tooth profile.

Next, the above formula of the clearance δ is derived. In Figure 7, the tooth depth of the straight portion of the end teeth of the two gears together with h _{the as,} the following expression is obtained by applying a k = 1 (3) formula motion trajectory l.

Here the pressure angle α is a function of the general theta _W, (3) tan [alpha from equation = 1 / 2tanθ _W - relation of (10). On the other hand, from the equation (3), at the point C ′, There is a relationship between this and (10) Is obtained, and this is put into equation (9) to obtain the following result.

I give specific numerical values. The reference module m of the reference rack is m = 0.3 mm, and the number of teeth of the internal gear and the external gear is z _c = 2.
02, if z _F = 200, r ₀ = 1/2 × 0.3 × 200 = 30 mm,
According to equation (2) It is. Here obtain h _as = 0.3m = When 0.09 mm (12) from the equation [delta] = 0.012 mm, also the alpha = 18.12 degrees from the (11) equation. These numerically support the foregoing.

Next, the root portion of the reference rack of the present invention may have an arbitrary shape as long as the meshing of the tooth tip portion is not interrupted, but this is constituted by a straight extension of the tooth tip portion and an arc of the fillet portion. Is reasonable. FIG. 8 shows an example. Computer simulation of the state of contact of the teeth of the flexible meshing gear device due to this tooth profile confirmed that the tooth profile was such that the meshing was sufficiently close to continuous contact.

In the present invention, when determining the specific shape of the reference rack tooth profile, it is first appropriately select tooth depth h _{the as} the straight portion of the end teeth, then (11) determining the pressure angle α of the straight line portion by the formula.
An arc having the radius shown in the equation (8) is smoothly connected to this. At that time, bamboo h _a at the end of the teeth can be selected as appropriate. In addition, the tooth height h _{fs of the} straight portion is h
_fs ≧ h _as is satisfied, and the arc of the fillet portion is formed so as not to interfere with the tooth tip of the counterpart (No. 8).
See figure).

Other Embodiments The case where k = 1 has been described above, but the same tooth profile configuration can be achieved in a certain range for k> 1 and k <1. Further, in the above-described example, the internal gear and the external gear as shown in FIG. 1 are described as a flexible meshing gear device of a type in which the internal gear and the external gear mesh at two places. However, the present invention relates to such a flexible meshing gear device. Not limited. For example, the gist of the present invention is also applied to a flexible meshing gear device of a type in which the number of teeth of both gears is 3n and meshes at three places.

According to the present invention, according to the present invention, the tooth profile of the reference rack on the tooth flank of each of the internal gear and the external gear is determined by both the movement trajectories of the teeth of the external gear with respect to the tooth grooves of the internal gear determined by the shape of the wave generator. Since it is formed from an arc best approximated to a mapping curve obtained by similarity conversion with a contraction ratio of 1/2 with the limit position of contact between the gear teeth as the origin, and a straight line smoothly connected to the arc, the tooth of both gears Substantially mesh with each other continuously. This leads directly to an increase in the rigidity and strength of the flexion gear device. Further, in the present invention, by setting the central portion of the tooth profile to be a straight line, the respective tooth shapes corresponding to this portion of the internal gear and the external gear become involute tooth profiles, and the advantages of the involute tooth profile in terms of machining, measurement, and maintaining accuracy. There is also an advantage that you can enjoy. As described above, according to the present invention, it is possible to realize a tooth profile capable of continuous contact using a simple arc and a straight line, so that it is possible to obtain a powerful flexible meshing gear device with high productivity and bottom cost.

[Brief description of the drawings]

FIG. 1 is a front view of a flexible meshing gear device. FIG. 2 is an explanatory diagram of a pitch line of a flexible external gear. FIG. 3 is an explanatory diagram showing a locus of movement of the teeth of the flexible external gear with respect to the tooth spaces of the rigid internal gear. FIG. 4 is an explanatory diagram of the formation of the tooth flank tooth profiles for making continuous contact between the internal gear and the external gear approximated by a rack. FIG. 5 is an explanatory diagram showing a change in a radius of curvature along the movement trajectory shown in FIG. FIG. 6 is an explanatory diagram showing the relationship between the motion trajectory shown in FIG. 3 and the tooth profile of the present invention. FIG. 7 is an explanatory view showing the relationship between the tooth flank of the reference rack of the rigid internal gear and the flexible external gear according to the present invention. FIG. 8 is an explanatory diagram showing an example of a reference rack tooth profile of the flexion gear device according to the present invention. DESCRIPTION OF SYMBOLS 1... Flexible gear 2... Internal gear 3... External gear 4... Wave generator 9... Motion locus C... Curvature circle α... Pressure angle MC. Straight section MA …… Linear part of the addendum of the internal gear

Claims (2)

(57) [Claims] 1. A rigid circular internal gear, a flexible external gear disposed inside the internal gear, and bending the external gear radially so that a part of the external gear becomes a part of the internal gear. With a meshing wave generator.
By rotating a generator, a meshing portion of the external gear and the internal gear is rotated in a circumferential direction to generate relative rotation between the external gear and the internal gear. In the gear device, each tooth profile of the internal gear and the external gear is created by a reference rack having a tooth shape having an arc portion and a toothed end portion having a linear portion smoothly connected thereto, and the arc portion Is characterized by adopting an arc shape having a radius of 1/2 of the maximum radius of curvature in a tooth motion locus of an external gear determined by a shape of the wave generator with respect to a tooth groove of an internal gear. Flexible meshing gear. 2. A reference rack according to claim 1, wherein said reference rack has a tooth profile having an addendum portion having said arc portion and a straight portion smoothly connected thereto.