JPS5986751A - Arc gear - Google Patents

Abstract

PURPOSE:To make the titled gear miniaturized and light-weighted by a method wherein, in the titled gear wherein an arc toothed external gear is meshed with an arc toothed internal gear inscribing with each other, the tooth thickness is reduced down to 1/2 or less than that of the conventional arc gear slightly miniaturizing the overall teeth. CONSTITUTION:In a gear mechanism wherein an arc toothed internal gear 11 is meshed with an external gear 12 inscribing with each other, the tooth numbers N1, N1+l1 of the respective gears 11, 12 are made (n) times of those of the conventional gears while the module M1 is made 1/n times of the conventional module M. Then the internal gear 11 is formed by two arc curves comprising two arcs wherein the deddendum thickness on a pitch circle is around 2M1, the center of tooth form is located outside the pitch circle at the point exceeding the specified distance of (d) and the radius R11 is around M while the two arcs are internally extended from respective deddendum to make them intersect acute- angularly near the end of the tooth form. On the other hand, the external gear 12 is formed of two curves with the deddendum thickness around (pi-2)M1 and the tooth form corresponding to that of the internal gear 11.

Description

DETAILED DESCRIPTION OF THE INVENTION The present invention relates to an improvement of an arc-shaped gear in which teeth J (v) are arc-shaped.

Conventional arc-shaped gears are those in which an external gear with an arc-shaped tooth profile with the number of teeth N is inscribed and meshed with an internal gear with an arc-shaped tooth profile with the number of teeth N+e, and has a single arc-shaped tooth profile. Therefore, the difference in the number of teeth ef can be made smaller than the number of teeth N of an external gear, and this arc-shaped gear is often used as a differential speed reducer.

However, since this arc-shaped tooth profile was originally used as a substitute for a cycloid tooth profile, accurate meshing could not be achieved. I was using it in a different way.

However, since multiple gear sets are stacked, the axial length of the device becomes longer, making it larger and more expensive. between 2
By forming a plurality of arc-shaped tooth shapes, the effect of multiple gear sets can be achieved with one gear set, and the axial length of the differential speed reduction device can be shortened, making the device compact, lightweight, and inexpensive. It is an object of the present invention to provide an arc-shaped gear that can be manufactured to

First, the relationship between the cycloidal tooth profile, which is the origin of the arcuate tooth profile, and the arcuate tooth profile will be explained with reference to FIG.

6 points are the centers of the internal gear 1, and 1a is its pitch circle. External gear 2 rotating inscribed in the pitch circle 1a
The center of is on the circumference of a circle 3 with a radius γ, which is the middle, middle, and end of the six points, and due to the rotation of the external gear 2, its center is D
o + D] + D2...Move.

Note that the radius of the pitch circle 2a of the external gear 2 is 4·γ. When the center of the external gear 2 is at Do, the point Aoi where the pitch circle 2a touches the pitch circle 1a is defined as the origin 0. When the center of the external gear 2 moves by θ around 6 points, the external gear 2 rotates and moves by - in the direction of the reflected force, so as the center moves to DI ID2... Therefore, the point Ao on the circumference of the pitch circle 2a is Ao.
Move to t + A2...

Now, if we take the y-axis in the straight line direction connecting points 0 and 6, and xill k in the direction perpendicular to the V-axis from point 0, then the coordinates of locus A are (x ry ) k, r.

becomes. This is Zykloi F.

If we take γ as a unit and set it to γ-1, then there is a point E on the X axis whose length from point 0 is L, and the length from this point E to the above point A2 is also the length ' 5 it W: do it. Here, Az point ke, 8 points 10''u1='ll (1+-y)・d.

Since XT+,: == L2.

As θ becomes larger, L also becomes larger, but since equation (3) is an approximate equation, the larger θ becomes, the larger the error will be. Now, let θ=1 radian, for example, 4=10
Then, L=0.999, which is approximately equal to γ. Therefore, if the tooth shape is an arc of radius γ from point 0 on the X-axis with length γ, it can be used up to the vicinity of θ=0 as a substitute for the cycloid tooth shape. Note that the length of the perpendicular drawn from point E to the pitch circle 1a of the internal gear 1 is d.

d= 1+4 ・7 +r −(1+A)−7=
(C○ko]) +1- (i-+-a) It becomes l・2.

The radius of the pitch circle 2a of the external gear 2 is between the internal gear 1 and the external gear 2! When the cliff, which is the value divided by the distance between . In this case, interference can be prevented by forming an arc between the F points outside the Jb'iE point in the arc as shown by the broken line. Also (3)
In the formula, there is no interference between A-1 and Gian.

Next, FIG. 2 shows a conventional arc-shaped gear shown in the right half from the center line 1b, and the modules of the internal gear 1 and the external gear 2 are denoted by M. The number of teeth of internal gear 1 and external gear 2 is N-
1-/, N, the inner diameter of the pitch circle 1a of the internal gear 1 is (N-1-/)·M, and the diameter of the pitch circle 2a of the external gear 2 is NM. Also, the pitch of each circumference is π·M. Here, the radius Rr' of the arc-shaped tooth profile of the internal gear 1 is set to <approximately M, and M=γ, and the center of the radius R is set to a position d outward from the pitch circle 1a as described above. And the tooth root thickness of the pitch circle 1al of the internal teeth and gear 1 is approximately 2γ, that is, 2MA
Therefore, the tooth bottom length is approximately (π-2)·γ, and it is established as a gear. If the radius R2 of the arc-shaped tooth profile of the external tooth i1j 2 is placed at a position away from the side, the thickness of the tooth tip on the pitch circle 2a of the external gear 2 is approximately (π-2)·γ, that is, (π -2)
・It becomes M. There is one arc-shaped tooth pattern between the circumferential pitches PIF2 of the internal gear 1 and between the circumferential pitches Qt and Q2 of the external gear 2, respectively.

FIG. 3 shows the arc-shaped gear according to the first embodiment of the present invention, showing the left half from the center line, and the pitch circle is the same as that of the conventional arc-shaped gear shown in FIG. The number of teeth is multiplied by gn. Number of teeth f of the internal gear 11 at that time
If N1+es, then N1+e.

= n・(N+/), and the number of teeth of the external gear 12 f Nl
Then, N1=n-N. Also module 1km+
Then, Ml=Ba. Therefore, the pitch circle 11a of the incisor gear 11 (7) @ diameter is (Nt+/l) ・Mt=(N
+e) ・As it becomes M, the pitch circle 1 of the external gear 12
The diameter of 2a is Nl-M1=N-M, and the pitch circle is the same as the conventional one. The tooth profile corresponds to the circumferential pitch πM of the conventional one, and since n teeth are provided between the abutment and the ``6'', the root thickness on the pitch circle 11a of the internal gear 11 is approximately 2Mt -LM, and the total tooth tip thickness on the pitch circle 12a of the external gear 12 (π-2) M1 = (π-
2) In addition, the arc notch 11] forming the arc-shaped tooth profile is approximately 2M1, but the arc radius R4 and RL2 of each tooth profile are the same as R1 and R2 in Fig. 2. and abbreviated as M. Note that the center of the arc radius R1'1 and the center of the arc radius R12 are at a predetermined distance d=(1+A) from the circumference of the pitch circle 11a and the circumference of the pitch circle 12a, respectively.
It is located on the outer circumference by ``-1-1-(1+A))-γ, and if the above le is large, it is placed further outside.

Each arc-shaped tooth profile of the internally toothed gear 11 consists of two circular arc curves that extend inward from the root point and intersect at an acute angle near the tip of the tooth profile. Each arc-shaped tooth profile consists of two arc curves each extending inward from a point at the tip of the tooth and intersecting at an acute angle at the base of the tooth.

Therefore, the tooth thickness of these tooth profiles is approximately - compared to the conventional one, but all the teeth are only slightly lower, and the gear set of the conventional external gear 2 and internal gear 1 described above is The same effect as shifting the phase by -hits occurs. In addition, the difference in the number of teeth between the internal gear 11 and the external gear 12 is 11k 4
Individual.

FIG. 4 shows an arc-shaped gear according to another embodiment of the present invention, in which the number of teeth is twice that of the first embodiment shown in FIG.
The difference in the number of teeth between the internal gear 11 and the external gear 12 is four, as in the first embodiment. Therefore, if the module is kMz, the diameter of the pitch circle 11a of the incisor gear 11 is (2Nj+el)
- M2, and the diameter of the pitch circle 12a of the external gear 12 is 2N1·M2.

In this embodiment, the tooth tips of the internal gear 11 are shortened, and the value A, which is the radius of the pitch circle 12a of the external gear 12 divided by the distance between the centers of the internal gear 11 and the external gear 12, is further increased. It was shown that interference between the tooth tips can be avoided even when

Next, as explained above, when the hardness is high, the arc-shaped tooth profile of the internal gear 11 may be scraped. In that case, the tip of the tooth, for example, the radius (005 to 0
．． 10) - Chamfer the R12 circle.

In addition, FIG. 5 shows another solution 7. Although FIG. 5 shows only a part of the arc-shaped gear, other parts are the same. A,
Point B is the intersection of the pitch circle 12a and the arc of the circular tooth shape of the external gear 12 with radius R12, and point H is the midpoint of the points A and B on the pitch circle 12a. External gear 12
Draw a straight line connecting point D, which is the center of
- Subtract J' and S-8'. The straight lines J-J' and S-
Let the points of contact between 8' and the circular arc be point T and point U, respectively, and
Let the intersections of the straight lines JJ' and ss' and the pitch circle 12a be point V and point W, respectively. The above points ■ and W are internal gear 1, respectively.
Since it is outside the arc-shaped tooth profile of No. 1, the straight line TV and the straight line U-W are each part of the tooth profile of the external gear 12, and from the remaining rT points and U points toward the tooth J, if.

The internal gear 11 and the external gear 12 contact each other near points T and U to transmit power, and the pressure angle changes only slightly from zero, and the force is transmitted to both teeth ip and rotates. , the amount of work that occurs there is small and the loss is small.

Further, the contact area at this time becomes larger, the surface pressure can be lowered, and the arc-shaped tooth profile of the internal gear 110 is prevented from being scraped.

As explained above, the present invention has a tooth thickness that is less than 1 inch compared to the conventional arc-shaped southeast tooth thickness, and moreover, by making only all teeth (machined) slightly lower, the tooth thickness can be reduced between the same circumferential pitch as the conventional gear. to 2
Since a plurality of arc-shaped tooth patterns are formed, a gear set h4L of an external gear and an internal gear circumscribing the external gear is stacked and the phases are shifted, and one set is used in a differential reduction gear. Compared to the conventional method, this is possible with one set of gears, the axial length of the device is shortened, and the device is small, lightweight, and inexpensive.
have

[Brief explanation of the drawing]

Fig. 1 is a relationship diagram between the cycloid tooth profile and the arc-shaped tooth profile, which is the origin of the arc-shaped tooth profile, Fig. 2 is a front view showing the right half of the conventional arc No. 1 gear from the center line, and Fig. 3. A front view showing the left half of the first embodiment of the arc-shaped gear according to the present invention from the center line r9, FIG. 4 is a front view showing another embodiment of the arc-shaped gear according to the present invention, and FIG. 5 is an outside view. FIG. 2 is an enlarged view showing a portion of the external gear shape for preventing the internal gear from being scraped by the tips of the teeth of the gear. In addition, 1st 1st middle - f? ] u indicates the same or equivalent part. 11...Internal tooth bacteria 11a...Pitch circle 12...
・External gear 12a... Pinch circle Rtt... Arc radius of internal gear R12... Arc radius of external gear 5n

Claims (1)

[Claims] 1) In an arc-shaped gear in which an external gear having an arc-shaped tooth profile is inscribed and meshed with an internal gear having a similar arc-shaped tooth profile, what is the number of teeth of the external gear and the internal gear? N1 (=n-
N ), N1 +lV1 (=nN+ne) and module k Mt (='), and the internal gear has a root thickness of approximately 2 on its pitch circumference.
Ml, and each tooth profile has a center located outside the pitch circle by a predetermined distance d or more, and a radius R11 of approximately M(""
The external gear consists of two circular arc curves, each extending inward from the tooth root point and intersecting at an acute angle near the tip of the tooth profile. The tip thickness is approximately (π-2)Ml, and the notch width by the arc forming the arc-shaped tooth profile is approximately 2M+6')・The center of each tooth profile is at a predetermined distance from the pitch circle of the external gear. It is understood that it consists of two circular arc curves, which are two circular arcs that are located on the outside by more than d and have a radius R12 of approximately M (=n#M+), each extending inward from the point of the tooth tip and intersecting at an acute angle at the root of the tooth. Characteristic arc-shaped gears.