CN1068105C - Flexible meshing type gear having a negative deflection over-running tooth profile - Google Patents

Abstract

In a flexible meshing gear device (1), it is stipulated that it is within a basic section defined perpendicular to the axis of the flexible external gear (3) at a predetermined point on the interdental curve of the flexible external gear (3) The radial deflection (W) is a negative deviation deflection less than the rated deflection (Wo). Both the rigid internal gear (2) and the flexible external gear (3) are spur gears, and the number of teeth of the flexible external gear is 2n (n is a positive integer) less than that of the rigid internal gear (2). The meshing of the two tooth shapes can make the connection contact in the basic section perpendicular to the axis through the meshing, which improves the performance of maintaining the lubricating oil film between the tooth surfaces.

Description

Flexible meshing gear unit with negative misalignment calibrated tooth profile

The present invention relates to a flexible meshing type gear unit, and more particularly, the present invention relates to tooth profiles of a rigid internal gear and a flexible external gear for a flexible meshing type gear unit.

A flexible meshing gear device is composed of a rigid circular internal gear, one placed inside the internal gear and having fewer teeth than the internal gear such as 2n (n is a positive integer) and can be flexed into an ellipse so that It consists of two flexible external gears meshing with the internal gear and a wave generator installed in the external gear to bend the external gear into an elliptical shape.

Although the basic tooth shape of the gear in the flexible meshing gear device is linear (see US Patent No. 2,906,143), the flexible meshing gear device using involute gears has also been successfully developed (see Japan Patent Heisei 45-411171). In addition, the present inventor once proposed a system (see Japanese Patent JP-A 63-115943) that adopts the curve obtained by transforming the similarity of the moving track as the tooth surface profile of the two gears. The tooth of the gear is carried out with a reduction ratio of 1/2 within the range specified by the meshing limit point on the approximate track of the tooth of the internal gear. This system is a system for achieving continuous contact between the tooth flank profiles of two gears.

A flexible meshing type gear unit of the prior art is equipped with an annular flexible external gear, and another kind of said gear unit of the prior art is equipped with a cup-shaped flexible external gear, in the latter gear unit, A three-dimensional deflection phenomenon called "cone surface" appears, and the elliptical wave generator inserted in it makes the deflection amount (the difference between the major axis and the minor axis of the ellipse) from the baffle plate of the flexible external gear to Towards the opening portion, it gradually increases approximately in proportion to the distance to the baffle. However, the tooth shape described in the above-mentioned separate document does not consider the problem of "forming a tapered surface". When the tooth profile meshes continuously, tooth interference and other problems will occur in other sections of the tooth line.

The present inventors later proposed a flexible meshing type gear device without disturbance of a wide meshing range on the entire interdental curve of a cup-shaped flexible external gear. Disclosed in 3-357037.

The performance required for a flexible meshing gear device is becoming increasingly stringent. In order to meet this requirement, the strength and wear resistance of the device must be further improved. In particular, it is necessary to improve the wear resistance of the tooth surface as much as possible.

The entirety of the above invention makes the gears mesh continuously along the interdental curve, however this meshing is a so-called "reverse motion" meshing and therefore inevitably has disadvantages from the standpoint of maintaining a lubricating oil film between tooth surfaces. The permissible transmission torque is somewhat limited due to tooth surface wear caused by oil film breakdown, and for the above reasons, an improvement in this area is strongly demanded.

In order to achieve the above-mentioned improvement, the present invention fundamentally improves the tooth profile of the rigid internal gear and the flexible external gear to replace the tooth profile of the prior art that performs reverse motion meshing including continuous contact between convex curves, specifically, adopts A new convex curve tooth shape is used as the working tooth shape of the rigid internal gear or flexible external gear and a concave curve tooth shape is used as the working tooth shape of the other gear. As a result, the two gears implement the convex tooth shape The passing mesh between the tooth profile and the concave profile is advantageous from a lubrication point of view.

More specifically, the present invention is characterized by a flexible meshing type transmission having the following structural features, the device comprising a rigid internal gear, a flexible external gear disposed within the rigid internal gear, and a The cross section of the external gear perpendicular to its axis is deflected into an ellipse, so that the flexible external gear is partially meshed with the rigid internal gear and the meshing position of the two gears is rotated in the circumferential direction. The rotation of the wave generator cause relative rotation between the two gears,

a) The radial deflection (W) in the basic section defined perpendicular to the axis of the flexible external gear at a specified point on the interdental curve of a gear is specified as a negative value less than the deflection rated deflection (Wo) deviation deflection;

b) Both the rigid internal gear and the flexible external gear are spur gears;

c) The number of teeth of the flexible external gear is 2n less than the number of teeth of the rigid internal gear (n is a positive integer);

d) The working tooth profile of a rigid internal gear or a flexible external gear (designated as the first gear) is defined as a convex curve whose shape is, or approximately The tooth top part of a tooth of a gear that approximates the rack’s moving track takes the apex of the moving track as the origin, and in the basic section of the tooth profile perpendicular to the axis, the convex curve of the exit is obtained by similarity transformation according to the magnification ratio λ, the above part is protruding relative to the other gear,

e) Define the working tooth profile of the other or second gear as a concave curve whose shape is or approximately passes through the same portion of the path of travel at magnification (in) and with the apex of the path of travel as The concave curve obtained by the similarity transformation of the origin, so that the meshing of the two tooth shapes becomes a continuous contact through meshing in the basic section of the vertical axis.

It is preferable to make a convex curve in proportion to the top of the concave profile of the working profile to the concave profile of the second gear to avoid tooth interference or to shorten the crown.

The tooth shape of the present invention can also be used in a flexible meshing type gear unit equipped with a cup-shaped flexible external gear. In order to achieve continuous contact along the inter-tooth curve in this case, it is best according to the need to avoid interference. Tooth reduction is performed proportionally toward the opening portion of the cup-shaped flexible external gear and the inner end portion on the gear fence side with respect to the basic section of the tooth line perpendicular to the axis.

The tooth form of the present invention can also be used in a flexible meshing type gear unit in which the flexible external gear flexes in a three-lobed shape to mesh with the rigid internal gear at three points on its periphery, in which case , the number of teeth of the flexible external gear is set to be 3n (n is a positive integer) less than the number of teeth of the rigid internal gear.

Fig. 1 is a perspective view of a flexible meshing type gear unit equipped with a cup-shaped flexible external gear;

Figure 2 is a schematic front view of the device of Figure 1;

Figure 3 is a set of diagrams illustrating how a cup-shaped flexible external gear deflects "to form a cone", where (a) is a section through the axis before deformation, and (b) is a section through the long axis containing the wave generator The section of the axis of , Figure (c) is a section through the axis including its minor axis;

Fig. 4 is the movement trajectory in the basic section perpendicular to the axis determined by the simulation of the rack in the case of a negative deviation of the teeth of the flexible external gear or the rigid internal gear relative to the other gears;

Fig. 5 is a diagram illustrating the tooth profile derivation method of the present invention;

Figure 6 is a diagram illustrating how the tooth crest portion of the concave surface of a gear is replaced by a convex envelope;

Fig. 7 is the meshing schematic diagram of the tooth shape of the present invention drawn with respect to the backlash of a gear in the basic section perpendicular to the tooth as a function of time;

Fig. 8 is a schematic diagram of the tooth profile of the present invention meshing in the basic section perpendicular to the tooth; this illustration relates to the tooth profile of the main part of the flexible external gear being convex and the tooth profile of the main part of the rigid internal gear being concave , and spatially draw all the teeth of the rigid internal gear;

Fig. 9 is a schematic diagram of the space drawn by the teeth meshing of the present invention;

The concavo-convex directions of the main parts of the two gears are just opposite to those shown in Figure 8;

Fig. 10 is a set of illustrations illustrating examples of meshing interference of the tooth shape of the present invention in each section except perpendicular to the basic section of the tooth, wherein Fig. 10 (a) is one on the opening side for the basic plane section perpendicular to the tooth Section, Figure 10(b) is a section on the side of the baffle for the basic section of the vertical teeth;

Fig. 11 is a diagram illustrating teeth of a flexible external gear performing tooth removal;

Fig. 12 is a set of schematic diagrams illustrating that the tooth shape of the present invention is in the shovel tooth section rather than the meshing situation perpendicular to the base plane section of the tooth, wherein Fig. 12 (a) is located on the opening side in the basic section perpendicular to the tooth The section of Fig. 12(b) is the section on the side of the baffle in the basic section perpendicular to

Fig. 13 is a set of schematic diagrams illustrating the meshing situation of the tooth profile of the present invention in different un-removed tooth sections, wherein the tooth profile of the cup-shaped flexible external gear is corrected, and Fig. 13 (a) is for the opening part The section of Fig. 13(b) is for the basic section, and Fig. 13(c) is for the section at the inner end;

Fig. 14 is a schematic diagram of the meshing of the tooth shape of the present invention in a basic section perpendicular to the teeth, the diagram relates to the case where the difference in the number of teeth of the internal and external gears is 3, and all the teeth are spatially drawn.

Embodiments of the present invention are described below with reference to the accompanying drawings:

1 and 2 are a perspective view and a front view, respectively, of a prior art flexible meshing type gear device to which the present invention is applicable. The flexible meshing gear device 1 has a cylindrical rigid internal gear 2, a cup-shaped flexible external gear 3 installed in the rigid internal gear 2, and an elliptical wave generator mounted in the cup-shaped flexible external gear 3. device 4. The cup-shaped flexible external gear 3 is in a deflected state caused by the wave generator 4. In the figure, the major axis direction and the minor axis direction of the ellipse of the wave generator 4 are marked with symbols 4a, 4b respectively.

Fig. 3 shows the deflection state in the section passing through the axis of the cup-shaped flexible external gear due to the so-called "tapering", that is, due to the deflection of the opening part of the flexible external gear, Fig. 3(a ) represents the state before deformation, and Fig. 3(b) is a section through the axis of the major axis 4a of the wave generator 4, and Fig. 3(c) is a section through the axis of the minor axis 4b of the wave generator 4, from It can be seen from these illustrations that the amount of deflection produced by the cup-shaped flexible external gear 3 is the largest at the opening side section 3a, and gradually decreases toward the inner end section 3c on the side of the baffle plate 3b.

Figure 4 is in a base plane section perpendicular to the tooth (an axis perpendicular to the axis used for the definition of the tooth profile, such as the section taken from the center of the tooth line shown in Figure 3 (a) IV-IV line), the flexure The trajectory of one tooth of a rigid external gear or a rigid internal gear (hereinafter referred to as the first gear 100) relative to the other gear (hereinafter referred to as the second gear 200), the movement trajectory L1 shown here is in the so-called negative In the case of deviation, the radial deflection (the difference between the pitch circle of the flexible external gear and its maximum radius when the pitch circle is deformed into an ellipse or trilobate) is less than its rated value Wo (when the rigid internal gear When fixed, the value obtained by dividing the pitch circle radius of the flexible external gear by the reduction ratio), that is, when the radial deflection is KWo value, K here is the standard deflection coefficient (K<1) . Moreover, the moving locus _L1 shown in FIG. 4 is under the condition that the flexible external gear is bent into an ellipse, and the arrow 101 indicates the moving direction of the first gear 100 (because the flexible meshing type gear device has many teeth, so its tooth meshing can be approximately regarded as meshing with a rack with infinite number of teeth, therefore, in the following discussion on the tooth shape derivation of Figure 4 and other figures, the gear meshing is approximated by the rack meshing deal with.)

Fig. 5 is a diagram for explaining the tooth shape derivation method of the present invention. In the figure, point O is the vertex of a tooth movement path _L1 of the first gear (the maximum entry point into a tooth gap of the second gear), and point V is the movement path path _L1 at this point from relative to The inflection point where the convex shape of the second gear turns into a concave shape. Point A is limited to the OV section of the moving track L ₁ , and point O is taken as the origin (similar center), and the curve L ₁ (O, A) between the point O and point A on the moving track L ₁ is carried out with the magnification A similar transformation of λ to obtain an analog curve L ₂ (O, B), which is used as the working tooth profile of the first gear, although this curve is not shown in the figure, it is also smoothly connected with an inner fillet The curves are connected, so the working tooth shape of the first gear is a convex tooth shape.

Taking point O as the origin (similar center) again, the curve L ₁ (O, A) is subjected to the similar transformation with the amplification ratio (λ+1) again to obtain a simulated curve L ₃ (O, C), and the curve is used As the basic tooth shape of the second gear, this tooth shape is a concave tooth shape.

The value of λ is selected such that the distance from point O to point C along the addendum direction (vertical direction in the figure) becomes the same as or close to the amplitude OM of the trajectory _L1 along the addendum direction. In other words, by selecting point C in this way, the lambda value can be determined relative to the earlier selected point A

λ=(OC/OA)-1

The following describes the case where the tooth profile of the first gear and the second gear are correctly meshed with the tooth profile determined by the above method.

In Fig. 5, take an arbitrary point P on the concave tooth shape L ₃ (O, C) of the second gear, draw a straight line OP, and stipulate that the straight line OP is consistent with the first gear convex tooth shape L ₂ (O, B ) and the intersection point with the moving track L ₁ (O,A) are Q and R respectively, according to the derivation method of tooth profile, we can get:

OP=(λ+1)×OR

OQ=λ×OR

therefore,

QP=OP-OQ=OR

Moreover, from the viewpoint of analog characteristics, the tangents of the curves at the three points P, Q and R are parallel to each other.

From the above two points, it can be seen that when the point Q of the convex tooth shape L ₂ (O, B) is located at point P, the convex tooth shape L ₂ (O, B) will meet the concave tooth surface L at point P ₃ (O,C), specifically, to ensure continuous meshing between the convex tooth shape L ₂ (O,B) and the concave tooth shape L ₃ (O,C). Also, since the meshing starts where points B and C meet (where point _O0 of the tooth profile of the first gear is at point A) and meshing ends at point O, this is called "through meshing".

However, the reality is that before the meshing reaches point A on the travel path, the hobbing action of the tooth profile of the first gear replaces the crown part of the second gear with a convex envelope, as shown in Figure 6 In this case, the envelope surface is part DE in FIG. 6 , and the meshing of this section belongs to the through-type meshing. Moreover, in a flexible meshing type gear unit equipped with a cup-shaped flexible external gear as shown in FIG. The degree of penetration into the second gear is greatest at the inner end portion (portion 3C in FIG. 3(a)).

Figure 7 illustrates the meshing of the tooth profile of the present invention with respect to a backlash of a second gear as a function of time in a basic section perpendicular to the tooth.

Figure 8 is a spatial diagram of all the teeth of the internal and external gears, in which the first gear 100 is a flexible external gear 3, and the second gear 200 is a rigid internal gear 2, and Figure 9 is also a spatial diagram of all the teeth of an internal and external gear , the difference is that the first gear 100 is a rigid internal gear 2, and the second gear 200 is a flexible external gear 3.

As mentioned above, in a device equipped with a cup-shaped flexible external gear, the shape of the curved surface of the second gear 200 enclosed by the crown of the first gear 100 depends on the position of the section perpendicular to the axis of the first gear (see Fig. 6). In this case, the meshing rigidity can be increased by specifying the convex tooth shape of the addendum portion of the second gear 200 as the envelope surface of the inner tooth end portion 3C. In order to increase the wear resistance or simply to shorten the tooth crown to achieve full through meshing, the envelope surface can also be given a certain amount of clearance, which is advantageous from a lubrication point of view.

Next, the characteristics of the tooth profile will be considered with regard to the conical surface of the flexible external gear of the flexible meshing type gear device equipped with the cup-shaped flexible external gear shown in FIG. 3 . The tooth shape of the invention is derived from the movement path in the basic section and cannot be used without modification for other sections. Figure 10 shows as an example the situation taken where the first gear 100 is a flexible external gear 3 and the second gear 200 is a rigid internal gear 2, this figure (Figure 10) is suitable for the basic section taken from the interdental curve The case of the midpoint (the position of the line IV-IV in Fig. 3(a)). Fig. 10(a) is a section for the opening side of the basic section, and Fig. 10(b) is a section for the baffle-side inner end of the basic section.

As can be seen from these figures, these teeth interfere with the sections towards the sides of the basic section. One way to avoid this tooth interference is to place a shovel matching the amount of interference from the basic section as shown in Figure 11. Tooth weight is added to opposite sides of the tooth.

Fig. 12(a) and Fig. 12(b) respectively show the meshing conditions of the tooth shape in the cross section of the opening side and the cross section of the inner end when cutting teeth. Another way to achieve continuous contact along the tooth-to-tooth curve is to properly correct the tooth profile of the flexible external gear without tooth removal.

Figure 13 shows the engagement in this case where Figure 13(a) is a section for the opening, Figure 13(b) is a basic section, and Figure 13(c) is a section for the inner end.

Although the above description is mainly for the case of elliptical flexures, the method of the present invention can be equally applied to the case of trilobal flexures with a tooth number difference of 3n. FIG. 14 shows an example of a meshing in this case in a basic section and spatially shows all the teeth of the gear.

As mentioned above, by introducing the through-meshing of the present invention, the ability to maintain the lubricating oil film between the tooth surfaces can be greatly enhanced, and the transmission allowed by the flexible meshing type gear device based on the wear of the tooth surfaces can be significantly improved. torque.

Moreover, the use of negative deviation can reduce the bending stress caused by deflection near the long and short axes of the flexible external gear, improve the rim strength of the flexible external gear, and, due to the continuous tooth contact, the meshing stiffness can be improved. improve.

In addition, since the present invention can be implemented at any conical angle of the cup-shaped flexible external gear, the present invention can also be applied to a short-bodied flexible external gear, and can also be used for cup-shaped flexible external gears that do not form a tapered surface. on flexible external gears.

Claims (14)

1. one kind has the flexible engagement type gearing that negative deviation is calibrated profile of tooth, contain: a rigid internal gear, flexible gear that is positioned at internal gear and one are used for making a cross section perpendicular to its axis of external gear to deflect into ellipse, thereby the wave-generator that makes flexible external gear be meshed with rigid internal gear and two gear meshing positions are along the circumferential direction rotated partly, the rotation of this wave-generator produces relatively rotating between two gears, it is characterized in that having following structural feature:

A) the radially deflection in the fundamental section that is limited perpendicular to flexible property external gear axis on the regulation point on a tooth trace of gear is defined as the negative deviation deflection less than specified deflection (Wo);

B) rigid internal gear and flexible external gear are spur wheel;

C) number of teeth of the gear ratio rigid internal gear of flexible external gear is few 2n, and n is a positive integer;

D) rigid internal gear or flexible external gear promptly the work profile of tooth in first gear be defined as a crest curve, the shape of this crest curve is exactly or is approximate is by in the fundamental section perpendicular to the tooth trace of Gear axis, summit with motion track, (O) be initial point, tooth to this first gear is the convex part of the approximate tooth bar motion track of second gear with respect to another gear, (OA) with magnification ratio, (λ) carry out similarity transformation, the crest curve that is drawn, it is protruding that described male portion is divided with respect to second gear, wherein

λ=(along the amplitude of tooth top direction motion track)/(distance that point is ordered to O along the tooth top direction from A)-1;

E) the work profile of tooth of another gear or second gear is defined as a concave curve, the shape of this concave curve is exactly or is similar to the concave curve that the similarity transformation carried out with magnification ratio (λ+1) as initial point with its summit by the same part of motion track draws, thus make first gear and the engagement of second tooth-formation of gear become in the fundamental section of vertical axis Continuous Contact pass through mesh.

2. the flexible engagement type gearing that has negative deviation calibration profile of tooth according to claim 1, it is characterized in that, the work profile of tooth is that the top of the recessed profile of tooth of second gear of sag vertical curve is limited by a crest curve, and convex first tooth-formation of gear that is limited with top and the convex curve of avoiding recessed profile of tooth disturbs mutually.

3. the flexible engagement type gearing that has negative deviation calibration profile of tooth according to claim 1, it is characterized in that the work profile of tooth is that the crown shortening of second gear of sag vertical curve is disturbed with convex first tooth-formation of gear that a convex curve is limited mutually with the crown of avoiding recessed profile of tooth.

4. a flexible engagement type device that has negative deviation calibration profile of tooth contains a rigid internal gear, a flexible external gear that is positioned at internal gear, with one be used for a cross section perpendicular to its axis of external gear is deflected into a trilobal, thereby the wave-generator that makes flexible external gear be meshed with rigid internal gear and two gear meshing positions are along the circumferential direction rotated partly, the rotation of this wave-generator produces relatively rotating between two gears, it is characterized in that having following structural feature:

A) the radially deflection in the fundamental section that is limited perpendicular to flexible external gear axis on the regulation point on a tooth trace of gear is defined as the negative deviation deflection less than specified deflection (Wo);

B) rigid internal gear and flexible external gear are spur wheel;

C) few 3n (n is a positive integer) of the gear ratio rigid internal gear number of teeth of flexible external gear;

D) rigid internal gear or flexible external gear promptly the work profile of tooth in first gear be defined as a crest curve, the shape of this crest curve is exactly or is approximate is by in the fundamental section perpendicular to the tooth trace of Gear axis, summit with motion track, (O) be initial point, tooth to this first gear is the convex part of the approximate tooth bar motion track of second gear with respect to another gear, (OA) with magnification ratio, (λ) carry out similarity transformation, the crest curve that is drawn, it is protruding that described male portion is divided with respect to second gear, wherein

λ=(along the amplitude of tooth top direction motion track)/(distance that point is ordered to O along the tooth top direction from A)-1;

E) the work profile of tooth of another gear or second gear is defined as a concave curve, the shape of this concave curve is or is approximate to be the concave curve that draws by in the same top of above-mentioned motion track and the similarity transformation carried out with magnification ratio (λ+1) as initial point with its summit, thus make first gear and the engagement of second tooth-formation of gear become in perpendicular to the fundamental section of axis Continuous Contact pass through mesh.

5. the flexible engagement type gearing that has the calibration profile of tooth of negative deviation according to claim 4, it is characterized in that this work profile of tooth is that the recessed profile of tooth top of second gear of a sag vertical curve is limited with the top of avoiding recessed profile of tooth by a convex curve and disturbs mutually with convex first form of gear tooth that a convex curve is limited.

6. the flexible engagement type gearing that has the calibration profile of tooth of negative deviation according to claim 4, it is characterized in that this work profile of tooth is that the crown shortening of second gear of a sag vertical curve is disturbed with convex first tooth-formation of gear that a convex curve is limited mutually with the crown of avoiding recessed profile of tooth.

7. the flexible engagement type gearing that has negative deviation calibration profile of tooth according to claim 1, it is characterized in that, the described flexible external gear that is positioned at internal gear is cup-shaped, and the deflection that is produced from a baffle plate end to an opening end is approximate to be directly proportional with the distance of baffle plate.

8. the flexible engagement type gearing that has the calibration profile of tooth of negative deviation according to claim 7, it is characterized in that, the recessed profile of tooth top of the gear that this work profile of tooth is a sag vertical curve is limited by a convex curve, and the double wedge shape that is limited with top and the convex curve of avoiding recessed profile of tooth is disturbed mutually.

9. the flexible engagement type gearing that has the calibration profile of tooth of negative deviation according to claim 7, it is characterized in that this work profile of tooth is that the crown shortening of second gear of a sag vertical curve is disturbed with convex first tooth-formation of gear that a convex curve is limited mutually with the crown of avoiding recessed profile of tooth.

10. according to Claim 8 or the 9 described flexible engagement type gearings that have the calibration profile of tooth of negative deviation, it is characterized in that, the open part that at least the first gear and the teeth directional of one of second gear the flexible external gear of cup-shaped is with in the fundamental section of relative tooth mark perpendicular to axis, teeth is carried out in the inner of its baffle plate side, to avoid making interference mutually between two profiles of tooth owing to the flexible external gear of cup-shaped forms the conical surface.

11. the flexible engagement type gearing that has negative deviation calibration profile of tooth according to claim 4, it is characterized in that, the described flexible external gear that is positioned at internal gear is cup-shaped, and the deflection that is produced from a baffle plate end to an opening end is approximate to be directly proportional with the distance of baffle plate.

12. the flexible engagement type gearing that has the calibration profile of tooth of negative deviation according to claim 11, it is characterized in that, the work profile of tooth is that the top of the recessed profile of tooth of second gear of sag vertical curve is limited by a crest curve, and convex first tooth-formation of gear that is limited with top and the convex curve of avoiding recessed profile of tooth disturbs mutually.

13. the flexible engagement type gearing that has the calibration profile of tooth of negative deviation according to claim 11, it is characterized in that the work profile of tooth is that the crown shortening of first gear of sag vertical curve is disturbed with convex first tooth-formation of gear that a convex curve is limited mutually with the crown of avoiding recessed profile of tooth.

14. according to claim 12 or the 13 described flexible engagement type gearings that have the calibration profile of tooth of negative deviation, it is characterized in that, the profile of tooth of at least the first gear and one of second gear towards the open part of the flexible external gear of cup-shaped with in the fundamental section of relative tooth mark perpendicular to axis, teeth is carried out in the inner of its baffle plate side, to avoid making interference mutually between two profiles of tooth owing to the flexible external gear of cup-shaped forms the conical surface.

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