JP2015075149A - Process of manufacture of wave gear device - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a wave gear device in which an internal tooth of a rigidity internal gear and an external tooth of a flexible external gear are accurately engaged to each other.SOLUTION: A tooth shape curve is determined in respect to a portion of an addendum side of an external tooth of a flexible external gear (S1: the first determination step). A wave generator is virtually rotated to calculate a relative movement locus of the tooth shape curve in respect to a rigidity internal gear is calculated and a tooth shape of the rigidity internal gear is determined under application of an envelope curve of the movement locus (S2: the second determination step). The wave generator is rotated, the relative movement locus of the internal tooth of the rigidity internal gear determining the tooth shape at the step S2 in respect to the flexible external gear is calculated and a tooth shape of remaining portion of the external tooth of the flexible external gear is determined under application of the envelope curve of the movement locus (S3: the third determination step).

Description

  The present invention relates to a method of manufacturing a wave gear device including a rigid internal gear, a flexible external gear, and a wave generator.

  Conventionally, a wave gear device has been known as a speed reducer that is lightweight and compact and can obtain a high reduction ratio by a single reduction. A general wave gear device has an annular rigid internal gear, a flexible external gear disposed inside the ring-shaped rigid internal gear, and a substantially elliptical wave generator disposed inside the inside.

  The flexible external gear is bent into a substantially elliptic shape by a wave generator, and meshes with the rigid internal gear at two locations in the major axis direction of the substantially elliptic shape. Further, the number of external teeth of the flexible external gear is smaller by 2 × n (n is a positive integer) than the number of internal teeth of the rigid internal gear. Therefore, when the wave generator is rotated, the two meshing positions of both gears are also moved in the circumferential direction along with this rotation, and as a result, both gears are relatively rotated according to the difference in the number of teeth.

  For example, the number of internal teeth of the rigid internal gear is 102, and the number of external teeth of the flexible external gear is 100. When the rigid internal gear is fixed, when the wave generator attached to the input shaft is rotated once, it is 1/50 (the difference in the number of teeth of both gears / the number of teeth of the flexible external gear). ) To obtain a decelerated output.

  Wave gear devices are classified into several types according to the shape of the flexible external gear. As a typical wave gear device, a so-called cup type having a cup-shaped flexible external gear, a so-called top hat type having a top-shaped flexible external gear, and a cylindrical flexible A so-called flat type having an external gear is known.

  Among these wave gear devices, in cup-type and top-hat type wave gear devices, one end of the body portion on which the external teeth of the flexible external gear are formed extends inward or outward in the radial direction to be a member to be attached. An attachment portion to be attached is formed. A fixed side member or a load side member is connected and fixed to the mounting portion.

  In the wave gear device having these cup-type and top-hat-type flexible external gears, when the wave generator is fitted inside the flexible external gear, the body of the flexible external gear is attached to the mounting portion. The amount of bending is increased according to the distance in the direction of the rotation axis from the side.

  Until now, many inventions have been proposed regarding the tooth profile of the wave gear device. For example, in Patent Document 1, the tooth profile of both gears is calculated by rack approximation of the movement trajectory of the flexible external gear with respect to the rigid internal gear, and the required point of the trajectory is determined from the meshing limit point on this trajectory. The range is a curve obtained by similarity conversion with a reduction ratio of 1/2.

  However, the tooth profile shown in Patent Document 1 is a member attachment in which the body portion of the flexible external gear is formed along the rotation axis direction by fitting a substantially elliptical wave generator inside the flexible external gear. The so-called “corning” phenomenon in which the amount of deflection increases according to the distance from the part side is not taken into consideration. Therefore, it is not suitable for meshing of a wave gear device having a cup-type / top-hat type flexible external gear. Further, in Patent Document 1, since the tooth profile is derived from the rack approximation, that is, the tooth movement in the case of an infinite number of teeth, the change in the tooth inclination and the movement locus that occurs in the case of a finite number of teeth is not considered.

  On the other hand, in Patent Document 2, in order to consider the phenomenon of cornering, one compound curve is obtained by superimposing movement trajectories calculated by rack approximation in a plurality of cross-sections perpendicular to the tooth trace direction. Yes. Then, from the meshing limit point selected on this curve, a similarity curve obtained by similarity conversion of a required portion of the composite curve with a reduction ratio of 1/2 is obtained as a basic tooth of the flexible external gear and the rigid internal gear. It has a tooth profile.

  Further, in Patent Document 2, the displacement in the rack axis direction from the rack approximate tooth profile at the contact point in each cross section perpendicular to the axis, which is caused by actual meshing, is broken down into two. That is, depending on the inclination angle of the tooth crest center line of the external tooth of the flexible external gear with respect to the root center line of the internal tooth of the rigid internal gear, and the rack movement locus of the external tooth movement locus of the flexible external gear It breaks down into those caused by deviation from Next, the basic tooth addendum of the external teeth and internal teeth is corrected so as to cancel out the algebraic sum of the respective displacements.

Japanese Unexamined Patent Publication No. 63-115943 JP-A-11-159588

  However, in Patent Documents 1 and 2, since the tooth profile is analytically derived from the approximate ellipse given by the equation of few parameters, the actual movements of both the rigid internal gear and the flexible external gear are mutually connected. There is a problem that the teeth do not mesh correctly.

  Therefore, the present invention provides a method of manufacturing a wave gear device in which the internal teeth of the rigid internal gear and the external teeth of the flexible external gear are accurately meshed with each other.

  The present invention relates to a rigid internal gear having a plurality of internal teeth, a flexible external gear having a plurality of external teeth and disposed inside the rigid internal gear, and the flexible external gear in a radial direction. In a method of manufacturing a wave gear device, comprising: a wave generator that bends and partially meshes with the rigid internal gear and moves the meshed portion in the circumferential direction by rotating around a rotation axis; A first determination step of determining a tooth profile curve for a part of the tooth tip side of one gear of the rigid internal gear and the flexible external gear, and the wave generator is rotated to rotate the rigid internal gear. And determining a relative movement locus of the tooth profile curve with respect to the other gear of the flexible external gears, and determining a tooth shape of the other gear using an envelope of the movement locus; and Rotate the wave generator against the one gear The relative movement trajectory of the tooth of the other gear whose tooth profile has been determined in the second determination step is obtained, and the tooth profile of the remaining portion of the tooth of the one gear is determined using the envelope of the movement trajectory. A third determination step.

  ADVANTAGE OF THE INVENTION According to this invention, the wave gear apparatus with which the internal tooth of a rigid internal gear and the external tooth of a flexible external gear mesh | engage correctly can be obtained.

It is explanatory drawing which shows schematic structure of the wave gear apparatus manufactured by the manufacturing method which concerns on 1st Embodiment. It is sectional drawing of the wave gear apparatus which follows the cut surface AA of Fig.1 (a). It is a cross-sectional schematic diagram which shows the flexible external gear elastically deformed by the wave generator. It is a flowchart of the process of determining the tooth profile of the rigid internal gear and flexible external gear in 1st Embodiment. It is a figure for demonstrating the 2nd determination process in the manufacturing method of the wave gear apparatus which concerns on 1st Embodiment. It is a figure for demonstrating the 2nd determination process in the manufacturing method of the wave gear apparatus which concerns on 1st Embodiment. It is a figure for demonstrating the 3rd determination process in the manufacturing method of the wave gear apparatus which concerns on 1st Embodiment. It is a figure for demonstrating the 3rd determination process in the manufacturing method of the wave gear apparatus which concerns on 1st Embodiment. It is a figure which shows the aspect of the meshing of the external tooth and internal tooth of the wave gear apparatus manufactured by the manufacturing method which concerns on 1st Embodiment. It is a flowchart of the process of determining the tooth profile of the rigid internal gear and flexible external gear in 2nd Embodiment. It is a figure for demonstrating the 2nd determination process in the manufacturing method of the wave gear apparatus which concerns on 2nd Embodiment. It is a figure for demonstrating the 2nd determination process in the manufacturing method of the wave gear apparatus which concerns on 2nd Embodiment. It is a figure for demonstrating the 3rd determination process in the manufacturing method of the wave gear apparatus which concerns on 2nd Embodiment. It is a figure for demonstrating the 3rd determination process in the manufacturing method of the wave gear apparatus which concerns on 2nd Embodiment. It is a figure which shows the aspect of the meshing | engagement of the external tooth and internal tooth of the wave gear apparatus manufactured with the manufacturing method which concerns on 2nd Embodiment. It is a figure which shows the external-tooth shape of the flexible external gear of the wave gear apparatus manufactured by the manufacturing method which concerns on 2nd Embodiment. The curvature of the tooth profile in the range of 0.4 × m is shown from the pitch circle of the external teeth of the flexible external gear manufactured by the manufacturing method according to the second embodiment to the tip side and the root side in the tooth direction. It is a graph. It is a graph which shows the approximate tooth profile of the external tooth of a flexible external gear.

  EMBODIMENT OF THE INVENTION Below, the form for implementing this invention is demonstrated in detail, referring drawings.

[First Embodiment]
FIG. 1 is an explanatory view showing a schematic configuration of a wave gear device manufactured by the manufacturing method according to the first embodiment of the present invention, FIG. 1 (a) is a front view of the wave gear device, and FIG. 1 (b). FIG. 3 is a side view of the wave gear device. FIG. 2 is a cross-sectional view of the wave gear device taken along a cutting plane AA in FIG.

  As shown in FIG. 2, the wave gear device 10 includes a rigid internal gear 20, a flexible external gear 30, and a wave generator 40 that are arranged coaxially with the rotation axis XX.

  As shown in FIG. 1A, the rigid internal gear 20 includes a gear main body 21 formed of an annular rigid member, and a plurality of rigid internal gears 20 formed on the inner periphery of the gear main body 21 at intervals in the circumferential direction. Internal teeth 22. The number of internal teeth 22 of the rigid internal gear 20 is, for example, 102 teeth. The rigid internal gear 20 is formed with a fixing bolt hole 23 for attachment to a fixing member (not shown).

  As shown in FIGS. 1B and 2, the flexible external gear 30 includes a cylindrical thin-walled body 31 and an end (one end) 31 a of the body 31, and the outer periphery of the body 31. It has the some external tooth 33 formed in the surface 31c, and the attaching part 32 connected to the edge part (other end part) 31b of the trunk | drum 31. As shown in FIG. The trunk | drum 31 has flexibility.

  The flexible external gear 30 is a so-called cup-shaped flexible external gear formed in a cup shape having an opening on the opposite side to the mounting portion 32. The attachment portion 32 is a member formed in a plate shape extending inward in the radial direction from the end portion 31 b of the body portion 31. A fixing bolt hole 32a is formed in the attachment portion 32, and is attached to a member to be attached (output shaft member) by a bolt (not shown).

  Further, the external teeth 33 of the flexible external gear 30 have fewer teeth than the internal teeth 22 of the rigid internal gear 20. For example, the number of teeth of the external teeth 33 of the flexible external gear 30 is 100, and is set to 2 less than the number of teeth of 102 of the internal teeth of the rigid internal gear 20.

  The external teeth 33 are formed such that the tooth trace direction is parallel to the direction along the outer peripheral surface 31 c of the trunk portion 31 in a state where the trunk portion 31 is not elastically deformed. The flexible external gear 30 is disposed inside the rigid internal gear 20 so that the external teeth 33 face the internal teeth 22 of the rigid internal gear 20.

  The wave generator 40 is fitted inside the flexible external gear 30, that is, inside the trunk portion 31, contacts the inner peripheral surface 31 d of the trunk portion 31 at the end 31 a of the trunk portion 31, and causes the trunk portion 31 to move. It is bent in the radial direction and elastically deformed into a substantially elliptical shape.

  The wave generator 40 includes an elliptical cam 41 and a thin bearing 42 provided on the outer periphery of the elliptical cam 41 and capable of elastic deformation. The elliptical cam 41 includes an input shaft member (not shown). Is formed with an input shaft mounting screw hole 43.

  When the flexible external gear 30 is elastically deformed into a substantially elliptical shape, the rigid internal gear 20 and the flexible external gear 30 have two meshing portions P and Q on the major axis of the substantially elliptical shape (see FIG. In 1 (a)), partial meshing is caused by a plurality of teeth. Then, when the elliptical cam 41 rotates about the rotation axis XX, the meshing portions P and Q of the rigid internal gear 20 and the flexible external gear 30 move in the circumferential direction. The flexible external gear 30 has a reduction ratio 50 (= the number of teeth of both gears / the number of teeth of the flexible external gear) based on the number of teeth difference between the rigid internal gear 20 and the flexible external gear 30. Rotate at a rotational speed reduced with respect to the rotational speed of the elliptical cam 41.

  FIG. 3 is a schematic cross-sectional view (hatching is omitted) showing the flexible external gear 30 elastically deformed by the wave generator 40. 3A is a schematic cross-sectional view of the flexible external gear 30 along the cutting plane AA of FIG. 1A including a substantially elliptical long axis, and FIG. 3B is a substantially elliptical short axis. It is a cross-sectional schematic diagram of the flexible external gear 30 along cut surface BB of FIG.

  In FIG. 3A, the amount of bending of the body portion 31 in the radial direction increases from the end portion 31 b toward the end portion 31 a in accordance with the distance, and the opening end 31 e of the body portion 31 outwards in the radial direction. The amount of bending is maximum. On the other hand, in FIG. 3B, the amount of bending of the body portion 31 inward in the radial direction increases according to the distance from the end portion 31 b to the end portion 31 a, and the radius at the opening end 31 e of the body portion 31 is increased. The amount of bending inward in the direction is the maximum. A phenomenon in which the amount of deflection of the body portion 31 of the flexible external gear 30 changes according to the distance from the mounting portion 32 side is referred to as “corning”.

  Next, the determination process of the tooth profile of the rigid internal gear 20 and the flexible external gear 30 which is a part of the manufacturing process of the wave gear device 10 will be described in detail. FIG. 4 is a flowchart of the process of determining the tooth profiles of the rigid internal gear 20 and the flexible external gear 30 in the first embodiment. Hereinafter, the tooth profiles of the rigid internal gear 20 and the flexible external gear 30 are obtained by computer simulation. At that time, the positional relationship between the rigid internal gear 20 and the flexible external gear 30 in consideration of the coning is obtained by simulation using a finite element method.

  First, a tooth profile curve is determined for a part on the tooth tip side of the external tooth 33 of the flexible external gear 30 (one gear) of the rigid internal gear 20 and the flexible external gear 30 (S1: first determination step). ). The part on the tooth tip side is a part (or all) of the end surface. The end of the external teeth 33 is outside the pitch circle.

  In the first embodiment, the tooth profile curve is an arc curve. This circular arc curve is a curve corresponding to one side when the end of the external teeth 33 is bisected by a line extending in the radial direction.

  Next, a simulation of rotating the wave generator 40 is performed to obtain a relative movement locus of the tooth profile curve with respect to the rigid internal gear 20 (the other gear), and the tooth profile of the rigid internal gear 20 is determined using the envelope of the movement locus. Determine (S2: second determination step).

  Hereinafter, the movement trajectory drawn by the tooth profile curve viewed from the rigid internal gear 20 will be described in detail. Drawing 5 is a figure for explaining the 2nd decision process in the manufacturing method of wave gear device 10 concerning a 1st embodiment of the present invention. FIG. 5 shows that when the wave generator is rotated, the external teeth of the flexible external gear located on the major axis of the substantially elliptical shape are in a rigid inner state during the movement to the position on the minor axis of the substantially elliptical shape. The relative movement locus | trajectory of the circular curve of the external tooth of the flexible external gear with respect to the internal tooth of a gear is shown.

  FIG. 5A shows the movement locus on the vertical section (first vertical section) C11 perpendicular to the rotation axis XX at the outer end portion (tooth opening portion) 33a (FIG. 3) of the external teeth 33. Is shown. FIG. 5B shows a movement locus on a vertical section (first vertical section) C12 perpendicular to the rotation axis XX at the central portion 33b (FIG. 3) of the external teeth 33. FIG. 5C shows a movement locus on a vertical section (first vertical section) C13 perpendicular to the rotation axis XX at the tooth trace inner end portion 33c (FIG. 3) of the external tooth 33.

  The coordinate system Xi-Yi is an orthogonal coordinate system fixed to the internal teeth 22 of the rigid internal gear 20, and the Yi axis coincides with the center line of the root of the internal teeth 22.

  Here, in step S2, in consideration of the coning of the flexible external gear 30, the tooth profile curve relative to the rigid internal gear 20 is obtained in a plurality of vertical sections C11, C12, C13 perpendicular to the rotation axis XX. Find the movement trajectory. Then, the tooth profile of the rigid internal gear 20 is determined from the outer shape of the envelope group obtained by projecting the envelope of the moving locus of the tooth profile curve in each vertical section C11, C12, C13 in the direction of the rotation axis XX.

  More specifically, as shown in FIG. 5 (a) on the vertical section C11, from the position on the major axis of the substantially elliptical shape when the wave generator 40 is virtually rotated, the short shape of the substantially elliptical shape is obtained. The movement trajectories 341a to 341z of the arc curve to the position on the axis are obtained on the coordinate system Xi-Yi. And the envelope 231 of these movement locus | trajectories 341a-341z is calculated | required.

  Similarly, on the vertical section C12, as shown in FIG. 5B, from the position on the major axis of the substantially elliptical shape when the wave generator 40 is virtually rotated, on the minor axis of the substantially elliptical shape. The movement trajectories 342a to 342z of the arc curve to the position are obtained on the coordinate system Xi-Yi. And the envelope 232 of these movement locus | trajectories 342a-342z is calculated | required.

  Similarly, on the vertical section C13, as shown in FIG. 5C, from the position on the major axis of the substantially elliptical shape when the wave generator 40 is virtually rotated, on the minor axis of the substantially elliptical shape. The movement trajectories 343a to 343z of the arc curve up to the position are obtained on the coordinate system Xi-Yi. And the envelope 233 of these movement locus | trajectories 343a-343z is calculated | required.

  In FIGS. 5A to 5C, curves 231 ′, 232 ′, and 233 ′ that are symmetric with respect to the Yi axis of the envelopes 231, 232, and 233 are also illustrated.

  Next, how the tooth profile of the rigid internal gear 20 is determined from the outer shape of the envelope group obtained by projecting the envelopes 231, 232, 233 in the direction of the rotation axis XX will be described.

  FIG. 6 is a view for explaining a second determination step in the method for manufacturing the wave gear device 10 according to the first embodiment of the present invention.

  As shown in FIG. 6A, the envelopes 231, 232, and 233 are projected in the direction of the rotation axis XX and superimposed on the coordinate system Xi-Yi to obtain an envelope group. In FIG. 6A, the long broken line indicates the envelope 231, the broken line indicates the envelope 232, and the dotted line indicates the envelope 233.

  Then, as shown in FIG. 6 (b), the rigid internal gear 20 which is the tooth profile of the counterpart gear from the envelope group obtained by projecting a plurality of envelopes 231, 232, 233 in the direction of the rotation axis XX. The tooth profile of the inner teeth 22 is determined.

  More specifically, the outermost peripheral lines of the envelope group (a plurality of envelopes 231, 232, 233) so that the circular arc curve and the internal teeth 22 of the rigid internal gear 20 do not interfere with each other on each vertical section C 11, C 12, C 13. Is the tooth profile of the internal teeth 22 of the rigid internal gear 20. That is, in the tooth profile of the internal tooth 22 of the rigid internal gear 20, the main range of the end surface is formed by the envelope 233, and the main range of the root surface is formed by the envelope 231.

  Next, after determining the tooth profile of the rigid internal gear 20 in step S2, the wave generator 40 is virtually rotated by simulation. Then, the relative movement trajectory of the internal teeth 22 with respect to the external teeth 33 of the flexible external gear 30 is obtained, and the tooth profile of the remaining portion of the external teeth 33 is determined using the envelope of the movement trajectory (S3: Third) Decision process).

  Hereinafter, a method for determining the tooth profile of the remaining portion of the external tooth 33 of the flexible external gear 30 will be described in detail. FIG. 7 is a view for explaining a third determination step in the method for manufacturing the wave gear device 10 according to the first embodiment of the present invention.

  FIG. 7 shows that when the wave generator is rotated, the external teeth of the flexible external gear positioned on the substantially elliptical long axis move flexibly to the position on the substantially elliptical short axis. The relative movement locus | trajectory of the internal tooth of a rigid internal gear with respect to the external tooth of a sexual external gear is shown.

  FIG. 7A shows a movement locus on the vertical section (second vertical section) C21 perpendicular to the rotation axis XX at the outer end portion (tooth opening portion) 22a (FIG. 2) of the internal teeth 22. Is shown. FIG. 7B shows a movement locus on a vertical section (second vertical section) C22 perpendicular to the rotation axis XX at the central portion 22b (FIG. 2) of the tooth trace of the internal tooth 22. FIG. 7C shows a movement locus on a vertical section (second vertical section) C23 perpendicular to the rotation axis XX at the tooth trace inner end portion 22c (FIG. 2) of the internal tooth 22.

  The coordinate system Xo-Yo is an orthogonal coordinate system fixed to the external tooth 33 of the flexible external gear 30, and the Yo axis coincides with the center line of the tooth crest of the external tooth 33.

  Here, in step S3, in consideration of the coning of the flexible external gear 30, the rigid internal gear 20 with respect to the flexible external gear 30 in a plurality of vertical sections C21, C22, C23 perpendicular to the rotation axis XX. The relative movement locus of the inner teeth 22 is obtained. Then, from the outer shape of the envelope group obtained by projecting the envelope of the movement trajectory of the internal teeth 22 of the rigid internal gear 20 in each vertical section C21, C22, C23 in the direction of the rotation axis XX, it is not flexible. The tooth profile of the gear 30 is determined.

  Specifically, on the vertical section C21, as shown in FIG. 7 (a), from the position on the major axis of the substantially elliptical shape when the wave generator 40 is virtually rotated, a short shape of the substantially elliptical shape is obtained. The movement trajectories 221a to 221z of the internal teeth 22 to the position on the axis are obtained on the coordinate system Xo-Yo. And the envelope 344 of these movement locus | trajectories 221a-221z is calculated | required.

  Similarly, on the vertical section C22, as shown in FIG. 7B, from the position on the major axis of the substantially elliptical shape when the wave generator 40 is virtually rotated, on the minor axis of the substantially elliptical shape. The movement trajectories 222a to 222z of the internal teeth 22 to the position are obtained on the coordinate system Xo-Yo. And the envelope 345 of these movement locus | trajectories 222a-222z is calculated | required.

  Similarly, on the vertical section C23, as shown in FIG. 7C, from the position on the major axis of the substantially elliptical shape when the wave generator 40 is virtually rotated, on the minor axis of the substantially elliptical shape. The movement trajectories 223a to 223z of the internal teeth 22 up to the position are obtained on the coordinate system Xo-Yo. And the envelope 346 of these movement locus | trajectories 223a-223z is calculated | required.

  In FIGS. 7A to 7C, curves 344 ′, 345 ′, and 346 ′ that are line-symmetric with respect to the Yo axis of the envelopes 344, 345, and 346 are also illustrated.

  Subsequently, the tooth profile of the remaining portion of the external tooth 33 of the flexible external gear 30 is determined from the outer shape of the envelope group obtained by projecting the envelopes 344, 345, and 346 in the direction of the rotation axis XX. Explain the situation.

  FIG. 8 is a view for explaining a third determination step in the method for manufacturing the wave gear device 10 according to the first embodiment of the present invention.

  As shown in FIG. 8A, the envelopes 344, 345, and 346 are projected in the direction of the rotation axis XX and superimposed on the coordinate system Xo-Yo to obtain an envelope group. In FIG. 8A, the long broken line indicates the envelope 344, the broken line indicates the envelope 345, and the dotted line indicates the envelope 346.

  And as shown in FIG.8 (b), it is flexible outside which is a tooth profile of the other party gear from the envelope group obtained by projecting a plurality of envelopes 344,345,346 in the direction of the rotation axis XX. The tooth profile of the external teeth 33 of the gear 30 is determined.

  More specifically, an envelope group (a plurality of envelopes 231, 232, 233) is arranged so that the external teeth of the flexible external gear and the internal teeth of the rigid internal gear do not interfere with each other on each vertical section C 21, C 22, C 23. Is the tooth profile of the external teeth 33 of the flexible external gear 30. That is, in the tooth profile of the external tooth 33 of the flexible external gear 30, the main range of the end surface is formed by the envelopes 344 and 346, and the main range of the root surface is formed by the envelope 344.

FIG. 9 is a diagram illustrating a state of meshing between the external teeth 33 and the internal teeth 22 of the wave gear device 10 manufactured by the manufacturing method according to the first embodiment. 9A is on the vertical cross section C11 of the external end 33a of the external teeth 33, FIG. 9B is on the vertical cross section C12 of the central portion 33b of the external teeth 33, and FIG. The state of meshing on the vertical section C13 of the tooth trace inner end 33c of the tooth 33 is shown. On the long axis of each vertical section C11, C12, C13 on outside teeth 33 _A are substantially elliptical shape, the external teeth 33 _Z represents the external teeth 33 positioned on the minor axis. As can be seen from FIGS. 9A to 9C, in each of the vertical sections C11, C12, and C13, a continuous meshing state is formed, and no interference or the like occurs.

  As described above, in the first embodiment, a tooth profile that takes into account the complexity of the flexure shape of the flexible external gear 30 and the angle change between the teeth is obtained by discrete coordinate calculation. Therefore, even when the deformation of the flexible external gear 30 cannot be expressed with a small number of parameters, the wave gear device 10 in which the internal teeth 22 and the external teeth 33 are accurately meshed can be obtained.

  In the first embodiment, the shape of the external teeth 33 of the flexible external gear 30 is determined to determine the shape of the internal teeth 22 of the rigid internal gear 20 and the external teeth 33 of the flexible external gear 30. The shape of the remaining teeth is uniquely determined. Further, the position of the boundary between a part of the external teeth 33 of the flexible external gear 30 and the remaining part is uniquely determined. For this reason, not only does the condition that the external teeth 33 of the flexible external gear 30 and the internal teeth 22 of the rigid internal gear 20 mesh with each other, but the tooth profile that does not cause a contradiction between a part and the remaining part of the external tooth 33 is formed. It is possible to have.

Further, the wave gear device 10 manufactured by the manufacturing method of the first embodiment has a substantially elliptical short axis on the vertical cross section C13 of the tooth trace inner end portion 33c, as shown in FIG. 9C. addendum between the external teeth 33 _Z and inner teeth 22 located in are in contact. Accordingly, the tooth profile is such that continuous meshing contact is made on the entire circumference of the substantially elliptical shape.

  In addition, when a processing error or the like is taken into account, in order to prevent interference, a tooth obtained by correcting any one of the external tooth tip and bottom and the internal tooth tip and bottom may be used. That is, in step S <b> 2, at least one of the bottom portion and the tip portion of the rigid internal gear 20 is provided with a relief portion that avoids interference with the flexible external gear 30, and the tooth profile of the rigid internal gear 20. May be determined. In step S <b> 3, at least one of the tooth bottom portion and the tooth tip portion of the flexible external gear 30 is provided with a relief portion that avoids interference with the rigid internal gear 20, so that the flexible external gear 30. The tooth profile may be determined.

  Furthermore, when a specific tooth profile is determined, the coning shape of the flexible external gear 30 may slightly change with respect to the initial design conditions. Therefore, it is desirable to repeat the steps from the simulation by the finite element method of the positional relationship between the rigid internal gear 20 and the flexible external gear 30 in consideration of the basic coning.

[Second Embodiment]
Next, the manufacturing method of the wave gear apparatus concerning 2nd Embodiment of this invention is demonstrated. FIG. 10 is a flowchart of the process of determining the tooth profiles of the rigid internal gear and the flexible external gear in the second embodiment. In addition, in the wave gear apparatus of 2nd Embodiment, about the structure similar to the wave gear apparatus of the said 1st Embodiment, the same code | symbol is attached | subjected and description is abbreviate | omitted.

  In the first embodiment, the case where one gear is the flexible external gear 30 and the other gear is the rigid internal gear 20 has been described. However, in the second embodiment, one gear is the rigid internal gear 20. The case where the other gear is the flexible external gear 30 will be described.

  Hereinafter, the tooth profiles of the rigid internal gear 20 and the flexible external gear 30 are obtained by computer simulation. At that time, the positional relationship between the rigid internal gear 20 and the flexible external gear 30 in consideration of the coning is obtained by simulation using a finite element method.

  First, a tooth profile curve is determined for a portion of the internal teeth 22 of the rigid internal gear 20 (one gear) on the tooth tip side of the rigid internal gear 20 and the flexible external gear 30 (S11: first determination step). The part on the tooth tip side is a part (or all) of the end surface. The end of the inner teeth 22 is the inside (center side) of the pitch circle.

  In the second embodiment, the tooth profile curve is an arc curve. This circular arc curve is a curve corresponding to one side when the end of the inner teeth 22 is bisected by a line extending in the radial direction.

  Next, a simulation of rotating the wave generator 40 is performed to obtain a relative movement locus of the tooth profile curve with respect to the flexible external gear 30 (the other gear), and the flexible external gear is used by using the envelope of the movement locus. 30 tooth profiles are determined (S12: second determination step).

  Hereinafter, the movement locus drawn by the tooth profile curve viewed from the flexible external gear 30 will be described in detail. FIG. 11 is a diagram for explaining a second determination step in the method for manufacturing the wave gear device 10 according to the second embodiment of the present invention. FIG. 11 shows that when the wave generator is rotated, the external teeth of the flexible external gear located on the substantially elliptical long axis move flexibly to the position on the substantially elliptical minor axis. The relative movement locus | trajectory of the circular arc curve of the internal tooth of a rigid internal gear with respect to the external tooth of a sexual external gear is shown.

  FIG. 11A shows a movement locus on a vertical section (second vertical section) C21 perpendicular to the rotation axis XX at the tooth trace outer end portion 22a (FIG. 2) of the internal tooth 22. FIG. 11B shows a movement locus on a vertical section (second vertical section) C22 perpendicular to the rotation axis XX at the central portion 22b (FIG. 2) of the tooth trace of the internal tooth 22. FIG. 11C shows a movement locus on a vertical section (second vertical section) C23 perpendicular to the rotation axis XX at the tooth trace inner end portion 22c (FIG. 2) of the internal tooth 22.

  The coordinate system Xo-Yo is an orthogonal coordinate system fixed to the external teeth 33 of the flexible external gear 30, and the Yo axis coincides with the center line of the tooth crest of the external teeth 33.

  Here, in step S12, in consideration of the coning of the flexible external gear 30, the tooth profile curve relative to the flexible external gear 30 in a plurality of vertical sections C21, C22, C23 perpendicular to the rotation axis XX. To obtain a realistic trajectory. Then, the tooth profile of the flexible external gear 30 is determined from the outer shape of the envelope group obtained by projecting the envelope of the movement locus of the tooth profile curve in each vertical section C21, C22, C23 in the direction of the rotation axis XX. To do.

  More specifically, on the vertical section C21, as shown in FIG. 11 (a), from the position on the major axis of the substantially elliptical shape when the wave generator 40 is virtually rotated, the short shape of the substantially elliptical shape is obtained. The movement trajectories 251a to 251z of the arc curve to the position on the axis are obtained on the coordinate system Xo-Yo. And the envelope 361 of these movement locus | trajectories 251a-251z is calculated | required.

  Similarly, on the vertical section C22, as shown in FIG. 11 (b), from the position on the major axis of the substantially elliptical shape when the wave generator 40 is virtually rotated, on the minor axis of the substantially elliptical shape. The movement trajectories 252a to 252z of the arc curve to the position are obtained on the coordinate system Xo-Yo. And the envelope 362 of these movement locus | trajectories 252a-252z is calculated | required.

  Similarly, on the vertical section C23, as shown in FIG. 11 (c), from the position on the major axis of the substantially elliptical shape when the wave generator 40 is virtually rotated, on the minor axis of the substantially elliptical shape. The movement trajectories 253a to 253z of the arc curve up to the position are obtained on the coordinate system Xo-Yo. And the envelope 363 of these movement locus | trajectories 253a-253z is calculated | required.

  In FIGS. 11A to 11C, curves 361 ′, 362 ′, and 363 ′ that are line-symmetric with respect to the Yo axis of the envelopes 361, 362, and 363 are also illustrated.

  Next, how the tooth profile of the flexible external gear 30 is determined from the outer shape of the envelope group obtained by projecting the envelopes 361, 362, and 363 in the direction of the rotation axis XX will be described.

  FIG. 12 is a diagram for explaining a second determination step in the method for manufacturing the wave gear device 10 according to the second embodiment of the present invention.

  As shown in FIG. 12A, the envelopes 361, 362, and 363 are projected in the direction of the rotation axis XX and superimposed on the coordinate system Xo-Yo to obtain an envelope group. In FIG. 12A, the long broken line indicates the envelope 361, the broken line indicates the envelope 362, and the dotted line indicates the envelope 363.

  And as shown in FIG.12 (b), it is flexible outside which is a tooth profile of the other party gear from the envelope group obtained by projecting a plurality of envelopes 361, 362, 363 in the direction of the rotation axis XX. The tooth profile of the external teeth 33 of the gear 30 is determined.

  More specifically, on each vertical section C21, C22, C23, the outermost of the envelope group (a plurality of envelopes 361, 362, 363) is arranged so that the circular arc curve and the external teeth 33 of the flexible external gear 30 do not interfere with each other. The inner circumferential line is the tooth profile of the external teeth 33 of the flexible external gear 30. That is, in the tooth profile of the external tooth 33 of the flexible external gear 30, the main range of the end surface is formed by the envelope 363 and the main range of the root surface is formed by the envelope 361.

  Next, after determining the tooth profile of the flexible external gear 30 in step S12, the wave generator 40 is virtually rotated by simulation. Then, the relative movement trajectory of the external teeth 33 with respect to the internal teeth 22 of the rigid internal gear 20 is obtained, and the tooth profile of the remaining portion of the internal teeth 22 is determined using the envelope of the movement trajectory (S13: third determination step). ).

  Hereinafter, a method for determining the tooth profile of the remaining portion of the internal tooth 22 of the rigid internal gear 20 will be described in detail. FIG. 13 is a diagram for explaining a third determination step in the method for manufacturing the wave gear device 10 according to the second embodiment of the present invention.

  FIG. 13 shows that when the wave generator is rotated, the external teeth of the flexible external gear located on the major axis of the substantially elliptical shape move in the rigid inner state in the movement to the position on the minor axis of the substantially elliptical shape. The relative movement locus of the external teeth of the flexible external gear with respect to the internal teeth of the gear is shown.

  FIG. 13A shows a movement locus on a vertical section (first vertical section) C11 perpendicular to the rotation axis XX at the external end portion 33a (FIG. 3) of the external teeth 33. FIG. 13B shows a movement locus on a vertical section (first vertical section) C12 perpendicular to the rotation axis XX at the central portion 33b (FIG. 3) of the external teeth 33. FIG. 13C shows a movement locus on a vertical section (first vertical section) C13 perpendicular to the rotation axis XX at the tooth trace inner end portion 33c (FIG. 3) of the external tooth 33. FIG.

  The coordinate system Xi-Yi is an orthogonal coordinate system fixed to the internal teeth 22 of the rigid internal gear 20, and the Yi axis coincides with the center line of the root of the internal teeth 22.

  Here, in step S13, in consideration of the coning of the flexible external gear 30, the flexible external gear 30 with respect to the rigid internal gear 20 in a plurality of vertical sections C11, C12, C13 perpendicular to the rotation axis XX. The relative movement trajectory of the external teeth 33 is obtained. Then, within the outer shape of the envelope group obtained by projecting the envelope of the movement locus of the external teeth 33 of the flexible external gear 30 in each vertical section C11, C12, C13 in the direction of the rotation axis XX, the rigidity is reduced. The tooth profile of the gear 20 is determined.

  More specifically, on the vertical section C11, as shown in FIG. 13 (a), from the position on the major axis of the substantially elliptical shape when the wave generator 40 is virtually rotated, the short shape of the substantially elliptical shape is obtained. The movement trajectories 331a to 331z of the external teeth 33 to the position on the axis are obtained on the coordinate system Xi-Yi. And the envelope 254 of these movement locus | trajectories 331a-331z is calculated | required.

  Similarly, on the vertical section C12, as shown in FIG. 13 (b), the position on the major axis of the substantially elliptical shape from the position on the major axis of the substantially elliptical shape when the wave generator 40 is virtually rotated is shown. The movement trajectories 332a to 332z of the external teeth 33 to the position are obtained on the coordinate system Xi-Yi. And the envelope 255 of these movement locus | trajectories 332a-332z is calculated | required.

  Similarly, on the vertical section C13, as shown in FIG. 13C, from the position on the major axis of the substantially elliptical shape when the wave generator 40 is virtually rotated, on the minor axis of the substantially elliptical shape. The movement trajectories 333a to 333z of the external teeth 33 up to the position are obtained on the coordinate system Xi-Yi. And the envelope 256 of these movement locus | trajectories 333a-333z is calculated | required.

  In FIGS. 13A to 13C, curves 254 ′, 255 ′, and 256 ′ that are symmetric with respect to the Yi axis of the envelopes 254, 255, and 256 are also illustrated.

  Subsequently, a state in which the tooth profile of the remaining portion of the internal tooth 22 of the rigid internal gear 20 is determined from the outer shape of the envelope group obtained by projecting the envelopes 254, 255, and 256 in the direction of the rotation axis XX. explain.

  FIG. 14 is a diagram for explaining a third determination step in the method for manufacturing the wave gear device 10 according to the second embodiment of the present invention.

  As shown in FIG. 14A, the envelopes 254, 255, and 256 are projected in the direction of the rotation axis XX and superimposed on the coordinate system Xi-Yi to obtain an envelope group. In FIG. 14A, the long broken line indicates the envelope 254, the broken line indicates the envelope 255, and the dotted line indicates the envelope 256.

  And as shown in FIG.14 (b), the rigid internal gear 20 which is a tooth profile of the other party gear from the envelope group obtained by projecting several envelope 254,255,256 to the direction of the rotating shaft XX. The tooth profile of the inner teeth 22 is determined.

  More specifically, an envelope group (a plurality of envelopes 254, 255, 256) is provided so that the external teeth of the flexible external gear and the internal teeth of the rigid internal gear do not interfere on each vertical section C11, C12, C13. Is the tooth profile of the internal teeth 22 of the rigid internal gear 20. That is, the tooth profile of the internal tooth 22 of the rigid internal gear 20 is formed by the envelopes 254 and 256 with the main range of the end surface and the main range of the root surface with the envelope 254.

FIG. 15 is a diagram illustrating a state of meshing of the external teeth 33 and the internal teeth 22 of the wave gear device 10 manufactured by the manufacturing method according to the second embodiment. 15A is on the vertical cross section C11 of the external end 33a of the external teeth 33, FIG. 15B is on the vertical cross section C12 of the central portion 33b of the external teeth 33, and FIG. The state of meshing on the vertical section C13 of the tooth trace inner end 33c of the tooth 33 is shown. On the long axis of each vertical section C11, C12, C13 on outside teeth 33 _A are substantially elliptical shape, the external teeth 33 _Z represents the external teeth 33 positioned on the minor axis. As can be seen from FIGS. 13A to 13C, in each of the vertical cross sections C11, C12, and C13, a continuous meshing state is formed and no interference or the like occurs.

  As described above, in the second embodiment, the tooth profile that takes into account the complexity of the flexure shape of the flexible external gear 30 and the angle change between the teeth is obtained by discrete coordinate calculation. Therefore, even when the deformation of the flexible external gear 30 cannot be expressed with a small number of parameters, the wave gear device 10 in which the internal teeth 22 and the external teeth 33 are accurately meshed can be obtained.

  In the second embodiment, by determining the shape of a part of the internal teeth 22 of the rigid internal gear 20, the shape of the external teeth 33 of the flexible external gear 30 and the remaining internal teeth 22 of the rigid internal gear 20. The shape of the tooth of this part is uniquely determined. Further, the position of the boundary between a part of the internal teeth 22 of the rigid internal gear 20 and the remaining part is uniquely determined. For this reason, a tooth profile that not only satisfies the condition in which the external teeth 33 of the flexible external gear 30 and the internal teeth 22 of the rigid internal gear 20 mesh with each other, but also does not cause a contradiction between a portion and the remaining portion of the internal teeth 22. It is possible to have.

  In addition, when a processing error or the like is taken into account, in order to prevent interference, a tooth obtained by correcting any one of the external tooth tip and bottom and the internal tooth tip and bottom may be used. That is, in step S12, at least one of the tooth bottom portion and the tooth tip portion of the flexible external gear 30 is provided with a relief portion that avoids the interference with the rigid internal gear 20, and the flexible external gear 30 is provided. The tooth profile may be determined. In step S <b> 13, at least one of the tooth bottom portion and the tooth tip portion of the rigid internal gear 20 is provided with a relief portion that avoids interference with the flexible external gear 30, and the tooth profile of the rigid internal gear 20. May be determined.

  Here, considering the curvature of the tooth profile determined according to the present invention, if it is impossible to express with a parameter with little gear deformation, each movement locus and envelope group obtained in the tooth profile derivation process are also the same. It is a curve that is difficult to express with a small number of parameters. Therefore, the tooth profile can be a curve whose curvature repeats increasing and decreasing.

  FIG. 16 shows the external tooth shape of the flexible external gear shown in the second embodiment, and FIG. 17 shows the teeth in the toothing direction from the pitch circle, where m is the external tooth module of the flexible external gear. It is the graph which showed the curvature of the tooth profile of the range of 0.4xm on the front side and the tooth bottom side, respectively.

  In FIG. 17, the point U of the external tooth shape is a portion where the envelopes on the cross sections perpendicular to each axis defined in the axial direction intersect, but as shown in the graph of FIG. 17, the curvature has a maximum value at the point U, and the tooth It becomes the maximum value in the range in the bamboo direction. In addition, in the external tooth shape on the tooth tip side in the direction of toothing from the point U, there is a portion where the value of curvature is negative, that is, there is a curve in which the external tooth shape repeats unevenness. The increase in the curvature of the tooth profile and the presence of the uneven surface on the tooth surface affect the increase in contact stress and stress concentration generated on the tooth surface, and cause the tooth surface to wear and deteriorate.

  Therefore, at least one tooth profile shape of the rigid internal gear and the flexible external gear has a maximum value of curvature within a range of 0.4 × m from the pitch circle to the tooth tip side and the tooth bottom side in the toothing direction. It is good to correct to a reduced tooth profile. Thereby, the contact stress of the tooth surface generated when the rigid internal gear meshes with the flexible external gear can be reduced.

  That is, the contact stress can be reduced and the stress concentration can be alleviated by reducing the maximum value of the curvature of the tooth profile and eliminating the unevenness within a predetermined range sandwiching the pitch circle. The solid line shown in the graph of FIG. 18 indicates the curvature of an external tooth shape of an example obtained by approximating the external tooth shape so as to suppress the maximum value of the curvature of the external tooth shape and eliminate the unevenness of the tooth shape. . It is useful to modify the external tooth shape and the internal tooth shape in order to obtain a desired tooth profile curvature within a range that does not hinder the precise meshing aimed at by the present invention.

  The present invention is not limited to the embodiments described above, and many modifications can be made by those having ordinary knowledge in the art within the technical idea of the present invention.

  In the first and second embodiments described above, the so-called cup-shaped flexible external gear 30 in which the attachment portion 32 extends inward in the radial direction from the end portion 31b of the trunk portion 31 has been described. However, the present invention is not limited to this. Absent. As shown by a broken line in FIG. 2, the present invention can also be applied to a so-called top hat-type flexible external gear in which the attachment portion 32 extends radially outward from the end portion 31 b of the body portion 31.

  In the first and second embodiments, the case where the output of the wave gear device is decelerated to 1/50 has been described. However, the present invention is not limited to this, and the wave gear device having an arbitrary reduction ratio and size can be used. A wave gear device which is adapted and meshes accurately can be obtained.

  In the first and second embodiments, the envelope is obtained from a plurality of vertical sections, and the tooth profile is determined based on the envelope group. However, there may be one vertical section, in which case the envelope The line may be a tooth profile.

  Moreover, although the case where the first vertical cross section C11, 12, 13 and the second vertical cross section C21, 22, 23 are different from each other has been described, the first vertical cross section and the second vertical cross section may be the same vertical cross section. .

DESCRIPTION OF SYMBOLS 10 ... Wave gear apparatus, 20 ... Rigid internal gear, 22 ... Internal tooth, 30 ... Flexible external gear, 33 ... External tooth, 40 ... Wave generator

Claims (9)

A rigid internal gear having a plurality of internal teeth; a flexible external gear having a plurality of external teeth; and being disposed inside the rigid internal gear; and bending the flexible external gear in a radial direction to In a manufacturing method of a wave gear device comprising: a wave generator that partially meshes with a rigid internal gear and moves the meshed portion in a circumferential direction by rotating around a rotation axis;
A first determination step of determining a tooth profile curve for a part of the tooth tip side of one of the rigid internal gear and the flexible external gear;
Rotating the wave generator to obtain a relative movement locus of the tooth profile curve with respect to the other gear of the rigid internal gear and the flexible external gear, and using the envelope of the movement locus, the other A second determination step for determining the tooth profile of the gear;
Rotating the wave generator to obtain a relative movement locus of the tooth of the other gear whose tooth shape has been determined in the second determination step with respect to the one gear, and using the envelope of the movement locus, the A third determination step for determining the tooth profile of the remaining portion of the tooth of one gear;
A method of manufacturing a wave gear device, comprising:   In the second determining step, relative movement trajectory of the tooth profile curve with respect to the other gear is obtained in a plurality of first vertical sections perpendicular to the rotation axis, and the tooth profile curve in each first vertical section is determined. 2. The method of manufacturing a wave gear device according to claim 1, wherein a tooth profile of the other gear is determined from an outer shape of an envelope group obtained by projecting an envelope of a movement locus in the direction of the rotation axis.   In the third determining step, a relative movement trajectory of the tooth of the other gear with respect to the one gear is obtained in a plurality of second vertical cross sections perpendicular to the rotation axis, and The tooth profile of the one gear is determined from the outer shape of the envelope group obtained by projecting the envelope of the movement locus of the tooth of the other gear in the direction of the rotation axis. Method of manufacturing the wave gear device of the present invention.   The method for manufacturing a wave gear device according to any one of claims 1 to 3, wherein the tooth profile curve is an arc curve.   In the second determining step, at least one of the tooth bottom portion and the tooth tip portion of the other gear is provided with a relief portion that avoids interference with the one gear, and the tooth shape of the other gear is determined. The method of manufacturing a wave gear device according to claim 1, wherein the wave gear device is determined.   In the third determining step, at least one of the tooth bottom portion and the tooth tip portion of the one gear is provided with a relief portion that avoids interference with the other gear, and the tooth profile of the one gear is determined. The method of manufacturing a wave gear device according to claim 1, wherein the wave gear device is determined.   The flexible external gear includes a flexible cylindrical body portion provided with the plurality of external teeth at one end portion, and a mounted member that extends radially inward from the other end portion of the body portion. The method for manufacturing a wave gear device according to any one of claims 1 to 6, further comprising an attachment portion to be attached.   The flexible external gear includes a flexible cylindrical body portion provided with the plurality of external teeth at one end portion, and a mounted member that extends radially outward from the other end portion of the body portion. The method for manufacturing a wave gear device according to any one of claims 1 to 6, further comprising an attachment portion to be attached.   When the module of the rigid internal gear and the flexible external gear is m, at least one tooth profile is in a range of 0.4 × m from the pitch circle to the tooth tip side and the tooth bottom side in the tooth direction. 8. The method for manufacturing a wave gear device according to claim 1, wherein the tooth profile is modified to a tooth profile shape in which the maximum value of curvature is reduced.

Images