Wave gear that has a tooth profile with three-dimensional contact

Abstract

Wave gear (1) with a tooth profile with three-dimensional contact, comprising: a rigid, internally toothed gear (2); a flexible, externally toothed gear (3) arranged coaxially within the internally toothed gear (2); and a wave generator (4) fitted into the interior of the externally toothed gear (3), wherein the flexible, externally toothed gear (3) has a flexible cylindrical drum section (31), a diaphragm (32) extending radially from a rear edge (31b) of the cylindrical drum section (31), and external teeth (34) formed on a region of an outer circumferential surface in the direction of an opening at the front edge (31a) of the cylindrical drum section (31); the flexible, externally toothed gear (3) is deformed into an elliptical shape by the wave generator (4) and partially engages with internal teeth (24) of the rigid, internally toothed gear (2);the rigid, internally toothed gear (2) and the flexible, externally toothed gear (3) are both spur gears with a module m; the number of teeth of the flexible, externally toothed gear (3) is 2n less than the number of teeth of the rigid, internally toothed gear (2), where n is a positive integer; the extent of deformation at a principal axis position on an elliptical boundary neutral curve of the flexible, externally toothed gear (3) relative to a boundary neutral circle, before the external teeth (34) have been deformed into an elliptical shape, in a cross-section perpendicular to the axis of the external teeth (34) at any position in the tooth path direction is 2kmn, where &kgr is a deviation factor;the extent of deformation along the tooth path direction of the external toothing (34) from an inner edge (34b) of the external toothing (34) at the membrane (32) to an outer edge (34a) of the external toothing (34) at the opening at the front end (31a) increases proportionally to the distance from the membrane (32); if a cross-section perpendicular to the axis at a position on the path between the inner edge (34b) of the external toothing (34) and the outer edge (34a) of the external toothing (34) in the tooth path direction of the external toothing (34) is defined as a principal cross-section (34c), a deformation state of the principal cross-section (34c) is defined as a zero-deviation deformation, wherein a deviation factor �kgr; = 1 is, a deformation state at the inner edge (34b) of the external toothing (34) is a deformation with negative deviation, where the deviation factor &kgr;< 1, and a deformation state at the outer edge (34a) of the external toothing (34) is a deformation with positive deviation, where the deviation factor &kgr; > 1 is; when the wave generator (4) rotates, in a case where the engagement between the external gear (34) and the internal gear (24) is approximated by a rack approximation, the x-axis is a tandem direction of movement of the rack, the y-axis is a direction perpendicular to the tandem direction of movement, and an origin of the y-axis is defined as a midpoint of an amplitude of the motion trajectory with respect to each cross-section perpendicular to the axis, a motion trajectory of the external gear (34) with respect to the internal gear (24) is defined by equation (1): x = 0.5mn(θ − sinθ) = mncosθa first similarity curve defined by equation (2) is a similarity curve BC obtained by subjecting a first curve region AB extending from a high point A to a low point B to a μ-fold transformation, using point B as the similarity center, where A is the highest point of the motion trajectory obtained on the main cross section (34c) of the external gearing (34), B is the nearest low point after the highest point A, and μ is set to a positive value less than 1: xFa=0.5(1−&lgr;)(&pgr;−&thgr;+sin&thgr;)yFa=(&lgr;−1)(1+cos&thgr;)(0≤&thgr;≤&pgr;).a second similarity curve defined by equation (3), a similarity curve AC, is obtained by taking a second curve obtained by rotating a first similarity curve BC by 180° about a point C on the first similarity curve BC, a {(1 - &lgr;) / &lgr;is subjected to a multi-fold transformation, using point C as the center of similarity; xCa=0.5{(1−&lgr;)&pgr;+&lgr;(&thgr;−sin&thgr;)}yCa=&lgr;(1+cos&thgr;)(0≤&thgr;≤&pgr;).a base tooth profile curve defining a tooth profile on the principal axis of the external gearing (34) is defined by: a tooth tip profile region (41) defined using a curve region between point A and an intersection point D on the second similarity curve AC; a straight tooth profile region (42) defined by a region of a straight line L extending from the intersection point D; and a flank tooth profile region (43) connected to the straight tooth profile region (42), wherein &agr; a positive value less than 20, L is the straight line passing through point C on the second similarity curve AC and having an angle of inclination of Σ with respect to the y-axis.has, and D is the intersection point between the straight line L and the second similarity curve AC; wherein the curve defining the flank tooth profile area (43) is a curve that does not contribute to the engagement of the gears (2, 3) and is chosen to avoid overlap with the internal teeth (24);a tooth profile in each cross-section perpendicular to the axis of the external toothing (34) between the main cross-section (34c) and the outer edge of the external toothing (34) is defined by a profile-shifted tooth profile, which is obtained by profile shifting in an x-axis direction and in a y-axis direction with respect to the base tooth profile in each cross-section perpendicular to the main axis until the straight tooth profile region on the motion trajectory described by the base tooth profile shape in each cross-section perpendicular to the main axis is consistent with the straight tooth profile region on the motion trajectory described by the base tooth profile shape on the main cross-section (34c);a tooth profile in each cross-section perpendicular to the axis of the external toothing (34) between the main cross-section (34c) and the inner edge of the external toothing (34) is defined by a shifted tooth profile obtained by shifting the profile in the y-axis direction with respect to the base tooth profile shape in each cross-section perpendicular to the axis, such that the motion trajectory described by the base tooth profile shape is, in each cross-section perpendicular to the axis, a tangent to a lower region of the motion trajectory described by the base tooth profile shape in the main cross-section (34c);and the tooth profile of the internal gearing (24) is defined by a tooth tip profile area (51) defined by a curved area between point B on the first similarity curve BC and an intersection point E, a straight tooth profile area (52) defined by an area on the straight line extending from the intersection point E, and a flank tooth profile area (53) connected to the straight tooth profile area, where E is the intersection point between the straight line L and the first similarity curve BC;wherein the curve defining the flank tooth profile region (53) is a curve that does not contribute to the engagement of the two gears (2, 3) and is chosen to avoid an intersection with the external toothing (34), wherein the magnitudes of the profile shifts in the x-axis direction and the y-axis direction, which are carried out on the external toothing region between the main cross-section (34c) of the external toothing (34) and the outer edge (34a) of the external toothing (34), are defined by equations (4a) and (4b). become: x=0.5(t−&kgr;sint)y=−&kgr;+1−0.5 / tan&agr;×(t−&kgr;sint)−&kgr;(1−cost),where=sin−12tan&agr; / &kgr;−1+(2tan&agr;)2−1 / &kgr;21+(2tan&agr;)2;

Description

Technical field

[0001] The present invention relates to a wave gear having a tooth profile with three-dimensional contact, in which a rigid, internally toothed gear and a flexible, externally toothed gear mesh in a three-dimensional contact state. In a three-dimensional contact state between the rigid, internally toothed gear and the flexible, externally toothed gear, an engagement state is formed in which both gears are in continuous contact in a cross-section perpendicular to the axis, which is fixed at a predetermined position in the gear path direction of the two gears. An engagement state is also formed in which the two gears are in partial contact in cross-sections perpendicular to the axis other than the previously mentioned cross-section in the gear path direction. State of the art

[0002] The wave gear was invented by C.W. Musser (Patent Document 1). Since then, wave gears have been the subject of various inventions by other researchers, including the inventor of the present invention. Even specifically regarding the tooth profile, inventions are numerous. For example, the inventor of the present invention proposed in Patent Document 2 to use an involute tooth profile as the base tooth profile; and in Patent Documents 3 and 4, proposed a method for constructing a tooth profile using a technique in which the engagement of a rigid, internally toothed gear and a flexible, externally toothed gear is approximated by a rack and pinion approximation to obtain the tooth tip profile of the two gears.

[0003] A wave gear typically has an annular rigid, internally toothed gear, a flexible, externally toothed gear arranged coaxially within the rigid, internally toothed gear, and a wave generator fitted into the flexible, externally toothed gear. The flexible, externally toothed gear has a flexible cylindrical drum section, a diaphragm extending radially from a rear edge of the cylindrical drum section, and external teeth formed on an outer circumferential surface of the cylindrical drum section leading to an opening at the front edge.

[0004] The flexible, externally toothed gear is deformed into an elliptical shape by the wave generator and caused to engage with the rigid, internally toothed gear in areas at both ends of the ellipse's major axis. The degree of deformation of the external teeth of the flexible, externally toothed gear, which has been deformed into an elliptical shape, increases along the tooth path direction of the external teeth from the inner edge of the external teeth at the membrane to the outer edge of the external teeth at the opening at the front end, with the degree of deformation being essentially proportional to the distance from the membrane. As the wave generator rotates, each section of the toothed areas of the flexible, externally toothed gear is repeatedly deformed radially outward and inward. This process of deformation of the teeth of the flexible, externally toothed gear is known as "coning."

[0005] When the flexible, externally toothed gear is deformed into an elliptical shape by the wave generator, a neutral circle of the external teeth of the flexible, externally toothed gear is deformed into an elliptical boundary neutral curve. If w is the extent of the radial deformation with respect to the boundary neutral circle at the longitudinal position of the boundary neutral curve before the deformation, the value obtained by dividing the radius of the boundary neutral circle by the reduction ratio of the wave generator becomes the regular (standard) deformation quantity w. o called, and the ratio of these values ​​(w / w) o ) is called the deviation factor κ. A deformation with the regular deformation quantity w o is called “zero deviation deformation”, deformation with a magnitude greater than the regular deformation magnitude where is (κ > 1) is called "deformation with positive deviation" and a deformation with a magnitude smaller than the regular deformation magnitude w o is (κ < 1) is called “deformation with negative deviation”. If m is the module of the flexible, externally toothed gear and n is the difference in the number of teeth between the flexible, externally toothed gear and the rigid, internally toothed gear, where n is a positive integer, then the magnitude of the deformation is w = 2 κmn.

[0006] In patent document 5, the inventor of the present invention proposed a wave gear having a tooth profile capable of continuous engagement, taking into account the conical shape of the teeth of the flexible, externally toothed gear. The wave gear proposed in patent document 5 is described below.

[0007] Any position in the tooth path direction of a cross-section perpendicular to the axis of the flexible, externally toothed gear is defined as the principal cross-section, and the deformation of the flexible, externally toothed gear in the principal cross-section is defined as a deformation with zero deviation (κ = 1). The engagement of the flexible, externally toothed gear and the rigid, internally toothed gear is approximated by a rack and pinion approximation. At each position along the tooth path direction of the flexible, externally toothed gear, including the principal cross-section, the motion trajectories of a tooth of the flexible, externally toothed gear relative to a tooth of the rigid, internally toothed gear are determined for a cross-section perpendicular to the axis while the shaft generator is rotating.A first similarity curve is determined, in which a curve region extending from a maximum point to a subsequent minimum point of a motion trajectory with zero deviation deformation, obtained on the main cross-section, is scaled down by a factor of λ (where λ < 1), with the minimum point being used as the similarity center. The first similarity curve is used as the base tooth profile of the tooth tips of the rigid, internally toothed gear.

[0008] A second similarity curve is determined, in which a curve obtained by rotating the first similarity curve 180° around an endpoint of the first similarity curve is scaled up by a factor of (1 – λ) / λ, using the endpoint as the similarity center. The second similarity curve is used as the base tooth profile for the tooth tips of the flexible, externally toothed gear.

[0009] Areas arranged in the tooth path direction of the external teeth on both sides of the flexible, externally toothed gear are profile-shifted such that both the first and second motion trajectories describe curves that are tangents to the minimum point of the motion trajectory with zero deviation deformation in the main cross-section, wherein the first motion trajectory is obtained perpendicular to the axis between the membrane and the main cross-section of the external teeth of the flexible, externally toothed gear for each cross-section in which a deformation with negative deviation (deviation factor κ < 1) occurs, and the second motion trajectory is obtained perpendicular to the axis between the opening at the front end and the main cross-section of the external teeth of the flexible, externally toothed gear in each cross-section in which a deformation with positive deviation (deformation factor κ > 1) occurs.

[0010] In a wave gear with a tooth profile designed as described, it is possible to achieve effective engagement over the area extending in the tooth path direction from the main cross-section to the outer end of the external teeth, and over the area of ​​the tooth path extending from the main cross-section to the inner end of the external teeth. This engagement is centered around a continuous tooth profile mesh that extends over a wide area of ​​the main cross-section. This allows for the transmission of a higher torque than with a conventional wave gear, where the mesh occurs over a narrower area of ​​the tooth path. State-of-the-art documents, patent documents

[0011] Patent Document 1: US Patent No. 2,906,143 Patent Document 2: JP-B 45-41 171 Patent Document 3: JP-A 63-115 943 Patent Document 4: JP-A 64-79 448 Patent document 5: WO 2010 / 070712 Disclosure of the invention Problems to be solved by the invention

[0012] An object of the present invention is to propose a tooth profile for a wave gear with three-dimensional contact, in which the tooth profiles of a rigid, internally toothed gear and a flexible, externally toothed gear form a composite tooth profile which has a curved tooth profile region and a straight tooth profile region, wherein the tooth profile with three-dimensional contact is able to achieve an engagement of the tooth profiles of the two gears over the entire tooth path, taking into account the cone of the flexible, externally toothed gear. Means for solving the tasks

[0013] In a wave gear according to the present invention, the tooth profiles of the rigid, internally toothed gear and the flexible, externally toothed gear are each defined as a composite tooth profile comprising a straight tooth profile region and a curved tooth profile region. The curve defining the curved tooth profile region is a homothetic curve obtained by homothetically converting a portion of the motion trajectory of a tooth of the flexible, externally toothed gear in a case where the engagement of the two gears is approximated by a rack engagement.

[0014] The cross-section perpendicular to the axis near the center of the tooth in the tooth path direction of the flexible, externally toothed gear is defined on the main cross-section where zero deviation deformation occurs. This results in a negative deviation deformation in a region of the toothing of the flexible, externally toothed gear that is located further towards the inner end in the tooth path direction than the main cross-section, and a positive deviation deformation in a region that is located further towards the opening at the front end than the main cross-section.

[0015] In the external gearing region, where the external teeth of the flexible, externally toothed gear are deformed with positive deviation, a negative profile shift occurs in the direction of tooth depth and tooth thickness. This causes the straight tooth profile regions of the external gear to contact the straight tooth profile regions of the internal teeth of the rigid, internally toothed gear, resulting in a meshing condition between the two gears. In the external gearing region, where deformation with negative deviation occurs, a negative profile shift is only performed in the direction of tooth depth. This causes the curved tooth profile regions of the external gear to continuously contact the curved tooth profile regions of the internal teeth of the rigid, internally toothed gear, resulting in a continuous meshing condition between the two gears.This ensures that the two gears mesh together across the entire tooth path. Effect of the invention

[0016] In the wave gear according to the present invention, a profile shift of a different form is applied to the external teeth to ensure that the tooth profiles mesh in the tooth path direction on both sides of the main cross-section of the flexible, externally toothed gear, taking the cone into account. It is therefore possible to achieve effective engagement of the two gears over the entire tooth path. As a result, the present invention provides a wave gear that allows for the transmission of a higher torque. Brief description of the drawings

[0017] Fig. Figure 1 is a schematic front view of a typical wave gear;

[0018] Fig. Figure 2 is an illustrative diagram showing a flexible, externally toothed gear in a deformed state, wherein (a) shows the state before deformation, (b) shows the state of a section enclosing a major axis of an elliptically deformed, flexible, externally toothed gear, and (c) shows the state of a section enclosing a minor axis of an elliptically deformed, flexible, externally toothed gear;

[0019] Fig. Figure 3 is an illustrative diagram showing motion trajectories of an external tooth relative to an internal tooth in cross-sections perpendicular to the axis of the external tooth of the flexible, externally toothed gear at a position at the outer edge, a principal cross-sectional position and a position at the inner edge in the tooth path direction, which are obtained in cases where the relative motion of the flexible, externally toothed gear and the rigid, internally toothed gear is approximated as a rack;

[0020] Fig. Figure 4 is an illustrative diagram showing the procedure to determine a tooth tip profile for each of the two gears based on the motion trajectory on the main cross-section (zero deviation cross-section) of an external toothing of the flexible, externally toothed gear;

[0021] Fig. Figure 5 is an illustrative diagram showing an example of a base tooth profile shape of an external tooth and the tooth profile shape of an internal tooth on the cross-section perpendicular to the axis (main cross-section) of the external tooth;

[0022] Fig. Figure 6 is a diagram showing the extent of the vertical profile shift for each cross-section of the tooth path of the flexible, externally toothed gear;

[0023] Fig. Figure 7 is an illustrative diagram showing the tooth profile shape in the direction of the tooth path and at right angles to the axis of a profile-shifted tooth of the external gearing on each cross-section;

[0024] Fig. Figure 8 is a diagram showing motion trajectories after profile shift at three points on the tooth path of the flexible, externally toothed gear between the main cross-section and the outer edge;

[0025] Fig. Figure 9 is a diagram showing motion trajectories after profile displacement at three points along the tooth path of the flexible, externally toothed gear between the main cross-section and the inner edge; and

[0026] Fig. Figure 10 is a diagram that, in the case of a rack and pinion approximation of the engagement of the two gears, shows the motion trajectories of an external toothing on the tooth path of the flexible, externally toothed gear at the outer edge, on the main cross-section, and at the inner edge. method of carrying out the invention

[0027] The following describes a wave gear according to the present invention with reference to the attached drawings. Overall structure of a wave gear

[0028] Fig. Figure 1 is a front view of a wave gear. Fig. Figure 2 is a cross-sectional view showing a section that includes an axis of the opening area of ​​the flexible, externally toothed gear of the wave gear. Fig. 1 contains, which is deformed into an elliptical shape, Fig. 2(a) shows the state before deformation, Fig. 2(b) shows a section after the deformation which contains a principal axis of an elliptic curve and Fig. Figure 2(c) shows a section after deformation, which includes a minor axis of an elliptic curve. In the Fig. 2(a) to (c) the solid line shows a cup-shaped flexible externally toothed gear, while the dashed line shows a cylindrical hat-shaped flexible externally toothed gear.

[0029] As shown in the figures, the wave gear 1 a ring-shaped, rigid, internally toothed gear 2 , a flexible, externally toothed gear 3 , which is inside the internally toothed gear 2is arranged, and an elliptically contoured wave generator 4 , which is inside the externally toothed gear 3 It is fitted. The rigid, internally toothed gear 2 and the flexible, externally toothed gear 3 Both spur gears have a module m. The difference in the number of teeth between the two gears is 2n (where n is a positive integer), with the rigid, internally toothed gear having more teeth. The flexible, externally toothed gear 3 is generated by the elliptically contoured wave generator 4 deformed into an elliptical shape and engages in areas at both ends of the main axis L1 of the elliptical curve with the stiff, internally toothed gear 2 one. If the wave generator 4 As the gears rotate, the engagement positions of the two gears move. 2 , 3 circumferentially and between the two gears 2 , 3A relative rotation occurs, corresponding to the difference in the number of teeth. The flexible, externally toothed gear 3 has a flexible cylindrical drum area 31 , a membrane 32 , which continuously extend from a rear edge 31b originating from the drum area and widening in a radial direction, a hub 33 , which continuously interact with the membrane 32 is formed, and has an external toothing. 34 , located on the outer circumferential surface area of ​​the cylindrical drum area 31 towards an open edge 31a is trained.

[0030] Since the elliptically contoured wave generator 4 into an inner circumferential surface area of ​​the externally toothed area of ​​the cylindrical drum area 31 The extent to which the cylindrical drum area is fitted is determined by the dimensions to which it extends. 31deformed, in a radial direction outwards or from the rear edge 31b at the membrane 32 to the open edge 31a to. As in the Fig. 2(b) shows that the extent of the deformation takes on an outward dimension in a section containing the major axis L1 of the ellipse, in the direction of the open edge. 31a proportional to the distance from the rear edge 31b to, and, as in the Fig. 2(c) shows the extent of the inward deformation in a section that follows the minor axis 12 the ellipse contains, towards the open edge 31a proportional to the distance from the rear edge 31b Therefore, the extent of deformation of the external gearing varies. 34 , which point towards the open edge 31a The deformation is formed on the outer circumferential surface area, perpendicular to the axis in the tooth path direction on every cross-section. In particular, the extent of the deformation decreases from the position at the inner edge. 34b, which in the tooth path direction of the external toothing 34 on the side of the membrane 32 is arranged to the position at the outer edge 34a , which is on the side of the open edge 31a is arranged proportionally to the distance from the rear edge 31b to.

[0031] In the present invention, the cross-section 34c perpendicular to the axis near the center of the tooth path direction of the external gearing 34 of the flexible, externally toothed gear 3 a cross-section that exhibits zero deviation deformation, and which serves as the main cross-section 34c This is referred to as... One result occurs in the area of ​​the external teeth of the flexible, externally toothed gear. 3 , which continues in the direction of the tooth path towards the inner edge 34b as the main cross-section 34cis arranged, a deformation with negative deviation on, and in the area that extends further in the tooth path direction towards the outer edge 34a as the main cross-section 34c When arranged, a deformation with a positive deviation occurs. Tooth profile shape of the two gears

[0032] Fig. Figure 5 is an illustrative diagram showing an example of the basic tooth profile shape of the two gears. 2 , 3 shows the tooth profile shape of the external teeth. 34 The tooth profile shown in the drawing is the base tooth profile shape used to determine the tooth profile shape for the main cross-section. 34c to define, which is located near the center of the tooth path direction of the external gearing 34 The basic tooth profile shape is defined by a convexly curved external tooth head profile area. 41 , a straight external tooth profile area 42, which is continuously formed with the previous area, a concave curved external tooth flank profile area 43 , which is continuously formed with the preceding area, and an external tooth root area 44 , which is continuously formed with the preceding area. The main cross-section 34c For example, a cross-section perpendicular to the axis through which the centerline of a ball in a wave bearing passes, as in Fig. 2 shown.

[0033] The tooth profile shape of the external teeth 34 between the main cross-section 34c and the outer edge 34a is, as described below, a profile-shifted tooth profile, which is created by applying a negative profile shift in the direction of tooth depth and tooth thickness to the in Fig. The tooth profile shape shown in section 5 is obtained. The tooth profile shape of the external teeth. 34between the main cross-section 34c and the inner edge 34b , is, as described below, a profile-shifted tooth profile, which is obtained by applying pressure to the in Fig. The basic tooth profile shown in section 5 only exhibits a negative profile shift in the direction of tooth depth.

[0034] The internal teeth 24 has the same tooth profile shape along its entire length in the tooth path direction, which is based on the in Fig. The tooth profile shape shown in section 5 is defined. In particular, the tooth profile shape of the internal teeth is defined. 24 through a convexly curved internal tooth profile area 51 , a straight internal tooth profile area 52 , which is continuously formed with the preceding area, an internal gear flank tooth profile area 53 , which is continuously formed with the preceding area, and an internal tooth root area 54, which is continuously trained in the preceding area, is defined.

[0035] Method for forming the tooth profiles for the two gears. The method for determining the base tooth profile shape of the external gearing and the tooth profile shape of the internal gearing. 24 The following refers to the Fig. 3, Fig. 4 and Fig. 5 described.

[0036] Trajectory of movement of the gearing according to the rack and pinion approximation

[0037] Fig. 3 is a diagram showing the motion trajectories of the external gearing. 34 of the flexible, externally toothed gear 3 shows. When the relative movement of the teeth of the two gears 2 , 3 of the wave gear 1 When approached by a rack and pinion, the motion trajectory of the external gearing is determined. 34 of the flexible, externally toothed gear 3 with regard to the internal teeth24 of the rigid, internally toothed gear 2 received. In Fig. 3 denotes the x-axis as the tandem movement direction of the rack, the y-axis as a direction perpendicular to it, and θ as the rotation angle of the wave generator. 4 In a cross-section perpendicular to the axis, at any position in the tooth path direction of the external gearing 34 of the flexible, externally toothed gear 3 the extent of deformation on the main axis in position L1 on an elliptical boundary neutral line of the external gearing 34 relative to a boundary neutral circle, before the external gearing 34 is deformed into an elliptical shape, 2 κmn, where κ is the deviation factor. The motion trajectory of the external gearing. 34 of the flexible, externally toothed gear 3 is described by the following equation: x = 0.5 mn(θ – κsinθ) y = κmncosθ (1)

[0038] For the sake of simplicity, with m = 1, n = 1 (the difference in the number of teeth is equal to 2), the motion trajectory is obtained from equation (1a): x = 0.5(θ – κsinθ) y = κcosθ. (1a)

[0039] In the Fig. 3 is the origin of the y-axis, the mean position of the amplitude of the motion trajectory. Of the motion trajectories, the zero-deviation motion trajectory M1 is located in the main cross-section. 34c The motion trajectory M2 is obtained in the case of zero-deviation deformation, where the deviation factor κ = 1. The motion trajectory M2 is obtained in the case of deformation with positive deviation, where the deviation factor κ > 1, and the motion trajectory M3 is obtained in the case of deformation with negative deviation, where the deviation factor κ < 1. In the present invention, the main cross-section34c , which forms the basis for the tooth profile shape of the two gears 2 , 3 is, as in the Fig. 2 shown, at a position near the center of the tooth path direction of the external gearing 34 The flexible, externally toothed gear is placed on a cross-section perpendicular to the axis. The motion trajectory M2 of positive deviation is the trajectory obtained on the cross-section perpendicular to the axis, which is in the tooth path direction of the external toothing. 34 with regard to the main cross-section 34c towards the outer edge 34 is arranged, and the motion trajectory M3 with negative deviation is the trajectory obtained on the cross-section perpendicular to the axis, which is in the tooth path direction of the external gearing. 34 with regard to the main cross-section 34c towards the inner edge 34b is arranged. Method for forming the tooth profile on a main cross-section

[0040] Fig. Figure 4 is an illustrative diagram showing a method for determining the tooth head profile of the external gearing. 34 and the internal teeth 24 The diagram shows the usage range defined for the motion trajectory M1 in a state of zero deviation deformation, in order to determine the tooth head profile. First, in the motion trajectory M1, the main cross-section 34c A parameter θ in a curved region is assigned a value between π (point B: minimum of the motion trajectory) and 0 (point A: maximum of the motion trajectory). This curved region of the motion trajectory M1 is subjected to a λ-fold (0 < λ < 1) similarity transformation, which uses point B as the similarity center, and a first similarity curve BC is obtained. Fig. Figure 4 shows a case where λ = 0.6. The first similarity curve BC is used as the tooth profile curve, which is used to determine the tooth tip profile of the stiff, internally toothed gear. 2 to define.

[0041] Using the endpoint C of the first similarity curve BC as its center, the first similarity curve BC is rotated by 180° to obtain curve B'C. Curve B'C is then subjected to a (1 – λ) / λ-fold similarity transformation, again using endpoint C as its similarity center, resulting in a second similarity curve AC.

[0042] The second similarity curve AC is used as the tooth profile curve, which is used to determine the tooth tip profile of the base tooth profile shape of the flexible, externally toothed gear. 3 to define.

[0043] When the tooth profile curves that define the tooth head profiles are expressed by equations, the following equations (2) and (3) are obtained.

[0044] Basic equation for the tooth head profile of the rigid, internally toothed gear: x Ca = 0.5{(1 – λ)π + λ(θ – sinθ)} y Ca =(1 + cosθ) (2) (0 ≤ θ ≤ π).

[0045] Basic equation for the tooth head profile of the flexible, externally toothed gear: x Fa = 0.5(1 – λ)(π – θ + sinθ) y Fa = (λ – 1)(1 + cosθ) (3) (0 ≤ θ ≤ π). Base tooth profile shape for the main cross-section of the external teeth

[0046] To define the found tooth head profile as described above, the main cross-section is used. 34c the external gearing 34 Using the tooth profile curve AC, a tooth profile shape is defined as follows with reference to the Fig. 4 and Fig. 5 is described.

[0047] Regarding the tooth profile curve AC for defining the tooth head profile based on the tooth profile shape of the flexible, externally toothed gear 3 A straight line is drawn through point C at a pressure angle α, and a curved region AD of the tooth profile curve AC is determined between an endpoint A and an intersection point D with respect to the straight line L. The curved region AD is used as the tooth profile curve, defining the regular tooth tip profile, and using this tooth profile curve, an external tooth tip profile region is calculated. 41 formed. A straight section on the straight line L extending from the intersection point D forms a straight section of the external gear tooth profile area. 42 defined. In this case, the external gear flank tooth profile area is defined. 43defined by a predefined concave curve, which defines the straight external gear tooth profile area 42 and the external tooth root area 44 , which is defined by a predetermined external tooth root curve, connects them so that a predetermined distance of the straight external tooth profile area is maintained. 42 from the internal teeth 24 is achieved. Tooth profile shape of the internal teeth

[0048] Similarly, the tooth profile curve DC, which is used to define the tooth head profile, is used to define the tooth profile of the internal gearing. 24 to train. As in the Fig. 4 and Fig. As shown in section 5, the intersection point between the straight line L and the curve BC is defined as point E, the curve area BE is used as the tooth profile curve, which defines the regular tooth tip profile, and the internal gear tooth tip profile area 51is formed using the tooth profile curve. The straight section of the internal gear tooth profile area. 52 is defined using the straight portion of the straight line extending from intersection point E. Furthermore, the internal gear flank tooth profile area is defined. 53 defined by a predefined concave curve, which defines the straight internal gear tooth profile area 52 and the internal tooth root area 54 , which is defined by a predetermined internal tooth root curve, connects them so that at the tip there is a distance of the straight internal tooth profile area 52 from the external gearing 34 is achieved.

[0049] The flank tooth profile areas 43 , 44 , 53 , 54 Neither gear engages in meshing. Therefore, the flank tooth profile areas 43 , 44 , 53 ,54 can be determined without restrictions, as long as there is no overlap with the respective tooth head profile areas. 51 , 52 , 41 , 42 occurs.

[0050] This is how the basic tooth profile shape is determined at the main cross-section 34c the external gearing, as in Fig. 5 shown, and the tooth profile shape of the internal teeth 24 The pressure angle α of the straight tooth profile is defined. In the present example, it is 9°. Considerations regarding the machining of gears make a small α value less desirable than having a straight tooth profile originating from a point with a pressure angle of 6° to 12° and combining it with the flank tooth profile.

[0051] The engagement of the tooth profile of the internal teeth 24 on the main cross-section 34c and the tooth profile of the external teeth 34, which is determined as described above, by contact between the tooth head profile areas of both gears 24 , 34 and is achieved through contact between the two straight tooth profile areas. When the external teeth... 34 of the flexible, externally toothed gear 3 with regard to the internal teeth 24 of the rigid, internally toothed gear 2 As the gears move along the motion trajectory M1, the tooth head profiles are defined by the similarity curve derived from the motion trajectory; therefore, continuous contact is ensured and continuous engagement of the two gears is achieved. Tooth profile shape of the external teeth at positions outside the outer cross-section

[0052] When the flexible, externally toothed gear 3 with regard to the rigid, internally toothed gear 2 along the motion trajectory M1, which is in Fig. As shown in section 3, the tooth head profiles of the two gears touch during the engagement of the tooth head profiles. 2 , 3 in the main cross-section 34c due to the properties of the similarity curves, it is continuous. In contrast, the deviation factor is such that in every cross-section perpendicular to the axis of the external gearing, 34 , which is relative to the main cross-section 34c is arranged in the direction of the outer edge, κ > 1, and the deviation factor is such that in each cross-section perpendicular to the axis of the external toothing 34 , which is relative to the main cross-section 34c is arranged in the direction of the inner edge, κ < 1. As in Fig. As shown in Figure 3, both the motion trajectory M2 with positive deviation and the motion trajectory M3 with negative deviation overlap with the zero-deviation motion trajectory M1; in this state it is not possible to obtain an engagement state in which both gears 24 , 34 are in mutual contact.

[0053] Accordingly, in the area of ​​the external gearing between the main cross-section 34c and the outer edge 34a based on the tooth profile shape, which is in Fig. As shown in Figure 5, a profile shift was performed so that the straight tooth profile area of ​​the tooth profile of each cross-section is perpendicular to the axis and consistent with the straight external gear profile areas. 42 of the tooth profile on the main cross-section 34c The resulting shifted tooth profile is positioned perpendicular to the axis between the main cross-section for each cross-section. 34cand the outer edge 34a used as a tooth profile.

[0054] The magnitude of the horizontal profile displacement x and the magnitude of the vertical profile displacement y required in this case are obtained by the following equations (4a), (4b). In these equations, α is the pressure angle of the straight section of the profile-displaced rack profile, where the straight rack profile section after the profile displacement is determined on the cross-section perpendicular to the axis such that it is consistent with the straight external gear tooth profile section. 42 on the main cross-section 34c is. x = 0.5(t – κsint) (4a) y = –κ + 1 – 0.5 / tanα × (t – κsint) – κ(1 – cost) (4b)

[0055] Where in equations (4a) and (4b)

[0056] Next, the deviation factor on each cross-section is perpendicular to the axis of the external gearing. 34between the main cross-section 34c and the inner edge 34b such that κ < 1, and the magnitude of the deviation is in comparison to the principal cross-section 34c small. Therefore, the area of ​​the external teeth overlaps with an area of ​​the internal teeth in the lower part of the motion trajectory. 20 In this condition, the procedure cannot be maintained.

[0057] Accordingly, the external gearing 34 between the main cross-section 34c and the inner edge 34b A vertical profile shift is performed. The amount of the profile shift is chosen such that the lower region of the motion trajectory M3 of the external gearing 34 of the flexible, externally toothed gear 3 with regard to the internal teeth 24 of the rigid, internally toothed gear 2a tangent to point B in the lower part of the motion trajectory M1 on the main cross-section 34c is (see Fig. 4) In this case, no horizontal profile shift is performed.

[0058] In particular, each cross-section perpendicular to the axis on the external gearing is examined. 34 between the position of the main cross-section 34c and the position of the inner edge 34b , which are in the direction of the membrane 32 The size of the profile displacement is arranged according to the deviation factor κ at each position of a cross-section perpendicular to the axis such that the motion trajectory M3 in each cross-section perpendicular to the axis forms a tangent to point B in the lower region of the motion trajectory M1 in the main cross-section 34c If m = 1 and n = 1, the profile shift is equal to y and the negative value is taken, which is expressed by the following equation (5): y = κ – 1 (5)

[0059] Fig. Figure 6 shows an example of the magnitude of the vertical profile shift at each position of the tooth path of the external gearing. 34 of the flexible, externally toothed gear 3 , as shown in equations (4b) and (5). The horizontal axis in the diagram shows the deviation factor κ of each cross-section perpendicular to the axis of the flexible, externally toothed gear. 3 , and the vertical axis shows the magnitude of the vertical profile shift shown by equations (4b) and (5), and corresponds to the deviation factor κ.

[0060] From a practical point of view, the profile shift curve C1, expressed by equation (4b), can be approximated by a tangent C2 drawn at the point on the curve where the deviation factor κ = 1. In this case, a disturbance in tooth thickness occurring during engagement can be used as a preload to eliminate backlash or overrun. The straight profile shift line C3 in Fig. Figure 6 shows the size of the profile shift at each position on the inner edge. 34b of the main cross-section 34c , as expressed by equation (5).

[0061] Here, the tooth profile contour of the external gearing, when viewed in the direction of the tooth path, describes the shape of a broken line with the position of the main cross-section. 34cas a tip, if based on the profile shift curve C1 or the tangent C2 and the straight profile shift line C3 onto an external gearing area outside the main cross-section 34c A profile shift is exerted. To make the area containing the tip smooth and continuous, it is advantageous to define the area containing the main cross-section. 34c contains, using the four-dimensional curve C4 as described in the Fig. As shown in Figure 6, a smooth, continuous tooth profile shape is used. The four-dimensional curve C4 is tangent to tangent C2 and the straight profile displacement line C3 and has its highest point at κ = 1. Accordingly, it is located near the tooth path of the main cross-section. 34cA flat area is formed, ensuring a uniform variation in profile shift. The treatment of dimensions during tooth cutting of the flexible, externally toothed gear is also addressed. 3 simplified.

[0062] Fig. 7(a) is an illustrative diagram showing the tooth profile contour along the tooth path direction of the external gearing. 34 and the internal teeth 25 , which are chosen as described above, and the state on the main axis 11 (maximum intervention) is shown. In the diagram, the area representing the main cross-section is shown. 34c the external gearing 34 The area defined by the four-dimensional curve C4 contains the region that extends further towards the outer edge. 34a The arrangement is defined by the tangent C2, which approximates the profile displacement curve C1, and the area that extends further towards the inner edge. 34bThe position of the main cross-section is defined by the straight profile displacement line C3.

[0063] The Fig. 7(b), (c) and (d) are illustrative diagrams showing tooth profile shapes on a cross-section perpendicular to the axis, each at the position of the outer edge. 34a , of the main cross-section 34c and the inner edge 34b the external gearing 34 The diagrams also show the state at a position on the main axis L1 (deepest engagement). The tooth profile shape of the internal gearing. 34 is the same as at any cross-section perpendicular to the axis in the tooth path direction. The tooth profile shape of the external gearing is defined by the base tooth profile shape, which is in Fig. 5 on the main cross-section 34c As shown, however, to make the upper part of the shape slightly flatter, the shape is defined by a straight line. 45defined. The tooth profile shape in a cross-section perpendicular to the axis, extending further towards the outer edge. 34a as the main cross-section 34c The tooth profile is arranged in a shape obtained by subjecting it to a vertical and a horizontal negative profile shift. The tooth profile shape at a cross-section perpendicular to the axis extends further towards the inner edge. 34b as the main cross-section 34c The arrangement has a shape that is obtained by subjecting the base tooth profile to a negative vertical profile shift.

[0064] Fig. Figure 8 shows the motion trajectories M1, M2(1) and M2(2) of the external gearing. 34 , which relate to the internal gearing 24 approximated by a rack and pinion, in cross-sections perpendicular to the axis at three points between the main cross-section 34c and the outer edge 34a the external gearing34 of the flexible, externally toothed gear 3 . In the area between the main cross-section 34c and the outer edge 34a the external gearing 34 do the two gears engage? 34 , 24 in a state intertwined, in which the straight tooth profile area 42 the external gearing 34 the straight tooth profile area 52 the internal teeth 24 touched.

[0065] Fig. Figure 9 shows the motion trajectories M1, M3(1) and M3(2) of the external gearing. 34 , which relate to the internal gearing 24 approximated by a rack and pinion, in cross-sections perpendicular to the axis at three positions between the main cross-section 34c and the outer edge 34a the external gearing 34 of the flexible, externally toothed gear 3 As in the Fig. As shown in Figure 9, the motion trajectories M3(1) and M3(2) touch at the point on the tooth profile of the external gearing after the profile shift has been carried out. 34 the motion trajectory M1 in its lower region on the main cross-section 34c The trajectories in this area, near the low points of the movement trajectories, closely approximate the movement trajectory M1, as discovered by the inventor. This creates an engagement with continuous contact between the tooth head profiles.

[0066] The Fig. Figures 10(a), (b) and (c) are illustrative diagrams that, using the rack and pinion approximation, depict the state of engagement of the external gearing. 34 and the internal teeth 24 show that have tooth profiles which are formed as described above. Fig. 10(a) is located at a position on the outer edge 34a the external gearing 34 receive, Fig.10(b) is located at the position of the main cross-section 34c obtained, and 10(c) is located at the position of the inner edge 34b the external gearing 34 obtained. A case of a motion trajectory is shown, which occurs at the main cross-section. 34c has a flat area. As can be clearly seen from the motion trajectories, the external gearing has 34 of the flexible, externally toothed gear 3 , although approximate, across all cross-sections from the outer edge 34a via the main cross-section 34c to the inner edge 34b adequate contact with the internal teeth 24 .

Claims

[1] Wave gear ( 1 ) with a tooth profile featuring three-dimensional contact, exhibiting: a rigid, internally toothed gear ( 2 ); a flexible, externally toothed gear ( 3 ), the coaxially within the internally toothed gear ( 2 ) is arranged; and a wave generator ( 4 ), which is inside the externally toothed gear ( 3 ) is fitted, whereby the flexible, externally toothed gear ( 3 ) a flexible cylindrical drum area ( 31 ), a membrane ( 32 ), extending radially from a rear edge ( 31b ) of the cylindrical drum area ( 31 ) extends from, and an external toothing ( 34 ) has, which is located on an area of ​​an outer circumferential surface in the direction of an opening at the front edge ( 31a ) of the cylindrical drum area ( 31 ) is trained; the flexible, externally toothed gear ( 3 ) through the wave generator ( 4 ) is deformed into an elliptical shape and partially incorporated into the internal teeth ( 24 ) of the rigid, internally toothed gear ( 2 ) intervenes; the rigid, internally toothed gear ( 2 ) and the flexible, externally toothed gear ( 3 ) both spur gears have a module m; the number of teeth of the flexible, externally toothed gear ( 3 ) by 2n less than the number of teeth of the rigid, internally toothed gear ( 2 ) where n is a positive integer; the extent of deformation at a principal axis position on an elliptical boundary neutral curve of the flexible, externally toothed gear ( 3 ) relative to a boundary neutral circle, before the external gearing ( 34) has been deformed into an elliptical shape, in a cross-section perpendicular to the axis of the external gearing ( 34 ) at any position in the tooth path direction 2 kmn, where κ is a deviation factor; the extent of deformation along the tooth path direction of the external gearing ( 34 ) from an inner edge ( 34b ) the external gearing ( 34 ) at the membrane ( 32 ) to an outer edge ( 34a ) the external gearing ( 34 ) at the opening at the front end ( 31a ) proportional to the distance from the membrane ( 32 ) increases; when a cross-section is perpendicular to the axis at a position on the path between the inner edge ( 34b ) the external gearing ( 34 ) and the outer edge ( 34a ) the external gearing ( 34 ) in the tooth path direction of the external gearing ( 34 ) as a main cross-section ( 34c) is defined as a deformation state of the main cross-section ( 34c ) is defined as a zero-deviation deformation, where a deviation factor κ = 1, a deformation state at the inner edge ( 34b ) the external gearing ( 34 ) is a deformation with negative deviation, where the deviation factor κ < 1, and a deformation state at the outer edge ( 34a ) the external gearing ( 34 ) is a deformation with positive deviation, where the deviation factor κ > 1; when the wave generator ( 4 ) rotates, in a case where the engagement between the external teeth ( 34 ) and the internal teeth ( 24) is approximated by a rack and pinion approximation, the x-axis is a tandem direction of motion of the rack, the y-axis is a direction perpendicular to the tandem direction of motion, and an origin of the y-axis is defined as a midpoint of an amplitude of the motion trajectory with respect to each cross-section perpendicular to the axis, a motion trajectory of the external gearing ( 34 ) with regard to the internal gearing ( 24 ) is defined by equation (1): x = 0.5 mn(θ – κsinθ) y = κmncosθ (1) a first similarity curve defined by equation (2) is a similarity curve BC obtained by subjecting a first curve region AB, extending from a maximum point A to a minimum point B, to a λ-fold transformation, using point B as the similarity center, where A is the highest point of the motion trajectory on the principal cross-section ( 34c) the external gearing ( 34 ) is obtained, B is the next minimum point after the highest point A, and λ is set to a positive value less than 1: x Fa = 0.5 (1 – λ)(π θ + sinθ) y Fa = (λ – 1)(1 + cosθ) (2) (0 ≤ θ ≤ π). a second similarity curve defined by equation (3) is a similarity curve AC obtained by subjecting a second curve obtained by rotating a first similarity curve BC by 180° about a point C on the first similarity curve BC to a {(1 – λ) / λ}-fold transformation, using the point C as the similarity center; x Ca = 0.5 {(1 – λ)π + λ(θ – sinθ)} y Ca = λ(1 + cosθ) (3) (0 ≤ θ ≤ π). a basic tooth profile curve, which defines a tooth profile on the main axis of the external gearing ( 34 ) defined, is defined by: a tooth head profile area ( 41 ), which is defined using a curve segment between point A and an intersection point D on the second similarity curve AC; a straight tooth profile area ( 42 ), which is defined by a region of a straight line L extending from the point of intersection D; and a flank tooth profile area ( 43 ), which is associated with the straight tooth profile area ( 42 ) is connected, where α is a positive value less than 20, L is the straight line passing through point C on the second similarity curve AC and has an angle of inclination of α with respect to the y-axis, and D is the intersection point between the straight line L and the second similarity curve AC; where the curve defining the flank tooth profile area is a curve that does not lead to the engagement of the gears ( 2 , 3) contributes and is chosen so that it overlaps with the internal teeth ( 24 avoids; a tooth profile in each cross-section perpendicular to the axis of the external teeth ( 34 ) between the main cross-section ( 34c ) and the outer edge of the external toothing ( 34 ) is defined by a profile-shifted tooth profile, which is obtained by profile shifting in an x-axis direction and in a y-axis direction with respect to the base tooth profile in each cross-section perpendicular to the principal axis until the straight tooth profile region on the movement trajectory, which is described by the base tooth profile shape in each cross-section perpendicular to the principal axis, is consistent with the straight tooth profile region on the movement trajectory, which is described by the base tooth profile shape on the principal cross-section ( 34c ) is described; a tooth profile in each cross-section perpendicular to the axis of the external teeth ( 34) between the main cross-section ( 34c ) and the inner edge of the external toothing ( 34 ) is defined by a shifted tooth profile, which is obtained by shifting the profile in the y-axis direction with respect to the base tooth profile shape in each cross-section perpendicular to the axis, such that the motion trajectory described by the base tooth profile shape is, in each cross-section perpendicular to the axis, a tangent to a lower region of the motion trajectory defined by the base tooth profile shape in the main cross-section ( 34c ) is described; and the tooth profile of the internal teeth ( 24 ) is defined by a tooth head profile area ( 51 ), which is defined by a curved region between point B on the first similarity curve BC and an intersection point E, a straight tooth profile region ( 52), which is defined by an area on the straight line extending from the intersection point E, and a flank tooth profile area ( 53 ), which is connected to the straight tooth profile area, where E is the intersection point between the straight line L and the first similarity curve BC; where the curve that defines the flank tooth profile area ( 53 ) defined, is a curve that does not lead to the engagement of the two gears ( 2 , 3 ) contributes and is chosen so that it overlaps with the external gearing ( 34 avoids. [2] Wave gears ( 1 ) with a tooth profile with three-dimensional contact according to claim 1, wherein the magnitudes of the profile displacements in the x-axis direction and the y-axis direction, which occur on the external gearing area between the main cross-section ( 34c ) the external gearing ( 34 ) and the outer edge ( 34a ) the external gearing (34 ) are carried out by which equations (4a) and (4b) are defined: x = 0.5(t – κsint) (4a) y = –κ + 1 – 0.5 / tanα × (t – κsint) – κ (1 – cost), (4b) where [3] Wave gears ( 1 ) with a tooth profile with three-dimensional contact according to claim 2, wherein instead of the profile displacement curve which defines the magnitude of the profile displacement in the y-axis direction of equation (4b), the magnitude of the profile displacement in the y-axis direction is a magnitude of the profile displacement defined by a straight profile displacement line expressed by a tangent drawn to a point on the profile displacement curve where the deviation coefficient κ = 1. [4] Wave gears ( 1) with a tooth profile with three-dimensional contact according to one of claims 1 to 3, wherein the magnitude of the profile displacement in the y-axis direction, which is on the external toothing area of ​​the external toothing ( 34 ) between the main cross-section ( 34c ) and the inner edge of the external toothing ( 34 ) is carried out, is defined by equation (5): y = (κ – 1)mn (5). [5] Wave gears ( 1 ) with a tooth profile with three-dimensional contact according to one of claims 1 to 4, wherein a region of the tooth path contour of an interrupted tooth path contour, which represents a position of the main cross-section ( 34c ) as its highest point and is formed by a profile shift in the direction of the y-axis, which extends towards the outer edge ( 34a ) the external gearing ( 34 ) and the inner edge ( 34b ) the external gearing ( 34 ) is carried out, whereby the main cross-section ( 34c) is used as a boundary and the area of ​​the tooth path contour contains the highest point, using a four-dimensional curve that has a highest point at the position of the main cross-section ( 34c ) has, is transformed into a smoothly connecting contour.

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