Wave gear with a compound tooth profile that engages upon positive deformation

Abstract

Wave gear (1) with a ring-shaped, fixed, internally toothed gear (2), a flexible, externally toothed gear (3) arranged inside the internally toothed gear (2), and a wave generator (4) which is inserted into the externally toothed gear (3), wherein the flexible, externally toothed gear (3) has a flexible, cylindrical body region (301) and an annular membrane (302) extending radially from a rear end (301a) of the cylindrical body region (301), and wherein a toothed region formed in a region of the cylindrical body region (301) near an open region at the front end (301b) is deformed into an elliptical shape by the wave generator (4) over a region extending from a rear end region near the diaphragm (302) to a front end region near the opening, such that the deformation is substantially proportional to the distance from the diaphragm (302), wherein the wave gear (1) has a compound tooth profile which is engaged during positive deformation, wherein: the fixed, internally toothed gear (2) is designed as a spur gear with a module (m); the flexible, externally toothed gear (3) is designed as a spur gear with a module (m); a number of teeth of the flexible, externally toothed gear (3) is smaller by the size 2n, where n is a positive integer, than the number of teeth of the fixed, internally toothed gear (2); the deformation of a principal axis of an elliptical boundary neutral line of the flexible, externally toothed gear (3) in a cross-section which is perpendicular to an axis and is hereinafter referred to as the principal cross-sectional area, and which is selected at a predetermined position of the toothing of the flexible, externally toothed gear (3) in a tooth path direction, is set to 2κmn (κ>1); the engagement of the teeth of the fixed, internally toothed gear (2) and the flexible, externally toothed gear (3) in the main cross-sectional area is approximated by rack engagement in order to calculate a motion position curve (M) of the teeth of the flexible, externally toothed gear (3) in relation to the teeth of the fixed, internally toothed gear (2) in connection with a rotation of the shaft generator (4); characterized by the fact that a curve region (AB) is obtained from a region of the motion position curve (M) extending from the main axis of the deepest engagement position of the two gears (2, 3) to a side where the engagement of the teeth is disengaged, such that the curve region (AB) begins at position (A) of the deepest engagement of the two gears (2, 3), which is the position where the inclination angle is 90°, and reaches a position (B) where the inclination angle of the motion position curve (M) relative to a radial line of the fixed, internally toothed gear (2) is α° (0°<α°<30°); and a main area of ​​the tooth profile (30) of the flexible, externally toothed gear (3) is defined by a first similarity transformation curve (AC) in which the curve area (AB) is enlarged by a multiple of λ, and by a straight line (33) smoothly connected to an endpoint of the first similarity transformation curve (AC); a main region of a tooth profile (20) of the fixed, internally toothed gear (2) by a second similarity transformation curve (AD) in which the curve region (AB) is enlarged by a multiple of (λ+1), and is defined by a straight line (24) smoothly connected to an endpoint of the second similarity transformation curve (AD); and a value of λ is less than a maximum value of λ, where the maximum value of λ is obtained when the curve region (AB) is subjected to a similarity transformation with the factor (λ+1), where the origin of the similarity transformation of the curve region (AB) is placed at the position of the deepest intervention (A), such that a remote end of the second similarity transformation curve (AD) is arranged on the motion position curve (M).

Description

Technical field

[0001] The present invention relates to a wave gear and in particular to a wave gear in which the tooth profiles of a fixed, internally toothed gear and a flexible, externally toothed gear are modified to obtain high strength and a high slip torque. State of the art

[0002] The wave gear was invented by C.W. Musser (Patent Document 1), and since then, numerous inventions relating to wave gears have been made by many researchers, including Musser and the present inventor. Numerous inventions relating to the tooth profiles of wave gears have also been proposed. For example, the present inventor has proposed making the base tooth profile an involute tooth profile (Patent Document 2) and has also proposed a design method for a tooth profile to obtain the tooth tip profile of two gears that are in contact with each other over a wide area by using a technique in which the engagement of the teeth of the fixed, internally toothed gear and the flexible, externally toothed gear is described by a rack and pinion approximation (Patent Documents 3, 4).The present inventor has also proposed an invention aimed at preventing impairment of the tooth profile caused by the rack approach (patent document 5).

[0003] The present inventor has further proposed a tooth profile which is provided with a large tooth height and a wide engagement area in order to avoid slippage under high load torque in a Weil gear with a high reduction ratio which contains over 160 teeth in the two gears (Patent document 6).

[0004] In patent document 7, the present inventor proposes a wave gear drive comprising a circular rigid inner gear; a flexible outer gear arranged within the rigid inner gear; and a wave generator arranged within the flexible outer gear. The flexible outer gear has a flexible cylindrical main section and an annular diaphragm extending radially from a rear end of the cylindrical main section. A toothed section is formed at an open area at the front end of the cylindrical main section, which is bent into an elliptical shape by an extent of bending generated by a wave generator, the extent of bending from a rear end section on the diaphragm side to a front end section on the open side of the cylindrical main section being approximately proportional to the distance from the diaphragm.A cross-section of the flexible external gear, perpendicular to the axis at a specific point along the direction of the tooth extension line of the flexible external gear, is defined as a principal cross-section. The rigid internal gear and the flexible external gear are gears with a module m, and the flexible external gear has a number of teeth that is 2n (n is a positive integer) less than the number of teeth of the rigid internal gear. If the meshing of the teeth in the principal cross-section is approximated by rack meshing, a path of motion M of a tooth of the flexible external gear relative to a tooth of the rigid internal gear is obtained, which accompanies the rotation of the shaft generator.At the entry side of the teeth meshing with the major axis of the path of motion M, a first similarity curve AC is obtained by similarity transformation of a pressure angle α, which is defined as an inclination angle in a direction orthogonal to the direction of motion M in a region ranging from 90° at point A in an initial meshing phase to a minimum of 0° at point B, or in a region that is an intermediate sub-region between point A and point B, using a similarity ratio (λ < 1) with point A as the similarity center. The first similarity curve AC is used as the base tooth profile at the tooth tip of the rigid internal gear.A second similarity curve CB is obtained by rotating the first similarity curve AC by an angle of 180° with endpoint C as the similarity center, and by similarity transformation, in which the first similarity curve AC is multiplied by a similarity ratio (1 - λ) / λ. The second similarity curve CB is used as the base tooth profile on the tooth tip of the flexible external gear. Patent document 1: US 2,906,143 A Patent Document 2: JP 45-41171 B Patent Document 3: JP 63-115943 A Patent Document 4: JP 64-79448 A Patent Document 5: JP 7-167228 A Patent document 6: WO 2005 / 043006 A1 Patent document 7: DE 10 2007 006 530 A1 Disclosure of the invention Problems to be solved by the invention

[0005] There is a need for further improvements to the tooth profile in order to prevent slippage under high load torque in a wave gear with a large reduction ratio, which has more than 200 teeth in the two gears.

[0006] In response to this need, the tooth height must be made as large as possible, the engagement area of ​​the fixed, internally toothed gear and the flexible, externally toothed gear must be increased, and the contact pressure between the tooth profiles of the two gears must be reduced in order to increase the torque capacity.

[0007] In view of these points, it is an object of the present invention to provide a wave gear which has a tooth profile which can be provided with a large tooth height, a wide engagement area and the ability to reduce the contact pressure of the two gears in order to prevent slippage under high load torque. Means used to solve the problems described above

[0008] To solve the problems described above, according to the present invention, a wave gear is provided comprising an annular, fixed, internally toothed gear, a flexible, externally toothed gear arranged inside the internally toothed gear, and a wave generator incorporated into the externally toothed gear, wherein the flexible, externally toothed gear has a flexible, cylindrical body region and an annular diaphragm extending radially from a rear end of the cylindrical body region, and wherein a toothed region formed in a region of the cylindrical body region near an open area at the front end is deformed into an elliptical shape by the wave generator over a region extending from the rear end region near the diaphragm to a region at the front end near the opening.that the deformation or bending is essentially proportional to the distance from the membrane; wherein the wave gear is characterized in that:, the fixed, internally toothed gear is designed as a spur gear with a module m; the flexible, externally toothed gear is designed as a spur gear with a module m; the number of teeth of the flexible, externally toothed gear is smaller by a size 2n (where n is a positive integer) than the number of teeth of the fixed, internally toothed gear; the deformation of the principal axis of the elliptical boundary neutral line of the flexible, externally toothed gear in a cross-section that is perpendicular to the axis (and is hereinafter referred to as the principal cross-section) and that is chosen at a predetermined position of the toothing of the flexible, externally toothed gear in the tooth path direction, is set to 2κmn (κ>1); the engagement of the teeth of the fixed, internally toothed gear and the flexible, externally toothed gear in the main cross-sectional area is approximated by rack engagement in order to calculate the motion locus curve of the teeth of the flexible, externally toothed gear in relation to the teeth of the fixed, internally toothed gear in connection with the rotation of the shaft generator; a curve region of a region of the motion position curve extending from the main axis of the lowest engagement position of the two gears to the side where the engagement of the teeth is disengaged, such that the curve region begins at the lowest engagement position of the two gears, which is the position where the inclination angle is 90°, and reaches the position where the inclination angle in the motion curve with respect to the radial line of the fixed, internally toothed gear is α° (0°<α°<30°); and a main area of ​​the tooth profile of the flexible, externally toothed gear is defined by a first similarity transformation curve, in which the curve area is enlarged by a multiple of λ, and by a straight line smoothly connected to an endpoint of the first similarity transformation curve; the main area of ​​the tooth profile of the fixed, internally toothed gear is defined by a second similarity transformation curve, in which the curve area is increased by a multiple of (λ + 1), and by a straight line smoothly connected to an endpoint of the second similarity transformation curve; where the value of λ is less than the maximum value of λ, where the maximum value of λ is obtained by multiplying the curve range by (λ+1), where the origin of the similarity transformation of the curve range is set to the position of the deepest intervention, so that the remote end of the second similarity transformation curve is positioned on the motion position curve.

[0009] For practical purposes, a value in the range of 0° to 15° is generally used for the inclination angle α°.

[0010] The straight section in the tooth head profile of the fixed, internally toothed gear is preferably chosen to be as large as possible without overlapping with the tooth head of the tooth head profile of the flexible, externally toothed gear.

[0011] To enlarge the root or foot region of the fixed, internally toothed gear, the tooth profile region located near the root and along the second similarity transformation curve, which defines the root region of the fixed, internally toothed gear, is preferably modified into the form of a tooth profile consisting of an arc having a radius of curvature greater than that of the second similarity transformation curve and a straight line connected to the arc.

[0012] The end of the straight line defining the root area of ​​the tooth profile of the flexible, externally toothed gear is preferably connected by an arc to a root circle in order to maintain a clearance above a tooth head of the fixed, internally toothed gear.

[0013] The tooth area of ​​the flexible, externally toothed gear is at least in the area from the main cross-section to the front end area near the opening taken back or chamfered.

[0014] The present invention can be used in wave gears that have a high reduction ratio and have more than 200 teeth on both the fixed, internally toothed gear and the flexible, externally toothed gear. Mode of operation of the invention

[0015] In the wave gear according to the present invention, the tooth height of the teeth of the fixed, internally toothed gear and the flexible, externally toothed gear depends on the bending or deformation of the flexible, externally toothed gear. Therefore, the bending or deformation of the flexible, externally toothed gear in the radial direction is set to 2κ]mn (κ>1), which is greater than the normal bending of 2mn (κ=1), and the tooth height of both gears is set greater than the standard tooth height (tooth height when κ=1).

[0016] The locus of the meshing motion of the teeth of the two gears is described by a rack approximation in the case κ>1. The main regions of the tooth root profile of the fixed, internally toothed gear and the tooth tip profile of the flexible, externally toothed gear are defined using curves obtained by similarity magnification of a curve at a point where the engagement in a post-engagement state is detached from the deepest point of engagement, which is the vortex of the motion locus of the rack. The two gears are kept in continuous contact with each other.

[0017] By using a compound tooth profile, where the tooth profiles of the two gears are defined by the first and second similarity transformation curves and the straight tooth profiles smoothly connected to the endpoints of the similarity transformation curves, the contact pressure of the teeth is reduced and the torque load capacity is increased.

[0018] According to the present invention, a wave gear is provided which has a tooth profile that allows the tooth height to be increased, the engagement area to be enlarged, and the contact pressure to be reduced. The present invention is therefore particularly suitable for use in wave gears with a high reduction ratio, which have more than 200 teeth in the two gears. Brief description of the drawings Fig. Figure 1 is a schematic front view of a wave gear which is the subject of the present invention; Fig. Figure 2 is an explanatory view showing the bent state of a flexible, externally toothed gear in cross-section through an axis, wherein (A) shows the state before deformation, (B) shows the cross-section including the major axis after elliptical deformation, and (C) shows a cross-section including the minor axis after elliptical deformation; Fig. 3 is a motion position curve of a rack when κ>1, which forms the basis for forming a tooth profile according to the present invention; Fig. Figure 4 is an explanatory view showing the area used to form a tooth profile within the motion curve according to Fig. 3 is used; Fig. Figure 5A is an explanatory view showing an example of similarity transformation curves used to determine the tooth profiles of the two gears; Fig. 5B is an explanatory view showing similarity transformation curves; Fig. 5C is an explanatory view showing similarity transformation curves when λ is set to its maximum value; Fig. 6A is an explanatory view showing an example of the tooth profiles of the two gears; Fig. 6B is an explanatory view that covers an area of Fig. 6A shows in enlarged form; and Fig. Figure 7 is an explanatory view showing the chamfering or beveling performed on a tooth of the flexible, externally toothed gear. Reference sign 1 wave gear 2 fixed, internally toothed gears 3 flexible, externally toothed gears 4-wave generator 20 Tooth profile of the fixed, internally toothed gear 21 Area of ​​a similarity transformation curve tooth profile 22, 25 sheets 23 straight line 24 straight tooth profile area 30 Tooth profile of the flexible, externally toothed gear 31 Area of ​​a similarity transformation curve tooth profile 32 straight line 33 Area of ​​a straight tooth profile 34 sheets 35 foot circle 300 Position of the main cross-section 301a rear end 301b open end 304 External gearing 304a rear end area in tooth path direction 304b in tooth path direction front end region M Motion position curve AB Curve area used to define a tooth profile AC first similarity transformation curve AD second similarity transformation curve A lowest point of the motion curve B Point at which the inclination angle of a tangent to the motion curve α is Best way to implement the invention

[0019] A wave gear in which the present invention is used is described below with reference to the figures. (Structure of the wave gear)

[0020] Fig. Figure 1 is a front view of a wave gear 1, which is the subject of the present invention. Fig. Figures 2(A) to 2(C) are cross-sectional views showing the flexible, externally toothed gear 3 of the wave gear 1, in which the opening area in a cross-section through an axis is bent into an elliptical shape. Fig. 2(A) shows a state before deformation, Fig. Figure 2(B) shows a cross-section that includes the principal axis of the elliptical shape after deformation, and Fig. Figure 2(C) shows a cross-section enclosing the minor axis of the ellipse after deformation. The solid lines in the Fig. Figures 2(A) to 2(C) show a flexible, externally toothed gear 3 that is cup-shaped, and the dashed lines show a flexible, externally toothed gear 3 that is cap-shaped.

[0021] A wave gear 1 has an annular, fixed, internally toothed gear 2, a flexible, externally toothed gear 3 arranged inside the gear 2, and an elliptically profiled wave generator 4 fitted into the gear 2, as shown in the figures. The difference in the number of teeth between the fixed, internally toothed gear 2 and the flexible, externally toothed gear 3 is 2n (where n is a positive integer). The flexible, externally toothed gear 3 of the wave gear 1 is deformed into an elliptical shape by the elliptically profiled wave generator 4 and engaged with the fixed, internally toothed gear 2 at both end regions of the elliptical shape in the direction of the main axis L1.The engagement position of the two gears 2, 3 moves circumferentially when the shaft generator 4 is rotated, and a relative rotation is generated between the two gears 2, 3, corresponding to the difference in the number of teeth between the two gears. The flexible, externally toothed gear 3 has a flexible cylindrical body region 301, a radially expanding membrane 302 that extends through a rear end 301a of the body region 301, a hub 303 that extends through the membrane 302, and external teeth 304 formed in the region of the outer circumferential surface of the cylindrical body region 301 on the side closer to the open end 301b.

[0022] The radial outward or inward deformation is gradually increased by the elliptically profiled wave generator 4, which is fitted into the area on the inner circumferential surface of the cylindrical body section 301 in which the external teeth are formed, from the rear end 301a on the membrane side of the cylindrical body section 301 toward the opening end 301b. The outward deformation is increased in the cross-section containing the principal axis L1 of the elliptical shape proportionally to the distance from the rear end 301a to the open end 301b, as shown in Fig. 2(B) shown; and the inward deformation in the cross-section containing the minor axis L2 of the elliptical shape is increased proportionally to the distance from the rear end 301a to the open end 301b, as shown in Fig. 2(C) shown. For the outer teeth 304, which are formed in the region of the external circumferential surface on the side near the open end 301b, the deformation is therefore increased from a rear end region 304a in the direction of the tooth path to a front end region 304b on the side near the opening proportionally to the distance from the rear end 301a of the cylindrical body region. (Method for forming the tooth profile in the main cross-sectional area)

[0023] Fig. Figure 3 is a view showing the locus of motion of a tooth of the flexible, externally toothed gear 3 relative to the fixed, internally toothed gear 2. The locus of motion is obtained by approximating the relative motion of the two gears 2, 3 of the wave gear 1 by a rack. The locus of motion M is obtained in a principal cross-section (the cross-section that is perpendicular to an axis and selected at a predetermined position of the outer teeth 304 of the flexible, externally toothed gear 3 in the tooth path direction), which forms the basis for forming the tooth profiles of the two gears. For example, the principal cross-section is defined as a cross-section arranged as shown by the solid line 300 passing through the center of a ball in the bearing of the wave generator 4, as in Fig. 2(A) can be seen. The locus M of motion of a tooth of gear 3 is described by the following formulas: x=0.5 mn(θ−κ sin θ) y=κmn(1−cos θ).

[0024] Here, κ is a deformation coefficient greater than 1 and m is a module. The total amplitude of the motion path M of the flexible, externally toothed gear 3 is 2κmn.

[0025] The Fig. Figure 4 is an explanatory view showing the working area defined for the loop region of the motion position curve M of a tooth. The curve region AB describes the area extending from point A, which is the region of deepest engagement, to the region where the engagement is disengaged. The curve region reaches point B, which has an angle α°, and extends from point A of the lowest position, which is the position where the angle of inclination (pressure angle) of a tangent to the motion position curve M relative to the y-axis (radial line of the fixed, internally toothed gear) is 90° (x-axis). The angle α° corresponds to the angle of least pressure of the resulting tooth profile. In particular, α° corresponds to the angle of least pressure of the tooth tip in the flexible, externally toothed gear 3 and the angle of least pressure of the tooth root in the fixed, internally toothed gear 2. The range of the angle α° is usually 0°<α<30° and in practice 0°<α<15°.A tooth profile is determined using the curve region AB as described below. During engagement with positive deformation (κ>1), there is no contact until the teeth of the flexible, externally toothed gear 3 enter the tooth grooves of the fixed, internally toothed gear 2 and reach the lowest position A, and contact with the tooth surface of the internally toothed gear 2 only occurs on the release side, where the engagement is disengaged.

[0026] A first similarity transformation curve AC, obtained by subjecting the motion position curve of the working area, i.e., the curve region AB, to a similarity transformation with the multiplier λ, is used as the tooth profile of the main region of the tooth tip profile of the flexible, externally toothed gear 3, as in Fig. 5A is shown. A second similarity transformation curve AD, obtained by subjecting the curve region AB to a similarity transformation with the multiplier (λ+1), is used as the tooth profile of the main region of the tooth root profile of the fixed, internally toothed gear 2. The two tooth profiles determined in this way can be continuously engaged with each other in the curve region AB due to the similarity properties, as shown by the principle in the Fig. 5B shown.

[0027] The tooth height must be increased as much as possible to increase the slippage torque. To achieve this, λ is increased as much as possible. The highest value is position D', where the tooth tip of the fixed, internally toothed gear 2 is at the apex of the motion path curve M. The tooth tips of the two gears interfere with each other when the value is greater than D'. Such a case is found in the Fig. 5C shown.

[0028] The maximum value of λ reaches an extreme value in cases where the tooth tip of the fixed, internally toothed gear 2 is selected as the location of the maximum amplitude of the motion position curve M. The contact of the tooth profiles is a point contact and lacks the necessary strength when the maximum value is chosen as the value for λ.

[0029] In this embodiment, a value slightly below the maximum value is therefore chosen for λ, while retaining the advantages of a tooth height greater than the standard tooth height. An approach is also pursued in which the main area of ​​the tooth profile of the two gears is defined by a composite tooth profile. This composite profile is formed from the tooth profile of a similarity transformation curve and the tooth profile of a straight line by smoothly connecting a straight line at the endpoints of the similarity transformation curves of each of the two gears. This can reduce the surface pressure of the tooth and achieve improvements related to stress.

[0030] The value of the angle θ (parameter) and the angle α (pressure angle), which corresponds to the maximum theoretical value of λ+1 (in this case excluding the straight section of the compound tooth profile), can be calculated using the following formula: tan α=dx / dy=0.5(1−κ cos θ) / (κ sin θ).

[0031] The scaling factor (λ+1) of the motion position curve is the following value: From the x-coordinate value: λ+1=0.5 mn(π−κ sin 180°) / 0.5 mn / (θ−κ sin θ)=π / (θ−κ sin θ). From the y-coordinate: λ+1=2κmn / κmn / (1−cos θ)=2 / (1−cos θ)=2 / (1−cos θ)

[0032] The value of θ can therefore be obtained from the formula above and can be calculated using the following formula: θ−κ sin θ+0.5 π cos θ−0.5 π=0.

[0033] For example, the values ​​of θ, α and λ+1 are as follows when the deformation coefficient is set to κ = 1.4, θ=−26.1272° α=11.7712° λ+1=19.5731°.

[0034] Fig. 6A and Fig. Figure 6B are explanatory views showing an example of a tooth profile of a fixed, internally toothed gear 2 and a flexible, externally toothed gear 3. In these figures, the upper line is a tooth profile 30 of a flexible, externally toothed gear 3 and the lower line is a tooth profile 20 of a fixed, internally toothed gear 2.

[0035] In the main region of the tooth profile 20 of the fixed, internally toothed gear 2, the root region is a tooth profile region 21 of a similarity transformation curve, wherein the similarity transformation curve tooth profile defined by the second similarity transformation curve AD has been slightly adapted, and the tip region is a straight tooth profile region 24 defined by a straight line smoothly connected to the similarity transformation curve tooth profile region 21. The region of the second similarity transformation curve AD near the root is adapted by a straight line 23 and by an arc 22, one end of which is connected to the straight line 23 and the other end smoothly connected to the similarity transformation curve tooth profile region 21, in order to enlarge the root in the tooth root region of the fixed, internally toothed gear 2.Conversely, an arc 25 smoothly transitions into the endpoint of a straight tooth profile area 24 on the near side of the tooth head, the other end of the arc 25 is connected to a straight line 26 extending perpendicular to the center line of the tooth of the fixed, internally toothed gear 2, and the flat tooth head is defined by the straight line 26.

[0036] Here, the area of ​​the straight tooth profile region 24 in the tooth head profile of the fixed, internally toothed gear 2 is preferably set to the maximum value up to the value at which an overlap with the tooth tip of the tooth head region profile of the flexible, externally toothed gear 3 occurs.

[0037] In the tooth profile 30 of the flexible, externally toothed gear 3, the tooth tip region is a similarity transformation curve tooth profile region 31 defined by a first similarity transformation curve AC, and the tooth root region is a straight tooth profile region 33 defined by a straight line smoothly connected to the endpoint of the similarity transformation curve tooth profile region 31. A root circle 35 is smoothly connected to the endpoint of the straight tooth profile region 33 in the tooth root region by an arc 34. Adequate clearance from the flat top surface of the fixed, internally toothed gear 2 is ensured by the root circle 35, the flat surface being defined by the straight line 32 extending perpendicular to the centerline of the tooth at the end of the similarity transformation curve tooth profile region 31 near the tooth tip.

[0038] A retraction or chamfering, which gradually increases towards the open end 301b, of the area of ​​the outer teeth 304 of the flexible, externally toothed gear 3 from the main cross-section (position shown by the line area 300) to the front end area 304b, as in Fig. The procedure shown in Figure 7 is carried out. The resulting effect is that a preload is generated by the bulging of the motion curve of the outer teeth 304 near the main axis in the region of the outer teeth 304, extending from the main cross-sectional area to the open end 301b. A disruption of the engagement is also prevented in the region of the outer teeth 304 near the membrane 302 and at a distance from the main cross-sectional area.

Images