Method for designing tooth profile of wave gear device

Abstract

In a method for designing a tooth profile of a wave gear device (1), a first curve is obtained for points A (φ=0) to B (φ=π / 2) on a locus of movement of an external tooth (30) relative to an internal tooth (20). A similar curve is obtained by making the first curve (1-λ) times with the center of similarity being point B, and a second curve is obtained by rotating the similar curve 180° with the center of similarity being a midpoint C of points A and B. A third curve is obtained by making only the x coordinate of the second curve α times (α<1), or a fourth curve is obtained by making only the y coordinate of the second curve β times (β>1). The addendum tooth profile of the external tooth (30) is defined using the third curve or the fourth curve. A tooth profile can be obtained in which a wide range of meshing can be maintained by using a tooth profile design method using a locus of movement, and the dedendum of the external tooth (30) is enlarged, and more portions of the tooth surface of the external tooth (30) can be used for meshing.

Description

Technical Field

[0001] The present invention relates to a method for setting the tooth profile of a rigid internal gear and a flexible external gear in a wave gear device. Background Technology

[0002] Japanese Patent No. 2055418 discloses a method for achieving high rotational accuracy and high load capacity in a wave gear device. Regarding the tooth profile, by utilizing the movement trajectory of the external gear relative to the internal gear, a tooth profile capable of meshing over a wide range in the circumferential direction is formed. Increasing the number of teeth meshing simultaneously averages the tooth profile error, resulting in high accuracy, and disperses the load, reducing the stress on individual teeth, thereby achieving high load capacity. In this specification, regarding the wave gear device, the tooth profile obtained by using the movement trajectory of the external gear relative to the internal gear for the tooth profile is referred to as the IH tooth profile.

[0003] Various tooth profiles have been patented based on methods that apply this movement trajectory to the tooth profile. For example, Japanese Patent No. 2055418 uses half of the movement trajectory for the tooth profile, while Japanese Patent No. 2675853 further generalizes this by using λ times the movement trajectory (λ being a positive value less than 1) for the tooth profile. In addition, there are several other patents that utilize λ times the movement trajectory, such as Japanese Patent No. 2612585, Japanese Patent No. 3230595, and Japanese Patent No. 3942249.

[0004] Existing technical documents

[0005] Patent documents

[0006] Patent Document 1: Japanese Patent No. 2055418

[0007] Patent Document 2: Japanese Patent No. 2612585

[0008] Patent Document 3: Japanese Patent No. 2675853

[0009] Patent Document 4: Japanese Patent No. 3230595

[0010] Patent Document 5: Japanese Patent No. 3942249 Summary of the Invention

[0011] Regarding wave gear mechanisms, the increasing load capacity of both internal and external gears necessitates a reduction in stress at the tooth root of the external gear. The stress at the tooth root is primarily divided into tensile stress due to torque and bending stress due to elliptic deformation. Load dispersion caused by the IH tooth profile reduces the value of the tensile load due to torque. Enlarging the tooth root portion is particularly effective in reducing bending stress.

[0012] To reduce bending stress, and in order to expand the tooth root using the IH tooth profile, it is necessary to increase the value of λ, reduce the tooth tip portion of the external teeth used for meshing, and shrink the shape of the tooth root side. In this case, only a narrow range of the tooth tip can be used, which may lead to wear and denting of the external teeth. Furthermore, since the meshing point is only at the tooth tip side, the stress in the tilting direction of the external teeth may increase.

[0013] In view of this problem, the object of the present invention is to provide a tooth profile design method for a wave gear device, which is used to improve the tooth profile of an IH gear, and can maintain a wide range of meshing, expand the tooth root of the external tooth of the external gear, and can use a larger portion of the tooth surface for meshing.

[0014] This invention relates to a method for designing the tooth profile of a wave gear device, which comprises: a rigid internal gear; a flexible external gear; and a wave generator that causes the external gear to bend into an elliptical shape and mesh with the internal gear at a position on the major axis containing the ellipse, and causes the meshing position of the external gear and the internal gear to move in a circumferential direction. The invention is characterized by...

[0015] With the rotation angle of the wave generator set to φ, and focusing on the internal teeth of the internal gear and the external teeth of the external gear located on the major axis when φ = 0, the movement trajectory of the external teeth relative to the internal teeth is obtained as the first curve during the period when the wave generator rotates from φ = 0 to φ = φ1 (0 < φ1 ≤ π / 2).

[0016] When the endpoint of the first curve when φ = 0 is set as point A, the endpoint when φ = φ1 is set as point B, the midpoint between point A and point B is set as point C, and λ is set as a positive value less than 1, a similar curve (1-λ) times the first curve is found with point B as the center of similarity. The second curve is then obtained by rotating this similar curve by 180 degrees with point C as the center.

[0017] When α is set to a positive value less than 1 and β is set to a positive value greater than 1, the curve obtained by making only the x-coordinate of the second curve α times is designated as the third curve. For the second curve, the curve obtained by making only the y-coordinate β times is designated as the fourth curve. At this time, either the third curve or the fourth curve is calculated, and the tooth tip profile of the external tooth is defined by this curve.

[0018] The tooth tip profile of the internal gear is defined by the curve enveloping the tooth tip profile of the external teeth.

[0019] The root profiles of the external teeth and the root profiles of the internal teeth are respectively set to shapes that do not interfere with the tip profiles of the other teeth.

[0020] Invention Effects

[0021] According to the method of the present invention, it is possible to obtain a tooth profile that can maintain a wide range of meshing and enlarge the tooth root of the external tooth by utilizing a tooth profile design method based on a movement trajectory, and can use a larger portion of the tooth surface of the external tooth for meshing. Attached Figure Description

[0022] Figure 1A This is an explanatory diagram showing a cross-section of the wave gear device.

[0023] Figure 1B This is an explanatory diagram showing the end face of the wave gear device.

[0024] Figure 2A This is an explanatory diagram showing an example of an IH tooth profile.

[0025] Figure 2B This is an explanatory diagram showing the meshing condition of the IH tooth profile.

[0026] Figure 3A This is an explanatory diagram showing an example of the tooth profile proposed in this invention.

[0027] Figure 3B This is an explanatory diagram illustrating the meshing condition of the tooth profile proposed in this invention.

[0028] Figure 3C This is a graph showing the relationship between θ and φ obtained through numerical calculation when λ = 0.5 and α = 0.7.

[0029] Figure 3D This is an explanatory diagram comparing the tooth profile proposed in this invention with the IH tooth profile. Detailed Implementation

[0030] [Structure of the Wave Gear Mechanism]

[0031] Figure 1A , Figure 1BThis is an explanatory diagram showing an example of a wave gear device to which the present invention can be applied. The illustrated example is a cup-shaped wave gear device with a cup-shaped external gear. The present invention can also be applied to a top hat-shaped gear device with a top hat-shaped external gear and a flat wave gear device with a cylindrical external gear.

[0032] The wave gear device 1 comprises: a rigid internal gear 2; a flexible external gear 3, coaxially disposed inside the internal gear 2; and a wave generator 4 with an elliptical profile, fitted inside the external gear 3. The wave generator 4 causes the external gear 3 to bend into an elliptical shape, with the external teeth 30 of the external gear 3 meshing with the internal teeth 20 of the internal gear 2 at both ends of the major axis L of the ellipse. The internal gear 2 has 2n more teeth than the external gear 3 (n is a positive integer). If the wave generator 4 rotates, a relative rotation corresponding to the difference in the number of teeth is generated between the internal gear 2 and the external gear 3. If the internal gear 2 is fixed in a non-rotating state, it can be removed from the external gear 3 on the load side (not shown) for deceleration rotation. Both the internal gear 2 and the external gear 3 are spur gears with a module m. The deflection in the diametrical direction of the external gear 3 is 2κmn. κ is the displacement coefficient, for example, set to the practical range of 0.6 < κ < 1.4.

[0033] [IH tooth profile method]

[0034] First, the method for IH tooth profile, which is the premise of this invention, will be described.

[0035] The rotation angle of the wave generator in the wave gear device is set as φ. Focusing on the internal teeth of the internal gear and the external teeth of the external gear on the long axis when φ = 0, the movement trajectory of the external teeth relative to the internal teeth, obtained by rotating the wave generator from 0 to π / 2, is set as curve l (Equation 1). Furthermore, regarding the IH tooth profile method, a portion of this movement trajectory curve is sometimes used, in which case the range of φ is less than 0 to π / 2.

[0036]

[0037] Let point A be the endpoint when φ = 0 and point B be the endpoint when φ = π / 2. Let point C be the midpoint between point A and point B. Use the similarity curve obtained by making curve l λ times (0 < λ < 1) with point B as the center of similarity to define the tooth tip profile of the internal teeth of the internal gear (Equation 2).

[0038] Here, the intermediate variable representing the tooth profile shape is set as θ.

[0039]

[0040] Using point B as the center of similarity, the curve l is multiplied by (1-λ) to obtain the similarity curve. The tooth tip profile of the external gear is defined by using the curve obtained by rotating the similarity curve by 180 degrees with point C as the center (Equation 3).

[0041]

[0042] Furthermore, the root profiles of the internal teeth and the root profiles of the external teeth are designed to be shapes that do not interfere with the tip profiles of the other teeth.

[0043] (Proof of continuous contact of IH tooth profile)

[0044] The internal and external gears of the wave gear device have a large number of teeth. Therefore, by considering the number of teeth as infinite, the meshing of the teeth of the two gears can be approximated as the meshing of a rack. If the approximation of the rack is used, there is no element of tooth slope. Therefore, the tooth tip profile of the external tooth (Equation 3) can be expressed as Equation 4 when the vertex of the tooth tip profile (Equation 3) moves along the movement trajectory (Equation 1).

[0045]

[0046] The envelope point of the tooth tip profile group of the external tooth is the meshing point. Regarding the condition for the envelope of the tooth tip profile group of the external tooth, for Equation 4, the Jacobian determinant is zero. That is, Equation 5.

[0047]

[0048] If we calculate Equation 5, it becomes Equation 6.

[0049]

[0050] Equation 6 always holds true when φ = θ. In Equation 4, φ = θ is used to obtain the envelope of the tooth tip profile group of the external tooth. If φ = θ is used in Equation 4, it becomes Equation 7.

[0051]

[0052] Comparing Equation 7 with Equation 2, it can be seen that the envelope of the tooth tip profile of the external tooth is consistent with that of the tooth tip profile of the internal tooth. Therefore, if the tooth tip profiles of the internal and external teeth are set as in Equations 2 and 3, it is proven that a large range of continuous contact can be achieved between the internal and external teeth.

[0053] [The tooth profile design method of the present invention]

[0054] In the tooth profile design method of the present invention, the tooth profile is set in the following manner.

[0055] (The tooth profile at the top of the external tooth 30)

[0056] Similar to the IH tooth profile method described above, the rotation angle of the wave generator 4 of the wave gear device 1 is set as φ, focusing on the internal tooth 20 of the internal gear 2 and the external tooth 30 of the external gear 3 on the long axis when φ = 0. The movement trajectory of the external tooth 30 relative to the internal tooth 20 obtained when φ is rotated from 0 to π / 2 is set as curve l (first curve) (keeping Equation 1 unchanged).

[0057]

[0058] Let point A be the endpoint of curve l when φ = 0, point B be the endpoint when φ = π / 2, and point C be the midpoint between points A and B. Up to this point, the method is the same as for the IH tooth profile.

[0059] Using point B as the center of similarity, make curve l (1-λ) times to obtain a similar curve. Using point C as the center, rotate the similar curve by 180 degrees to obtain the second curve.

[0060] For the second curve, the third curve (Equation 8) is obtained by simply multiplying the x-coordinate by α. The tooth profile of the external tooth 30 is defined using this third curve. In Equation 8, θ is an intermediate variable representing the shape of the tooth profile.

[0061]

[0062] Alternatively, a fourth curve, derived in the following manner, can be used instead of the third curve to define the tooth tip profile of the external tooth 30. Specifically, a similarity curve is derived by multiplying curve l by (1-λ) with point B as the center of similarity. A second curve is derived by rotating the similarity curve by 180 degrees with point C as the center. Then, for the second curve, the fourth curve (Equation 9) is obtained by multiplying the y-coordinate by β. This fourth curve is used to define the tooth tip profile of the external tooth 30.

[0063]

[0064] (The tooth profile at the crest of internal tooth 20)

[0065] The tooth profile of the inner tooth 20 is set as the tooth profile obtained by the envelope of the tooth profile of the outer tooth 30.

[0066] When the tooth tip profile of the external tooth 30 is set as in Equation 8, the tooth tip profile set of the external tooth 30 when implementing the rack approximation becomes Equation 10.

[0067]

[0068] The envelope condition in this case becomes Equation 11.

[0069]

[0070] Equation 11 cannot be solved analytically; therefore, the relationship between φ and θ is determined through numerical calculation. Substituting the result into Equation 10 yields the tooth profile of the internal tooth 20.

[0071] Furthermore, when the tooth tip profile of the external tooth 30 is set as in Equation 9, the tooth tip profile set of the external tooth 30 when implementing the rack approximation becomes Equation 12, and the envelope condition becomes Equation 13.

[0072]

[0073]

[0074] The tooth profile of the internal tooth 20 is obtained by solving Equation 13 numerically and substituting it into Equation 12.

[0075] (tooth root and tooth profile)

[0076] In addition, similar to the IH tooth profile, the root profiles of the internal tooth 20 and the external tooth 30 are set to not interfere with the tip profile of the other tooth.

[0077] (Effects)

[0078] In Equation 8, if α < 1, then relative to the IH tooth profile with the same λ value, the tooth thickness of the external tooth 30 of the external gear 3 can be reduced and its tooth root enlarged. Alternatively, when the respective λ is adjusted to make the tooth thickness the same, the tooth surface used for meshing of the external tooth 30 is enlarged relative to the IH tooth profile. This means that the range of energy subjected to tooth friction is dispersed over a larger range. Furthermore, the radius of curvature of the tooth surface of the external tooth 30 also increases, thus reducing the contact stress on the tooth surface. These factors combined result in enhanced resistance to wear, dents, and other damage to the tooth surface.

[0079] In Equation 9, if λ = λ0 is set as in Equation 8, and β > 1 and λ = 1 - λ0 / β, then the same effect as in Equation 8 can be obtained.

[0080] [Example of tooth profile design]

[0081] When the external gear 3 is set to an ellipse shape using tangential polar coordinates as in Equation 14, the movement trajectory of the external gear 3 relative to the internal gear 2 as the case of rack meshing is represented by Equation 15.

[0082] p = r n +κmncos(2ψ) 0≤ψ≤2π Equation 14

[0083]

[0084] p: The distance from the origin to the tangent when drawing a tangent line for an elliptical shape.

[0085] rn: The radius of the external gear in its circular state before elliptical deformation.

[0086] ψ: The angle between the x-axis and the tangent when drawing a tangent to an ellipse.

[0087] xl: Coordinate of the pitch line direction of the rack

[0088] yl: Coordinate of the rack in the tooth height direction

[0089] m: Modulus

[0090] n: 1 / 2 of the difference in the number of teeth between the internal and external gears.

[0091] φ: The rotation angle of the wave generator, which is consistent with ψ in the rack approximation.

[0092] κ: Offset coefficient

[0093] An example of calculating the tooth profile for the movement trajectory of Equation 15 is shown. Here, m = 1, n = 1 (the difference in the number of teeth is 2), and κ = 1 are set.

[0094] (Comparative example: IH tooth profile)

[0095] Figure 2A Together with the movement trajectory shown in Equation 15 (φ=0~π / 2), the tooth tip profiles of the external teeth and the internal teeth obtained by the IH tooth profile method are shown with λ=0.65. Figure 2B The diagram shows the meshing of the external teeth relative to the internal teeth in this case.

[0096] (An example of a tooth profile obtained based on the method proposed in this invention)

[0097] Figure 3A Together with the movement trajectory shown in Equation 15 (φ = 0 ~ π / 2), the tooth profiles (tooth tip profiles of external tooth 30 and internal tooth 20) obtained by the method proposed in this invention are illustrated under the condition that λ = 0.5 and α = 0.7. The tooth thickness (x-coordinate of the connection between tooth tip and tooth root) of the tooth profile obtained based on this proposed method is formed as follows: Figure 2A The tooth thickness of the IH tooth profile shown is the same.

[0098] 1-0.65(=1-λ)=0.5×0.7(=λ·α)=0.35

[0099] Figure 3B The diagram illustrates the meshing of the external tooth 30 with the internal tooth 20 in this case. Additionally, Figure 3C The figure shows the relationship between θ and φ obtained by numerical calculation with λ = 0.5 and α = 0.7 in order to define the tooth tip profile of internal tooth 20. Figure 3DThe diagram shows tooth profiles and IH tooth profiles obtained based on the method proposed in this invention.

Claims

1. A method for designing the tooth profile of a wave gear device, the wave gear device comprising: a rigid internal gear; a flexible external gear; and a wave generator, which causes the external gear to bend into an elliptical shape and mesh with the internal gear at a position including the major axis of the elliptical shape, and causes the meshing position of the external gear relative to the internal gear to move in a circumferential direction, characterized in that, Let the rotation angle of the wave generator be φ. Focusing on the internal teeth of the internal gear and the external teeth of the external gear located on the major axis when φ = 0, the movement trajectory of the external teeth relative to the internal teeth is obtained as the first curve during the period when the wave generator rotates from φ = 0 to φ = φ1, where 0 < φ1 ≤ π / 2. When the endpoint of the first curve when φ = 0 is set as point A, the endpoint when φ = φ1 is set as point B, the midpoint between point A and point B is set as point C, and λ is set as a positive value less than 1, a similar curve is found that makes the first curve 1 - λ times larger, with point B as the center of similarity. Then, the second curve is obtained by rotating this similar curve by 180 degrees with point C as the center. When α is set to a positive value less than 1 and β is set to a positive value greater than 1, the curve obtained by making only the x-coordinate of the second curve α times is designated as the third curve. For the second curve, the curve obtained by making only the y-coordinate β times is designated as the fourth curve. At this time, either the third curve or the fourth curve is calculated, and the tooth tip profile of the external tooth is defined by this curve. The tooth tip profile of the internal gear is defined by the curve enveloping the tooth tip profile of the external teeth. The root profiles of the external teeth and the root profiles of the internal teeth are respectively set to shapes that do not interfere with the tip profiles of the other teeth.

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