Wave gear device

Abstract

A wave gear device (1A) is configured such that an annular, flexible external gear (2) meshes with an internal gear (3) inside the internal gear (3) while deforming into a waveform. The Young's modulus E (GPa) of the external gear (2) satisfies 2.0<E<120. The external gear (2) comprises a cylindrical wall (21). The cylindrical wall (21) is formed from a tooth part (21a) that has external teeth (2a) at an outer surface and a body part (21b) that connects to the tooth part (21a). A tooth width a of the tooth part (21a) and a body width b (b≥0) of the body part (21b) satisfy b / (a + b)<0.5.

Description

Strain wave gearing

[0001] The present invention relates to a strain wave gear device.

[0002] In recent years, there has been an increasing demand for smaller, lighter robots in the robotics industry, such as for industrial or collaborative robots. For this reason, wave gearing devices (strain wave gear reducers) that can be used as main components of robots have been developed to be smaller, lighter, and have a higher allowable torque.

[0003] One such wave gearing device, for example, is one in which the outer diameter dimension of a flexible external gear, which is one of the components of the wave gearing device, is increased while the axial length is shortened, thereby flattening the external gear and realizing a smaller space (see, for example, Patent Document 1).

[0004] WO 98 / 53224

[0005] However, with the strain wave gear device described in Patent Document 1, it is difficult to flatten the external gear while maintaining an increased allowable torque.

[0006] An object of the present invention is to provide a strain wave gear device that has a short axial length and an increased allowable torque.

[0007] (1) A wave gearing device according to the present invention is a wave gearing device in which a flexible annular external gear deforms in a wave pattern while meshing with an internal gear on the inside of the internal gear, wherein the Young's modulus E [GPa] of the external gear is 2.0<E<120, the external gear has a cylindrical wall that is composed of a tooth portion on whose outer surface the external teeth of the external gear are provided, and a body portion that is continuous with the tooth portion, and wherein the face width a (a>0), which is the axial length of the tooth portion, and the body width b (b≧0), which is the axial length of the body portion, satisfy the relationship b / (a+b)<0.5. With the wave gearing device according to the present invention, the axial length can be kept short and the allowable torque can be increased.

[0008] (2) In the strain wave gearing device of (1) above, the Young's modulus E [GPa] of the external gear preferably satisfies the relationship 2.0<E<30. In this case, by using a resin gear for the external gear, the axial length can be further reduced and the allowable torque can be further increased. Furthermore, in the strain wave gearing device of (1) above, it is preferable that b / (a+b)<0.4.

[0009] (3) In the strain wave gearing device of (1) or (2) above, it is preferable that the tip circle diameter Df of the external gear, the tip circle diameter Dr of the internal gear, and the total tooth depth h of the external gear satisfy the relationship 0.1h < (Df - Dr) < h. In this case, manufacturing is easier without reducing the allowable torque.

[0010] (4) In the strain wave gearing device of (3) above, it is preferable that the tip circle diameter Df of the external gear, the tip circle diameter Dr of the internal gear, and the total tooth depth h of the external gear satisfy the relationship 0.3h < (Df - Dr) < h. In this case, the allowable torque can be improved by increasing the number of meshing teeth.

[0011] (5) In the wave gear device of any one of (1) to (4) above, the external gear may have a bottom wall connected to one end of the cylindrical wall, and the bottom wall may have a plurality of slit holes arranged discontinuously in an annular shape around the axis, and the plurality of annularly arranged slit holes may be arranged on at least one circle centered on the axis. In this case, efficient torque transmission can be achieved.

[0012] (6) In the strain wave gear device of (5) above, the length of each of the plurality of slit holes in the circumferential direction can be made longer than its length in the radial direction, thereby enabling efficient torque transmission.

[0013] (7) In the strain wave gear device of (5) or (6) above, the plurality of slit holes may be arranged in a plurality of rows concentrically around the axis so that the radial distances from the axis are different. In this case, even more efficient torque transmission can be achieved.

[0014] (8) In the strain wave gear device of (7) above, it is preferable that the plurality of slits arranged in the plurality of rows are arranged concentrically around the axis so that the positions of the circumferential ends of the slits in each row are different between adjacent rows. In this case, more efficient torque transmission can be achieved.

[0015] According to the present invention, it is possible to provide a strain wave gear device in which the axial length is kept short and the allowable torque is increased.

[0016] FIG. 1 is a front view schematically showing a strain wave gearing according to a first embodiment of the present invention. FIG. 2 is a cross-sectional view schematically showing the strain wave gearing of FIG. 1 along the X-X cross section. FIG. 3 is a cross-sectional view schematically showing the external gear of FIG. 2 in a halved state. FIG. 4 is a cross-sectional view schematically showing a portion of the external gear to explain coning. FIG. 5 is an enlarged view schematically showing the state when the external gear is assembled inside the internal gear, showing an enlarged view of the interference portion between the internal gear and the external gear. FIG. 6 is a view schematically showing the deflection state of the external gear to explain an example of a method for calculating an appropriate deflection amount of the external gear when the external gear is attached to the internal gear of a strain wave gearing, in the case where the external gear is attached to an elliptical wave generator. FIG. 7 is an enlarged view schematically showing the meshing state with the internal gear when the external teeth of the external gear have a positive deflection tooth profile. FIG. 8 is an enlarged view schematically showing the meshing state with the internal gear when the external teeth of the external gear have a negative deflection tooth profile. FIG. 9 is a bottom view schematically showing a modified example of the external gear of FIG. 3. Fig. 2 is a cross-sectional view showing, in a manner equivalent to the X-X cross section of Fig. 1, an external gear that can be applied to a wave gearing device according to the present invention, and the cross-sectional view shows the states before and after tooth profile modification of the external teeth. Fig. 3 is a cross-sectional view showing, in a manner equivalent to the X-X cross section of Fig. 1, an external gear that can be applied to a wave gearing device according to the present invention, and the cross-sectional view shows the states before and after profile shifting of the external teeth. Fig. 4 is a cross-sectional view showing, in a manner equivalent to the cross section of Fig. 2, another external gear that can be applied to a wave gearing device according to the present invention. Fig. 5 is a front view showing, in a manner equivalent to the cross section of Fig. 2, a wave gearing device according to a second embodiment of the present invention.

[0017] A wave gear device according to an exemplary embodiment of the present invention will now be described with reference to the drawings.

[0018] A wave gearing device 1A according to a first embodiment of the present invention is shown schematically in Figure 1. The wave gearing device 1A is capable of transmitting power by meshing an internal gear 3 on the inside of the internal gear 3 while a flexible annular external gear 2 deforms in a wave pattern.

[0019] The strain wave gearing 1A includes a flexible external gear 2, an internal gear 3 with the external gear 2 disposed on its inner periphery, and a wave generator 4 disposed on the inner periphery of the external gear 2. The external gear 2 is an annular gear with a plurality of external teeth 2a. Each of the plurality of external teeth 2a protrudes radially outward. The internal gear 3 is an annular gear with a plurality of internal teeth 3a. Each of the plurality of internal teeth 3a protrudes radially inward. In the present disclosure, the internal gear 3 is a rigid gear with high rigidity that is difficult to deform. The internal gear 3 is formed of an iron-based material such as cast iron, alloy steel, or carbon steel. The wave generator 4 includes a non-circular cam member 41 rotatable about an axis O and a bearing 42 disposed on the outer periphery of the cam member 41. In the present disclosure, the cam member 41 is a two-lobe (two-lobe) elliptical shape when viewed in the axial direction, as shown in the figure.

[0020] Figure 2 shows a schematic cross section of the strain wave gear device 1A taken along line X-X in Figure 1. In the present disclosure, the bearing 42 includes an outer ring 42a, an inner ring 42b, and a plurality of rolling elements (e.g., rollers or balls) 42c interposed between them. However, at least one of the outer ring 42a and the inner ring 42b may be omitted from the bearing 42. The bearing 42 may also include a cage (not shown) that holds the rolling elements 42c.

[0021] The wave generator 4 is attached to the inner peripheral surface of the external gear 2, thereby deflecting the external gear 2 non-circularly so that the external teeth 2 a of the external gear 2 mesh with the internal teeth 3 a of the internal gear 3. In the present disclosure, the external gear 2 and the internal gear 3 mesh at two positions on the major axis of the cam member 41. In FIG. 1 , the symbol P indicates the meshing portion between the external teeth 2 a of the external gear 2 and the internal teeth 3 a of the internal gear 3. As shown in FIG. 1 , in the present disclosure, the meshing portion P is located on both major axis sides of the cam member 41. However, there is a difference in the number of teeth (e.g., 2) between the number of teeth Zf of the external teeth 2 a of the external gear 2 and the number of teeth Zr of the internal teeth 3 a of the internal gear 3.

[0022] The cam member 41 has a mounting hole 43 formed therein for mounting an input shaft (not shown) coaxially with the axis O. In the present disclosure, the mounting hole 43 has a key groove 43 a formed therein for preventing rotation of the input shaft.

[0023] In the wave generator 4, the cam member 41 rotates around the axis O together with the input shaft. As a result, the cam member 41 can rotate the external gear 2 relative to the cam member 41 via the rolling elements 42c of the bearing 42. On the other hand, the internal gear 3 is fixed to a housing case or the like. Therefore, when the cam member 41 is rotated, a relative rotation occurs between the external gear 2 and the internal gear 3 due to the difference in the number of teeth. As a result, the meshing portion P of the external gear 2 moves in the circumferential direction of the internal gear 3 in the opposite direction to the rotational direction of the cam member 41. In the present disclosure, the meshing portion P moves in the opposite direction to the rotational direction of the wave generator 4 relative to the internal gear 3 every time the cam member 41 rotates 180 degrees around the axis O. In other words, in the present disclosure, the input rotation from the input shaft is reversed and output as a reduced rotation from the external gear 2.

[0024] As described above, the external gear 2 has flexibility, allowing it to bend non-circularly to conform to the external shape of the cam member 41. In this embodiment, specifically, the Young's modulus E [GPa] of the external gear 2 is 2.0<E<120. Examples of materials having such a Young's modulus E include resin, light metal, and graphite. Specific examples of resin include POM (polyacetal), PEEK (polyether ether ketone), FRP (fiber reinforced plastic), nylon, and PE (polyurethane). Specific examples of light metals include titanium alloy, copper alloy, and aluminum alloy. Preferably, the Young's modulus E [GPa] of the external gear 2 is 2.0<E<30. Examples of materials having such a Young's modulus E include resin, light metal, and graphite. Specific examples of resin include POM (polyacetal), PEEK (polyether ether ketone), FRP (fiber reinforced plastic), nylon, and PE (polyurethane). Specific examples of light metals include titanium alloys, copper alloys, and aluminum alloys.

[0025] FIG. 3 shows a schematic halved cross section of the external gear 2. As shown in FIG. 3, the external gear 2 has a cup-like appearance with a front end opening A1 formed at one axial end. In the present disclosure, the external gear 2 includes a cylindrical wall 21 and a bottom wall 22 connected to the cylindrical wall 21. In the present disclosure, the front end opening A1 is formed at one axial end of the cylindrical wall 21. In the present disclosure, the bottom wall 22 is connected to the other axial end of the cylindrical wall 21. Furthermore, in the present disclosure, a boss (mounting portion) 23 is provided on the bottom wall 22 coaxially with the axis O. In the present disclosure, a mounting hole 24 for mounting an output shaft (not shown) coaxially with the axis O is formed in the boss 23. Furthermore, in the present disclosure, a key groove 24a is formed in the mounting hole 24 for preventing rotation of the output shaft. In the present disclosure, input rotation from the input shaft is reversed and output as reduced rotation from the output shaft connected to the external gear 2.

[0026] The cylindrical wall 21 is composed of a tooth portion 21a, on whose outer surface the external teeth 2a of the external gear 2 are provided, and a body portion 21b connected to the tooth portion 21a. In the present disclosure, the tooth width a is the axial length of the tooth portion 21a. Specifically, the tooth width a is the axial width of the external teeth 2a cut into. The range of the tooth width a is a range having the same value as the tooth width of the meshing internal teeth 3a. In the present disclosure, the body width b is the axial length of the body portion 21b. In the present disclosure, the body width b is the axial length between the front end 2e of the external gear 2 and the upper surface 22a of the bottom wall 22 of the external gear 2. Furthermore, in the present disclosure, the axial length (total width) L of the cylindrical wall 21 is L = a + b.

[0027] In this embodiment, the tooth width a (a > 0), which is the axial length of the tooth portion 21a, and the body width b (b ≧ 0), which is the axial length of the body portion 21b, satisfy the relationship b / (a + b) < 0.5.

[0028] When flattening the external gear 2 by shortening the axial length (total width L) of the cylindrical wall 21 of the external gear 2 in order to make the strain wave gear device smaller and lighter, there is a problem in the configuration of conventional strain wave gear devices in that the allowable torque of the strain wave gear device is reduced.

[0029] In contrast, the wave gearing device 1A according to this embodiment focuses on the meshing between the external teeth 2a of the external gear 2 and the internal teeth 3a of the internal gear 3, and recognizes that this meshing is caused by coning, which will be described later, and aims to improve the allowable torque of the wave gearing device 1A.

[0030] FIG. 4 shows a schematic cross section of a portion of the external gear 2 to explain the coning.

[0031] The external gear 2 is deflected non-circularly by the cam member 41 of the wave generator 4, and as shown in FIG. 4 , the amount of deflection increases along the tooth trace direction (axial direction) of the external teeth 2a from the bottom wall 22 side toward the front end opening A1, approximately proportional to the axial distance from the bottom wall 22. In FIG. 4 , the amount of deflection is shown as a deflection angle θ with the connecting portion between the cylindrical wall 21 and the bottom wall 22 as the base point. Furthermore, as the wave generator 4 rotates, each circumferential portion of the tooth portion 21a of the external gear 2 repeatedly deflects in the radial direction (direction perpendicular to the axial direction). This type of deflection of the external gear 2 caused by the operation of the wave generator 4 is called "coning."

[0032] As shown in FIG. 4 , the meshing width between the external teeth 2 a of the external gear 2 and the internal teeth 3 a of the internal gear 3 is reduced by coning. In particular, when the rigidity of the external gear 2 is high, it becomes difficult for the deflection of the cylindrical wall 21 to follow the external shape of the cam member 41 of the wave generator 4. As a result, as shown in FIG. 4 , the cylindrical wall 21 deflects by bending at an angle θ with the connecting portion between the cylindrical wall 21 and the bottom wall 22 as the base point. In this case, the meshing width between the external teeth 2 a of the external gear 2 and the internal teeth 3 a of the internal gear 3 also decreases. In addition, when the axial length (total width L) of the cylindrical wall 21 is shortened to flatten the external gear 2, the rigidity of the cylindrical wall 21 increases. Furthermore, in this case, since the total width L of the cylindrical wall 21 is shortened, the meshing width between the external teeth 2 a of the external gear 2 and the internal teeth 3 a of the internal gear 3 tends to decrease. Therefore, if the external gear 2 is flattened, the allowable torque of the strain wave gear device will decrease.

[0033] In contrast, the strain wave gearing 1A according to this embodiment specifies the Young's modulus E [GPa] of the external gear 2 in the range 2.0 < E < 120, thereby making the external gear 2 more flexible. In this case, for example, as shown by arrow D in FIG. 4 , the cylindrical wall 21 of the external gear 2 itself is more flexible. As a result, as shown in FIG. 2 , the strain wave gearing 1A makes it possible to shape the external gear 2 so as to increase the meshing ratio in the tooth width direction between the external teeth 2 a of the external gear 2 and the internal teeth 3 a of the internal gear 3. Furthermore, with an external gear 2 having a Young's modulus E within the above range, the external gear 2 is less susceptible to the effects of coning due to deformation, as shown by arrow D in FIG. 4 . Therefore, the strain wave gearing 1A can increase the allowable torque of the strain wave gearing 1A by the amount of increase in the meshing width between the external teeth 2 a of the external gear 2 and the internal teeth 3 a of the internal gear 3 while suppressing the effects of coning. In addition, according to the wave gear device 1A, the cylindrical wall 21 of the external gear 2 itself becomes more flexible, so the allowable torque of the wave gear device 1A can be improved while the axial length (total width L) of the cylindrical wall 21 can be shortened, thereby flattening the external gear 2.

[0034] Additionally, the wave gearing 1A is configured so that the tooth width a (a > 0) and the body width b (b ≥ 0) satisfy the relationship b / (a + b) < 0.5. In this case, the tooth portion 21a where the external teeth 2a are arranged accounts for more than half of the overall width L of the cylindrical wall 21. In other words, if the tooth width a (a > 0) and the body width b (b ≥ 0) satisfy the relationship b / (a + b) < 0.5, the area occupying the meshing portion between the external teeth 2a of the external gear 2 and the internal teeth 3a of the internal gear 3 can be ensured to be larger than the body portion 21b of the cylindrical wall 21 of the external gear 2. Therefore, in this case, the allowable torque of the wave gearing 1A is selected within a range that enables a larger allowable torque to be obtained.

[0035] Furthermore, the wave gearing 1A is configured so that the Young's modulus E of the external gear 2 exceeds 2.0 GPa. For example, if the Young's modulus E is 2.0 GPa or less, the external gear 2 is more likely to twist when torque is applied, and the rigidity required for a reducer may not be maintained. In contrast, if the Young's modulus E exceeds 2.0 GPa, for example, the allowable torque obtainable by the external gear 2 tends to make the external gear 2 less likely to twist when power is input to the external gear 2. In other words, if the Young's modulus E of the external gear 2 is set to exceed 2.0 GPa, the rigidity required for a wave gearing reducer can be maintained. Additionally, the wave gearing 1A is configured so that the Young's modulus E of the external gear 2 is less than 120 GPa. If the Young's modulus E is 120 GPa or more, the external gear 2 is less likely to bend, and it may be difficult to make b / (a+b) less than 0.5. On the other hand, if Young's E is less than 120 GPa, deflection is likely to occur in the external gear 2. This makes it easy for the face width a (a > 0) and the body width b (b ≥ 0) to satisfy the relationship b / (a + b) < 0.5.

[0036] Therefore, the strain wave gear device 1A according to this embodiment can provide a strain wave gear device in which the axial length is kept short and the allowable torque is increased.

[0037] Incidentally, in wave gearing, the tooth tip circle diameter Df of the external gear 2 is often designed to be equal to or slightly interfere with the tooth tip circle diameter Dr of the internal gear 3. The reason for this is that, for example, if the design is such that Df > Dr, as shown in Figure 5, when the external gear 2 is inserted into the internal gear 3, the tooth tips 2p of the external teeth 2a on the external gear 2 and the tooth tips 3p of the internal teeth 3a on the internal gear 3 will interfere with each other, making it difficult to assemble the external gear 2 to the internal gear 3.

[0038] On the other hand, in the case of a small wave gearing device, the thickness of the flexible external gear 2 becomes thinner as the wave gearing device becomes smaller. In this case, the stress on the external gear 2 also becomes smaller as the thickness of the external gear 2 becomes thinner. For this reason, the external gear 2 can be bent into a non-circular meshing shape without being attached to the wave generator 4 in advance. Therefore, when the thickness of the external gear 2 is made thinner, it may be possible to assemble it by bending the external gear 2.

[0039] Therefore, as an example of improving the meshing ratio between the external gear 2 and the internal gear 3, it is possible to increase the tooth depth of the external teeth 2 a of the external gear 2 to prevent ratcheting, while reducing the overall thickness of the external gear 2. If the tooth depth of the external teeth 2 a is increased, this is also effective in preventing ratcheting that may occur between the external gear 2 and the internal gear 3.

[0040] However, if the tooth depth of the external teeth 2a is set large while the external gear 2 is thinned, there is a possibility that the external gear 2 may break due to the load torque received by the external gear 2. Furthermore, further thinning the thin external gear 2 increases the difficulty of processing. For this reason, it is not realistic to set the tooth depth of the external teeth 2a large while thinning the external gear 2 as a means of improving the meshing ratio between the external gear 2 and the internal gear 3.

[0041] In contrast, the strain wave gearing 1A uses a material with a low Young's modulus E for the external gear 2, which makes it easier for the external gear 2 to flex when it is assembled to the internal gear 3. As a result, with strain wave gearing 1A, the external gear 2 can be made thin, and the strain wave gearing can be easily manufactured without further thinning.

[0042] Furthermore, the Young's modulus E [GPa] of the external gear 2 preferably satisfies 2.0<E<30. In this case, if the Young's modulus E of the external gear 2 is E<30, for example, by using a resin gear for the external gear 2, the axial length can be further reduced and the allowable torque can be further increased. As a specific example, by using PEEK (Young's modulus E=4) as the material for the external gear 2, the relationship between the face width a (a>0) and the body width b (b≧0) can be made to satisfy the relationship b / (a+b)<0.4. In this case, the meshing width between the external teeth 2a of the external gear 2 and the internal teeth 3a of the internal gear 3 can be further increased. Therefore, in this case, the allowable torque of the strain wave gearing 1A can be further improved.

[0043] Also, referring to FIG. 5, in this embodiment, it is preferable that the tip circle diameter Df of the external gear 2, the tip circle diameter Dr of the internal gear 3, and the total tooth depth h of the external gear 2 satisfy the relationship 0.1h<(Df-Dr)<h.

[0044] If 0.1h<(Df-Dr), the allowable torque can be increased without reducing the number of meshing teeth. Furthermore, if (Df-Dr)<h, the external gear 2 can be assembled to the internal gear 3 without causing significant interference between the external teeth 2a of the external gear 2 and the internal teeth 3 of the internal gear 3. Therefore, if the tip circle diameter Df of the external gear 2, the tip circle diameter Dr of the internal gear 3, and the total tooth depth h of the external gear 2 are set to satisfy the relationship 0.1h<(Df-Dr)<h, the wave gear device 1A can be easily manufactured without reducing the allowable torque.

[0045] Furthermore, in this embodiment, it is preferable that the tooth tip circle diameter Df of the external gear 2, the tooth tip circle diameter Dr of the internal gear 3, and the total tooth depth h of the external gear 2 satisfy the relationship 0.3h < (Df - Dr) < h. In this case, the allowable torque can be further increased by increasing the number of meshing teeth.

[0046] Furthermore, one method for improving the allowable torque of a wave gearing device that has been flattened by making the external gear 2 flat is to adjust the deflection amount d, which is a value indicating the amount of deflection of the external gear 2, as shown in Fig. 6, for example. Here, the deflection amount d can be defined as d = (Zr - Zf) x m based on the relationship between the module m, the number of teeth Zf of the external gear 2, and the number of teeth Zr of the internal gear 3. As a specific example, in a wave gearing device with a module m = 1 and a reduction ratio of 50, when the difference in the number of teeth is 2, the deflection amount d is d = (102 - 100) x 1, so d = 2.

[0047] On the other hand, if the tooth depth of the external gear 2 is made excessively short to avoid interference when assembling the external gear 2 and the internal gear 3, the number of meshing teeth or the meshing area will be reduced. For this reason, if the tooth depths of the external gear 2 and the internal gear 3 are made excessively short, the allowable torque of the strain wave gear device will decrease, or there will be concerns about ratcheting. For this reason, there is a certain degree of restriction on the tooth depth in a strain wave gear device; for example, as an element that can adjust the tip circle diameter Df of the external gear 2, a tooth depth that does not exceed d / 2, that is, half the value of the deflection amount d, is required.

[0048] In response to this, the deflection amount d is sometimes intentionally adjusted to improve the lifespan or gear strength of strain wave gearing. A known tooth profile obtained by adjusting the deflection amount d is known as the "deviation tooth profile," as described in Japanese Patent Publication No. 45-41171. Deviation gears are considered to be compatible with materials that are easily deformed. The deviation tooth profile can be specified, for example, by the deflection amount d expressed by the following equation (1):

[0049] d = (Zr - Zf) x m x K (1) (K: deviation coefficient)

[0050] For example, in the case of a wave gearing device with a large reduction ratio, the module m between the external gear 2 and the internal gear 3 becomes small, which inevitably results in a problem of a smaller tooth depth. Therefore, to compensate for the smaller tooth depth itself, a positive deviation tooth profile is sometimes used, which increases the effective height of the tooth depth by increasing the deflection amount d. Here, the positive deviation tooth profile can be expressed as (d = (Zr - Zf) x m x K: (K > 1)). In other words, the positive deviation tooth profile satisfies K > 1 in equation (1). Figure 7 shows a schematic and partial meshing model of a positive deviation tooth profile.

[0051] Conversely, in the case of a wave gear device with a small reduction ratio, the tooth depth can be increased. However, this increases the deflection amount d. This increases the load stress on the bearing 42 of the wave generator 4, resulting in a problem of reduced reducer life. Therefore, a negative deviation tooth profile may be used, which increases the number of meshing teeth by reducing the deflection amount d. Here, the negative deviation tooth profile can be expressed as (d = (Zr - Zf) x m x K: (K < 1)). In other words, the negative deviation tooth profile satisfies K < 1 in Equation (1). Figure 8 shows a schematic and partial meshing model of a negative deviation tooth profile. When using a negative deviation tooth profile, increasing the number of meshing teeth can improve the allowable torque and alleviate the stress on the wave generator 4.

[0052] However, the technology described in the above publication does not prescribe the relationship between the tooth shape of the external gear 2 and the optimal material properties for the external gear 2. In contrast, the strain wave gear device 1A according to this embodiment can be applied to either a positive deviation tooth profile or a negative deviation tooth profile.

[0053] For example, in the case of a positive deviation tooth profile, the deflection amount d is larger than usual, so a material with a lower Young's modulus E is considered better. However, if Young's modulus E is simply low, the allowable torque of the wave gear device may be reduced. Therefore, in the wave gear device 1A according to this embodiment, if the external teeth 2a and internal teeth 3a are shaped as positive deviation tooth profiles, meshing in the face width direction is improved. Therefore, in the wave gear device 1A, the deflection amount d can be set to a value that satisfies K > 1 in equation (1). Furthermore, if the coning angle of the external gear 2 is θ, the wave gear device 1A can ensure sufficient allowable torque if it is a wave gear device that satisfies (b × sin(θ) + Df) > Dr.

[0054] In contrast, in the case of a negative deviation tooth profile, the deflection amount d is smaller than usual, so even a material with a high Young's modulus E can be used. However, as mentioned above, if Df > Dr, interference occurs between the external teeth 2a of the external gear 2 and the internal teeth 3a of the internal gear 3, making it difficult to assemble the external gear 2 to the internal gear 3. However, in the case of the external gear 2 of the strain wave gearing 1A according to this embodiment, the external gear 2 is formed of a material with a smaller Young's modulus E and greater flexibility than a typical external gear. Therefore, when the external teeth 2a and internal teeth 3a have a negative deviation tooth profile, the value of the deviation coefficient K in equation (1) is K<1, making it possible to further reduce K and increase the number of meshing teeth. Therefore, even in the case of a negative deviation tooth profile, reducing the deviation coefficient K can ensure sufficient allowable torque.

[0055] Next, FIG. 9 is a bottom view schematically showing a modified example of the external gear 2. As shown in FIG.

[0056] The external gear 2 has a bottom wall 22 that is continuous with one end of the cylindrical wall 21. A plurality of slit holes 25 are intermittently arranged in an annular shape around the axis O in the bottom wall 22. The plurality of annularly arranged slit holes 25 are arranged on at least one circle centered on the axis O. The slit holes 25 are through-holes that penetrate the bottom wall 22.

[0057] For the external gear 2, a shape in the bottom wall 22 that is easily deformed in the radial direction but not easily twisted is advantageous for torque transmission. As in the present embodiment, if a plurality of slit holes 25 are formed annularly around the axis O in the bottom wall 22 of the external gear 2, and the annularly arranged slit holes 25 are arranged on at least one circle centered on the axis O, the bottom wall 22 of the external gear 2 has a structure that is easily deformed in the radial direction but is resistant to twisting in the circumferential direction. That is, according to this embodiment, the rigidity of the bottom wall 22 can be made anisotropic. As a result, the external gear 2 according to this embodiment has a shape that is easily deformed in the radial direction but not easily twisted, thereby enabling efficient torque transmission. Therefore, according to this embodiment, the axial length can be made shorter while still providing efficient torque transmission. Furthermore, in this case, the allowable torque can be increased. Therefore, according to this embodiment, the axial length can be made shorter while increasing the allowable torque.

[0058] Furthermore, as shown in Figure 9, in this embodiment, the length of each of the multiple slit holes 25 in the circumferential direction is longer than its length in the radial direction. In this embodiment, the slit holes 25 are elongated holes extending in the circumferential direction. In this case, the external gear 2 is more susceptible to deformation in the radial direction, but is also less susceptible to twisting, allowing for efficient torque transmission. Therefore, according to this embodiment, efficient torque transmission is possible. Furthermore, in this case, the allowable torque can be further increased.

[0059] Furthermore, in this embodiment, the multiple slit holes 25 are arranged in multiple concentric rows around the axis O so that the radial distances from the axis O are different. Referring to FIG. 9 , in this embodiment, the multiple slit holes 25 are arranged in three concentric rows around the axis O so that the radial distances from the axis O are different. In this embodiment, the twelve annular slit holes 25 are arranged on each of three concentric circles centered on the axis O. When the multiple slit holes 25 are arranged in multiple concentric rows around the axis O so that the radial distances from the axis O are different, as in this embodiment, the external gear 2 is more susceptible to radial deformation, but is also less susceptible to twisting, resulting in more efficient torque transmission. Therefore, this embodiment enables more efficient torque transmission. Furthermore, in this case, the allowable torque can be further increased.

[0060] In addition, in this embodiment, the plurality of slit holes 25 arranged in a plurality of rows are arranged concentrically around the axis O such that the circumferential end positions of the slit holes 25 in each row are different between adjacent rows. For example, as shown in Fig. 9 , in this embodiment, three radially arranged slit holes 25 are arranged in three radial rows such that the radially inner and outer slit holes 25 are aligned in the radial direction, while the radially central slit hole 25 is shifted in the circumferential direction relative to the radially inner and outer slit holes 25. In other words, in this embodiment, the plurality of slit holes 25 arranged discontinuously and annularly around the axis O are aligned in the radial direction on the radially inner and radially outer sides, while in the radial center, they are arranged so that they are shifted in the circumferential direction to one side relative to the radially inner and radially outer sides while leaving portions that overlap with each other in the radial direction.

[0061] In a bottom view as shown in FIG. 9 , if the circumferential arrangement angles of the multiple rows of slit holes 25 arranged on concentric circles around the axis O are the same, and the multiple rows of slit holes 25 are arranged so that they overlap in the radial direction, the torsional rigidity of the bottom wall 22 will decrease. For this reason, in this embodiment, it is preferable that the multiple rows of slit holes 25 arranged in the radial direction are arranged at positions offset in the circumferential direction. Therefore, as in this embodiment, if the multiple rows of slit holes 25 are arranged concentrically around the axis O so that the circumferential end positions of the slit holes 25 in each row are different between adjacent rows, more efficient torque transmission can be achieved. Therefore, according to this embodiment, more efficient torque transmission can be achieved. Furthermore, in this case, the allowable torque can be further increased. In addition, in this case, the axial length can be further shortened, thereby further flattening the strain wave gear device 1A. Therefore, in this case, the axial length can be further shortened while further increasing the allowable torque.

[0062] Next, FIG. 10 is a cross-sectional view showing an external gear 2 applicable to the strain wave gearing 1A, taken along the X-X cross section of FIG. 1, and shows the state before and after tooth profile modification of the external teeth 2a.

[0063] According to this embodiment, the body width b of the external gear 2 can be set to 0 (zero). That is, according to this embodiment, the tooth width a of the external gear 2 can be increased up to the bottom wall 22.

[0064] However, in general, when the tooth width a is increased up to the bottom wall 22, the deflection amount d is substantially reduced on the side of the bottom wall 22. Therefore, when the tooth width a is increased up to the bottom wall 22, there is a possibility that the tooth width direction end portions of the tooth flanks of the external teeth 2 a and the tooth width direction end portions of the tooth flanks of the internal teeth 3 a may end up interfering excessively.

[0065] In contrast to this, with the wave gearing 1A according to this embodiment, if excessive interference occurs between the external gear 2 and the internal gear 3 due to the face width a of the external gear 2 being increased up to the bottom wall 22, it is possible to form a taper (inclined surface) or an R (curved surface) by modifying the end portion in the face width direction of the tooth flank of the external teeth 2a, as shown in Figure 10. Methods for such tooth profile modification include, for example, crowning and end relief.

[0066] 10 , when tooth profile modification is performed on the end portions of the tooth flanks of the external teeth 2 a in the tooth width direction, the tooth thickness of the end portions of the tooth flanks of the external teeth 2 a in the tooth width direction becomes smaller. This suppresses excessive interference between the external gear 2 and the internal gear 3 that can occur when the tooth width a of the external gear 2 is increased up to the bottom wall 22. In particular, in this case, the tip circle becomes smaller in a small module wave gear device, which is effective in avoiding excessive interference between the external gear 2 and the internal gear 3.

[0067] Next, FIG. 11 is a cross-sectional view showing an external gear 2 applicable to the strain wave gearing 1A, taken along the line X-X in FIG. 1, and the cross-sectional view shows the state before and after profile shifting of the external teeth 2a.

[0068] If excessive interference occurs between the external gear 2 and the internal gear 3 due to the increased face width a of the external gear 2 up to the bottom wall 22, it is possible to impart profile shifts to the external teeth 2a of the external gear 2 in proportion to the distance toward the bottom wall 22, similar to tooth profile modification. This suppresses excessive interference between the external gear 2 and the internal gear 3, which may occur due to the increased face width a of the external gear 2 up to the bottom wall 22, similar to tooth profile modification. Also in this case, the tip circle of the external teeth 2a becomes smaller, which is effective in avoiding excessive interference between the external gear 2 and the internal gear 3. Note that when the face width a is increased, a gap may occur in the meshing between the external gear 2 and the internal gear 3 in the direction of the face width a, depending on the deflection amount d. In such a case, the meshing can be improved by imparting profile shifts in the opposite direction to the external gear 2, thereby increasing the allowable torque.

[0069] Furthermore, in the wave gear device 1A according to this embodiment, in order to improve the strength and ease of flexural deformation of the external gear 2, it is preferable that the average thickness of the body width b of the body portion 21b be 30 to 90% of the maximum thickness of the tooth width a of the tooth portion 21a. In this case, the strength and ease of flexure of the external gear 2 can be improved.

[0070] Next, FIG. 12 is a cross-sectional view that schematically shows another external gear 2 that can be applied to the strain wave gear device 1A, which corresponds to the cross-section of FIG. 2.

[0071] In the strain wave gearing 1A, the external gear 2 is a cup-shaped external gear, but the external gear 2 can also be a top hat-shaped external gear as shown in Fig. 12. In the present disclosure, the external gear 2 includes a cylindrical wall 21 and a flange 26 connected to the cylindrical wall 21. In the present disclosure, the flange 26 is connected to the lower end of the cylindrical wall 21 and protrudes radially outward in an annular shape in the circumferential direction around the axis O.

[0072] In the present disclosure, the cylindrical wall 21 is composed of a tooth portion 21a, on whose outer surface the external teeth 2a of the external gear 2 are provided, and a body portion 21b connected to the tooth portion 21a. In the present disclosure, the tooth width a is also the axial length of the tooth portion 21a. In the present disclosure, the body width b is also the axial length of the body portion 21b. In the present disclosure, the axial length (total width) L of the cylindrical wall 21 is also L = a + b. However, in the present disclosure, the body width b is the axial length between the front end 2e of the external gear 2 and the upper surface 26a of the flange 26 of the external gear 2.

[0073] Furthermore, a wave gear device 1B according to a second embodiment of the present invention is shown schematically in Fig. 13. In Fig. 13, parts, members, and other elements that are substantially the same as those in the wave gear device 1A are designated by the same reference numerals, and description thereof will be omitted.

[0074] The wave gearing according to the present invention can be a multi-lobe wave gearing with three or more meshing points. The wave gearing 1B in Fig. 13 is a three-lobe wave gearing in which there are three meshing points P between the external teeth 2a of the external gear 2 and the internal teeth 3a of the internal gear 3. In this embodiment, the cam member 41 has a triangular three-lobe shape. Also, in this embodiment, the bearing 42 includes a cage 42d that holds the rolling elements 42c. The matters described in relation to the wave gearing 1A can also be applied to a multi-lobe wave gearing with three or more lobes, such as the wave gearing 1B.

[0075] Furthermore, in the wave gear device according to the present invention, when the outer radius of the body portion 21 b of the external gear 2 is rD (however, when b = 0, the root radius of the external gear 2 is rD), and the thickness of the body portion 21 b is t, the relationship between Young's modulus E and b / (a + b) can satisfy the following formula:

[0076] 0.4<Y<30...(2)

[0077]

[0078] For example, if the Young's modulus E of a commonly used external gear 2 exceeds 200 and b / (a+b)<0.5 is satisfied, then equation (3) becomes less than 0.4. In this case, the thickness t of the trunk portion 21b must be made extremely small. Therefore, in this case, it becomes difficult to establish a strain wave gearing device.

[0079] On the other hand, there is a method of increasing the outer circumferential radius rD of the trunk portion 21b. However, this method increases the outer diameter of the external gear 2, making it difficult to achieve the object of the present invention, which is to reduce the size of the external gear 2, i.e., the strain wave gear device.

[0080] In contrast to this, the relationship of the above formula (2) can be satisfied if, for example, PEEK (Young's modulus E=4) is used as the material for the external gear 2. In this case, the allowable torque can be improved while keeping the strain wave gear device 1A (1B) compact.

[0081] Furthermore, it is preferable that the formula (3) satisfies the relationship of the following formula (4).

[0082] 0.5<Y<20...(4)

[0083] When formula (3) satisfies the relationship of formula (4), it is possible to further increase the meshing width between the external teeth 2 a of the external gear 2 and the internal teeth 3 a of the internal gear 3. Therefore, in this case, it is possible to further improve the allowable torque of the strain wave gear device 1A (1B).

[0084] The above merely illustrates an exemplary embodiment of the present invention, and various modifications are possible within the scope of the claims. Furthermore, in the above explanation, the power transmission path of the strain wave gearing device has the wave generator 4 as an input and the external gear 2 as an output, but this is not limited to this. For example, the power transmission path of the strain wave gearing device may have the external gear 2 as an input and the wave generator 4 as an output.

[0085] 1A: Strain wave gearing (first embodiment), 1B: Strain wave gearing (second embodiment), 2: External gear, 2a: External teeth of external gear, 2e: Front end of external gear, 2p: Tooth tips of external teeth, 21: Cylindrical wall, 21a: Tooth portion of cylindrical wall, 21b: Body portion of cylindrical wall, 22: Bottom wall, 22a: Upper surface of bottom wall, 23: Boss (mounting portion), 24: Mounting hole, 24a: Keyway, 25: Slit hole, 26: Flange, 26a: Upper surface of flange, 3: Internal gear, 3a: Internal teeth of internal gear, 3p: Tooth tips of internal teeth, 4: Wave generator, 41: Cam member, 42: Bearing, 42a: Outer ring, 42b: Inner ring, 42c: Rolling elements, 42d: Cage 43: Mounting hole, 43a: Keyway, A1: Front end opening of external gear, a: Tooth width of external gear, b: Body width of external gear, Df: Tip diameter of external gear, Dr: Tip diameter of internal gear, L: Overall width of cylindrical wall, P: Meshing portion, Zf: Number of teeth of external gear, Zr: Number of teeth of internal gear

Claims

1. A harmonic gear device in which an annular external gear having flexibility meshes with an internal gear inside the internal gear while being deformed into a waveform, wherein the Young's modulus E [GPa] of the external gear satisfies 2.0 < E < 120, the external gear includes a cylindrical wall, and the cylindrical wall is composed of a tooth portion provided with external teeth on the outer surface of the external gear and a body portion continuous with the tooth portion, and a tooth width a (a > 0) which is the axial length of the tooth portion and a body width b (b ≧ 0) which is the axial length of the body portion satisfy the relationship b / (a + b) < 0.

5.

2. The harmonic gear device according to claim 1, wherein the Young's modulus E [GPa] of the external gear satisfies 2.0 < E < 30.

3. The harmonic gear device according to claim 1 or 2, wherein a tip circle diameter Df of the external gear, a tip circle diameter Dr of the internal gear, and a total tooth height h of the external gear satisfy the relationship 0.1h < (Df - Dr) < h.

4. The harmonic gear device according to claim 3, wherein a tip circle diameter Df of the external gear, a tip circle diameter Dr of the internal gear, and a total tooth height h of the external gear satisfy the relationship 0.3h < (Df - Dr) < h.

5. The harmonic gear device according to claim 1 or 2, wherein the external gear includes a bottom wall continuous with one end of the cylindrical wall, and a plurality of slit holes are intermittently arranged annularly around the axis on the bottom wall, and the plurality of annularly arranged slit holes are arranged on at least one circle centered on the axis.

6. The harmonic gear device according to claim 5, wherein each of the plurality of slit holes has a length along the circumferential direction longer than the length in the radial direction.

7. The harmonic gear device according to claim 6, wherein the plurality of slit holes are arranged in a plurality of concentric circles centered on the axis so that the radial distances from the axis are different.

8. The harmonic gear device according to claim 7, wherein the plurality of slit holes arranged in a plurality of concentric circles are arranged in a plurality of concentric circles centered on the axis so that the circumferential end positions of the slit holes in each row are different between adjacent rows.

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