Gear

Abstract

Provided is a gear that can suppress the occurrence of poor rotation even when the diameter is small and the number of teeth is small. A gear (1) has different amounts of profile shift set in the tooth trace direction, and the tooth shape at each position in the tooth trace direction is formed by a curve corresponding to the amount of profile shift.

Description

Technical Field

[0001] The present invention relates to a gear. Background Art

[0002] In a gear, when the manufacturing error is large or the parallelism of the rotation axis of the gear is insufficient, etc., there may be a problem of poor rotation due to tooth jamming caused by the disappearance of backlash, or noise caused by local contact.

[0003] In order to suppress the occurrence of such poor rotation or local contact, Patent Document 1 proposes a gear having a tooth shape in which the tooth tip is cut (implementing tooth tip crowning) as it goes toward the end in the tooth trace direction and the tooth shape in the tooth trace direction is maintained in the same shape.

[0004] Prior Art Documents

[0005] Patent Documents

[0006] [Patent Document 1] Japanese Unexamined Patent Application Publication No. 2018-135899 Summary of the Invention

[0007] Problems to be Solved by the Invention

[0008] However, in the gear described in Patent Document 1, when there is a position deviation or shaft skew of the rotation axis, etc., when the amount of modification is small, the diameter is large, and the number of teeth is large, it will rotate without problems, but when the amount of modification is large, the diameter is small, and the number of teeth is small, there may be a problem of poor rotation.

[0009] Therefore, an object of the present invention is to provide a gear that can suppress the occurrence of poor rotation even when the diameter is small and the number of teeth is small.

[0010] Solutions for Solving the Problems

[0011] The present invention aims to solve the above problems, and provides a gear in which the tooth shape at each position in the tooth trace direction is formed by a curve set corresponding to the amount of modification, and is configured such that the tooth shape continuously changes in the tooth trace direction.

[0012] Effects of the Invention

[0013] According to the present invention, it is possible to provide a gear that can suppress the occurrence of poor rotation even when the diameter is small and the number of teeth is small. Brief Description of the Drawings

[0014] Figure 1 It is a view showing a gear according to an embodiment of the present invention, (a) is a perspective view, and (b) is a sectional view showing the A-A section of (a).

[0015] Figure 2 is Figure 1 Cross-sectional views taken along line B-B, C-C, and D-D of (b) of , and enlarged views of the main parts in each cross-section.

[0016] Figure 3 is a diagram for explaining the amount of displacement.

[0017] Figure 4 (a) of is a diagram showing the cross-sectional shapes of the teeth at one end, the central part, and the other end of the tooth line direction in a standard gear, and (b) is a diagram for explaining the meshing state of the standard gear in the case of a large amount of displacement.

[0018] Figure 5 (a) of is a diagram showing the cross-sectional shapes of the teeth at one end, the central part, and the other end of the tooth line direction in the gear of Comparative Example 1 in which crowning of the tooth surface has been performed, and (b) is a diagram for explaining the meshing state of the gear of Comparative Example 1 in the case of a large amount of displacement.

[0019] Figure 6 (a) of is a diagram showing the cross-sectional shapes of the teeth at one end, the central part, and the other end of the tooth line direction in the gear of Comparative Example 2 in which crowning of the tooth tip has been performed, and (b) is a diagram for explaining the meshing state of the gear of Comparative Example 2 in the case of a large diameter and a large number of teeth.

[0020] Figure 7 is a diagram for explaining the meshing state of the gear of Comparative Example 2 in the case of a small diameter and a small number of teeth.

[0021] Figure 8 is a cross-sectional view showing an example of the tooth shape of the gear of Comparative Example 3.

[0022] Figure 9 (a) of is a diagram showing the cross-sectional shapes of the teeth at one end, the central part, and the other end of the tooth line direction in the tooth shape of the gear of Comparative Example 4 in which crowning of the tooth surface and crowning of the tooth tip have been performed, and (b) is a diagram for explaining the meshing state of the gear of Comparative Example 4.

[0023] Figure 10 (a) and (b) of are diagrams showing the cross-sectional shapes of the teeth at one end, the central part, and the other end of the tooth line direction in the gear of a modification example of the present invention.

[0024] Figure 11 is a diagram for explaining the change in the tooth shape when the amount of displacement is changed.

[0025] Figure 12Fig. (a) is a cross-sectional view of the teeth at the central part and the end part in the tooth line direction when the displacement amount at the end part in the tooth line direction is set to -0.5, and Fig. (b) is a cross-sectional view of the teeth at the central part and the end part in the tooth line direction when the displacement amount in the tooth line direction is set to -1.0.

[0026] Figure 13 Fig. (a) is Figure 12 Fig. (a) is a cross-sectional view of the teeth at the central part and the end part in the tooth line direction when the tip part of the tooth of the reference rack tool is composed only of a curve with a specified radius of curvature in Fig. (a), and Fig. (b) is Figure 12 Fig. (a) is a cross-sectional view of the teeth at the central part and the end part in the tooth line direction when the tip part of the tooth of the reference rack tool is composed only of a straight line in Fig. (a).

[0027] Figure 14 Fig. (a) is a diagram for explaining the influence of deviation in a gear, and Fig. (b) is a coordinate diagram showing an example of the relationship between the pitch circle diameter and the movement amount.

[0028] Figure 15 is a flowchart showing the procedure of a method for manufacturing a resin gear according to an embodiment of the present invention.

[0029] Figure 16 is a perspective view of an electrode formed by an electrode forming process.

[0030] Figure 17 Figs. (a) and (b) are diagrams for explaining a mold forming process.

[0031] Figure 18 Figs. (a) to (d) are diagrams for explaining the rotation of the electrode during the mold forming process.

[0032] Explanation of Reference Numerals

[0033] 1... Gear

[0034] 2... Shaft portion

[0035] 3... Tooth

[0036] 31... Tooth tip

[0037] 32... Tooth bottom

[0038] 33... Thickness reduction portion Detailed Description of the Invention

[0039] [Embodiment]

[0040] Hereinafter, embodiments of the present invention will be described with reference to the drawings.

[0041] (Outline of the gear)

[0042] Figure 1This is a diagram showing the gear of the present embodiment. (a) is a top view, and (b) is a perspective view. Figure 2 The (a) of Figure 1 is a perspective view showing the tooth shape of the gear of Figure 2 The (b) of

[0043] As Figure 1 and Figure 2 shown, the gear 1 integrally includes: a substantially cylindrical shaft portion 2 having a shaft hole 2a into which a rotation shaft (not shown) is inserted; and a plurality of teeth 3 formed on the outer peripheral surface of the shaft portion 2. In addition, the shape of the shaft portion 2 and the like are not particularly limited and can be appropriately changed. Hereinafter, the direction parallel to the rotation shaft is referred to as the axial direction, the direction perpendicular to the rotation shaft is referred to as the radial direction. In addition, the rotation direction around the rotation shaft is referred to as the circumferential direction. Here, the case where the gear 1 is a spur gear in which the teeth 3 are formed parallel to the axial direction is described, but it may also be a helical gear in which the teeth 3 are formed inclined with respect to the axial direction.

[0044] In the present embodiment, the gear 1 includes resin. However, it is not limited thereto, and the material of the gear 1 is not limited to resin.

[0045] In the gear 1 of the present embodiment, the tooth shape at each position in the tooth line direction is constituted by a curve set corresponding to the amount of modification, and is configured such that the tooth shape continuously changes in the tooth line direction.

[0046] By configuring in this way, when a position deviation or shaft skew occurs in the rotation shaft, even in the case of a small diameter and a small number of teeth, the occurrence of rotation failure can be suppressed. The reasons are described below.

[0047] (Regarding the amount of modification)

[0048] First, the amount of modification is described. The amount of modification in this specification refers to the change amount of the distance between the rotation shaft of the mating gear and the rotation shaft of its own gear due to the position deviation or shaft skew of the rotation shaft, or misalignment, etc. The term "amount of modification" is generally used as the change amount of the distance between the rotation shaft of the gear and the rotation shaft of the hob when the gear is generated by the hob, or the change amount of the radial position of the teeth of the gear. However, the generation of the gear 1 in the present embodiment is not limited to the hob, and such a definition is not used in this specification.

[0049] More specifically, as Figure 3As shown, when the rotational axis of the mating gear 1b inclines toward the self gear 1a side (shaft skew occurs), the tip position of the mating gear 1b protrudes toward the self gear 1a side. The amount of protrusion, that is, the distance from the tip position in the state where the rotational axis of the mating gear 1b is not inclined to the tip position in the state where the rotational axis of the mating gear 1b is inclined (or the state where the position of the rotational axis deviates due to the deviation of the position of the rotational axis or the like) is equal to the amount of modification. Thus, the amount of modification can be renamed as the protrusion amount of the mating gear 1b relative to the self gear 1a (the protrusion amount from the normal position).

[0050] (Investigation of the Optimal Tooth Shape)

[0051] Here, an investigation is made on the optimal tooth shape that can suppress rotational malfunction or local contact. Hereinafter, performing a crowning process on the tooth surface in such a manner that the tooth thickness gradually becomes thicker from both end portions in the tooth line direction to the central portion is referred to as tooth surface crowning. In addition, performing a crowning process on the tooth tip in such a manner that the tooth tip gradually protrudes radially outward from both end portions in the tooth line direction to the central portion is referred to as tooth tip crowning.

[0052] First, an investigation is made on a standard gear 100 having a tooth shape in which neither tooth surface crowning nor tooth tip crowning is performed and the tooth shape in the tooth line direction is maintained in the same shape as shown in (a) of Figure 4 .

[0053] As shown in (b) of Figure 4 , in the standard gear 100 in which neither tooth surface crowning nor tooth tip crowning is performed, when the amount of modification becomes large, the meshing becomes deep at the end portion in the tooth line direction of the tooth 101, and there may occur rotational malfunctions such as so-called bottoming where the tooth tip on the driving gear side or the driven gear side interferes with the tooth bottom on the driven gear side or the driving gear side that meshes therewith, and disappearance of backlash. Particularly in the resin-made standard gear 100, when a force acts on the tooth 101, the tooth 101 elastically deforms and the meshing position changes, increasing the possibility of occurrence of rotational malfunctions.

[0054] Next, an investigation is made on a gear 110 of Comparative Example 1 in which only tooth surface crowning is performed on the standard gear 100 as shown in (a) of Figure 5 . In the gear 110 of Comparative Example 1, by performing tooth surface crowning on the tooth 111, the tooth thickness at the end portion in the tooth line direction is reduced. Therefore, as shown in (b) of Figure 5 , even when the amount of modification is large, backlash can be ensured and the occurrence of rotational malfunctions and local contact can be suppressed. However, the gear 110 in which only tooth surface crowning is performed needs to be manufactured by grinding or machining, and thus the productivity is poor and it is difficult to manufacture inexpensively and in large quantities.

[0055] Next, an investigation is made on a gear as shown in (a) of Figure 6A discussion is made of the gear 120 of Comparative Example 2 in which only a tip crowning is implemented in the standard gear 100 as shown in (a). Figure 6 (b) of shows the meshing state in the case where the module is 1.5, the number of teeth is 40, the pressure angle is 20°, and the pitch diameter is 60 mm. As Figure 6 shown in (b) of, in the gear 120 of Comparative Example 2, by implementing a tip crowning on the tooth 121, similar to the case where a flank crowning is implemented, when the amount of modification is small, backlash can be ensured and the occurrence of rotational irregularities and local contact can be suppressed.

[0056] Thus, in the gear 120 of Comparative Example 2, when the amount of modification is small, the diameter is large, and the number of teeth is large, rotation will proceed without problems. However, as Figure 7 shown, in the case where the amount of modification is large, the diameter is small, and the number of teeth is small, when the crowning amount is set to be the same as that in the case of Figure 6 (b), rotational irregularities may be caused due to the disappearance of backlash, or noise may be caused due to local contact. In addition, in Figure 7 , the meshing state in the case where the module is 0.5, the number of teeth is 15, the pressure angle is 20°, and the pitch diameter is 7.5 mm is shown.

[0057] In order to solve the problems in the gear 120 of Comparative Example 2, it can be considered to form a tooth shape such as the gear 130 of Comparative Example 3 shown in Figure 8 by setting the entire region in the tooth line direction to a constant negative modification. However, in this case, although the occurrence of rotational irregularities and local contact can be suppressed, there may be looseness during meshing at the central part in the tooth line direction, and in addition, since the root part becomes thinner than necessary, the tooth root strength may also be insufficient.

[0058] As another configuration for solving the problems in the gear 120 of Comparative Example 2, it can be considered to implement both a tip crowning and a flank crowning on the tooth 141 as in the gear 140 of Comparative Example 4 shown in (a) of Figure 9 . However, in this case, as Figure 9 (b) shows, the crowning amount becomes large and looseness may occur. More specifically, in the gear 140, in order to avoid interference at the tooth bottom, the crowning amount in the flank crowning needs to be set to match the part corresponding to the undercut in the ideal tooth shape shown by the dashed line in Figure 9 (b). This requires cutting the part where the tooth surface abuts according to the ideal tooth shape and performing a matching cut on the entire tooth surface region. Therefore, compared with the gear 120 of Comparative Example 2 where a tip crowning is implemented and the ideal tooth shape, a larger crowning amount needs to be set. As a result, the crowning amount becomes too large and looseness may occur. Moreover, since the backlash becomes too large at the end in the tooth line direction, it may cause looseness and noise.

[0059] Therefore, in the gear 1 of the present embodiment, as Figure 1 and Figure 2 shown, the tooth shape at each position in the tooth trace direction is formed by a curve corresponding to the amount of modification. Thus, due to adopting the optimal tooth shape, compared with the gear 140 of Comparative Example 4, the crowning amount can be suppressed, and looseness and noise can be suppressed. Moreover, by implementing tip crowning, the tooth shape can be optimized for the protruding amount of the tooth tip, the reduction amount of the thickness at the tooth root can be suppressed, and the strength of the entire gear 1 can be increased.

[0060] In the present embodiment, the case of implementing tip crowning has been described, but it is also possible to omit tip crowning as in the gear 1a shown in Figure 10 (a) as long as the tooth shape at each position in the tooth trace direction is formed by a curve corresponding to the amount of modification. In addition, in the present embodiment, the curve of the tooth tip 31 and the curve of the tooth root 32 are formed by curves with the same curvature, but it is also possible to have different curvatures for the curve of the tooth tip 31 and the curve of the tooth root 32 as in the gear 1b shown in Figure 10 (b). However, in this case, it becomes difficult to perform generation by a hob (hobbing machine). Therefore, it is more desirable that, as in the present embodiment, the curve of the tooth tip 31 and the curve of the tooth root 32 are formed by curves with the same curvature so as to be able to perform generation by a hob and improve productivity.

[0061] (Details of tooth shape)

[0062] Hereinafter, the details of the tooth shape of the gear 1 of the present embodiment will be described. In the gear 1 of the present embodiment, it is set that the amount of modification continuously changes in the tooth trace direction, and the tooth shape in the cross-section (radial cross-section) perpendicular to the rotation axis at each position in the tooth trace direction is formed by a curve corresponding to the amount of modification at that position. The amount of modification mentioned here is, as described above, the amount of change in the distance between the rotation axis of the mating gear and the rotation axis of its own gear due to shaft deviation or shaft skew of the rotation axis, etc. Therefore, when the amount of modification changes, the meshing state of the gear 1 changes, so it is necessary to set the tooth shape to a suitable shape. That is to say, the "curve corresponding to the amount of modification" is a curve that forms the following tooth shape: when meshing with the set amount of modification, the gear 1 can rotate normally without faults such as rotation problems and looseness.

[0063] In addition, the gear 1 of the present embodiment has implemented tip crowning. By implementing tip crowning, the protruding amount of the tooth tip can be reduced at the end in the tooth trace direction, thereby ensuring the thickness at the tooth root and increasing the strength of the tooth 3.

[0064] More specifically, in the gear 1 of the present embodiment, the tooth shape at each position in the tooth trace direction is composed of an involute curve and a trochoid curve corresponding to the amount of modification at that position, and has a transition point where the involute curve and the trochoid curve are switched. Hereinafter, the "involute curve and trochoid curve corresponding to the amount of modification" will be described.

[0065] When the involute curve constituting the tooth profile of the gear 1 is represented by XY coordinates with the gear center as the origin, its coordinate position (Xi, Yi) can be represented by the following equations (1) and (2).

[0066] Xi = (dx × sinδi × cosβi) / 2…(1)

[0067] Yi = {(d - dx) × cosδi} / 2…(2)

[0068] In addition, when the trochoid curve constituting the tooth profile of the gear 1 is represented by XY coordinates with the gear center as the origin, its coordinate position (Xt, Yt) can be represented by the following equations (3) and (4).

[0069] Xt = dx × sinδt × cosβt…(3)

[0070] Yt = {(d - dx) × cosδt} / 2…(4)

[0071] In addition, each variable in the equations (1) to (4) represents the following values.

[0072] d: Pitch diameter of the gear

[0073] dx: Diameter of the circle centered on the gear center and passing through the coordinate position (Xi, Yi)

[0074] δi: Angle formed by the straight line connecting the coordinate position (Xi, Yi) and the gear center and the straight line extending from the intersection of the reference rack tool node (Pitchpoint) and the gear pitch circle to the gear center

[0075] βi: Torsion angle at the diameter dx

[0076] δt: Angle formed by the straight line connecting the coordinate position (Xt, Yt) and the gear center and the straight line extending from the intersection of the reference rack tool node (Pitchpoint) and the gear pitch circle to the gear center

[0077] βt: Torsion angle at the diameter dx

[0078] Here, when the displacement amount changes and the displacement coefficient Xn changes, although the base circle diameter remains unchanged, the addendum circle diameter, the dedendum circle diameter, the tooth thickness, the addendum height, and the phase difference between the dedendum height of the reference rack tool and the meshing pitch line will change. In addition, the value obtained by multiplying the displacement coefficient Xn by the module m is the displacement amount. If a specific example is given, the addendum circle diameter da of the gear is given by the following formula (5):

[0079] da = d / (cosβ)+2(hac + Xn)…(5)

[0080] Wherein, hac: can be represented by the addendum height coefficient in the reference rack tool, and it can be seen that when the displacement coefficient Xn becomes smaller, the addendum circle diameter also becomes smaller.

[0081] Moreover, δi and δt in the above formulas (1) to (4) can be represented using the displacement coefficient Xn. As Figure 11 and Figure 12 shown, the smaller the displacement coefficient Xn, the larger the radius of curvature between the bottom of the tooth and the meshing end position of the trochoid curve forming the tooth root vicinity. That is to say, in the gear 1 of the present embodiment, the radius of curvature between the bottom of the tooth and the meshing end position of the trochoid curve at the end in the tooth line direction is smaller than the radius of curvature between the bottom of the tooth and the meshing end position of the trochoid curve at the center in the tooth line direction.

[0082] In addition, in Figure 11 and Figure 12 , a radial sectional view of the tooth 3 is shown in the case where the module is set to 1.0, the pressure angle is set to 20°, and the number of teeth is set to 20. In addition, in (a) and (b) of Figure 12 , a diagram showing the radial sectional view (displacement amount is 0) at the center in the tooth line direction and the radial sectional view (displacement amount is -0.5 or -1.0) at the end in the tooth line direction overlapped is shown. In addition, Figure 11 , 12 , the dashed line A represents the meshing end position in the gear 1.

[0083] In addition, the smaller the displacement coefficient Xn (or the displacement amount) (the more negative displacement is performed), the more the proportion of the trochoid curve in the entire tooth surface increases. Therefore, at the end in the tooth line direction, the switching position between the involute curve and the trochoid curve is more radially outward than at the center in the tooth line direction. In addition, since each point at the tip of the reference rack tool (hob) for cutting teeth during gear generation (or during electrode formation described later) draws a trochoid curve, the trochoid curve described in the present embodiment actually refers to a curve that envelopes a plurality of trochoid curves.

[0084] Moreover, by reducing the radius of curvature between the tooth bottom and the meshing end position that forms the hypocycloid curve near the tooth root, the thickness at the meshing end position is reduced. Therefore, in gear 1, at the end in the tooth trace direction, the thickness at the meshing end position is smaller than that at the central part in the tooth trace direction. In other words, in gear 1, at the end in the tooth trace direction, there is a thickness reduction portion 33 with a reduced thickness compared to the central part in the tooth trace direction, radially inward of the meshing end position.

[0085] Gear 1 has the following tooth shape: from the central part to both ends in the tooth trace direction, the amount of thickness reduction of the thickness reduction portion 33 gradually increases. The thickness reduction portion 33 is formed in a recessed manner in the circumferential direction at least at both ends in the tooth trace direction. By having the thickness reduction portion 33, even when the influence of deviation is large, the clearance at the tooth tip can be ensured, bottoming can be avoided, and thus poor rotation can be suppressed. The minimum thickness of tooth 3 in the part where the thickness reduction portion 33 is formed becomes thinner as it gets closer to the end in the tooth trace direction.

[0086] Moreover, in gear 1, when comparing the central part (the amount of profile shift is 0) in the tooth trace direction with the end in the tooth trace direction, the thickness of tooth 3 at the meshing end position is smaller at the end in the tooth trace direction than at the central part in the tooth trace direction. In Figure 12 the case of example (a) of

[0087] that is, when the amount of profile shift at the end in the tooth trace direction is set to -0.5, the thickness W1 at the meshing end position of the central part in the tooth trace direction is 1.734 mm, and the thickness W2 at the meshing end position of the end in the tooth trace direction is 1.322 mm. Figure 12 In addition, in example (a) of

[0088] Figure 12 that, the difference in thickness ΔW between the meshing end positions of the central part and the end in the tooth trace direction is W1 - W2 = 1.755 - 1.413 = 0.342 mm. On the other hand, the amount of profile shift is the value obtained by multiplying the profile shift coefficient Xn by the module. Therefore, the amount of profile shift at the end in the tooth trace direction is -0.5 × 1 = -0.5 mm. So, the difference in the amount of profile shift between the central part and the end in the tooth trace direction is 0.5 mm. In this way, in gear 1, the difference in thickness ΔW between the meshing end positions of the central part and the end in the tooth trace direction is smaller than the difference in the amount of profile shift between the central part and the end in the tooth trace direction. By setting it like this, the thickness of tooth 3 at the meshing position that is easily affected by the acting stress can be ensured, which helps to improve the strength of gear 1. Compared with a metal gear, the resin gear 1 has a higher possibility of elastic deformation due to stress, and there may be a failure in stress transmission due to tooth skipping or the like caused by elastic deformation. Therefore, in the resin gear 1, the effect of ensuring the thickness of tooth 3 is particularly remarkable.

[0088] In addition, here, the case where the thickness and the amount of modification at the meshing end position in the central part in the tooth line direction are the largest and the thickness and the amount of modification at the meshing end position at the end in the tooth line direction are the smallest (the case of negative modification from the central part to the end) is described. However, the thickness and the amount of modification at the meshing end position in the central part in the tooth line direction may not be the largest, and the thickness and the amount of modification at the meshing end position at the end in the tooth line direction may not be the smallest either. For example, in addition to setting the amount of modification at one end in the tooth line direction to be the largest and the amount of modification at the other end to be the smallest, the amount of modification may be the largest at a position between the central part and the end in the tooth line direction. In this case, it is sufficient that the difference between the maximum thickness and the minimum thickness of the meshing end positions in the entire region in the tooth line direction (corresponding to ΔW above) is smaller than the difference between the maximum amount of modification and the minimum amount of modification in the entire region in the tooth line direction. At this time, the meshing node at the end in the tooth line direction will be located at a position radially inside the meshing node in the central part in the tooth line direction, and thus it is easier to ensure the clearance at the tooth tip. In addition, in this case, the meshing pitch line viewed from the tooth surface side is taken as a curve gentler than the tooth bottom outline line and the tooth tip outline line. In addition, in the present embodiment, the conversion point where the involute curve and the trochoid curve are switched becomes the meshing end position of the gear.

[0089] In Figure 12 the example of (b) (in the case where the amount of modification at the end in the tooth line direction is set to -1.0), the thickness W1 at the meshing end position in the central part in the tooth line direction is 1.755 mm, the thickness W2 at the meshing end position at the end in the tooth line direction is 1.062 mm, and the difference ΔW in thickness between the meshing end positions in the central part and the end in the tooth line direction is 0.693 mm. Since the difference in the amount of modification between the central part and the end in the tooth line direction is 1.0 mm, ΔW is smaller than the difference in the amount of modification between the central part and the end in the tooth line direction. In addition, in the gear 1, parameters such as the amount of modification at the end in the tooth line direction, the module, the pressure angle, and the number of teeth can be appropriately changed as long as the condition that ΔW is smaller than the difference in the amount of modification between the central part and the end in the tooth line direction is satisfied.

[0090] In addition, the radius of curvature between the tooth bottom and the meshing end position of the trochoid curve at the end in the tooth line direction and the difference ΔW in thickness between the meshing end positions in the central part and the end in the tooth line direction can also be controlled by changing the tooth shape of the reference rack tool for forming the electrode. In Figure 11 , Figure 12 the case where the tooth shape of the reference rack tool is trapezoidal and its corners are rounded with a specified radius of curvature is shown. In contrast, in the case where the tip of the tooth of the reference rack tool is composed only of a curve with a specified radius of curvature, the cross-sectional views of the teeth 3 in the central part and the end in the tooth line direction are as in Figure 13 (a). In addition, Figure 13(a) is set to the same conditions as Figure 10 (a) except for changing the tooth shape of the reference rack tool. In Figure 13 (a) case, W1 = 1.765 mm, W2 = 1.430 mm, ΔW = 0.335. It can be seen that in this case, compared with Figure 12 (a) case (ΔW = 0.342), ΔW becomes smaller.

[0091] Similarly, when the tip of the tooth of the reference rack tool is composed of only straight lines and is a trapezoid without rounded corners, the cross-sectional view of the tooth 3 at the center and end in the tooth line direction is as shown in Figure 13 (b). In addition, Figure 13 (b) is set to the same conditions as Figure 12 (a) except for changing the tooth shape of the reference rack tool. In Figure 13 (b) case, W1 = 1.734 mm, W2 = 1.322 mm, ΔW = 0.412. It can be seen that in this case, compared with Figure 12 (a) case (ΔW = 0.342), ΔW becomes larger.

[0092] In addition, by changing the composition of the tip of the tooth of the reference rack tool in this way, the position and number of each point of the tip of the reference rack tool for drawing the hypocycloid curve also change. Therefore, the shape or number of multiple hypocycloid curves constituting the hypocycloid curve near the tooth root will change.

[0093] (Effect of shaft skew)

[0094] Next, the effect of the shaft skew of the rotating shaft in the gear is described. As shown in Figure 14 (a), a gear with a pitch diameter of d and a tooth width of b is discussed. In addition, for simplicity of explanation, a spur gear without crowning is discussed here. As an example, when the angle of the rotating shaft C is inclined by θ with respect to the center O of the bottom surface of the gear, assuming that the angle θ is small enough, the distance f from the rotating shaft C before inclination (the rotating shaft C at the normal assembly position) to the pitch circle of the gear can be expressed by the following formula (6).

[0095] f = (ytanθ + d / 2)cosθ…(6)

[0096] Thus, the protrusion amount e from the normal assembly position can be expressed by the following formula (7).

[0097] e = f - d / 2 = (ytanθ + d / 2)cosθ - d / 2…(7)

[0098] Here, the protrusion amount e refers to the amount by which the gear protrudes radially due to the inclination of the rotating shaft C.

[0099] As shown in formula (7), the smaller the pitch diameter d is, the larger the protrusion amount e is. If an example of the relationship between the pitch diameter d and the protrusion amount e is shown in a coordinate graph, it will be as shown in Figure 14 (b) of. Thus, even if the inclination θ of the rotation axis C is constant, the smaller the pitch diameter d of the gear, that is, the smaller the diameter of the gear, the larger the protrusion amount e. As a result, problems such as the disappearance of backlash and bottoming are likely to occur.

[0100] Here, the pitch diameter d is obtained by multiplying the number of teeth z by the module m. Therefore, when the module m is fixed, the smaller the value of the number of teeth z, or when the number of teeth z is fixed, the smaller the module m, the larger the protrusion amount e will be. Generally speaking, as an index of the size of a gear, the module m is used, and a gear with a smaller module m is generally considered to be a gear with a smaller diameter. In particular, in small-diameter gears with a module m of 1.0 or less, if only crowning is performed, in the case where the cross-sectional shape is the same along the tooth line, problems such as the disappearance of backlash and bottoming are likely to occur.

[0101] In contrast, in the gear 1 of the present embodiment, the tooth shape in the tooth line direction is formed by a curve corresponding to the amount of profile shift at that position. Therefore, even when the protrusion amount e is large, it is possible to suppress the disappearance of backlash and bottoming, and suppress the occurrence of rotation failure. In small-diameter gears with a module m of 1.0 or less, rotation failure can also be suppressed.

[0102] (Manufacturing method of gear 1)

[0103] The gear 1 of the present embodiment includes resin and is formed by injection molding using a mold. The gear 1 has a tooth shape in which the axial central portion protrudes radially outward. In addition, since the gear 1 has a tooth shape with a thickness reduction portion 33 at the end in the tooth line direction, a mold having a so-called undercut needs to be formed. Conventionally, the formation of such a mold has been difficult, but in the present embodiment, a mold with an undercut can be formed by performing electrical discharge machining while rotating the electrode in the mold.

[0104] As shown in Figure 15 , first, in step S1, an electrode forming process is performed. In the electrode forming process, as shown in Figure 16 , an electrode 4 having a shape substantially the same as (similar shape) that of the gear 1 is formed at the tip portion. When forming the electrode 4, hobbing is performed on the outer peripheral surface of a cylindrical metal substrate 41 made of, for example, copper as the electrode to form teeth 42. At this time, by performing gear generation while moving the reference rack tool in an arc shape, a tooth shape with crowning and tooth thickness crowning can be obtained.

[0105] After the electrode forming process, in step S2, a mold forming process is performed. In the mold forming process, using the electrode 4 formed in step S1, a mold 5 is formed by electrical discharge machining. Specifically, as shown in (a) and (b) of Figure 17 , first, the mold 5 is disposed in the liquid L, and the electrode 4 is continuously moved closer to the inside of the mold 5. In this state, a voltage is applied between the electrode 4 and the mold 5 to generate a spark. Then, the mold 5 melts due to the heat of the spark, and the melted metal is rapidly cooled and dispersed by the liquid L, while forming the holes 51, and the shape of the electrode 4 is transferred to the mold 5. In the present embodiment, during the electrical discharge machining, as shown in (a) to (d) of Figure 18 , by performing the machining while swinging the electrode 4, a mold 5 with an undercut can be formed.

[0106] After the mold forming process, in step S3, an injection molding process is performed. In the injection molding process, using the mold 5 formed by the mold forming process, a gear 1 is formed by injection molding. According to the above, a resin gear 1 can be obtained.

[0107] (Functions and effects of the embodiment)

[0108] As described above, in the gear 1 of the present embodiment, the tooth shape at each position in the tooth trace direction is constituted by a curve set corresponding to the amount of modification, and is configured such that the tooth shape continuously changes in the tooth trace direction.

[0109] As a conventional gear, generally, the tooth shape has the same cross-sectional shape along the tooth trace. However, in such a gear, especially in a small-diameter gear, the protrusion amount (amount of modification) of the mating gear relative to its own gear is large, and there may be a rotation failure due to the disappearance of backlash or the interference between the tooth tip of the mating gear and the tooth bottom of its own gear. In contrast, in the gear 1 of the present embodiment, the tooth shape in the tooth trace direction is constituted by a curve corresponding to the amount of modification set at that position. Therefore, the occurrence of rotation failure can be suppressed, and particularly, in the case where the diameter is small, the number of teeth is small, and the influence of the shaft deviation or shaft skew of the rotation axis is large, a remarkable effect can be obtained.

[0110] (Summary of the embodiment)

[0111] Next, the technical idea grasped from the above-described embodiment is described by referring to the reference numerals in the embodiment. However, the reference numerals and the like in the following description are not used to limit the constituent elements in the claims to the components specifically shown in the embodiment.

[0112] [1] A gear (1), wherein the tooth shape at each position in the tooth trace direction is constituted by a curve set corresponding to the amount of modification, and is configured such that in the tooth trace direction, the tooth shape continuously changes.

[0113] [2] The gear (1) according to [1] is subjected to crowning treatment.

[0114] [3] The gear (1) according to [1] or [2], the above curve is a curve that at least includes an involute curve.

[0115] [4] The gear (1) according to any one of [1] to [3], the above curve is a curve that at least includes an involute curve and a trochoid curve, and has a transition point where the involute curve and the trochoid curve are switched.

[0116] [5] The gear (1) according to [4], the above transition point is the meshing terminal position of the gear.

[0117] [6] The gear (1) according to [4] or [5], the above trochoid curve is composed of an envelope of a plurality of trochoid curves.

[0118] [7] The gear (1) according to any one of [1] to [6], the difference between the maximum thickness and the minimum thickness of the meshing terminal position in the entire region of the tooth trace direction is less than the difference between the maximum modification amount and the minimum modification amount in the entire region of the tooth trace direction.

[0119] [8] The gear (1) according to any one of [1] to [7], the difference in thickness between the meshing terminal positions at the central part and the end part in the tooth trace direction is less than the difference in modification amount between the central part and the end part in the tooth trace direction.

[0120] [9] The gear (1) according to any one of [1] to [8], at the end part in the tooth trace direction, there is a thickness reduction part (33) with a reduced thickness compared to the central part in the tooth trace direction at a position radially inward of the meshing terminal position.

[0121]

[10] The gear (1) according to [9], has the following tooth shape: from the central part to both end parts in the tooth trace direction, the amount of thickness reduction of the above thickness reduction part (33) gradually increases.

[0122]

[11] The gear (1) according to [9] or

[10] , at least at both end parts in the tooth trace direction, the above thickness reduction part (33) is formed in a recessed manner in the circumferential direction.

[0123] Above, the embodiments of the present invention have been described, but the above-described embodiments do not limit the invention related to the claims. In addition, it should be noted that not all combinations of the features described in the embodiments are necessary for the solution to the problem of the invention.

[0124] The present invention can be implemented with appropriate modifications without departing from its gist. For example, in the above-described embodiment, the amount of modification is set such that it gradually becomes a negative modification from the central portion to both end portions in the tooth line direction, but it is not limited thereto. For example, the amount of modification may also be set such that it gradually becomes a positive modification from the central portion to the end portions in the tooth line direction. In addition, the amount of modification may also be set such that the amount of modification at one end portion in the tooth line direction is different from the amount of modification at the other end portion in the tooth line direction.

Claims

1. A gear, characterized in that the tooth shape at each position in the tooth trace direction is formed by a curve set corresponding to the amount of modification, and is configured such that in the above-mentioned tooth trace direction, the above-mentioned tooth shape changes continuously, the above-mentioned curve is a curve that at least includes an involute curve and a trochoid curve, has a conversion point where the involute curve and the trochoid curve are switched, the difference in thickness at the meshing end positions between the central portion and the end portion in the above-mentioned tooth trace direction is smaller than the difference in the amount of modification between the central portion and the end portion in the above-mentioned tooth trace direction.

2. The gear according to claim 1, which has been subjected to crowning treatment.

3. The gear according to claim 1, wherein the above-mentioned conversion point is the meshing end position of the gear.

4. The gear according to claim 1, wherein the above-mentioned trochoid curve is composed of the envelope of a plurality of trochoid curves.

5. The gear according to any one of claims 1 to 4, at the end portion in the tooth trace direction, has a thickness reduction portion with a reduced thickness compared to the central portion in the tooth trace direction at a position radially inward of the meshing end position.

6. The gear according to claim 5, has the following tooth shape: from the central portion to both end portions in the tooth trace direction, the amount of thickness reduction of the above-mentioned thickness reduction portion gradually increases.

7. The gear according to claim 5, at least at both end portions in the tooth trace direction, the above-mentioned thickness reduction portion is formed in a concave manner in the circumferential direction.

8. A gear, characterized in that the tooth shape at each position in the tooth trace direction is formed by a curve set corresponding to the amount of modification, and is configured such that in the above-mentioned tooth trace direction, the above-mentioned tooth shape changes continuously, the difference between the maximum thickness and the minimum thickness of the meshing end positions in the entire tooth trace direction region is smaller than the difference between the maximum amount of modification and the minimum amount of modification in the entire tooth trace direction region.

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