Gear grinding method and gear grinding device

Abstract

This method for grinding a gear comprises a grinding step (Sb) for grinding a tooth flank of a gear (Gb1) by: making an axial intersection angle between a rotational axis (B2) of a workpiece (W2) and a rotational axis (C) of a thread-shaped grinding wheel (T) a combined axial intersection angle (θ2) obtained by combining a reference axial intersection angle (θ1) with a corrected axial intersection angle (Δθ); rotating the thread-shaped grinding wheel (T) and the workpiece (W2) in a synchronized manner; and relatively moving the thread-shaped grinding wheel (T) in a direction parallel to the rotational axis (B2) of the workpiece (W2). The reference axial intersection angle (θ1) is an axial intersection angle determined on the basis of a torsion angle (ϕw) on a reference circle of the gear (Gb1) and a torsion angle (ϕt) on a reference circle of the thread-shaped grinding wheel (T). The corrected axial intersection angle (Δθ) is an axial intersection angle for forming a grinding mark (Gr_W2), which is formed on the tooth flank of the gear (Gb1) by the thread-shaped grinding wheel (T), in a direction inclined at a predetermined angle (Σ) with respect to a tooth trace direction (D_Tr).

Description

[Technical Field]

[0001] The present disclosure relates to a gear grinding method and a gear grinding apparatus. [Background technology]

[0002] Patent Document 1 describes the generation of noise due to minute steps formed on the gear tooth flanks during gear meshing. The minute steps on the gear tooth flanks are generated, for example, by grinding the gear tooth flanks with a grinding wheel. Specifically, when the gear tooth flanks are ground with abrasive grains from the grinding wheel, minute groove-like grinding marks are formed on the gear tooth flanks in the direction of movement of the abrasive grains at the grinding points on the tooth flanks. Generally, minute groove-like grinding marks are formed in a direction parallel to the tooth trace direction of the gear tooth flanks. In other words, multiple grinding marks form steps on the gear tooth flanks in the tooth depth direction. Patent Document 1 also describes the use of honing or gear dressing after grinding the gear tooth flanks with a grinding wheel to reduce the steps on the tooth flanks. [Prior art documents] [Patent documents]

[0003] [Patent Document 1] Japanese Patent Application Laid-Open No. 2000-52145 Summary of the Invention [Problem to be solved by the invention]

[0004] However, with conventional methods, additional processing such as honing or dressing gears is required after grinding with a grinding wheel to reduce the steps on the gear tooth flanks. The additional processing increases the number of processing steps and increases the processing costs.

[0005] The present disclosure has been made in consideration of such problems, and aims to provide a gear grinding method and gear grinding device that can reduce noise caused by steps on the gear tooth flanks when the gears mesh, without requiring additional processing. [Means for solving the problem]

[0006] One aspect of the present disclosure is a gear grinding method for grinding a tooth flank of a gear using a threaded grinding wheel, comprising the steps of: a grinding step in which an intersecting-axis angle between a rotation axis of a workpiece and a rotation axis of the threaded grinding wheel is set to a composite intersecting-axis angle obtained by combining a reference intersecting-axis angle and a correction intersecting-axis angle, the threaded grinding wheel and the workpiece are rotated synchronously, and the threaded grinding wheel is moved relatively in a direction parallel to the rotation axis of the workpiece to grind the tooth flank of the gear, the reference crossed axes angle is an axis crossed angle determined based on a helix angle on a reference circle of the gear and a helix angle on a reference circle of the threaded grinding wheel, In the gear grinding method, the corrected cross-axis angle is an axis-crossing angle for forming grinding marks on the tooth flanks of the gear by the threaded grinding wheel in a direction inclined at a predetermined angle with respect to the tooth trace direction.

[0007] Another aspect of the present disclosure is a gear grinding apparatus that grinds a tooth surface of a gear using a threaded grinding wheel, comprising: a grinding processing unit that grinds the tooth flanks of the gear by setting an axis-crossing angle between a rotation axis of the workpiece and a rotation axis of the threaded grinding wheel to a composite axis-crossing angle obtained by combining a reference axis-crossing angle and a correction axis-crossing angle, rotating the threaded grinding wheel and the workpiece synchronously, and moving the threaded grinding wheel relatively in a direction parallel to the rotation axis of the workpiece, the reference crossed axes angle is an axis crossed angle determined based on a helix angle on a reference circle of the gear and a helix angle on a reference circle of the threaded grinding wheel, The corrected cross-axis angle is an axis-crossing angle for forming grinding marks on the tooth surfaces of the gear by the threaded grinding wheel in a direction inclined at a predetermined angle with respect to the tooth trace direction, in a gear grinding device. [Effects of the Invention]

[0008] When grinding the tooth flanks of a gear using a threaded grinding wheel, a crossed-axes angle between the rotation axis of the workpiece and the rotation axis of the threaded grinding wheel is set. The crossed-axes angle obtained by the helix angle on the reference circle of the gear and the helix angle on the reference circle of the threaded grinding wheel is defined as the reference crossed-axes angle. For example, when the helix angle on the reference circle of the gear is 0°, the reference crossed-axes angle is equal to the helix angle on the reference circle of the threaded grinding wheel. When the helix angle on the reference circle of the gear is not 0°, the reference crossed-axes angle is determined by taking the helix angle on the reference circle of the gear into account when comparing the helix angle on the reference circle of the threaded grinding wheel.

[0009] If the gear tooth flanks are ground with the cross-axis angle set to the reference cross-axis angle, the grinding marks formed on the gear tooth flanks by the threaded grinding wheel will be parallel to the tooth trace direction. Therefore, in the gear grinding method and gear grinding apparatus described above, the cross-axis angle between the rotation axis of the workpiece and the rotation axis of the threaded grinding wheel is set to a composite cross-axis angle that is a combination of the reference cross-axis angle and the corrected cross-axis angle.

[0010] The corrected cross-axis angle is an angle for forming grinding marks on the tooth flanks of a gear by the threaded grinding wheel in a direction inclined at a predetermined angle relative to the tooth trace direction. In other words, by setting the cross-axis angle during grinding to a composite cross-axis angle obtained by combining the reference cross-axis angle and the corrected cross-axis angle, the grinding marks are not parallel to the tooth trace direction but are inclined relative to the tooth trace direction.

[0011] Because the grinding marks can be formed in a direction inclined toward the tooth trace, for example, when the gear to be ground and the mating gear mesh, the direction in which the grinding marks extend can be aligned with the meshing progression direction on the tooth flank of the gear to be ground. When these two directions are aligned, the mating gear does not climb over the grinding marks on the tooth flank as the gears mesh. Since the grinding marks do not climb over the grinding marks, noise generated during gear meshing can be reduced.

[0012] Furthermore, even if the direction of the grinding marks does not coincide with the direction of meshing, by bringing the direction of the grinding marks closer to the direction of meshing, it is possible to reduce the grinding marks' overstepping action, thereby reducing noise generated during gear meshing.

[0013] As described above, according to the above aspects, it is possible to provide a gear grinding method and gear grinding device that can reduce noise caused by steps on the gear tooth flanks when the gears mesh, without performing additional processing.

[0014] It should be noted that the reference symbols in parentheses in the claims indicate the correspondence with the specific means described in the embodiments to be described later, and do not limit the technical scope of the present invention. [Brief explanation of the drawings]

[0015] [Figure 1] FIG. 1 is a diagram showing a gear grinding device. [Figure 2] FIG. 2 is a view of the gear grinding machine of FIG. 1 as seen from the left. [Figure 3] FIG. 1(a) is a diagram showing the meshing state of a drive gear and a driven gear, and FIG. 1(b) is a diagram explaining the meshing line and meshing direction in the case of helical gears. [Figure 4] 1A and 1B are diagrams illustrating the mechanism by which meshing noise occurs, in which FIG. 1A shows a case in which the grinding marks are aligned with the meshing progression direction, and FIG. 1B shows a case in which the grinding marks are inclined toward the meshing progression direction. [Figure 5] 4 is a flowchart showing processing by a grinding condition determination unit included in the gear grinding device according to the first embodiment. [Figure 6] 6A and 6B are diagrams illustrating the reference axis intersecting angle determination step S3 in FIG. 5, in which (a) shows the state of the threaded grinding wheel and the workpiece, (b) shows the threaded grinding wheel and the teeth to be ground on the gear of the workpiece, and (c) shows the threaded grinding wheel and the workpiece as viewed from the rotation axis of the threaded grinding wheel. [Figure 7]6A and 6B are diagrams illustrating the reference axis intersecting angle determining step S3 in FIG. 5, in which (a) is a perspective view showing a part of the convex cutting edge of the threaded grinding wheel and a part of the gear tooth of the workpiece, (b) is a diagram showing a part of the grinding marks on the tooth surface of the workpiece, and (c) is a perspective view showing the grinding marks on the tooth surface of the gear of the workpiece. [Figure 8] 6A and 6B are diagrams illustrating the corrected axis-crossing angle determination step S4 in FIG. 5, in which (a) shows the state of the threaded grinding wheel and the workpiece, (b) shows the threaded grinding wheel and the teeth to be ground on the gear of the workpiece, and (c) shows the threaded grinding wheel and the workpiece as viewed from the rotation axis of the threaded grinding wheel. [Figure 9] 6A and 6B are diagrams illustrating the corrected axis-crossing angle determination step S4 in FIG. 5, in which (a) is a perspective view showing a part of the convex cutting edge of the threaded grinding wheel and a part of the gear tooth of the workpiece, (b) is a diagram showing a part of the grinding marks on the tooth surface of the gear of the workpiece, and (c) is a perspective view showing the grinding marks on the tooth surface of the gear of the workpiece. [Figure 10] FIG. 1 is a diagram showing grinding points on a tooth surface, velocity vectors, and tooth surface normal component vectors on a tooth surface of a gear of a workpiece. [Figure 11] FIG. 10 is a diagram showing a grinding wheel velocity vector, a grinding wheel normal component vector, and a tangent vector in a convex cutting edge of a threaded grinding wheel. [Figure 12] 3 is a diagram showing grinding points on the tooth surface of a gear of a workpiece and grinding wheel shape points on a threaded grinding wheel in the first embodiment. FIG. [Figure 13] FIG. 10 is a diagram showing grinding points on the tooth surface of a gear of a workpiece and grinding wheel shape points of a threaded grinding wheel in a reference example. [Figure 14] FIG. 10 is a perspective view showing the meshing progression direction and grinding marks in the case of a spur gear according to a second embodiment. [Figure 15] FIG. 10 is a view showing a threaded grinding wheel according to a third embodiment. DETAILED DESCRIPTION OF THE INVENTION

[0016] (Embodiment 1) 1. Gear grinding equipment 1 The configuration of the gear grinding device 1 will be described with reference to Figures 1 and 2. The gear grinding device 1 grinds the tooth flanks of a gear using a threaded grinding wheel T. In detail, the gear grinding device 1 grinds the tooth flanks of a gear-shaped workpiece W using the threaded grinding wheel T, thereby forming the tooth flanks of a desired gear.

[0017] 2, the gear grinding device 1 sets the axis-crossing angle between the rotation axis B of the workpiece W and the rotation axis C of the threaded grinding wheel T to a composite axis-crossing angle θ2. The composite axis-crossing angle θ2 is an angle obtained by combining the reference axis-crossing angle θ1 and the corrective axis-crossing angle Δθ. The reference axis-crossing angle θ1 and the corrective axis-crossing angle Δθ will be described later.

[0018] The gear grinding device 1 rotates the threaded grinding wheel T around the C-axis, which is the central axis of the threaded grinding wheel T, and rotates the workpiece W around the B-axis, which is the central axis of the workpiece W, while moving the threaded grinding wheel T relative to the workpiece W in the direction of its central axis, thereby grinding the gear-shaped tooth surface of the workpiece W.

[0019] Therefore, the gear grinding device 1 is configured to allow relative movement between the workpiece W and the threaded grinding wheel T in the directions of three orthogonal axes. Furthermore, the gear grinding device 1 is configured so that the workpiece W is rotatable about the B axis and the threaded grinding wheel T is rotatable about the C axis, and so that the workpiece W or the threaded grinding wheel T can be rotatable in order to change the relative position between the workpiece W and the threaded grinding wheel T.

[0020] The gear grinding device 1 may be, for example, a six-axis machine, i.e., a machine with three linear axes and three rotational axes. In this embodiment, the gear grinding device 1 allows the workpiece W to rotate about the B axis, the threaded grinding wheel T to rotate about the A axis and the C axis, and the threaded grinding wheel T to move in the X, Y, and Z axes. The A axis is an axis perpendicular to the rotation axis B of the workpiece W and the rotation axis C of the threaded grinding wheel T. The B axis coincides with the central axis of the workpiece W. The C axis coincides with the central axis of the threaded grinding wheel T. Note that the mechanical configuration of the gear grinding device 1 is not limited to the above, and various configurations can be applied. For example, the gear grinding device 1 can be applied to a horizontal machining center or a vertical machining center with a different configuration.

[0021] The gear grinding machine 1 includes, for example, a bed 2, a column 3, a Y-axis slide 4, a rotating member 5, a grinding wheel support member 6, a threaded grinding wheel T, a workpiece support member 7, a grinding condition determination unit 8, and a grinding processing unit 9. The bed 2 is placed on an installation surface. The column 3 is guided by an X-axis guide provided on the upper surface of the bed 2 and is provided so as to be movable in the X-axis direction (horizontal direction in FIG. 1 ) relative to the bed 2. Although not shown, the column 3 is driven by a ball screw mechanism, a linear motor, or the like.

[0022] The Y-axis slide 4 is guided by a Y-axis guide provided on a side surface of the column 3 extending in the vertical direction, and is provided so as to be movable in the Y-axis direction (up and down direction in FIG. 1) relative to the column 3. The rotation member 5 is provided on the Y-axis slide 4 and is provided so as to be rotatable around the A-axis, which is a horizontal axis. The rotation member 5 is provided so as to be rotatable within a range of 360°, for example.

[0023] The grindstone support member 6 is guided by a Z-axis guide provided on the rotating member 5 and is provided so as to be movable in the Z-axis direction. The Z-axis direction changes direction as the rotating member 5 rotates around the A-axis. In the initial state, the Z-axis direction is, for example, horizontal and perpendicular to the X-axis and Y-axis directions.

[0024] The grinding wheel support member 6 supports the threaded grinding wheel T rotatably around the C axis. The C axis coincides with the central axis of the threaded grinding wheel T and is an axis parallel to the Z axis. The threaded grinding wheel T has a spiral convex cutting edge that protrudes radially outward. The threaded grinding wheel T may have a single thread or a multiple-thread thread. In the case of a multiple-thread thread, the threaded grinding wheel T will have multiple spiral convex cutting edges. The workpiece support member 7 is provided on the bed 2 and supports the workpiece W rotatably around the B axis.

[0025] The grinding condition determination unit 8 is configured to include at least a processor (arithmetic processing device). The grinding condition determination unit 8 determines grinding conditions including the convex cutting edge shape of the threaded grinding wheel T and a composite axis-crossing angle θ2 (grinding condition determination step Sa). The composite axis-crossing angle θ2 is an angle obtained by combining the reference axis-crossing angle θ1 and the correction axis-crossing angle Δθ. The method for determining the grinding conditions will be described later.

[0026] The grinding processing unit 9 is configured to include at least a processor (arithmetic processing device). Based on the determined grinding conditions, the grinding processing unit 9 executes a process of grinding the gear tooth flank of the workpiece W using the threaded grinding wheel T (grinding step Sb). The grinding method for the gear tooth flank of the workpiece W by the grinding processing unit 9 of the gear grinding device 1 is as follows: In this embodiment, the rotating member 5 is rotated by a predetermined angle around the A axis to achieve a grinding posture in which the cross-axis angle between the rotation axis B of the workpiece W and the rotation axis C of the threaded grinding wheel T is θ2. Next, the grinding processing unit 9 synchronously rotates the workpiece W and the threaded grinding wheel T. More specifically, the workpiece W is rotated around the B axis, and the threaded grinding wheel T is rotated around the C axis, thereby synchronizing the rotations of both.

[0027] Next, the column 3 is moved in the X-axis direction, the Y-axis slide 4 is moved in the Y-axis direction, and the grinding wheel support member 6 is moved in the Z-axis direction, thereby moving the threaded grinding wheel T to the initial grinding position. Next, the Y-axis slide 4 is moved to move the threaded grinding wheel T in the direction of the central axis of the workpiece W (a direction parallel to the rotation axis B), and grinding of the gear tooth surface of the workpiece W is performed.

[0028] In this embodiment, the gear grinding method by the gear grinding device 1 is a process in which the grinding condition determination unit 8 performs a process (grinding condition determination step Sa) and then the grinding processing unit 9 performs a process (grinding step Sb).

[0029] 2. Gear meshing direction D_La The meshing progression direction D_La will be described with reference to Fig. 3. As shown in Fig. 3(a), the drive gear Ga and the driven gear Gb are in meshing state. The drive gear Ga and the driven gear Gb are gears having a helix angle.

[0030] In this case, as shown by the dashed line in Fig. 3(b), on the tooth flank of the driven gear Gb, the line of contact (meshing line) La with the drive gear Ga is inclined with respect to the tooth trace direction D_Tr and the tooth depth direction D_Hi. In detail, first, the tooth flank corner Ea, which is the tooth tip and one end of the tooth trace direction D_Tr on the tooth flank of the driven gear Gb, meshes, and then the line of contact (meshing line) La moves toward the tooth flank corner Eb, which is the tooth root and the other end of the tooth trace direction D_Tr.

[0031] 3. Mechanism of meshing noise and methods for suppressing it The mechanism by which meshing noise occurs and a method for suppressing it will be described with reference to Fig. 4. Noise generated when the drive gear Ga and driven gear Gb mesh is affected by steps formed on the tooth flanks of the drive gear Ga and the driven gear Gb. Here, the tooth flank of the driven gear Gb will be described.

[0032] Fig. 4(a) shows a case where grinding marks Gr1 formed on the tooth flank of driven gear Gb1 extend in a direction inclined relative to the tooth trace direction D_Tr and the tooth depth direction D_Hi, while Fig. 4(b) shows a case where grinding marks Gr2 formed on the tooth flank of driven gear Gb2 extend in a direction parallel to the tooth trace direction D_Tr.

[0033] The grinding marks Gr1 and Gr2 are microgrooves formed by grinding the tooth surfaces of the driven gears Gb1 and Gb2 with the threaded grinding wheel T shown in Fig. 1. The extending direction of the grinding marks Gr1 and Gr2 coincides with the direction in which the contact abrasive grains that make up the threaded grinding wheel T advance and come into contact with the tooth surfaces of the driven gears Gb1 and Gb2.

[0034] On the tooth flank of the driven gear Gb1 shown in FIG. 4(a), the contacting abrasive grains of the threaded grinding wheel T proceed in a direction inclined relative to the tooth trace direction D_Tr and the tooth depth direction D_Hi. In particular, on the driven gear Gb1, the extension direction of the grinding marks Gr1 coincides with the meshing progression direction D_La. The grinding marks Gr1 are formed in a direction inclined at a predetermined angle Σ relative to the tooth trace direction D_Tr. However, since the grinding marks Gr1 are not, in detail, linear but are composed of multiple arcs with small angles, the predetermined angle Σ has an angular range.

[0035] On the other hand, on the tooth flank of the driven gear Gb2 shown in Fig. 4(b), the contacting abrasive grains of the threaded grinding wheel T advance in a direction parallel to the tooth trace direction D_Tr. Therefore, on the driven gear Gb2, the extending direction of the grinding marks Gr2 does not coincide with the meshing advancing direction D_La.

[0036] In the driven gear Gb1 shown in FIG. 4(a), as meshing with the drive gear Ga progresses, the meshing point does not go over the grinding marks Gr1. Therefore, noise caused by the meshing point going over the grinding marks Gr1 does not occur. On the other hand, in the driven gear Gb2 shown in FIG. 4(b), as meshing with the drive gear Ga progresses, the meshing point goes over the grinding marks Gr2. Therefore, noise caused by the meshing point going over the grinding marks Gr2 occurs.

[0037] 4(a), by making the extension direction of the grinding marks Gr1 coincide with the meshing direction D_La, it is possible to suppress the generation of noise (mesh noise) caused by the grinding marks Gr1 going over the grinding marks Gr1. Note that even if the extension direction of the grinding marks Gr1 does not completely coincide with the meshing direction D_La, the closer the extension direction of the grinding marks Gr1 is to the meshing direction D_La, the more the generation of mesh noise can be suppressed. Therefore, even if the extension direction of the grinding marks Gr1 does not completely coincide with the meshing direction D_La, bringing the extension direction of the grinding marks Gr1 closer to the meshing direction D_La is effective in reducing mesh noise.

[0038] 4. Processing by the grinding condition determination unit 8 The processing (grinding condition determination step Sa) by the grinding condition determination unit 8 will be described with reference to Figs. 5 to 12. As described above, the grinding condition determination unit 8 determines grinding conditions including the convex cutting edge shape of the threaded grinding wheel T and the axis crossing angle θ2. In particular, the grinding condition determination unit 8 determines grinding conditions that can align the extending direction of the grinding marks Gr1 with the target direction, as shown in Fig. 4(a).

[0039] The grinding condition determination unit 8 executes a gear specification acquisition step S1, a threaded grinding wheel specification determination step S2, a reference intersecting axis angle determination step S3, a corrected intersecting axis angle determination step S4, a composite intersecting axis angle determination step S5, and a convex cutting edge shape determination step S6.

[0040] The grinding condition determination unit 8 first acquires the specifications of the gear Gb to be ground (S1). The specifications of the gear Gb include the module, normal pressure angle, reference circle helix angle φw, number of teeth, addendum modification coefficient, reference pitch circle diameter, base circle diameter, tip circle diameter, and root circle diameter.

[0041] Next, the grinding condition determination unit 8 determines the specifications of the threaded grinding wheel T (S2). The specifications of the threaded grinding wheel T are determined as follows: The grinding condition determination unit 8 determines the pressure angle of the threaded grinding wheel T based on the acquired specifications of the gear Gb (S21). Next, the grinding condition determination unit 8 determines the grinding wheel module and pitch (S22). Next, the grinding condition determination unit 8 calculates the helix angle on the reference circle φt corresponding to the grinding wheel diameter (S23).

[0042] Next, the reference crossed-axes angle θ1 is determined (S3). The reference crossed-axes angle θ1 will be described with reference to FIGS. 6 and 7. In determining the reference crossed-axes angle θ1, the workpiece W1 is defined as W1 and the rotation axis B1 of the workpiece W is defined as B1. The workpiece W1 and rotation axis B1 are used to distinguish them from the workpiece W2 and rotation axis B2 used in determining the corrected crossed-axes angle Δθ, which will be described later.

[0043] 6(a) and 6(b) are views viewed from a direction perpendicular to the rotation axis B1 of the workpiece W1 and perpendicular to the rotation axis C of the threaded grinding wheel T. As shown in FIGS. 6(a) and 6(b), the reference crossing axes angle θ1 is the crossing axes angle between the rotation axis B1 of the workpiece W1 and the rotation axis C of the threaded grinding wheel T. The reference crossing axes angle θ1 is determined based on the helix angle φw on the reference circle of the gear of the workpiece W1 and the helix angle φt on the reference circle of the threaded grinding wheel T. More specifically, when the tooth trace direction D_Tr of the portion to be ground on the workpiece W1 coincides with the tooth trace direction on the reference circle of the convex cutting edge ground by the threaded grinding wheel T, the crossing axes angle between the rotation axis B1 of the workpiece W1 and the rotation axis C of the threaded grinding wheel T is the reference crossing axes angle θ1.

[0044] If the tooth flanks of the gear of the workpiece W1 are ground with the threaded grinding wheel T with the reference intersecting axes angle set to θ1, then as shown in Figures 6(b) and 6(c), a grinding point P1a on one tooth flank and a grinding point P1b on the other tooth flank of the workpiece W1 will be ground by the threaded grinding wheel T. When projected in the direction shown in Figure 6(b), the grinding points P1a and P1b are located on the rotation axis C of the threaded grinding wheel T. When projected in the direction shown in Figure 6(c), the grinding points P1a and P1b are located on Xt and Xw.

[0045] As shown in Fig. 6(c), at grinding points P1a and P1b, the threaded grinding wheel T rotates around the C axis, and therefore the abrasive grains on the convex cutting edge of the threaded grinding wheel T rotate around the C axis. Therefore, at grinding points P1a and P1b, the abrasive grains on the convex cutting edge of the threaded grinding wheel T move directly upward in Fig. 6(c).

[0046] At the grinding points P1a and P1b, the movement direction vectors of the abrasive grains on the convex cutting edge of the threaded grinding wheel T are represented by V1a and V1b, respectively. As shown in FIG. 6(c), when viewed from the axial direction of the threaded grinding wheel T (when projected in the axial direction of the threaded grinding wheel T), the tooth trace direction D_Tr of the gear of the workpiece W1 coincides with the velocity vector (the on-plane components of V1a and V1b in FIG. 6(c)) due to the rotation of the threaded grinding wheel T at the grinding points P1a and P1b on the convex cutting edge of the threaded grinding wheel T. In other words, when projected onto an action plane representing the tooth surface of the workpiece W1, the on-plane component of the tooth trace direction D_Tr of the gear of the workpiece W1 coincides with the on-plane component of the velocity vector due to the rotation of the threaded grinding wheel T at the grinding points P1a and P1b.

[0047] The enlarged view of FIG. 7(a) shows a movement direction vector V1a of the abrasive grains of the convex cutting edge of the threaded grinding wheel T at a grinding point P1a on one tooth flank of the workpiece W1. As shown in FIGS. 7(b) and 7(c), grinding marks Gr_W1 are formed on one tooth flank of the workpiece W1 by the abrasive grains of the convex cutting edge of the threaded grinding wheel T. That is, the grinding marks Gr_W1 are formed substantially parallel to the tooth trace direction D_Tr on the tooth flank of the workpiece W1. Although the grinding marks Gr_W1 are not linear but comprised of numerous arcs with small angles, overall, they are substantially parallel to the tooth trace direction D_Tr. Therefore, the reference crossed-axes angle θ1 can be considered the crossed-axes angle for forming the grinding marks Gr_W1 on the gear tooth flank of the workpiece W1 by the threaded grinding wheel T in a direction parallel to the tooth trace direction D_Tr.

[0048] Returning to Figure 5, the following explanation will be given. Once the reference crossed-axes angle θ1 is determined (S3), a corrected crossed-axes angle Δθ is then determined (S4). As shown in Figure 4(a), the corrected crossed-axes angle Δθ is the angle for forming grinding marks Gr1 on the tooth flank of the gear on the workpiece W by the threaded grinding wheel T in a direction inclined by a predetermined angle Σ with respect to the tooth trace direction D_Tr.

[0049] The corrective axis-crossing angle Δθ will be described with reference to FIGS. 8 and 9. As shown in FIGS. 8(a) and 8(b), the corrective axis-crossing angle Δθ is an axis-crossing angle that is added to the reference axis-crossing angle θ1. In other words, by adding the corrective axis-crossing angle Δθ, the axis-crossing angle between the rotation axis B2 of the workpiece W2 and the rotation axis C of the threaded grinding wheel T becomes a composite axis-crossing angle θ2, which is a combination of the reference axis-crossing angle θ1 and the corrective axis-crossing angle Δθ. The corrective axis-crossing angle Δθ may be either a positive value or a negative value.

[0050] When the tooth flanks of the gear of the workpiece W1 are ground with the threaded grinding wheel T in a state where a resultant cross-axis angle θ2 is set, where the corrected cross-axis angle Δθ is added to the reference cross-axis angle θ1, a grinding point P2a on one tooth flank and a grinding point P2b on the other tooth flank of the workpiece W2 are ground with the threaded grinding wheel T, as shown in FIGS. 8(b) and 8(c). When projected in the direction shown in FIG. 8(b), the grinding point P2a is located above the rotation axis C of the threaded grinding wheel T, and the grinding point P2b is located below the rotation axis C of the threaded grinding wheel T. When projected in the direction shown in FIG. 8(c), the grinding point P2a is located above Xt and Xw, and the grinding point P2b is located below Xt and Xw.

[0051] As shown in Figure 8(c), at grinding points P2a and P2b, the threaded grinding wheel T rotates around the C axis, and therefore the abrasive grains on the convex cutting edge of the threaded grinding wheel T rotate around the C axis. Therefore, at grinding point P2a, the abrasive grains on the convex cutting edge of the threaded grinding wheel T move in the upper right direction in Figure 8(c). On the other hand, at grinding point P2b, the abrasive grains on the convex cutting edge of the threaded grinding wheel T move in the upper left direction in Figure 8(c).

[0052] At grinding points P2a and P2b, the movement direction vectors of the abrasive grains on the convex cutting edge of the threaded grinding wheel T are denoted as V2a and V2b, respectively. As shown in FIG. 8(c), when viewed from the axial direction of the threaded grinding wheel T (when projected in the axial direction of the threaded grinding wheel T), angles α and β are formed between the tooth trace direction D_Tr of the gear of the workpiece W2 and the velocity vector due to the rotation of the threaded grinding wheel T at grinding points P2a and P2b on the convex cutting edge of the threaded grinding wheel T (the components of V2a and V2b on the paper in FIG. 8(c)). In other words, when projected onto an action plane representing the tooth surface of the workpiece W2, an angle is formed between the component on the action plane of the tooth trace direction D_Tr of the gear of the workpiece W2 and the component on the action plane of the velocity vector due to the rotation of the threaded grinding wheel T at grinding points P2a and P2b.

[0053] The enlarged view of FIG. 9(a) shows a movement direction vector V2a of the abrasive grains of the convex cutting edge of the threaded grinding wheel T at a grinding point P2a on one tooth flank of the workpiece W2. As shown in FIGS. 9(b) and 9(c), grinding marks Gr_W2 are formed on one tooth flank of the workpiece W2 by the abrasive grains of the convex cutting edge of the threaded grinding wheel T. That is, the grinding marks Gr_W2 are formed in a direction inclined at a predetermined angle Σ with respect to the tooth trace direction D_Tr of the tooth flank of the workpiece W2. Although the grinding marks Gr_W2 are not linear but comprised of numerous arcs with small angles, they are generally formed in a direction inclined at a predetermined angle Σ with respect to the tooth trace direction D_Tr. Therefore, the corrected cross-axis angle Δθ can be considered to be the cross-axis angle for forming the grinding marks Gr_W2 on the gear tooth flank of the workpiece W1 by the threaded grinding wheel T in a direction inclined at a predetermined angle Σ with respect to the tooth trace direction D_Tr.

[0054] As shown in Fig. 9(c), grinding marks Gr_W2 on one tooth flank of the gear of workpiece W2 are formed in a direction inclined at a predetermined positive angle Σ with respect to the tooth trace direction D_Tr. Although not shown, grinding marks Gr_W2 on the other tooth flank of the gear of workpiece W2 are formed in a direction inclined at a predetermined negative angle (-Σ) with respect to the tooth trace direction D_Tr.

[0055] The method for determining the correction axis-crossing angle Δθ, i.e., the correction axis-crossing angle determining step S4, will be described in detail with reference to Fig. 5 and Figs. 10 to 12. First, as shown in Fig. 5, a temporary correction axis-crossing angle Δθ' is determined (S41). The temporary correction axis-crossing angle Δθ' that is initially determined is an arbitrary value and serves as an initial value for determining the correction axis-crossing angle Δθ.

[0056] Next, as shown in FIGS. 5 and 10, when the workpiece W2 is rotated around the B2 axis, a tooth surface normal component vector Gv (referred to as a tooth surface normal component vector) of the velocity vector Gm of a grinding point P2 on the tooth surface of the gear of the workpiece W2 is calculated (S42). Here, the grinding point P2 is set as a plurality of discrete points on a cross section perpendicular to the tooth trace direction D_Tr on the tooth surface of the workpiece W2. The plurality of grinding points P2 are indicated by white and black circles in FIG. 10. Also, in FIG. 10, the velocity vector Gm and the normal component vector Gv are indicated for the grinding point P2 indicated by the black circle.

[0057] Next, a provisional corrected cross-axis angle Δθ' is applied as the corrected cross-axis angle Δθ. That is, a provisional resultant cross-axis angle θ2' is set by adding the provisional corrected cross-axis angle Δθ' to the reference cross-axis angle θ1. Here, as shown in FIG. 11 , when the threaded grinding wheel T is moved relative to the workpiece W2, the velocity vector (referred to as the grinding wheel velocity vector) of point Pt' on the convex cutting edge of the threaded grinding wheel T is designated as Tm'. Then, the tooth flank normal component vector Gv at grinding point P2 on the tooth flank of the workpiece W2 shown in FIG. 10 and the component Tv' (referred to as the grinding wheel normal component vector) in the direction of the tooth flank normal component vector Gv of the grinding wheel velocity vector Tm' at point Pt' of the threaded grinding wheel T shown in FIG. 11 are calculated. That is, the direction of the tooth flank normal component vector Gv on the workpiece W2 coincides with the direction of the grinding wheel normal component vector Tv' on the threaded grinding wheel T. Then, a point Pt' on the convex cutting edge of the threaded grinding wheel T is determined when the magnitude of the tooth surface normal component vector Gv of the workpiece W2 matches the magnitude of the grinding wheel normal component vector Tv' of the threaded grinding wheel T. The determined point Pt' on the convex cutting edge is set as a temporary grinding wheel point Pt' (S43).

[0058] Next, as shown in Fig. 5 and Fig. 11, a tangent vector Th' of the convex cutting edge of the threaded grinding wheel T is calculated (S44). More specifically, by determining the temporary grinding wheel point Pt' in S43, the normal cross-sectional shape of the convex cutting edge of the threaded grinding wheel T is determined, as shown by the two-dot chain line in Fig. 11. Then, a tangent vector Th' is calculated, which is a vector in a direction perpendicular to the normal cross-section of the convex cutting edge, out of the grinding wheel velocity vector Tm' of the temporary grinding wheel point Pt' on the convex cutting edge of the threaded grinding wheel T. This tangent vector Th' corresponds to the movement direction vector V2a of the abrasive grains of the convex cutting edge of the threaded grinding wheel T shown in Fig. 9(a).

[0059] Next, it is determined whether or not the tangent vector Th' of the threaded grinding wheel T at a predetermined grinding point P2 (for example, the center point of the tooth depth) on the tooth surface of the workpiece W2 coincides with the direction of a preset target grinding mark Gr_W2 (S45). At this time, when comparing with the meshing progression angle, the tangent vector Th' is projected onto the plane of action representing the tooth surface of the workpiece W2 and compared with the angle on the plane of action.

[0060] If it is determined that the tangent vector Th' coincides with the direction of the target grinding streak Gr_W2 (S45: Yes), the temporary grinding wheel point Pt' is determined as the grinding wheel shape point Pt, and the temporary corrected axis-crossing angle Δθ' when they coincide is determined as the corrected axis-crossing angle Δθ (S46). On the other hand, if it is determined that the tangent vector Th' does not coincide with the direction of the target grinding streak Gr_W2 (S45: No), the process returns to S41, a new temporary corrected axis-crossing angle Δθ' is determined, and the processes from S42 onwards are carried out.

[0061] That is, in the corrected-axis-crossing-angle determining step S4, a provisional corrected axis-crossing-angle Δθ' is found so that the tangent vector Th' of the threaded grinding wheel T at a predetermined grinding point P2 (for example, a point at the center of the tooth depth) on the tooth surface of the workpiece W2 coincides with the direction of the target grinding mark Gr_W2. Then, in the process of the corrected-axis-crossing-angle determining step S4, as shown in Fig. 10, the same process is performed for multiple grinding points P2 on the tooth surface of the workpiece W2, and grinding wheel shape points Pt corresponding to all of the grinding points P2 are determined.

[0062] Next, as shown in FIG. 5, a composite axis-crossing angle θ2 is determined by combining the reference axis-crossing angle θ1 determined in S3 with the correction axis-crossing angle Δθ determined in S4 (S5).

[0063] Next, as shown in Fig. 5, with the cross-axis angle between the rotation axis B2 of the workpiece W2 and the rotation axis C of the threaded grinding wheel T set to a composite cross-axis angle θ2, the shape of the convex cutting edge of the threaded grinding wheel T is determined based on a plurality of grinding wheel form points Pt (S6). Specifically, as shown in Fig. 12, the cross-sectional shape of the convex cutting edge of the threaded grinding wheel T is determined based on the grinding wheel form points Pt that correspond to each grinding point P2 on the gear tooth flank of the workpiece W2.

[0064] If the corrected cross-axis angle Δθ is zero, that is, if the cross-axis angle between the rotation axis B1 of the workpiece W1 and the rotation axis C of the threaded grinding wheel T as shown in Figures 6 and 7 is set to the reference cross-axis angle θ1, the cross-sectional shape of the convex cutting edge of the threaded grinding wheel T will be the shape shown in Figure 13. In other words, grinding wheel form points Pt corresponding to each grinding point P1 on the gear tooth flank of the workpiece W1 are determined, and the cross-sectional shape of the convex cutting edge of the threaded grinding wheel T is determined based on the grinding wheel form points Pt.

[0065] It can be seen that the cross-sectional shape of the convex cutting edge of the threaded grinding wheel T when the correction axis-crossing angle Δθ shown in FIG. 12 is taken into consideration has a smaller width (left-right width in FIGS. 12 and 13 ) and a larger protrusion amount (up-down height in FIGS. 12 and 13 ) than the cross-sectional shape of the convex cutting edge of the threaded grinding wheel T when the correction axis-crossing angle Δθ is not taken into consideration, as shown in FIG. 13 .

[0066] As described above, the grinding condition determination unit 8 determines the reference crossed-axes angle θ1 and the corrected crossed-axes angle Δθ, and determines the resultant crossed-axes angle θ2 as one of the grinding conditions by combining the determined reference crossed-axes angle θ1 and the corrected crossed-axes angle Δθ. Furthermore, the grinding condition determination unit 8 determines the convex cutting edge shape of the threaded grinding wheel T as one of the grinding conditions. The determined convex cutting edge of the threaded grinding wheel T is configured to be able to simultaneously grind both tooth flanks of the gear on the workpiece W2.

[0067] 5. Processing by Grinding Processing Unit 9 The following describes the processing (grinding step Sb) performed by the grinding processing unit 9. The grinding processing unit 9 applies the grinding conditions determined by the grinding condition determination unit 8 and grinds the tooth flank of the gear of the workpiece W with a threaded grinding wheel T.

[0068] 8(a), (b), and (c), the grinding processing unit 9 positions the workpiece W2, which is a helical gear, and the threaded grinding wheel T. The cross-axis angle between the rotation axis B2 of the workpiece W2 and the rotation axis C of the threaded grinding wheel T is set to a composite cross-axis angle θ2. The workpiece W2 and the threaded grinding wheel T are then rotated synchronously, and the threaded grinding wheel T is moved relatively in a direction parallel to the rotation axis B2 of the workpiece W2.

[0069] As a result, as shown in FIG. 8(b), both tooth flanks of the gear of the workpiece W2 are ground simultaneously using the threaded grinding wheel T. As shown in FIGS. 9(b) and 9(c), grinding marks Gr_W2 are formed on the tooth flank of the ground workpiece W2 by the threaded grinding wheel T. The formed grinding marks Gr_W2 are formed in a direction inclined at a predetermined angle Σ with respect to the tooth trace direction D_Tr. In particular, the extension direction of the formed grinding marks Gr_W2 coincides with the meshing progression direction D_La on the tooth flank of the workpiece W2. In other words, the predetermined angle Σ is set to the angle between the tooth trace direction D_Tr of the tooth flank of the driven gear Gb (shown in FIG. 3) as the workpiece W2 and the meshing progression direction D_La of the driving gear Ga, which is the mating gear. This reduces meshing noise.

[0070] 6.Effects According to this embodiment, when grinding the tooth flank of the gear of the workpiece W2 using the threaded grinding wheel T, a crossed-axes angle between the rotation axis B2 of the workpiece W2 and the rotation axis C of the threaded grinding wheel T is set. The crossed-axes angle obtained by the helix angle φw on the reference circle of the gear of the workpiece W2 and the helix angle φt on the reference circle of the threaded grinding wheel T is defined as the reference crossed-axes angle θ1. In this embodiment, the gear of the workpiece W2 is a helical gear. Therefore, the helix angle φw on the reference circle of the gear of the workpiece W2 is not 0°. In this case, the reference crossed-axes angle θ1 is an angle that takes into account the helix angle φw on the reference circle of the gear of the workpiece W2 relative to the helix angle φt on the reference circle of the threaded grinding wheel T.

[0071] 6 and 7, if the cross-axis angle is set to the reference cross-axis angle θ1 and the gear tooth flank of the workpiece W1 is ground, the grinding marks Gr_W1 formed on the gear tooth flank of the workpiece W1 by the threaded grinding wheel T will be parallel to the tooth trace direction D_Tr on the tooth flank. Therefore, in this embodiment, the cross-axis angle between the rotation axis B2 of the workpiece W2 and the rotation axis C of the threaded grinding wheel T is set to a composite cross-axis angle θ2 obtained by combining the reference cross-axis angle θ1 and the corrected cross-axis angle Δθ, as shown in FIGS.

[0072] The corrected cross-axis angle Δθ is the cross-axis angle for forming grinding marks Gr_W2 on the tooth surface of the gear of the workpiece W2 by the threaded grinding wheel T in a direction inclined at a predetermined angle Σ with respect to the tooth trace direction D_Tr. In other words, by setting the cross-axis angle during grinding to a composite cross-axis angle θ2 obtained by combining the reference cross-axis angle θ1 and the corrected cross-axis angle Δθ, the grinding marks Gr_W2 are not parallel to the tooth trace direction D_Tr but are inclined toward the tooth trace direction D_Tr.

[0073] Because the grinding marks Gr_W2 can be formed in a direction inclined toward the tooth trace direction D_Tr, for example, when the gear to be ground and the mating gear mesh, the direction in which the grinding marks Gr_W2 extend can be aligned with the meshing progression direction D_La on the tooth flank of the gear to be ground. When these two directions are aligned, the mating gear Ga does not climb over the grinding marks Gr_W2 on the tooth flank as the gears mesh. Since the grinding marks Gr_W2 do not climb over the grinding marks Gr_W2, noise generated during gear meshing can be reduced.

[0074] Furthermore, even if the direction in which the grinding marks Gr_W2 extend is not aligned with the meshing direction D_La, by bringing the direction in which the grinding marks Gr_W2 extend closer to the meshing direction D_La, it is possible to reduce the overriding action of the grinding marks Gr_W2, thereby reducing noise generated during meshing of the gears.

[0075] In particular, by using a helical gear as the workpiece W2, it is possible to make the direction in which the grinding marks Gr_W2 extend substantially coincide with the meshing direction D_La, thereby reducing noise generated when the helical gears mesh.

[0076] As a result, noise caused by the influence of steps on the gear tooth surfaces during gear meshing can be reduced without additional processing.

[0077] In this embodiment, as shown in FIG. 8, the threaded grinding wheel T is configured to be able to simultaneously grind both tooth flanks of the gear on the workpiece W2, and the grinding process Sb by the grinding processing unit 9 simultaneously grinds both tooth flanks of the gear on the workpiece W2 with the threaded grinding wheel T. As shown in FIG. 9, the grinding marks Gr_W2 on one tooth flank of the gear on the workpiece W2 are formed in a direction inclined at a predetermined positive angle Σ with respect to the tooth trace direction D_Tr. Meanwhile, the grinding marks Gr_W2 on the other tooth flank of the gear on the workpiece W2 are formed in a direction inclined at a predetermined negative angle (-Σ) with respect to the tooth trace direction D_Tr. In this way, when the direction of the grinding marks Gr_W2 satisfies the above condition, both tooth flanks can be ground simultaneously, thereby reducing the number of grinding man-hours.

[0078] (Embodiment 2) In the first embodiment, the workpiece W is described as a helical gear having a helix angle φw. Alternatively, the workpiece W may be a spur gear, as shown in FIG. 14. When the workpiece W is a spur gear, the helix angle on the reference circle is 0°. As shown in FIG. 14, in the workpiece W, which is a spur gear, the meshing direction D_La of the mating gear coincides with the tooth depth direction D_Hi.

[0079] If the extension direction of the grinding marks Gr_W were formed parallel to the tooth trace direction D_Tr, the meshing point would have to cross the grinding marks Gr_W many times, causing meshing noise. Therefore, as shown in Fig. 14, the extension direction of the grinding marks Gr_W is inclined at an angle relative to the tooth trace direction D_Tr and also at an angle relative to the tooth depth direction D_Hi. In other words, the extension direction of the grinding marks Gr_W is inclined relative to the meshing progression direction D_La, but at an angle smaller than perpendicular.

[0080] As explained in the first embodiment, by aligning the extension direction of the grinding marks Gr_W with the meshing direction D_La, noise caused by the meshing point climbing over the grinding marks Gr_W can be significantly reduced. However, the grinding marks Gr_W cannot be formed in a direction parallel to the tooth depth direction D_Hi. Therefore, the grinding marks Gr_W are set in a direction as close as possible to the meshing direction D_La.

[0081] (Embodiment 3) In the above embodiment, an example has been given in which both tooth flanks of a gear on a workpiece W are ground simultaneously by the threaded grinding wheel T. Alternatively, the threaded grinding wheel T may be configured to grind only one tooth flank of a gear on a workpiece W. The threaded grinding wheel T is formed as shown in FIG. 15. In other words, the convex cutting edge of the threaded grinding wheel T has only one side of the convex cutting edge of the threaded grinding wheel T determined in embodiment 1.

[0082] In the first embodiment, both tooth flanks of the workpiece W are ground simultaneously, and thus when the extending direction of the grinding marks Gr_W2 on one tooth flank is determined, the extending direction of the grinding marks Gr_W2 on the other tooth flank is necessarily determined. Therefore, in order to freely set the extending direction of the grinding marks Gr_W2 for each tooth flank, it is advisable to use a threaded grinding wheel T as shown in Fig. 15. In this case, one tooth flank is ground with the threaded grinding wheel T shown in Fig. 15, and the other tooth flank is ground with a threaded grinding wheel not shown.

Claims

1. A gear grinding method for grinding a tooth surface of a gear (Gb1) using a threaded grinding wheel (T), comprising: a grinding step (Sb) in which an axis-crossing angle between a rotation axis (B2) of a workpiece (W2) and a rotation axis (C) of the threaded grinding wheel is set to a composite axis-crossing angle (θ2) obtained by combining a reference axis-crossing angle (θ1) and a corrected axis-crossing angle (Δθ), the threaded grinding wheel and the workpiece are rotated synchronously, and the threaded grinding wheel is moved relatively in a direction parallel to the rotation axis of the workpiece to grind the tooth flank of the gear, the reference crossed axes angle is an axis crossed angle determined based on a helix angle (φw) on a reference circle of the gear and a helix angle (φt) on a reference circle of the threaded grinding wheel, the corrected cross-axis angle is an axis-crossing angle for forming grinding marks (Gr_W2) on the tooth surface of the gear by the threaded grinding wheel in a direction inclined at a predetermined angle (Σ) with respect to a tooth trace direction (D_Tr).

2. 2. The gear grinding method according to claim 1, wherein the reference crossed axes angle is an axis-crossed angle for forming the grinding marks on the tooth flanks of the gear by the threaded grinding wheel in a direction parallel to a tooth trace direction.

3. 3. The gear grinding method according to claim 1, wherein, when viewed from an axial direction of the threaded grinding wheel, an angle exists between a tooth trace direction of the gear and a velocity vector caused by rotation of the threaded grinding wheel at a grinding point on a convex cutting edge of the threaded grinding wheel.

4. the threaded grinding wheel is configured to be able to simultaneously grind both tooth flanks of the gear of the workpiece, the grinding marks on one tooth surface of the gear are formed in a direction inclined at a positive predetermined angle with respect to the tooth trace direction, the grinding marks on the other tooth surface of the gear are formed in a direction inclined at a predetermined negative angle with respect to the tooth trace direction, 4. The gear grinding method according to claim 1, wherein the grinding step simultaneously grinds both tooth flanks of the gear on the workpiece with the threaded grinding wheel.

5. the threaded grinding wheel is configured to be capable of grinding only one tooth surface of the gear of the workpiece, 4. The gear grinding method according to claim 1, wherein the grinding step grinds only one tooth flank of the gear in the workpiece with the threaded grinding wheel.

6. a grinding condition determination step (Sa) of determining grinding conditions including the convex cutting edge shape of the threaded grinding wheel and the composite axis crossing angle; a grinding step (Sb) of grinding the tooth flank of the gear using the threaded grinding wheel based on the determined grinding conditions; The gear grinding method according to any one of claims 1 to 5, comprising:

7. The grinding condition determination step (Sa) a reference crossed axes angle determining step (S3) of determining the reference crossed axes angle based on the helix angle on the reference circle of the gear and the helix angle on the reference circle of the threaded grinding wheel; a corrected-axis-crossing-angle determining step (S4) of determining a corrected-axis-crossing-angle angle for forming the grinding marks on the tooth surface of the gear on the workpiece by the threaded grinding wheel in a direction inclined by the predetermined angle with respect to a tooth trace direction; a convex cutting edge shape determination step (S6) of determining the convex cutting edge shape of the threaded grinding wheel in a state in which an axis-crossing angle between the rotation axis of the workpiece and the rotation axis of the threaded grinding wheel is set to the composite axis-crossing angle; 7. The gear grinding method of claim 6, comprising:

8. The corrected axis-crossing angle determining step includes: calculating a tooth surface normal component vector (Gv) that is a normal component vector of the tooth surface of the velocity vector of the grinding point on the tooth surface of the gear when the workpiece is rotated; a temporary corrected cross-axes angle is set as the corrected cross-axes angle, and the threaded grinding wheel is moved relative to the workpiece; calculating a grinding wheel normal component vector (Tv') that is a component in the direction of the tooth flank normal component vector of a velocity vector of a temporary grinding wheel point (Pt') on the convex cutting edge of the threaded grinding wheel, and determining the temporary grinding wheel point when a magnitude of the tooth flank normal component vector and a magnitude of the grinding wheel normal component vector match; Calculating a tangent vector (Th') of the convex cutting edge from among the velocity vectors of the determined temporary grindstone point; determining whether the tangent vector coincides with a predetermined direction of the grinding streak, and determining the temporary grinding wheel point when the tangent vector coincides as a grinding wheel shape point (Pt), and determining the temporary corrected axis-crossing angle when the tangent vector coincides as the corrected axis-crossing angle; The gear grinding method according to claim 7 , further comprising determining the convex cutting edge shape of the threaded grinding wheel based on the determined grinding wheel shape points.

9. the gear is a helical gear, 9. The gear grinding method according to claim 1, wherein the predetermined angle is set to an angle between a tooth trace direction of a tooth surface of the gear and a meshing direction of a mating gear.

10. the gear is a spur gear, The gear grinding method according to any one of claims 1 to 8, wherein the predetermined angle is set to an angle inclined with respect to a tooth trace direction of the tooth flank of the gear and with respect to a meshing progression direction of a mating gear.

11. A gear grinding device (1) that grinds the tooth surface of a gear (Gb1) using a threaded grinding wheel (T), a grinding processing unit (9) that grinds the tooth flanks of the gear by setting an axis-crossing angle between a rotation axis (B2) of a workpiece (W2) and a rotation axis (C) of the threaded grinding wheel to a composite axis-crossing angle (θ2) obtained by combining a reference axis-crossing angle (θ1) and a corrected axis-crossing angle (Δθ), rotating the threaded grinding wheel and the workpiece synchronously, and moving the threaded grinding wheel relatively in a direction parallel to the rotation axis of the workpiece; the reference crossed axes angle is an axis crossed angle determined based on a helix angle (φw) on a reference circle of the gear and a helix angle (φt) on a reference circle of the threaded grinding wheel, the corrected cross-axis angle is an axis-crossing angle for forming grinding marks (Gr_W2) on the tooth surface of the gear by the threaded grinding wheel in a direction inclined at a predetermined angle (Σ) with respect to a tooth trace direction (D_Tr).

12. a grinding condition determination unit (8) that determines grinding conditions including the convex cutting edge shape of the threaded grinding wheel and the composite axis crossing angle; the grinding processing unit (9) that grinds the tooth surface of the gear using the threaded grinding wheel based on the determined grinding conditions; 12. The gear grinding apparatus of claim 11, comprising:

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