Machining method for Gothic arc-shaped grooves

Abstract

When forming a Gothic arc-shaped groove in a workpiece using a form tool, even when using a form tool with low shape accuracy, the contact angle and the difference in contact angle between the left and right sides can be easily adjusted, enabling the satisfaction of tolerance requirements. [Solution] A mold tool 1 is used in which the width W1 of the cutting edge 2 is narrower than the width W2 of the groove 4 to be formed. A first machining step P1 is performed in which the cutting edge 2 is driven into the workpiece 3. A second machining step P2 is performed in which the position of the cutting edge 2 is shifted within the range of the width W2 of the groove 4 to be formed, and the cutting edge 2 is driven into the workpiece 3 again. Then, by adjusting (1) the cutting depth D1 when forming the arc 4a of the groove 4, (2) the cutting depth D2 when forming the arc 4b, and (3) the distance S of the positional shift between (1) and (2), the contact angles θa, θb and the difference between the left and right contact angles (the difference between θa and θb) are adjusted. In addition, if the shape accuracy of the mold tool 1 is low, the cutting depths D1 and D2 are made different.

Description

Technical Field

[0001] The present disclosure relates to a method of forming a Gothic arc-shaped groove in a workpiece by cutting using a master tool.

Background Art

[0002] As a mechanism for transporting and positioning a workpiece in a machine tool, a ball screw mechanism may be employed. The screw groove in which balls (steel balls) roll in the ball screw mechanism typically has a Gothic arc-shaped cross-sectional shape.

[0003] When forming a Gothic arc-shaped groove, in many cases, a master tool 100 as shown in FIG. 7 is used, and a Gothic arc-shaped groove 300 is formed in a workpiece 200 by cutting. The cutting edge portion 110 of the master tool 100 has the same cross-sectional shape as the groove 300 to be processed. Specifically, the cutting edge portion 110 has an arc-shaped cutting edge portion 110a with the same radius as the arc 300a of the groove 300, and an arc-shaped cutting edge portion 110b with the same radius as the arc 300b.

[0004] When the Gothic arc-shaped groove 300 is ideally formed, the groove 300 has two arcs 300a and 300b that are symmetrically formed with respect to the groove center line 300x. The radii Ra and Rb of the arcs 300a and 300b are equal dimensions. The centers Oa and Ob of the arcs 300a and 300b are located on the opposite sides of the arcs 300a and 300b across the groove center line 300x, respectively. Also, the centers Oa and Ob of the arcs 300a and 300b are displaced by the same distance in the groove width direction (left-right direction in FIG. 7) with respect to the groove center line 300x.

[0005] As shown in FIG. 8, a ball 400, which is a component of the ball screw mechanism, contacts the groove 300 at contact points A and B. In an ideally formed groove 300, the contact angle θa on the arc 300a side (left side) and the contact angle θb on the arc 300b side (right side) are equal angles. That is, the difference between the contact angle θa and the contact angle θb (hereinafter, the difference between the contact angle θa and the contact angle θb is referred to as the "left-right contact angle difference") is zero.

[0006] Although not using a form tool, Patent Documents 1 and 2 disclose methods for forming Gothic arc-shaped grooves in a workpiece.

[0007] In the embodiment disclosed in Patent Document 1 (see Figures 1 to 5 in particular), when forming a Gothic arc-shaped groove 1 having an arc 2a on the left side of the groove centerline S and an arc 2b on the right side, a left-hand cutting tool 11a and a right-hand cutting tool 11b are used. The cutting tools 11a and 11b are tools for machining the left and right cross-sections of the groove 1, respectively. The cutting tools 11a and 11b each have arc-shaped cutting edges 14a and 14b for forming the arcs 2a and 2b of the groove 1.

[0008] The left-handed cutting tool 11a and the right-handed cutting tool 11b are held in the tool holder 20, respectively, with their positions offset from each other in the cutting direction. Adjustment shims 26 of the same thickness are interposed between the left-handed cutting tool 11a and the tool holder 20, and between the right-handed cutting tool 11b and the tool holder 20. By changing the thickness of the adjustment shims 26, the distance between the cutting tools 11a, 11b and the tool holder 20 is adjusted. Along with this adjustment, the contact angle α on the arc 2a side (left side) and the contact angle α on the arc 2b side (right side) when the groove 1 and the rolling element 3 come into contact are adjusted.

[0009] In the embodiment disclosed in Patent Document 2 (see Figure 1 in particular), when forming a Gothic arc-shaped groove 5, a general-purpose cutting tool 8 is used in which the radius of curvature of the nose of the cutting edge 8a is smaller than the radius of curvature of the arc of the groove 5. Specifically, the general-purpose cutting tool 8 is moved multiple times for the effective length of the groove 5, and the entire groove 5 is formed by sequentially shifting the movement paths P1, P2 to Pn in the arc direction of the cross-sectional shape of the groove 5. [Prior art documents] [Patent Documents]

[0010] [Patent Document 1] Japanese Patent Publication No. 2005-1003 [Patent Document 2] Japanese Patent Application Publication No. 6-249317 [Overview of the project] [Problems that the invention aims to solve]

[0011] In Gothic arc grooves, strict tolerance requirements must be met for the contact angle and the difference in contact angle between the left and right sides. In other words, the contact angle must be set to the desired angle, and the difference in contact angle between the left and right sides must be approximately zero. For this reason, when forming grooves using a form tool, it was necessary to prepare a form tool with high shape accuracy to satisfy the tolerance requirements, but this was difficult. Specifically, in the cutting edge portion 110 of the form tool 100 shown in Figure 7, it is extremely difficult to form the arc-shaped cutting edge portion 110a and the arc-shaped cutting edge portion 110b substantially symmetrically to the extent that the tolerance requirements are satisfied.

[0012] Therefore, instead of forming grooves using a form tool, it is conceivable to adopt the embodiments disclosed in the above-mentioned Patent Documents 1 and 2, and to satisfy strict tolerance requirements by adjusting the contact angle and the difference in contact angle between the left and right sides.

[0013] However, in the embodiment disclosed in Patent Document 1, the thickness of the adjustment shim 26 had to be changed each time to adjust the left and right contact angles α, α, making it impossible to quickly adjust the left and right contact angles α, α. Furthermore, in the embodiment disclosed in Patent Document 1, it is not possible to adjust the difference in contact angles between the left and right sides (the difference between the left contact angle α and the right contact angle α).

[0014] On the other hand, in the embodiment disclosed in Patent Document 2, both the contact angle and the difference in contact angle between the left and right sides can be adjusted, but it is not possible to perform these adjustments quickly. This is because, in that embodiment, it is necessary to move the general-purpose cutting tool 8 by the effective length of the groove 5 over the same number of times as the number of movement paths P1, P2 to Pn. Therefore, the time required for machining the groove 5 itself inevitably becomes long.

[0015] As previously described, the embodiments disclosed in Patent Documents 1 and 2 cannot be considered an effective alternative to groove formation using a full-form tool in satisfying tolerance requirements for contact angle and left-right contact angle difference. Therefore, there has been a need for a technology that can easily adjust the contact angle and left-right contact angle difference, and satisfy tolerance requirements, even when using a full-form tool with low shape accuracy.

[0016] In light of the circumstances described above, the challenge to be addressed is to enable easy adjustment of the contact angle and the difference in contact angle between left and right sides, even when using a form tool with low shape accuracy, when forming a Gothic arc-shaped groove in a workpiece using a form tool, thereby ensuring that tolerance requirements are met. [Means for solving the problem]

[0017] A first method for machining a Gothic arc-shaped groove to solve the above problems is a method for machining a Gothic arc-shaped groove that includes a machining step of cutting a workpiece with the cutting edge of a die tool to form a Gothic arc-shaped groove in the workpiece, wherein the machining step uses a die tool whose cutting edge width is narrower than the width of the groove to be formed, and the machining step includes a first machining step of cutting the cutting edge into the workpiece, and a second machining step of shifting the position of the cutting edge in the width direction from the first machining step within the width range of the groove to be formed, and then cutting the cutting edge into the workpiece again.

[0018] In the first method for machining a Gothic arc-shaped groove, a full-form tool is used in the machining process, in which the width of the cutting edge is narrower than the width of the groove formed in the same process. With a machining process using such a full-form tool, the contact angle and the difference in contact angle between the left and right sides of the groove can be easily adjusted in conjunction with the execution of the first and second machining processes. In other words, the contact angle can be easily set to the desired angle, and the difference in contact angle between the left and right sides can be easily reduced to approximately zero. Specifically, in this machining process, all that is required to adjust the contact angle and the difference in contact angle between the left and right sides of the groove is to adjust (1) to (3) in conjunction with the execution of the first and second machining processes: (1) the depth to which the cutting edge is cut into the workpiece when forming the arc on one side of the groove, (2) the depth to which the cutting edge is cut into the workpiece when forming the arc on the other side of the groove, and (3) the positional displacement distance in the groove width direction between the cutting position in (1) and the cutting position in (2). Here, if the shape accuracy of the mold tool (blade portion) is low and the arc-shaped blade portion on one side of the blade portion is not formed symmetrically with respect to the other side, the depth of cut in (1) above and the depth of cut in (2) above are made different. On the other hand, if the shape accuracy of the mold tool (blade portion) is high and the arc-shaped blade portion on one side of the blade portion is formed substantially symmetrically with respect to the other side, the depth of cut in (1) above and the depth of cut in (2) above are made substantially the same. As described above, according to the first Gothic arc groove machining method, even when using a mold tool with low shape accuracy, the contact angle and the difference in contact angle between the left and right sides can be easily adjusted by simply adjusting (1) to (3) above, and tolerance requirements can be satisfied.

[0019] The second method for machining a Gothic arc groove involves performing the second machining step multiple times in the first machining method described above. These multiple steps include shifting the position of the cutting edge to one side in the width direction and shifting it to the other side in the width direction. The depth to which the cutting edge penetrates the workpiece differs between the shift to one side and the shift to the other side.

[0020] In the second method for machining Gothic arc grooves, one side of the groove can be formed by shifting the position of the cutting edge to one side in the width direction during one of the multiple second machining steps. Conversely, the other side of the groove can be formed by shifting the position of the cutting edge to the other side in the width direction during one of the steps. Furthermore, since the depth to which the cutting edge penetrates the workpiece differs between the steps where the edge is shifted to one side and the steps where it is shifted to the other side, it is possible to adjust the contact angle of the groove and the difference in contact angle between the left and right sides, even if the arc-shaped cutting edge on one side and the arc-shaped cutting edge on the other side are not formed symmetrically. Moreover, both the steps where the edge is shifted to one side and the steps where it is shifted to the other side are performed after the first machining step. Therefore, in the steps where the edge is shifted to one side and the steps where it is shifted to the other side, the amount of material to be cut is reduced because the workpiece has already been cut in the first machining step, thus reducing the load on the cutting process. As a result, in the second method for machining a Gothic arc-shaped groove, the first machining step can be used for rough machining and the second machining step for finishing, allowing for the precise formation of the arcs on one side and the other side of the groove.

[0021] The third method for machining a Gothic arc-shaped groove is a modification of the first machining method described above, in which the depth to which the cutting edge penetrates the workpiece is differed between the first and second machining steps.

[0022] In the third method for machining Gothic arc-shaped grooves, the first machining step can form the arc on one side of the groove. Furthermore, the second machining step can form the arc on the other side of the groove. In addition, since the depth to which the cutting edge penetrates the workpiece is different between the first and second machining steps, it is possible to adjust the contact angle and the difference in contact angle between the left and right sides of the groove, even if the arc-shaped cutting edge on one side of the cutting edge is not formed symmetrically. Moreover, in the third method for machining Gothic arc-shaped grooves, the groove can be formed by performing the first and second machining steps only once each. This makes it possible to complete the groove formation quickly.

[0023] The processing method of the fourth Gothic arc-shaped groove is that in the above-mentioned processing method of any one of the first to third, in the second processing step, a master tool different from the master tool used in the first processing step is used, and the different master tool has a form in which the width of the blade part is narrower than the width of the groove formed in the processing step.

[0024] Even when different master tools are used in the first processing step and the second processing step as in the processing method of the fourth Gothic arc-shaped groove, it is possible to easily adjust the contact angle of the groove and the difference in the contact angle between the left and right.

Advantages of the Invention

[0025] According to the processing method of the Gothic arc-shaped groove of the present disclosure, even when the shape accuracy of the master tool is low, the contact angle and the difference in the contact angle between the left and right can be easily adjusted, and it is possible to satisfy the tolerance requirements.

Brief Description of the Drawings

[0026] [Figure 1] It is a cross-sectional view showing a ball screw mechanism. [Figure 2] It is a perspective view showing a processing step in the processing method of a Gothic arc-shaped groove. [Figure 3] It is a cross-sectional view showing a master tool (blade part) and a workpiece. [Figure 4] Fig. 4(a) is a cross-sectional view showing the first processing step in the processing process, and Figs. 4(b) and 4(c) are cross-sectional views showing the second processing step in the processing process. [Figure 5] It is a cross-sectional view showing a Gothic arc-shaped groove formed in a workpiece. [Figure 6] Fig. 6(a) is a cross-sectional view showing the first processing step in the processing process, and Fig. 6(b) is a cross-sectional view showing the second processing step in the processing process. [Figure 7] It is a cross-sectional view showing a master tool and a Gothic arc-shaped groove formed in a workpiece. [Figure 8] It is a cross-sectional view showing a Gothic arc-shaped groove formed in a workpiece. [Modes for carrying out the invention]

[0027] The following describes an embodiment of the method for machining a Gothic arc groove, with reference to the attached drawings. In this embodiment, we will use the method for machining a Gothic arc groove that will become the screw groove of a ball screw mechanism as an example. First, before describing the method for machining a Gothic arc groove, we will explain the overview of the ball screw mechanism.

[0028] In the following explanation, "axial direction" refers to the direction in which the axis of the screw shaft 20 constituting the ball screw mechanism 10 extends, and "radial direction" refers to the direction radiating from the axis of the screw shaft 20.

[0029] Figure 1 is a cross-sectional view of the ball screw mechanism 10. The ball screw mechanism 10 shown in the figure comprises a screw shaft 20 having a helical male screw groove 20a formed on its outer circumference, a nut 30 having a helical female screw groove 30a formed on its inner circumference, a plurality of balls (e.g., steel balls) 40 interposed in a track 60 formed between the opposing male screw grooves 20a and female screw grooves 30a, and a circulating member 50 attached to the nut 30. The male screw groove 20a and female screw groove 30a are Gothic arc-shaped grooves.

[0030] The ball screw mechanism 10 can be used as a screw shaft rotation type or as a nut rotation type. In the screw shaft rotation type ball screw mechanism 10, the nut 30 moves back and forth in the axial direction (linear motion) as the screw shaft 20 rotates around its axis. On the other hand, in the nut rotation type ball screw mechanism 10, the screw shaft 20 moves back and forth in the axial direction as the nut 30 rotates around its axis. In the screw shaft rotation type ball screw mechanism 10, a rotation restricting means (not shown) is provided to restrict the rotation of the nut 30. On the other hand, in the nut rotation type ball screw mechanism 10, a rotation restricting means (not shown) is provided to restrict the rotation of the screw shaft 20.

[0031] The nut 30 is formed in a cylindrical shape from a metal material. End caps 50A, 50A, which serve as circulating members 50, are attached to one end and the other end of the nut 30 in the axial direction. Therefore, this ball screw mechanism 10 is an end cap type ball screw mechanism.

[0032] The nut 30 has a through hole 30b formed on the radially outer side of the female screw groove 30a, which penetrates the nut 30 axially. Each end cap 50A is annular (short cylindrical), and a groove 50a is formed on the end face facing the nut 30 to connect (connect) the longitudinal end of the track 60 and the longitudinal end of the through hole 30b. The groove 50a and the through hole 30b formed in the nut 30 form a circulation section 70 for circulating the balls 40 interposed in the track 60. When the screw shaft 20 and the nut 30 rotate relative to each other, the multiple balls 40 arranged in the ball passage 80 circulate along a series of ball passages 80 consisting of the track 60 and the circulation section 70. As a result, the rotating side of the screw shaft 20 and the nut 30 rotates smoothly, and the linear side moves smoothly in a straight line.

[0033] Next, we will explain the machining method for Gothic arc-shaped grooves.

[0034] <First Embodiment> As shown in Figure 2, the machining method for a Gothic arc-shaped groove according to the first embodiment includes a machining step P in which the workpiece 3 is cut by the cutting edge 2 of the general-purpose tool 1 to form a Gothic arc-shaped groove 4 in the workpiece 3. Machining step P includes a first machining step P1 and a second machining step P2, which will be described later, and both steps P1 and P2 are performed in the manner shown in Figure 2.

[0035] In the embodiment shown in Figure 2, the position and orientation of the form tool 1 are fixed. Meanwhile, the workpiece 3 is continuously fed in the direction indicated by arrow F in Figure 2. The workpiece 3 is formed in a cylindrical shape. In this embodiment, the workpiece 3 is fed in the direction of arrow F while rotating it around the axis of the cylinder, and the inner circumferential surface 3a of the workpiece 3 is continuously cut by the cutting edge 2 of the form tool 1 to form a groove 4.

[0036] Herein, as a modification of this embodiment, a Gothic arc-shaped groove may be formed on the outer surface of a cylindrical workpiece.

[0037] Figure 3 shows the form tool 1 used in machining process P. The form tool 1 is used in both the first and second machining processes P1 and P2, which will be described later. The form tool 1 has a cutting edge 2 for cutting the workpiece 3. The width W1 of the cutting edge 2 is narrower than the width W2 of the groove 4 formed in the workpiece 3 during machining process P. In Figure 3, the groove 4 formed in the workpiece 3 upon completion of machining process P is shown by a dashed line. The dimensional difference between the width W1 of the cutting edge 2 and the width W2 of the groove 4 is approximately 0.4 mm as an example.

[0038] The blade portion 2 of the overall tool 1 has a cross-sectional shape perpendicular to the cutting direction (perpendicular to the plane of the paper in Figure 3) that is formed in the shape of a Gothic arc. The blade portion 2 has two arc-shaped blade portions 2a and 2b, flanking a reference line 2x located approximately in the center of its width direction (left-right direction in Figure 3).

[0039] The form tool 1 of this embodiment has low shape accuracy, and the two arc-shaped cutting edges 2a and 2b of the cutting edge 2 are not formed symmetrically. Note that Figure 3 exaggerates the low shape accuracy of the form tool 1. The radius Ra of the arc-shaped cutting edge 2a is smaller than the radius Rb of the arc-shaped cutting edge 2b. The centers Oa and Ob of the arc-shaped cutting edges 2a and 2b are located on opposite sides of the reference line 2x from the arc-shaped cutting edges 2a and 2b, respectively. The distance shifted in the width direction from the reference line 2x is different between the center Oa of the arc-shaped cutting edge 2a and the center Ob of the arc-shaped cutting edge 2b.

[0040] The following describes the flow of the machining process P using the above-mentioned general-purpose tool 1, with reference to Figures 4(a) to 4(c). In this embodiment, the machining process P is performed to form a Gothic arc-shaped groove 4 with a cross-sectional shape having two arcs 4a and 4b.

[0041] The machining process P includes the first machining process P1 shown in Figure 4(a) and the second machining process P2 shown in Figures 4(b) and 4(c). The first machining process P1 is a process for rough machining of the groove 4, and the second machining process P2 is a process for finishing the groove 4. In this embodiment, the first machining process P1 is performed once and the second machining process P2 is performed twice.

[0042] In this Gothic arc groove machining method, three elements are adjusted: the cutting depth D1 shown in Figure 4(b), the cutting depth D2 shown in Figure 4(c), and the positional displacement distance S shown in Figure 4(c). By adjusting these three elements, the contact angles θa, θb and the left-right difference in contact angles (the difference between contact angle θa and contact angle θb) of groove 4 shown in Figure 5 are adjusted.

[0043] As shown in Figure 4(a), in the first machining step P1, the cutting edge 2 of the form tool 1 is made to cut into the inner circumferential surface 3a of the workpiece 3. At this time, the workpiece 3 is cut by both the arc-shaped cutting edge 2a and the arc-shaped cutting edge 2b of the cutting edge 2. This performs rough machining of the groove 4. In this embodiment, the cutting edge 2 is made to cut into the inner circumferential surface 3a of the workpiece 3 with the reference line 2x of the cutting edge 2 aligned with the center line 4x in the width direction of the groove 4 formed in machining step P.

[0044] At the completion of the first machining process P1, the two arcs 4a and 4b of the groove 4 are not yet formed. That is, there is remaining material to be cut on one side (left) and the other side (right) in the width direction, flanking the center line 4x of the groove 4. This material to be cut is the portion to be removed in the second machining process P2, following the first machining process P1. As an example, the width of the material to be cut on one side and the other side of the center line 4x of the groove 4 is approximately 0.2 mm (width on the inner circumferential surface 3a of the workpiece 3).

[0045] Here, the depth D into which the cutting edge 2 cuts into the workpiece 3 in the first machining step P1 can be any depth as long as it is less than or equal to the design depth of the groove 4. However, from the viewpoint of reducing the load on the workpiece 3 during the subsequent second machining step P2, it is preferable to determine the cutting depth D such that only a small amount of material remains to be removed when the first machining step P1 is completed.

[0046] As shown in Figures 4(b) and 4(c), in the second machining step P2, the position of the cutting edge 2 is shifted in the width direction from that of the first machining step P1, within the range of the width W2 of the groove 4 formed in machining step P. Then, the cutting edge 2 of the form tool 1 is made to cut into the inner circumferential surface 3a of the workpiece 3 again. This completes the finishing of the groove 4.

[0047] As previously described, the second machining process P2 is performed twice. In the first second machining process P2 shown in Figure 4(b), the position of the blade 2 is shifted to one side (left) in the width direction, relative to the position at the time of the first machining process P1. In contrast, in the second second machining process P2 shown in Figure 4(c), the position of the blade 2 is shifted to the other side (right) in the width direction, relative to the position at the time of the first machining process P1. The distance S shown in Figure 4(c) is the distance of the positional shift in the width direction between the position at which the blade 2 cuts into the workpiece 3 in the first second machining process P2 and the position at which the blade 2 cuts into the workpiece 3 in the second second machining process P2.

[0048] As shown in Figure 4(b), when the first second machining step P2 is performed, the workpiece 3 is cut by the arc-shaped cutting edge 2a of the cutting edge 2 by the amount of the cutting allowance mentioned above. As a result, of the two arcs 4a and 4b of the groove 4, the arc 4a, which has a relatively smaller radius, is formed. The radius of arc 4a is the same as the radius Ra of the arc-shaped cutting edge 2a.

[0049] On the other hand, as shown in Figure 4(c), when the second machining process P2 is performed a second time, the workpiece 3 is cut by the arc-shaped cutting edge 2b of the cutting edge 2 by the amount of the cutting allowance mentioned above. As a result, of the two arcs 4a and 4b of the groove 4, the arc 4b with a relatively larger radius is formed. The radius of arc 4b is the same as the radius Rb of the arc-shaped cutting edge 2b.

[0050] In the second machining step P2, the position of the cutting edge 2 is shifted by a distance S in the width direction (to the right in this embodiment) relative to the position of the first machining step P2. Here, the longer the distance S, the smaller the contact angles θa, θb of the groove 4 (see Figure 5) can be.

[0051] The cutting depth D2 in the second machining step P2 is made larger than the cutting depth D1 in the first machining step P2. In other words, the cutting depth is increased when cutting the workpiece 3 with the arc-shaped cutting edge 2b, which has a relatively larger radius than the two arc-shaped cutting edges 2a and 2b of the cutting edge 2. Here, the larger the dimensional difference between the radius Ra of the arc-shaped cutting edge 2a and the radius Rb of the arc-shaped cutting edge 2b, the larger the dimensional difference between the cutting depth D1 and the cutting depth D2, thereby reducing the difference in the left-right contact angle (the difference between the contact angle θa and the contact angle θb in Figure 5).

[0052] Once the machining process P (both the first and second machining processes P1 and P2) is completed, a Gothic arc-shaped groove 4, as shown in Figure 5, is formed in the workpiece 3. The ball 5, a component of the ball screw mechanism, contacts the groove 4 at contact points A and B. This Gothic arc-shaped groove machining method makes it possible to make the contact angle θa on the arc 4a side (left side) and the contact angle θb on the arc 4b side (right side) approximately equal. In other words, the difference in contact angles between the left and right sides (the difference between contact angle θa and contact angle θb) can be made approximately zero.

[0053] Here, as a modification of this embodiment, the order of the first second processing step P2 and the second second processing step P2 may be reversed. That is, in this embodiment, the arc 4b of the groove 4 is formed after the arc 4a is formed, but as a modification of this embodiment, the arc 4a of the groove 4 may be formed after the arc 4b is formed.

[0054] Furthermore, as a modification of this embodiment, the second processing step P2 may be performed three or more times, and the width of the groove 4 being formed may gradually widen each time the second processing step P2 is performed. In this modification, the cutting depth D1 is the cutting depth in the time when the cutting position of the blade 2 into the workpiece 3 is furthest to the left among the multiple second processing steps P2. The cutting depth D2 is the cutting depth in the time when the cutting position of the blade 2 into the workpiece 3 is furthest to the right among the multiple second processing steps P2. Furthermore, the distance S is the distance of the difference in cutting position between the time when the cutting position of the blade 2 into the workpiece 3 is furthest to the left and the time when it is furthest to the right among the multiple second processing steps P2.

[0055] <Second Embodiment> The machining method for the Gothic arc-shaped groove of the second embodiment will be described below with reference to Figures 6(a) and 6(b). Only the differences between the second embodiment and the first embodiment will be described. The differences between the second embodiment and the first embodiment are that in machining step P, the first machining step P1 and the second machining step P2 are each performed only once, and the execution of the first machining step P1 forms the arc 4a of the groove 4.

[0056] In this Gothic arc groove machining method, three elements are adjusted: the cutting depth D3 shown in Figure 6(a), the cutting depth D4 shown in Figure 6(b), and the positional displacement distance S shown in Figure 6(b). By adjusting these three elements, the contact angles θa and θb of the groove 4 and the left-right difference in contact angles (the difference between contact angle θa and contact angle θb) are adjusted.

[0057] As shown in Figure 6(a), in the first machining step P1, the reference line 2x of the cutting edge 2 is shifted to one side (left side) in the width direction, using the center line 4x of the groove 4 formed in machining step P as a reference. Then, the cutting edge 2 of the form tool 1 is made to cut into the inner circumferential surface 3a of the workpiece 3. At this time, the workpiece 3 is cut by both the arc-shaped cutting edge 2a and the arc-shaped cutting edge 2b of the cutting edge 2. As a result of this cutting, the arc 4a of the groove 4 is formed.

[0058] At the completion of the first machining process P1, of the two arcs 4a and 4b of the groove 4, arc 4b is still unformed. That is, with respect to the center line 4x of the groove 4, there is still material remaining on the other side (right side) in the width direction. This material is the part that will be machined in the second machining process P2 after the first machining process P1.

[0059] As shown in Figure 6(b), in the second machining step P2, the reference line 2x of the cutting edge 2 is shifted to the other side (right side) in the width direction, using the center line 4x of the groove 4 formed in machining step P as a reference. Then, the cutting edge 2 of the form tool 1 is made to cut into the inner circumferential surface 3a of the workpiece 3 again. At this time, the workpiece 3 is cut by the arc-shaped cutting edge 2b of the cutting edge 2 by the amount of the cutting allowance mentioned above. As a result of this cutting, the arc 4b of the groove 4 is formed.

[0060] In the second machining step P2, the position of the cutting edge 2 is shifted by a distance S in the width direction (to the right in this embodiment) relative to the first machining step P1. The longer the distance S, the smaller the contact angles θa and θb of the groove 4 can be.

[0061] The cutting depth D4 in the second machining step P2 is made larger than the cutting depth D3 in the first machining step P1. The larger the dimensional difference between the radius Ra of the arc-shaped cutting edge 2a and the radius Rb of the arc-shaped cutting edge 2b, the larger the dimensional difference between the cutting depth D3 and the cutting depth D4, which reduces the difference in the contact angle from side to side.

[0062] <Other variations> Herein, the following modifications can be applied to the above embodiments. That is, as modifications of the first and second embodiments above, a different mold tool 1 may be used in the second machining step P2 than the mold tool 1 used in the first machining step P1. The different mold tool 1 used in the second machining step P2 may differ from the mold tool 1 used in the first machining step P1 in terms of the width W1 of the blade portion 2, the radii Ra and Rb of the arc-shaped blade portions 2a and 2b of the blade portion 2, and the positions of the centers Oa and Ob. However, the width W1 of the blade portion 2 of the different mold tool 1 is narrower than the width W2 of the groove 4 formed in machining step P. As an example, the different mold tool 1 may have undergone wear due to repeated use, and the dimensions of the width W1 of the blade portion 2 and the radii Ra and Rb of the arc-shaped blade portions 2a and 2b of the blade portion 2 may have changed from the original mold tool 1.

[0063] Furthermore, as a variation of the first and second embodiments described above, if the shape accuracy of the overall tool 1 is high and the two arc-shaped blade portions 2a and 2b of the blade portion 2 are formed substantially symmetrically, the cutting depth D1 and cutting depth D2 in the first embodiment may be substantially the same. Similarly, if the shape accuracy of the overall tool 1 is high, the cutting depth D3 and cutting depth D4 in the second embodiment may be substantially the same. [Explanation of Symbols]

[0064] 1 General mold tool 2. Cutting edge of a general-purpose tool 3 Workpiece 4 Gothic arc-shaped grooves D1 Cutting depth D2 Cutting depth D3 Cutting depth D4 Cutting depth P Machining process P1 First processing process P2 Second processing process W1 Width of the blade W2 Groove width

Claims

1. A method for machining a Gothic arc-shaped groove, comprising a machining step of cutting a workpiece with the cutting edge of a form tool to form a Gothic arc-shaped groove in the workpiece, In the aforementioned machining process, a form tool is used in which the width of the cutting edge is narrower than the width of the groove to be formed. The aforementioned processing step is A first processing step involves cutting the blade into the workpiece, A second processing step involves shifting the position of the blade portion in the width direction from the first processing step within the width range of the groove to be formed, and then causing the blade portion to cut into the workpiece again. A method for machining Gothic arc-shaped grooves, characterized by including [a specific element].

2. The second processing step is performed multiple times, The aforementioned multiple operations include operations in which the position of the blade is shifted to one side in the width direction and operations in which it is shifted to the other side in the width direction. The method for machining a Gothic arc-shaped groove according to claim 1, characterized in that the depth to which the cutting edge is inserted into the workpiece is different between the rotation in which the cutting edge is shifted to one side and the rotation in which the cutting edge is shifted to the other side.

3. The method for machining a Gothic arc-shaped groove according to claim 1, characterized in that the depth to which the cutting edge is inserted into the workpiece is different between the first machining step and the second machining step.

4. In the method for machining a Gothic arc-shaped groove according to any one of claims 1 to 3, A method for machining a Gothic arc-shaped groove, characterized in that the second machining step uses a different type of type tool than the one used in the first machining step, and the width of the cutting edge of the different type of type tool is narrower than the width of the groove to be formed.

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