Machining method of super-hemispherical shape

Abstract

To provide a machining method of a super-hemispherical shape using a cup grinding wheel capable of machining the super-hemispherical shape using a standard curve generator by devising a machining step of a workpiece.SOLUTION: A machining method of a super-hemispherical shape includes the steps of: using a curve generator comprising a spindle 2, a lifting device 3, a sliding table 4, a turning device 5, a rotating device 6 and a cup grinding wheel 7, setting an inclination angle α of the cup grinding wheel 7 to be greater than 45°, arranging a grinding point at a position deviated in an X-axis direction from a rotation axis E of the spindle 2, the grinding point being a contact point of a workpiece W in the cup grinding wheel 7 and located at the highest position in a Z-axis direction, and raising the workpiece W in the Z-axis direction in a state that the spindle 2 and the cup grinding wheel 7 are rotated; and, after an upper end of the workpiece W reaches the grinding point of the cup grinding wheel 7, moving the grinding point of the cup grinding wheel 7 in the X-axis direction so as to coincide with the rotation axis E of the spindle 2.SELECTED DRAWING: Figure 1

Description

[Technical field]

[0001] The present invention relates to a method for machining a super-hemispherical shape using a cup grinding wheel, and more specifically, to a method for machining a super-hemispherical shape using a cup grinding wheel, which makes it possible to machine a super-hemispherical shape using a standard curve generator by devising a workpiece machining process. [Background technology]

[0002] It has been proposed that a conventional lens processing machine can process a lens into any shape by simultaneously controlling three axes: an axis that holds and rotates the lens (Z-axis), an X-axis perpendicular to the Z-axis, and an axis on the tool side that grinds the lens (B-axis) (see, for example, Patent Document 1). However, with such simultaneous control of three axes, it is difficult to control each axis with high precision, and there is also the problem that it is difficult to maintain sufficient precision so that the processed lens has the desired target processed shape.

[0003] In addition, in the conventional processing method using a curve generator, the cup grindstone is tilted and raised in the Z-axis direction to process the workpiece, so that the workpiece becomes a physically accurate sphere, and the accuracy is superior to the processing method using three-axis simultaneous control described in the previous paragraph. However, when processing a super-hemispherical shape using a conventional curve generator, if the lens is raised in the Z-axis direction while the tool (e.g., cup grindstone) is tilted at an angle of more than 45° with respect to the Z-axis, the cup grindstone and the lens interfere with each other, and the super-hemispherical shape cannot be processed. Specifically, as shown in Figs. 6(a) to (c), if a super-hemispherical shape is processed based on the conventional processing method while the cup grindstone 7 is tilted at an angle of, for example, about 55° with respect to the Z-axis, when the unmachined workpiece W is raised in the Z-axis direction, a part of the cup grindstone interferes with the side of the workpiece W, and the side of the workpiece W is ground, so that the super-hemispherical shape cannot be obtained. [Prior art documents] [Patent documents]

[0004] [Patent Document 1] JP 2008-068337 A Summary of the Invention [Problem to be solved by the invention]

[0005] An object of the present invention is to provide a method for machining a hyper-hemispherical shape using a cup grinding wheel, which makes it possible to machine a hyper-hemispherical shape using a standard curve generator by devising a workpiece machining process. [Means for solving the problem]

[0006] In order to achieve the above object, the machining method of the present invention for machining a super hemispherical shape includes a curve generator including a spindle which detachably holds a workpiece and has a rotation axis in a Z-axis direction, a lifting device which raises and lowers the spindle in the Z-axis direction, a slide table which is configured to be able to advance and retreat along an X-axis direction perpendicular to the rotation axis of the spindle, a turning device which is configured to be able to turn on the slide table around a B-axis which is perpendicular to the Z-axis direction and the X-axis direction, a rotating device which is mounted on the turning device and has a rotation axis perpendicular to the B-axis, and a cup grinding wheel which is detachably attached to the rotating device. the inclination angle α of the cup grinding wheel relative to the rotation axis of the spindle being set to more than 45°, the grinding point of the cup grinding wheel, which is the contact point with the workpiece and is located at the highest position in the Z-axis direction, being positioned away from the rotation axis of the spindle in the X-axis direction, and while the spindle and the cup grinding wheel are rotating, lifting the workpiece in the Z-axis direction; and after the upper end of the workpiece reaches the grinding point of the cup grinding wheel, moving the grinding point of the cup grinding wheel in the X-axis direction so as to coincide with the rotation axis of the spindle. Effect of the Invention

[0007] In the method for machining a super hemispherical shape of the present invention, a spindle that detachably holds a workpiece and has a rotation axis in the Z-axis direction, a lifting device that raises and lowers this spindle in the Z-axis direction, a slide table configured to be able to advance and retreat along the X-axis direction perpendicular to the rotation axis of the spindle, a turning device configured to be able to turn on this slide table around a B-axis perpendicular to the Z-axis direction and the X-axis direction, a turning device mounted on this turning device and having a rotation axis perpendicular to the B-axis, and a cup grinding wheel detachably attached to this turning device are provided. Therefore, while having the configuration of a standard curve generator, it is possible to machine a super hemispherical shape that could not be machined in the past by going through two machining steps: a step of setting the inclination angle α of the cup grinding wheel with respect to the rotation axis of the spindle to more than 45° and locating the grinding point of the cup grinding wheel at a position deviated from the rotation axis of the spindle in the X-axis direction and lifting the workpiece in the Z-axis direction, and a step of moving the grinding point of the cup grinding wheel in the X-axis direction so that it coincides with the rotation axis of the spindle. In particular, since the standard curve generator configuration is provided, the advantage that the workpiece can be continuously machined while the inclination angle α of the cup grinding wheel is fixed can be maintained, so that sufficient precision can be easily ensured and high precision can be obtained for the target machined shape. Furthermore, even when the shape of the workpiece is corrected, the correction can be made based on the measurement results obtained by the conventional ring spherometer, so the correction work is simple and very advantageous.

[0008] In the machining method for a super hemispherical shape of the present invention, it is preferable to include a calculation unit that calculates the inclination angle α of the cup grindstone relative to the rotation axis of the spindle and the movement amount Δd of the cup grindstone in the X-axis direction based on shape data including the target machining shape of the workpiece and the shape of the cup grindstone, and a control unit that controls the movement of the lifting device, the slide table, and the turning device based on the calculated value calculated by the calculation unit, calculates the inclination angle α of the cup grindstone and the movement amount Δd of the cup grindstone in the X-axis direction, and based on the calculated value, the cup grindstone rotates around the B-axis so that it has an inclination angle α with respect to the rotation axis of the spindle, and moves the cup grindstone by the movement amount Δd in the X-axis direction from the rotation axis of the spindle, the workpiece rises in the Z-axis direction and the workpiece and the cup grindstone come into contact with each other, and after the cup grindstone grinds a predetermined amount of the workpiece, it moves by the movement amount Δd in the X-axis direction so that the grinding point of the cup grindstone coincides with the rotation axis of the spindle, and the cup grindstone grinds the workpiece to the target machining shape. This contributes to obtaining high accuracy for the target machining shape of the workpiece.

[0009] It is preferable that the movement amount Δd [mm] of the cup grinding wheel in the X-axis direction and the virtual interference amount Xd [mm] in the X-axis direction where the workpiece and the cup grinding wheel interfere with each other when the workpiece is raised so that the central axis of the workpiece and the tip of the cup grinding wheel come into contact with each other with the cup grinding wheel set at the inclination angle α satisfy the relationship Xd≦Δd≦Xd+3mm. In this way, making the movement amount Δd of the cup grinding wheel in the X-axis direction as small as possible contributes to obtaining high accuracy for the target machining shape of the workpiece.

[0010] Before machining the workpiece, it is preferable to raise the workpiece so that the central axis of the workpiece comes into contact with the cup grindstone with the inclination angle α of the cup grindstone set to 0°, pre-register the position of the workpiece in the Z-axis direction when the workpiece comes into contact with the cup grindstone as a reference position, calculate the displacement amount Zd of the cup grindstone in the Z-axis direction when the inclination angle α of the cup grindstone is set from 0° to more than 45°, calculate the movement amount Wz of the workpiece in the Z-axis direction based on position data including the previously registered reference position of the workpiece and the calculated displacement amount Zd of the cup grindstone in the Z-axis direction, and move the workpiece in the Z-axis direction based on this calculated value for grinding. This contributes to obtaining high accuracy for the target machining shape of the workpiece. [Brief description of the drawings]

[0011] [Figure 1] FIG. 2 is a perspective view showing a curve generator used in the present invention. [Diagram 2] 1 is a flowchart based on a processing method of the present invention. [Diagram 3] 5A to 5C are explanatory diagrams showing changes in the shape of a workpiece due to the machining method of the present invention. [Figure 4] 4 is an explanatory diagram for calculating various dimensions in the processing method of the present invention. FIG. [Diagram 5] 4 is an explanatory diagram for calculating various dimensions in the processing method of the present invention. FIG. [Figure 6] 1A to 1C are explanatory diagrams showing changes in the shape of a workpiece caused by a conventional machining method. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0012] The configuration of the present invention will be described in detail below with reference to the accompanying drawings. Fig. 1 shows a curve generator used in the present invention. In Fig. 1, the direction perpendicular to the rotation axis E of the spindle is the X-axis direction, and the direction parallel to the rotation axis E of the spindle is the Z-axis direction.

[0013] As shown in FIG. 1, the curve generator 1 includes a spindle 2 that detachably holds a workpiece W and has a rotation axis E in the Z-axis direction, a lifting device 3 that raises and lowers the spindle 2 in the Z-axis direction, a slide table 4 that is configured to be able to advance and retreat along the X-axis direction, a turning device 5 that is configured to be able to turn around a B-axis perpendicular to the X-axis and Z-axis directions on the slide table 4, a turning device 6 that is mounted on the turning device 5 and has a rotation axis F perpendicular to the B-axis, and a cup grindstone 7 that is detachably attached to the turning device 6. The rotation axis E of the spindle 2 coincides with the rotation axis of the workpiece W, and the rotation axis F of the turning device 6 coincides with the rotation axis of the cup grindstone 7. The cup grindstone 7 has a cylindrical grindstone body 7a with a bottom and a tip portion 7b with a diamond grindstone attached to one end of the grindstone body 7a. Depending on the shape and size of the workpiece W, various shapes such as a cylindrical one are used.

[0014] Furthermore, the curve generator 1 includes a calculation unit that calculates various dimensions required for machining the workpiece W, and a control unit that controls each unit based on the calculated values ​​calculated by the calculation unit. The calculation unit calculates dimensions required for machining the workpiece W, including the inclination angle α of the cup grindstone 7 relative to the rotation axis E of the spindle 2, the movement amount Δd of the cup grindstone 7 in the X-axis direction, the displacement amount Zd in the Z-axis direction, and the movement amount Wz of the workpiece W in the Z-axis direction, based on shape data and position data including the target machining shape of the workpiece W and the shape of the cup grindstone 7. The control unit also controls the movement of the lifting device 3, the slide table 4, and the turning device 5, and the rotation of the spindle 2 and the rotating device 6. These calculation units and control units can be configured as calculation devices and control devices, respectively, and may be mounted inside the curve generator 1, or may be arranged outside the curve generator 1 and connected thereto.

[0015] A method for machining a workpiece W using the above-mentioned curve generator 1 will be described. Figures 2 to 5 show the machining method of the present invention. In the present invention, as shown in Figure 2, the workpiece W can be ground into a desired super-hemispherical shape (target machining shape) through steps S1 to S5.

[0016] In step S1, as a presetting process, as shown in Figure 3(a), before machining the workpiece W, the inclination angle α of the cup grinding wheel 7 is set to 0°, and the workpiece W is raised from the lowest position of the spindle 2 so that the central axis of the unmachined workpiece W (the rotation axis E of the spindle 2) comes into contact with the tip of the cup grinding wheel 7. The position of the workpiece W in the Z-axis direction when the workpiece W and the cup grinding wheel 7 come into contact is measured, and this position of the workpiece W in the Z-axis direction is registered in advance as a reference position.

[0017] Then, in step S2, as a positioning process for the cup grinding wheel 7 before machining, the inclination angle α and the movement amount Δd [mm] in the X-axis direction of the cup grinding wheel 7 (see FIG. 3(b)) are calculated based on various shape data. Specifically, as shown in FIG. 4, the inclination angle α and the movement amount Δd in the X-axis direction of the cup grinding wheel 7 are calculated based on the target machining shape of the workpiece W and the position of the cup grinding wheel 7. Here, the movement amount Δd in the X-axis direction is the distance measured along the X-axis direction between the rotation axis E of the spindle 2 and the grinding point Gp of the cup grinding wheel 7. This grinding point Gp of the cup grinding wheel 7 is the contact point between the cup grinding wheel 7 and the workpiece W when the cup grinding wheel 7 is tilted at the inclination angle α, and is the highest point in the Z-axis direction on the grinding surface of the cup grinding wheel 7. First, the inclination angle α [°] is calculated by the following formula 1 using the outer diameter D1 [mm] and inner diameter D2 [mm] of the cup grinding wheel 7, the machining radius of curvature R [mm] of the target machining shape of the workpiece W, and the curvature radius r [mm] of the tip portion 7b of the cup grinding wheel 7. The calculated inclination angle α of the cup grinding wheel 7 is in the range of more than 45° and not more than 60°.

[0018]

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[0019] Then, the virtual interference amount D [mm] in the first X-axis direction is calculated by the following formula 2 using the machining radius of curvature R and the tilt angle α of the target machining shape of the workpiece W, and the virtual interference amount d [mm] in the second X-axis direction is calculated by the following formula 3 using the radius of curvature r and the tilt angle α of the tip portion 7b of the cup grindstone 7. Here, as shown in FIG. 4, the virtual interference amount D in the first X-axis direction and the virtual interference amount d in the second X-axis direction are both virtual overlap amounts in the X-axis direction. The virtual interference amount D in the first X-axis direction corresponds to the interference amount above the contact point P between the workpiece W and the cup grindstone 7, and the virtual interference amount d in the second X-axis direction corresponds to the interference amount below the contact point P, and the virtual interference amount d is small compared to the virtual interference amount D. Then, the virtual interference amount Xd [mm] in the X-axis direction of the cup grindstone 7 is calculated by the following formula 4. If the calculated virtual interference amount Xd of the cup grinding wheel 7 in the X-axis direction is set as the movement amount Δd of the cup grinding wheel 7 in the X-axis direction, the workpiece W and the cup grinding wheel 7 will not interfere with each other even if the workpiece W is raised with the cup grinding wheel 7 set at the inclination angle α.

[0020]

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[0021]

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[0022]

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[0023] The virtual interference amount Xd of the cup grindstone 7 in the X-axis direction calculated as above may be set as the movement amount Δd of the cup grindstone 7 in the X-axis direction, but the movement amount Δd of the cup grindstone 7 in the X-axis direction may be set to satisfy the following relationship in consideration of deviation during machining. It is preferable that the movement amount Δd [mm] of the cup grindstone 7 in the X-axis direction and the virtual interference amount Xd [mm] in the X-axis direction satisfy the relationship Xd≦Δd≦Xd+3mm. In particular, it is more preferable to satisfy the relationship Xd≦Δd≦Xd+2mm, and it is most preferable to satisfy the relationship Xd≦Δd≦Xd+1mm. In this way, by making the movement amount Δd of the cup grindstone 7 in the X-axis direction as small as possible, it contributes to obtaining high accuracy for the target machining shape of the workpiece W.

[0024] In step S2, furthermore, the final movement amount Wz of the workpiece W in the Z-axis direction is calculated based on various position data of the cup grindstone 7. Specifically, as shown in FIG. 5, the displacement amount Zd of the cup grindstone 7 in the Z-axis direction is calculated assuming a state in which the inclination angle α of the cup grindstone 7 is 0° and a state in which the cup grindstone 7 is inclined at the inclination angle α with respect to the target machining shape of the workpiece W. Then, the angle θ1 [°] is calculated by the following formula 5 using the distance KC [mm] in the X-axis direction from the B-axis to the axis center of the cup grindstone 7 when the inclination angle α of the cup grindstone 7 is 0°, the distance KX [mm] in the Z-axis direction from the reference plane S to the B-axis when the inclination angle α of the cup grindstone 7 is 0°, the outer diameter D1 and the inner diameter D2 of the cup grindstone 7, the grindstone length LW [mm] in the Z-axis direction from the reference plane S to the tip of the cup grindstone 7 when the inclination angle α of the cup grindstone 7 is 0°, and the curvature radius r of the tip portion 7b of the cup grindstone 7. This angle θ1 is the angle between a line connecting the center of the radius of curvature r of the tip 7b of the cup grindstone 7 and the B-axis, and a line parallel to the X-axis direction passing through the B-axis. Furthermore, the length L [mm] is calculated by the following formula 6 using the distance KC, the distance KX, the outer diameter D1 and inner diameter D2 of the cup grindstone 7, the grindstone length LW, the radius of curvature r of the tip 7b of the cup grindstone 7, the angle θ1, and the inclination angle α, and the angle θ2 [°]. This length L is the length measured along the Z-axis direction from a line parallel to the X-axis direction passing through the B-axis to the center of the radius of curvature r of the tip 7b of the cup grindstone 7, when the cup grindstone 7 is inclined at the inclination angle α (angle θ2). Here, the angle θ2 is the angle between a line parallel to the X-axis direction passing through the B-axis and a line inclined downward in the X-axis direction with respect to the line. Then, the following formula 7 is used to calculate the displacement Zd [mm] of the cup grindstone 7 in the Z-axis direction when the inclination angle α of the cup grindstone 7 is set from 0° to more than 45°. Finally, based on the reference position of the workpiece W registered in advance in step S1 and the calculated displacement Zd of the cup grindstone 7 in the Z-axis direction, the movement amount Wz of the workpiece W in the Z-axis direction is calculated, which is the difference between the two (the value obtained by subtracting the latter from the former). This movement amount Wz of the workpiece W in the Z-axis direction corresponds to the total movement amount from the lowest point position of the spindle 2 until the upper end of the workpiece W reaches the grinding point Gp of the cup grindstone 7. The reference plane S, which is the reference for the distance KX and the grindstone length LW, can be set at the lower end of the rotating device 6, for example.

[0025]

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[0026]

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[0027]

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[0028] Next, in step S3, as a setting process for the cup grindstone 7 before machining, the cup grindstone 7 is moved to a predetermined position. Specifically, based on the calculated values ​​calculated in step S2, as shown in Fig. 3(b), the grinding point Gp of the cup grindstone 7 is tilted around the B-axis to have an inclination angle α with respect to the rotation axis E of the spindle 2, and is moved by a movement amount Δd in the X-axis direction so as to move away from the rotation axis E of the spindle 2 in the X-axis direction.

[0029] Then, in step S4, the workpiece W is raised in the Z-axis direction, and grinding of the workpiece W by the cup grindstone 7 is started. Specifically, the workpiece W is gradually raised in the Z-axis direction by the amount of movement Wz in the Z-axis direction calculated in step S2, and a predetermined amount of the upper part of the workpiece W is ground (first grinding step). At that time, the workpiece W moves from the lowest position of the spindle 2 to the grinding point Gp of the cup grindstone 7. At the end of such a first grinding step, a circular unmachined portion is formed on the upper part of the workpiece W, as shown in FIG. 3(c).

[0030] Next, in step S5, the cup grinding wheel 7 moves in the X-axis direction, and the cup grinding wheel 7 starts grinding the remaining part of the workpiece W. Specifically, the cup grinding wheel 7 gradually moves by a movement amount Δd in the X-axis direction so that the grinding point Gp of the cup grinding wheel 7 coincides with the rotation axis E of the spindle 2, thereby grinding the remaining part of the workpiece W to a predetermined machining radius of curvature R (second grinding step). At the end of such second grinding step, the workpiece W is ground into a desired super-hemispherical shape (target machining shape), as shown in Fig. 3(d).

[0031] The above-mentioned machining method for a super hemispherical shape of the present invention includes the spindle 2 which detachably holds the workpiece W and has a rotation axis E in the Z-axis direction, the lifting device 3 which raises and lowers the spindle 2 in the Z-axis direction, the slide table 4 which is configured to be able to advance and retreat along the X-axis direction, the turning device 5 which is configured to be able to turn around the B-axis on the slide table 4, the turning device 6 which is mounted on the turning device 5 and has a rotation axis F which is perpendicular to the B-axis, and the cup grinding wheel 7 which is detachably attached to the turning device 6. Therefore, it is possible to perform machining operations similar to those of a standard curve generator. While having the configuration of the ring generator, the inclination angle α of the cup grindstone 7 is set to more than 45°, the grinding point Gp of the cup grindstone 7 is positioned at a position deviated from the rotation axis E of the spindle 2 in the X-axis direction, and the workpiece W is raised in the Z-axis direction. After the upper end of the workpiece W reaches the grinding point Gp of the cup grindstone 7, the grinding point Gp of the cup grindstone 7 is moved in the X-axis direction so as to coincide with the rotation axis E of the spindle 2. This allows machining into a super-hemispherical shape that could not be machined conventionally. In particular, since the configuration of the standard curve generator is provided, the advantage that the workpiece W can be continuously machined while keeping the inclination angle α of the cup grindstone 7 fixed can be maintained, so that sufficient accuracy can be easily ensured and high accuracy can be obtained for the target machined shape. Furthermore, even when the shape of the workpiece W is corrected, the correction can be performed based on the measurement results using a conventional ring spherometer, which is very advantageous. [Explanation of symbols]

[0032] 1. Curve Generator 2 Spindle 3 Lifting device 4 Slide table 5 Swivel 6 Rotating device 7 Cup Grindstone Gp Grinding Point

Claims

1. A curve generator is used, which includes a spindle that detachably holds a workpiece and has a rotation axis in the Z-axis direction, a lifting device that raises and lowers the spindle in the Z-axis direction, a slide table that is configured to be able to advance and retreat along the X-axis direction perpendicular to the rotation axis of the spindle, a turning device that is configured to be able to turn on the slide table around a B-axis perpendicular to the Z-axis direction and the X-axis direction, a rotating device that is mounted on the turning device and has a rotation axis perpendicular to the B-axis, and a cup grinding wheel that is detachably attached to the rotating device, a step of setting an inclination angle α of the cup grinding wheel with respect to the rotation axis of the spindle to be greater than 45°, disposing a grinding point, which is a contact point of the cup grinding wheel with the workpiece and is located at the highest position in the Z-axis direction, at a position offset from the rotation axis of the spindle in the X-axis direction, and raising the workpiece in the Z-axis direction while the spindle and the cup grinding wheel are rotating; and after the upper end of the workpiece reaches the grinding point of the cup grinding wheel, moving the grinding point of the cup grinding wheel in the X-axis direction so as to coincide with the rotation axis of the spindle.

2. a calculation unit that calculates an inclination angle α of the cup grinding wheel relative to the rotation axis of the spindle and a movement amount Δd of the cup grinding wheel in the X-axis direction based on shape data including a target machining shape of the workpiece and a shape of the cup grinding wheel, and a control unit that controls movement of the lifting device, the slide table and the rotating device based on the calculated values ​​calculated by the calculation unit, the inclination angle α and the movement amount Δd in the X-axis direction of the cup grindstone are calculated, and based on the calculated values, the cup grindstone is rotated around the B-axis so that the cup grindstone has the inclination angle α with respect to the rotation axis of the spindle, and the cup grindstone is moved from the rotation axis of the spindle by the movement amount Δd in the X-axis direction; The method for machining a super-hemispherical shape as described in claim 1, characterized in that the workpiece rises in the Z-axis direction, the workpiece comes into contact with the cup wheel, and the cup wheel grinds a predetermined amount of the workpiece.After that, the cup wheel moves a distance Δd in the X-axis direction so that the grinding point of the cup wheel coincides with the rotation axis of the spindle, thereby grinding the workpiece into the target machining shape.

3. The method for machining a super-hemispherical shape as described in claim 2, characterized in that the movement amount Δd [mm] of the cup grinding wheel in the X-axis direction and the virtual interference amount Xd [mm] in the X-axis direction where the workpiece and the cup grinding wheel interfere with each other when the workpiece is raised so that the central axis of the workpiece and the cup grinding wheel come into contact with each other with the cup grinding wheel set at the inclination angle α satisfy the relationship Xd≦Δd≦Xd+3 mm.

4. Before machining the workpiece, the inclination angle α of the cup grindstone is set to 0°, and the workpiece is raised so that the central axis of the workpiece comes into contact with the cup grindstone. The position of the workpiece in the Z-axis direction when the workpiece comes into contact with the cup grindstone is registered in advance as a reference position. Calculating a displacement amount Zd of the cup grindstone in the Z-axis direction when the inclination angle α of the cup grindstone is set from 0° to more than 45°, and calculating a movement amount Wz of the workpiece in the Z-axis direction based on position data including a previously registered reference position of the workpiece and the calculated displacement amount Zd of the cup grindstone in the Z-axis direction; 4. The method for machining a super-hemispherical shape according to claim 2 or 3, wherein the workpiece is moved in the Z-axis direction based on the calculated value and ground.

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