JP2002144128A - Machining method and apparatus for scroll-like work piece - Google Patents

Abstract

PROBLEM TO BE SOLVED: To machine an involute curved part of a scroll-like wall in a work piece regardless of existence/absence of eccentricity between the center of rotation of the work piece and the center of the involute base circle. SOLUTION: Circular interpolation is performed for the wall surface shape of the involute curved part 35. A scroll-like work piece is rotated so that the normal direction of the wall surface at a contact point of the wall surface and a tool 16 is always pointed in a fixed direction of X-axis, and the tool is relatively moved in the X-axis direction to the work piece and in the Y-axis direction along the circular arc.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method and an apparatus for processing a scroll-shaped workpiece used for a compressor or the like in an air conditioner.

[0002]

2. Description of the Related Art Conventionally, as a method of processing a scroll-shaped workpiece, for example, a method disclosed in Japanese Patent Application Laid-Open No. 62-88507 is known. In this method, the center position of the tool is set on the inner wall or the outer wall of the involute curve in the workpiece by the radius of the base circle in the Y-axis direction matching the radial direction from the center of the base circle of the involute curve. With the tool shifted,
The wall surface is processed by rotating the workpiece around the center of the base circle while moving the tool and the workpiece relative to each other in the X axis direction perpendicular to the axial direction. Things.

According to such a method, the wall surface can be machined by the relative movement between the tool and the workpiece in the X-axis direction and the rotation of the workpiece.

[0004]

In the above-mentioned scroll machining, in order to machine an involute curved scroll-shaped wall with high accuracy, the center of rotation of the workpiece and the center of the base circle of the involute curve must be exactly matched. Must be. In other words, when there is a deviation between the rotation center of the workpiece and the center of the involute base circle (for example, when there is an error in the setting position of the workpiece on the chuck or the like, or when there is a deviation of the rotation center of the chuck itself) Has the disadvantage that the deviation of the rotation center has a significant adverse effect on the accuracy of involute curve machining.

In recent years, scroll-type workpieces in which the center of the involute base circle is intentionally shifted from the center of the circular workpiece have been put to practical use in order to reduce the size of the entire workpiece (for example, see Japanese Patent Application Laid-Open Publication No. H11-163873). In order to machine a workpiece having such an eccentric shaft by the above-described method, a complicated mechanism is required to rotate the workpiece around an eccentric shaft deviated from the center of the outer circle. Therefore, an increase in cost cannot be avoided.

In view of such circumstances, the present invention is capable of processing an involute curve portion of a scroll-like wall of a workpiece with high accuracy regardless of whether or not the center of rotation of the workpiece and the center of an involute base circle are eccentric. It is an object of the present invention to provide a method and a device that can do this.

[0007]

As a means for solving the above-mentioned problems, the present invention has a scroll-shaped wall, on which an involute curve portion whose wall forms an involute curve is formed. A method for machining the wall surface of the involute curve portion of the scroll-shaped workpiece, wherein the shape of the wall surface in the involute curve portion is circularly interpolated, and the normal direction of the wall surface at the contact point between the wall surface and the tool is While rotating the scroll-shaped workpiece around the center of the base circle of the involute curve or a point near the center so that the scroll-shaped workpiece always faces the fixed X-axis direction, the scroll-shaped workpiece is moved along the arc. Relative to the X-axis direction and the Y-axis direction orthogonal thereto.

The present invention also provides a scroll-shaped workpiece having a scroll-shaped wall, on which a scroll-shaped wall is formed with an involute curve having an involute curve, for machining the wall of the involute curve. A rotating drive means for rotating the workpiece around a center or a point near the center of the base circle, and rotating the tool and the workpiece in the X-axis direction parallel to the diameter of the base circle of the involute curve. X-axis driving means for relatively moving;
Y-axis drive means for relatively moving the tool and the workpiece in the Y-axis direction parallel to the diameter of the base circle of the involute curve and orthogonal to the X-axis direction, and circularly interpolating the shape of the wall surface in the involute curve portion Interpolation calculating means, and the scroll-shaped workpiece is formed so that the normal direction of the wall surface at the contact point between the interpolated wall surface and the tool always faces the constant X-axis direction. Each of the driving units is moved so as to move the tool relative to the scroll-shaped workpiece along the arc in the X-axis direction and in the Y-axis direction orthogonal thereto, while rotating about a center or a point near the center. Processing control means for operating the means.

In these methods and apparatuses, the wall shape of the involute curve portion is circularly interpolated (that is, approximated to a shape obtained by joining a plurality of circular arcs), and the tool is moved relative to the workpiece along the circular arc. Therefore, the wall surface of the involute curved portion can be machined with high accuracy regardless of whether or not the rotation center of the workpiece coincides with the center of the involute base circle. Therefore, it is also possible to machine the wall surface of the involute curve portion while rotating the workpiece around an axis that is displaced from the center of the involute base circle within a range not more than the radius of the base circle. In addition, since the workpiece is rotated such that the normal line at the contact point between the tool and the arc always points in the fixed X-axis direction, the relative movement of the tool with respect to the workpiece is not complicated.

In order to circularly interpolate the curve of the wall surface of the involute curve portion, for example, the curve is divided at the same pitch angle (the expansion angle of the involute curve), and each of the divided curves approximates the curve. Should be assigned.

[0011]

DESCRIPTION OF THE PREFERRED EMBODIMENTS Preferred embodiments of the present invention will be described with reference to the drawings.

FIG. 1 shows an example of a processing apparatus for carrying out the present invention. In the figure, a Y-axis column 12 is erected on a bed 10, and a tool table 14 is mounted so as to be able to move up and down along the Y-axis column 12, that is, to be movable along a Y-axis direction which is a vertical direction. Have been. The tool base 14 includes a chuck (not shown) for detachably holding a tool (here, an end mill) 16.
2 and a Y-axis motor (Y-axis drive means) 13 shown in FIG.

On the bed 10, a rail 18 extending in the Z-axis direction parallel to the central axis of the tool 16 is installed.
The Z-axis table 2 is slidable along the rail 18.
0 is attached. The Z-axis table 20 is slid in the Z-axis direction by a Z-axis motor 22 and a ball screw mechanism (not shown).

The Z-axis table 20 has an X-axis slidable in an X-axis direction orthogonal to the Z-axis direction and the Y-axis direction.
A shaft table 24 is mounted. This X axis table 2
Reference numeral 4 is slidably driven in the X-axis direction by an X-axis motor (X-axis driving means) 25 and a ball screw mechanism (not shown) shown in FIG.

A headstock 26 stands on the X-axis table 24. The headstock 26 supports a spindle (not shown) so as to be rotatable about a C-axis parallel to the Z-axis. The main shaft is driven to rotate around the C-axis by a C-axis motor (rotation driving means) 28, and is configured to detachably grip a scroll-shaped workpiece 30 via a chuck (not shown).

FIG. 2 shows an example of the scroll-shaped workpiece 30. As shown in FIG. The workpiece 30 has a circular outer peripheral surface, and a scroll-like wall 32 protrudes forward from a front side surface (a front side surface in FIG. 2). The scroll-shaped wall 32 includes a central portion 34 and an involute curved portion 35. The center portion 34 is formed in a predetermined region sandwiching a boundary point between the inner wall surface and the outer wall surface of the scroll-shaped wall 32, and is formed in a shape other than an involute curve, such as an arc, a straight line, or the like. The involute curved portion 35 has an outer wall surface 35A and an inner wall surface 35B sandwiching the center portion 34. Before processing according to the present invention, the two wall surfaces 35A and 35B have substantially the same circle as a base circle. It is formed in an involute curve. Therefore, both the X-axis direction and the Y-axis direction are set in directions that match the radial direction of the base circle.

This processing device includes an NC control device (drive control means) 40 as shown in FIG. The NC control device 40 operates the Z-axis motor 22 to position the workpiece 30 with respect to the tool 16, and to control the X-axis motor 25, the Y-axis motor 13,
The operation control of the shaft motor 28 causes the scroll-shaped wall 32 of the workpiece 30 to be machined. The functions related to the machining control include a data reading unit 42, an interpolation data calculation unit 44, and a pulse distribution unit. 46
It has.

The data reading section 42 reads and stores NC data (such as the processing shape and the feed speed of the scroll-like wall 32) input from the outside. The interpolation data calculation unit 44 calculates and outputs interpolation data (described later in detail) for processing the scroll-shaped wall 32 based on the data read by the data reading unit 42. The pulse distribution unit 46 calculates an X-axis, a Y-axis,
The pulse is distributed to each axis, and each axis motor 25,13,2
8 is output.

Next, a method of processing the scroll-shaped wall 32 performed by this apparatus will be described.

First, the involute curve portion 35A,
Circular interpolation is performed on the wall surface of 35B. As a specific method, for example, as shown in FIG. 4, the shape of the wall surface is divided at the same pitch angle (extending angle of the involute curve) φ, and each divided involute curve is approximated by an approximate arc as shown in FIG. C may be assigned. In order to determine such an approximate arc C, for example, a center of curvature Oc and a radius of curvature R at a midpoint M of the divided involute curve I (broken line in the figure) are obtained, and the center of curvature Oc and the radius of curvature R are obtained. A method of allocating an arc C (solid line in the figure) can be used.

As shown in FIG. 4, the involute music
Arcs C1, C2, C3, C4, C assigned to lines
Radius of curvature R1, R2, R3, R4, R of 5, C6, ...
5, R6, ... become larger as they move away from the center
Go. Each of the arcs C1, C2, C3, C4, C5, C
The center of curvature of 6, ... is a circle approximating the involute base circle
C _AI will ride on

In the present invention, whether or not the center portion 34 is processed is irrelevant. However, if the center portion 34 is also processed continuously with the involute curve portion 35, the shape of the center portion 34 is changed to an arc shape in the same manner as described above. What is necessary is just to prepare data that has been subjected to interpolation (local linear interpolation depending on the shape).

In actual machining, as shown in FIG. 6A, the center of the tool 16 is shifted in the negative direction (downward) along the Y-axis direction with respect to the center of the base circle BC of the involute curve. The tool 16 is relatively shifted by an amount substantially equal to ro and the tool 16 is brought into contact with the radially outer portion of the inner wall surface 35B of the involute curved portion 35 from the right side to the left side in the drawing at this Y-axis position. At this time, it is also possible to make the outermost end of the scroll-shaped wall come into contact with a predetermined position by processing the X-axis and the C-axis. In this state, the tool 16
The normal direction of the inner wall surface 35B at the point of contact between the inner wall surface 35B and the inner wall surface 35B matches the X-axis direction.

Next, from this state, while rotating the workpiece 30 around the C axis so that the normal direction always faces the X axis direction, the tool is moved so that the tool 16 follows each arc. It is moved relative to 30 in the X-axis direction and the Y-axis direction (that is, the respective axis motors 25, 13, and 28 are simultaneously operated). By such control, the tool 16 moves substantially linearly in the X-axis direction when viewed macroscopically while vibrating with a small amplitude in the Y-axis direction (FIGS. 6B and 6C).

As the machining proceeds, the tool 16 approaches the central portion 34 from the involute curved inner wall surface 35B, and further, as shown in FIG.
In the region where is to be processed, the center portion 34 is continuously processed by keeping the normal direction of the wall surface of the center portion 34 at the contact point between the two at the X-axis direction based on the data interpolated as described above. Alternatively, the central portion 34 may be separately processed.

When the machining of the center portion 34 is advanced as described above, when the end point of the center portion 34 is reached, the tool 16
Is automatically located at a position shifted from the center of the base circle by about the base circle radius ro in the Y-axis direction in the opposite direction (that is, in the positive direction). From this state, FIG.
As shown in (a) to (c), the tool 16 is machined while rotating the workpiece 30 so that the normal direction at the contact point between the involute curve portion 35 and the tool 16 is maintained in the X-axis direction. The object 30 is relatively moved in the X-axis direction and the Y-axis direction. As a result, as shown in FIGS. 7B and 7C, the outer wall surface 35A of the involute curved portion 35 can be continuously processed from the radially inner portion to the radially outer portion.

In order to execute the above involute machining, the NC control device 40 may be configured to perform, for example, the following arithmetic control operation.

First, the NC data is read, and the processed figure of the scroll-shaped wall 32 is grasped (step S in FIG. 8).
1). In addition, a deviation amount between the center of the workpiece 30 when the workpiece 30 is actually set in the processing apparatus and the rotation center when the workpiece 30 is actually driven to rotate is detected (step S2). . The amount of this deviation is, for example, when a chuck is used to grip a workpiece or a master work manufactured in correspondence with the workpiece, and the chuck is rotated with a tester applied to the outer peripheral surface of the workpiece or the master work. It can be detected by a method such as measuring the runout of the outer peripheral surface.

Next, as shown in FIG. 4, the involute curves of the inner and outer walls 35A and 35B in the involute curve portion 35 are approximated to a shape in which a plurality of arcs are connected. That is, the involute curve is divided at the same pitch angle, and an arc similar to this is assigned to each divided curve (step S3). Further, each arc is divided into a plurality of point groups P1, P2,... Which are separated from each other by a predetermined distance S (step S4).

After the point group division in this way, the point Pn is determined based on the designated feed rate F (mm / min) input from the outside.
Is calculated from the following equation (step S5).

[0031]

Tn = α · S / F (msec) α: coefficient If the distances S are all constant irrespective of n, all the values of Tn are equal, but the distance S changes with n. If the value Sn is set to be equal to Tn, Tn also changes depending on n.

Next, the distance for relatively moving the tool 16 and the workpiece 30 in both the X and Y directions during this movement time Tn, and C
Interpolation data Dn, which is combination data on the angle at which the workpiece 30 is rotated around the axis, is calculated (step S
6).

For the calculation of the data, for example, a method as shown in FIG. 9 may be used.

First, a normal line (that is, a straight line passing through the center A1 of the tool 16 and the contact point P1) at the contact point P1 in a state where the tool 16 is in contact with the arc at the point P1, is drawn. The intersection of the perpendicular and the normal when the perpendicular is lowered from the rotation center O of the workpiece 30 is B1. Thereby, the workpiece rotation center O and the tool center A
A right-angled triangle OA1B with the line segment OA1 connecting to 1 as the hypotenuse
1 will be formed.

Similarly, when the tool 16 moves relative to the workpiece 30 by a distance S from the point P1 and reaches the point P2, a normal line at the point P2 is drawn. A perpendicular triangle OA2B2 having a line segment OA2 connecting the workpiece rotation center O and the tool center A2 as an oblique side, with an intersection of the perpendicular and the normal when the perpendicular is lowered from the rotation center O of the object 30 as B2. Form.

Focusing on each right triangle, the method of the present invention always maintains the normal direction in the X-axis direction. Therefore, the normal line at the point P1 and the normal line at the point P2 are used. the angle formed angle gamma ₁₂ that there straight A2B2 must rotate the workpiece 30 in a journey S (i.e. C axis rotation angle). Then, the tool 16 the difference X ₁₂ of the length of the line segment A2B2 line segment A1B1 is at journey S
Is the amount that must be moved relative to the X-axis direction relative to the workpiece 30, Y-axis difference Y ₁₂ is a tool 16 relative to the workpiece 30 of the length of the line segment OB2 line segment OB1 That is, the amount that must be relatively moved.

Thus, the X axis,
Interpolation data for the Y axis and the C axis can be calculated. Further, when the deviation amount between the center of the workpiece and the actual center of rotation of the workpiece is detected in step S2,
Each of the interpolation data is corrected based on the shift amount. Then, based on the interpolation data Dn, a pulse is distributed to each of the X, Y, and C axes and is output to each of the axis motors 25, 13, and 28 (step S7). A method of processing the inner and outer walls 35A and 35B of the involute curved portion 35 while always keeping the normal direction of the scroll-shaped wall 32 at the contact point between the tool 16 and the wall surface in the X-axis direction can be realized.

In the processing and apparatus described above, the processing is not performed along the involute curve as in the related art,
Since the involute curve is circularly interpolated and the tool 16 is moved relative to the workpiece 30 along the circular arc, the actual rotation center of the workpiece 30 is eccentric from the center of the involute base circle. However, high machining precision can be maintained, and even for a workpiece intentionally deviated between the two centers, the scroll-like shape can be obtained only by simple rotation without rotating the workpiece 30 eccentrically as in the related art. The wall 32 can be machined. Moreover,
Since the workpiece 30 is rotated so that the normal line at the contact point between the tool 16 and each arc always points in the X-axis direction, the movement of the tool 16 is not so complicated as compared with the conventional involute machining, and smooth. Processing can be advanced with a simple movement.

FIG. 10 shows the relative movement of the tool in the X-axis direction and the Y-axis direction with respect to the workpiece when the workpiece in which the rotation center of the workpiece coincides with the center of the involute base circle is machined according to the present invention. It is shown macroscopically. As shown in the figure, in the involute curve portion, at a position shifted from the tool rotation center (Y = 0) by a dimension almost equal to the involute basic circle radius ro in the Y-axis direction, no large movement occurs in the Y-axis direction. Processing can be performed (that is, only by a substantially linear movement in the X-axis direction).

FIG. 11A is a microscopic view of the movement at the involute curve. That is, the tool 16 reciprocates with a small amplitude (about 26 μm) in the Y-axis direction for each of the allocated arcs, and its vibration center is located slightly more from the center than the radius (3.0 mm) of the involute base circle. ing.

On the other hand, in the case of machining a workpiece whose center of rotation is eccentric by only 15 μm from the center of the involute base circle even if the radius of the base circle is the same of 3.0 mm, FIG. As shown in FIG.
In addition to micro-vibration in the axial direction,
It will undulate at a cycle of °.

Further, the amount of eccentricity is 1/1/3 of the base circle radius of 3.0 mm.
In the case of a workpiece having a diameter of 1.8 mm exceeding 2 (for example, a compressor of a car air conditioner), as shown in FIG. 11C, the movement of the tool 16 vibrates in the Y-axis direction with a considerably large amplitude even when viewed macroscopically. (Amplitude about 3.5mm).

According to the present invention, highly accurate machining can be realized for any workpiece by simple movement and control.

It should be noted that the present invention is not limited to such an embodiment, and the following embodiments can be taken as examples.

(1) In the above embodiment, the workpiece 30 is
Although the tool 16 is moved in the axial direction and the tool 16 is moved in the Y-axis direction, the tool 16 may be moved in the X-axis direction, or the workpiece 30 may be moved in the Y-axis direction. . Further, the X-axis direction and the Y-axis direction in the present invention can be freely set as long as they are directions orthogonal to each other and parallel to the diameter of the base circle of the involute curve.

(2) In the present invention, regardless of the type of the tool 16, various tools suitable for wall machining, such as end mills and grindstones, can be applied.

(3) The present invention is widely applicable to at least a part of the scroll-shaped wall 32 in which the inner and outer wall surfaces are formed in an involute shape, and other parts, for example, the outermost scroll end 36 ( The shape such as FIG. 2) may be any shape. About the processing,
As with the central portion 34, the processing method according to the present invention or another processing method may be used as appropriate.

(4) In the present invention, when the involute curve is divided at the same pitch angle, the pitch angle can be set arbitrarily. However, it goes without saying that the smaller the division pitch angle, the higher the processing accuracy.

FIG. 12 shows division pitch angles (5 °, 10 °,
15 °, 20 °, 25 °) and the relationship between the base circle radius and the theoretical error amount are shown in a graph. As shown in the figure, if the division pitch angle is set to 15 ° or less, the base circle radius becomes
Even if it is 3.50 mm, the error amount can be theoretically suppressed to 0.50 μm or less. On the other hand, in the processing apparatus as shown in FIG. 1, the deviation of centering of the workpiece 30 mounted on the spindle (the deviation between the target rotation center and the actual rotation center) is generally 10%.
Since it exceeds μm, it is clear that the method of the present invention can process the involute curve with higher accuracy than the conventional method.

[0050]

As described above, according to the present invention, the wall shape of the involute curve portion is circularly interpolated so that the normal direction of the wall surface at the contact point between the wall surface and the tool always faces the fixed X-axis direction. Rotating the scroll-like workpiece, and
Since the tool is moved relative to the scroll-shaped workpiece in the X-axis direction and the Y-axis direction orthogonal to the scroll-shaped workpiece so as to follow the arc, the rotation center of the workpiece and the center of the involute base circle are shifted. Regardless of the presence or absence of eccentricity, there is an effect that the involute curve portion of the scroll-shaped wall in the workpiece can be processed with high accuracy.

[Brief description of the drawings]

FIG. 1 is an overall perspective view of a scroll processing device according to an embodiment of the present invention.

FIG. 2 is a front view showing an example of a scroll-shaped workpiece processed by the processing device.

FIG. 3 is a block diagram showing a functional configuration of an NC control device provided in the processing device.

FIG. 4 is a diagram showing a method of circularly interpolating a wall shape of an involute curve portion in the scroll-shaped workpiece.

FIG. 5 is a diagram showing an example of a method for determining the curvature of the arc.

FIGS. 6 (a), (b) and (c) are front views showing how an inner wall surface of an involute curve portion in the scroll-shaped workpiece is machined.

FIG. 7A is a front view showing a state of processing a central portion of the scroll-shaped workpiece, and FIGS. 7B and 7C are views showing a state of processing an outer wall surface of an involute curved portion of the scroll-shaped workpiece. It is a front view.

FIG. 8 is a flowchart showing an arithmetic control operation performed by the NC control device.

FIG. 9 is a diagram showing an example of a principle of calculating interpolation data in the NC control device.

FIG. 10 is a graph showing macroscopic relative movement amounts of a tool in an X-axis direction and a Y-axis direction with respect to a workpiece during processing according to the present invention.

FIGS. 11A to 11C are graphs showing microscopic relative movement amounts of a tool in an X-axis direction and a Y-axis direction with respect to a workpiece during processing according to the present invention.

FIG. 12 is a graph showing a relationship between a curve division pitch angle, a base circle radius, and a theoretical error amount in the method of the present invention.

[Explanation of symbols]

 13 Y-axis motor (Y-axis driving means) 25 X-axis motor (X-axis driving means) 28 C-axis motor (rotation driving means) 30 Scroll-like workpiece 32 Scroll-like wall 34 Center part 35 Involute curve part 35A Involute curve part Outer wall surface 35B Inner wall surface of involute curve portion 40 NC controller (drive control means) BC Basic circle of involute curve C1, C2, C3, C4, C5, C6, ... Arc ro Basic circle radius

Claims (5)

[Claims] 1. A method for processing a wall surface of an involute curved portion of a scroll-shaped workpiece having a scroll-shaped wall, wherein the scroll-shaped wall is formed with an involute curved portion having an involute curved surface. The scroll-shaped workpiece is interpolated by circularly interpolating the shape of the wall surface in the involute curve portion, and the normal direction of the wall surface at the contact point between the wall surface and the tool always faces a constant X-axis direction. While rotating about the center of the base circle of the involute curve or a point near the center, the tool is relatively moved in the X-axis direction and the Y-axis direction orthogonal to the scroll-like workpiece along the arc. A method for processing a scroll-shaped workpiece. 2. The method for processing a scroll-like workpiece according to claim 1, wherein a curve of a wall surface of the involute curve portion is divided at the same pitch angle, and an arc that approximates the curve is assigned to each of the divided curves. A method for processing a scroll-shaped workpiece, comprising: 3. The method for processing a scroll-shaped workpiece according to claim 1, wherein the workpiece is centered on an axis which is displaced from the center of the involute base circle within a radius equal to or smaller than the radius of the base circle. A method for processing a scroll-shaped workpiece, wherein the wall surface of the involute curve portion is processed while rotating. 4. An apparatus for machining a wall surface of an involute curved portion of a scroll-shaped workpiece having a scroll-shaped wall, wherein the scroll-shaped wall is formed with an involute curved portion whose wall surface forms an involute curved shape. Rotating drive means for rotating the workpiece about or at a point near the center of the base circle; and X and X parallel to the diameter of the base circle of the involute curve.
X-axis driving means for relatively moving in the axial direction, Y-axis driving means for relatively moving the tool and the workpiece in the Y-axis direction parallel to the diameter of the base circle of the involute curve and orthogonal to the X-axis direction Interpolating means for circularly interpolating the shape of the wall surface in the involute curve portion, and the normal direction of the wall surface at the contact point between the interpolated wall surface and the tool always faces the constant X-axis direction. While rotating the scroll-shaped workpiece about the center of the base circle of the involute curve or a point near the center, the tool is moved along the arc in the X-axis direction and orthogonal to the scroll-shaped workpiece along the arc. A machining control means for operating each of the driving means so as to relatively move in the Y-axis direction. 5. The scroll-shaped workpiece processing apparatus according to claim 4, wherein a curve on the wall surface of the involute curve portion is divided at the same pitch angle, and an arc that approximates the curve is assigned to each of the divided curves. A scroll-shaped workpiece processing apparatus, wherein the interpolation calculation means is configured as described above.