JPH105918A - Rolling method of annular body - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a rolling device of an annular body capable of improving finish precision of the inner diameter of an annular work. SOLUTION: An outer diameter of an annular body, which is worked to the extent the tip part of a probe is inserted in the inner diameter of annular work, is investigated beforehand, corresponding thereto a setting position for a start switch of a proximity switch is decided (step S1). When rolling of the annular work starts and the proximity switch detects a start switch main body, the probe is moved to an inner diameter measuring position by a back/forth direction cylinder and left/right direction cylinder, at the same time, the probe is energized so as to always slide on the inner peripheral face of annular work by the left/right direction cylinder (step S2, S3, S4, S5, S6). While measuring the inner diameter of annular work, rolling is continued, until the inner diameter is made to a desired size, the annular work is rolled/expanded for completion.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for rolling an annular body, and more particularly, to a method for rolling an annular body in which an outer diameter and an inner diameter of an annular work are formed to desired dimensions.

[0002]

2. Description of the Related Art FIG. 8 shows a conventional annular body rolling processing apparatus, particularly an annular body which performs cold rolling in which an annular work is rolled in the circumferential direction at room temperature and expanded to a desired outer diameter and inner diameter. It is a figure showing the schematic structure of a rolling processing device.

In this conventional apparatus for rolling an annular body, an outer peripheral surface of an annular workpiece 801 is formed by a forming roll 80.
2 and the inner peripheral surface of the annular work 801 is pressed by the mandrel 803 to perform rolling.

That is, a forming roll 802 supported by a processing feed slide 804 is in contact with an outer peripheral surface of an annular workpiece 801, and a mandrel 803 is in contact with an inner peripheral surface thereof. While the forming roll 802 is rotated by a motor (not shown), the mandrel 8 is rotated by the processing feed slide 804.
Move toward 03. Thereby, the annular work 8
01 is pressed between the forming roll 802 and the mandrel 803, and is rolled and expanded.

[0005] On the opposite side of the mandrel 803 from the forming roll 802, two support rolls (not shown) are arranged. The mandrel 803 is urged by the two support rolls in a state where the annular work 801 is extrapolated, and presses the forming roll 802 and the annular work 801.
The two support rolls have the same radius, rotate around a common rotation axis, and are arranged on both sides of the annular work 801 so as to sandwich the annular work 801.

On the other side of the forming roll 802, the measuring element 8 is brought into contact with the outer peripheral surface of the annular work 801.
05 is provided, and a gauge 806 with a contact point is connected to the measuring element 805. The tracing stylus 805 is displaced leftward in the figure as the annular work 801 is rolled and expanded. The gauge with contact 806 measures the amount of displacement of the tracing stylus 805, and when the measured amount of displacement of the tracing stylus 805 reaches a predetermined amount, the annular workpiece 801 is rolled and expanded to a desired outer diameter. Then, the rolling process is completed.

[0007]

As described above, the annular workpiece 801 has been conventionally subjected to rolling while measuring its outer diameter, including the case where the accuracy of the inner diameter is particularly required. In addition, the rolling process of the annular work 801 based on the outer diameter is performed because the inner diameter of the annular work 801 before being processed is small and both sides of the annular work 801 are sandwiched between the two support rolls. This is because it is difficult to insert a measuring member into the inside diameter, and it is therefore difficult to perform a rolling process while measuring the inside diameter.

For this reason, the annular workpiece 801 is usually subjected to rolling while measuring the outer diameter, and the inner diameter is indirectly measured on the assumption that the volume of the annular workpiece 801 is constant. That is, for example, by providing a circumferential groove or the like on the outer peripheral surface of the forming roll 802 and defining the width of the annular work 801 to be rolled, indirectly by measuring the outer diameter of the annular work 801 having a constant volume. The annular workpiece 801 can be rolled while measuring the inner diameter.

However, in the above-described method, the accuracy of the pre-machining is rough, so that each annular workpiece 80
Since there is actually a variation in the volume of No. 1, there is a disadvantage that it is easy to include an error in the inner diameter measured indirectly through this volume, and it is difficult to accurately process the annular work 801. For this reason, when the inner diameter of the machined ring is important, for example, when a bearing ring of a bearing part is to be formed, the inner diameter of the ring-shaped work 801 which is rolled on the basis of the outer diameter can be obtained. The finished dimensions were within the tolerance.

FIG. 9 is an explanatory view of the stamping in the conventional example.

In FIG. 1, a ring 801 'processed based on an outer diameter is fixed by a ring fixing jig 901 and an inner diameter sizing die 902 is inserted into the inner diameter.

However, the method of processing the annular workpiece 801 while indirectly measuring the inner diameter from the outer diameter and the volume tends to include an error, as described above, and therefore, the inner diameter is sufficiently corrected even when the die is threaded. There is a disadvantage that the sizing die 902 cannot be formed or the sizing die 902 is damaged when the die-cutting is performed.

Further, for example, the average value of the inner diameter and the outer diameter of the annular work, or the thickness (ie, 1 / (the difference between the inner diameter and the outer diameter) of the annular work)
2) to a predetermined target value, it is desirable to directly measure the inner diameter in addition to the outer diameter. However, conventionally, since the processing was performed based only on the measured outer diameter,
Also in this case, there is a disadvantage that the annular workpiece cannot be machined with high accuracy.

SUMMARY OF THE INVENTION The present invention has been made to solve the above problems, and it is possible to improve the finishing accuracy of the inner diameter of an annular workpiece and to omit the sizing processing. It is intended to provide a device.

[0015]

In order to achieve the above object, an invention according to claim 1 comprises a forming roll for pressing an annular work from its outer peripheral surface and a mandrel for pressing the annular work from its inner peripheral surface. By rotating at least one of them and bringing the forming roll and the mandrel close to each other, the annular work is nipped between the forming roll and the mandrel, and the annular work is rolled in the circumferential direction to expand the diameter. In the method for rolling an annular body, the outer diameter of the annular work to be rolled and expanded is monitored, and the monitored outer diameter of the annular work is different from the tip where the mandrel contacts. When the probe reaches a predetermined outer diameter at which the tip of the probe configured to slide on the inner peripheral surface of the annular work can be inserted, the tip of the probe is moved forward. The annular workpiece is moved from a position not in sliding contact with the inner peripheral surface to a position in which it is in sliding contact with the annular workpiece, and a displacement amount of the tracing stylus caused by rolling and expanding the annular workpiece is detected. Based on this, the inner diameter of the annular work is calculated.

In order to achieve the above object, a forming roll for pressing the annular work from its outer peripheral surface, a mandrel for pressing the annular work from its inner peripheral surface, and at least one of the forming roll and the mandrel are provided. A rotating means for rotating, and a sliding means for moving at least one of the forming roll and the mandrel to bring the forming roll and the mandrel close to each other, wherein at least one of the forming roll and the mandrel is rotated by the rotating means. By bringing the forming roll and the mandrel close to each other while rotating, the annular work is pressed between the forming roll and the mandrel, and the annular work is rolled in the circumferential direction and expanded. In a rolling device for rolling an annular body,
A measuring element configured such that its tip is in sliding contact with the inner peripheral surface of the annular work at a part different from the part with which the mandrel contacts, and a position where its distal end is in sliding contact with the inner peripheral surface of the annular work. Moving means for moving the probe between a position where it does not come into sliding contact with the workpiece, detecting means for detecting the amount of displacement of the tracing stylus accompanying rolling and expanding of the annular work, and displacement of the tracing stylus detected by the detecting means Calculating means for calculating the inner diameter of the annular work based on the amount, and monitoring the outer diameter of the annular work to be rolled and expanded, and monitoring the outer diameter of the annular work to determine the inner diameter of the annular work. The moving means is controlled such that when the tip of the tracing stylus reaches a predetermined outer diameter into which the tip can be inserted, the tracing stylus is moved to a position where the tip comes into sliding contact with the inner peripheral surface of the annular work. Having control means It may be characterized.

In the apparatus for rolling an annular body according to the first aspect, the control means may control the annular workpiece when the inner diameter of the annular work calculated by the arithmetic means reaches a predetermined size. Rolling and expanding of the work may be terminated.

[0018] The control means may be arranged such that, when the measured difference between the outer diameter and the inner diameter of the annular work or the average value of the outer diameter and the inner diameter of the annular work reaches a predetermined value, Rolling and diameter expansion may be terminated. You may do so.

[0019]

Embodiments of the present invention will be described below with reference to the drawings.

FIG. 1 is a diagram showing a schematic configuration of an apparatus for rolling an annular body according to an embodiment of the present invention.

As shown in FIG. 1, a rolling apparatus according to an embodiment of the present invention comprises a forming roll 102 for pressing an annular work 101 from an outer peripheral surface thereof,
And a mandrel 103 which presses the inner surface 1 from its inner peripheral surface. The forming roll 102 and the mandrel 103 have rotation axes parallel to each other, and cooperate to clamp the annular work 101.

The forming roll 102 has an outer peripheral surface shape corresponding to the finished shape of the outer peripheral surface of the annular work 101, and the mandrel 103 has an outer peripheral surface shape corresponding to the finished shape of the inner peripheral surface of the annular work 101. Have. The forming roll 102 is driven in the left and right directions in the figure by a slide mechanism (not shown).

The mandrel 103 is mounted on the mandrel support 10.
4 and is urged by two support rolls 105 a and 105 b (see FIGS. 4 and 5) from the opposite side of the forming roll 102 to pinch the annular work 101 with the forming roll 102.

The support rolls 105a and 105b have the same radius, and the forming roll 102 and the mandrel 10
3 rotates about a common rotation axis parallel to each rotation axis.
FIG. 1 shows only the support roll 105b disposed on the front rear side in the figure. The support roll 105b is provided with an accommodation groove 105c for accommodating a later-described measuring element 108, which is a part of a mechanism for measuring the inner diameter of the annular work 101.

On the opposite side of the annular work 101 from the forming roll 102, the outer peripheral surface of the annular work 101 is contacted.
A contact 106 is provided, and the contact 106 is fixed to a start switch 107 fixed to move integrally with the forming roll 102.

Further, between the support roll 105a and the support roll 105b, a stylus 108 whose leading end is inserted into the inner diameter of the annular work 101 at a stage where the rolling of the annular work 101 has progressed to some extent. The tracing stylus 108 is connected to the front-rear cylinder 1
The front-rear direction cylinder 110 is fixed to the left-right direction cylinder 111.

Next, referring to FIG.
A mechanism for measuring the outer diameter of the device will be described. FIG. 2 is a diagram showing a configuration of a mechanism for measuring the outer diameter of the annular workpiece 101. FIG. 2A is a view of the mechanism as viewed from the front in FIG. 1, and FIG. 2B is a view of the mechanism as viewed from the right in FIG.

As shown in FIG. 2, the mechanism for measuring the outer diameter of the annular work 101 is composed of a contact 106 and a start switch 107. Also, the start switch 107
Are a main body 501, a base 502, and a guide bar 503.
, Linear guide 504, spring 505, slide 5
06 and a proximity switch 507.

The contact 106 is fixed to the main body 501 of the start switch 107. The base 502 is shown in FIG.
The guide bar 5 has a substantially U-shape when viewed from above.
2A and the linear guide 504 are supported at both ends, and a proximity switch 507 is provided on the wall at the front rear side in FIG.
Is attached. The main body 501 has a slide 506
Is attached, and the guide bar 503 is attached to the main body 501.
Directly, and the linear guide 504 guides the movement of the main body 501 indirectly via the slide 506.

The spring 505 urges the main body 501 rightward in FIG. Due to the urging force of the spring 505, the contact 106 is always in sliding contact with the outer periphery of the annular workpiece 101 during rolling. The proximity switch 507 is connected to the base 50
2 can be changed, and when the main body 501 is displaced to the installation position, a detection signal is output.

The installation position is determined in advance by examining the outer diameter of the annular work 101 when the tip of the tracing stylus 108 has been machined to such an extent that it can be inserted into the inner diameter of the annular work 101. As the proximity switch 507 outputs a detection signal corresponding to the position of the main body 501,
The position of the proximity switch 507 is adjusted on the base 502.

Next, referring to FIG.
A mechanism for measuring the inner diameter of the device will be described. FIG. 3 is a diagram illustrating a configuration of a mechanism for measuring the inner diameter of the annular workpiece 101. FIG. 2A is a view of the mechanism as viewed from the front in FIG. 1, and FIG. 2B is a view of the mechanism as viewed from the right in FIG.

As shown in FIG. 3, the mechanism for measuring the inner diameter of the annular workpiece 101 includes a tracing stylus 108, a displacement measuring device 109, a front-rear direction cylinder 110, and a left-right direction cylinder 111.

The tracing stylus 108 is supported by the support roll 105b.
3 so that it can be stored in the storage groove 105c provided in FIG.
It has a substantially arc shape when viewed from the front in FIG. For this reason, in a standby state in which the measurement of the inner diameter of the annular workpiece 101 is not performed, the measuring element 108 is used by the supply device (not shown) to supply / discharge the annular workpiece 101.
01 does not interfere.

The tracing stylus 108 has a substantially U-shape when viewed from the front in FIG. 3B. Therefore, when measuring the inner diameter of the annular work 101, the annular work 1
The distal end of the tracing stylus 108 provided with the stylus 108a can be inserted into the inner diameter of the annular workpiece 101, avoiding the outer surface of the stylus 01 (see FIG. 4).

The front-rear direction cylinder 110 causes the tracing stylus 108 to stroke in the left-right direction in FIG. 3B within a range of about 10 mm. The front-rear direction cylinder 110 is mounted on a slider 111a of the left-right direction cylinder 111. The left-right direction cylinder 111 moves the measuring element 108 in a range of about 30 mm in conjunction with the movement of the front-rear direction cylinder 110 in FIG. Stroke in the left and right directions. The right end of the stroke of the left-right cylinder 111 is set so that the tracing stylus 108 does not interfere with the mandrel 103.

Further, a connecting rod 111b which is in sliding contact with the displacement measuring instrument 109 is attached to the left-right cylinder 111. The displacement measuring device 109 is connected to the mandrel support 104.
And outputs an electric signal whose value changes in accordance with the contact position with the connecting rod 111b.

FIG. 4 is a diagram showing a correlation between the annular workpiece 101 and the measuring element 108 when the measuring element 108 is at the inner diameter measuring position. At the inner diameter measuring position, the tracing stylus 108 moved in the direction of arrow A in the figure by the sliding operation of the front-rear direction cylinder 110 is
01 is placed in the inside diameter.

FIG. 5 is a diagram showing a correlation between the annular workpiece 101 and the tracing stylus 108 when the tracing stylus 108 is in the standby state. In the standby state, the tracing stylus 108 moved in the direction of arrow B in the figure by the sliding operation of the front-rear direction cylinder 110 is
01 is not located within the inner diameter.

Next, the operation of the rolling machine according to this embodiment will be described. FIG. 6 is a block diagram showing a schematic configuration of a control mechanism of the rolling device for an annular body according to one embodiment of the present invention. FIG. 7 is a flowchart of a process by the control mechanism of the rolling device for an annular body according to one embodiment of the present invention.

The control mechanism of the rolling processing apparatus according to the present embodiment has a processing control device 601, which includes a displacement measuring device 109 and a longitudinal cylinder 11.
0, an actuator means 604 for rotating and moving the left / right direction cylinder 111, the proximity switch 507, and the forming roll 102 is connected thereto. Note that a monitor for monitoring the displacement value may be connected to the processing control device 601.

The processing control device 601 includes the detection signal from the proximity switch 507 and the displacement measuring device 109.
Is input. Further, the processing control device 601 outputs a signal notifying the start and end of the processing of the annular workpiece 101 to the actuator means 604, and an advancing / retreating command for driving the front-rear direction cylinder 110 and the left-right direction cylinder 111 in desired directions. Is output.

In FIG. 7, first, when the inner diameter of the annular workpiece 101 reaches the inner diameter at the time of completion of machining, the displacement measuring device 1
09 is set as a reference value for indicating the completion of the processing.

That is, a master ring manufactured in advance so as to exactly match the inner and outer diameters at the time of completion of processing is prepared, and this master ring is attached to the annular workpiece 108 in FIG.
In the same manner as above, the probe 1 is actually passed through the mandrel 103.
08 contact the inner diameter of the master ring.
In a state where the maximum distance from the tip of 08 to the outer diameter surface of the mandrel 103 is equal to the inner diameter of the master ring, the value of the electric signal output from the displacement measuring device 109 is set as a reference value for indicating the completion of processing. . This reference value is stored in a memory unit (not shown) in the processing control device 601.

In the case where a large number of annular workpieces 108 are continuously processed, the reference value setting process in step S1 may be executed only when the first one is processed.
In the processing of the second and subsequent annular workpieces 108, it is not necessary to further perform the processing of step S1.

Next, the annular workpiece 101 is set between the forming roll 102 and the mandrel 103 by the supply device (not shown) (step S2). Annular work 101
Is completed, a signal instructing the start of the machining operation is input from the machining control device 601 to the actuator means 604, the forming roll 102 is moved, the annular work 101 is sandwiched between the mandrel 103, and then, By rotating the forming roll 102, the annular workpiece 1
01 is started (step S3).
At this point, the contact 106 is in contact with the outer peripheral surface of the annular workpiece 101, but the space formed by the inner peripheral portion of the annular workpiece 101 and the mandrel 103 is narrow, and the measuring element 108
Since it is impossible to insert the
In the standby position shown in FIG.

Next, it is determined whether or not the proximity switch 507 has output a detection signal (step S4). When no detection signal is output from the proximity switch 507,
Assuming that the tip of the tracing stylus 108 cannot be inserted into the inner diameter of the annular workpiece 101, this determination is repeated at appropriate minute time intervals.

In step S4, the proximity switch 507
Is determined to have output the detection signal, the annular workpiece 10
It is assumed that the front and rear cylinders 1 have been machined to a size that allows the tip of the tracing stylus 108 to be inserted into the inner diameter thereof.
An advancing / retreating command is output to 10 and the tracing stylus 108 is moved to the inner diameter measuring position shown in FIG. 4 (step S5).

Next, the tracing stylus 108 is moved to the left in FIG. 1 by the left and right cylinders to bring the stylus provided at the tip of the tracing stylus into contact with the inner peripheral surface of the ring-shaped workpiece 101, and the stylus is moved The tracing stylus 108 is urged to the left in FIG. 1 with a force of about 0.1 N so as to always be in sliding contact with the inner peripheral surface of the 101 (step S6).

Next, the machining control device 601 measures the inner diameter of the annular work 101 at that time based on the electric signal output from the displacement measuring device 603 (step S7), and determines whether the inner diameter has reached a desired inner diameter. It is determined whether or not it is (step S8). Specifically, the data of the measured current position is taken into the processing control device 601 and compared with the reference value stored in the memory unit in step S1 by a comparator (not shown). If the inside diameter has not reached the desired inside diameter,
The above determination is repeated at appropriate small time intervals, and when it is determined that the inner diameter has reached the desired inner diameter, the comparator outputs an electric signal. That is, the actuator means 6
A signal for instructing the end of the machining operation is input to 04.

As described above, according to the annular body rolling processing apparatus of the present embodiment, the inner diameter is measured directly from the time when the tip of the measuring element 108 can be inserted into the inner diameter of the annular work 101. In addition, since the annular work 101 can be rolled, the difference in the inner diameter of the processed annular body can be reduced. As a result, the accuracy of the repetitive machining of the inner diameter is improved, so that the allowance for the inner diameter turning or the inner diameter grinding, which is the next step, can be made constant. For this reason, the processing time in the next step can be stabilized, the machining allowance can be reduced, and the productivity in the next step can be further improved.

In the above embodiment, the annular work 1 is controlled by the proximity switch 507 of the start switch 107.
Start switch 10 when the inner diameter of 01 becomes measurable
7, the position of the body 501 was detected.
Instead of the proximity switch 507, a start switch 107
A displacement measuring device such as a linear scale for measuring the displacement of the main body 501 may be provided, and the start time of the measurement of the inner diameter and the end time of the processing may be determined based on the output of the displacement measuring device.

That is, the outer diameter of the annular work 101 is calculated from the output of the displacement measuring device provided in the start switch 107 in place of the proximity switch 507, and when the outer diameter reaches a predetermined outer diameter, the inner diameter is measured. To start. Further, at the end time of the processing, the rolling processing of the annular work 101 is ended when the calculated difference between the outer diameter and the inner diameter of the annular work 101 or the average value of the outer diameter and the inner diameter each reaches a predetermined value. It may be.

[0054]

According to the method for rolling an annular body according to the first aspect, the outer diameter of the annular work to be rolled and expanded is monitored, and the monitored outer diameter of the annular work is determined by the mandrel. When the tip reaches a predetermined outer diameter at which the tip of the probe comes into sliding contact with the inner peripheral surface of the annular work at a portion different from the contacting portion, the tip of the probe is moved to the annular workpiece. Is moved from a position not in sliding contact with the inner peripheral surface to a position in which it is in sliding contact with the inner peripheral surface of the annular work. Since the inner diameter of the annular work is calculated, the annular work can be machined while directly measuring the inner diameter of the annular work, so that the finishing accuracy of the inner diameter of the annular work can be improved.

Further, with the above-described configuration, the finished size of the inner diameter of the ring after processing is fixed without being affected by the variation in the volume of each annular work material. Therefore, the inner diameter is corrected by sizing processing such as through a die. Thus, the amount of straightening becomes constant, so that the working efficiency of the sizing process is improved and the life of the through die is prolonged.

Further, since the finished size of the inner diameter of the ring after processing is made constant, it is not necessary to perform die threading for an annular work having a relatively simple cross-sectional shape, thus simplifying the ring processing step. Therefore, the sizing processing cost, which accounts for a large portion of the ring processing cost, can be reduced.

Further, by making the finished dimensions of the inner diameter of the ring after machining constant, the amount of machining required in the next step (inner diameter turning, inner diameter grinding, etc.) is reduced, and the work efficiency is improved. Can be. Further, the work material volume can be reduced by reducing the amount of processing in the next step, so that the yield can be improved.

Further, it is easy to make the average value of the inner diameter and the outer diameter uniform and to make the thickness in the radial direction uniform.

[Brief description of the drawings]

FIG. 1 is a diagram showing a schematic configuration of an annular body rolling processing apparatus according to one embodiment of the present invention.

FIG. 2 is a diagram showing a configuration of a mechanism for measuring an outer diameter of an annular workpiece 101 of the annular body rolling apparatus according to one embodiment of the present invention.

FIG. 3 is a diagram showing a configuration of a mechanism for measuring an inner diameter of an annular workpiece 101 of the annular body rolling processing apparatus according to one embodiment of the present invention.

FIG. 4 is a diagram showing a correlation between the annular workpiece 101 and the tracing stylus 108 when the tracing stylus 108 of the annular body rolling processing apparatus according to one embodiment of the present invention is at the inner diameter measuring position.

FIG. 5 is a diagram illustrating a correlation between the annular workpiece 101 and the tracing stylus 108 when the tracing stylus 108 of the annular body rolling processing apparatus according to one embodiment of the present invention is in the standby state.

FIG. 6 is a block diagram showing a schematic configuration of a control mechanism of the rolling device for an annular body according to one embodiment of the present invention.

FIG. 7 is a flowchart of a process by a control mechanism of the annular body rolling processing apparatus according to one embodiment of the present invention.

FIG. 8 is a view showing a schematic configuration of a conventional annular body rolling processing apparatus.

FIG. 9 is a diagram showing a method of performing die cutting of a ring processed by a conventional processing method.

[Explanation of symbols]

 Reference Signs List 101 annular workpiece 102 forming roll 103 mandrel 104 mandrel support base 105a, 105b support roll 106 contact 107 activation switch 108 measuring element 109 displacement measuring instrument 110 front-back direction cylinder 111 left-right direction cylinder 507 approach switch 601 control processing device

Claims (1)

[Claims] 1. By rotating at least one of a forming roll for pressing an annular work from its outer peripheral surface and a mandrel for pressing the annular work from its inner peripheral surface, the forming roll and the mandrel are brought close to each other,
The method according to claim 1, wherein the annular work is squeezed between the forming roll and the mandrel, and the annular work is rolled in the circumferential direction to expand the diameter.
The outer diameter of the annular work to be expanded is monitored, and the monitored outer diameter of the annular work is different from the part where the mandrel contacts, so that the tip thereof slides on the inner peripheral surface of the annular work. When a predetermined outer diameter is reached at which the tip of the tracing stylus configured to be inserted can be inserted, the tip is moved from a position at which the tip does not slid to the inner peripheral surface of the annular work to a position at which the tip comes into sliding contact, A rolling process for an annular body, comprising detecting a displacement amount of the tracing stylus caused by rolling and expanding the diameter of the annular work, and calculating an inner diameter of the annular work based on the detected displacement amount of the tracing stylus. Method.