JP3837359B2 - Workpiece dimension measuring method and workpiece dimension measuring apparatus - Google Patents

Description

[0001]
BACKGROUND OF THE INVENTION
The present invention measures the radius of the inner surface of each of a plurality of segments that are annularly arranged around the axis and divided in the circumferential direction with the segments biased radially inward toward the axis. The present invention relates to a workpiece dimension measuring method and a workpiece dimension measuring apparatus directly used for carrying out the method.
[0002]
[Prior art]
In Japanese Patent Laid-Open No. 8-152318, in order to measure the inner diameter of a cylindrical material, the first and second movable members that can be expanded and contracted by a rotating shaft disposed at the center of the cylindrical material are supported. There is described what measures the inner diameter of a cylindrical material based on the amount of expansion and contraction of the first and second movable members while rolling a roller provided at the tip of the movable member along the inner peripheral surface of the cylindrical material. Yes.
[0003]
Japanese Patent Laid-Open No. 2000-356597 discloses a laser-type distance measuring device provided at the tip of a measuring arm that rotates around the center of the core shroud to measure the inner diameter of the core shroud. An instrument for measuring the inner diameter of a core shroud is described.
[0004]
[Problems to be solved by the invention]
By the way, what was described in the said Unexamined-Japanese-Patent No. 8-152318 and Unexamined-Japanese-Patent No. 2000-356597 is a thing in which the to-be-measured object is integrated and the internal diameter which should be measured does not change. On the other hand, for example, a shroud covering a turbine wheel of a gas turbine engine is composed of a plurality of segments divided in the circumferential direction, and each segment is loosely fitted so as to move relative to each other. When the gas turbine engine is operated, the segments are urged radially inward by the action of air pressure to closely fit, and the gap with the tip of the turbine wheel is kept constant. Since it is impossible to measure the inner diameter of the shroud during operation of the gas turbine engine, the segments are urged radially inward to reproduce the shape of the actual operating state, and in that state the inner diameter of the shroud is measured. There is a need to do.
[0005]
The present invention has been made in view of the above-described circumstances, and an object thereof is to make it possible to easily and accurately measure the radius of the inner surface of each of a plurality of segments that are divided in the circumferential direction and can move relative to each other. To do.
[0006]
[Means for Solving the Problems]
In order to achieve the above object, according to the first aspect of the present invention, the radius of the inner surface of each of a plurality of segments arranged in an annular shape around the axis and divided in the circumferential direction is set to the segments. In the workpiece dimension measurement method for measuring in a state in which the workpiece is urged radially inward toward the axis, a plurality of segments are sucked by the suction means and are urged radially inward toward the axis. Laser light is transmitted to the gap between the outer surface of the annular reference shield having a radius and centered on the axis and the inner surface of each segment, and the gap is based on the amount of laser light received through the gap. A dimension measurement method for workpieces is proposed, in which the radius of the inner surface of each segment is measured by adding the size of the gap to the predetermined radius.
[0007]
According to the above configuration, the measurement is performed in a state where a plurality of segments arranged in an annular shape around the axis and divided in the circumferential direction are sucked by the suction means and biased radially inward toward the axis. In addition, the segment position can be adjusted to a position in accordance with the actual use state, and measurement can be performed, thereby improving measurement accuracy. In addition, a laser beam is transmitted to the gap between the outer surface of the annular reference shield arranged around the axis and the inner surface of each segment to calculate the size of the gap, and the gap is calculated at a predetermined radius of the reference shield. Since the size is added to measure the radius of the inner surface of each segment, the radius of the segment can be measured in a non-contact manner to prevent damage.
[0008]
According to the invention described in claim 2, the radius of the inner surface of each of the plurality of segments arranged in an annular shape around the axis and divided in the circumferential direction is set so that the segments are directed in the radial direction toward the axis. In a workpiece dimension measuring apparatus for measuring in a state of being biased inward, a frame arranged to face the inner surfaces of a plurality of segments assembled so as to be movable in a radial direction, and a frame arranged on an axis A center shaft that is supported so as to be movable up and down relative to the frame, a plurality of guide rods that are supported by the frame so as to be movable in a radial direction and are urged radially inward by springs, and the radial directions of the respective guide rods An adsorbing means provided at the outer end and capable of adsorbing to the inner surface of the corresponding segment, and a cap formed on the center shaft and capable of pressing the radial inner end of the guide rod. An annular reference shield supported by the frame so as to face the inner surfaces of the plurality of segments with a predetermined radius centered on the axis, and a gap between the inner surface of each segment and the outer surface of the reference shield There is proposed a workpiece dimension measuring apparatus comprising a gap measuring means for measuring the size of the workpiece.
[0009]
According to the above configuration, when the center shaft is moved up and down relative to the frame, the guide rod whose inner end in the radial direction is pressed against the cam surface of the center shaft moves outward in the radial direction, and the suction provided at the outer end in the radial direction. Means adhere to the inner surface of the corresponding segment. When the center shaft is returned to the original position from this state, the segment adsorbed by the adsorbing means moves inward in the radial direction together with the guide rod by the spring force of the spring, and the position of the segment becomes a position that matches the actual use state. It is arranged. In this state, by measuring the size of the gap between the outer surface of the annular reference shield having a predetermined radius centered on the axis and the inner surface of each segment by the gap measuring means, each according to the actual use state The radius of the inner surface of each segment can be measured.
[0010]
According to the invention described in claim 3, in addition to the configuration of claim 2, the gap measuring means includes a laser transmitter and a laser receiver disposed at both ends in the axial direction across the gap, A workpiece dimension measuring apparatus is proposed in which the laser light receiving unit measures the size of the gap based on the amount of received laser light.
[0011]
According to the above configuration, since the gap measuring means is configured by the laser transmitter and the laser receiver arranged at both ends in the axial direction across the gap between the inner surface of the segment and the outer surface of the reference shield, it passes through the gap. Thus, the size of the gap can be accurately measured based on the amount of laser light received by the laser light receiving unit. Moreover, since the measurement is performed without contact, there is no possibility of damaging the segment.
[0012]
According to the invention described in claim 4, in addition to the structure of claim 2, there is proposed a workpiece dimension measuring apparatus characterized in that the gap measuring means is rotatable together with the center shaft.
[0013]
According to the above configuration, the radius of the inner surfaces of the plurality of segments can be efficiently measured by rotating the gap measuring means together with the center shaft.
[0014]
According to the fifth aspect of the present invention, in addition to the configuration of the second aspect, the rotation position detection means for detecting the rotation position of the center shaft is provided, and the gap measurement means is based on the detection result of the rotation position detection means. A workpiece dimension measuring apparatus is proposed which measures the size of the gap.
[0015]
According to the above configuration, since the gap measuring means measures the size of the gap based on the rotational position of the center shaft detected by the rotational position detecting means, the radius of the inner surface of the plurality of segments can be obtained simply by rotating the center shaft. It can be measured automatically.
[0016]
The support plate 85 and the guide plate 95 of the embodiment correspond to the frame of the present invention, and the suction pad 102 of the embodiment corresponds to the suction means of the present invention, and the laser transmitter 113 and the laser receiver 116 of the embodiment. Corresponds to the gap measuring means of the present invention, and the limit switch 118 and the detected member 119 of the embodiment correspond to the rotational position detecting means of the present invention.
[0017]
DETAILED DESCRIPTION OF THE INVENTION
Hereinafter, embodiments of the present invention will be described based on examples of the present invention shown in the accompanying drawings.
[0018]
1 to 10 show an embodiment of the present invention. FIG. 1 is a diagram for explaining the overall structure of a turbofan engine. FIG. 2 is an overall side view of the measuring apparatus (cross-sectional view taken along line 2-2 in FIG. 3). 3 is a view taken in the direction of arrow 3 in FIG. 2, FIG. 4 is an enlarged view of a portion 4 in FIG. 2, FIG. 5 is a sectional view taken along line 5-5 in FIG. 7 is an enlarged view of a portion 7 in FIG. 4, FIG. 8 is an operation explanatory diagram corresponding to FIG. 7, FIG. 9 is an operation explanatory diagram corresponding to FIG. 5, and FIG. .
[0019]
First, the overall structure of the turbofan engine will be described with reference to FIG. The turbofan engine includes an inner shaft 11 and an outer shaft 12 that is fitted to the outer periphery of the inner shaft 11 so as to be relatively rotatable. An axial flow type fan 13 is provided at the front end of the inner shaft 11, and an axial flow type first stage low pressure turbine wheel 14 and a second stage low pressure turbine wheel 15 are provided at the rear end. A centrifugal compressor wheel 16 is provided at the front end of the outer shaft 12 shorter than the inner shaft 11, and an axial flow type high-pressure turbine wheel 17 is provided at the rear end.
[0020]
A part of the air sucked from the front part of the engine and compressed by the fan 13 is discharged from the rear part of the engine through the bypass passage 18 arranged along the outer periphery of the engine, and the remainder of the air is the bypass passage. The air is guided to the compressor wheel 16 through a compressed air passage 19 disposed radially inward of the air pipe 18. The air further compressed by the compressor wheel 16 is supplied to an annular combustor 20 where it is mixed with the fuel injected from the fuel injection nozzle 21 and burned. The fuel gas generated in the combustor 20 includes a high-pressure turbine wheel 17 provided at the upstream end of the combustion gas passage 22, and first and second-stage low-pressure turbine wheels 14 and 15 provided in an intermediate portion of the combustion gas passage 22. It is discharged from the rear part of the engine through.
[0021]
Next, the structure of a measuring apparatus that measures the radius of the turbine shroud covering the outer periphery of the high-pressure turbine wheel 17 will be described with reference to FIGS.
[0022]
The measuring device includes a disk-shaped base member 81, and the lower end of the intermediate case 43 of the turbofan engine is placed on the upper surface of the base member 81 and positioned by a plurality of knock pins 82. A substantially cylindrical gas generator case 44 is coupled to the upper peripheral portion of the intermediate case 43, a turbine case 45 is coupled to the upper peripheral portion of the gas generator case 44, and the intermediate case 43, the gas generator case 44, and the like. Are connected by a centrifugal shroud 46. A turbine shroud 47 supported by the inner peripheral portion of the turbine case 45 and surrounding the outer peripheral portion of the high-pressure turbine wheel 17 is composed of a plurality of (in the embodiment, 16) segments 48. (See FIG. 5). Each segment 48 is loosely supported on the inner periphery of the turbine case 45 via a holder 49 so as to be able to move relative to each other (see FIG. 7). During the operation of the turbofan engine, the high-pressure air compressed by the compressor wheel 16 acts on the outer periphery of the turbine shroud 47, so that the plurality of segments 48 are urged radially inward and closely contact each other, A minute gap is secured between the outer peripheral portion of the high-pressure turbine wheel 17.
[0023]
The measuring device includes an annular frame 83 that is fitted and fixed to a circular opening of a turbine case 45 of a turbofan engine, and a disk-shaped support plate 85 is provided on the lower surface thereof via a plurality of stays 84. Fixed. A lid member 87 is fixed by bolts 88 so as to cover the upper surface of the cylindrical member 86 fixed to the center portion of the support plate 85, and an opening portion 87a at the center of the lid member 87 and an opening portion 85a at the center of the support plate 85. In addition, a center shaft 90 having a knob 89 at its upper end is supported so as to be rotatable and vertically movable. That is, the center shaft 90 includes a first shaft 91 having a small diameter and a second shaft 92 having a large diameter fixed to the outer periphery of the first shaft 91, and the first shaft 91 has an opening 87 a of the lid member 87. The second shaft 92 passes through the opening 85a of the support plate 85. A spring 93 is contracted between the lower surface of the flange 92 a formed at the upper end of the second shaft 92 and the peripheral edge of the opening 85 a of the support plate 85, and the flange 92 a becomes a lid member 87 by the elastic force of the spring 93. The center shaft 90 is urged upward so as to abut against the lower surface of the center shaft 90. The center shaft 90 is disposed on the axis L of the turbine shroud 47.
[0024]
A guide plate 95 is fixed to the lower surface of the support plate 85 by a plurality of bolts 94... And eight guide cylinders 96 are fixed radially to the guide plate 95. A guide rod 97 is slidably fitted in each guide cylinder 96 and is urged radially inward by a spring 98 disposed between the guide cylinders 96. A bolt-shaped cam follower 99 is provided at the radially inner end of the guide rod 97, and a conical cam surface 92 b that can come into contact with the head of the cam follower 99 is formed at the lower end of the second shaft 92.
[0025]
Four suction pads 102... Are radially supported by arcuate brackets 101 fixed to the radially outer ends of the respective guide rods 97 with nuts 100. These four suction pads 102 are sucked by two each on one and the other of the two adjacent segments 48, 48. Further, the short cylindrical reference shield 104 fixed to the lower surface of the support plate 85 with bolts 103... Has a gap β between the outer surfaces of the sixteen segments 48 of the turbine shroud 47 (see FIGS. 9 and 10). Opposite through. As shown in FIGS. 7 and 9, the radius of the outer surface of the reference shield 104 around the axis L is R. The reference shield 104 is formed with 32 openings 104a through which the 32 suction pads 102 can pass.
[0026]
An annular header 105 is fixed to the lower surface of the guide plate 95 by bolts 106. An annular passage 105 a sealed by a pair of O-rings 108 is formed between the header 105 and the header cover 107. The annular passage 105a is connected to a vacuum pump (not shown) via a vacuum tube 109, and eight radiation passages 105b radially branching from the annular passage 105a are provided with eight brackets 101 ... Connected to. A branch passage 101a formed in each bracket 101 communicates with the four suction pads 102.
[0027]
A laser transmitter 113 is fixed to the tip of an upper arm 112 fixed in the radial direction by a bolt 111 near the upper end of the center shaft 90, and a lower arm fixed in the radial direction by a bolt 114 at the lower end of the center shaft 90. A laser receiving unit 116 is fixed to the tip of 115. The collar 117 fitted to the outer circumference of the first shaft 91 is disposed between the lower arm 115 and the second shaft 92 and has a function of positioning the second shaft 92 in the axial direction. The laser transmitting unit 113 and the laser receiving unit 116 face each other in the vertical direction, and a part of the 5 mm-wide laser beam transmitted from the laser transmitting unit 113 is blocked by the reference shield 104 and the other part is blocked. It is blocked by the segment 48 and the remaining part passes through the gap β and is received by the laser receiving unit 116.
[0028]
A limit switch 118 composed of a photoelectric switch is provided on the upper arm 112, and 16 detected members 119 detected by the limit switch 118 are arranged on the upper surface of the lid member 87 at equal intervals in the circumferential direction. . When the limit switch 118 detects one of the detected members 119..., The laser beam transmitter 113 transmits the laser beam for a predetermined time, and the laser beam passes through the gap β in the central portion in the circumferential direction of the corresponding segment 48. Then, the laser light receiving unit 116 receives the light.
[0029]
Next, the operation of the embodiment of the present invention having the above configuration will be described.
[0030]
As shown in FIG. 2, an intermediate case 43, a gas generator case 44, a turbine case 45, a centrifugal shroud 46, a turbine shroud 47, and a holder 49 of a turbofan engine are assembled and sub-assembled into a measuring device. After setting on the base member 81, the annular frame 83 is fixed to the circular opening of the turbine case 45. In this state, the outer surface of the reference shield 104 fixed to the disk-shaped support plate 85 supported by the annular frame 83 via the stays 84 is formed between the inner surface of the 16 segments 48 of the turbine shroud 47 with a clearance β. Opposite through.
[0031]
Subsequently, when the knob 89 at the upper end of the first shaft 91 of the center shaft 90 is pushed down, a cam surface 92b formed at the lower end of the second shaft 92 of the center shaft 90 is formed as shown in FIGS. The eight guide rods 97 are pushed outward in the radial direction, and the four suction pads 102 provided on the bracket 101 fixed to the tip of each guide rod 97 pass through the opening 104a of the reference shield 104 to be 2 Adhere to the inner surfaces of the segments 48, 48. Subsequently, when the knob 89 is released, the eight guide rods 97 are retreated inward in the radial direction together with the suction pads 102 by the spring force of the spring 98, and as shown in FIG. The 16 segments 48 adsorbed by 102... Move inward in the radial direction toward the axis L. As a result, the 16 segments 48 are closely adhered and integrated with each other, and the shape of the turbine shroud 47 during operation of the turbofan engine is reproduced.
[0032]
In this state, when the knob 89 is gripped and the center shaft 90 is rotated, the laser transmitter 113 and the laser receiver 116 together with the upper arm 112 and the lower arm 115 rotate around the axis L, and the limit switch provided on the upper arm 112 Each time 118 detects any of the 16 detected members 119..., The laser transmitter 113 transmits a laser beam. As shown in FIG. 10, the transmitted laser light passes through a gap β between the outer surface of the reference shield 104 and the inner surface of the segment 48 between two adjacent suction pads 102, 102. The light is received by the unit 116.
[0033]
As is clear from FIG. 10, the width of the laser light transmitted from the laser light transmitting unit 113 is a predetermined width (for example, 5.0 mm), part of which is blocked by the reference shield 104 and the other one. The part is blocked by the segment 48. Since the positional relationship in the radial direction between the laser transmitter 113 and the reference shield 104 is constant, the amount of light blocked by the reference shield 104 is constant, but the radial position of the segment 48 is not constant, so the segment The amount of light blocked by 48 changes. Accordingly, the amount of received light received by the laser light receiving unit 116 changes according to the radial position of the segment 48, that is, according to the gap β between the inner surface of the segment 48 and the outer surface of the reference shield 104. The gap β can be calculated according to the above.
[0034]
Since the radius R (see FIG. 10) from the axis L of the center shaft 90 to the outer surface of the reference shield 104 is known, the value (R + β) obtained by adding the gap β to the radius R is the inner surface of each segment 48. It becomes the radius of. Therefore, when the center shaft 90 is rotated by 360 °, the size of the gap β is measured for each of the 16 segments 48..., And the radius of the inner surface of each of the 16 segments 48. it can. Then, the radius of the segment 48 where the gap β is minimum is the minimum radius of the turbine shroud 47.
[0035]
As described above, the radius of the inner surface of the 16 segments 48 of the turbine shroud 47 in accordance with the actual operating state of the turbofan engine can be measured by only rotating the center shaft 90 once, and the turbine shroud can be measured. Turbine efficiency can be improved by accurately grasping the gap with the outer surface of the high-pressure turbine wheel 17 housed in the 47 and adjusting the gap.
[0036]
Further, since the measurement is performed in a non-contact manner using laser light, not only the turbine shroud 47 can be prevented from being damaged, but also the versatility is improved because the measurement is not hindered by the material of the turbine shroud 47.
[0037]
As mentioned above, although the Example of this invention was explained in full detail, this invention can perform a various design change in the range which does not deviate from the summary.
[0038]
For example, in the embodiment, a non-contact photoelectric switch is employed as the limit switch 118, but a contact mechanical limit switch can be employed instead.
[0039]
In the embodiment, the measurement of the radius of the inner surface of the segment 48... Constituting the turbine shroud 47 of the turbofan engine is exemplified. However, the present invention can be applied to the measurement of the radius of the inner surface of the segment 48 for other appropriate applications. it can.
[0040]
Further, an electromagnet can be adopted as the suction means instead of the suction pad 102.
[0041]
【The invention's effect】
As described above, according to the first aspect of the present invention, the plurality of segments that are annularly arranged around the axis and divided in the circumferential direction are attracted by the suction means and radially inward toward the axis. Since the measurement is performed in the state of being energized, it is possible to perform the measurement by adjusting the position of the segment to a position corresponding to the actual use state, and the measurement accuracy is improved. In addition, a laser beam is transmitted to the gap between the outer surface of the annular reference shield arranged around the axis and the inner surface of each segment to calculate the size of the gap, and the gap is calculated at a predetermined radius of the reference shield. Since the size is added to measure the radius of the inner surface of each segment, the radius of the segment can be measured in a non-contact manner to prevent damage.
[0042]
According to the second aspect of the present invention, when the center shaft is moved up and down relative to the frame, the guide rod whose inner end in the radial direction is pressed against the cam surface of the center shaft moves outward in the radial direction. Adsorption means provided at the outer end in the direction adsorbs to the inner surface of the corresponding segment. When the center shaft is returned to the original position from this state, the segment adsorbed by the adsorbing means moves inward in the radial direction together with the guide rod by the spring force of the spring, and the position of the segment becomes a position that matches the actual use state. It is arranged. In this state, by measuring the size of the gap between the outer surface of the annular reference shield having a predetermined radius centered on the axis and the inner surface of each segment by the gap measuring means, each according to the actual use state The radius of the inner surface of each segment can be measured.
[0043]
According to the invention described in claim 3, the gap measuring means is configured by the laser beam transmitters and the laser beam receivers disposed at both ends in the axial direction across the gap between the inner surface of the segment and the outer surface of the reference shield. Therefore, the size of the gap can be accurately measured based on the amount of received laser light that passes through the gap and is received by the laser receiver. Moreover, since the measurement is performed without contact, there is no possibility of damaging the segment.
[0044]
According to the invention described in claim 4, the radius of the inner surfaces of the plurality of segments can be efficiently measured by rotating the gap measuring means together with the center shaft.
[0045]
According to the fifth aspect of the present invention, the gap measuring means measures the size of the gap based on the rotational position of the center shaft detected by the rotational position detecting means. The radius of the inner surface of the segment can be automatically measured.
[Brief description of the drawings]
FIG. 1 is a diagram illustrating the overall structure of a turbofan engine. FIG. 2 is an overall side view of the measuring apparatus (cross-sectional view taken along line 2-2 in FIG. 3).
3 is a cross-sectional view taken along arrow 3 in FIG. 2. FIG. 4 is an enlarged view of a portion 4 in FIG. 2. FIG. 5 is a cross-sectional view taken along line 5-5 in FIG. 7 is an enlarged view of a portion 7 in FIG. 4. FIG. 8 is an explanatory diagram corresponding to FIG. 7. FIG. 9 is an explanatory diagram corresponding to FIG. 5. FIG. 10 is a sectional view taken along line 10-10 in FIG. Explanation】
48 segment 85 support plate (frame)
90 Center shaft 92b Cam surface 95 Guide plate (frame)
97 Guide rod 98 Spring 102 Suction pad (Suction means)
104 Reference shield 113 Laser transmitter (gap measuring means)
116 Laser receiver (gap measuring means)
118 Limit switch (rotational position detection means)
119 Detected member (rotation position detecting means)
L Axis line R Radius β Clearance

Claims (5)

A plurality of segments (48) arranged in an annular shape around the axis (L) and divided in the circumferential direction are set to have a radius on the inner surface, and the segments (48) are directed radially inward toward the axis (L). In the workpiece dimension measurement method for measuring in a state of being biased,
A plurality of segments (48) are adsorbed by the adsorbing means (102) and biased radially inward toward the axis (L), and have a predetermined radius (R) and are arranged around the axis (L). Laser light is transmitted to the gap (β) between the outer surface of the annular reference shield (104) and the inner surface of each segment (48), and based on the amount of received laser light that has passed through the gap (β) The size of the gap (β) is calculated, and the radius of the inner surface of each segment (48) is measured by adding the size of the gap (β) to the predetermined radius (R). Dimension measurement method. A plurality of segments (48) arranged in an annular shape around the axis (L) and divided in the circumferential direction are set to have a radius on the inner surface, and the segments (48) are directed radially inward toward the axis (L). In the workpiece dimension measuring device for measuring in the state of being biased,
A frame (85, 95) disposed to face the inner surface of a plurality of segments (48) assembled in a radially movable manner;
A center shaft (90) disposed on the axis (L) and supported so as to be movable up and down and rotatable with respect to the frame (85, 95);
A plurality of guide rods (97) supported radially by the frames (85, 95) and biased radially inward by springs (98);
An adsorbing means (102) provided at the radially outer end of each guide rod (97) and adsorbable on the inner surface of the corresponding segment (48);
A cam surface (92b) formed on the center shaft (90) and capable of pressing the radially inner end of the guide rod (97);
An annular reference shield (104) supported on the frame (85, 95) so as to face the inner surfaces of the plurality of segments (48) having a predetermined radius (R) centered on the axis (L);
Gap measuring means (113, 116) for measuring the size of the gap (β) between the inner surface of each segment (48) and the outer surface of the reference shield (104);
An apparatus for measuring a size of a workpiece, comprising: The gap measuring means (113, 116) includes a laser transmitter and a laser receiver arranged at both ends in the axis (L) direction with the gap (β) in between, and the laser receiver is based on the amount of received laser light. 3. The workpiece dimension measuring apparatus according to claim 2, wherein the size of the gap (β) is measured. 3. The workpiece dimension measuring device according to claim 2, wherein the gap measuring means (113, 116) is rotatable together with the center shaft (90). Rotation position detection means (118, 119) for detecting the rotation position of the center shaft (90) is provided, and the gap measurement means (113, 116) is based on the detection result of the rotation position detection means (118, 119). The workpiece dimension measuring apparatus according to claim 2, wherein the dimension of β) is measured.

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