JP5652631B2 - Method of calculating the amount of misalignment in a roundness measuring device - Google Patents

Description

  The present invention relates to a method of calculating the amount of misalignment in a roundness measuring apparatus, and in particular, shows a deviation between a detection point where a measuring element of a detector of a roundness measuring apparatus is brought into contact with a measured object and a bus bar of the measured object. The present invention relates to a method of calculating the amount of misalignment in a roundness measuring apparatus having a function of calculating the amount of misalignment and correcting the amount of misalignment.

  Conventionally, a roundness measuring device (roundness measuring machine) that measures the roundness of a circular object such as a cylindrical object is known. This roundness measuring device, for example, places a measurement object (workpiece) having a circular cross section such as a cylindrical object on a rotatable mounting table, and contacts a tip (measurement element) on the surface of the work The outer shape of the circular cross section is measured by measuring and detecting the displacement of the tip terminal accompanying the rotation of the workpiece.

  For example, in Patent Document 1, in a roundness measuring machine, a horizontal arm that guides a contact of a first detector horizontally and diametrically with respect to a cylindrical workpiece, and a tip of the arm are provided. A first detector support frame that enables the contact of the first detector to contact two points in the diameter position, and a second detector of diameter reading that detects the horizontal movement amount of the horizontal arm. A diameter measuring device of a roundness measuring machine composed of: This device first sets the master piece on the turntable, places the contact of the first detector on the right side of the master piece, obtains the reading of the second detector, and then places the contact on the left side of the master piece. Then, the reading of the second detector is obtained, and the error value of this apparatus is calculated from the two readings of the second detector according to the known dimensions of the master. Then, a workpiece is set instead of the master, and the diameter dimension is measured in the same manner to perform error correction.

  Patent Document 2 discloses a reference jig for a roundness measuring machine that performs origin calibration of a roundness measuring machine and calibrates a detector that measures the surface shape of a measurement object. A pedestal that is detachably mounted on the upper surface of the XY table on the rotary table, and a calibration master that enables calibration of the sensitivity of the probe (detector) on the upper stage of the pedestal. Provided with an origin ball (reference sphere) disposed above the calibration master so that measurement can be performed in the X-axis direction and the right-side surface of the lowermost surface, the right-side surface, and the Z-axis direction of the left-side surface. Are described in which a positional deviation of a stylus (sensor) provided on the probe in each posture is obtained as a correction value. This is to obtain the origin information of the roundness measuring machine by placing the reference jig for the roundness measuring machine on the measured object rotating mechanism and bringing the sensor of the roundness measuring machine's detector into contact with the reference sphere. At the same time, the sensitivity of the detector is calibrated by involving the sensor of the detector in the calibration master.

JP-A-1-259211 Japanese Patent No. 4163545

  However, when the measurement object is placed on the table of the roundness measuring device and the detection element of the detector is brought into contact with the measurement object, detection is performed so that the bus bar of the measurement object and the measurement element are in contact with the measurement object. It is very difficult to match the points, and there is a problem in that an accurate diameter value cannot be measured for a measurement object having a diameter value different from the diameter value of the measurement object that has been the standard.

  The present invention has been made in view of such problems, and calculates and corrects the amount of misalignment, which is the amount of deviation between the bus of the measurement object and the detection point, thereby correcting the diameter value of the measurement object serving as a reference. It is an object of the present invention to provide a method for calculating the amount of misalignment in a roundness measuring apparatus capable of calculating an accurate diameter value even for a measurement object having a diameter value different from that of a circle.

  In order to achieve the above object, the method of calculating the amount of misalignment in the roundness measuring device according to the present invention causes the measured object to rotate relative to the detector by matching the center of the measured object with the center of rotation. A method of calculating the amount of misalignment in a roundness device for measuring the roundness of a measured object, comprising: means for linearly moving the detector in a predetermined direction with respect to the measured object; The tip sphere of the instrument is parallel to a generatrix that is a straight line parallel to the direction in which the detector horizontally moves through the center of the reference measurement object with respect to one reference measurement object having a known diameter value. Moving and measuring the reference measurement object by measuring the reference measurement object at two detection points facing each other and detecting the measurement difference with respect to the reference measurement object. Deviation between the bus of the measured object and the detection point A misalignment amount calculating step of calculating a certain misalignment amount, characterized by comprising a.

  As a result, by calculating and correcting the amount of misalignment, which is the amount of deviation between the bus of the measurement object and the detection point, even a measurement object having a diameter value different from the diameter value of the reference measurement object can be accurately obtained. It is possible to calculate a correct diameter value.

  In one embodiment, it is preferable that the misalignment amount calculating step calculates a diameter value of a tip sphere of the detector together with the misalignment amount based on each measurement difference.

  As a result, the diameter value of the tip sphere of the detector can be calculated, so even if the tip sphere is deteriorated due to wear, the accurate diameter value can be obtained, so the measurement system can be further improved. Can do.

  As described above, according to the present invention, a diameter value different from the diameter value of the reference measurement object is obtained by calculating and correcting the amount of misalignment, which is the deviation amount between the bus of the measurement object and the detection point. It is possible to calculate an accurate diameter value even in the case of a measurement object having a diameter.

It is a perspective view which shows the external appearance of the roundness measuring apparatus which concerns on one Embodiment of this invention. It is a block diagram which shows the structure of the roundness measuring apparatus of FIG. It is a perspective view which shows the external appearance of the measuring machine main body of a detector rotation type roundness measuring apparatus. It is a top view which shows the ideal case without misalignment when measuring a measurement object with a roundness measuring device. It is a top view which shows the case where there exists a center shift | offset | difference when measuring a measurement object with a roundness measuring apparatus. It is a top view which shows a mode that the reference | standard measured object which has a known diameter is measured by two right and left points which oppose in the position which shifted | deviated from the bus-line, and calculates | requires the amount of misalignment. It is a top view which shows the method of correct | amending the measured diameter value using the calculated amount of misalignment Y. FIG. It is a top view which shows the method of measuring two reference | standard measurement objects which have a known different diameter value in two right and left points which oppose in the position which shifted | deviated from the bus line, and calculates the amount of eccentricity and the diameter value of a tip sphere.

  Hereinafter, a method for calculating the amount of misalignment in a roundness measuring apparatus according to the present invention will be described in detail with reference to the accompanying drawings.

  FIG. 1 is a perspective view showing an appearance of a roundness measuring apparatus used in the present invention.

  This roundness measuring apparatus is composed of a measuring machine main body and an arithmetic processing unit. FIG. 1 shows a measuring machine main body 11 of a roundness measuring apparatus 10.

  The measuring machine main body 11 is provided with a mounting table (XY / tilting table) 12 on which a measuring object (not shown here) is mounted on a base (base) 14. The mounting table (XY / tilting table) 12 includes an X direction fine movement knob 22 and a Y direction fine movement knob 24. The X direction fine movement knob 22 and the Y direction fine movement knob 24 are respectively connected to the mounting table moving shaft, and the fine movement knobs 22 and 24 can finely feed the mounting table 12 in the X direction and the Y direction. The horizontal position of the stage 12 can be finely adjusted.

  Further, the stage 12 is provided with an X-direction tilt knob 25 and a Y-direction tilt knob 23 so that the tilt can be adjusted in the X direction and the Y direction.

  A rotation mechanism 15 is provided at the lower part of the stage 12. The rotating mechanism 15 rotates the workpiece placed on the stage 12 by rotating the stage 12.

  Further, a column (support) 27 extending vertically upward is provided on the base 14, and a slider 28 is mounted on the column 27 so as to be movable up and down. A horizontal arm (radial movement axis) 29 is mounted on the slider 28 so as to be driven in the horizontal direction.

  A detector 30 is provided at the tip of the horizontal arm 29, and the detector 30 includes a probe 31. The roundness measuring apparatus 10 measures the measured object by bringing the measuring element 31 into contact with the measured object placed on the mounting table 12, and calculates a detection signal obtained by the measurement via the detector 30. The data is sent to the apparatus and processed by an arithmetic processing unit. A center misalignment adjusting mechanism 32 is provided at the tip of the horizontal arm 29.

  FIG. 2 is a block diagram showing the configuration of the roundness measuring apparatus 10.

  As shown in FIG. 2, the roundness measuring device 10 includes a measuring machine main body 11 and an arithmetic processing device 13. The measuring machine main body 11 will be described again although there are some points that overlap the description of FIG.

  The measuring machine main body 11 is provided with a mounting table 12 that is rotated by a rotating mechanism 15 on a base 14. The mounting table 12 is provided with an X-direction fine adjustment knob 22, a Y-direction fine adjustment knob 24, an X-direction inclination knob 25, and a Y-direction inclination knob 23 for fine adjustment in the horizontal direction and inclination adjustment in the vertical direction. Yes.

  The stage 12 is rotated by a rotation mechanism 15 including a bearing 16, an encoder 18, a motor 20, and the like. The stage 12 is rotatably supported by a motor 20 via a bearing 16. An encoder 18 is attached to the rotation shaft of the motor 20, and the rotation angle is read with high accuracy. For example, an ultra-high precision static pressure air bearing is used as the bearing 16, and the mounting table 12 is rotated with very high rotational accuracy (for example, 0.005 μm).

  Further, a slider 28 is mounted on a column (post) 27 erected on the base 14 so as to be movable up and down, and a horizontal arm (radial movement axis) 29 is mounted on the slider 28 so as to be driven in the horizontal direction. . A detector 30 is provided at the tip of the horizontal arm 29, and a probe 31 is installed on the detector 30. In addition, an electric micrometer using a differential transformer is used for the detector 30 to detect the amount of displacement of the probe 31 that contacts the measurement object 26.

  At the time of measurement, the measurement object 26 is placed on the mounting table 12, and the measuring element 31 is brought into contact with the measurement object to perform measurement. A detection signal obtained by the measurement is sent to the arithmetic processing unit 13 via the detector 30.

  The arithmetic processing unit 13 includes an amplifier 33, an A / D converter 34, an arithmetic / processing unit 36, and a program 38 stored in a memory for controlling these, and further includes a display unit for displaying the processing result. Yes.

  A detection signal obtained by bringing the probe 31 into contact with the measurement object 26 is sent to the arithmetic processing unit 13 via the detector 30. In the arithmetic processing unit 13, the signal is first amplified by the amplifier 33, converted into a digital signal by the A / D converter 34, and input to the arithmetic / processing means 36.

  When the roundness of the measuring object 26 is measured by the roundness measuring apparatus 10, after the measuring object 26 is placed on the mounting table 12, first, the center of rotation of the mounting table 12 and the measuring object are measured. The eccentricity correction with respect to the center of the object 26 and the inclination correction of the measurement object 26 with respect to the rotation axis of the mounting table 12 are performed. As a result, it is assumed that the center of rotation of the stage 12 and the center of the measurement object 26 coincide with each other.

  Next, in a state where the probe 31 of the detector 30 is in contact with the side surface of the measurement object 26, the mounting table 12 is rotated once by the motor 20, and the data for one round of the side surface of the measurement object 26 is converted into an analog voltage value. Collected. The detection signal obtained as an analog voltage value is amplified by the amplifier 33 as described above, converted into a digital signal by the A / D converter 34, and input to the arithmetic / processing means 36. The calculation / processing unit 36 calculates the roundness of the measurement object 26 from the rotation angle data input from the encoder 18 and the displacement data detected by the detector 30, and displays the calculation result on the display unit 40.

  In the roundness measuring apparatus 10 described above, the stage 12 on which the measurement object 26 is placed rotates, and the measuring element 31 moves in the front-rear direction (movement direction of the horizontal arm 29) and in the vertical direction (movement of the slider 28). In this case, the measuring element 31 does not rotate and moves in the direction), and the roundness measuring device of the mounting table rotation type is used. However, the present invention is limited to such a mounting table rotation type roundness measuring device. Is not to be done. It can also be applied to a roundness measuring device with a rotating detector, where the stage does not rotate, the probe moves in the front-rear and up-down directions, and the probe rotates around the workpiece. is there.

  FIG. 3 is a perspective view showing an appearance of a measuring machine main body of the detector rotation type roundness measuring apparatus.

  As shown in FIG. 3, the measuring machine main body 111 of the roundness measuring apparatus 100 is provided with a mounting table 112 on which a measuring object is placed on a base 114. The stage 112 has an X direction fine movement knob 122 and a Y direction fine movement knob 124. Although omitted here, an X-direction tilt knob and a Y-direction tilt knob may be provided as in the previous example.

  On the base 114, a column (post) 127 extending substantially vertically upward is erected, and a slider 128 is mounted on the column 127 so as to be movable up and down. The slider 128 is moved up and down by a feeding device 150 provided in the column 127. A horizontal arm (radial movement axis) 129 is attached to the lower side of the slider 128, and a detector 130 and a measuring element 131 are installed on the horizontal arm 129.

  The roundness measuring apparatus 100 measures the measurement object by rotating the measurement element 131 around the measurement object while bringing the measurement element 131 into contact with the measurement object placed on the mounting table 112. A detection signal obtained by the measurement is sent to an arithmetic processing device (not shown) via the detector 130 and processed by the arithmetic processing device. A misalignment adjusting mechanism 132 is installed between the horizontal arm 129 and the detector 130.

  Hereinafter, calculation of the amount of misalignment by the roundness measuring apparatus 10 (or 100) of the present embodiment and a method of correcting the amount of misalignment using this will be described.

  At the time of roundness measurement, as shown in FIG. 4, the tip sphere 31a of the probe 31 is brought into contact with the measuring object 26 placed on the mounting table 12 (not shown here).

  Then, in the case of the mounting table rotation type roundness measuring apparatus 10, the measuring object 26 is rotated by rotating the mounting table 12 as indicated by an arrow A in FIG. 4. Further, in the case of the detector rotation type roundness measuring apparatus 100, as shown by an arrow B in FIG. 4, the probe 31 (tip sphere 31a) is rotated along the outer periphery of the measurement object 26. It is assumed that the center of the measurement object 26 and the center of rotation of the mounting table 12 coincide with each other. Here, the center of the measuring object 26 refers to a figure forming the outer periphery of the measuring object 26 (more precisely, a point (detection point) measured by bringing the tip sphere 31a into contact with the surface of the mounting table 12). Suppose that it is the center of the least square circle of the outer periphery of the parallel section.

  At this time, the tip sphere 31a of the probe 31 is in contact with the measurement object 26 in any case. For example, in the case of the mounting table rotation type roundness measuring apparatus 10, as shown by an arrow D in FIG. 4, while the tip sphere 31 a is always pressed against the outer surface of the measured object 26, the measured object 26 is moved to the arrow. Rotate in direction A. At this time, if the measured object 26 is not a perfect circle and the radius changes as the measured object 26 rotates, the tip sphere 31a moves toward or away from the center of rotation, and its position changes in the direction of arrow D.

  The change in the position of the tip sphere 31a is detected via the detector 30 and processed by the arithmetic processing unit 13, whereby the roundness of the measurement object 26 is detected.

  As shown in FIG. 4, a detection point P at which measurement is performed by moving the tip sphere 31 a of the probe 31 in the detection direction indicated by the arrow D and making contact with the measurement object 26 is a bus M passing through the center of the measurement object 26. , The roundness of the measurement object 26 can be accurately measured.

  However, in actual measurement, the detection point P of the tip sphere 31 a of the probe 31 with respect to the measurement object 26 does not always coincide with the bus M of the measurement object 26.

  Depending on the apparatus, for example, as shown in FIG. 5, the detection point Q at which the tip sphere 31 a of the probe 31 contacts the measurement object 26 may not coincide with the bus M of the measurement object 26. In this case, the measurement error is the distance ε between the centers of the tip spheres 31a in the detection direction D of the tip sphere 31a at the detection point P that coincides with the bus M of the measurement object 26 and the detection point Q in the actual measurement. Occurs.

  Further, the distance Y between the centers of the tip spheres 31a in the detection point P and the detection point Q in the direction perpendicular to the detection direction D represents the deviation of the detection point Q from the bus M, and this value Y Is the amount of misalignment.

  Next, a method for obtaining the misalignment amount Y will be described.

  In the method described below, two points opposite to the detection direction of the probe 31 of the reference measurement object having a known diameter value are measured, the amount of misalignment is calculated from the measurement error, and correction is performed. .

  As shown in FIG. 6, with respect to a reference measurement object 26-1 having a known diameter value, a measuring element of the roundness measuring device 10 from the right side and the left side in a direction parallel to the detection direction indicated by the arrow D in the figure. Measurement is performed by bringing 31 tip balls 31a into contact with each other.

  The diameter value of the reference measurement object 26-1 is D0, and the diameter of the tip sphere 31a is d.

  Here, it is assumed that the right detection point is P1 and the left detection point is P2 when it is assumed that the tip sphere 31a of the probe 31 has no misalignment and is correctly in contact with the reference measurement object 26-1. That is, it is assumed that the detection point P1 and the detection point P2 coincide with the bus M of the reference measurement object 26-1. In this case, the detection value at the right side detection point at P1 is R1, and the detection point at the left detection point at P2 is R2. Here, from the figure, the difference R1-R2 between the detection value R1 and the detection value R2 is the sum of the diameter value D0 of the reference measurement object 26-1 and the diameter d of the tip sphere 31a.

  That is, R1-R2 = D0 + d.

  Next, when the tip sphere 31a of the measuring element 31 is misaligned, that is, the measuring element 31 and the reference measuring object 26-1 are relatively relative to each other in a direction orthogonal to the generatrix M of the reference measuring object 26-1. Suppose you have moved to. At this time, the tip sphere 31a of the probe 31 of the roundness measuring device 10 is brought into contact with the reference measurement object 26-1 from the right side and the left side in a direction parallel to the detection direction indicated by the arrow D in the drawing. taking measurement.

  At this time, the right detection point where the tip sphere 31a contacts the reference measured object 26-1 from the right side is Q1, and the detection value at that time is R1 '. Further, the left detection point where the tip sphere 31a contacts the reference measured object 26-1 from the left is Q2, and the detection value at that time is R2 '.

  Then, when the amount of misalignment, which is the distance by which the probe 31 and the reference measurement object 26-1 are displaced in the direction orthogonal to the bus M, is Y, the right and left sides of the reference measurement object 26-1 are measured. The measured value (R1′-R2 ′) obtained is represented by the following formula (1).

R1′−R2 ′ = 2√ [{(D0 / 2) + (d / 2)} 2−Y2] (1)
Here, √ [*] represents the square root of *.

  Therefore, if R1'-R2 'is measured, D0 and d are already known. Therefore, if the above equation (1) is solved, the misalignment amount Y can be obtained as the following equation (2).

Y = √ [{(D0 / 2) + (d / 2)} 2- (R1′−R2 ′) 2/4] (2)
Next, a method of correcting the measured diameter value and the like using the calculated misalignment amount Y will be described.

  In FIG. 7, when measuring the outer diameter of the measurement object (when the tip sphere 31a circumscribes the outer circle C1 of the circular measurement object) and when measuring the inner diameter of the measurement object (the tip sphere 31a is the cylindrical measurement object). The case of inscribed in the inner circle C2 will be described.

  That is, in FIG. 7, the tip sphere 31a circumscribes the circle C1 and inscribes the circle C2. Further, when the tip sphere 31a is located at positions E and F facing each other with respect to the diameter of the circle C1, the distance between the centers of the tip spheres 31a at each position is represented by δ. The diameter of the circle C1 is D1, and the diameter of the tip sphere 31a is d.

  At this time, the tip sphere 31a is contacted from the right side at the position E with respect to the circle C1, and the tip is viewed from the left side with respect to the circle C1 at the position G facing the position E in the direction parallel to the generatrix M with respect to the circle C1. Measurement is performed by bringing the ball 31a into contact.

  A detection value measured by bringing the tip sphere 31a into contact with the circle C1 from the right side at the position E is R1 ″, and a detection value measured by bringing the tip sphere 31a from the left side into contact with the circle C1 at the position G is R2 ″.

  Then, the misalignment amount Y, which is the distance from the generatrix M of the tip sphere 31a at the position E, can be obtained as described above.

  As can be seen from the figure, the distance δ between the centers of the tip spheres 31a at the two positions E and F described above can be expressed by the following equation (3) using this amount of misalignment Y.

δ = √ [(R1 ″ −R2 ″) 2+ (2Y) 2] (3)
Therefore, by correcting the measured diameter (R1 ″ −R2 ″) with the amount of misalignment Y, the diameter D1 of the circle C1 measured by circumscribing the tip sphere 31a can be obtained by the following equation (4).

D1 = √ [(R1 ″ −R2 ″) 2+ (2Y) 2] −d (4)
Similarly, the diameter D2 of the circle C2 measured with the tip sphere 31a inscribed can be obtained by the following equation (5).

D2 = √ [(R1 ″ −R2 ″) 2+ (2Y) 2] + d (5)
As described above, according to the present embodiment, the amount of misalignment Y can be calculated by measuring a reference measurement object having a known diameter value from two left and right positions facing each other in a direction parallel to the generatrix M. . In addition, the true diameter value of an arbitrary measured object can be calculated by correcting the diameter value obtained by measuring the arbitrary measured object by using the calculated misalignment amount Y.

  Further, according to the present invention, as shown in FIG. 8, by measuring two reference measurement objects having known diameter values, a circle C3 and a circle C4, the amount of misalignment Y is calculated, and the tip sphere 31a A diameter value can be calculated.

  According to this, even when the tip sphere 31a is worn and its diameter value is different from the initial value, the true diameter value of the worn tip sphere 31a can be obtained.

  In FIG. 8, the diameter value of the circle C3 is D3, the diameter value of the circle C4 is D4, and the diameter value of the tip sphere 31a is d.

  At this time, similarly to the above example, when there is no misalignment, the measured diameter value R3-R4 when the circle C3 is measured from the left and right directions is expressed by the following equation (6).

R3-R4 = D3 + d (6)
Similarly, when there is no misalignment, the measured diameter value R5-R6 when the circle C4 is measured from the left and right directions is expressed by the following equation (7).

R5-R6 = D4 + d (7)
Further, when there is a misalignment (center misalignment amount Y), a measured diameter value R3′-R4 ′ when the circle C3 is measured from the left and right directions is expressed by the following equation (8).

R3′−R4 ′ = 2√ [{(D3 / 2) + (d / 2)} 2-Y2] (8)
Similarly, the measured diameter value R5′-R6 ′ when the circle C4 is measured from the left and right directions when there is a misalignment (center misalignment amount Y) is expressed by the following equation (9).

R5′−R6 ′ = 2√ [{(D4 / 2) + (d / 2)} 2-Y2] (9)
Therefore, if the measured diameter values R3′-R4 ′ and R5′-R6 ′ are obtained by measuring the two circles C3 and C4 whose diameter values D3 and D4 are known, respectively, the two equations (8) and From (9), the amount of misalignment Y and the diameter value d of the tip sphere 31a can be calculated.

  As described above, according to the present embodiment, a diameter different from the diameter value of the reference measurement object is obtained by calculating and correcting the misalignment amount that is the deviation amount between the bus of the measurement object and the detection point. Even for a measured object having a value, an accurate diameter value can be calculated.

  As described above, the method of calculating the amount of misalignment in the roundness measuring device of the present invention has been described in detail, but the present invention is not limited to the above examples, and various improvements and modifications can be made without departing from the scope of the present invention. Of course, deformation may be performed.

  DESCRIPTION OF SYMBOLS 10 ... (mounting table rotation type) Roundness measuring device, 11 ... Measuring machine main body, 12 ... Mounting table (XY / tilting table), 13 ... Arithmetic processing device, 14 ... Base (base), 15 ... Rotation Mechanism: 16 ... Bearing, 18 ... Encoder, 20 ... Motor, 22 ... X direction fine adjustment knob, 23 ... Y direction fine adjustment knob, 24 ... Y direction fine adjustment knob, 25 ... X direction fine adjustment knob, 26 ... Measurement object, 27 ... Column (Posts), 28 ... slider, 29 ... horizontal arm (radial movement axis), 30 ... detector, 31 ... measuring element, 31a ... tip ball, 32 ... decentering adjustment mechanism, 33 ... amplifier, 34 ... A / D Converter, 36 ... arithmetic / processing means, 38 ... program, 40 ... display means, 100 ... (detector rotation type) roundness measuring device

Claims (1)

A method of calculating the amount of misalignment in a roundness device that measures the roundness of a measured object by rotating the measured object relative to a detector while aligning the center of the measured object with the center of rotation. ,
Means for linearly moving the detector in a predetermined direction with respect to the measurement object;
A bus tip that is a straight line parallel to a direction in which the detector horizontally moves linearly through the center of the reference measurement object with respect to one reference measurement object having a diameter value with a known diameter value. A step of moving in parallel and making contact with the reference measurement object at two detection points opposed to the reference measurement object, and measuring a difference in the reference measurement object; and
A misalignment amount calculating step of calculating a misalignment amount, which is a shift amount between the bus of the reference measurement object and the detection point, based on the measurement difference;
A method of calculating the amount of misalignment in a roundness measuring apparatus comprising:

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