A method and system for measuring inner hole of a part

Abstract

The present invention relates to the technical field of measuring inner holes of parts, and specifically to a method and system for measuring inner holes of parts, which are used to perform micron-level precision measurement on equal-diameter holes. The technical solution of the present invention freely moves the first laser probe to the radial measurement position in the equal-diameter hole, and the vertical deviation between the ranging laser emitted by the first laser probe along the hole radial direction and the hole axis is within a preset range; after controlling the first laser probe to perform the radial rough measurement task on the equal-diameter hole at the radial measurement position, the estimated inner diameter of the equal-diameter hole can be obtained; according to the estimated inner diameter, the first laser probe is controlled to perform the circumferential precision measurement task on the equal-diameter hole with the corresponding precision measurement rotation step, so as to obtain a circumferential data set characterized as an elliptical profile, and the estimated inner diameter and the precision measurement rotation step are inversely proportional; after the circumferential data set is analyzed and processed, the short semi-axis of the elliptical profile is determined as the measured radius of the equal-diameter hole. This technical solution improves the measurement accuracy of equal-diameter holes when measuring equal-diameter holes.

Description

Technical Field

[0001] The invention relates to the technical field of measuring inner holes of parts, and in particular to a method and system for measuring inner holes of parts. Background Art

[0002] Laser bore measurement technology is used to detect the machining accuracy of inner holes on mechanical parts. This type of solution plays an important role in industrial manufacturing and maintenance, especially in fields where accurate measurement of the geometry of the hole is required, such as aerospace and automotive industries. Laser bore ranging is the process of accurately measuring the inner surface of a hole using laser technology. The principle is to emit a laser beam into the hole through an optical system. The laser beam is reflected back to the sensor after irradiating the hole wall. The sensor captures the reflected light and calculates the distance of laser propagation through phase difference or time delay. The advantage of this technology lies in its high precision and non-contact measurement capability, which can achieve high-resolution measurement without contacting the hole wall. This makes laser bore ranging particularly suitable for measuring inner holes that are difficult to access or easily damaged by measuring tools. The laser system can quickly capture data and generate measurement results in real time, greatly improving measurement efficiency and quality control level. Taking equal-diameter hole measurement as an example, this type of hole has the same diameter in its length direction. The current technical means need to calibrate the parts or equal-diameter holes before implementing laser hole measurement. The calibration process is time-consuming and labor-intensive, and the calibration error directly affects the measurement accuracy of equal-diameter holes. Summary of the invention

[0003] In order to solve the technical problem of how to accurately measure equal-diameter holes, the purpose of the present invention is to provide a method and system for measuring the inner holes of parts, thereby improving the measurement accuracy of equal-diameter holes. The technical solutions adopted are as follows:

[0004] In a first aspect, an embodiment of the present invention provides a method for measuring the inner hole of a part, which is applied to perform micron-level precision measurement of equal-diameter holes on a part; the method comprises:

[0005] The first laser probe is freely moved to a radial measurement position in the equal-diameter hole, wherein the part provided with the equal-diameter hole is fixed by a positioning device so that the vertical deviation between the distance measuring laser emitted by the first laser probe along the radial direction of the hole and the axis of the hole is within a preset range;

[0006] Controlling the first laser probe to perform a radial rough measurement task on the equal-diameter hole at a radial measurement position to obtain an estimated inner diameter of the equal-diameter hole;

[0007] According to the estimated inner diameter, the first laser probe is controlled to perform a circumferential precision measurement task on the equal-diameter hole with a corresponding precision measurement rotation step, so as to obtain a circumferential data set characterized as an elliptical profile, wherein the estimated inner diameter and the precision measurement rotation step are inversely proportional to each other;

[0008] The circumferential data set is analytically processed to determine the minor semi-axis of the elliptical profile as the measured radius of the equal-diameter hole.

[0009] In an optional embodiment, controlling the first laser probe to perform a radial rough measurement task on the equal-diameter hole at a radial measurement position to obtain an estimated inner diameter of the equal-diameter hole includes:

[0010] According to the data configured in the radial coarse measurement task, the radial ranging number and the corresponding coarse measurement rotation step of the radial coarse measurement task are determined, wherein the radial ranging number is a positive integer greater than or equal to 3, and the rotation angle represented by the coarse measurement rotation step is greater than a preset angle, so that the angle measurement range of the radial coarse measurement task is greater than or equal to 120°;

[0011] According to the number of radial distance measurements and the coarse measurement rotation step, the first laser probe is controlled to perform multi-point distance measurement along the radial direction of the equal-diameter hole at the radial measurement position to obtain the measurement distance of each measurement point;

[0012] Determine the estimated inside diameter of a hole of equal diameter based on the average of all measured distances.

[0013] In an optional embodiment, after obtaining the measurement distance of each measurement point, the method further includes:

[0014] Determine whether the measured distance of each measuring point is less than the distance threshold;

[0015] If so, the first laser probe is controlled to move radially in the equal-diameter hole so that the first laser probe is in a radial target area for performing a circumferential precision measurement task, wherein the radial target area is an area where any radial distance between the first laser probe and the equal-diameter hole is greater than a preset value.

[0016] In an optional embodiment, the distance measurement method of the circumferential precision measurement task is a phase distance measurement method; before controlling the first laser probe to perform the circumferential precision measurement task on the equal-diameter hole with a corresponding precision measurement rotation step according to the estimated inner diameter, the method further includes:

[0017] Based on the data obtained from the radial rough measurement task, determine the deflection level of the part fixed by the positioning device;

[0018] When the skew level is greater than the level threshold and the estimated inner diameter is greater than the inner diameter threshold, the circumferential precision measurement task is configured as dual-wavelength laser ranging;

[0019] When the skew level is less than or equal to the level threshold, or the estimated inner diameter is less than or equal to the inner diameter threshold, the circumferential precision measurement task is configured as single-wavelength laser ranging.

[0020] In an optional embodiment, parsing the circumferential data set includes:

[0021] When the circumferential data set is a data set obtained by single-wavelength laser ranging, each measured distance and corresponding direction angle in the circumferential data set of the single-wavelength laser ranging is input into the analytical model of the ellipse profile;

[0022] The first short semi-axis analyzed by the analytical model in single-wavelength laser ranging is determined as the measured radius of the equal-diameter hole in single-wavelength laser ranging;

[0023] When the circumferential data set is a data set obtained by dual-wavelength laser ranging, the measured distances and corresponding direction angles of two wavelengths in the circumferential data set of the dual-wavelength laser ranging are sequentially input into the analytical model of the ellipse profile;

[0024] According to the analytical results of the distance and direction angle measured under two wavelengths by the analytical model, the second minor semi-axis and the third minor semi-axis are obtained;

[0025] According to the second minor semi-axis and the third minor semi-axis, the measured radius of the equal-diameter hole in the dual-wavelength laser ranging is obtained.

[0026] In an optional embodiment, obtaining the measured radius of the equal-diameter hole in dual-wavelength laser ranging according to the second short semi-axis and the third short semi-axis includes:

[0027] According to the short semi-axis corresponding to the long wavelength in the second short semi-axis and the third short semi-axis, a value of the measured radius in the range of ten micrometers to millimeters is determined;

[0028] The micrometer-order value of the measured radius is determined based on the short semi-axis of the second short semi-axis and the third short semi-axis corresponding to the short wavelength.

[0029] In an optional embodiment, before freely moving the first laser probe to a radial measurement position in the equal-diameter hole, the method further comprises:

[0030] When it is determined that the equal-diameter hole is a non-through hole structure, the second laser probe is controlled to perform an axial distance measurement task on the equal-diameter hole to obtain the hole bottom position and hole mouth position of the equal-diameter hole;

[0031] The first area from the hole bottom position to the hole mouth direction and the second area from the hole mouth position to the hole depth direction are configured as the no-stopping area for the first laser probe to move freely.

[0032] In an optional embodiment, after parsing the circumferential data set, the method further includes:

[0033] Control the positioning device to rotate the part around its hole axis at multiple angles, and perform circumferential precision measurement and data analysis at each angle to obtain the actual measured radius at each angle;

[0034] Outputs the radial runout of holes of equal diameter based on all measured radii.

[0035] In an optional embodiment, after parsing the circumferential data set, the method further includes:

[0036] Controlling the first laser measuring head to move a third preset distance in the axial direction of the equal-diameter hole, and performing the circumferential precision measuring task again, so as to obtain the measured radius of the equal-diameter hole again;

[0037] The taper measurement result of the equal-diameter hole is output based on the first measured radius and the second measured radius.

[0038] In a second aspect, an embodiment of the present invention further provides a system for measuring inner holes of a part, which is used to perform micron-level precision measurement of equal-diameter holes on a part; the system comprises:

[0039] A positioning device, used to fix the part with equal-diameter holes so that the vertical deviation between the distance measuring laser emitted by the first laser measuring head along the diameter of the hole and the axis of the hole is within a preset range;

[0040] A measuring device is used to control its first laser probe to move freely to a radial measurement position in an equal-diameter hole; control the first laser probe to perform a radial rough measurement task on the equal-diameter hole at the radial measurement position to obtain an estimated inner diameter of the equal-diameter hole; control the first laser probe to perform a circumferential fine measurement task on the equal-diameter hole with a corresponding fine measurement rotation step according to the estimated inner diameter to obtain a circumferential data set characterized as an elliptical profile, wherein the estimated inner diameter and the fine measurement rotation step are inversely proportional; and perform analytical processing on the circumferential data set to determine the minor semi-axis of the elliptical profile as the measured radius of the equal-diameter hole.

[0041] The present invention has the following beneficial effects:

[0042] The technical solution of the present invention freely moves the first laser probe to the radial measurement position in the equal-diameter hole. Since the part with the equal-diameter hole is fixed by the positioning device, the vertical deviation between the distance measuring laser emitted by the first laser probe along the hole radial direction and the hole axis is within a preset range, and the distance can be accurately measured by laser. After controlling the first laser probe to perform the radial rough measurement task on the equal-diameter hole at the radial measurement position, the estimated inner diameter of the equal-diameter hole can be obtained. Then, according to the estimated inner diameter, the first laser probe is controlled to perform the circumferential fine measurement task on the equal-diameter hole with the corresponding fine measurement rotation step to obtain a circumferential data set characterized as an elliptical profile. The estimated inner diameter and the fine measurement rotation step are inversely proportional. The adopted fine measurement rotation step is suitable for the measurement of the equal-diameter hole with the estimated inner diameter. The amount of data presented by the circumferential data set can ensure that the equal-diameter hole is accurately measured. After the circumferential data set is analyzed and processed, the short semi-axis of the elliptical profile is determined as the measured radius of the equal-diameter hole. When measuring equal-diameter holes, the vertical deviation of this technical solution is within the preset range to ensure the accuracy of the laser distance measurement method; since there is no need to clamp and calibrate the parts, the influence of calibration accuracy on the measurement results is eliminated, and the precision rotation step adopted can be applied to the micron-level measurement accuracy requirements, and the measurement accuracy is controlled from multiple dimensions, so that the measurement accuracy of equal-diameter holes can meet the micron-level requirements. At the same time, since the measurement process does not require the clamping and calibration of the parts, the measurement efficiency of equal-diameter holes is taken into account. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] In order to more clearly illustrate the technical solutions and advantages in the embodiments of the present invention or the prior art, the drawings required for use in the embodiments or the prior art descriptions are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0044] Figure 1 A flow chart of a method for measuring an inner hole of a part provided by an embodiment of the present invention;

[0045] Figure 2 A schematic diagram of the structure of a system for measuring inner holes of parts provided by one embodiment of the present invention;

[0046] Figure 3 A schematic diagram of the principle of calculating the estimated inner diameter provided by one embodiment of the present invention;

[0047] Figure 4 A first principle example diagram of equal-diameter hole measurement provided by an embodiment of the present invention;

[0048] Figure 5 A second principle example diagram of equal-diameter hole measurement provided by an embodiment of the present invention.

[0049] Description of reference numerals: 1-measuring device, 2-positioning device, 3-part;

[0050] 11-first laser measuring head, 12-second laser measuring head, 13-vertical plate, 14-horizontal driving mechanism. DETAILED DESCRIPTION

[0051] In order to further explain the technical means and effects adopted by the present invention to achieve the predetermined invention purpose, the following is a detailed description of a method and system for measuring the inner hole of a part proposed by the present invention, its specific implementation, structure, features and effects, in conjunction with the accompanying drawings and preferred embodiments. In the following description, different "one embodiment" or "another embodiment" does not necessarily refer to the same embodiment. In addition, specific features, structures or characteristics in one or more embodiments may be combined in any suitable form.

[0052] Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs.

[0053] At present, for the measurement of equal-diameter holes, it is necessary to calibrate the equal-diameter holes or parts first, so that the ranging laser emitted by the laser probe is perpendicular to the hole axis. However, due to the inherent error of the calibration instrument and the operational error of the calibration operation, the accuracy of the inner diameter measurement results of equal-diameter holes is insufficient. In particular, micron-level accuracy cannot be guaranteed, and due to the influence of calibration operation errors, for inner holes with a large aspect ratio (Aspect Ratio), for example, when the aspect ratio is greater than 7-10 times, the calibration error in the measurement process will be further amplified, resulting in the laser measurement method being unable to obtain accurate inner diameter measurement results. The following will specifically describe a specific scheme of a method and system for measuring the inner hole of a part provided by the present invention in conjunction with the accompanying drawings.

[0054] See also Figure 1 , Figure 1 A flow chart of a method for measuring the inner hole of a part provided by an embodiment of the present invention. The method can be applied to a measuring device to measure the diameter of equal-diameter holes. The method is run by a controller on the measuring device. The controller can be any terminal capable of implementing control and data processing, such as an industrial computer or an embedded control board, as long as it can run the method. No specific restrictions are imposed on it. The measuring method is used to measure equal-diameter holes on parts with micron-level precision; the measuring method includes:

[0055] S11. Freely move the first laser probe to a radial measurement position in the equal-diameter hole, wherein the part with the equal-diameter hole is fixed by a positioning device so that the vertical deviation between the ranging laser emitted by the first laser probe along the radial direction of the hole and the axis of the hole is within a preset range.

[0056] For details, please refer to Figure 2 , Figure 2 It is a structural diagram of the part inner hole measurement system, and the measurement system includes a measuring device 1 and a positioning device 2. The positioning device 2 is used to fix the part 3, and the fixing method can be clamping. For example, for parts with smaller mass and volume, the part is clamped and fixed by a three-jaw chuck; of course, the part can also be fixed by setting a positioning mechanism on the positioning device, such as setting a V-shaped groove on the base to fix the part. After the part is placed in the V-shaped groove, it can be positioned and fixed on the V-shaped groove by its own gravity. It can be understood that since the three-jaw clamp and the base with a V-shaped groove are only used for preliminary fixing and positioning of the part, the ranging laser emitted in the aperture radial direction cannot be completely perpendicular to the hole wall of the equal-diameter hole, and can only ensure that the vertical deviation between the ranging laser and the hole axis is within a preset range. It can be understood that the vertical deviation is caused by the deflection of the part 3 when clamped on the definition device 2. For example, the three-jaw chuck clamps the part 3 in an automatic centering manner, which cannot ensure that the ranging laser is completely perpendicular to the hole axis. The ideal vertical state cannot be achieved through instrument calibration, and it takes a lot of calibration time.

[0057] The parts to be measured by the embodiments of the present invention are parts that require micron-level precision measurement, and cannot be accurately measured by traditional measuring tools. Controlling the vertical deviation between the ranging laser and the hole axis within a preset range can effectively reduce unexpected changes in the ranging laser when it is reflected on the hole wall. The reflected light of the ranging laser on the hole wall of the equal-diameter hole can be returned and received more regularly, and the intensity and stability of the reflected light are better. At the same time, the influence of calibration accuracy on the measurement results is also eliminated, so that the measurement accuracy of the equal-diameter hole can reach the micron level.

[0058] like Figure 2 As shown in the figure, the measuring device 1 includes a first laser probe 11, a second laser probe 12, a vertical plate 13 and a horizontal driving mechanism 14. The first laser probe 11 and the second laser probe 12 are installed on the vertical plate 13, and the vertical plate 13 is installed on the horizontal driving mechanism 14. The horizontal driving mechanism 14 can drive the vertical plate 13 to move along the axial direction of the equal-diameter hole.

[0059] The first laser probe is used to measure the aperture of equal-diameter holes. The first laser probe is a long rod structure. The light is emitted from one end close to the part, and is emitted to the hole wall along the aperture of the equal-diameter hole, and is received after being reflected by the hole wall. A motor is provided at one end of the first laser probe close to the vertical plate, and an encoder is provided at the end of the motor. The rotation angle of the motor can be determined based on the rotation stroke of the motor. The first laser probe is driven by the motor to rotate, so as to achieve circumferential measurement of the equal-diameter hole. The first laser probe can be freely moved into the equal-diameter hole by controlling the horizontal drive mechanism. For example, a preset button connects the power supply and the horizontal drive mechanism. The user triggers the button to connect the power supply to the horizontal drive mechanism to power on the horizontal drive mechanism, and the horizontal drive mechanism drives the first laser probe to move into the equal-diameter hole. After releasing the button, the horizontal drive mechanism is powered off, and the first laser probe stops in the equal-diameter hole. The horizontal drive mechanism can be a drive mechanism composed of an electric telescopic rod. It can be understood that since the equal-diameter holes have the same diameter in the length direction, the first laser probe can be located in the middle area of ​​the hole when measuring the inner diameter thereof, and the operation can be based on the user's experience.

[0060] In practical applications, some equal-diameter holes may be blind holes or have step structures. If the radial measurement position is close to the bottom or mouth of the hole, it will cause the subsequent inability to obtain an accurate circumferential data set. Based on this, in a specific implementation, before executing step S11, the method further includes:

[0061] When it is determined that the equal-diameter hole is a non-through hole structure, the second laser probe is controlled to perform axial distance measurement on the equal-diameter hole to obtain the hole bottom position and hole mouth position of the equal-diameter hole. The non-through hole structure means that the equal-diameter hole on the part is a blind hole, or there is a step structure, such as Figure 2 As shown in . The equal-diameter hole structure can be determined by reading the drawing of the part, for example, by taking an image of the drawing, and determining whether the equal-diameter hole is a non-through hole structure through the hole structure represented by the image; of course, the second laser probe can also perform the axial distance measurement task, which is the task of the second laser probe to perform axial measurement of the part. During the axial measurement, the second laser probe moves in the Z direction and measures the distance, and can measure the position of the end face of the part, which is used as the hole mouth position; the position of the inner hole step structure, that is, the hole bottom position, can also be measured.

[0062] Configure the first area from the hole bottom to the hole mouth and the second area from the hole mouth to the hole depth as the no-stop area for the first laser probe to move freely. Figure 4 , Figure 4This is a first principle example diagram of equal-diameter hole measurement. In the figure, the ranging laser emitted by the first laser probe along the hole radial direction is G1, the hole axis is G2, G1 and G2 are in a non-vertical state, and the angle α between the ranging laser G1 and the hole wall is less than 90°. If the first laser probe is too close to the hole bottom or hole mouth, part of the ranging laser cannot be emitted to the hole wall during circumferential measurement. Therefore, the first area K2 and the second area K3 are configured as no-stop areas, and the radial measurement position can only be located in the middle area K1 to ensure that the ranging laser can be emitted to the hole wall during circumferential measurement of equal-diameter holes.

[0063] It should be noted that the method of freely moving the first laser probe can also be based on manual operation of the user. The first laser probe can be manually moved to the middle area of ​​the hole. After the first laser probe is freely moved into the equal-diameter hole, step S12 is entered.

[0064] S12, controlling the first laser probe to perform a radial rough measurement task on the equal-diameter hole at the radial measurement position to obtain an estimated inner diameter of the equal-diameter hole.

[0065] Specifically, the radial rough measurement task is to perform preliminary measurement of the radial direction of the equal-diameter hole by the first laser probe, and its purpose is to estimate the inner diameter of the equal-diameter hole to obtain the estimated inner diameter of the equal-diameter hole. The estimated inner diameter can be the estimated diameter or radius of the equal-diameter hole, which can characterize the aperture size of the equal-diameter hole. The center angle of 180° or 360° can be used as the distance measurement range of the radial rough measurement task, and multiple points are measured within the above center angle, and the estimated inner diameter is obtained by the distance measured by multiple points.

[0066] It should be noted that when determining the estimated inner diameter, the estimated inner diameter can be estimated based on multiple measurement distances obtained by performing the radial rough measurement task at the radial measurement position. Figure 3 , Figure 3 The schematic diagram is a principle diagram for calculating the estimated inner diameter. Three-point measurement can be performed in the radial rough measurement task, and the three measurement points are recorded as P1, P2 and P3 respectively; point O1 in the figure is the radial measurement position, and the distances from point O1 to the three measurement points P1, P2 and P3 are recorded as d1, d2 and d3 respectively. The triangle formed by the three measurement points is recorded as △P1P2P3. The center of the circle O2 is determined by the circumcenter of the triangle. The center of the circle O2 is the intersection of the perpendicular bisectors of the line segments P1P2 and P2P3. The radius r of the circle is calculated using the circumscribed circle radius formula, and the estimated inner diameter of the equal-diameter hole can be obtained.

[0067] Specifically, a rectangular coordinate system is established based on point O1, with the horizontal coordinate being the X-axis and the vertical coordinate being the Y-axis. The coordinates of the three measuring points are marked as P1 (x1, y1), P2 (x2, y3) and P3 (x3, y3). The area of ​​△P1P2P3 is marked as S, and the area S is calculated based on the following formula. , when calculating the area, all coordinate values ​​can be taken as positive values, and then the area of ​​△P1P2P3 can be obtained based on the above formula. The radius of the circumscribed circle formula is , and then the estimated inner diameter is obtained. It can be understood that the above formula can accurately calculate the radius when the ranging laser is perpendicular to the hole axis. Since the part is not calibrated, the calculated radius r can only be used as the estimated inner diameter of the equal diameter hole.

[0068] Exemplarily, step S12 includes sub-steps S12-1 to S12-2, which are specifically described as follows:

[0069] S12-1. According to the data configured in the radial rough measurement task, determine the number of radial ranging measurements and the corresponding rough measurement rotation step of the radial rough measurement task, wherein the number of radial ranging measurements is a positive integer greater than or equal to 3, and the rotation angle represented by the rough measurement rotation step is greater than the preset angle, so that the angle measurement range of the radial rough measurement task is greater than or equal to 120°. The data configured in the radial rough measurement task can be independently configured based on the measurement requirements of equal-diameter holes of a single specification, or can be combined and configured based on the measurement requirements of equal-diameter holes of different specifications. The number of radial ranging measurements is the number of ranging measurements to be performed by the first laser probe in the radial rough measurement task, and the rough measurement rotation step is the rotation angle of the first laser probe under adjacent radial ranging times. When the number of radial ranging measurements is 3, the rough measurement rotation step can be configured to be 40-60° to prevent the angle measurement range of the radial rough measurement task from being too small, causing insufficient accuracy in estimating the inner diameter.

[0070] S12-2, according to the number of radial distance measurements and the rough measurement rotation step, control the first laser probe to perform multi-point distance measurement along the radial direction of the equal diameter hole at the radial measurement position to obtain the measured distance of each measuring point. After the first laser probe rotates the rough measurement rotation step, a distance measurement is performed, and the distance measurement is stopped when the number of rotations reaches the number of radial distance measurements, and the measured distance of each measuring point is obtained based on the measurement results obtained after each rotation.

[0071] In practical applications, since the first laser probe is freely movable into the hole, if the first laser probe is too close to the hole wall, the accuracy of the nearby distance measurement may be affected. Based on this, in an optional embodiment, after obtaining the measured distance of each measuring point, the method further includes:

[0072] Determine whether the measured distance of each measurement point is less than the distance threshold. The distance threshold can be set based on the actual situation. For example, it can be determined based on data such as laser wavelength and scattering angle (or divergence angle). Short-wavelength lasers (such as visible light lasers) usually have smaller scattering angles, while long-wavelength lasers (such as infrared lasers) may have larger scattering angles. Generally, the shorter the wavelength, the easier it is for the laser to remain stable near the reflective surface, and the hole wall and the first laser probe remain larger than the range affected by the laser scattering angle. The distance threshold can be based on the formula: , calculate the distance threshold L min , where D is the desired spot diameter of the ranging laser emitted to the hole wall, is the laser wavelength, d is the initial spot diameter of the ranging laser without contacting the hole wall, so It is characterized by the change in the spot diameter caused by the scattering angle. From the above analysis, it can be seen that if the measurement distance is too small, it will lead to the inability to obtain an accurate measurement distance after the laser is scattered. The distance threshold can be set to 10-20mm.

[0073] When the measured distance is greater than or equal to the distance threshold, it means that the distance between the first laser probe and the hole wall is reasonable and will not affect the accuracy of the subsequent circumferential precision measurement task, and no other operations are performed. On the contrary, when the measured distance is less than the distance threshold, it means that the first laser probe is too close to the hole wall in the hole, and the first laser probe is controlled to move radially in the equal-diameter hole so that the first laser probe is in the radial target area for performing the circumferential precision measurement task. The radial target area is the area where any radial distance between the first laser probe and the equal-diameter hole is greater than a preset value, and the preset value can be set to the above-mentioned distance threshold L min , or it can be greater than this value to reduce the measurement error caused by scattering factors of the ranging laser.

[0074] S12-3, determine the estimated inner diameter of the equal-diameter hole according to the mean of all measured distances. The mean of all measured distances can be calculated based on the mean function, and the calculation result is determined as the estimated inner diameter. This implementation has high accuracy and effectively reduces the calculation redundancy of data. After determining the estimated inner diameter of the equal-diameter hole, enter step S13.

[0075] S13, controlling the first laser probe to perform circumferential precision measurement on the equal-diameter hole with a corresponding precision measurement rotation step according to the estimated inner diameter, so as to obtain a circumferential data set characterized by an elliptical profile, wherein the estimated inner diameter and the precision measurement rotation step are inversely proportional.

[0076] Specifically, the precision measurement rotation step is the rotation angle between adjacent measuring points when the first laser probe performs the circumferential precision measurement task. When determining the precision measurement rotation step, it can be obtained based on the estimated inner diameter. For example, a corresponding relationship is established between different estimated inner diameters and precision measurement rotation steps so that the two change in inverse proportion. The change can be linear or nonlinear. Based on the estimated inner diameter obtained from the current radial rough measurement task, the precision measurement rotation step of the current circumferential precision measurement task is determined in the corresponding relationship, so as to perform the circumferential precision measurement task based on the current precision measurement rotation step. Since the ranging laser is not in a perpendicular state to the hole axis, after circumferential ranging is performed on equal-diameter holes based on the circumferential precision measurement task, the contour represented by all measured distances is an elliptical contour.

[0077] It can be understood that when performing circumferential precision measurement tasks, the larger the estimated inner diameter, the larger the diameter of the equal-diameter hole. If the precision measurement rotation step is too large, the accuracy of the elliptical profile fitting will be insufficient. Therefore, the estimated inner diameter and the precision measurement rotation step are set to an inversely proportional relationship, so that the adopted precision measurement rotation step is suitable for measuring equal-diameter holes of different specifications. This measurement method has good applicability for inner holes of different specifications.

[0078] Furthermore, when performing circumferential precision measurement tasks, the precision measurement rotation step can be set to a fixed value, for example, radial distance measurement is performed once each time the precision measurement rotation step is rotated until the 360° circumferential rotation distance measurement is completed, and the set composed of all distance measurement values ​​is determined as a circumferential data set. Of course, after completing 180° rotation distance measurement based on the precision measurement rotation step, half of the precision measurement rotation step can be rotated, and 180° rotation distance measurement can be continued with the precision measurement rotation step to capture more comprehensive data as a circumferential data set. For example, when the precision measurement rotation step is 20°, a point is measured every 20°. After 9 times, basic data within this angle range can be obtained, providing preliminary contour information; after the 180° measurement is completed, rotate 10° and measure once, so that an intermediate point can be added every 20°, so that the details of the elliptical contour can be captured more accurately, especially at the four turning points of the elliptical contour; then continue to measure in 20° mode until the 180° scanning distance measurement is completed. This method can more comprehensively reflect the true contour of the equal-diameter hole in the deflected state without increasing the number of measurements. In this way, more comprehensive data points can be obtained, so that the subsequent fitting algorithm (such as the least squares method) can better capture the true shape of the equal-diameter hole, thereby improving the fitting accuracy of the elliptical contour.

[0079] In practical applications, the laser distance measurement method is mostly based on the time difference between laser emission and reception to obtain the measurement time, and the product of the measurement time and the speed of light is determined as the measurement distance. This distance measurement method is mostly suitable for the measurement of large-sized parts; for small-sized parts, the phase distance measurement method can be used, but when the degree of deviation of the part clamping is large, the conventional phase distance measurement method may not be able to obtain an accurate measurement distance. Based on this, in a specific implementation, the distance measurement method for the circumferential precision measurement task is the phase distance measurement method; before performing the circumferential precision measurement task on equal-diameter holes, the method also includes:

[0080] According to the data obtained from the radial rough measurement task, the deflection level of the part fixed by the positioning device is determined. The deflection level characterizes the degree of vertical deviation between the ranging laser and the hole axis, and can be set to multiple levels to characterize the magnitude of the vertical deviation. The larger the deflection level, the larger the vertical deviation level; conversely, the smaller the deflection level, the smaller the corresponding vertical deviation level. The deflection level can be determined based on multiple measurement distances obtained from the radial rough measurement task. For example, when estimating the estimated inner diameter based on the above method, multiple radial rough measurement tasks are performed, and each radial rough measurement task can obtain the corresponding estimated inner diameter. The larger the deviation between all estimated inner diameters, the higher the deflection level; conversely, the smaller the deflection level.

[0081] When the skew level is greater than the level threshold and the estimated inner diameter is greater than the inner diameter threshold, the circumferential precision measurement task is configured as dual-wavelength laser ranging. Dual-wavelength laser ranging uses two wavelengths of laser to perform circumferential ranging on equal-diameter holes. Lasers of different wavelengths have different responses to the reflection and scattering characteristics of the inner surface of equal-diameter holes. Some wavelengths may be greatly affected by surface roughness and reflectivity, while other wavelengths are less sensitive to these effects. Therefore, by combining or comparing the measurement results of different wavelengths, the error caused by scattering can be reduced, while the phase ambiguity problem in phase ranging can be reduced.

[0082] When the skew level is less than or equal to the level threshold, or the estimated inner diameter is less than or equal to the inner diameter threshold, the circumferential precision measurement task is configured as single-wavelength laser ranging. Single-wavelength laser ranging is to measure the distance of equal-diameter holes using a ranging laser of one wavelength. The configured laser wavelength can be determined based on the estimated inner diameter and skew level, and it can be applied to accurate ranging in this environment. It will not be described in detail here.

[0083] At this point, circumferential distance measurement is performed on the equal-diameter holes based on the configured single-wavelength distance measurement method or dual-wavelength distance measurement method to obtain a circumferential data set, and the process proceeds to step S14.

[0084] S14, performing analytical processing on the circumferential data set to determine the minor semi-axis of the elliptical profile as the measured radius of the equal-diameter hole.

[0085] Specifically, the circumferential data set can be processed based on the analytical model. The circumferential data set is a data set consisting of different measurement distances and corresponding direction angles. Figure 5 , Figure 5 This is an example diagram of the second principle of equal-diameter hole measurement. The coordinate system xO1y is established based on the radial measurement position. The direction angle is the angle θ between the measurement distance and the x-axis. The major semi-axis of the elliptical profile is set to a and the minor semi-axis is set to b. The following relationship exists:

[0086]

[0087] Among them, di is a different measurement distance, that is, Figure 5 The distance between the midpoint O1 and point P. All measured distances d are obtained from this i The relationship between the major semi-axis a and the minor semi-axis b is solved using the least squares method, and the minor semi-axis b is determined as the measured radius of the equal-diameter hole. Figure 5 The middle curve R is the curve represented by the elliptical profile, and the curve D is the curve represented by the equal-diameter hole. The first laser probe measures the distance from point O1 to the circumference of the equal-diameter hole, and point P is the measurement point emitted by the first laser probe to the hole wall. It can be seen from the figure that the short semi-axis of curve R is the radius of curve D.

[0088] It should be noted that when the amount of data in the circumferential data set is small, the analysis of the major and minor semi-axes of the elliptical contour based on the least squares method cannot meet the micron-level requirements of aperture measurement. The method of the embodiment of the present invention can implement circumferential distance measurement on equal-diameter holes by accurately and precisely measuring the rotation step, and then analyze the accurate minor semi-axis, so that it can meet the micron-level measurement accuracy requirements.

[0089] It can be understood that it is difficult to achieve micron-level measurement accuracy through laser measurement, which is affected by many factors. In order to minimize the impact of the measuring device, precision calibration can be performed before measuring the part. For example, a ring with a standard inner diameter is fixed by a positioning device, and the ring with a standard inner diameter is measured by a measuring device to obtain the measured inner diameter of the ring. The calibration coefficient is determined based on the measured inner diameter and the actual standard inner diameter of the ring. The short semi-axis of the elliptical profile is calibrated based on the calibration coefficient, and the calibration result is determined as the measured radius of the equal-diameter hole. Calibration can reduce the influence of the measuring device's own error on the measurement accuracy, and ensure that the measurement accuracy of the equal-diameter hole reaches the micron level. Similarly, after the ring is fixed, there is also a vertical deviation caused by clamping, which will introduce a systematic error. This error will affect the result in a similar way in each measurement. If the degree of deflection of the clamping is controlled, the short semi-axis obtained in each measurement can be effectively calibrated based on the calibration coefficient. Therefore, by controlling the degree of deflection of the clamping and implementing calibration, the measurement system can work more stably, reduce the systematic error caused by the clamping factor, and thus improve the measurement accuracy of the equal-diameter hole.

[0090] When implementing the above calibration, you can also choose a standard inner diameter ring with a similar inner diameter to the equal-diameter hole to implement the determination of the parameters of the spot and wavelength. For example, the inner diameter of the ring can be measured based on spots of different diameters and different wavelengths. The target spot diameter and target wavelength suitable for equal-diameter hole measurement can be determined based on the measured inner diameter and the actual standard inner diameter of the ring. In the actual circumferential precision measurement task, the target spot diameter and target wavelength can be selected to implement the measurement, so as to reduce the measurement error caused by inaccurate configuration of the spot and wavelength of the ranging laser emitted along the radial direction of the aperture.

[0091] Exemplarily, step S14 includes sub-steps S14-1 to S14-5, which are specifically described as follows:

[0092] S14-1. When the circumferential data set is a data set obtained by single-wavelength laser ranging, each measured distance and corresponding direction angle in the circumferential data set of the single-wavelength laser ranging is input into the analytical model of the ellipse profile. As described above, the analytical model is constructed based on the measured distance, direction angle, major semi-axis and minor semi-axis.

[0093] S14-2, the first minor semi-axis analyzed by the analytical model in single-wavelength laser ranging is determined as the measured radius of the equal-diameter hole in single-wavelength laser ranging. The analytical model is solved based on the above relationship and the least squares method, and the solved first minor semi-axis is output as the measured radius obtained by single-wavelength laser ranging.

[0094] S14-3. When the circumferential data set is a data set obtained by dual-wavelength laser ranging, the measured distances and corresponding azimuths of the two wavelengths in the circumferential data set of the dual-wavelength laser ranging are sequentially input into the analytical model of the elliptical profile. The measured distances and azimuths obtained at different wavelengths can be stored in the circumferential data set as corresponding data subsets, each data subset being a measured distance and azimuth obtained at one wavelength, and the data of each data subset is input into the analytical model.

[0095] S14-4. According to the analytical results of the analytical model for measuring distance and direction angle at two wavelengths, the second minor semi-axis and the third minor semi-axis are obtained. The numerical precision of the second minor semi-axis and the third minor semi-axis can be configured to be in the micron level.

[0096] S14-5. According to the second minor semi-axis and the third minor semi-axis, the measured radius of the equal-diameter hole in the dual-wavelength laser ranging is obtained. The second minor semi-axis and the third minor semi-axis are obtained based on different wavelength measurements. In order to reduce the error caused by phase ambiguity, the measured radius is determined by combining the second minor semi-axis and the third minor semi-axis.

[0097] For example, according to the short semi-axis corresponding to the long wavelength in the second and third short semi-axis, the value of the measured radius in the range of ten microns to millimeters is determined; according to the short semi-axis corresponding to the short wavelength in the second and third short semi-axis, the value of the measured radius in microns is determined. The second short semi-axis is determined to be 58.233mm based on the long wavelength ranging laser measurement, and the third short semi-axis is determined to be 58.225mm based on the short wavelength ranging laser measurement. The measured radius is determined to be 58.235mm. It can be understood that when implementing aperture measurement, the millimeter-level value is used as the unit of measurement, and the size of the measured radius is expressed in millimeters. Ten microns is the second decimal place of the measured radius, and microns is the third decimal place of the measured radius.

[0098] In practical applications, the radial runout of the inner hole is also an indicator for detecting whether the inner hole is reasonable. After the circumferential data set is analyzed and processed, the method further includes:

[0099] S15, controlling the positioning device to rotate the part around its hole axis at multiple angles, and performing circumferential precision measurement tasks and data analysis processing at each angle to obtain the actual measured radius at each angle.

[0100] Specifically, a motor can be installed on the positioning device to drive the part to rotate around its hole axis. The rotation angle can be determined based on the estimated inner diameter. When the estimated inner diameter is larger, it means that more intensive measurements are required for holes of equal diameter, and the angle of each rotation is smaller. Conversely, when the estimated inner diameter is smaller, 3-6 circumferential precision measurement tasks can be performed, that is, one circumferential precision measurement task is performed every 60-120° rotation.

[0101] S16. Output the radial runout of the equal-diameter hole according to all the measured radii. The radial runout characterizes the changes between all the measured radii. The maximum measured radius and the minimum measured radius can be extracted from all the measured radii. The radial runout of the equal-diameter hole can be determined based on the difference between the maximum measured radius and the minimum measured radius. Of course, all the measured radii can also be analyzed based on the least squares method to obtain the radial runout of the equal-diameter hole.

[0102] The equal-diameter holes have the same diameter in their length direction. Precision machining methods include grinding, fine boring, lapping, etc. Only measuring the equal-diameter holes at a single radial measurement position cannot fully reflect the actual accuracy of the equal-diameter holes. Based on this, in a specific implementation, after parsing the circumferential data set, the method further includes:

[0103] S17, control the first laser probe to move a third preset distance along the axial direction of the equal-diameter hole, and perform the circumferential precision measurement task again to obtain the actual measured radius of the equal-diameter hole again. Figure 4 In the figure, point A is the radial measurement position of the initial circumferential precision measurement task. After completing the task, the first laser probe is controlled to move to point B, and the circumferential precision measurement task is performed again to obtain the actual radius measured at point B.

[0104] S18. Output the taper measurement result of the equal-diameter hole according to the measured radius obtained for the first time and the measured radius obtained for the second time. If the measured radii obtained by the two circumferential precision measurement tasks are the same, it means that the equal-diameter hole has no taper; on the contrary, if there is a difference between the measured radii obtained by the two circumferential precision measurement tasks, it means that the equal-diameter hole has taper. The taper of the equal-diameter hole is calculated based on the trigonometric function and output as the taper measurement result.

[0105] Based on the same technical concept as the measuring method, an embodiment of the present invention further provides a system for measuring inner holes of parts, which is used to perform micron-level precision measurement of equal-diameter holes on parts; the system includes a positioning device and a measuring device.

[0106] The positioning device can be a three-jaw chuck or other fixture that can fix the part. The positioning device is used to fix the part with equal-diameter holes so that the vertical deviation between the ranging laser emitted by the first laser probe along the radial direction of the hole and the hole axis is within a preset range.

[0107] The measuring device is used to control its first laser probe to move freely to a radial measurement position in an equal-diameter hole; control the first laser probe to perform a radial rough measurement task on the equal-diameter hole at the radial measurement position to obtain an estimated inner diameter of the equal-diameter hole; control the first laser probe to perform a circumferential fine measurement task on the equal-diameter hole with a corresponding fine measurement rotation step according to the estimated inner diameter to obtain a circumferential data set characterized as an elliptical profile, wherein the estimated inner diameter and the fine measurement rotation step are inversely proportional; and perform analytical processing on the circumferential data set to determine the minor semi-axis of the elliptical profile as the actual measured radius of the equal-diameter hole.

[0108] The technical solution provided in the embodiments of the present invention has at least the following technical effects or advantages:

[0109] The technical solution of the present invention freely moves the first laser probe to the radial measurement position in the equal-diameter hole. Since the part with the equal-diameter hole is fixed by the positioning device, the vertical deviation between the distance measuring laser emitted by the first laser probe along the hole radial direction and the hole axis is within a preset range, and the distance can be accurately measured by laser. After controlling the first laser probe to perform the radial rough measurement task on the equal-diameter hole at the radial measurement position, the estimated inner diameter of the equal-diameter hole can be obtained. Then, according to the estimated inner diameter, the first laser probe is controlled to perform the circumferential fine measurement task on the equal-diameter hole with the corresponding fine measurement rotation step to obtain a circumferential data set characterized as an elliptical profile. The estimated inner diameter and the fine measurement rotation step are inversely proportional. The adopted fine measurement rotation step is suitable for the measurement of the equal-diameter hole with the estimated inner diameter. The amount of data presented by the circumferential data set can ensure that the equal-diameter hole is accurately measured. After the circumferential data set is analyzed and processed, the short semi-axis of the elliptical profile is determined as the measured radius of the equal-diameter hole. When measuring equal-diameter holes, the vertical deviation of this technical solution is within the preset range to ensure the accuracy of the laser distance measurement method; since there is no need to clamp and calibrate the parts, the influence of calibration accuracy on the measurement results is eliminated, and the precision rotation step adopted can be applied to the micron-level measurement accuracy requirements, and the measurement accuracy is controlled from multiple dimensions, so that the measurement accuracy of equal-diameter holes can meet the micron-level requirements. At the same time, since the measurement process does not require the clamping and calibration of the parts, the measurement efficiency of equal-diameter holes is taken into account.

[0110] It should be noted that the sequence of the above embodiments of the present invention is only for description and does not represent the advantages and disadvantages of the embodiments. The processes depicted in the accompanying drawings do not necessarily require the specific order or continuous order shown to achieve the desired results. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0111] The various embodiments in this specification are described in a progressive manner, and the same or similar parts between the various embodiments can be referenced to each other, and each embodiment focuses on the differences from other embodiments.

Claims

1. A method for measuring the inner hole of a part, characterized in that: The method is applied to implement micron-level precision measurement of equal-diameter holes on parts; the method comprises: Freely move the first laser probe to a radial measurement position in the equal-diameter hole, wherein the part with the equal-diameter hole is fixed by a positioning device so that the vertical deviation between the distance measuring laser emitted by the first laser probe along the radial direction of the hole and the hole axis is within a preset range; Controlling the first laser probe to perform a radial rough measurement task on the equal-diameter hole at the radial measurement position to obtain an estimated inner diameter of the equal-diameter hole; Controlling the first laser probe to perform a circumferential precision measurement task on the equal-diameter hole with a corresponding precision measurement rotation step according to the estimated inner diameter, so as to obtain a circumferential data set characterized by an elliptical profile, wherein the estimated inner diameter and the precision measurement rotation step are inversely proportional to each other; Analytically processing the circumferential data set to determine the minor semi-axis of the elliptical profile as the measured radius of the equal-diameter hole; The controlling the first laser probe to perform a radial rough measurement task on the equal-diameter hole at the radial measurement position to obtain an estimated inner diameter of the equal-diameter hole includes: Determine the number of radial ranging and the corresponding coarse measurement rotation step of the radial coarse measurement task according to the data configured in the radial coarse measurement task, wherein the number of radial ranging is a positive integer greater than or equal to 3, and the rotation angle represented by the coarse measurement rotation step is greater than a preset angle, so that the angle measurement range of the radial coarse measurement task is greater than or equal to 120°; According to the radial distance measurement times and the coarse measurement rotation step, the first laser probe is controlled to perform multi-point distance measurement along the radial direction of the equal-diameter hole at the radial measurement position to obtain the measurement distance of each measurement point; The estimated inner diameter of the equal-diameter hole is determined according to the average of all measured distances.

2. The method for measuring the inner hole of a part according to claim 1, characterized in that: After obtaining the measured distance of each measuring point, the method further includes: Determine whether the measured distance of each measuring point is less than a distance threshold; If so, the first laser probe is controlled to move radially in the equal-diameter hole so that the first laser probe is in a radial target area for performing the circumferential precision measurement task, wherein the radial target area is an area where any radial distance between the first laser probe and the equal-diameter hole is greater than a preset value.

3. The method for measuring the inner hole of a part according to claim 1, characterized in that: The distance measurement method of the circumferential precision measurement task is a phase distance measurement method; before the first laser probe is controlled according to the estimated inner diameter to perform the circumferential precision measurement task on the equal-diameter hole with a corresponding precision measurement rotation step, the method further includes: Determining the deflection level of the part fixed by the positioning device according to the data obtained from the radial rough measurement task; When the deflection level is greater than a level threshold and the estimated inner diameter is greater than an inner diameter threshold, configuring the circumferential precision measurement task to be dual-wavelength laser ranging; When the deflection level is less than or equal to the level threshold, or the estimated inner diameter is less than or equal to the inner diameter threshold, the circumferential precision measurement task is configured as single-wavelength laser ranging.

4. The method for measuring the inner hole of a part according to claim 1, characterized in that: The parsing and processing of the circumferential data set includes: When the circumferential data set is a data set obtained by single-wavelength laser ranging, each measured distance and corresponding direction angle in the circumferential data set of the single-wavelength laser ranging is input into the analytical model of the ellipse profile; Determine the first minor semi-axis analyzed by the analytical model in the single-wavelength laser ranging as the measured radius of the equal-diameter hole in the single-wavelength laser ranging; When the circumferential data set is a data set obtained by dual-wavelength laser ranging, the measured distances and corresponding direction angles of two wavelengths in the circumferential data set of the dual-wavelength laser ranging are sequentially input into the analytical model of the elliptical profile; According to the analytical results of the analytical model for measuring distances and azimuths at two wavelengths, a second minor semi-axis and a third minor semi-axis are obtained; According to the second short semi-axis and the third short semi-axis, the measured radius of the equal-diameter hole in the dual-wavelength laser ranging is obtained.

5. The method for measuring the inner hole of a part according to claim 4, characterized in that: The step of obtaining the measured radius of the equal-diameter hole in the dual-wavelength laser ranging according to the second minor semi-axis and the third minor semi-axis includes: Determine a value of the measured radius in the range of ten micrometers to millimeters according to the second semi-minor axis and the third semi-minor axis corresponding to the long wavelength; The micrometer-order value of the measured radius is determined according to the minor semi-axis corresponding to the short wavelength among the second minor semi-axis and the third minor semi-axis.

6. The method for measuring the inner hole of a part according to claim 1, characterized in that: Before freely moving the first laser probe to a radial measurement position in the equal-diameter hole, the method further includes: When it is determined that the equal-diameter hole is a non-through hole structure, controlling the second laser probe to perform an axial distance measurement task on the equal-diameter hole to obtain the hole bottom position and hole mouth position of the equal-diameter hole; The first area from the hole bottom position to the hole mouth direction and the second area from the hole mouth position to the hole depth direction are configured as the no-stopping area for the first laser probe to move freely.

7. The method for measuring the inner hole of a part according to claim 1, characterized in that: After parsing the circumferential data set, the method further includes: Controlling the positioning device to rotate the part around its hole axis at multiple angles, and performing the circumferential precision measurement task and data analysis processing at each angle to obtain the measured radius at each angle; According to all the measured radii, the radial circular runout of the equal-diameter hole is output.

8. The method for measuring the inner hole of a part according to claim 1, characterized in that: After parsing the circumferential data set, the method further includes: Controlling the first laser measuring head to move a third preset distance along the axial direction of the equal-diameter hole, and performing the circumferential precision measuring task again, so as to obtain the measured radius of the equal-diameter hole again; The taper measurement result of the equal-diameter hole is outputted according to the measured radius obtained initially and the measured radius obtained again.

9. A system for measuring inner holes of parts, characterized in that: The measuring system is a system corresponding to any one of the measuring methods of claims 1 to 8, and is used to perform micron-level precision measurement of equal-diameter holes on parts; the system comprises: A positioning device, used to fix the part with equal-diameter holes so that the vertical deviation between the distance measuring laser emitted by the first laser measuring head along the diameter of the hole and the axis of the hole is within a preset range; A measuring device is used to control its first laser probe to move freely to a radial measurement position in the equal-diameter hole; control the first laser probe to perform a radial rough measurement task on the equal-diameter hole at the radial measurement position to obtain an estimated inner diameter of the equal-diameter hole; control the first laser probe to perform a circumferential fine measurement task on the equal-diameter hole with a corresponding fine measurement rotation step according to the estimated inner diameter to obtain a circumferential data set characterized as an elliptical profile, wherein the estimated inner diameter and the fine measurement rotation step are inversely proportional; and perform analytical processing on the circumferential data set to determine the minor semi-axis of the elliptical profile as the measured radius of the equal-diameter hole.

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