CN114295063A - Spline gauge parameter measuring method and device - Google Patents
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Abstract
The invention discloses a spline gauge parameter measuring method and device, and belongs to the field of calibration of measuring instruments. The device comprises a base, a workbench, a moving shaft, a measuring head, a stand column, an upper tip and a lower tip. The measuring head is a three-dimensional scanning measuring head, a sensor for measuring the position of an X axis of the tangential motion axis is arranged on a U axis, and a sensor for measuring the position of a Y axis of the radial motion axis is arranged at a position close to the Y axis motion guide rail. The method comprises the steps of scanning a spline working surface in a contact measurement mode, and calculating to obtain tooth thickness and tooth groove width; the cross-rod distance M value is directly measured by using a self-centering mode. The layout of the spline mathematical models and the measuring device such as the base circle mathematical model, the reference circle mathematical model, the spline tooth form mathematical model and the like adopted by the invention accords with parameter definition, can meet the calibration requirements of various types of splines, particularly can solve the calibration problem of the spline with odd teeth substantially, eliminates the influence of the actual pressure angle deviation theoretical value on the measuring result, and improves the measuring efficiency and the more accurate degree of the measuring result.
Description
Technical Field
The invention relates to a spline gauge parameter measuring method and device, and belongs to the field of calibration of measuring instruments.
Background
The spline is a common coupling form in mechanical transmission, mainly used for circumferential fixation between a shaft and a part on the shaft to transmit torque, and consists of an external spline on the shaft and an internal spline of a hub hole. The splines may be divided into involute splines, rectangular splines, and triangular splines according to tooth profiles. The involute spline is the most widely used, most complex in structure and most parametric spline form at present. The spline ring gauge and the spline plug gauge are main standard measuring tools for comprehensively inspecting splines and are divided into a go gauge and a no-go gauge.
Tooth thickness and tooth groove width are important parameters of the spline. At present, the tooth thickness and the tooth groove width are difficult to calibrate by a direct method, the measurement precision is difficult to guarantee, and the quantity values are difficult to unify. According to the GB/T5106-2006 cylindrical straight tooth involute spline gauge standard, the tooth thickness and the tooth groove width are converted into the cross-bar distance (namely M value) for judgment. The M value is the primary parameter used in current spline gauge calibration.
At present, the cross-rod distance M value of the spline plug gauge can be measured by a length measuring instrument and three pins. This method has the following outstanding problems: calculating upper and lower limits of an M value through a tooth thickness tolerance and a pressure angle theoretical value, only judging the qualification of an actually measured M value, and not accurately and reversely calculating an actual tooth thickness or tooth space width value; ② the deviation of the pressure angle is not taken into account; the operation is complicated, and the best position is difficult to find when the spline with odd teeth is used; and fourthly, when the spline with the odd number of teeth is measured, the measurement position does not pass through the center of the spline, so that the measurement accuracy is difficult to ensure.
Disclosure of Invention
Aiming at the problems in the prior art, the invention discloses a spline gauge parameter measuring method and device, aiming at improving the spline gauge parameter measuring efficiency and accuracy.
The purpose of the invention is realized by the following technical method:
the invention discloses a spline gauge parameter measuring method, which comprises the steps of scanning a spline working surface in a contact measuring mode through a five-axis linkage control method, and calculating to obtain tooth thickness and tooth space width; the cross-rod distance M value is directly measured by using a self-centering mode.
The invention discloses a spline gauge parameter measuring method, which is a method for precisely measuring the tooth thickness, the tooth groove width and the cross-bar distance M value of a spline gauge by using a linkage contact scanning method, and comprises the following steps:
(1) cleaning each tooth socket of the gauge, placing on a rotary worktable of the spline gauge parameter measuring device, clamping the bottom of the spline gauge parameter measuring device, and enabling the top end of the spline gauge parameter measuring device to be propped by an upper tip so as to fix the gauge. Selecting a measuring head with the diameter smaller than the width of the tooth groove at the base circle position;
(2) the rotary working table rotates to drive the gauge to a proper position, a spline workpiece coordinate system is constructed, and a measurement path is planned according to the spline workpiece coordinate system:
the proper position is that the central line position of the two tooth profile surfaces is opposite to the Y-axis direction;
the workpiece coordinate system is that the intersection point of the central line of the base circle mathematical model and the rotating shaft of the rotary table is used as the coordinate origin, the horizontal direction is specified to be the right direction and is the X-axis positive direction, the Y-axis is constructed according to the coordinate system orthogonal principle, and the vertical direction is specified to be the Z-axis positive direction.
(3) The stylus probe contacts the tooth surface in one direction of the key teeth, the linear axis being from P in the Y direction0Starting scanning the tooth profile to PnAfter finishing the point, acquiring the actual shape of the contour;
(4) the stylus is moved to the opposite side position, and the stylus on the other side of the stylus is brought into contact with the tooth surface and moved from P 'in the Y direction'0Point to Start scanning tooth Profile, to P'nAfter finishing the point, controlling the measuring head to withdraw from the tooth groove after the measurement is finished;
(5) obtaining coordinates (x) of the intersection position of the reference circle and the two side tooth surfaces according to the reference circle mathematical model through the coordinate point data obtained by scanning1,y1,z1) And (x)2,y2,z2) And calculating to obtain the result of the tooth thickness or the tooth space width.
The included angle between the intersection position of the tooth surfaces at two sides and the connecting line of the origin of coordinates is calculated according to the formula:
the tooth thickness is calculated according to the formula:
wherein S is the tooth thickness, D is the reference circle diameter, DbIs base circle diameter
The implementation method for measuring the cross-rod distance M value comprises the following steps:
(1) cleaning each tooth socket of the gauge, placing on a rotary worktable of the spline gauge parameter measuring device, clamping the bottom of the spline gauge parameter measuring device, and enabling the top end of the spline gauge parameter measuring device to be propped by an upper tip so as to fix the gauge. Obtaining a nominal pressure angle and tooth thickness or tooth groove width according to a spline tooth profile mathematical model, and selecting an optimal radius measuring needle through calculation;
the spline mathematical model comprises a base circle mathematical model, a reference circle mathematical model and a spline tooth profile mathematical model, and the spline tooth profile mathematical model comprises an involute mathematical model, a rectangular mathematical model and a triangular mathematical model.
And the optimal radius measuring needle is tangent to the tooth grooves of the spline teeth and is used for measuring the cross-rod distance M. The diameter of a measuring needle for measuring the plug gauge is calculated according to the formula:
the diameter of the measuring needle for measuring the ring gauge is calculated according to the formula:
wherein, PbIs a base junction.
(2) The rotary working table rotates to drive the gauge to a proper position, a spline workpiece coordinate system is constructed, and a measurement path is planned according to the spline workpiece coordinate system:
the tooth socket to be measured is right opposite to the Y-axis direction at a proper position;
the workpiece coordinate system is that the intersection point of the central line of the base circle mathematical model and the rotating shaft of the rotary table is used as the coordinate origin, the horizontal direction is specified to be the right direction and is the X-axis positive direction, the Y-axis is constructed according to the coordinate system orthogonal principle, and the vertical direction is specified to be the Z-axis positive direction.
(3) The measuring head moves along the radial direction to enter the tooth socket and simultaneously contacts the tooth surfaces at two sides for measurement to obtain a radial position P0Controlling the measuring head to exit from the tooth groove after the measurement is finished;
(4) the rotary worktable drives the spline to rotate to the next measured position, the step (3) is repeated, and the next tooth P is measured1Carrying out measurement;
(5) repeating the step (4) and measuring all the key teeth P in sequencenAnd then, calculating the actual reference circle diameter according to the measured coordinates of the sphere center of the measuring head.
The equation of the reference circle is
(x-a)2+(y-b)2=r2
Let A be 2a, B be 2B, and C be a2+b2-r2The equation is
x2+y2-Ax-By+C=0
Substituting the spherical center coordinate matrix to obtain
The fitting calculation can be obtained
The cross rod distance M value of the plug gauge is calculated according to a formula:
MRe=DM+DRe
the cross-rod distance M value of the ring gauge is calculated according to a formula:
MRe=DM-DRe
wherein M isReTo span a rod distance, DMFor actually measuring the diameter, alpha, of the reference circleDIs the pressure angle, DReFor measuring the diameter of the needle
The invention discloses a spline gauge parameter measuring device which mainly comprises a base, a workbench, a moving shaft (a motor, a guide rail and a support), a measuring head, an upright post, an upper tip and a lower tip. The motion shafts comprise four linear motion shafts of tangential, radial, axial 1 and axial 2 and a rotary motion shaft, and correspond to an X shaft, a Y shaft, a Z shaft, a U shaft and a C shaft in sequence. The X-axis is horizontally arranged on the workbench, the Z-axis is arranged above the X-axis support along the vertical direction, a sliding support is arranged on the Z-axis, the Y-axis is arranged on the Z-axis support and is perpendicular to the Z-axis and the X-axis, the U-axis is arranged on the workbench, the upper tip mechanism is arranged on the stand column, the C-axis is arranged on the workbench, the lower tip mechanism is arranged on the C-axis and is coaxial with the C-axis, the upper tip mechanism and the lower tip mechanism are coaxial, the spline gauge to be measured is arranged between the upper tip mechanism and the lower tip mechanism, and the measuring head is arranged on the radial movement axis, and the size of the measuring head measuring needle meets the requirement of the optimal radius.
The measuring head is a three-dimensional scanning measuring head.
The tangential and radial movement shafts adopt a sensor of a laser interferometry principle as a length reference, a sensor for measuring the X-axis position of the tangential movement shaft is arranged on a U-axis, and a sensor for measuring the Y-axis position of the radial movement shaft is arranged at a position close to a Y-axis movement guide rail.
During measurement, a motor of the C shaft drives a spline measuring gauge to be measured to rotate, motors of the X shaft, the Y shaft and the Z shaft drive a measuring head to linearly move, the U shaft and the Z shaft synchronously move, and the position of the X shaft is measured in real time.
Has the advantages that:
1. the invention discloses a spline gauge parameter measuring method and device, which uses a contact measuring mode to scan a spline working surface and obtains tooth thickness and tooth groove width through calculation; the cross-rod distance M value is directly measured by using a self-centering mode. The layout of the spline mathematical models and the measuring device such as the base circle mathematical model, the reference circle mathematical model, the spline tooth form mathematical model and the like adopted by the invention accords with the parameter definition, can meet the calibration requirements of various types of splines, particularly can solve the calibration problem of the spline with odd teeth substantially, eliminates the influence of the actual pressure angle deviation theoretical value on the measuring result, and improves the measuring efficiency and the more accurate degree of the measuring result.
2. The invention discloses a spline gauge parameter measuring method and device, wherein a measuring head is a three-dimensional scanning measuring head, tangential and radial movement shafts adopt a sensor of a laser interference measurement principle as a length reference, a sensor for measuring the X-axis position of the tangential movement shaft is arranged on a U-axis, and a sensor for measuring the Y-axis position of the radial movement shaft is arranged at a position close to a Y-axis movement guide rail; during measurement, the C-axis motor drives the spline measuring gauge to be measured to rotate, the X-axis motor, the Y-axis motor and the Z-axis motor drive the measuring head to linearly move, the U-axis motor and the Z-axis motor synchronously move, the position of the X-axis is measured in real time, and the measuring efficiency and the measuring precision can be further improved.
Drawings
FIG. 1 is a schematic diagram of tooth thickness of a cylindrical straight tooth involute spline plug gauge;
FIG. 2 is a schematic view of the tooth thickness (tooth space width) measurement process of the present invention;
wherein: 1-probe, 2-stylus, 3-left side key tooth flank, 4-right side key tooth flank, 5-left side measurement start position P06-left measurement end position Pn7-Right measurement starting position P'08-Right side measurement end position P'n。
FIG. 3 is a schematic diagram of a cross-bar distance M of a cylindrical straight tooth involute spline plug gauge;
FIG. 4 is a schematic view of the measurement process of the cross-rod distance M according to the present invention.
Wherein: 1-measuring head, 2-measuring needle, 3-left side key tooth surface, 4-right side key tooth surface and 5-key tooth radial position.
FIG. 5 is a schematic view of a measuring device according to the present invention.
Wherein: the method comprises the following steps of 1-base, 2-workbench, 3-rotary motion shaft (C shaft), 4-measuring head, 5-upright post and upper top, 6-axial 2 motion shaft (U shaft), 7-laser interference measurement sensor, and 8-tangential, radial and axial 1 motion shaft (X shaft, Y shaft and Z shaft).
FIG. 6 is a schematic view of the installation position of the length measuring reference of the moving axis of the measuring device of the present invention.
Wherein: 1-measuring head, 2-motion axis, 3-reflector and 4-laser head.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and examples. The technical problems and the advantages solved by the technical solutions of the present invention are also described, and it should be noted that the described embodiments are only intended to facilitate the understanding of the present invention, and do not have any limiting effect.
Example 1:
selecting a 24-tooth M5 spline plug gauge, wherein the reference circle diameter D is 120mm, the tooth number Z is 24, and the base circle diameter D isb103.923mm, pressure angle alphaDIs 30 DEG, using the actual diameter DReThe measuring needle is 10.0mm, the tooth thickness is calibrated by a contact method, and the operation steps are as follows:
(1) cleaning each tooth groove of the plug gauge, placing the tooth grooves on a rotary worktable of the spline gauge parameter measuring device, clamping the bottom of the tooth grooves, and enabling the top end of the tooth grooves to be propped by a tip to fix the plug gauge. Selecting a measuring head with the diameter smaller than the width of the tooth groove at the base circle position;
(2) the rotary worktable rotates to drive the gauge to enable the position of the center line of the two tooth profile surfaces to be opposite to the Y-axis direction, a spline workpiece coordinate system is constructed, and a measurement path is planned according to the spline workpiece coordinate system:
(3) referring to fig. 2 and 6, the Z-axis movement drives the X-axis, the Y-axis and the measuring head to the height to be measured, the Y-axis movement drives the X-axis and the measuring head to face the middle of the measured tooth surface, the X-axis and the Y-axis are slightly moved, the contact pin 2 of the measuring head 1 contacts with the tooth surface at one side of the key tooth surface 3, and the linear axis moves from the initial position P to the linear axis along the Y direction0Point 5 begins scanning the tooth profile to the end position PnEnding the point 6, and acquiring the actual shape of the contour;
(4) as shown in FIG. 2, the probe is moved to the measurement position 5 by fine movement in the X-axis and Y-axis directions so that the stylus 2 of the probe 1 is brought into contact with the key tooth surface 4 side and moved from the start position P 'in the Y-direction'0Point 7 begins scanning the tooth profile to an end position P'nAfter the point 8 is finished, controlling the measuring head to withdraw from the tooth groove after the measurement is finished;
(5) obtaining coordinates (x) of the intersection position of the reference circle and the tooth surface according to the reference circle mathematical model through the coordinate point data obtained by scanning1,y1,z1) And (x)2,y2,z2) From the intersection position of the two side tooth surfaces to the coordinateThe included angle of the original point connecting line is calculated according to the formula:
the tooth thickness is calculated according to the formula:
during measurement, a plurality of teeth are measured at approximately equal positions, and then the arithmetic mean value is taken as the tooth thickness to be measured; the actual tooth thickness range of the plug gauge is (7.858-7.862) mm, and the arithmetic mean value is 7.860 mm.
Example 2:
selecting a 24-tooth M5 spline plug gauge and a nominal pressure angle alphaDThe angle is 30 degrees and the nominal reference circle diameter is 120mm, the cross-rod distance M value is calibrated by a contact method, and the operation steps are as follows:
(1) cleaning each tooth groove of the plug gauge, placing the tooth grooves on a rotary worktable of the spline gauge parameter measuring device, clamping the bottom of the tooth grooves, and enabling the top end of the tooth grooves to be propped by a tip to fix the plug gauge. Obtaining a nominal pressure angle and tooth thickness (or tooth groove width) according to a spline tooth profile mathematical model, and selecting an optimal radius measuring needle 2 and an actual radius D by calculationReA stylus of 15.869 mm;
(2) the rotary working table rotates to drive the gauge to the measured tooth socket to be opposite to the Y-axis direction, a spline workpiece coordinate system is constructed, and a measurement path is planned according to the spline workpiece coordinate system:
(3) as shown in fig. 4 and 6, the Z-axis moves to drive the X-axis, the Y-axis and the measuring head to the height to be measured, the Y-axis moves to drive the X-axis and the measuring head to face the middle of the measured tooth surface, the X-axis moves to enable the measuring head 1 to enter the tooth socket along the radial direction, the measuring needle 2 simultaneously contacts the tooth surfaces 4 on the two sides 3 to measure, the radial position 5 is obtained, and the measuring head is controlled to exit the tooth socket after the measurement is finished;
(4) the rotary worktable drives the spline to rotate to the next measured position, and the step (3) is repeated to measure the next tooth;
(5) repeating the step (4) and measuring all the key teeth in sequence. Constructing a fitting circle according to the measured coordinates of the sphere center of the measuring head to obtain the reference circle diameter of 120.126 mm;
(6) substituting the diameter D of the stylusReIs 15.869mm, calculate
MRe=DM+DRe=120.126+15.869=135.995
An M value of 135.995mm was obtained.
The method has the advantages that: by the method for measuring the tooth thickness, the tooth groove width and the cross-rod distance M of the cylindrical straight tooth involute spline plug gauge, a result which accords with the definition can be directly obtained; the method can meet the calibration requirements of various types of splines, particularly the calibration of the spline with the odd number of teeth is solved substantially, the influence of the deviation of an actual pressure angle from a theoretical value on a measurement result is eliminated, and the measurement principle and the method are high in detection efficiency.
The above detailed description is intended to illustrate the objects, aspects and advantages of the present invention, and it should be understood that the above detailed description is only exemplary of the present invention and is not intended to limit the scope of the present invention, and any modifications, equivalents, improvements and the like within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (10)
1. A spline gauge parameter measuring method is characterized by comprising the following steps: is a method for realizing the precise measurement of the spline gauge tooth thickness and the tooth groove width by a linkage contact scanning method, and the realization method comprises the following steps,
cleaning each tooth socket of a gauge, placing the tooth socket on a rotary worktable of a spline gauge parameter measuring device, clamping the bottom of the tooth socket, and enabling the top end of the tooth socket to be propped by an upper tip to fix the gauge; selecting a measuring head with the diameter smaller than the width of the tooth groove at the base circle position;
step two, the rotary working table rotates to drive the gauge to a proper position, a spline workpiece coordinate system is constructed, and a measurement path is planned according to the spline workpiece coordinate system:
step three, the stylus measuring head contacts with the tooth surface in one direction of the key teeth, and the linear axis is from P along the Y direction0Point start scanningTooth profile to PnAfter finishing the point, acquiring the actual shape of the contour;
step four, moving the measuring head to the opposite side position, enabling the measuring head other side contact pin to be in contact with the tooth surface, and enabling the measuring head other side contact pin to contact with the tooth surface from P 'along the Y direction'0Point to Start scanning tooth Profile, to P'nAfter finishing the point, controlling the measuring head to withdraw from the tooth groove after the measurement is finished;
and step five, obtaining coordinates of the intersection positions of the reference circle and the tooth surfaces on two sides according to the reference circle mathematical model through scanning the obtained coordinate point data, and calculating to obtain the tooth thickness or the tooth space width.
2. The spline gauge parameter measuring method according to claim 1, wherein: the proper position, namely the position of the midline of the two tooth profile surfaces is opposite to the Y-axis direction; the working coordinate system is that the intersection point of the central line of the base circle mathematical model and the rotating shaft of the rotary table is the coordinate origin, the horizontal direction is specified to be the X-axis positive direction, the Y-axis is constructed according to the coordinate system orthogonal principle, and the vertical direction is specified to be the Z-axis positive direction.
3. The spline gauge parameter measuring method according to claim 1, wherein: the implementation method of the fifth step is that,
the included angle between the intersection position of the tooth surfaces at two sides and the connecting line of the origin of coordinates is calculated according to the formula:
the tooth thickness is calculated according to the formula:
wherein S is the tooth thickness, D is the reference circle diameter, DbIs the base circle diameter.
4. A spline gauge parameter measuring method is characterized by comprising the following steps: is a method for realizing the precise measurement of the cross-bar distance M value of the spline gauge by using a linkage contact scanning method, and the realization method comprises the following steps,
cleaning each tooth socket of a gauge, placing the tooth socket on a rotary worktable of a spline gauge parameter measuring device, clamping the bottom of the tooth socket, and enabling the top end of the tooth socket to be propped by an upper tip to fix the gauge; obtaining a nominal pressure angle and tooth thickness or tooth groove width according to a spline tooth profile mathematical model, and selecting an optimal radius measuring needle through calculation;
step two, the rotary working table rotates to drive the gauge to a proper position, a spline workpiece coordinate system is constructed, and a measurement path is planned according to the spline workpiece coordinate system:
step three, the measuring head moves into the tooth socket along the radial direction and simultaneously contacts the tooth surfaces at two sides for measurement to obtain a radial position P0Controlling the measuring head to exit from the tooth groove after the measurement is finished;
fourthly, the rotary working table drives the spline to rotate to the next measured position, the third step is repeated, and the next tooth P is measured1Carrying out measurement;
step five, repeating the step four, and measuring all the key teeth P in sequencenAnd then, calculating the actual reference circle diameter according to the measured coordinates of the sphere center of the measuring head.
5. The spline gauge parameter measurement method according to claim 4, wherein: the implementation method of the step one is that,
the spline mathematical model comprises a base circle mathematical model, a reference circle mathematical model and a spline tooth profile mathematical model, and the spline tooth profile mathematical model comprises an involute mathematical model, a rectangular mathematical model and a triangular mathematical model;
the optimal radius measuring needle is tangent to the tooth grooves of the spline teeth and used for measuring the rod spanning distance M; the diameter of a measuring needle for measuring the plug gauge is calculated according to the formula:
the diameter of the measuring needle for measuring the ring gauge is calculated according to the formula:
wherein, PbIs a base junction.
6. The spline gauge parameter measurement method according to claim 4, wherein: in the second step, the proper position, namely the measured tooth socket, is opposite to the Y-axis direction; the workpiece coordinate system is that the intersection point of the central line of the base circle mathematical model and the rotating shaft of the rotary table is the coordinate origin, the horizontal direction is specified to be the X-axis positive direction, the Y-axis is constructed according to the coordinate system orthogonal principle, and the vertical direction is specified to be the Z-axis positive direction.
7. The spline gauge parameter measurement method according to claim 4, wherein: the implementation method of the fifth step is that,
the reference circle equation is (x-a)2+(y-b)2=r2
Let A be 2a, B be 2B, and C be a2+b2-r2The equation is
x2+y2-Ax-By+C=0
Substituting the spherical center coordinate matrix to obtain
Calculated by fitting
The cross rod distance M value of the plug gauge is calculated according to a formula:
MRe=DM+DRe
the cross-rod distance M value of the ring gauge is calculated according to a formula:
MRe=DM-DRe
wherein,MReTo span a rod distance, DMFor actually measuring the diameter, alpha, of the reference circleDIs the pressure angle, DReThe stylus diameter is measured.
8. The utility model provides a spline gauge parameter measurement device which characterized in that: the measuring device mainly comprises a base, a workbench, a moving shaft, a measuring head, a stand column, an upper tip and a lower tip;
the motion shafts comprise four linear motion shafts of tangential, radial, axial 1 and axial 2 and a rotary motion shaft, and correspond to an X shaft, a Y shaft, a Z shaft, a U shaft and a C shaft in sequence; the X-axis is horizontally arranged on the workbench, the Z-axis is arranged above the X-axis support along the vertical direction, a sliding support is arranged on the Z-axis, the Y-axis is arranged on the Z-axis support and is perpendicular to the Z-axis and the X-axis, the U-axis is arranged on the workbench, the upper tip mechanism is arranged on the stand column, the C-axis is arranged on the workbench, the lower tip mechanism is arranged on the C-axis and is coaxial with the C-axis, the upper tip mechanism and the lower tip mechanism are coaxial, the spline gauge to be measured is arranged between the upper tip mechanism and the lower tip mechanism, and the measuring head is arranged on the radial movement axis, and the size of the measuring head measuring needle meets the requirement of the optimal radius.
9. A spline gauge parameter measuring device according to claim 8, wherein: the measuring head is a three-dimensional scanning measuring head; the tangential and radial movement shafts adopt a sensor of a laser interferometry principle as a length reference, a sensor for measuring the X-axis position of the tangential movement shaft is arranged on a U-axis, and a sensor for measuring the Y-axis position of the radial movement shaft is arranged at a position close to a Y-axis movement guide rail.
10. A spline gauge parameter measuring device according to claim 8, wherein: during measurement, a motor of the C shaft drives a spline measuring gauge to be measured to rotate, motors of the X shaft, the Y shaft and the Z shaft drive a measuring head to linearly move, the U shaft and the Z shaft synchronously move, and the position of the X shaft is measured in real time.
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