CN111561882A - Dynamic measuring device and method for six degrees of freedom of rotating shaft - Google Patents

Dynamic measuring device and method for six degrees of freedom of rotating shaft Download PDF

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Publication number
CN111561882A
CN111561882A CN202010565143.2A CN202010565143A CN111561882A CN 111561882 A CN111561882 A CN 111561882A CN 202010565143 A CN202010565143 A CN 202010565143A CN 111561882 A CN111561882 A CN 111561882A
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displacement sensor
rotating shaft
measuring
error
displacement
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CN111561882B (en
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周怡帆
刘兴宝
米良
夏仰球
滕强
唐强
陈衡
杜坤
韩林
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Institute of Mechanical Manufacturing Technology of CAEP
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Institute of Mechanical Manufacturing Technology of CAEP
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01BMEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B11/00Measuring arrangements characterised by the use of optical techniques
    • G01B11/26Measuring arrangements characterised by the use of optical techniques for measuring angles or tapers; for testing the alignment of axes
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01BMEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B21/00Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant
    • G01B21/02Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring length, width, or thickness

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Abstract

The invention discloses a dynamic measuring device with six degrees of freedom of a rotating shaft, which comprises a rack, a power mechanism, a data acquisition system and a data analysis system, wherein the rack is provided with a measuring mechanism and a moving joint mechanism; the data acquisition system is connected with the measuring mechanism and is used for acquiring the measuring data of the measuring mechanism; the data analysis system is connected with the data acquisition system and is used for analyzing the data acquired by the data acquisition system; the measuring mechanism comprises an angle measuring mechanism and a displacement measuring mechanism; the invention also discloses a measuring method of the dynamic measuring device for the six-degree-of-freedom of the rotating shaft, which comprises the steps of S1 installation, S2 adjustment, S3 data acquisition and S4 data processing; the invention can complete the six-degree-of-freedom measurement of the rotating shaft in the same equipment, and solves the problems of more time consumption, complicated measurement process and the like caused by multi-plane separation measurement and angle error separation measurement of the rotating shaft error; the device has the advantages of high measurement efficiency, simple structure, convenience in installation and the like, and meanwhile, the detection cost is greatly reduced.

Description

Dynamic measuring device and method for six degrees of freedom of rotating shaft
Technical Field
The invention relates to space geometric accuracy detection, in particular to a dynamic measuring device and a measuring method for six degrees of freedom of a rotating shaft.
Background
The six degrees of freedom of the rotating shaft comprise the degrees of freedom of movement along the directions of X, Y, Z three orthogonal coordinate axes and the degrees of freedom of rotation around the three coordinate axes, the six degrees of freedom of the rotating shaft can be divided according to the standards ISO230-2 and ISO230-7, the degree of freedom of rotation around the Z axis is the position precision of the rotating shaft, and the other 5 degrees of freedom are the full-attitude dynamic rotation precision of the rotating shaft. In the aspect of technical research, the six degrees of freedom of a rotating shaft is an important technical index for evaluating the dynamic performance of the rotating shaft, taking a machine tool as an example, the six degrees of freedom of a main shaft of the machine tool directly influences the processing quality of a processed part, and in the aspect of engineering application, foreign precision machine tools already take the measurement of the rotation error of the main shaft as a necessary option for detecting the precision of the machine tool.
At present, the measurement of the six degrees of freedom of the rotating shaft is separately measured, two detection devices mainly comprise a rotating shaft position precision detection device and a rotating precision detection device, the position precision detection device mainly detects displacement errors of the rotating shaft along X, Y, Z orthogonal coordinate axis directions, and the rotating precision detection device mainly detects angle errors of the rotating shaft rotating around X, Y and Z axes. The two detection devices have limited information for measurement, and are difficult to complete all the six-degree-of-freedom measurement of the rotating shaft in one measurement, so that the problems of long measurement time, complex measurement process and the like are caused.
The rotary shaft position precision detection is mainly based on two measurement principles of a circular grating encoder and laser interference, special detection equipment is needed, the special detection equipment is expensive, and the detection cost is improved. The gyration accuracy includes two types, namely a static measurement method and a dynamic measurement method based on a precise steel ball or a ceramic ball. The static measurement method is essentially used for measuring the bounce of the rotating shaft and the ball, and when the rotating shaft runs at a high speed, the quasi-static measurement data of the rotating shaft is greatly different from the actual working condition state; the measuring reference of the rotating shaft dynamic rotation precision measuring instrument is separated from the mounting connector, a spring chuck clamping mode is mostly adopted, the assembling precision is not high, the rotation precision is amplified, the measuring precision is reduced, and the spring structure influences the dynamic balance of a measuring structure, so that high-speed measurement cannot be realized; meanwhile, the dynamic rotation precision measuring instrument mostly adopts external time triggering to acquire detection data, the position of a rotation shaft cannot be accurately positioned, the influence of speed fluctuation on a measuring result is difficult to remove, and the measuring precision is reduced.
Disclosure of Invention
The invention provides a dynamic measuring device and a dynamic measuring method for six degrees of freedom of a rotating shaft, aiming at solving the technical problems that the prior art can not synchronously measure the six degrees of freedom of the rotating shaft at one time and has low measuring precision.
The technical scheme adopted by the invention is as follows: the dynamic measuring device of the six degrees of freedom of the revolving shaft comprises:
a machine tool;
the moving joint mechanism is arranged on the rack and is used for connecting the rotating shaft;
the power mechanism is connected with the rack and is used for driving the motion joint unit to rotate;
the measuring mechanism is arranged on the rack and used for measuring relevant parameters of the rotating shaft;
the data acquisition system is connected with the measuring mechanism and is used for acquiring the measuring data of the measuring mechanism;
the data analysis system is connected with the data acquisition system and is used for analyzing the data acquired by the data acquisition system; the measuring mechanism comprises an angle measuring mechanism and a displacement measuring mechanism.
The invention installs the tested revolving shaft on the moving joint mechanism, the moving joint mechanism is installed on the frame, the frame is connected with the machine tool, the real-time data tested by the measuring mechanism is collected by the data collecting system, and the six degrees of freedom of the revolving shaft is calculated by the data analyzing system. The problems of more measurement time consumption, complex measurement process and the like caused by the rotary shaft error multi-plane separate measurement and the angle error separate measurement are solved; the invention can complete six-degree-of-freedom measurement of the rotating shaft in one device, has the advantages of high measurement efficiency, simple structure, convenient installation and the like, and greatly reduces the detection cost.
Furthermore, the movement joint mechanism comprises an installation platform, one end of the installation platform is provided with a measuring shaft, the other end of the installation platform is provided with an installation joint for installing a rotating shaft, and the installation joint and the measuring shaft are coaxially arranged; one side of the mounting table close to the measuring shaft is a mounting surface which is vertical to the measuring shaft; a first measuring surface and a second measuring surface are arranged at a certain distance in the axial direction of the measuring shaft, and the end part of the measuring shaft far away from the mounting table is a third measuring surface; the first measuring surface and the second measuring surface are parallel to each other, and the third measuring surface is perpendicular to the first measuring surface.
The measuring shaft and the measured revolving shaft are coaxially arranged, so that the relevant data of the revolving shaft can be measured through the relevant data of the measuring shaft. The first measuring surface and the second measuring surface are used for detecting reference surfaces of displacement errors of the rotating shaft on the X axis and the Y axis, and the third measuring surface is used for detecting the displacement errors of the rotating shaft on the Z axis. And the angular error of the rotation shaft rotating around X, Y and Z axis is determined again through the measured displacement error. Compared with one measuring surface, the two measuring surfaces, namely the first measuring surface and the second measuring surface, are arranged in the X-axis direction and the Y-axis direction, so that the vertical precision of the rotating shaft can be ensured, the installation error is reduced, and the measured data is more accurate.
Further, the motion joint mechanism is integrally formed. Compared with a structure that an installation joint and an inspection standard are separated in the prior art, the moving joint mechanism is integrally formed, on one hand, the assembly precision is obviously improved, the measurement precision is improved, on the other hand, the dynamic balance of the structure is changed, and high-speed measurement can be realized.
Further, the angle measuring mechanism comprises a circular grating arranged on the mounting surface, and the motion joint mechanism is connected with the rack through the circular grating; the rack is provided with at least one reading head for reading the circular grating data, and the reading head is connected with a data acquisition system through a wiring harness;
the displacement measuring mechanism comprises five displacement sensors arranged on a rack, namely a displacement sensor I, a displacement sensor II, a displacement sensor III, a displacement sensor IV and a displacement sensor V, wherein the displacement sensor I and the displacement sensor IV are arranged on two mutually vertical surfaces of the rack, and the displacement sensor I and the displacement sensor IV are both arranged on a plane where a first measuring surface is located; the displacement sensor II and the displacement sensor V are arranged on two mutually vertical surfaces of the frame, the displacement sensor I and the displacement sensor II are arranged coaxially, and the displacement sensor IV and the displacement sensor V are arranged coaxially; the displacement sensor II and the displacement sensor V are both arranged on the plane where the second measuring surface is located; the displacement sensor III is arranged below the third measuring surface and is vertical to the third measuring surface; the five sensors are connected with a data acquisition system through wiring harnesses.
The first measuring surface and the second measuring surface are arranged in the Z-axis direction, so that the axial precision of the rotating shaft is guaranteed, and the measured data is more accurate. Displacement errors of the rotating shaft on the X axis and the Y axis can be measured through two displacement sensors on the first measuring surface or the second measuring surface and positioned on the X axis and the Y axis, namely a displacement sensor I and a displacement sensor IV or a displacement sensor II and a displacement sensor V can be read; and the displacement sensor III can measure the displacement error of the rotating shaft on the Z axis. The angular error of the revolving shaft rotating around X, Y and Z axis is obtained by measuring the displacement error. In addition, installation errors are reduced by adopting a plurality of circular grating reading heads, an error separation algorithm is added into a data analysis system, rotation errors are removed, and higher-precision measurement of the positioning precision of the rotating shaft is realized.
Further, the first measuring surface, the second measuring surface and the third measuring surface are one of a plane and a spherical surface. As the plane or spherical measuring surface, the corresponding measurement can be completed; however, the spherical surface is a loose surface, and the change curvature is large, so that the error is large; the width and radius of the plane are consistent, so that the error is smaller, the measurement accuracy is higher, and the plane is obviously better than the spherical surface although both can be used as the measurement reference.
Furthermore, the five displacement sensors are all non-contact displacement sensors. The measuring shaft of the invention synchronously rotates along with the rotating shaft, so the non-contact displacement sensor can meet the motion working condition of the invention.
Further, the displacement sensor is detachably connected with the rack; the rack is provided with a mounting hole and a pressure joint, one end of the pressure joint penetrates through the mounting hole, the other end of the pressure joint is communicated with the outside of the rack, the rack is provided with a threaded hole facing the pressure joint, and a bolt is arranged in the threaded hole; the inner wall of the mounting hole is of an arc structure matched with the shape of the displacement sensor.
The invention has unique installation mode for the displacement sensor, and the displacement sensor is firstly installed in the installation hole with the size slightly larger than that of the displacement sensor, thereby facilitating the insertion of the displacement sensor; when the displacement sensor is installed, friction or interference cannot be generated between the displacement sensor and the installation hole, so that the displacement sensor is damaged; after the displacement sensor is installed, the pressure seam is arranged, so that the pressure seam is compressed through the rotation of the bolt in the threaded hole, the width of the pressure seam is narrowed, and the installation hole is pressed tightly, so that the fixation of the displacement sensor is completed. Compared with the clamping mode in the prior art, the fixing effect is better, the installation mode is simpler, meanwhile, the displacement sensor cannot be damaged, and the assembly precision is improved. In addition, the inner wall of mounting hole is the arc structure that matches with the displacement sensor appearance, consequently can make more inseparabler of displacement sensor and mounting hole laminating, and then improves stability.
The measuring method of the dynamic measuring device for the six-degree-of-freedom of the rotating shaft comprises the following steps of:
s1 installation:
the moving joint mechanism is coaxially installed with the rotating shaft to be tested through an installation joint, and the circular grating is installed on the installation surface of the moving joint mechanism; connecting the multi-reading head with a data acquisition system through a wire harness; the frame is fixedly connected with a machine tool through bolts;
mounting a displacement sensor I, a displacement sensor II, a displacement sensor III, a displacement sensor IV and a displacement sensor V in the mounting hole;
and S2, adjusting:
retracting the five displacement sensors into the mounting holes, and moving the tested rotating shaft in the X-axis and Y-axis directions until the tested rotating shaft is positioned at the center position of a displacement sensor III in the Z-axis direction; moving the tested rotating shaft in the Z-axis direction to enable the displacement sensor I and the displacement sensor IV to be positioned on a first measuring surface; the displacement sensor II and the displacement sensor V are positioned on a second measuring surface;
observing through a data acquisition system, and firstly adjusting a displacement sensor III in the Z-axis direction to enable the measurement value to be located in the middle of the measurement stroke; then, the position of the tested revolving shaft is adjusted along the X-axis direction, so that the measured value of the displacement sensor IV (54) is positioned in the middle position of the measuring stroke; then, the position of the tested revolving shaft is adjusted along the Y axis, so that the measured value of the displacement sensor I (51) is positioned in the middle position of the measuring stroke; continuously adjusting the measured values of the displacement sensor II and the displacement sensor V to the middle position of the stroke; finally, fixing the five displacement sensors on the frame through bolts;
and S3, data acquisition:
before measurement, the round grating and five displacement sensors are subjected to zero setting, and a data acquisition system takes a signal output by a reading head of the round grating as a trigger signal of the displacement sensors;
mounting the rack on a machine tool, preheating the machine tool for 20-30 min, starting measurement, and collecting data measured by the circular grating and the five displacement sensors;
signals output by a reading head of the circular grating are subjected to frequency division through different counters, and fixed-angle data acquisition is achieved;
and S4 data processing: and the data acquisition system transmits the acquired data to the data analysis system, and calculates the displacement error of the revolving shaft along X, Y and Z axis and the angle error of the revolving shaft rotating around X, Y and Z axis.
In step S2, each displacement sensor is adjusted to make its measurement value located at the middle position of the stroke, so as to better read and measure the error of the deflection; in step S3, the machine tool is preheated for 20-30 min before measurement, so that the influence of temperature rise on the measurement result can be effectively eliminated, and the working state of the measured revolving shaft is determined, so that the measuring equipment is prevented from being damaged by violent shaking; in step S3, the data acquisition system uses the signal output by the circular grating reading head as the trigger signal of the displacement sensor, and compared with the existing data acquisition triggered by external time, the data acquisition system synchronously acquires angle and displacement data and transmits the angle and displacement data to the data analysis system for analysis; the position of the rotary shaft can be accurately positioned, the high repeatability of each acquisition point position is ensured, the influence of the speed fluctuation of the rotary shaft on a measurement result is removed, and the measurement precision is improved.
Further, the step S4 specifically includes:
the displacement error of the rotating shaft along the X axis is measured by a displacement sensor IV or a displacement sensor V;
the displacement error of the rotating shaft along the Y axis is measured by a displacement sensor I or a displacement sensor II;
the displacement error of the rotating shaft along the Z axis is measured by a displacement sensor III;
the angle error of the rotation of the rotating shaft around the X axis or the Y axis is calculated by data measured by a pair of displacement sensors which are axially arranged along the rotating shaft, and the data can be measured by a displacement sensor I and a displacement sensor II; or the data measured by the displacement sensor IV and the displacement sensor V can be adopted; the following calculation is carried out by using data measured by the displacement sensor I and the displacement sensor II, and the calculation formula is as follows:
Figure BDA0002547552770000041
in formula (1):
θxis the angular error of rotation about the X axis;
ΔYI(theta) is the measured value of a displacement sensor I which is positioned at the near end of the Y-axis axial distance from the rotating shaft;
ΔYII(theta) is the measured value of a displacement sensor II which is positioned at the far end of the Y-axis axial distance from the rotating shaft;
d is the axial distance between the displacement sensor I and the displacement sensor II.
And dividing the difference value of the output values of the displacement sensor I and the displacement sensor II by the axial distance between the two sensors in the detection device to obtain a sine value of the rotation angle of the rotating shaft around the X axis, so that the angle error of the rotation of the rotating shaft around the X axis can be obtained.
Figure BDA0002547552770000051
In formula (2):
θyis the angular error of rotation about the Y axis;
ΔXIV(theta) is the measured value of a displacement sensor IV which is positioned at the axial direction of the X axis and is far away from the near end of the rotating shaft;
ΔXV(theta) is the measurement value of a displacement sensor V which is positioned at the far end of the X-axis axial distance from the rotating shaft;
d is the axial distance between the displacement sensor IV and the displacement sensor V.
The angle error of the rotation of the rotating shaft around the Y axis can be calculated through the formula (2);
the angular error of the revolving shaft rotating around the Z axis can be directly measured by a circular grating.
Further, calculating the radial error and the inclination error of the rotating shaft through a data processing system;
the method comprises the following specific steps of calculating the radial error of the rotating shaft:
generating a polar coordinate graph through the measurement values of two displacement sensors in the X-axis direction and the Y-axis direction on the same measurement surface, and calculating the radial motion error of the rotating shaft, wherein the calculation formula is as follows:
r(θ)=r0+ΔXIV(θ)cosθ+ΔYI(θ)sinθ (3)
in formula (3):
theta is the angular position of the rotating shaft;
r (theta) is the radial motion error of the rotating shaft at the angular position theta;
ΔXIV(theta) is a measurement value of a displacement sensor IV located in the X-axis direction
ΔY1(theta) is a measured value of the displacement sensor I positioned in the X-axis direction;
r0the radius value of the first measuring surface is taken as the radius value of the first measuring surface;
calculating the radial motion error of the rotating shaft at the angular position theta through the formula (3), selecting r (theta) and equally dividing into n sections, wherein each section is the radial motion error of one rotation of the rotating shaft; adding the obtained n sections of measured data and averaging to obtain the radial synchronous motion error of the measured revolving shaft; subtracting the obtained radial synchronous motion error from the radial synchronous motion error to obtain a radial asynchronous motion error;
the method comprises the following specific steps of calculating the inclination error of the rotating shaft:
generating a polar coordinate graph through the measurement values of two displacement sensors coaxially arranged along the rotating shaft, calculating the inclination motion error of the rotating shaft, and further measuring the inclination of the rotating shaft, wherein the calculation formula is as follows:
Figure BDA0002547552770000061
in the formula:
theta is the angular position of the rotating shaft;
beta (theta) is the inclination motion error of the rotating shaft at the angular position theta;
ΔXIV(theta) is a measurement value of a displacement sensor IV positioned in the X-axis direction;
ΔXV(theta) is a measurement value of the displacement sensor V located in the X-axis direction;
d is the axial distance between the displacement sensor IV and the displacement sensor V;
calculating the tilt motion error of the rotating shaft at the angle position theta through the formula (4), wherein the tilt motion error comprises a tilt synchronous motion error and a tilt asynchronous motion error, selecting beta (theta) and equally dividing the beta (theta) into n sections, and each section is a radial motion error of the rotating shaft rotating for one circle; adding the obtained n sections of measured data and averaging to obtain the radial synchronous motion error of the measured revolving shaft; and subtracting the obtained radial synchronous motion error from the radial synchronous motion error to obtain a radial asynchronous motion error.
The invention can not only measure the displacement error of the revolving shaft along X, Y, Z three orthogonal coordinate axes and the angle error of the revolving shaft rotating around X, Y and Z axes; the radial error and the inclination error of the rotating shaft can be measured. Radial error testing is very practical and effective for industries such as boring, milling, drilling, etc. where a tool rotates within a spindle. The tilt error indicates that the error source increases progressively as the workpiece or tool extends distally from the spindle face.
The invention has the beneficial effects that:
1. the invention can complete the six-degree-of-freedom measurement of the rotating shaft in the same equipment, and solves the problems of more time consumption, complicated measurement process and the like caused by multi-plane separation measurement and angle error separation measurement of the rotating shaft error; the device has the advantages of high measurement efficiency, simple structure, convenience in installation and the like, and meanwhile, the detection cost is greatly reduced.
2. Compared with the clamping mode in the prior art, the invention has better fixing effect on the displacement sensor and simpler installation mode, and simultaneously, the displacement sensor is not damaged, thereby improving the assembly precision; in addition, the inner wall of mounting hole is the arc structure that matches with the displacement sensor appearance, consequently can make more inseparabler of displacement sensor and mounting hole laminating, and then improves stability.
3. The motion joint mechanism is integrally formed, so that on one hand, the assembly precision is obviously improved, the measurement precision is improved, on the other hand, the dynamic balance of the structure is changed, and the high-speed measurement can be realized.
4. The data acquisition system takes the signal output by the circular grating reading head as the trigger signal of the displacement sensor, and compared with the existing data acquisition triggered by external time, the data acquisition system synchronously acquires angle and displacement data and transmits the angle and displacement data to the data analysis system for analysis; the position of the rotary shaft can be accurately positioned, the high repeatability of each acquisition point position is ensured, the influence of the speed fluctuation of the rotary shaft on a measurement result is removed, and the measurement precision is improved.
5. The invention can not only measure the displacement error of the revolving shaft along X, Y, Z three orthogonal coordinate axes and the angle error of the revolving shaft rotating around X, Y and Z axes; the radial error and the inclination error of the rotating shaft can be measured.
Drawings
Fig. 1 is a diagram of the operating state of the invention.
Fig. 2 is a schematic structural diagram of the present invention.
Fig. 3 is a schematic view of the mounting of the kinematic joint mechanism and the frame.
Fig. 4 is a schematic structural view of the rack.
Fig. 5 is a schematic view of the structure of the kinematic joint mechanism.
Fig. 6 is a schematic diagram of the arrangement of displacement sensors.
Fig. 7 is a top view of fig. 6.
Fig. 8 is a schematic view of the structure of the mounting hole.
Labeled as:
1. a machine tool; 2. a frame; 3. a kinematic joint mechanism; 6. a data acquisition system; 7. a data analysis system; 8. a rotating shaft;
21. mounting holes; 22. pressing a seam; 23. a threaded hole;
31. an installation table; 32. a measuring shaft; 33. installing a connector;
41. a circular grating; 42. a reading head;
51. a displacement sensor I; 52. a displacement sensor II; 53. a displacement sensor III; 54. a displacement sensor IV;
310. a mounting surface; 321. a first measuring surface; 322. a second measuring surface; 323. and (7) measuring the third surface.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
The first embodiment is as follows:
referring to fig. 1 and 2, in this embodiment, a machine tool is taken as an example, a power mechanism is a machine tool, and a measured rotating shaft is a rotating shaft of the machine tool. The invention relates to a dynamic measuring device of six degrees of freedom of a rotating shaft, which comprises a machine tool 1; the machine frame 2 is arranged on the machine tool 1 and is connected with the machine tool 1 through bolts; the moving joint mechanism 3 is arranged on the frame 2 and is used for connecting a rotating shaft 8; the measuring mechanism is arranged on the frame 2 and used for measuring relevant parameters of the rotating shaft 8; the data acquisition system is connected with the measuring mechanism and is used for acquiring the measuring data of the measuring mechanism; the data analysis system is connected with the data acquisition system and is used for analyzing the data acquired by the data acquisition system; the measuring mechanism comprises an angle measuring mechanism and a displacement measuring mechanism. The invention installs the tested revolving shaft on the moving joint mechanism, the moving joint mechanism is installed on the frame, the frame is connected with the machine tool, the real-time data tested by the measuring mechanism is collected by the data collecting system, and the six degrees of freedom of the revolving shaft is calculated by the data analyzing system. The problems of more measurement time consumption, complex measurement process and the like caused by the rotary shaft error multi-plane separate measurement and the angle error separate measurement are solved; the invention can complete six-degree-of-freedom measurement of the rotating shaft in one device, has the advantages of high measurement efficiency, simple structure, convenient installation and the like, and greatly reduces the detection cost.
Referring to fig. 5, the kinematic joint mechanism 3 includes a mounting table 31, one end of the mounting table 31 is provided with a measuring shaft 32, the other end is provided with a mounting joint 33 for mounting the revolving shaft 8, and the mounting joint 33 is arranged coaxially with the measuring shaft 32; one side of the mounting table 31 close to the measuring shaft 33 is a mounting surface 310, and the mounting surface 310 is perpendicular to the measuring shaft 32; a first measuring surface 321 and a second measuring surface 322 are arranged at a certain distance in the axial direction of the measuring shaft 32, and the end of the measuring shaft 32 far away from the mounting table 31 is a third measuring surface 323; the first measuring surface 321 and the second measuring surface 322 are parallel to each other, and the third measuring surface 323 is perpendicular to the first measuring surface 321. The measuring shaft and the measured revolving shaft are coaxially arranged, so that the relevant data of the revolving shaft can be measured through the relevant data of the measuring shaft. The first measuring surface and the second measuring surface are used for detecting reference surfaces of displacement errors of the rotating shaft on the X axis and the Y axis, and the third measuring surface is used for detecting the displacement errors of the rotating shaft on the Z axis. And the angular error of the rotation shaft rotating around X, Y and Z axis is determined again through the measured displacement error. Compared with one measuring surface, the two measuring surfaces, namely the first measuring surface and the second measuring surface, are arranged in the X-axis direction and the Y-axis direction, so that the vertical precision of the rotating shaft can be ensured, the installation error is reduced, and the measured data is more accurate.
Referring to fig. 5, the kinematic joint mechanism 3 is integrally formed. Compared with a structure that an installation joint and an inspection standard are separated in the prior art, the moving joint mechanism is integrally formed, on one hand, the assembly precision is obviously improved, the measurement precision is improved, on the other hand, the dynamic balance of the structure is changed, and high-speed measurement can be realized.
Referring to fig. 4, 6 and 7, the angle measuring mechanism includes a circular grating 41 disposed on the mounting surface 310, and the kinematic joint mechanism 3 is connected to the frame 2 through the circular grating 41; at least one reading head 42 for reading the data of the circular grating 41 is arranged on the frame 2, and the reading head 42 is connected with the data acquisition system 6 through a wiring harness; the displacement measuring mechanism comprises five displacement sensors arranged on the rack 2, namely a displacement sensor I51, a displacement sensor II 52, a displacement sensor III 53, a displacement sensor IV 54 and a displacement sensor V, wherein the displacement sensor I51 and the displacement sensor IV 54 are arranged on two mutually vertical surfaces of the rack, and the displacement sensor I51 and the displacement sensor IV 54 are both arranged on a plane where the first measuring surface 321 is located; the displacement sensor II 52 and the displacement sensor V are arranged on two mutually vertical surfaces of the rack, the displacement sensor I51 and the displacement sensor II 52 are arranged coaxially, and the displacement sensor IV 54 and the displacement sensor V are arranged coaxially; the displacement sensor II 52 and the displacement sensor V are both arranged on the plane where the second measuring surface 322 is located; the displacement sensor iii 53 is arranged below the third measuring plane 323 and perpendicular to the third measuring plane 323; the five sensors are all connected with the data acquisition system 6 through wiring harnesses. The first measuring surface and the second measuring surface are arranged in the Z-axis direction, so that the axial precision of the rotating shaft is guaranteed, and the measured data is more accurate. Displacement errors of the rotating shaft on the X axis and the Y axis can be measured through two displacement sensors on the first measuring surface or the second measuring surface and positioned on the X axis and the Y axis, namely a displacement sensor I and a displacement sensor IV or a displacement sensor II and a displacement sensor V can be read; and the displacement sensor III can measure the displacement error of the rotating shaft on the Z axis. The angular error of the revolving shaft rotating around X, Y and Z axis is obtained by measuring the displacement error. In addition, installation errors are reduced by adopting a plurality of circular grating reading heads, an error separation algorithm is added into a data analysis system, rotation errors are removed, and higher-precision measurement of the positioning precision of the rotating shaft is realized.
The first measuring surface 321, the second measuring surface 322 and the third measuring surface 323 are one of a plane and a spherical surface. As the plane or spherical measuring surface, the corresponding measurement can be completed; however, the spherical surface is a loose surface, and the change curvature is large, so that the error is large; the width and the radius of the plane are consistent, so that the error is smaller, the measurement precision is higher, and the plane is obviously better than the spherical surface although both can be used as the measurement reference; this embodiment is therefore preferably planar.
Referring to fig. 2, the five displacement sensors of the present embodiment are all non-contact displacement sensors. The measuring shaft of the invention synchronously rotates along with the rotating shaft, so the non-contact displacement sensor can meet the motion working condition of the invention.
The mounting joint is one of a BT series, an SK series or an HSK series of a tool shank of a main shaft of the machine tool.
Example two:
referring to fig. 4 and 8, in the present embodiment, on the basis of the first embodiment, the displacement sensor is detachably connected to the frame 2; the rack 2 is provided with a mounting hole 21 and a pressure seam 22, one end of the pressure seam 22 penetrates through the mounting hole 21, the other end of the pressure seam is communicated with the outside of the rack 2, the rack is provided with a threaded hole 23 facing the pressure seam, and a bolt is arranged in the threaded hole 23; the inner wall of the mounting hole 21 is of an arc structure matched with the shape of the displacement sensor.
The invention has unique installation mode for the displacement sensor, and the displacement sensor is firstly installed in the installation hole with the size slightly larger than that of the displacement sensor, thereby facilitating the insertion of the displacement sensor; when the displacement sensor is installed, friction or interference cannot be generated between the displacement sensor and the installation hole, so that the displacement sensor is damaged; after the displacement sensor is installed, the pressure seam is arranged, so that the pressure seam is compressed through the rotation of the bolt in the threaded hole, the width of the pressure seam is narrowed, and the installation hole is pressed tightly, so that the fixation of the displacement sensor is completed. Compared with the clamping mode in the prior art, the fixing effect is better, the installation mode is simpler, meanwhile, the displacement sensor cannot be damaged, and the assembly precision is improved. In addition, the inner wall of the mounting hole is of an arc structure matched with the shape of the displacement sensor, so that the displacement sensor and the mounting hole can be attached more tightly, and the stability is further improved;
example three:
the measuring method is used for the dynamic measuring device with six degrees of freedom of the rotating shaft in the first embodiment or the second embodiment and comprises the following steps:
s1 installation:
the motion joint mechanism 3 is coaxially installed with the tested rotating shaft through an installation joint 33, and a circular grating 41 is installed on the installation surface of the motion joint mechanism 3; connecting the multi-reading head 42 with the data acquisition system 6 through a wire harness; the frame 2 is fixedly connected with the machine tool 1 through bolts;
installing a displacement sensor I51, a displacement sensor II 52, a displacement sensor III 53, a displacement sensor IV 54 and a displacement sensor V in the mounting hole 21;
and S2, adjusting:
retracting the five displacement sensors into the mounting hole 21, moving the tested rotating shaft in the X-axis and Y-axis directions until the five displacement sensors are positioned at the central position of the displacement sensor III 53 in the Z-axis direction; moving the tested rotating shaft in the Z-axis direction to enable the displacement sensor I51 and the displacement sensor IV 54 to be positioned on the first measuring surface 321; the displacement sensor II 52 and the displacement sensor V are positioned on the second measuring surface 322;
observing through a data acquisition system, and firstly adjusting a displacement sensor III 53 in the Z-axis direction to enable the measurement value to be positioned in the middle of the measurement stroke; then, the position of the tested revolving shaft is adjusted along the X-axis direction, so that the measured value of the displacement sensor IV (54) is positioned in the middle position of the measuring stroke; then, the position of the tested revolving shaft is adjusted along the Y axis, so that the measured value of the displacement sensor I (51) is positioned in the middle position of the measuring stroke; continuously adjusting the measured values of the displacement sensor II 52 and the displacement sensor V to the middle position of the stroke; finally, fixing the five displacement sensors on the frame through bolts;
and S3, data acquisition:
before measurement, the circular grating 41 and five displacement sensors are zeroed, and a data acquisition system takes a signal output by a reading head 42 of the circular grating as a trigger signal of the displacement sensors;
preheating the machine tool 1 for 20-30 min, and then starting to measure, and collecting data measured by the circular grating 41 and the five displacement sensors;
signals output by a reading head of the circular grating are subjected to frequency division through different counters, and fixed-angle data acquisition is achieved;
and S4 data processing: and the data acquisition system transmits the acquired data to the data analysis system, and calculates the displacement error of the revolving shaft along X, Y and Z axis and the angle error of the revolving shaft rotating around X, Y and Z axis.
Step S4 specifically includes:
the displacement error of the rotating shaft along the X axis is measured by a displacement sensor IV or a displacement sensor V;
the displacement error of the rotating shaft along the Y axis is measured by a displacement sensor I or a displacement sensor II;
the displacement error of the rotating shaft along the Z axis is measured by a displacement sensor III;
the angle error of the rotation of the rotating shaft around the X axis or the Y axis is calculated by data measured by a pair of displacement sensors which are arranged along the axial direction of the rotating shaft, and the calculation formula is as follows:
Figure BDA0002547552770000101
in formula (1):
θxis the angular error of rotation about the X axis;
ΔYI(theta) is the measured value of a displacement sensor I which is positioned at the near end of the Y-axis axial distance from the rotating shaft;
ΔYII(theta) is the measured value of a displacement sensor II which is positioned at the far end of the Y-axis axial distance from the rotating shaft;
d is the axial distance between the displacement sensor I and the displacement sensor II.
Dividing the difference value of the output values of the displacement sensor I and the displacement sensor II by the axial distance between the two sensors in the inspection device to obtain a sine value of the rotation angle around the X axis, and then calculating the angle error of the rotation of the rotating shaft around the X axis;
Figure BDA0002547552770000102
in formula (2):
θyis the angular error of rotation about the Y axis;
ΔXIV(theta) is the measured value of a displacement sensor IV which is positioned at the axial direction of the X axis and is far away from the near end of the rotating shaft;
ΔXV(theta) is the measurement value of a displacement sensor V which is positioned at the far end of the X-axis axial distance from the rotating shaft;
d is the axial distance between the displacement sensor IV and the displacement sensor V.
The angle error of the rotation of the rotating shaft around the Y axis can be calculated through the formula (2);
the angular error of the revolving shaft rotating around the Z axis can be directly measured by a circular grating.
The invention can complete the six-degree-of-freedom measurement of the rotating shaft in the same equipment, and solves the problems of more time consumption, complicated measurement process and the like caused by multi-plane separation measurement and angle error separation measurement of the rotating shaft error; the device has the advantages of high measurement efficiency, simple structure, convenience in installation and the like, and meanwhile, the detection cost is greatly reduced.
In step S2, each displacement sensor is adjusted to make its measurement value located at the middle position of the stroke, so as to better read and measure the error of the deflection; in step S3, the machine tool is preheated for 20-30 min before measurement, so that the influence of temperature rise on the measurement result can be effectively eliminated, and the working state of the measured revolving shaft is determined, so that the measuring equipment is prevented from being damaged by violent shaking; in step S3, the data acquisition system uses the signal output by the circular grating reading head as the trigger signal of the displacement sensor, and compared with the existing data acquisition triggered by external time, the data acquisition system synchronously acquires angle and displacement data and transmits the angle and displacement data to the data analysis system for analysis; the position of the rotary shaft can be accurately positioned, the high repeatability of each acquisition point position is ensured, the influence of the speed fluctuation of the rotary shaft on a measurement result is removed, and the measurement precision is improved.
Example four:
on the basis of the third embodiment, the radial error and the inclination error of the rotating shaft are calculated by the data processing system;
the method comprises the following specific steps of calculating the radial error of the rotating shaft:
generating a polar coordinate graph through the measurement values of two displacement sensors in the X-axis direction and the Y-axis direction on the same measurement surface, and calculating the radial motion error of the rotating shaft, wherein the calculation formula is as follows:
r(θ)=r0+ΔXIV(θ)cosθ+ΔYI(θ)sinθ (3)
in formula (3):
theta is the angular position of the rotating shaft;
r (theta) is the radial motion error of the rotating shaft at the angular position theta;
ΔXIV(theta) is a measurement value of a displacement sensor IV located in the X-axis direction
ΔY1(theta) is a measured value of the displacement sensor I positioned in the X-axis direction;
r0the radius value of the first measuring surface is taken as the radius value of the first measuring surface;
calculating the radial motion error of the rotating shaft at the angular position theta through the formula (3), selecting r (theta) and equally dividing into n sections, wherein each section is the radial motion error of one rotation of the rotating shaft; adding the obtained n sections of measured data and averaging to obtain the radial synchronous motion error of the measured revolving shaft; subtracting the obtained radial synchronous motion error from the radial synchronous motion error to obtain a radial asynchronous motion error;
the method comprises the following specific steps of calculating the inclination error of the rotating shaft:
generating a polar coordinate graph through the measurement values of two displacement sensors coaxially arranged along the rotating shaft, calculating the inclination motion error of the rotating shaft, and further measuring the inclination of the rotating shaft, wherein the calculation formula is as follows:
Figure BDA0002547552770000111
in the formula:
theta is the angular position of the rotating shaft;
beta (theta) is the inclination motion error of the rotating shaft at the angular position theta;
ΔXIV(theta) is a measurement value of a displacement sensor IV positioned in the X-axis direction;
ΔXV(theta) is a measurement value of the displacement sensor V located in the X-axis direction;
d is the axial distance between the displacement sensor IV and the displacement sensor V;
calculating the tilt motion error of the rotating shaft at the angle position theta through the formula (4), wherein the tilt motion error comprises a tilt synchronous motion error and a tilt asynchronous motion error, selecting beta (theta) and equally dividing the beta (theta) into n sections, and each section is a radial motion error of the rotating shaft rotating for one circle; adding the obtained n sections of measured data and averaging to obtain the radial synchronous motion error of the measured revolving shaft; and subtracting the obtained radial synchronous motion error from the radial synchronous motion error to obtain a radial asynchronous motion error.
The invention can not only measure the displacement error of the revolving shaft along X, Y, Z three orthogonal coordinate axes and the angle error of the revolving shaft rotating around X, Y and Z axes; the radial error and the inclination error of the rotating shaft can be measured. Radial error testing is very practical and effective for industries such as boring, milling, drilling, etc. where a tool rotates within a spindle. The tilt error indicates that the error source increases progressively as the workpiece or tool extends distally from the spindle face.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (10)

1. The dynamic measuring device of the six degrees of freedom of the revolving shaft is characterized by comprising:
a frame (2);
the moving joint mechanism (3) is arranged on the rack (2) and is used for connecting the rotating shaft (8);
the power mechanism is connected with the rack and is used for driving the motion joint unit to rotate;
the measuring mechanism is arranged on the frame (2) and is used for measuring relevant parameters of the rotating shaft (8);
the data acquisition system is connected with the measuring mechanism and is used for acquiring the measuring data of the measuring mechanism;
the data analysis system is connected with the data acquisition system and is used for analyzing the data acquired by the data acquisition system;
the measuring mechanism comprises an angle measuring mechanism and a displacement measuring mechanism.
2. The dynamic measuring device of the rotating shaft with six degrees of freedom according to claim 1, characterized in that the kinematic joint mechanism (3) comprises a mounting table (31), one end of the mounting table (31) is provided with a measuring shaft (32), the other end is provided with a mounting joint (33) for mounting the rotating shaft (8), and the mounting joint (33) and the measuring shaft (32) are coaxially arranged; one side of the mounting table (31) close to the measuring shaft (33) is a mounting surface (310), and the mounting surface (310) is perpendicular to the measuring shaft (32); a first measuring surface (321) and a second measuring surface (322) are arranged at a certain distance in the axial direction of the measuring shaft (32), and the end part of the measuring shaft (32) far away from the mounting table (31) is a third measuring surface (323); the first measuring surface (321) and the second measuring surface (322) are parallel to each other, and the third measuring surface (323) and the first measuring surface (321) are perpendicular to each other.
3. The device for six degrees of freedom dynamic measurement of a rotating shaft according to claim 2, wherein the kinematic joint mechanism (3) is formed in one piece.
4. The rotary shaft six-degree-of-freedom dynamic measurement device according to claim 2, wherein the angle measurement mechanism comprises a circular grating (41) arranged on the mounting surface (310), and the motion joint mechanism (3) is connected with the frame (2) through the circular grating (41); the rack (2) is provided with at least one reading head (42) for reading data of the circular grating (41), and the reading head (42) is connected with the data acquisition system (6) through a wiring harness;
the displacement measurement mechanism comprises five displacement sensors arranged on a rack (2), namely a displacement sensor I (51), a displacement sensor II (52), a displacement sensor III (53), a displacement sensor IV (54) and a displacement sensor V, wherein the displacement sensors I (51) and IV (54) are arranged on two mutually vertical surfaces of the rack, and the displacement sensors I (51) and IV (54) are arranged on a plane where a first measurement surface (321) is located; the displacement sensor II (52) and the displacement sensor V are arranged on two mutually vertical surfaces of the rack, the displacement sensor I (51) and the displacement sensor II (52) are arranged coaxially, and the displacement sensor IV (54) and the displacement sensor V are arranged coaxially; the displacement sensor II (52) and the displacement sensor V are both arranged on the plane where the second measuring surface (322) is located; the displacement sensor III (53) is arranged below the third measuring surface (323) and is perpendicular to the third measuring surface (323); the five sensors are connected with a data acquisition system (6) through wiring harnesses.
5. The dynamic six-degree-of-freedom measurement device of the rotating shaft according to claim 4, wherein the first measurement surface (321), the second measurement surface (322) and the third measurement surface (323) are one of a plane and a spherical surface.
6. The dynamic measurement device for six degrees of freedom of a rotating shaft according to claim 4, wherein the five displacement sensors are all non-contact displacement sensors.
7. The rotating shaft six-degree-of-freedom dynamic measurement device according to claim 4, wherein the displacement sensor is detachably connected with the frame (2); the rack (2) is provided with a mounting hole (21) and a pressure seam (22), one end of the pressure seam (22) penetrates through the mounting hole (21), the other end of the pressure seam is communicated with the outside of the rack (2), the rack is provided with a threaded hole (23) facing the pressure seam, and a bolt is arranged in the threaded hole (23);
the inner wall of the mounting hole (21) is of an arc structure matched with the shape of the displacement sensor.
8. The measuring method for the dynamic measuring device for the six degrees of freedom of the revolving shaft according to any one of claims 4 to 7 is characterized by comprising the following steps of:
s1 installation:
the moving joint mechanism (3) is coaxially installed with the tested rotating shaft through an installation joint (33), and the circular grating (41) is installed on the installation surface of the moving joint mechanism (3); connecting the multi-reading head (42) with a data acquisition system (6) through a wire harness; the frame (2) is fixedly connected with the machine tool (1) through bolts;
installing a displacement sensor I (51), a displacement sensor II (52), a displacement sensor III (53), a displacement sensor IV (54) and a displacement sensor V in the mounting hole (21);
and S2, adjusting:
retracting the five displacement sensors into the mounting holes (21), moving the tested rotating shaft in the X-axis and Y-axis directions until the five displacement sensors are positioned at the central position of a displacement sensor III (53) in the Z-axis direction; moving the tested rotating shaft in the Z-axis direction to enable the displacement sensor I (51) and the displacement sensor IV (54) to be positioned on a first measuring surface (321); the displacement sensor II (52) and the displacement sensor V are positioned on a second measuring surface (322);
observing through a data acquisition system, and firstly adjusting a displacement sensor III (53) in the Z-axis direction to enable the measured value to be positioned in the middle position of the measuring stroke; then, the position of the tested revolving shaft is adjusted along the X-axis direction, so that the measured value of the displacement sensor IV (54) is positioned in the middle position of the measuring stroke; then, the position of the tested revolving shaft is adjusted along the Y axis, so that the measured value of the displacement sensor I (51) is positioned in the middle position of the measuring stroke; continuously adjusting the measured values of the displacement sensor II (52) and the displacement sensor V to the middle position of the stroke; finally, fixing the five displacement sensors on the frame through bolts;
and S3, data acquisition:
before measurement, the round grating (41) and five displacement sensors are subjected to zero setting, and a data acquisition system takes a signal output by a reading head (42) of the round grating as a trigger signal of the displacement sensors;
preheating the machine tool (1) for 20-30 min, then starting to measure, and collecting data measured by the circular grating (41) and the five displacement sensors;
signals output by a reading head of the circular grating are subjected to frequency division through different counters, and fixed-angle data acquisition is achieved;
and S4 data processing: and the data acquisition system transmits the acquired data to the data analysis system, and calculates the displacement error of the revolving shaft along X, Y and Z axis and the angle error of the revolving shaft rotating around X, Y and Z axis.
9. The method for measuring a six-degree-of-freedom dynamic measurement device of a rotating shaft according to claim 8, wherein the step S4 is specifically as follows:
the displacement error of the rotating shaft along the X axis is measured by a displacement sensor IV or a displacement sensor V;
the displacement error of the rotating shaft along the Y axis is measured by a displacement sensor I or a displacement sensor II;
the displacement error of the rotating shaft along the Z axis is measured by a displacement sensor III;
the angle error of the rotation of the rotating shaft around the X axis or the Y axis is calculated by data measured by a pair of displacement sensors which are arranged along the axial direction of the rotating shaft, and the calculation formula is as follows:
Figure FDA0002547552760000031
in formula (1):
θxis the angular error of rotation about the X axis;
ΔYI(theta) is the measured value of a displacement sensor I which is positioned at the near end of the Y-axis axial distance from the rotating shaft;
ΔYII(theta) is the measured value of a displacement sensor II which is positioned at the far end of the Y-axis axial distance from the rotating shaft;
d is the axial distance between the displacement sensor I and the displacement sensor II.
Dividing the difference value of the output values of the displacement sensor I and the displacement sensor II by the axial distance between the two sensors in the inspection device to obtain a sine value of the rotation angle around the X axis, and then calculating the angle error of the rotation of the rotating shaft around the X axis;
Figure FDA0002547552760000032
in formula (2):
θyis the angular error of rotation about the Y axis;
ΔXIV(theta) is the measured value of a displacement sensor IV which is positioned at the axial direction of the X axis and is far away from the near end of the rotating shaft;
ΔXV(theta) is the measurement value of a displacement sensor V which is positioned at the far end of the X-axis axial distance from the rotating shaft;
d is the axial distance between the displacement sensor IV and the displacement sensor V.
The angle error of the rotation of the rotating shaft around the Y axis can be calculated through the formula (2);
the angular error of the revolving shaft rotating around the Z axis can be directly measured by a circular grating.
10. The measuring method of the dynamic measuring device for the six degrees of freedom of the rotating shaft according to claim 9, wherein the radial error and the tilt error of the rotating shaft are calculated by a data processing system;
the method comprises the following specific steps of calculating the radial error of the rotating shaft:
generating a polar coordinate graph through the measurement values of two displacement sensors in the X-axis direction and the Y-axis direction on the same measurement surface, and calculating the radial motion error of the rotating shaft, wherein the calculation formula is as follows:
r(θ)=r0+ΔXIV(θ)cosθ+ΔYI(θ)sinθ (3)
in formula (3):
theta is the angular position of the rotating shaft;
r (theta) is the radial motion error of the rotating shaft at the angular position theta;
ΔXIV(theta) is a measurement value of a displacement sensor IV located in the X-axis direction
ΔY1(theta) is a measured value of the displacement sensor I positioned in the X-axis direction;
r0the radius value of the first measuring surface is taken as the radius value of the first measuring surface;
calculating the radial motion error of the rotating shaft at the angular position theta through the formula (3), selecting r (theta) and equally dividing into n sections, wherein each section is the radial motion error of one rotation of the rotating shaft; adding the obtained n sections of measured data and averaging to obtain the radial synchronous motion error of the measured revolving shaft; subtracting the obtained radial synchronous motion error from the radial synchronous motion error to obtain a radial asynchronous motion error;
the method comprises the following specific steps of calculating the inclination error of the rotating shaft:
generating a polar coordinate graph through the measurement values of two displacement sensors coaxially arranged along the rotating shaft, calculating the inclination motion error of the rotating shaft, and further measuring the inclination of the rotating shaft, wherein the calculation formula is as follows:
Figure FDA0002547552760000041
in the formula:
theta is the angular position of the rotating shaft;
beta (theta) is the inclination motion error of the rotating shaft at the angular position theta;
ΔXIV(theta) is a measurement value of a displacement sensor IV positioned in the X-axis direction;
ΔXV(theta) is a measurement value of the displacement sensor V located in the X-axis direction;
d is the axial distance between the displacement sensor IV and the displacement sensor V;
calculating the tilt motion error of the rotating shaft at the angle position theta through the formula (4), wherein the tilt motion error comprises a tilt synchronous motion error and a tilt asynchronous motion error, selecting beta (theta) and equally dividing the beta (theta) into n sections, and each section is a radial motion error of the rotating shaft rotating for one circle; adding the obtained n sections of measured data and averaging to obtain the radial synchronous motion error of the measured revolving shaft; and subtracting the obtained radial synchronous motion error from the radial synchronous motion error to obtain a radial asynchronous motion error.
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