CN113814870B - Method for measuring and calculating pose of magnetorheological polished workpiece and polishing method - Google Patents

Method for measuring and calculating pose of magnetorheological polished workpiece and polishing method Download PDF

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CN113814870B
CN113814870B CN202111151173.XA CN202111151173A CN113814870B CN 113814870 B CN113814870 B CN 113814870B CN 202111151173 A CN202111151173 A CN 202111151173A CN 113814870 B CN113814870 B CN 113814870B
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workpiece
coordinate system
point
measuring
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CN113814870A (en
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周涛
张云飞
曾靖超
郑永成
黄文�
张建飞
陈立
李凯隆
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Institute of Mechanical Manufacturing Technology of CAEP
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B24—GRINDING; POLISHING
    • B24B—MACHINES, DEVICES, OR PROCESSES FOR GRINDING OR POLISHING; DRESSING OR CONDITIONING OF ABRADING SURFACES; FEEDING OF GRINDING, POLISHING, OR LAPPING AGENTS
    • B24B29/00—Machines or devices for polishing surfaces on work by means of tools made of soft or flexible material with or without the application of solid or liquid polishing agents
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B24—GRINDING; POLISHING
    • B24B—MACHINES, DEVICES, OR PROCESSES FOR GRINDING OR POLISHING; DRESSING OR CONDITIONING OF ABRADING SURFACES; FEEDING OF GRINDING, POLISHING, OR LAPPING AGENTS
    • B24B1/00—Processes of grinding or polishing; Use of auxiliary equipment in connection with such processes
    • B24B1/005—Processes of grinding or polishing; Use of auxiliary equipment in connection with such processes using a magnetic polishing agent
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B24—GRINDING; POLISHING
    • B24B—MACHINES, DEVICES, OR PROCESSES FOR GRINDING OR POLISHING; DRESSING OR CONDITIONING OF ABRADING SURFACES; FEEDING OF GRINDING, POLISHING, OR LAPPING AGENTS
    • B24B49/00—Measuring or gauging equipment for controlling the feed movement of the grinding tool or work; Arrangements of indicating or measuring equipment, e.g. for indicating the start of the grinding operation
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B24—GRINDING; POLISHING
    • B24B—MACHINES, DEVICES, OR PROCESSES FOR GRINDING OR POLISHING; DRESSING OR CONDITIONING OF ABRADING SURFACES; FEEDING OF GRINDING, POLISHING, OR LAPPING AGENTS
    • B24B49/00—Measuring or gauging equipment for controlling the feed movement of the grinding tool or work; Arrangements of indicating or measuring equipment, e.g. for indicating the start of the grinding operation
    • B24B49/12—Measuring or gauging equipment for controlling the feed movement of the grinding tool or work; Arrangements of indicating or measuring equipment, e.g. for indicating the start of the grinding operation involving optical means

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  • Mechanical Engineering (AREA)
  • Automatic Control Of Machine Tools (AREA)
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Abstract

The invention discloses a method for measuring and calculating the pose of a magnetorheological polished workpiece and a polishing method, wherein the method for measuring and calculating the pose comprises the following steps: constructing a geometric pose measurement model of the workpiece; measuring the position of the central point of the workpiece according to the geometric pose measurement model; establishing a theoretical coordinate system of the workpiece by taking the position of the central point as an origin; constructing a geometric pose theoretical model of the position of the workpiece in a theoretical coordinate system; planning the path of the workpiece according to the geometric pose theoretical model and the CCOS technology; and correcting the planned track points according to the coordinate transformation matrix to obtain the actual processing track of the workpiece. The invention aims to provide a method for measuring and calculating the pose of a magnetorheological polishing workpiece and a polishing method, which utilize a three-coordinate measuring head integrated in a machine tool numerical control system to measure the center of the workpiece and points on a polishing surface, complete the acquisition of the pose data of the workpiece and solve the problem that the precision of the workpiece is influenced by manual experience in the accurate leveling process.

Description

Method for measuring and calculating pose of magnetorheological polished workpiece and polishing method
Technical Field
The invention relates to the technical field of numerical control optical manufacturing, in particular to a method for measuring and calculating the pose of a magnetorheological polishing workpiece and a polishing method.
Background
The magnetorheological polishing technology has the advantages of stable removal function, high removal efficiency, good surface shape convergence and the like, and is widely applied to polishing of optical workpieces with various shapes and surface types. When the magneto-rheological polishing technology is used for polishing optical workpieces with high certainty, the position and the posture of the workpieces in a machine tool need to be measured accurately. The traditional method is to use a dial indicator to accurately level a workpiece, and use a measuring system matched with a machine tool to carry out edge finding measurement on the position information of the leveled workpiece so as to establish an accurate workpiece coordinate system. When the processed workpiece is an aspheric surface with a large size or a small surface curvature radius, the efficiency of manual accurate leveling is very low, and when the workpiece is processed by multiple iterative processing, the posture of the workpiece needs to be manually adjusted again in each processing round, so that the processing precision and efficiency are greatly influenced.
Disclosure of Invention
The invention aims to provide a method for measuring and calculating the pose of a magnetorheological polished workpiece and a polishing method, and solves the problems that the precision is influenced by manual experience in the accurate leveling process of the workpiece, the efficiency is low and the like.
The invention is realized by the following technical scheme:
a method for measuring and calculating the pose of a magnetorheological polished workpiece comprises the following steps:
s1: constructing a geometric pose measurement model of the workpiece;
s2: acquiring the position of the central point of the workpiece according to the geometric pose measurement model;
s3: establishing a theoretical coordinate system of the workpiece by taking the position of the central point as an origin, wherein the theoretical coordinate system is parallel to a machine tool coordinate system;
s4: measuring and calculating whether the pitching deflection angle of the actual coordinate system and the theoretical coordinate system of the workpiece is larger than a preset pitching deflection angle, adjusting the posture of the workpiece when the pitching deflection angle is larger than the preset pitching deflection angle, and repeatedly executing the steps S1-S3; otherwise, S5 is executed
S5: constructing a geometric pose theoretical model of the position of the workpiece in the theoretical coordinate system;
s6: according to the geometric pose theoretical model, path planning is carried out on the workpiece by using a CCOS technology, and a path point set is obtained;
s7: correcting the track points in the track point set according to the coordinate transformation matrix to obtain the actual processing track of the workpiece; wherein the coordinate transformation matrix is a rigid body transformation matrix between the actual coordinate system of the workpiece and the theoretical coordinate system.
When the magneto-rheological polishing technology is used for polishing an optical workpiece with high certainty, the position and the posture of the workpiece in a machine tool need to be accurately measured. The traditional method is to utilize a dial indicator to accurately level a workpiece, and utilize a measuring system matched with a machine tool to carry out edge finding measurement on the position information of the leveled workpiece so as to establish an accurate workpiece coordinate system. When a processed workpiece is an aspheric surface with a large size or a small surface curvature radius, the efficiency of manual precise leveling is very low, when the workpiece is processed repeatedly in an iterative manner, the workpiece posture needs to be manually adjusted again in each processing round, and the processing precision and efficiency are greatly influenced.
Preferably, said S1 comprises the following sub-steps:
s11: taking the center of the C-axis turntable as a coordinate origin, and establishing a measurement coordinate system in the same direction as the coordinate system of the machine tool;
s12: acquiring the geometric shape, the size, the surface concave-convex type, the aspheric surface coefficient, the off-axis quantity and the optical axis included angle of the workpiece;
s13: and establishing the geometric pose measurement model according to the geometric shape, the size, the surface concave-convex type, the aspheric surface coefficient, the off-axis quantity, the optical axis included angle and the measurement coordinate system.
Preferably, said S2 comprises the following sub-steps:
s21: acquiring the surface position of a workpiece corresponding to the axis of the C shaft;
s22: generating a first driving signal according to the geometric pose measurement model and the workpiece surface position;
s23: the three-coordinate measuring head responds to the first driving signal to measure the side position of the workpiece in different directions;
s24: and calculating the position of the central point according to the measurement result of the side position and the geometric pose measurement model.
Preferably, said S4 comprises the following sub-steps:
s41: generating a second driving signal according to the geometric pose measurement model;
s42: the three-coordinate measuring head responds to the second driving signal to measure a preset point on the upper surface of the workpiece so as to acquire the coordinate of the preset point under the machine tool coordinate system;
s43: judging whether the following formula is satisfied according to the coordinates of the preset point in the machine tool coordinate system:
max{tan -1 ((z x+ -z x- )/2D x )，tan -1 ((z y+ -z y- )/2D y )}≤σ；
wherein z is x+ Representing a positive offset D from the center point X x Z-direction measurement of the measuring point, Z x- Representing a negative bias D from the center point X x Z-direction measurement of the measuring point, Z y+ Representing a positive offset D from said centre point Y y Z-direction measurement of the measuring points, Z y- Representing a negative bias D from said centre point Y y Z-direction measurement of the measuring points, D x Representing an X-offset distance, D, from said centre point y Represents a Y-direction offset distance from the center point;
s44: when the above formula is satisfied, executing the S5; otherwise, adjusting the workpiece attitude, and repeatedly executing S1-S3.
Preferably, said S5 comprises the following sub-steps:
s51: acquiring the geometric shape, the size, the surface concave-convex type, the aspheric surface coefficient, the off-axis quantity and the optical axis included angle of the workpiece;
s52: and establishing the geometric pose theoretical model according to the geometric shape, the size, the surface concave-convex type, the aspheric surface coefficient, the off-axis quantity, the optical axis included angle and the theoretical coordinate system.
Preferably, the generation of the coordinate transformation matrix comprises the sub-steps of:
x in the actual coordinate system r O r Z r Within the cross section, an initial value Δ Z is set x =0, with the cycle cutoff condition of
Figure GDA0003328505950000031
Solving theta sequentially through a cyclic solving method x 、X cm And Δ Z x ；
Figure GDA0003328505950000032
Figure GDA0003328505950000033
ΔZ x ＝
F t (GShp，GDim，CType，AspCoe，d，OpAng，D x +
Xcm,0-FtGShp,G im,CType,AspCoe,d,OpAng,Dx,0；
Wherein, Δ Z x Indicating the Z-directional deviation, X, resulting from the correction of the X-direction of the measuring point cm Indicating the deviation of the workpiece center correction point from the X direction of the measuring point,
Figure GDA0003328505950000034
the calculation result of the rotation angle of the i +1 th iteration actual coordinate system around the X axis of the theoretical coordinate system is shown,
Figure GDA0003328505950000035
representing the ith iteration around the theoretical coordinate systemX-axis rotation angle calculation result, ε x The iterative calculation of the convergence threshold value theta around the rotation angle of the X axis of the theoretical coordinate system is expressed by the actual coordinate system x Representing the rotation angle, X, of the actual coordinate system about the X-axis of the theoretical coordinate system 2 Indicates the X-direction position of the edge side point in the X positive direction 1 Showing the X-direction position of the edge side point in the X negative direction;
at X r O r Z r Within the cross section, an initial value Δ Z is set y =0, cycle cutoff condition is
Figure GDA0003328505950000036
Solving theta sequentially through a cyclic solving method y 、Y cm And Δ Z y ；
Figure GDA0003328505950000037
Figure GDA0003328505950000038
ΔZ y ＝F t (GShp，GDim，CType，AspCoe，d，OpAng，0，D y +Y cm )
-F t (GShp，GDim，CType，AspCoe，d，OpAng，0，D y )；
Wherein, Δ Z y Indicating the Z-direction deviation, Y, resulting from Y-direction correction of the measuring points cm Indicating the deviation of the center correction point of the workpiece from the Y direction of the measuring point,
Figure GDA0003328505950000039
the calculation result of the rotation angle of the i +1 th iteration actual coordinate system around the Y axis of the theoretical coordinate system is shown,
Figure GDA00033285059500000310
representing the calculation result of the rotation angle of the ith iteration actual coordinate system around the Y axis of the theoretical coordinate system, epsilon y Iteratively calculating the convergence threshold value theta around the rotation angle of the X axis of the theoretical coordinate system in the actual coordinate system y Representing realityAngle of rotation of the coordinate system about the Y axis of the theoretical coordinate system, Y 2 Indicates the Y-direction position of the edge side point in the Y-direction 1 The Y-direction position of the edge side point in the Y negative direction is shown;
the three-coordinate measuring head responds to the second driving signal, and (x) rc +X cm 、y rc +Y cm ) The corresponding workpiece is subjected to Z-direction position measurement to obtain the actual Z-direction position of the geometric center of the workpiece r ；
Calculating the rigid body transformation matrix:
Figure GDA0003328505950000041
wherein T represents a coordinate transformation matrix, Z rc Representing the Z-position of the center point.
A polishing method of a workpiece polishes the workpiece according to the actual processing track obtained by the method for measuring and calculating the posture of the magnetorheological polished workpiece.
Compared with the prior art, the invention has the following advantages and beneficial effects:
by constructing a geometric pose theoretical model of the workpiece and automatically converting the trajectory planning of the workpiece in the theoretical coordinate system into the actual coordinate system based on the coordinate system change relationship between the actual coordinate system of the workpiece in the test process and the wheel-managing coordinate system in an ideal state, the workpiece to be polished does not need to be accurately leveled manually in the polishing process, and therefore the problems that the precision is influenced by manual experience in the accurate workpiece leveling process, the efficiency is low and the like are solved.
Drawings
The accompanying drawings, which are included to provide a further understanding of the embodiments of the invention and are incorporated in and constitute a part of this application, illustrate embodiment(s) of the invention and together with the description serve to explain the principles of the invention. In the drawings:
FIG. 1 is a schematic view of the detection of pose of a magnetorheological polishing workpiece according to the present invention;
reference numbers and corresponding part names in the drawings:
1. a machine tool coordinate system; 2. a B axis; 3. a magnetorheological polishing wheel assembly; 4. an A axis; 5. a Z axis; 6. a three-coordinate measuring head; 7. a geometric centerline of the workpiece; 8. measuring a coordinate system; 9. a C-axis; 10. a workpiece; 11. a work table; 12. a C axis; 13. a Y axis; 14. marking the side surface of the workpiece; 15. an X axis; 16. a vision-aided measurement system; 17. an upper computer; 18. the ideal pose of the workpiece; 19. the actual pose of the workpiece; 20. an actual coordinate system; 21. a theoretical coordinate system.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail below with reference to examples and accompanying drawings, and the exemplary embodiments and descriptions thereof are only used for explaining the present invention and are not meant to limit the present invention.
Example 1
As shown in fig. 1, the device used in this embodiment includes a mechanical contact type three-coordinate measuring head 6, a vision auxiliary measuring system 16, an upper computer 17, a magnetorheological polishing wheel assembly 3, and a magnetorheological machine tool with X, Y, Z linear axes and a, B, C rotating axes. The three-coordinate measuring head 6 and the magnetorheological polishing wheel component 3 are integrated on the B shaft 2, the workbench 11 of the machine tool is installed on the C shaft 12, the C shaft 12 is installed on the Y shaft 13, the Y shaft 13 is installed on the X shaft 15, the Z shaft 5 is installed on the machine tool body, the A shaft 4 and the B shaft 2 form a double-swing shaft and are installed on the Z shaft 5, and the upper computer 17 runs a machine tool control system and a vision auxiliary measuring system 16. Based on the device, the method for measuring and calculating the pose of the magnetorheological polished workpiece provided by the application is described as follows:
a method for measuring and calculating the pose of a magnetorheological polished workpiece comprises the following steps:
s1: constructing a geometric pose measurement model of the workpiece 10;
a measurement coordinate system 8 (corresponding to the coordinate system O in fig. 1) is constructed s -X s Y s Z s ) The measuring coordinate system 8 in this embodiment is used to obtain the approximate position of the workpiece 10 on the worktable 11, so that the apparatus can perform the measuring operation according to the approximate position in the following process, and the instrument and the workpiece 10 are prevented from being damaged; specifically, the method comprises the following steps:
establishing a workpiece measurement coordinate system 8 in the same direction as the machine tool coordinate system 1 by taking the center of the C-axis turntable as the origin of coordinates; when the approximate position of a workpiece 10 on a workbench 11 is acquired subsequently, the workpiece 10 to be measured is installed on the workbench 11 of the machine tool, the pose of the workpiece 10 is roughly adjusted, the geometric center line 7 of the workpiece is approximately superposed with the center line of a C-axis turntable (C-axis 9), and the workpiece is fixed, namely the geometric center of the workpiece 10 is superposed with the center of the C-axis turntable as much as possible; meanwhile, observing a side marking 14 of the workpiece by using a vision auxiliary measuring system 16, rotating the C shaft 12, and adjusting the direction of the workpiece 10 to the processing direction;
constructing a geometric pose measurement model:
inputting parameters such as geometric shape, size, concave-convex type of workpiece surface, aspheric coefficient, off-axis quantity, optical axis included angle and the like of the workpiece 10 through an upper computer 17, and establishing a geometric pose measurement model of the workpiece on the machine according to an established measurement coordinate system 8, namely: each point on the surface of the workpiece satisfies the relation shown in the formula (1):
z s ＝F s (GShp，GDim，CType，AspCoe，d，OpAng，x s ，y s ) (1)
wherein x is s 、y s 、z s Representing the coordinates of a point on the workpiece 10 in the measurement coordinate system 8, F s And representing a geometric pose measurement model, wherein the model is determined by parameters such as the geometric shape, the size, the concave-convex type of the surface of the workpiece, aspheric coefficients, off-axis quantity, an optical axis included angle and the like of the workpiece 10, GShp represents the geometric shape, GDim represents the size, CType represents the concave-convex type of the surface of the workpiece, aspCoe represents the aspheric coefficients, d represents the off-axis quantity, and Opang represents the optical axis included angle.
S2: acquiring the position of a central point of the workpiece 10 according to the geometric pose measurement model; specifically, the method comprises the following steps:
as the geometric center line 7 of the workpiece is approximately coincident with the center line of the C-axis turntable (C-axis 9), the position of the central point of the workpiece 10 can be approximately obtained by measuring the surface position of the workpiece 10 corresponding to the C-axis 9, and based on the obtained position of the central point and in combination with a geometric pose measurement model, an NC program for measuring the side surface and the geometric center of the workpiece can be generated on line by using the upper computer 17, and the measurement of the side surface and the geometric center of the workpiece can be realizedThe quantity NC program is used for driving the three-coordinate measuring head 6 to measure the side position of the workpiece from different directions. In this embodiment, the measurement of the side positions of the workpiece from different directions refers to measuring different side positions of the workpiece along different directions, such as obtaining the side positions of the workpiece in the positive and negative directions of the X axis, obtaining the side positions of the workpiece in the positive and negative directions of the Y axis, and the like; wherein the Z-position of the measuring point is Z c Selecting l, i, which needs to consider the chamfer of the surface edge of the workpiece 10 and the range of a measuring rod of the three-coordinate measuring head 6, wherein l takes a positive value when the workpiece 10 is a convex surface and a plane, and l takes a negative value when the surface of the workpiece 10 is a concave surface; the measuring direction is selected according to the actual shape of the workpiece 10;
according to the side measurement result and the geometric pose measurement model, the central position of the workpiece 10 is geometrically solved, namely: obtaining the positions of the geometric center of the workpiece in the X and Y directions under the machine tool coordinate system according to the side measurement result rc And y rc Program-driven three-coordinate measuring head 6 pairs (x) rc 、y rc ) Measuring the Z-direction position of the workpiece to obtain the Z-direction position of the geometric center of the workpiece rc ；
S3: with the position of the central point as an origin, a theoretical coordinate system 21 of the workpiece 10 (corresponding to the coordinate system O in fig. 1) is established t -X t Y t Z t ) And the theoretical coordinate system 21 is parallel to the machine coordinate system 1 (corresponding to the coordinate system O-XYZ in fig. 1);
s4: detecting whether the pitching deflection angle of the actual coordinate system 20 and the theoretical coordinate system 21 of the workpiece 10 is larger than a preset pitching deflection angle or not, adjusting the posture of the workpiece 10 when the pitching deflection angle is larger than the preset pitching deflection angle, and repeatedly executing S1-S3; otherwise, executing S5;
because there is uncertainty in the placement of the workpiece 10, there are errors in translation and yaw between the actual attitude and the theoretical attitude, and when the yaw angle is too large, the measurement accuracy is affected, so to reduce the error between the theoretical coordinate system 21 and the actual coordinate system 20, this embodiment further needs to detect whether the pitch yaw angle between the theoretical coordinate system 21 and the actual coordinate system 20 is greater than the preset pitch yaw angle, and when the pitch yaw angle is greater than the preset pitch yaw angle, S1 is repeated, specifically, including:
the upper computer 17 generates an NC program for measuring the upper surface of the workpiece according to the geometric pose measurement model;
the NC program for measuring the upper surface of the workpiece drives the three-coordinate measuring head 6 to measure the preset points of the upper surface of the workpiece, wherein the measuring points are selected at a distance P in the X and Y directions rc Respective offset distance D x+ 、D x- 、D y+ And D y- Four points of (1), under the machine tool coordinate system, the measurement result of each measuring point is marked as P x+ (x rc +D x ，y rc ，z x+ )、P x- (x rc -D x ，y rc ，z x- )、P y+ (x rc ，y rc +D y ，z y+ ) And P y- (x rc ，y rc -D y ，z y- ). Wherein D is x And D y According to the geometric shape and the size of the workpiece, the measuring points are ensured to fall into the polishing area of the workpiece and are matched with P rc When the measurement result meets the following formula, executing S5, otherwise, repeatedly executing S1-S3;
max{tan -1 ((z x+ -z x- )/2D x )，tan -1 ((z y+ -z y- )/2D y )}≤σ；
wherein z is x+ Representing a positive offset D from the center point X x Z-direction measurement of the measuring point, Z x- Representing a negative bias D from said centre point X x Z-direction measurement of the measuring point, Z y+ Representing a positive offset D from said centre point Y y Z-direction measurement of the measuring points, Z y- Representing a negative bias D from said centre point Y y Z-direction measurement of the measuring points, D x Representing an X-offset distance, D, from the center point y Representing a Y-offset distance from the center point.
S5: constructing a geometric pose theoretical model of the position of the workpiece 10 in a theoretical coordinate system 21;
and (3) according to the workpiece model parameters input by the upper computer 17 in the S3 and the established theoretical coordinate system 21, establishing a workpiece theoretical model, namely: each point on the surface of the workpiece 10 satisfies the relationship shown in formula (2):
z t ＝F t (GShp，GDim，CType，AspCoe，d，OpAng，x t ，y t ) (2)
wherein x is t 、y t 、z t Representing the coordinates, F, of a point on the workpiece 10 in a theoretical coordinate system 21 t And the model is determined by parameters such as the geometric shape and size of the workpiece, the concave-convex type of the surface of the workpiece, aspheric coefficients, off-axis quantity, an optical axis included angle and the like.
S5: according to the geometric pose theoretical model, the workpiece 10 is subjected to track planning by using a CCOS (computer-controlled optical surface forming) technology to obtain a track point set M, M = { M = i |m i ＝(xt i ，yt i ，zt i ) T ，i＝1...N m }，m i Represents the ith trace point, xt i The X-directional component, yt, representing the ith trace point i The Y-component, zt, representing the ith trace point i Z-component, N, representing the ith trace point m Representing the number of track points;
s6: correcting the track points in the track point set M according to the coordinate transformation matrix to obtain an actual processing track P, P = { P = { of the workpiece 10 j |p j ＝(xt j ，yt j ，zt j ) T ，j＝1…N m }，p j Represents the jth revised trace point, xt j 、yt j 、zt j Respectively representing the X, Y and Z direction components of the jth track point; wherein the coordinate transformation matrix is an actual coordinate system (corresponding to the coordinate system O in fig. 1) r -X r Y r Z r ) 20 and a theoretical coordinate system 21, specifically, the relationship between the coordinate transformation matrix, the track point set M and the actual processing track P is: p = T · M, T being a coordinate transformation matrix.
The actual coordinate system 20 in this embodiment refers to a real coordinate system of the workpiece 10 in the polishing process, the theoretical coordinate system 21 is only a coordinate system in an ideal state, and because the placement of the workpiece 10 is uncertain, the established theoretical coordinate system 21 and the actual coordinate system 20 have a translational and yaw deviation. Based on this, in the scheme, the track planning of the workpiece 10 in the theoretical coordinate system 21 is converted into the actual coordinate system 20 by establishing the conversion relation between the theoretical coordinate system 21 and the actual coordinate system 20, so that the workpiece 10 to be polished does not need to be accurately leveled manually in the polishing process, and the problems that the precision is influenced by manual experience and the efficiency is low in the accurate leveling process of the workpiece 10 are solved.
The following describes a method for calculating the coordinate transformation matrix as follows:
(1) At X r O r Z r In the cross section, max { tan } is satisfied when the inclination angle between the actual attitude 19 and the theoretical attitude 18 of the workpiece is small -1 ((z x+ -z x- )/2D x )，tan -1 ((z y+ -z y- )/2D y ) When the } is less than or equal to sigma, the geometrical relationship shown in the following formula can be obtained. Setting an initial value Δ Z x =0, solving θ sequentially by a circular solution method x 、X cm 、ΔZ x The cycle cutoff conditions are as follows:
Figure GDA0003328505950000071
Figure GDA0003328505950000072
Figure GDA0003328505950000081
ΔZ x ＝
F t (GShp，GDim，CType，AspCoe，d，OpAng，D x +X cm ，0)-
F t (GShp，GDim，CType，AspCoe，d，OpAng，D x ，0)
wherein, Δ Z x Indicating the Z-directional deviation, X, resulting from the correction of the X-direction of the measuring point cm Indicates the deviation between the center correction point of the workpiece and the X direction of the measuring point,
Figure GDA0003328505950000082
the calculation result of the rotation angle of the i +1 th iteration actual coordinate system around the X axis of the theoretical coordinate system is shown,
Figure GDA0003328505950000083
representing the calculation result of the rotation angle of the ith iteration actual coordinate system around the X axis of the theoretical coordinate system, epsilon x Representing the iterative calculation of the convergence threshold value theta around the rotation angle of the X axis of the theoretical coordinate system in the actual coordinate system x Representing the rotation angle, X, of the actual coordinate system about the X-axis of the theoretical coordinate system 2 Indicates the X-direction position of the edge side point in the X positive direction 1 The X-direction position of the edge side point in the X negative direction is shown;
(2) At X r O r Z r In the cross section, max { tan ] is satisfied when the inclination angle between the actual attitude 19 of the workpiece and the theoretical attitude 18 of the workpiece is small -1 ((zx +- z x- )/2D x )，tan -1( (z y+ -z y- )/2D y ) When the } is less than or equal to sigma, the geometrical relationship can be obtained as shown in the following formula. Setting an initial value Δ Z y =0, solving θ sequentially by a circular solution method y 、Y cm 、ΔZ y The cycle cutoff conditions are as follows:
Figure GDA0003328505950000084
Figure GDA0003328505950000085
Figure GDA0003328505950000086
ΔZ y ＝
F t (GShp，GDim，CType，AspCoe，d，OpAng，0，D y +Y cm )-
F t (GShp，GDim，CType，AspCoe，d，OpAng，0，D y ) (8)
wherein, Δ Z y Indicating the Z-direction deviation, Y, resulting from Y-direction correction of the measuring points cm Indicating the center of the workpieceThe deviation of the correction point and the measuring point in the Y direction,
Figure GDA0003328505950000087
the calculation result of the rotation angle of the i +1 th iteration actual coordinate system around the Y axis of the theoretical coordinate system is shown,
Figure GDA0003328505950000088
represents the calculation result of the rotation angle of the ith iteration actual coordinate system around the Y axis of the theoretical coordinate system, epsilon y Iteratively calculating the convergence threshold value theta around the rotation angle of the X axis of the theoretical coordinate system in the actual coordinate system y Representing the angle of rotation of the actual coordinate system about the Y-axis of the theoretical coordinate system, Y 2 Indicates the Y-direction position of the edge side point in the Y-direction 1 Showing the Y-direction position of the edge side point in the Y negative direction;
(3) NC program driven three-coordinate measuring head 6 pairs (x) for measuring side surface and geometric center of workpiece rc +X cm 、y rc +Y cm ) Measuring the Z-direction position of the workpiece to obtain the actual Z-direction position of the geometric center of the workpiece r Thus, a rigid body transformation matrix between the actual coordinate system 20 and the theoretical coordinate system 21 of the workpiece is obtained:
Figure GDA0003328505950000091
wherein T represents a coordinate transformation matrix, Z rc Indicating the Z-position of the center point.
Example 2
A method for polishing a workpiece according to the actual processing trajectory obtained by the method for measuring and calculating the pose of a magnetorheological polished workpiece as provided in embodiment 1.
The above-mentioned embodiments are intended to illustrate the objects, technical solutions and advantages of the present invention in further detail, and it should be understood that the above-mentioned embodiments are merely exemplary embodiments of the present invention, and are not intended to limit the scope of the present invention, and any modifications, equivalent substitutions, improvements and the like made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (6)

1. A method for measuring and calculating the pose of a magnetorheological polishing workpiece is characterized by comprising the following steps:
s1: constructing a geometric pose measurement model of the workpiece (10);
s2: acquiring the position of a central point of the workpiece (10) according to the geometric pose measurement model;
s3: establishing a theoretical coordinate system (21) of the workpiece (10) by taking the central point as an origin, wherein the theoretical coordinate system (21) is parallel to a machine tool coordinate system (1);
s4: measuring and calculating whether the pitch yaw angle of the actual coordinate system (20) and the theoretical coordinate system (21) of the workpiece (10) is larger than a preset pitch yaw angle, adjusting the posture of the workpiece (10) when the pitch yaw angle is larger than the preset pitch yaw angle, and repeatedly executing the steps S1-S3; otherwise, executing S5;
s5: constructing a geometric pose theoretical model of the position of the workpiece (10) in the theoretical coordinate system;
s6: according to the geometric pose theoretical model, path planning is carried out on the workpiece (10) by utilizing a CCOS technology, and a path point set is obtained;
s7: correcting the track points in the track point set according to the coordinate transformation matrix to obtain the actual processing track of the workpiece (10); wherein the coordinate transformation matrix is a rigid body transformation matrix between an actual coordinate system (20) of the workpiece (10) and the theoretical coordinate system (21);
the S4 comprises the following substeps:
s41: generating a second driving signal according to the geometric pose measurement model;
s42: the three-coordinate measuring head (6) responds to the second driving signal to measure a preset point on the upper surface of the workpiece (10) so as to acquire the coordinate of the preset point under the machine tool coordinate system (1);
s43: according to the coordinates of the preset point in the machine tool coordinate system (1), judging whether the following formula is met:
max{tan -1 ((z x+ -z x- )/2D x )，tan -1 ((z y+ -z y- )/2D y )}≤σ；
wherein z is x+ Representing a positive offset D from the center point X x Z-direction measurement of the measuring point, Z x- Representing a negative bias D from the center point X x Z-direction measurement of the measuring point, Z y+ Representing a positive offset D from said centre point Y y Z-direction measurement of the measuring point, Z y- Representing a negative bias D from said centre point Y y Z-direction measurement of the measuring points, D x Representing an X-offset distance, D, from said centre point y Represents a Y-direction offset distance from the center point;
s44: when the above formula is satisfied, executing the S5; otherwise, adjusting the posture of the workpiece (10), and repeatedly executing S1-S3.
2. The method for measuring and calculating the pose of the magnetorheological polishing workpiece according to claim 1, wherein the S1 comprises the following substeps:
s11: establishing a measuring coordinate system (8) in the same direction as the machine tool coordinate system (1) by taking the center of the C-axis turntable as a coordinate origin;
s12: acquiring the geometric shape, the size, the surface concave-convex type, the aspheric surface coefficient, the off-axis quantity and the optical axis included angle of the workpiece (10);
s13: and establishing the geometric pose measurement model according to the geometric shape, the size, the surface concave-convex type, the aspheric surface coefficient, the off-axis quantity, the optical axis included angle and the measurement coordinate system (8).
3. The method for measuring and calculating the pose of the magnetorheological polishing workpiece according to claim 1, wherein the S2 comprises the following substeps:
s21: acquiring the surface position of a workpiece corresponding to the axis of the C shaft;
s22: generating a first driving signal according to the geometric pose measurement model and the workpiece surface position;
s23: the three-coordinate measuring head (6) responds to the first driving signal to measure the side position of the workpiece (10) in different directions;
s24: and calculating the position of the central point according to the measurement result of the side position and the geometric pose measurement model.
4. The method for measuring and calculating the pose of the magnetorheological polishing workpiece according to claim 1, wherein the S5 comprises the following substeps:
s51: acquiring the geometric shape, the size, the surface concave-convex type, the aspheric surface coefficient, the off-axis quantity and the optical axis included angle of the workpiece (10);
s52: and establishing the geometric pose theoretical model according to the geometric shape, the size, the surface concave-convex type, the aspheric surface coefficient, the off-axis quantity, the optical axis included angle and the theoretical coordinate system (21).
5. The method for measuring and calculating the pose of the magnetorheological polishing workpiece according to claim 1, wherein the generating of the coordinate transformation matrix comprises the following sub-steps of:
x in the actual coordinate system r O r Z r Within the cross section, an initial value Δ Z is set x =0, with the cycle cutoff condition of
Figure FDA0003776253100000021
Solving theta sequentially through a cyclic solving method x 、X cm And Δ Z x ；
Figure FDA0003776253100000022
Figure FDA0003776253100000023
ΔZ x ＝F t (GShp，GDim，CType，AspCoe，d，OpAng，D x +X cm ，0)-F t (GShp，GDim，CType，AspCoe，d，OpAng，D x ，0)；
Wherein, Δ Z x Indicating the Z-direction deviation, X, resulting from correcting the X-direction of the measuring point cm Indicates the deviation between the center correction point of the workpiece and the X direction of the measuring point,
Figure FDA0003776253100000024
the calculation result of the rotation angle of the i +1 th iteration actual coordinate system around the X axis of the theoretical coordinate system is shown,
Figure FDA0003776253100000025
representing the calculation result of the rotation angle of the ith iteration actual coordinate system around the X axis of the theoretical coordinate system, epsilon x Representing the iterative calculation of the convergence threshold value theta around the rotation angle of the X axis of the theoretical coordinate system in the actual coordinate system x Representing the rotation angle, X, of the actual coordinate system about the X-axis of the theoretical coordinate system 2 Indicates the X-direction position of the edge side point in the X positive direction 1 Representing the X-direction position of the edge side point in the X negative direction;
at X r O r Z r Within the cross section, an initial value Δ Z is set y =0, cycle cutoff condition is
Figure FDA0003776253100000026
Solving theta sequentially through a cyclic solving method y 、Y cm And Δ Z y ；
Figure FDA0003776253100000031
Figure FDA0003776253100000032
ΔZ y ＝F t (GShp，GDim，CType，AspCoe，d，OpAng，0，D y +Y cm )-F t (GShp，GDim，CType，AspCoe，d，OpAng，0，D y )；
Wherein, Δ Z y Indicating the z-direction resulting from y-direction correction of the measured pointsDeviation, Y cm Indicating the deviation of the center correction point of the workpiece from the Y direction of the measuring point,
Figure FDA0003776253100000033
the calculation result of the rotation angle of the i +1 th iteration actual coordinate system around the Y axis of the theoretical coordinate system is shown,
Figure FDA0003776253100000034
represents the calculation result of the rotation angle of the ith iteration actual coordinate system around the Y axis of the theoretical coordinate system, epsilon y Iteratively calculating the convergence threshold value theta around the rotation angle of the X axis of the theoretical coordinate system in the actual coordinate system y Representing the angle of rotation of the actual coordinate system about the Y-axis of the theoretical coordinate system, Y 2 Indicates the Y-direction position of the edge side point in the Y-direction 1 The Y-direction position of the edge side point in the Y negative direction is shown;
a three-coordinate stylus (6) responsive to the second drive signal, pair (x) rc +X cm 、y rc +Y cm ) The corresponding workpiece (10) is subjected to Z-direction position measurement to obtain the actual Z-direction position of the geometric center of the workpiece r ；
Calculating the rigid body transformation matrix:
Figure FDA0003776253100000035
wherein T represents a coordinate transformation matrix, Z rc Representing the Z-position of the center point.
6. A polishing method of a workpiece, characterized in that the workpiece is polished according to the actual processing track obtained by the calculation method of the posture of the magnetorheological polished workpiece according to any one of claims 1 to 5.
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