CN108067939B - Space point location measurement reference error compensation method - Google Patents

Space point location measurement reference error compensation method Download PDF

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CN108067939B
CN108067939B CN201611022909.2A CN201611022909A CN108067939B CN 108067939 B CN108067939 B CN 108067939B CN 201611022909 A CN201611022909 A CN 201611022909A CN 108067939 B CN108067939 B CN 108067939B
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高鑫
沈昕
阮超
汪裕杰
孙超
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Chengdu Aircraft Industrial Group Co Ltd
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B23—MACHINE TOOLS; METAL-WORKING NOT OTHERWISE PROVIDED FOR
    • B23Q—DETAILS, COMPONENTS, OR ACCESSORIES FOR MACHINE TOOLS, e.g. ARRANGEMENTS FOR COPYING OR CONTROLLING; MACHINE TOOLS IN GENERAL CHARACTERISED BY THE CONSTRUCTION OF PARTICULAR DETAILS OR COMPONENTS; COMBINATIONS OR ASSOCIATIONS OF METAL-WORKING MACHINES, NOT DIRECTED TO A PARTICULAR RESULT
    • B23Q15/00—Automatic control or regulation of feed movement, cutting velocity or position of tool or work
    • B23Q15/007—Automatic control or regulation of feed movement, cutting velocity or position of tool or work while the tool acts upon the workpiece
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Abstract

The invention discloses a space point location measurement reference error compensation method. The method can effectively solve the problem that the measurement result has measurement reference errors due to the fact that the actual measurement coordinate system of the part is not consistent with the theoretical measurement coordinate system. And only considering the error of the measurement result in the vector direction of the measurement method during calculation, constructing a target function according to a least square method, solving a coordinate transformation matrix between an actual measurement value and a theoretical value, and further performing measurement reference error compensation on the actual measurement value. The method can realize effective compensation of the measurement reference error, improve the measurement precision and provide effective data basis for the evaluation of the part machining precision.

Description

Space point location measurement reference error compensation method
Technical Field
The invention relates to an error compensation method, in particular to an error compensation method for space point location measurement, and specifically relates to a reference error compensation method for space point location measurement.
Background
In the numerical control machining process of the part, in order to obtain the current machining state of the part, the point position of the part is usually measured in an on-line detection or three-coordinate measuring machine measurement mode. In the process of measuring the part, because the theoretical measurement coordinate system and the actual measurement coordinate system of the part have deviation, the measurement result of the space point position of the part has measurement reference error. Such an error will have a great influence on the evaluation of the machining accuracy of the part.
According to related technologies and documents, the small iris (2013) published a paper "blade profile measurement programming and error processing technology" in academic journal "journal of metrology" 2013,34(2), p128-133 discloses a method for eliminating measurement system errors, theoretical coordinate values of measurement points are extracted based on a known blade CAD model, a normal vector is calculated by adopting a micro-plane method, and an ICP algorithm is adopted for registration to eliminate the system errors.
Liuyuanpun (2005) published a paper "study on the optimal matching problem of measured data of complex curved surfaces" in academic journal, "Chinese mechanical engineering," 2005,16(12), p1080-1082, and discloses a method for matching measured data of complex curved surface parts, which realizes the optimal matching of measured data by initial matching and accurate matching, wherein the accurate matching constructs a target function according to the principle of least square, and the matching problem of the measured data of complex curved surface parts and curved surfaces can be effectively solved by applying an L-BFGS-B algorithm to perform the accurate matching.
When the probe is used for measurement, the probe measures the error of the measuring point along the normal vector direction of the measuring point. As shown in FIG. 1, when the actual measurement coordinate system of the part is not consistent with the theoretical coordinate system, and the measurement is performed by using the probe, the measurement error only exists in the normal vector direction of the measurement. When the method is used for matching measurement data, the problem is simplified, the influence of the measurement vector on the measurement error is not considered, and the measurement reference error cannot be effectively compensated by adopting the method.
Disclosure of Invention
The invention aims to solve the problem that a measurement result has a measurement reference error due to the deviation between an actual measurement coordinate system and a theoretical measurement coordinate system when a part is measured, and provides a compensation method for the measurement reference error of a spatial point location.
The technical scheme of the invention is as follows:
a space point location measurement reference error compensation method comprises the following steps:
step 1, acquiring actual measurement coordinate values of part space measurement points from a measuring machine or a machine tool;
step 2, acquiring theoretical coordinate values of the part space measuring points and a measuring normal vector of each measuring point based on the part design model and the measuring file;
step 3, defining the actual measurement coordinate value, the theoretical coordinate value, the measurement normal vector and the measurement error of different points of the space point position as pa，ptV and e;
step 4, supposing that the space point position theoretical value ptP 'is obtained after three translations and three rotations'tWherein the amount of translational rotation is deltax,δy,δz,εx,εy,εz；
Step 5, mixing p'tEach inSetting the sum of squares of the difference between the error of the corresponding point in the measuring direction before the translational rotation and the error of the actual measured value of the point as a least square method target function for solving the translational rotation amount delta in the step 2x,δy,δz,εx,εy,εz；
Step 6, when the objective function value is minimum, the translation rotation amount of the spatial point location is the position relation between the actual coordinate system and the theoretical coordinate system of the spatial point location measurement, and in order to solve the translation rotation amount of the spatial point location, the objective function is used for the translation rotation amount deltax,δy,δz,εx,εy,εzRespectively deriving and assigning values to 0;
step 7, obtaining an equation set by simultaneously establishing derivation equations, and solving the translation rotation amount delta of the space point positionx,δy,δz,εx,εy,εz；
Step 8, according to the translation rotation amount of the spatial point location, translating and rotating the spatial point location theoretical value to obtain a transformed spatial point location coordinate value p't；
Step 9, according to the transformed space point position coordinate value p 'solved in the step 6'tAnd the actual measured value p of the spatial point positionaSolving a space point location error e' subjected to the reference error compensation along the measuring direction;
step 10, according to the error e' and the space point position theoretical value ptSolving the space point location measurement value p 'subjected to benchmark error compensation'a。
And 11, inputting the space point position measurement value subjected to the reference error compensation into a measuring machine measuring system or a machine tool system to be used as a basis for judging the machining error of the part.
The actual measurement coordinate value, the theoretical coordinate value, the measurement vector and the measurement error of different points of the space point position can be expressed as
Figure BDA0001156221620000021
vm(im jm km)、em，
Figure BDA0001156221620000022
Wherein m represents the mth spatial point, m is 1,2,3, … n, and n is the number of spatial points;
p 'obtained after translation and rotation of space point position theoretical value'tAfter the translation rotation amount is small and the high-order infinitesimal amount in the calculation process is omitted, the following expression can be used for representing the translation rotation amount:
Figure BDA0001156221620000031
wherein deltax,δy,δz,εx,εy,εzRespectively the translation amount and the rotation amount along the X, Y and Z directions;
the least squares objective function can be expressed by the following formula:
Figure BDA0001156221620000032
the derivation process of the target function on the translation rotation amount is calculated as follows:
order to
Figure BDA0001156221620000033
By
Figure BDA0001156221620000034
Obtaining:
Figure BDA0001156221620000035
by
Figure BDA0001156221620000036
Obtaining:
Figure BDA0001156221620000037
by
Figure BDA0001156221620000038
Obtaining:
Figure BDA0001156221620000039
by
Figure BDA00011562216200000310
Obtaining:
Figure BDA00011562216200000311
by
Figure BDA00011562216200000312
Obtaining:
Figure BDA00011562216200000313
by
Figure BDA00011562216200000314
Obtaining:
Figure BDA00011562216200000315
the solution process of the translational rotation amount is as follows:
and (3) simultaneously obtaining an equation set by using the derivation equations as shown in the following formula:
Figure BDA0001156221620000041
then
Figure BDA0001156221620000042
The spatial point location measurement error e' compensated by the reference error can be expressed as:
Figure BDA0001156221620000043
the space point location measurement value p 'subjected to benchmark error compensation'aCan be expressed as:
Figure BDA0001156221620000044
aiming at the characteristic that the space point location measurement error only exists in the measurement normal vector direction, the method takes the measurement normal vector direction error as a least square method target function, can accurately solve a space point location transformation matrix, and realizes the compensation of the space point location measurement reference error.
The invention has the following beneficial effects:
1. by considering the influence of the measurement vector on the measurement error, a least square method target function is constructed, a transformation matrix between an actual measurement coordinate system and a theoretical coordinate system of the spatial point location is solved, and further the reference error compensation of the measurement result is realized;
2. by realizing the reference error compensation of the measurement result, the measurement precision can be effectively improved, and a data basis is provided for the evaluation of the part machining precision.
Drawings
FIG. 1 is a schematic diagram of measurement errors of a part.
Wherein: 1. the method comprises the following steps of (1) theoretical position of a part, (2) actual position of the part, (3) a measuring probe, (4) actual spatial position of a part measuring point, 5 measuring normal vector at the part measuring point, 6 theoretical spatial position of the part measuring point, and 7) part measuring error along the direction of the measuring normal vector.
FIG. 2 is a schematic view of a point location of a part.
Wherein: 8. standard S specimen, 9. spatial measurement point location on the S specimen, 10. measurement normal vector at the spatial point location.
Table 1 shows theoretical coordinates of spatial measurement point positions of the S test piece, measurement normal vectors and tolerance values.
And table 2 shows coordinate values and error values of the spatial point position of the S specimen before and after error compensation.
Detailed Description
The method for compensating the spatial point location measurement reference error proposed by the present invention is described below with reference to the accompanying drawings and embodiments, but the present invention is not limited to the present example.
The method proposed by the invention is described by taking an S test piece proposed in the patent "S" shaped test piece for comprehensively detecting the precision of a numerical control milling machine and a detection method (ZL200710048269.7) "as an example, and is shown as 8 in FIG. 2. And (3) selecting 15 space measurement point positions on the S test piece, wherein the theoretical coordinates, the measurement normal vectors and the tolerance of the measurement point positions are shown in the table 1.
TABLE 1
Spatial point location ptTheoretical coordinate value/mm v/measurement of Normal vector Tolerance/mm
Point 1 (-52.975，-70.603，23) (-0.976，0.071，0.206) ±0.05
Point 2 (-51.491，-20.917，23) (-0.973，-0.006，0.233) ±0.05
Point 3 (-50.243，28.747，23) (-0.979，0.126，0.161) ±0.05
Point 4 (-28.083，71.213，23) (-0.482，0.858，0.178) ±0.05
Point 5 (-4.153，76.97，23) (-0.017，0.982，0.189) ±0.05
Point 6 (20.317，73.269，23) (0.306，0.935，0.179) ±0.05
Point 7 (55.853，40.676，23) (0.895，0.425，0.137) ±0.05
Dot 8 (70.763，-6.683，23) (0.967，0.256，-0.010) ±0.05
Point 9 (87.823，-53.218，23) (0.853，0.507，-0.123) ±0.05
Dot 10 (126.998，-81.098，23) (0.186，0.972，-0.140) ±0.05
Dot 11 (151.731，-81.533，23) (-0.159，0.978，-0.136) ±0.05
Dot 12 (174.337，-71.932，23) (-0.638，0.753，-0.160) ±0.05
Point 13 (191.549，-26.65，23) (-0.987，0.074，-0.143) ±0.05
Dot 14 (191.776，23.054，23) (-0.981，-0.006，-0.195) ±0.05
Point 15 (193.367，72.737，23) (-0.979，0.070，-0.190) ±0.05
1. Selecting 15 space measurement points on the S test piece, wherein the theoretical coordinate values of the space points and the measurement normal vectors are respectively defined as
Figure BDA0001156221620000061
vm(im jm km)；
2. Using a measuring machine to measure points in space on an S specimenMeasuring the position to obtain the actual measurement coordinate value of the space point position, which is defined as
Figure BDA0001156221620000062
Defining the measurement error of each spatial point location as em，
Figure BDA0001156221620000063
m＝1,2,3,…15；
2. Suppose that p 'is obtained after the space point position theoretical value is translated and rotated'tAfter the translation rotation amount is small and the high-order infinitesimal amount in the calculation process is omitted, the following expression can be used for representing the translation rotation amount:
Figure BDA0001156221620000064
wherein deltax,δy,δz,εx,εy,εzRespectively the translation amount and the rotation amount along the X, Y and Z directions;
3. p 'obtained after translation and rotation'tSetting the sum of squares of the difference between the error of each point and the corresponding point before translation and rotation in the measuring direction and the error of the actual measured value of the point as a least square method objective function, and expressing the sum by the following formula:
Figure BDA0001156221620000065
4. when the target function value is minimum, the translation rotation amount of the space point location is the position relation between the space point location measurement actual coordinate system and the theoretical coordinate system, and in order to solve the translation rotation amount of the space point location, the target function is used for the translation rotation amount deltax,δy,δz,εx,εy,εzRespectively deriving and assigning the values to 0;
5. and (3) obtaining an equation set by simultaneous derivation equations, solving the translation rotation amount of the spatial point position, and expressing by the following formula:
Figure BDA0001156221620000066
the spatial point location translation rotation amount result obtained by the above formula calculation is as follows:
(δx,δy,δz,εx,εy,εz)＝(0.0168，-0.037,0.4834，-0.0008，-0.0007，0.0004)
6. obtaining transformed space point location coordinate value p 'according to space point location translation rotation amount'tAnd then solve for p'tAnd the spatial point location measured value paThe error in the measurement direction, that is, the spatial point location error e' after the reference error compensation, is as shown in table 2, the average error before the compensation is 0.066mm, and the average error after the error compensation is 0.017 mm;
7. according to the error e' and the theoretical value p of the spatial point positiontSolving the space point location measurement value p 'subjected to benchmark error compensation'aAs shown in table 2.
TABLE 2
Figure BDA0001156221620000071
8. And inputting the space point position measurement value subjected to the reference error compensation into a measuring system of a measuring machine to serve as a judgment basis for the machining error of the S test piece.
The parts not involved in the present invention are the same as or can be implemented using the prior art.

Claims (4)

1. A space point location measurement reference error compensation method comprises the following steps:
step 1, acquiring actual measurement coordinate values of spatial point positions of parts from a measuring machine or a machine tool;
step 2, acquiring a theoretical coordinate value of a space point location of the part and a measurement vector of each measurement point based on the part design model and the measurement file;
step 3, defining the actual measurement coordinate value of the spatial point location, the theoretical coordinate value of the spatial point location, the measurement vector and the measurement error at different points as pa，ptV and e;
step 4, supposing that the space point position theoretical coordinate value ptP 'is obtained after three translations and three rotations'tWherein the amount of translational rotation is deltax,δy,δz,εx,εy,εz；
Step 5, mixing p'tSetting the sum of squares of the difference between the error of each point and the corresponding point before translation and rotation in the measuring direction and the error of the actual measured value of the point as a least square method objective function for solving the translation and rotation amount delta in the step 4x,δy,δz,εx,εy,εz；
Step 6, when the target function value is minimum, the translation rotation amount is the position relation between the space point location measurement actual coordinate system and the theoretical coordinate system, and in order to solve the translation rotation amount, the target function is used for the translation rotation amount deltax,δy,δz,εx,εy,εzRespectively deriving and assigning values to 0;
step 7, obtaining an equation set by simultaneously establishing derivation equations, and solving the translational rotation quantity deltax,δy,δz,εx,εy,εz；
Step 8, according to the translation rotation amount, translating and rotating the space point position theoretical coordinate value to obtain a transformed space point position coordinate value p't；
Step 9, according to the transformed space point position coordinate value p 'solved in the step 8'tAnd the actual measurement coordinate value p of the spatial point positionaSolving a space point position measurement error e' compensated by the reference error along the measurement direction;
step 10, according to the error e' and the theoretical coordinate value p of the spatial point locationtSolving the actual measurement coordinate value p 'of the space point position compensated by the reference error'a；
Step 11, inputting the space point position measurement value after the reference error compensation into a measuring machine measuring system or a machine tool system as a basis for judging the machining error of the part;
the actual measurement coordinate value of the space point position and the theoretical coordinate value of the space point positionThe value, the measured normal vector and the measurement error at different points can be expressed as
Figure FDA0003069066290000021
vm(im jm km)、em，
Figure FDA0003069066290000022
Wherein m represents the mth spatial point, m is 1,2,3, … n, and n is the number of spatial points;
p 'obtained by translating and rotating theoretical coordinate values of spatial point positions'tAfter the high-order infinitesimal quantity in the calculation process is omitted, the method can be represented by the following formula:
Figure FDA0003069066290000023
wherein deltax,δy,δz,εx,εy,εzRespectively the translation amount and the rotation amount along the X, Y and Z directions;
the derivation process of the target function on the translation rotation amount is calculated as follows:
order to
Figure FDA0003069066290000024
By
Figure FDA0003069066290000025
Obtaining:
Figure FDA0003069066290000026
by
Figure FDA0003069066290000027
Obtaining:
Figure FDA0003069066290000028
by
Figure FDA0003069066290000029
Obtaining:
Figure FDA00030690662900000210
by
Figure FDA00030690662900000211
Obtaining:
Figure FDA00030690662900000212
by
Figure FDA00030690662900000213
Obtaining:
Figure FDA00030690662900000214
by
Figure FDA00030690662900000215
Obtaining:
Figure FDA00030690662900000216
the least squares objective function can be expressed by the following formula:
Figure FDA00030690662900000217
2. the method as claimed in claim 1, wherein the solution of the translational rotation amount is as follows:
and (3) simultaneously obtaining an equation set by using the derivation equations as shown in the following formula:
Figure FDA0003069066290000031
then
Figure FDA0003069066290000032
3. The method as claimed in claim 1, wherein the spatial point location measurement error e' after being compensated by the reference error is represented as:
Figure FDA0003069066290000033
4. the method for compensating the spatial point location measurement reference error according to claim 1, wherein the spatial point location actual measurement coordinate value p 'after the reference error compensation'aCan be expressed as:
Figure FDA0003069066290000034
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