CN111797482A - Sensitive error weight calculation method for scanning measurement of cartesian coordinate system profile - Google Patents

Sensitive error weight calculation method for scanning measurement of cartesian coordinate system profile Download PDF

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CN111797482A
CN111797482A CN202010639446.4A CN202010639446A CN111797482A CN 111797482 A CN111797482 A CN 111797482A CN 202010639446 A CN202010639446 A CN 202010639446A CN 111797482 A CN111797482 A CN 111797482A
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CN111797482B (en
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彭小强
赖涛
戴一帆
陈善勇
翟德德
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National University of Defense Technology
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Abstract

The application relates to a sensitive error weight calculation method for scanning measurement of a cartesian coordinate system profile. The method comprises the following steps: and acquiring 21 geometric error parameters of the machine tool under a Cartesian coordinate system, and expressing the geometric error parameters as a normalized geometric error function. And acquiring a nominal profile coordinate of a workpiece to be scanned and measured, inputting the normalized geometric error function and the nominal profile coordinate into a pre-constructed linearity measurement error model and an angle measurement error model, and calculating the measurement point coordinate of the workpiece to obtain the sensitive error weight values of 21 geometric error parameters. The sensitive error weight value of the geometric error parameter is the ratio of the measurement error amplitude value when the machine tool measures the workpiece to the corresponding geometric error amplitude value. The method can accurately reflect the influence of various geometric error parameters of the machine tool on the coordinates of the measuring points, quantizes the degree of the influence of the various geometric error parameters on the measuring errors, and provides a calculation basis for error correction of the machine tool.

Description

Sensitive error weight calculation method for scanning measurement of cartesian coordinate system profile
Technical Field
The application relates to the technical field of machine tool design and manufacture and error measurement compensation, in particular to a sensitive error weight calculation method for scanning and measuring a cartesian coordinate system profile.
Background
Each machine has its own typical major sources of error and process characteristics, subject to the machine topology and manufacturing process. In order to rapidly and accurately control the main error source of the machine tool and obtain higher compensation efficiency, the error source of the machine tool needs to be predicted with higher reliability.
Geometric errors are the main sources of errors affecting the accuracy of machine tools. In equipment such as a three-coordinate measuring machine, a three-axis processing machine tool and the like, 21 geometric error parameters are generally adopted to describe basic geometric errors of the equipment, and specifically, the basic geometric errors include three positioning errors, six straightness errors, nine angular pendulum errors (including a rolling angle error, a deflection angle error and a pitch angle error) and three perpendicularity errors among three axes. When the equipment is produced, measuring instruments such as a double-frequency laser interferometer, an electronic level meter, a square, a high-precision inductance micrometer and the like are required to be used for detecting the geometric error parameters so as to correct errors. In addition, due to the influence of installation and use environment of the equipment, the equipment also needs to be subjected to similar detection during use so as to perform error compensation.
For the positioning error of the machine tool, researchers obtain the influence of the positioning error on the machine tool by statically analyzing the positioning error characteristic of the numerical control milling machine, and on the basis, the machining error of a workpiece can be reduced by 40% by using a software correction technology; a method and a system for measuring and automatically compensating the positioning error of the micro-tool are also provided, the positioning error of the cutter in the y direction is reduced from-0.25 mm to 0.01mm, and the total processing error is reduced from-0.25 mm to 0.001 mm. For the straightness, a learner researches the influence of a working position on the straightness of vertical movement, and points out a straightness error model and a compensation strategy, which are beneficial to improving the precision of a machine tool; many new methods are applied to measure straightness, also based on error separation techniques. As for the Roll angle error (Roll), since it is difficult to directly measure using an interferometer, a multi-step and multi-probe method of measuring the Roll error has been proposed by the researchers, and also a high inclinometer has been applied to measure the Roll error, the Roll angle is measured by a complicated optical system, and a measurement resolution of 0.13 arcsec and less than 5 μ rad is achieved. For Yaw angle error (Yaw), measurement instruments such as laser autocollimators, laser interferometers, and Doppler scales are used to measure Yaw error. Due to abbe offset, the deflection angle error has a large effect on the machine tool. For Pitch angle error (Pitch), the accuracy of the machine is directly dependent on the accuracy of the Pitch angle error measurement. The machining precision is effectively improved by compensating the pitch angle error, and a learner obtains a model with the influence of the pitch angle error on the machine tool. For perpendicularity errors, the national defense science and technology university studied a new error separation-based method for measuring perpendicularity with optical bricks, and after calibration, the perpendicularity increased from 19.71 "to 3.2".
In addition to the classification research of the geometric errors, in order to achieve micrometer-scale measurement accuracy or positioning accuracy, the machine tool is generally regarded as a multi-body system (MBS), and various geometric errors are comprehensively modeled, so that the geometric error identification and compensation method for the machine tool is implemented on the basis. But at present, the study on the perpendicularity error of the machine tool is less, and the study does not discuss the influence degree of various geometric errors on the measurement error of the machine tool.
Disclosure of Invention
In view of the above, there is a need to provide a sensitive error weight calculation method for cartesian coordinate system profile scanning measurement, which can quantify the influence degree of each geometric error on the measurement error of the machine tool.
A method of sensitive error weight calculation for cartesian coordinate system profile scan measurements, the method comprising:
and acquiring 21 geometric error parameters of the machine tool under a Cartesian coordinate system, and expressing the geometric error parameters as a normalized geometric error function.
And acquiring the nominal profile coordinate of the workpiece to be scanned and measured, inputting the normalized geometric error function and the nominal profile coordinate into a pre-constructed measurement error model, and calculating the measurement point coordinate of the workpiece. The measurement error model comprises a linearity measurement error model and an angle measurement error model. The linearity measurement error model is expressed as:
Figure BDA0002570946180000021
wherein EXX is X-axis positioning error, EYX is X-axis Y-direction straightness error, EZX is X-axis Z-direction straightness error, EXY and EZY are Y-axis X-direction and Z-direction straightness respectively, EYY is Y-axis positioning error, EXZ and EYZ are Z-axis X-direction and Y-direction straightness respectively, EZZ is Z-axis positioning error, and Deltax islinear、Δylinear、ΔzlinearRespectively, are the measurement errors of the linearity error generated in X, Y, Z three directions.
The angle measurement error model is expressed as:
Figure BDA0002570946180000031
Figure BDA0002570946180000032
Figure BDA0002570946180000033
Figure BDA0002570946180000034
wherein x isp、yp、zpThe zero compensation distance constant of the grating ruler of the machine tool is provided, EAX, EBX and ECX are X-axis three-item angle errors, EAY, EBY and ECY are Y-axis three-item angle errors, EAZ, EBZ and ECZ are Z-axis three-item angle errors, AOZ, BOZ and COY are three-item verticality errors, X, Y and Z are nominal profile coordinates, and delta X is equal to that of the machine tooli、Δyi、ΔziAnd the value of i is 1 to 12, and the measurement errors generated by the angle errors in X, Y, Z are respectively.
And obtaining the sensitive error weight values of 21 geometric error parameters according to the normalized geometric error function, the coordinates of the measuring points and the nominal profile coordinates. The sensitive error weight value is the ratio of the measurement error amplitude and the corresponding geometric error amplitude when the machine tool measures the workpiece.
In one embodiment, the step of obtaining the sensitive error weight values of the 21 geometric error parameters according to the normalized geometric error function, the coordinates of the measurement point, and the coordinates of the nominal profile includes:
and obtaining the geometric error amplitude when the machine tool measures the workpiece according to the normalized geometric error function and the nominal profile coordinate.
And obtaining the measurement error amplitude when the machine tool measures the workpiece according to the measurement point coordinate and the nominal profile coordinate.
And obtaining the sensitive error weight values of the 21 geometric error parameters according to the ratio of the measurement error amplitude to the corresponding geometric error amplitude.
In one embodiment, the method comprises the steps of obtaining 21 geometric error parameters of the machine tool in a cartesian coordinate system, and representing the geometric error parameters as a normalized geometric error function, including:
the 21 geometric error parameters of the machine tool are acquired under a Cartesian coordinate system. And taking the coordinate values as variables, and expressing the geometric error parameters as Fourier series of preset amplitude values and periodic values.
The basic wavelength component of the Fourier series is taken as a normalized geometric error function.
In one embodiment, the measurement error model is constructed in a manner that:
and (3) carrying out motion analysis on the machine tool under a Cartesian coordinate system, and obtaining a linearity measurement error model and an angle measurement error model of the machine tool according to the corresponding relation between the error value of the measuring point of the machine tool and the geometric error value.
A sensitive error weight calculation device for cartesian coordinate system profile scan measurements, the device comprising:
and the normalized geometric error function construction module is used for acquiring 21 geometric error parameters of the machine tool in a Cartesian coordinate system and expressing the geometric error parameters as a normalized geometric error function.
And the measuring point coordinate function building module is used for obtaining the nominal profile coordinates of the workpiece to be scanned and measured, inputting the normalized geometric error function and the nominal profile coordinates into a pre-built measuring error model, and calculating the measuring point coordinates of the workpiece. The measurement error model comprises a linearity measurement error model and an angle measurement error model, and the linearity measurement error model is expressed as:
Figure BDA0002570946180000041
wherein EXX is X-axis positioning error, EYX is X-axis Y-direction straightness error, EZX is X-axis Z-direction straightness error, EXY and EZY are Y-axis X-direction and Z-direction straightness respectively, EYY is Y-axis positioning error, EXZ and EYZ are Z-axis X-direction and Y-direction straightness respectively, EZZ is Z-axis positioning error, and Deltax islinear、Δylinear、ΔzlinearRespectively, are the measurement errors of the linearity error generated in X, Y, Z three directions.
The angle measurement error model is expressed as:
Figure BDA0002570946180000042
Figure BDA0002570946180000043
Figure BDA0002570946180000044
Figure BDA0002570946180000045
wherein x isp、yp、zpThe zero compensation distance constant of the grating ruler of the machine tool is provided, EAX, EBX and ECX are X-axis three-item angle errors, EAY, EBY and ECY are Y-axis three-item angle errors, EAZ, EBZ and ECZ are Z-axis three-item angle errors, AOZ, BOZ and COY are three-item verticality errors, X, Y and Z are nominal profile coordinates, and delta X is equal to that of the machine tooli、Δyi、ΔziI has a value of 1 to 12, eachAre the measurement errors of the angular error in X, Y, Z three directions.
And the sensitive error weight value calculation module is used for obtaining the sensitive error weight values of 21 geometric error parameters according to the normalized geometric error function, the measurement point coordinates and the nominal contour coordinates. The sensitive error weight value is the ratio of the measurement error amplitude and the corresponding geometric error amplitude when the machine tool measures the workpiece.
In one embodiment, the sensitive error weight value calculation module is configured to:
and obtaining the geometric error amplitude when the machine tool measures the workpiece according to the normalized geometric error function and the nominal profile coordinate.
And obtaining the measurement error amplitude when the machine tool scans and measures the workpiece according to the measurement point coordinate function and the nominal profile coordinate.
And obtaining the sensitive error weight values of the 21 geometric error parameters according to the ratio of the measurement error amplitude to the corresponding geometric error amplitude.
In one embodiment, the normalized geometric error function construction module is configured to:
and acquiring the geometric error parameters of the 21 items of the machine tool under a Cartesian coordinate system. And taking the coordinate values as variables, and expressing the geometric error parameters as Fourier series of preset amplitude values and periodic values.
The basic wavelength component of the Fourier series is taken as a normalized geometric error function.
In one embodiment, the method further includes a measurement error model building module, configured to:
and (3) carrying out motion analysis on the machine tool under a Cartesian coordinate system, and obtaining a linearity measurement error model and an angle measurement error model of the machine tool according to the corresponding relation between the error value of the measuring point of the machine tool and the geometric error value.
A machine error compensation device, comprising a memory and a processor, wherein the memory stores a computer program, and the processor implements the steps of the method in any one of the above embodiments when executing the computer program, outputs a sensitive error weight value of 21 geometric error parameters, and performs machine error compensation according to the sensitive error weight value.
A computer-readable storage medium, on which a computer program is stored, which, when being executed by a processor, implements the steps of the method according to any of the preceding embodiments, and outputs a sensitive error weight value for 21 geometric error parameters, and performs machine error compensation according to the sensitive error weight value.
The sensitive error weight calculation method, the sensitive error weight calculation device and the sensitive error weight calculation computer equipment for the scanning measurement of the outline of the Cartesian coordinate system and the machine tool error compensation system provide a measurement error model for describing 21 geometric errors of the machine tool and the measurement error of the machine tool, and after the 21 geometric errors of the Cartesian coordinate system are normalized, the normalized geometric errors and the nominal outline coordinates of a workpiece to be scanned are input into the measurement error model, so that the coordinates of the measurement point of the workpiece can be calculated, and the influence of various geometric error parameters of the machine tool on the coordinates of the measurement point can be accurately reflected. In addition, according to the normalized geometric error function, the coordinates of the measuring points and the nominal profile coordinates, the ratio of the measuring error amplitude value when the machine tool measures the workpiece to the corresponding geometric error amplitude value is obtained and used as the sensitive error weight value of 21 geometric error parameters, the influence degree of each geometric error parameter on the measuring error is quantized, and a calculation basis is provided for error correction of the machine tool.
Drawings
FIG. 1 is a diagram illustrating an exemplary application of the method for calculating the error-sensitive weights for a Cartesian coordinate system profile scan measurement;
FIG. 2 is a schematic flow chart diagram illustrating a method for error-sensitive weight calculation for Cartesian coordinate system profile scan measurements, according to one embodiment;
FIG. 3 is a schematic diagram showing the relationship between 12 angle errors and measurement errors;
FIG. 4 is a schematic diagram illustrating the relationship between the X-axis positioning error and the position of the workpiece under test in one embodiment
FIG. 5 is a schematic illustration of an embodiment of an X-axis positioning error and measurement errors caused thereby;
FIG. 6 is a schematic diagram of the geometric errors of 21 items and the measurement errors caused by the geometric errors in one embodiment;
FIG. 7 is a diagram illustrating the total measurement error due to 21 geometric errors in one embodiment;
FIG. 8 is a diagram illustrating the weighting of the 9-term linear geometric errors in one embodiment;
FIG. 9 is a diagram illustrating weighting of 12-term angular geometric errors according to an embodiment;
FIG. 10 is a graph comparing a calculated geometric error weight value to an experimentally obtained geometric error weight value in one embodiment.
Detailed Description
In order to make the objects, technical solutions and advantages of the present application more apparent, the present application is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the present application and are not intended to limit the present application.
The sensitive error weight calculation method for the scanning measurement of the profile of the Cartesian coordinate system can be applied to the application environment shown in FIG. 1. Specifically, the initial position point of the measuring head is an original point O, the moving direction of a moving bridge of the machine tool is taken as an X axis, the moving direction of the sliding block along the moving bridge is taken as a Y axis, the moving direction of the measuring column along the sliding block is taken as a Z axis, and a Cartesian coordinate system O-XYZ is established. O is1X1Y1Z1Is a coordinate system established on the Y axis, O2X2Y2Z2Is a coordinate system established on the X axis, O3X3Y3Z3Is a coordinate system established in the Z axis, where xp、yp、zpIs the zero compensation distance constant of the grating ruler of the machine tool.
In one embodiment, a method for calculating the sensitive error weight for cartesian coordinate system profile scanning measurement is provided, which is illustrated by taking the method as an example applied to a machine tool in the figure, as shown in fig. 2, and includes the following steps:
step 202: and acquiring 21 geometric error parameters of the machine tool under a Cartesian coordinate system, and expressing the geometric error parameters as a normalized geometric error function.
Through the normalization process, the distribution of the 21 geometric error parameters can be kept consistent, and meanwhile, the same geometric error amplitude value is obtained. Compared with the method that geometric error parameters are expressed by a plurality of binomials, the method provided by the embodiment can enable the geometric error parameter values to be more comparable by unifying the amplitude values of the geometric errors, avoids introducing new variables, and enables the sensitive error weight values of the geometric error parameters obtained on the basis to be more accurate.
Step 204: and acquiring the nominal profile coordinate of the workpiece to be scanned and measured, inputting the normalized geometric error function and the nominal profile coordinate into a pre-constructed measurement error model, and calculating the measurement point coordinate of the workpiece. The measurement error model comprises a linearity measurement error model and an angle measurement error model. The linearity measurement error model is expressed as:
Figure BDA0002570946180000071
wherein EXX is X-axis positioning error, EYX is X-axis Y-direction straightness error, EZX is X-axis Z-direction straightness error, EXY and EZY are Y-axis X-direction and Z-direction straightness respectively, EYY is Y-axis positioning error, EXZ and EYZ are Z-axis X-direction and Y-direction straightness respectively, EZZ is Z-axis positioning error, and Deltax islinear、Δylinear、ΔzlinearRespectively, are the measurement errors of the linearity error generated in X, Y, Z three directions.
The effect of angular error on measurement error is shown in fig. 3, and the angular measurement error model is expressed as:
Figure BDA0002570946180000081
Figure BDA0002570946180000082
Figure BDA0002570946180000083
Figure BDA0002570946180000084
wherein x isp、yp、zpThe zero compensation distance constant of the grating ruler of the machine tool is provided, EAX, EBX and ECX are X-axis three-item angle errors, EAY, EBY and ECY are Y-axis three-item angle errors, EAZ, EBZ and ECZ are Z-axis three-item angle errors, AOZ, BOZ and COY are three-item verticality errors, X, Y and Z are nominal profile coordinates, and delta X is equal to that of the machine tooli、Δyi、ΔziAnd the value of i is 1 to 12, and the measurement errors generated by the angle errors in X, Y, Z are respectively.
The nominal profile coordinates refer to the external profile coordinates of the workpiece in the cartesian coordinate system established in this embodiment, which are obtained according to the external profile data of the workpiece to be scanned and measured and the placement position of the workpiece on the machine tool. The measurement error model is obtained on the basis of measuring the geometric error value of the machine tool and the corresponding measurement error value, and the adopted modeling method comprises a secondary transfer matrix and the like.
Step 206: and obtaining the sensitive error weight values of 21 geometric error parameters according to the normalized geometric error function, the coordinates of the measuring points and the nominal profile coordinates. The sensitive error weight value is the ratio of the measurement error amplitude and the corresponding geometric error amplitude when the machine tool measures the workpiece.
In particular, the sensitive error weight value of the geometric error parameter may reflect the sensitivity of the measurement error to the geometric error. The larger the sensitive error weight value is, the more sensitive the measurement error is to the geometric error, i.e. the larger the measurement error caused by the geometric error in unit value is.
According to the sensitive error weight calculation method for scanning and measuring the profile of the cartesian coordinate system, based on the measurement error model describing 21 geometric errors of the machine tool and the measurement error of the machine tool, after the 21 geometric errors of the cartesian coordinate system are normalized, the normalized geometric errors and the nominal profile coordinates of the workpiece to be scanned are input into the measurement error model, the coordinates of the measurement point of the workpiece can be calculated, and the influence of various geometric error parameters of the machine tool on the coordinates of the measurement point can be accurately reflected. In addition, according to the normalized geometric error function, the coordinates of the measuring points and the nominal profile coordinates, the ratio of the measuring error amplitude value when the machine tool measures the workpiece to the corresponding geometric error amplitude value is obtained and used as the sensitive error weight value of 21 geometric error parameters, the influence degree of each geometric error parameter on the measuring error is quantized, and a calculation basis is provided for error correction of the machine tool.
In one embodiment, the stroke of the machine tool is 1280mm × 1280mm × 720mm, and the zero compensation distance constant x of the grating ruler of the machine toolp、ypAnd zpAre all 100 mm. The workpiece to be measured is a concave spherical surface, the sphere radius of the concave spherical surface is R, and the caliber of the spherical surface is D. The method for calculating the sensitive error weight for the scanning measurement of the profile of the cartesian coordinate system provided by the embodiment comprises the following steps:
step 402: and (3) carrying out motion analysis on the machine tool under a Cartesian coordinate system, and obtaining a linearity measurement error model and an angle measurement error model of the machine tool according to the corresponding relation between the error value of the measuring point of the machine tool and the geometric error value.
Compared with a geometric error model obtained by a traditional method such as a secondary transfer matrix and the like, the geometric error model obtained by analyzing the actual motion process of the machine tool has higher accuracy and more accurate description on the relationship between the geometric error and the measurement error.
Step 404: the 21 geometric error parameters of the machine tool are acquired under a Cartesian coordinate system.
Step 406: and taking the coordinate values as variables, and expressing the geometric error parameters as Fourier series of preset amplitude values and periodic values.
The general geometric error is expressed by a polynomial, which can be expressed as a fourier series, and is expressed as:
Figure BDA0002570946180000091
where E (t) is the geometric error, t is the coordinate value associated with the geometric error, which may be X, Y or the coordinate value of the Z axis, An、ωnAnd
Figure BDA0002570946180000092
respectively, an amplitude value, an angular acceleration value and a phase error value of the nth harmonic component of the fourier series.
Step 408: the basic wavelength component of the Fourier series is taken as a normalized geometric error function.
The geometric error may be represented by a fourier series, and in order to simplify the calculation, the geometric error may be represented by a fundamental wavelength component of the fourier series in the direction of the shift coordinate axis. In addition, in order to normalize the geometric error, no other variable (for example, the amplitude of the straightness error changes after being descaled) is introduced, and the 21 geometric errors are approximately represented as fundamental wavelength components corresponding to the fourier series using the same amplitude a and angular acceleration ω, so that the amplitude PV (the difference between the maximum peak and the minimum valley) of the geometric error is 2A, and the distribution of the 21 geometric errors is the same.
Step 410: and obtaining the geometric error amplitude when the machine tool measures the workpiece according to the normalized geometric error function and the nominal profile coordinate.
Step 412: and obtaining the measurement error amplitude when the machine tool measures the workpiece according to the measurement point coordinate and the nominal profile coordinate.
Specifically, the description will be given taking as an example the calculation of the geometric error weight of the X-axis positioning Error (EXX), and fig. 4 shows the relationship between the X-axis positioning error of the machine tool and the workpiece position. Substituting the nominal profile coordinates of the workpiece into the measurement error model to obtain measurement point coordinates; by matching the nominal profile coordinates with the coordinates of the measurement points, the difference between the two, i.e. the measurement error value as shown in fig. 5, can be obtained, so that the measurement error amplitude corresponding to the X-axis positioning error is obtained to be 0.28 μm.
Similarly, it can be seen that measurement errors are affected by various geometric errors. As shown in fig. 6, lines 1 to 3 are the influence of the geometric errors of the X-axis, the Y-axis and the Z-axis, respectively, on the measurement error, and line 4 is the influence of the perpendicularity error of the 10 μ rad value on the measurement error. It can be seen that the measurement error distribution caused by the perpendicularity error is not affected by the position of the workpiece or the steepness value. Even if the magnitude of each normalized geometric error is the same, different geometric errors will result in different measurement error distributions, and the corresponding measurement error magnitudes are different. Fig. 7 is a top view of the final measurement error affected by all geometric errors.
Step 414: and obtaining the sensitive error weight values of the 21 geometric error parameters according to the ratio of the measurement error amplitude to the corresponding geometric error amplitude.
Specifically, the measurement error magnitude and corresponding geometric error magnitude ratio Q is defined as:
Figure BDA0002570946180000101
wherein E isPVIs the magnitude of the measurement error, EAVIs the magnitude of the geometric error. Q can reflect the sensitivity degree of the measurement error to the geometric error, and the larger the Q value is, the more sensitive the measurement error to the geometric error is, namely the larger the measurement error caused by the geometric error is due to the unit value. The ratio of the measurement error magnitude and the corresponding geometric error magnitude can thus be used as a sensitive error weight value for the geometric error parameter.
According to the above definition, 21 terms of geometric error weights can be obtained, wherein 9 terms of linear geometric error weights are shown in fig. 8, and 12 terms of angular geometric error weights are shown in fig. 9. The total measurement error amplitude shown in fig. 7 is 20.2 μm, and the main geometric errors causing the measurement errors are 7 items of EZX, EZY, EAX, and the like in sequence according to the order of the weighted values from large to small.
The embodiment provides a specific implementation manner for calculating the geometric error weight by using the sensitive error weight calculation method for scanning and measuring the cartesian coordinate system profile, which is provided by the application, and the method can be used for a three-axis processing machine tool and a three-axis measuring machine, and can be applied to factory detection, installation and real-time error compensation of the machine tool for processing and measuring machine tools of common planes, spherical surfaces, aspheric surfaces, free curved surfaces and high-gradient complex curved surfaces.
In order to verify the sensitive error weight calculation method for the scanning measurement of the contour of the Cartesian coordinate system, the geometric error weight calculated by using the method provided by the application is compared with the geometric error weight obtained by experiments. Specifically, geometric errors of the machine tool are obtained through actual measurement by using a laser interferometer, the actual geometric errors are brought into a top view for obtaining all the geometric errors, and geometric error weights are calculated on the basis. Fig. 10 shows the comparison between the calculation results of the geometric error weights and the experimental results. It can be seen that the difference between the two is small, so that the method provided by the application has higher reliability and can be applied to error compensation of a measuring machine.
It should be understood that, although the steps in the flowchart of fig. 2 are shown in order as indicated by the arrows, the steps are not necessarily performed in order as indicated by the arrows. The steps are not performed in the exact order shown and described, and may be performed in other orders, unless explicitly stated otherwise. Moreover, at least a portion of the steps in fig. 2 may include multiple sub-steps or multiple stages that are not necessarily performed at the same time, but may be performed at different times, and the order of performance of the sub-steps or stages is not necessarily sequential, but may be performed in turn or alternately with other steps or at least a portion of the sub-steps or stages of other steps.
A sensitive error weight calculation device for cartesian coordinate system profile scan measurements, the device comprising:
and the normalized geometric error function construction module is used for acquiring 21 geometric error parameters of the machine tool in a Cartesian coordinate system and expressing the geometric error parameters as a normalized geometric error function.
And the measuring point coordinate function building module is used for obtaining the nominal profile coordinates of the workpiece to be scanned and measured, inputting the normalized geometric error function and the nominal profile coordinates into a pre-built measuring error model, and calculating the measuring point coordinates of the workpiece. The measurement error model comprises a linearity measurement error model and an angle measurement error model, and the linearity measurement error model is expressed as:
Figure BDA0002570946180000111
wherein EXX is X-axis positioning error, EYX is X-axis Y-direction straightness error, EZX is X-axis Z-direction straightness error, EXY and EZY are Y-axis X-direction and Z-direction straightness respectively, EYY is Y-axis positioning error, EXZ and EYZ are Z-axis X-direction and Y-direction straightness respectively, EZZ is Z-axis positioning error, and Deltax islinear、Δylinear、ΔzlinearRespectively, are the measurement errors of the linearity error generated in X, Y, Z three directions.
The angle measurement error model is expressed as:
Figure BDA0002570946180000121
Figure BDA0002570946180000122
Figure BDA0002570946180000123
Figure BDA0002570946180000124
wherein x isp、yp、zpThe zero compensation distance constant of the grating ruler of the machine tool is provided, EAX, EBX and ECX are X-axis three-item angle errors, EAY, EBY and ECY are Y-axis three-item angle errors, EAZ, EBZ and ECZ are Z-axis three-item angle errors, AOZ, BOZ and COY are three-item verticality errors, X, Y and Z are nominal profile coordinates, and delta X is equal to that of the machine tooli、Δyi、ΔziAnd the value of i is 1 to 12, and the measurement errors generated by the angle errors in X, Y, Z are respectively.
And the sensitive error weight value calculation module is used for obtaining the sensitive error weight values of 21 geometric error parameters according to the normalized geometric error function, the measurement point coordinates and the nominal contour coordinates. The sensitive error weight value is the ratio of the measurement error amplitude and the corresponding geometric error amplitude when the machine tool measures the workpiece.
In one embodiment, the sensitive error weight value calculation module is configured to:
and obtaining the geometric error amplitude when the machine tool measures the workpiece according to the normalized geometric error function and the nominal profile coordinate.
And obtaining the measurement error amplitude when the machine tool scans and measures the workpiece according to the measurement point coordinate function and the nominal profile coordinate.
And obtaining the sensitive error weight values of the 21 geometric error parameters according to the ratio of the measurement error amplitude to the corresponding geometric error amplitude.
In one embodiment, the normalized geometric error function construction module is configured to:
the method comprises the steps of obtaining 21 geometric error parameters of the machine tool under a Cartesian coordinate system, taking coordinate values as variables, and representing the geometric error parameters as Fourier series of preset amplitude values and periodic values.
The basic wavelength component of the Fourier series is taken as a normalized geometric error function.
In one embodiment, the method further includes a measurement error model building module, configured to:
and (3) carrying out motion analysis on the machine tool under a Cartesian coordinate system, and obtaining a linearity measurement error model and an angle measurement error model of the machine tool according to the corresponding relation between the error value of the measuring point of the machine tool and the geometric error value.
For specific limitations of the error-sensitive weight calculation apparatus for cartesian coordinate system profile scan measurement, reference may be made to the above limitations of the error-sensitive weight calculation method for cartesian coordinate system profile scan measurement, which are not described herein again. The various modules in the sensitive error weight calculation apparatus for cartesian coordinate system profile scan measurement described above may be implemented in whole or in part by software, hardware, and combinations thereof. The modules can be embedded in a hardware form or independent from a processor in the computer device, and can also be stored in a memory in the computer device in a software form, so that the processor can call and execute operations corresponding to the modules.
In one embodiment, a machine error compensation device is provided, which includes a memory and a processor, the memory storing a computer program, wherein the processor when executing the computer program implements the following steps, outputting a sensitive error weight value of 21 geometric error parameters, and performing machine error compensation according to the sensitive error weight value:
and acquiring 21 geometric error parameters of the machine tool under a Cartesian coordinate system, and expressing the geometric error parameters as a normalized geometric error function. And acquiring the nominal profile coordinate of the workpiece to be scanned and measured, inputting the normalized geometric error function and the nominal profile coordinate into a pre-constructed measurement error model, and calculating the measurement point coordinate of the workpiece. The measurement error model comprises a linearity measurement error model and an angle measurement error model. The linearity measurement error model is expressed as:
Figure BDA0002570946180000131
wherein EXX is X-axis positioning error, EYX is X-axis Y-direction straightness error, EZX is X-axis Z-direction straightness error, EXY and EZY are Y-axis X-direction and Z-direction straightness respectively, EYY is Y-axis positioning error, EXZ and EYZ are Z-axis X-direction and Y-direction straightness respectively, EZZ is Z-axis positioning error, and Deltax islinear、Δylinear、ΔzlinearRespectively, are the measurement errors of the linearity error generated in X, Y, Z three directions.
The angle measurement error model is expressed as:
Figure BDA0002570946180000141
Figure BDA0002570946180000142
Figure BDA0002570946180000143
Figure BDA0002570946180000144
wherein x isp、yp、zpThe zero compensation distance constant of the grating ruler of the machine tool is provided, EAX, EBX and ECX are X-axis three-item angle errors, EAY, EBY and ECY are Y-axis three-item angle errors, EAZ, EBZ and ECZ are Z-axis three-item angle errors, AOZ, BOZ and COY are three-item verticality errors, X, Y and Z are nominal profile coordinates, and delta X is equal to that of the machine tooli、Δyi、ΔziAnd the value of i is 1 to 12, and the measurement errors generated by the angle errors in X, Y, Z are respectively.
And obtaining 21 geometric error weight values according to the normalized geometric error function, the coordinates of the measuring points and the nominal outline coordinates. The sensitive error weight value of the geometric error parameter is the ratio of the measurement error amplitude value when the machine tool measures the workpiece to the corresponding geometric error amplitude value.
In one embodiment, the processor, when executing the computer program, further performs the steps of: and obtaining the geometric error amplitude when the machine tool measures the workpiece according to the normalized geometric error function and the nominal profile coordinate. And obtaining the measurement error amplitude when the machine tool measures the workpiece according to the measurement point coordinate and the nominal profile coordinate. And obtaining the sensitive error weight values of the 21 geometric error parameters according to the ratio of the measurement error amplitude to the corresponding geometric error amplitude.
In one embodiment, the processor, when executing the computer program, further performs the steps of: the 21 geometric error parameters of the machine tool are acquired under a Cartesian coordinate system. And taking the coordinate values as variables, and expressing the geometric error parameters as Fourier series of preset amplitude values and periodic values. The basic wavelength component of the Fourier series is taken as a normalized geometric error function.
In one embodiment, the processor, when executing the computer program, further performs the steps of: and (3) carrying out motion analysis on the machine tool under a Cartesian coordinate system, and obtaining a linearity measurement error model and an angle measurement error model of the machine tool according to the corresponding relation between the error value of the measuring point of the machine tool and the geometric error value.
In one embodiment, a computer-readable storage medium is provided, on which a computer program is stored, which when executed by a processor performs the following steps, outputting a sensitive error weight value for 21 geometric error parameters, and performing machine error compensation according to the sensitive error weight value:
and acquiring 21 geometric error parameters of the machine tool under a Cartesian coordinate system, and expressing the geometric error parameters as a normalized geometric error function.
And acquiring the nominal profile coordinate of the workpiece to be scanned and measured, inputting the normalized geometric error function and the nominal profile coordinate into a pre-constructed measurement error model, and calculating the measurement point coordinate of the workpiece. The measurement error model comprises a linearity measurement error model and an angle measurement error model. The linearity measurement error model is expressed as:
Figure BDA0002570946180000151
wherein EXX is X-axis positioning error, EYX is X-axis Y-direction straightness error, EZX is X-axis Z-direction straightness error, EXY and EZY are Y-axis X-direction and Z-direction straightness respectively, EYY is Y-axis positioning error, EXZ and EYZ are Z-axis X-direction and Y-direction straightness respectively, EZZ is Z-axis positioning error, and Deltax islinear、Δylinear、ΔzlinearRespectively, are the measurement errors of the linearity error generated in X, Y, Z three directions.
The angle measurement error model is expressed as:
Figure BDA0002570946180000152
Figure BDA0002570946180000153
Figure BDA0002570946180000154
Figure BDA0002570946180000155
wherein x isp、yp、zpThe zero compensation distance constant of the grating ruler of the machine tool is provided, EAX, EBX and ECX are X-axis three-item angle errors, EAY, EBY and ECY are Y-axis three-item angle errors, EAZ, EBZ and ECZ are Z-axis three-item angle errors, AOZ, BOZ and COY are three-item verticality errors, X, Y and Z are nominal profile coordinates, and delta X is equal to that of the machine tooli、Δyi、ΔziAnd the value of i is 1 to 12, and the measurement errors generated by the angle errors in X, Y, Z are respectively.
And obtaining 21 geometric error weight values according to the normalized geometric error function, the coordinates of the measuring points and the nominal outline coordinates. The sensitive error weight value of the geometric error parameter is the ratio of the measurement error amplitude value when the machine tool measures the workpiece to the corresponding geometric error amplitude value.
In one embodiment, the computer program when executed by the processor further performs the steps of: and obtaining the geometric error amplitude when the machine tool measures the workpiece according to the normalized geometric error function and the nominal profile coordinate. And obtaining the measurement error amplitude when the machine tool measures the workpiece according to the measurement point coordinate and the nominal profile coordinate. And obtaining the sensitive error weight values of the 21 geometric error parameters according to the ratio of the measurement error amplitude to the corresponding geometric error amplitude.
In one embodiment, the computer program when executed by the processor further performs the steps of: the 21 geometric error parameters of the machine tool are acquired under a Cartesian coordinate system. And taking the coordinate values as variables, and expressing the geometric error parameters as Fourier series of preset amplitude values and periodic values. The basic wavelength component of the Fourier series is taken as a normalized geometric error function.
In one embodiment, the computer program when executed by the processor further performs the steps of: and (3) carrying out motion analysis on the machine tool under a Cartesian coordinate system, and obtaining a linearity measurement error model and an angle measurement error model of the machine tool according to the corresponding relation between the error value of the measuring point of the machine tool and the geometric error value.
It will be understood by those skilled in the art that all or part of the processes of the methods of the embodiments described above can be implemented by hardware instructions of a computer program, which can be stored in a non-volatile computer-readable storage medium, and when executed, can include the processes of the embodiments of the methods described above. Any reference to memory, storage, database, or other medium used in the embodiments provided herein may include non-volatile and/or volatile memory, among others. Non-volatile memory can include read-only memory (ROM), Programmable ROM (PROM), Electrically Programmable ROM (EPROM), Electrically Erasable Programmable ROM (EEPROM), or flash memory. Volatile memory can include Random Access Memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in a variety of forms such as Static RAM (SRAM), Dynamic RAM (DRAM), Synchronous DRAM (SDRAM), Double Data Rate SDRAM (DDRSDRAM), Enhanced SDRAM (ESDRAM), Synchronous Link DRAM (SLDRAM), Rambus Direct RAM (RDRAM), direct bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM).
The technical features of the above embodiments can be arbitrarily combined, and for the sake of brevity, all possible combinations of the technical features in the above embodiments are not described, but should be considered as the scope of the present specification as long as there is no contradiction between the combinations of the technical features.
The above-mentioned embodiments only express several embodiments of the present application, and the description thereof is more specific and detailed, but not construed as limiting the scope of the invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the concept of the present application, which falls within the scope of protection of the present application. Therefore, the protection scope of the present patent shall be subject to the appended claims.

Claims (10)

1. A method of sensitive error weight calculation for cartesian coordinate system profile scan measurements, the method comprising:
obtaining 21 geometric error parameters of a machine tool under a Cartesian coordinate system, and expressing the geometric error parameters as a normalized geometric error function;
acquiring a nominal profile coordinate of a workpiece to be scanned and measured, inputting the normalized geometric error function and the nominal profile coordinate into a pre-constructed measurement error model, and calculating a measurement point coordinate of the workpiece; the measurement error model comprises a linearity measurement error model and an angle measurement error model, and the linearity measurement error model is expressed as:
Figure FDA0002570946170000011
wherein EXX is X-axis positioning error, EYX is X-axis Y-direction straightness error, EZX is X-axis Z-direction straightness error, EXY and EZY are Y-axis X-direction and Z-direction straightness respectively, EYY is Y-axis positioning error, EXZ and EYZ are Z-axis X-direction and Y-direction straightness respectively, EZZ is Z-axis positioning error, and Deltax islinear、Δylinear、ΔzlinearRespectively measuring errors generated by linearity errors in X, Y, Z three directions;
the angle measurement error model is expressed as:
(a)
Figure FDA0002570946170000012
(b)
Figure FDA0002570946170000013
(c)
Figure FDA0002570946170000014
(d)
Figure FDA0002570946170000015
(e)
Figure FDA0002570946170000016
(f)
Figure FDA0002570946170000017
(h)
Figure FDA0002570946170000018
(i)
Figure FDA0002570946170000019
(j)
Figure FDA00025709461700000110
(k)
Figure FDA00025709461700000111
(m)
Figure FDA00025709461700000112
(n)
Figure FDA00025709461700000113
wherein x isp、yp、zpThe zero point compensation distance constant of the grating ruler of the machine tool is obtained by taking EAX, EBX and ECX as X-axis three-item angle errors, EAY, EBY and ECY as Y-axis three-item angle errors, EAZ, EBZ and ECZ as Z-axis three-item angle errors, AOZ, BOZ and COY as three-item verticality errors, X, Y and Z are the nominal profile coordinates, and delta X and COY are the nominal profile coordinatesi、Δyi、ΔziThe value of i is 1 to 12, which are the measurement errors generated by the angle error in X, Y, Z three directions respectively;
obtaining a sensitive error weight value of 21 geometric error parameters according to the normalized geometric error function, the coordinates of the measuring points and the nominal outline coordinates; and the sensitive error weight value is the ratio of the measurement error amplitude to the corresponding geometric error amplitude when the machine tool measures the workpiece.
2. The method of claim 1, wherein the step of deriving a sensitive error weight value for 21 geometric error parameters from the normalized geometric error function, the measurement point coordinates, and the nominal profile coordinates comprises:
obtaining the geometric error amplitude when the machine tool scans and measures the workpiece according to the normalized geometric error function and the nominal profile coordinate;
obtaining a measurement error amplitude when the machine tool scans and measures the workpiece according to the measurement point coordinate and the nominal profile coordinate;
and obtaining the sensitive error weight value of 21 geometric error parameters according to the ratio of the measurement error amplitude to the corresponding geometric error amplitude.
3. The method according to claim 1, wherein the step of obtaining 21 geometric error parameters of the machine tool in a cartesian coordinate system, the step of representing the geometric error parameters as a normalized geometric error function comprises:
obtaining 21 geometric error parameters of the machine tool under a Cartesian coordinate system;
taking the coordinate values as variables, and expressing the geometric error parameters as Fourier series of preset amplitude values and periodic values;
and taking the basic wavelength component of the Fourier series as a normalized geometric error function.
4. The method according to any one of claims 1 to 3, wherein the measurement error model is constructed in a manner that includes:
and carrying out motion analysis on the machine tool under a Cartesian coordinate system, and obtaining a linearity measurement error model and an angle measurement error model of the machine tool according to the corresponding relation between the measurement point error value and the geometric error value of the machine tool.
5. A sensitive error weight calculation device for cartesian coordinate system profile scan measurements, the device comprising:
the normalized geometric error function building module is used for acquiring 21 geometric error parameters of the machine tool in a Cartesian coordinate system and expressing the geometric error parameters as a normalized geometric error function;
a measuring point coordinate function building module for obtaining the nominal contour coordinate of the workpiece to be scanned and measured
Inputting the normalized geometric error function and the nominal profile coordinate into a pre-constructed measurement error model, and calculating the measurement point coordinate of the workpiece; the measurement error model comprises a linearity measurement error model and an angle measurement error model, and the linearity measurement error model is expressed as:
Figure FDA0002570946170000031
wherein EXX is X-axis positioning error, EYX is X-axis Y-direction straightness error, EZX is X-axis Z-direction straightness error, EXY and EZY are Y-axis X-direction and Z-direction straightness respectively, EYY is Y-axis positioning error, EXZ and EYZ are Z-axis X-direction and Y-direction straightness respectively, EZZ is Z-axis positioning error, and Deltax islinear、Δylinear、ΔzlinearRespectively measuring errors generated by linearity errors in X, Y, Z three directions;
the angle measurement error model is expressed as:
(a)
Figure FDA0002570946170000032
(b)
Figure FDA0002570946170000033
(c)
Figure FDA0002570946170000034
(d)
Figure FDA0002570946170000035
(e)
Figure FDA0002570946170000036
(f)
Figure FDA0002570946170000037
(h)
Figure FDA0002570946170000038
(i)
Figure FDA0002570946170000039
(j)
Figure FDA00025709461700000310
(k)
Figure FDA00025709461700000311
(m)
Figure FDA00025709461700000312
(n)
Figure FDA00025709461700000313
wherein x isp、yp、zpThe zero point compensation distance constant of the grating ruler of the machine tool is obtained by taking EAX, EBX and ECX as X-axis three-item angle errors, EAY, EBY and ECY as Y-axis three-item angle errors, EAZ, EBZ and ECZ as Z-axis three-item angle errors, AOZ, BOZ and COY as three-item verticality errors, X, Y and Z are the nominal profile coordinates, and delta X and COY are the nominal profile coordinatesi、Δyi、ΔziThe value of i is 1 to 12, which are the measurement errors generated by the angle error in X, Y, Z three directions respectively;
the sensitive error weight value calculation module is used for obtaining the sensitive error weight values of 21 geometric error parameters according to the normalized geometric error function, the measurement point coordinates and the nominal contour coordinates; and the sensitive error weight value is the ratio of the measurement error amplitude value to the corresponding geometric error amplitude value when the machine tool scans and measures the workpiece.
6. The apparatus of claim 5, wherein the sensitive error weight value calculation module is configured to:
obtaining the geometric error amplitude when the machine tool scans and measures the workpiece according to the normalized geometric error function and the nominal profile coordinate;
obtaining a measurement error amplitude when the machine tool scans and measures the workpiece according to the measurement point coordinate function and the nominal profile coordinate;
and obtaining the sensitive error weight value of 21 geometric error parameters according to the ratio of the measurement error amplitude to the corresponding geometric error amplitude.
7. The apparatus of claim 5, wherein the normalized geometric error function construction module is configured to:
obtaining 21 geometric error parameters of the machine tool under a Cartesian coordinate system;
taking the coordinate values as variables, and expressing the geometric error parameters as Fourier series of preset amplitude values and periodic values;
and taking the basic wavelength component of the Fourier series as a normalized geometric error function.
8. The apparatus of any one of claims 5 to 7, further comprising a measurement error model building module configured to:
and carrying out motion analysis on the machine tool under a Cartesian coordinate system, and obtaining a linearity measurement error model and an angle measurement error model of the machine tool according to the corresponding relation between the measurement point error value and the geometric error value of the machine tool.
9. A machine error compensator apparatus comprising a memory and a processor, the memory storing a computer program, wherein the processor when executing the computer program implements the steps of the method according to any of claims 1 to 4, outputs a sensitive error weight value for 21 geometric error parameters, and performs machine error compensation according to the sensitive error weight value.
10. A computer-readable storage medium, on which a computer program is stored, which, when being executed by a processor, carries out the steps of the method according to one of claims 1 to 4, outputs a sensitive error weight value for 21 geometric error parameters, and carries out a machine error compensation in accordance with the sensitive error weight value.
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