CN118463807B - Marble platform movement position temperature error calibration and compensation method and system - Google Patents
Marble platform movement position temperature error calibration and compensation method and system Download PDFInfo
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Abstract
The invention relates to the technical field of error compensation, and discloses a marble platform movement position temperature error calibration and compensation method and system, wherein the calibration method comprises the following steps: constructing an error model based on measuring the motion position of the grating ruler: e=a×p (t-t 0)+B(t-t0); moving the axes from the origin at equal intervals at the temperature t 0 and the different temperatures t, recording the measured value and the actual position of the grating ruler at the movement position, and obtaining the temperature t 0 and the actual position errors at the different temperatures t according to the measured value and the actual position of the grating ruler; determining the values of A and B based on the error model and the actual position error fit; and calculating the actual position error e at each temperature according to an error model formula, and completing calibration. The scheme is used for processing errors influenced by temperature, and the values calculated according to the model can be used for compensating errors caused by most of temperature changes, so that the errors can be reduced to within 25% of the maximum errors in a certain temperature change range.
Description
Technical Field
The invention relates to the technical field of error compensation, in particular to a marble platform movement position temperature error calibration and compensation method and system.
Background
The marble has the characteristics of uniform texture, good stability, high strength, high hardness, extremely wear resistance, acid resistance, alkali resistance, very high corrosion resistance, no rust and capability of keeping the precision under heavy load. Conventionally, the marble Dan Pingtai used in industrial production and laboratories is derived from a layer of rock of good quality under the ground, which has failed naturally for hundreds of millions of years without internal stress. In addition, the marble non-metallic material has no magnetic reaction or plastic deformation, so the precision retention is good, the performance is superior to that of precision measurement reference parts made of high-quality cast iron and steel, and the high and stable precision can be obtained. Thus, the marble platform is generally used as a machine for high-precision equipment for producing high-precision automation equipment or providing a high-precision inspection reference because of its easy processing, good flatness, no internal stress, etc.
However, the materials have thermal expansion and contraction, and in precision machining, the temperature problem is not ignored. Temperature is a precise adversary and the heat generated by the room temperature and the machine itself can change shape and length. The specific amount of expansion and contraction of the material depends on the material and the change value of temperature. For example, when the length of a steel material is linearly expanded to a length of 12 μm per meter at a temperature of 1 ℃, stable machining accuracy can be obtained only in a stable temperature environment and a thermal equilibrium state even in a high-precision machine tool. The marble platform also has the problems described above, and the marble can maintain the straightness and flatness of μm level in a constant temperature state; however, marble has a thermal expansion coefficient of 6.8 μm/(mK) so that its thermal expansion is remarkable, and when the ambient temperature and the stage temperature are changed, the accuracy is directly lowered drastically. In addition, the position measuring sensor commonly used for marble platforms also has thermal expansion, for example, the grating scale has a thermal expansion coefficient of 12 μm/(mK), and the sensor is also affected by significant temperature changes.
To overcome the deformation errors of marble platforms caused by thermal expansion, the existing methods generally have two directions: one direction is to establish a complete constant temperature system, reform the factory environment and inhibit the temperature change of the working environment; the specific platform is subjected to heat radiation design and a heat radiation system is added, and the platform is controlled to generate heat; this method is generally costly and complicated to operate. The other direction is to use temperature compensation, but this approach typically requires accumulating a large amount of data, and performing interpolation and complex nonlinear calculations to compensate for temperature.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides a method and a system for calibrating and compensating the temperature error of the movement position of a marble platform, which overcome the problem of error increase caused by different temperatures to a large extent and ensure that the accuracy of the movement position of the marble platform in a certain temperature change range does not generate obvious change.
In order to achieve the above object, a first aspect of the present invention provides a marble platform movement position temperature error calibration method, comprising the steps of:
An error model based on the measuring motion position of the grating ruler is constructed, and the formula is as follows: e=a×p (t-t 0)+B(t-t0), where a is a position coefficient, B is a position bias coefficient, p is a target position of the platform movement, t is an actual temperature of a current grating ruler measurement position, t 0 is an initial reference temperature, and e is an actual position error caused by the temperature;
Moving the axes from the origin at equal intervals at the temperature t 0 and the different temperatures t, recording the measured value and the actual position of the grating ruler at the movement position, and obtaining the temperature t 0 and the actual position errors at the different temperatures t according to the measured value and the actual position of the grating ruler;
determining the values of A and B based on the error model and the actual position error fit;
And calculating the actual position error e at each temperature according to an error model formula for error compensation, and completing calibration.
The second aspect of the present invention provides a temperature compensation method for a marble platform movement position, after an error e is obtained by the calibration method, the error e is compensated to a preset target position p r, and the calculation formula is as follows: p r = p-e, the axis of the stage is moved to the actual target position, and the actual position of the axis of the stage is kept consistent with the actual position at the initial temperature.
A third aspect of the present invention provides a marble platform movement position temperature compensation system, comprising:
The error model module is used for constructing an error model based on the measuring motion position of the grating ruler, and the formula is as follows: e=a×p (t-t 0)+B(t-t0), where a is a position coefficient, B is a position bias coefficient, p is a target position of the platform movement, t is an actual temperature of a current grating ruler measurement position, t 0 is an initial reference temperature, and e is an actual position error caused by the temperature;
The position measurement module is used for respectively moving the axes from the origin at equal intervals at the temperature t 0 and the different temperatures t, recording the measured value and the actual position of the grating ruler at the movement position, and obtaining the actual position errors at the temperature t 0 and the different temperatures t at the different temperatures t according to the measured value and the actual position of the grating ruler;
the fitting module is used for fitting the error model and the actual position error to determine the values of A and B;
and the compensation module is used for driving the axis of the platform to move at the temperature t, calculating a corresponding error e by the error model, compensating the error e into a preset target position, and enabling the axis of the platform to move to an actual target position.
A fourth aspect of the application provides a machine-readable storage medium having stored thereon instructions for causing a machine to perform the calibration method of the application as described above.
A fifth aspect of the present invention provides a processor for executing a program, wherein the program is executed to perform: the temperature compensation method for the marble platform movement position comprises the steps.
A sixth aspect of the present invention provides a marble stage movement position temperature compensation stage, comprising a marble stage, a grating ruler, an interferometer and a temperature measurement device,
The grating ruler is respectively arranged on an X axis and a Y axis of the marble platform and is used for acquiring position coordinates of the X axis and the Y axis;
The interferometer is used for measuring the actual positions of the XY axes at different temperatures respectively, so that the position change caused by the temperature can be obtained;
the temperature measuring device is used for measuring the temperature of the installation position of the grating ruler.
According to the error caused by temperature change of the marble platform and the grating ruler, an error calculation model is provided; the model processes the errors influenced by the temperature, and the values obtained by calculation according to the model can be used for compensating the errors caused by most of temperature changes, so that the errors can be reduced to within 25% of the maximum errors in a certain temperature change range; the scheme is simple and easy to realize, and can be realized by building a simple platform; the calibration is carried out once, and the stability of the precision can be ensured based on the calibration result; in addition, the calculation is simple, the calculation time is short, complex nonlinear calculation is not needed to be carried out by accumulating a large amount of data, and the requirement of the marble platform on the environmental temperature is effectively reduced.
Additional features and advantages of embodiments of the invention will be set forth in the detailed description which follows.
Drawings
The accompanying drawings are included to provide a further understanding of embodiments of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain, without limitation, the embodiments of the invention. In the drawings:
FIG. 1 is a schematic diagram of a marble platform motion position temperature error compensation platform structure of the present invention;
FIG. 2 is a schematic diagram of error analysis performed on an X-axis structure according to an embodiment of the present invention;
FIG. 3 is a flow chart of a method for calibrating and compensating temperature errors at a movement position of a marble platform according to an embodiment of the invention;
FIG. 4 is a schematic diagram of a test case temperature compensation use and verification process according to the present invention;
FIG. 5 is a graph showing the error at various temperatures at various locations of the test case compensation platform of the present invention;
FIG. 6 shows the error after compensation according to the test example of the present invention.
Detailed Description
The following describes the detailed implementation of the embodiments of the present invention with reference to the drawings. It should be understood that the detailed description and specific examples, while indicating and illustrating the invention, are not intended to limit the invention.
The marble platform structure is shown in fig. 1, a marble base is fixed on a supporting structure, and then a Y-axis is arranged on the marble base, wherein the Y-axis consists of a grating ruler, a guide rail, a linear motor and a Y-axis marble; an X axis is arranged on the Y axis, and consists of a grating ruler, a guide rail, a linear motor and an X-axis marble; other workloads can be carried on the X-axis platform, and XY plane movement is achieved with the workloads. It should be noted that, the embodiments of the present invention are described by taking the above marble platform structure as an example, and the structure to which the present invention is applicable is not limited to the above marble platform structure, but may be a structure in which the X axis is located below the Y axis, or a marble platform including a Z axis structure, etc.
At a fixed temperature, the precision of the marble platform can meet certain requirements; however, after temperature change, the accuracy cannot meet the index requirement. Colloquially, when the marble platform X is moved 10.000mm, the actual exact spatial displacement is not necessarily exact, which may be 10.020mm or other values, and therefore requires compensation; furthermore, if the temperature changes, the actual position may further change to 10.050mm.
Taking the X-axis structure for error analysis as an example (Y-axis equivalent), as shown in fig. 2, error analysis was performed with respect to the model shown in fig. 2. When the platform is used, the platform returns to the original position, and then all positions take the original point as a reference. Then, the upper computer control shaft moves to a desired position, and the position is based on the grating ruler. The model of fig. 2 shows that the mounting of the grating ruler is not ideal, such as inclination in the drawing, or partial wave shape, etc., which can lead to incorrect true position; in addition, the motor continuously generates heat in continuous operation, so that temperature change can be caused, and the ambient temperature can rise and fall along with time; the measured value of the grating ruler can be further changed along with the thermal expansion or contraction of the ruler and the thermal expansion or contraction of marble, and errors of the real position can be further increased.
Based on the above description, it can be known that the stage needs to compensate for both the error of the grating ruler itself and the error caused by temperature in order to run to an accurate position. The embodiment of the invention provides a temperature error calibration method for a marble platform movement position, which is used for temperature error compensation, and as shown in fig. 3, comprises the following steps:
S1, constructing an error model based on measuring a motion position by a grating ruler, wherein the formula is as follows: e=a×p (t-t 0)+B(t-t0), where a is a position coefficient, B is a position bias coefficient, p is a target position of the platform movement, t is an actual temperature of a current grating ruler measurement position, t 0 is an initial reference temperature, and e is an actual position error caused by the temperature;
S2, respectively moving the axes from the original point at equal intervals at the temperature t 0 and the different temperatures t, recording the measured value and the actual position of the grating ruler at the movement position, and obtaining the actual position errors at the temperature t 0 and the different temperatures t at the different temperatures t according to the measured value and the actual position of the grating ruler;
S3, determining the values of A and B based on an error model and actual position error fitting;
S4, calculating the actual position error e at each temperature according to an error model formula, and completing calibration.
Further, in step S2, the axes are moved from the origin at equal intervals at the temperature t 0 and the different temperatures t, and the measured value and the actual position of the moving position grating ruler are recorded, and the process is as follows:
Firstly, measuring an actual position by adopting an interferometer, measuring a platform coordinate position by adopting a grating ruler, returning a machine to the original position, and synchronizing the platform coordinate position and the interferometer position;
Moving the axes at fixed intervals, recording the interferometer position and the platform position at the moment, and recording the current temperature t 0;
continuously and repeatedly operating the platform to generate temperature rise on the platform;
repeating steps 2) -3) at the current temperature after operation;
Data for n different positions at m temperatures are obtained.
Subtracting the two measured values of the interferometer value and the platform position to obtain an actual error value.
Taking t 0 as an initial temperature and the actual error values at different positions at t 0 as initial error values; subtracting t 0 from each temperature value to obtain a temperature difference, and subtracting the initial error value from each error value to obtain a new error value; thus obtaining the temperature difference and the change of the position error caused by the temperature difference.
Further, in step S3, the determining the values of a and B based on the error model and the actual position error fitting is as follows:
the measured changes in the m temperature differences and the errors at the n locations are recorded as follows:
the temperature difference is an independent variable, and the sign is:
；
The position error is a dependent variable, and the sign is:
；
The dependent variable t s expands to become t:
；
Calculating a coefficient matrix theta s:
；
taking the part with the '2' of the result inner corner mark to form a slope matrix theta as a new dependent variable
；
New argument is set platform positionThe argument p s extends to p 0:
；
Then there is a final coefficient calculation method:
。
the coefficients A and B can be obtained by calculation, and a calculation formula can be obtained after substituting the coefficients A and B into an error model. And A, B and t 0 can be obtained, the model can be determined, and the error value e is calculated based on the model.
Based on the same inventive concept, a second aspect of the present invention provides a marble platform movement position temperature compensation method, after obtaining an error value e by adopting the above marble platform movement position temperature calibration method, performing compensation calculation based on the error, and compensating e to a preset target position p r , wherein p r =p-e
The axis of the platform is moved to the actual target position p r.
The temperature induced errors may be compensated for in large part, illustratively from a maximum error of over 30 microns to a maximum error value of within 5 microns.
According to the technical scheme, the first-order model calculation is used, after the model is built, each position can be directly brought into calculation, the compensation value of the whole length can be obtained without other additional interpolation or nonlinear calculation, the calculation is simple, and the calculation time is short; the compensation method can continuously ensure the precision after being separated from the temperature control environment, greatly reduce the high requirement of marble on the environmental temperature control in order to exert the highest precision, reduce the use cost to a certain extent and reduce the requirement on the temperature control capability of a factory.
Based on the same inventive concept, a third aspect of the embodiments of the present invention provides a marble platform movement position temperature compensation system, comprising:
The error model module is used for constructing an error model based on the measuring motion position of the grating ruler, and the formula is as follows: e=a×p (t-t 0)+B(t-t0), where a is a position coefficient, B is a position bias coefficient, p is a target position of the platform movement, t is an actual temperature of a current grating ruler measurement position, t 0 is an initial reference temperature, and e is an actual position error caused by the temperature;
The position measurement module is used for respectively moving the axes from the origin at equal intervals at the temperature t 0 and the different temperatures t, recording the measured value and the actual position of the grating ruler at the movement position, and obtaining the actual position errors at the temperature t 0 and the different temperatures t at the different temperatures t according to the measured value and the actual position of the grating ruler;
the fitting module is used for fitting the error model and the actual position error to determine the values of A and B;
and the compensation module is used for driving the axis of the platform to move at the temperature t, calculating a corresponding error e by the error model, compensating the error e into a preset target position, and enabling the axis of the platform to move to an actual target position.
Based on the same inventive concept, a fourth aspect of the present invention provides a marble stage movement position temperature compensation platform, as shown in fig. 2, comprising a marble stage, a grating ruler, an interferometer and a temperature measurement device,
The grating ruler is respectively arranged on an X axis and a Y axis of the marble platform and is used for acquiring position coordinates of the X axis and the Y axis;
An interferometer for measuring the actual positions at different temperatures of the XY axes, respectively, so that a temperature-induced positional change can be obtained.
And the temperature measuring equipment is used for measuring the temperature of the installation position of the grating ruler.
Further, the method further comprises a processor for executing the marble stage movement position temperature compensation method according to the data of the grating ruler, the interferometer and the temperature measuring device. The interferometer is preferably a laser interferometer.
The platform provided by the invention has the advantages of simple structure, easiness in operation, one-time calibration, and capability of ensuring the temperature stability of precision based on a calibration result.
Firstly, building and arranging a set of system, wherein a marble base is fixed on a supporting structure, and then a Y-axis is arranged on the marble base, wherein the Y-axis consists of a grating ruler, a guide rail, a linear motor and a Y-axis marble; an X axis is arranged on the Y, and consists of a grating ruler, a guide rail, a linear motor and an X-axis marble; other workloads can be carried on the X platform, and XY plane movement is achieved with the workloads.
According to the invention, a temperature compensation mathematical model is constructed, and then model coefficients are obtained by calculation based on error and temperature difference data, so that the temperature drift of the position can be suppressed by using the model, and further an accurate movement position can be obtained. The detailed process comprises the following steps: firstly, based on a two-dimensional XY marble platform, correcting the temperature error of one dimension; in the dimension, an optical system for interferometer measurement is added to measure the actual position, and meanwhile, a temperature probe is added at the installation position of the grating ruler; then, after the platform returns to the original state, synchronizing the interferometer and the platform position data, and recording the current temperature; then, equidistant movement is carried out from the origin, the interferometer positions and the platform positions of a plurality of points are measured, and the interferometer measured values and the platform position errors are calculated; then, carrying out long-time platform movement to heat the platform, raising the ambient temperature, repeating the measurement for more than one time, and recording temperature and error data; after a plurality of groups of data are recorded, the coefficient calculation is carried out by using the calculation method of the invention, and the final calculation formula is formed after the coefficient calculation is substituted into a model; the other dimension may be treated in the same way.
Based on the same inventive concept, a fifth aspect of the embodiments of the present application provides a machine-readable storage medium having instructions stored thereon for causing a machine to perform the above-mentioned method for calibrating a temperature error of a moving position of a marble platform according to the present application.
Based on the same inventive concept, a sixth aspect of the embodiments of the present invention proposes a processor for running a program, wherein the program is executed to perform the steps of the above-mentioned marble platform movement position temperature compensation method.
Test example:
The flow shown in fig. 4 is tested, and the temperature compensation platform is based on the movement position of the marble platform shown in fig. 1, and the errors at different temperatures at each position of the compensation platform are tested first as shown in fig. 5. The error after test compensation is carried out by adopting the marble platform movement position temperature compensation method of the invention, and the result is shown in figure 6. In the figure, the series 1-9 are represented as 9 position points, the abscissa is the temperature difference, and the temperature difference is obtained by subtracting t 0 from each temperature value; the ordinate is the error caused by the temperature difference, the position of the platform is subtracted from the measured value of the interferometer to obtain an error, the error corresponding to t 0 is taken as an initial error, and the initial error value is subtracted from each error value to obtain the change value of the position error caused by the temperature difference. As can be seen from a comparison of the data in fig. 6 and 5, most of the errors are compensated, the compensated errors are significantly reduced, and the maximum error is reduced from more than 30 μm to less than 5 μm and is reduced to less than 17% of the maximum error when the temperature is changed at 5 ℃.
In summary, the technical scheme of the invention considers the errors caused by temperature change of the marble platform and the grating ruler, provides a temperature error calculation model, processes the errors influenced by the temperature in the temperature error calculation model, can be used for compensating most of the errors caused by temperature change, and can reduce the errors to within 17% of the maximum errors in a certain temperature change range; the scheme is simple and easy to realize, and can be realized by constructing a simple platform and performing primary calibration; based on the calibration result, the temperature stability of the precision can be ensured; in addition, the calculation is simple, the calculation time is short, complex nonlinear calculation or interpolation is not needed to be carried out by accumulating a large amount of data, and the requirement of the marble platform on the environmental temperature is effectively reduced.
It should also be noted that the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus.
The foregoing is merely exemplary of the present application and is not intended to limit the present application. Various modifications and variations of the present application will be apparent to those skilled in the art. Any modification, equivalent replacement, improvement, etc. which come within the spirit and principles of the application are to be included in the scope of the claims of the present application.
Claims (8)
1. The marble platform movement position temperature error calibration method is characterized by comprising the following steps:
An error model based on the measuring motion position of the grating ruler is constructed, and the formula is as follows: e=a×p (t-t 0)+B(t-t0), where a is a position coefficient, B is a position bias coefficient, p is a target position of the platform movement, t is an actual temperature of a current grating ruler measurement position, t 0 is an initial reference temperature, and e is an actual position error caused by the temperature;
Moving the axes from the origin at equal intervals at the temperature t 0 and the different temperatures t, recording the measured value and the actual position of the grating ruler at the movement position, and obtaining the temperature t 0 and the actual position errors at the different temperatures t according to the measured value and the actual position of the grating ruler;
The values of A and B are determined based on an error model and an actual position error fit, specifically: taking the temperature of t 0 as an initial temperature, and taking the position error at the temperature as an initial error; subtracting initial temperature from data of different temperatures t, and subtracting initial errors from corresponding position error data to form m new temperature difference data and n position error data so as to reflect position error change caused by temperature difference; m new temperature difference data are used as independent variables, the symbol is t s, n position error data e s are used as independent variables, wherein, ，；
The dependent variable t s expands to become t:
；
Calculating a coefficient matrix theta s:
taking the part with the "_2" of the inner corner mark of the coefficient matrix theta s to form a slope matrix theta as a new dependent variable:
; new argument is set platform position The argument p s extends to p 0:
，
The final coefficients a and B are calculated as follows: The coefficients A and B can be obtained through calculation, and a calculation formula can be obtained after substituting the coefficients A and B into an error model;
And calculating the actual position error e at each temperature according to an error model formula for error compensation, and completing calibration.
2. The method of claim 1, wherein the moving position grating ruler measured value and the actual position are recorded by moving the axes from the origin at equal intervals at a temperature t 0 and a plurality of different temperatures t, respectively, by the following procedures:
S1, returning to the original machine, and resetting the coordinates of the grating ruler;
s2, moving the shaft at equal intervals, recording the actual moving position through a measuring instrument, and simultaneously recording the measured value of the grating ruler and the current temperature t 0;
s3, respectively raising the platforms to different temperatures t, and repeating the steps S1-S2 at the current temperature t.
3. The method of claim 2, wherein the measuring instrument is an interferometer.
4. The method for compensating the temperature of the movement position of the marble platform is characterized in that after an error e is obtained by adopting the calibration method according to any one of claims 1-3, the e is compensated to a preset target position p r, and the calculation formula is as follows: p r = p-e, the axis of the stage is moved to the actual target position, and the actual position of the axis of the stage is kept consistent with the actual position at the initial temperature.
5. A marble platform motion position temperature compensation system, comprising:
The error model module is used for constructing an error model based on the measuring motion position of the grating ruler, and the formula is as follows: e=a×p (t-t 0)+B(t-t0), where a is a position coefficient, B is a position bias coefficient, p is a target position of the platform movement, t is an actual temperature of a current grating ruler measurement position, t 0 is an initial reference temperature, and e is an actual position error caused by the temperature;
The position measurement module is used for respectively moving the axes from the origin at equal intervals at the temperature t 0 and the different temperatures t, recording the measured value and the actual position of the grating ruler at the movement position, and obtaining the actual position errors at the temperature t 0 and the different temperatures t at the different temperatures t according to the measured value and the actual position of the grating ruler;
The fitting module is used for fitting the error model and the actual position error to determine the values of A and B, and specifically comprises the following steps: taking the temperature of t 0 as an initial temperature, and taking the position error at the temperature as an initial error; subtracting initial temperature from data of different temperatures t, and subtracting initial errors from corresponding position error data to form m new temperature difference data and n position error data so as to reflect position error change caused by temperature difference; m new temperature difference data are used as independent variables, the symbol is t s, n position error data e s are used as independent variables, wherein, ，；
The dependent variable t s expands to become t:
；
Calculating a coefficient matrix theta s:
Taking the part with the "_2" of the inner corner mark of the coefficient matrix theta s to form a slope matrix theta as a new dependent variable:
; new argument is set platform position The argument p s extends to p 0:
，
The final coefficients a and B are calculated as follows: The coefficients A and B can be obtained through calculation, and a calculation formula can be obtained after substituting the coefficients A and B into an error model; and the compensation module is used for driving the axis of the platform to move at the temperature t, calculating a corresponding error e by the error model, compensating the error e into a preset target position, and enabling the axis of the platform to move to an actual target position.
6. A machine-readable storage medium having stored thereon instructions for causing a machine to perform the method of any of the preceding claims 1-3.
7. A processor configured to execute a program, wherein the program is configured to, when executed, perform: the method for temperature compensation of a moving position of a marble slab according to claim 4.
8. A marble platform movement position temperature compensation platform is characterized by comprising a marble platform, a grating ruler, an interferometer and temperature measuring equipment,
The grating ruler is respectively arranged on an X axis and a Y axis of the marble platform and is used for acquiring position coordinates of the X axis and the Y axis;
The interferometer is used for measuring the actual positions of the XY axes at different temperatures respectively, so that the position change caused by the temperature can be obtained;
The temperature measuring device is used for measuring the temperature of the installation position of the grating ruler;
a processor as claimed in claim 7 for performing the marble stage movement position temperature compensation method based on data of the grating scale, interferometer and temperature measuring device.
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