CN109240204B - Numerical control machine tool thermal error modeling method based on two-step method - Google Patents
Numerical control machine tool thermal error modeling method based on two-step method Download PDFInfo
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- G05B19/18—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form
- G05B19/404—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form characterised by control arrangements for compensation, e.g. for backlash, overshoot, tool offset, tool wear, temperature, machine construction errors, load, inertia
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Abstract
The invention discloses a numerical control machine tool thermal error modeling method based on a two-step method, which solves the problem of low prediction precision of actually measured thermal errors in the prior art, and the thermal errors obtained by prediction are closer to the actually measured thermal errors, so that the numerical control machine tool thermal error modeling method has good prediction precision; the technical method isThe scheme is as follows: firstly, modeling the thermal deformation of a driving system by using a BP neural network, then obtaining the relation between the actual thermal error y and the actual thermal deformation x of the driving system by polynomial interpolation fitting, and constructing a thermal error prediction model x*、y*。
Description
Technical Field
The invention relates to the technical field of numerical control machines, in particular to a numerical control machine thermal error modeling method based on a two-step method.
Background
Along with the gradual development of numerical control machine tools, the requirements of the machine tools on the machining precision are higher and higher. Machine tool errors include thermal errors, geometric errors, and force-induced errors, where thermal deformation-induced errors account for 40% -70% of machine tool errors. The ball screw is used as an important transmission part of a machine tool and widely applied to servo feeding systems, such as a numerical control machine tool and a high-precision feeding platform, and the precision of the machine tool is directly influenced by the positioning error of the ball screw. The friction of the feed system during operation generates heat, which causes the temperature of the screw to rise, and generates large thermal errors, which affect the accuracy of the machine tool. Therefore, the mathematical modeling research is carried out on the temperature distribution, the thermal deformation rule and the thermal error compensation technology of the ball screw, and the influence of the thermal error on the machining precision of the machine tool can be better researched.
Aiming at the thermal error of a driving system, scholars at home and abroad carry out extensive research on modeling and compensating the thermal error of a machine tool. The main method comprises the following steps: a neural network model method, a multiple linear regression method, a finite element method, a method for establishing a thermal error model by a multiple theory and the like.
In most researches, the emphasis is on how the temperature rise of the system affects the accuracy of movement and how to reduce the thermal effect, and in most thermodynamic experiments, the measured thermal error is directly used for replacing the thermal error caused by the thermal deformation of a machine tool screw without accurately formulating the relationship between the measured thermal error and the thermal error.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a numerical control machine tool thermal error modeling method based on a two-step method, the thermal error obtained by prediction is closer to the actually measured thermal error, and the prediction precision is good.
The invention adopts the following technical scheme:
a numerical control machine tool thermal error modeling method based on a two-step method comprises the steps of firstly modeling thermal deformation of a driving system by a BP neural network, then obtaining the relation between an actual measurement thermal error y and an actual thermal deformation x of the driving system by polynomial interpolation fitting, and constructing a thermal error prediction model x*、y*。
Further, the concrete modeling process is as follows:
initializing a network topology structure, a BP neural network weight and a threshold value to obtain a BP neural network structure;
training by utilizing the thermal deformation data under different running conditions, and calculating errors;
and (3) judging whether a termination condition is met:
when the termination condition is not met, updating the weight value and the threshold value, and repeating the step (2);
when the end condition is met, obtaining the predicted thermal deformation x according to the input parameters of the driving system*；
Step (4) of predicting the amount of thermal deformation x*And obtaining the predicted thermal error y by the variable relation obtained by polynomial interpolation fitting*。
Further, in the step (1), for the thermal deformation part, training the BP neural network according to the temperature rise and thermal deformation data.
Further, a thermal deformation model is established for the ball screw feeding system by the BP neural network, the temperature rise value of the temperature measuring point is used as an input variable to be input into the BP neural network, and the thermal deformation of the ball screw is used as an output variable.
Further, in the step (2), the change of the operation condition is performed with the table speed v, the operation time t, and the operation stroke l in the thermal error experiment as input amounts.
Further, in the step (3), when the termination condition is met, inputting the speed of the workbench, the running time, the working stroke and the rotating speed of the nut to obtain the predicted thermal elongation x of the screw rod*。
Further, in the step (4), the polynomial interpolation fitting process is as follows:
1) inputting experimental data x and y, and determining a final fitting order by comparing polynomial fitting precision;
2) and training the multiple groups of data according to the final fitting order of the polynomial to obtain a polynomial concrete model between two errors.
Further, in the step 1), thermal errors of different-order polynomials under the same experimental conditions are accurately fitted and compared, and a plurality of groups of experiments are analyzed to select a proper order as a final fitting order; wherein the evaluation indexes are sum variance SSE and root mean square error RMSE.
Furthermore, in the ball screw feeding system, a laser displacement sensor is arranged at the end of the screw shaft to measure the thermal deformation of the end of the screw shaft, and the positioning error of the workbench is obtained through the measurement of a laser interferometer.
Further, for the actual measurement thermal error test, except the measurement stage, the movement mode is constant-speed reciprocating movement with a fixed stroke from the start-up of the machine tool to the achievement of thermal balance, and a set of data is measured by stopping the machine at set intervals.
Compared with the prior art, the invention has the beneficial effects that:
(1) modeling the thermal deformation of the lead screw by using a BP neural network, and then obtaining the relation between y and the actual thermal deformation x of the lead screw by polynomial interpolation fitting to construct a thermal error prediction model; compared with a direct method, the method has better prediction precision and is more suitable for engineering application;
(2) the invention can obtain the relation between the actually measured thermal error of the workbench and the actual thermal deformation of the screw rod through polynomial interpolation fitting, and has high reliability.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this application, illustrate embodiments of the application and, together with the description, serve to explain the application and are not intended to limit the application.
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a schematic diagram of a ball screw platform measurement of the present invention;
FIG. 3 is a diagram of a neural network architecture;
FIG. 4 is a graph of the temperature rise of experiment I of the present invention;
FIG. 5 is a graph of the measured thermal error of experiment I of the present invention;
FIG. 6 is a graph of the temperature rise of experiment II of the present invention;
FIG. 7 is a statistical graph of measured thermal error and prediction model for experiment II of the present invention;
FIG. 8 is a graph of measured error composition;
FIG. 9 is a graph of the temperature rise of experiment III of the present invention;
FIG. 10 is a statistical plot of the thermal distortion error and prediction model for experiment III of the present invention;
FIG. 11 is a graph of the temperature rise of experiment IV of the present invention;
FIG. 12 is a statistical graph of measured thermal error and prediction model for experiment IV of the present invention;
the system comprises a laser interferometer 1, a laser interferometer 2, a reflecting mirror 3, a magnetic base 4, a nut 5, a far-end bearing 6, a PC 7, a base 8, a ball screw 9, a near-end bearing 10, a motor 11 and a workbench 12.
Detailed Description
It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the disclosure. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments according to the present application. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, and it should be understood that when the terms "comprises" and/or "comprising" are used in this specification, they specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof, unless the context clearly indicates otherwise.
As introduced in the background art, the prior art has the defect of low prediction precision of the actually measured thermal error, and in order to solve the technical problems, the application provides a numerical control machine tool thermal error modeling method based on a two-step method.
In a typical embodiment of the present application, as shown in fig. 1, a numerically controlled machine tool thermal error modeling method based on a two-step method is provided, that is, a thermal deformation amount of a driving system is modeled by a BP neural network, and then a relationship between an actual thermal error y and an actual thermal deformation amount x of the driving system is obtained by polynomial interpolation fitting, so as to construct a thermal error prediction model x*、y*。
The positioning error of the feed drive system is mostly caused by the thermal deformation of the screw pair, and is expressed by the axial thermal deformation x of the screw:
x＝s(t)-s (1)
in formula (1): s represents the position of a certain point of the screw pair.
And starting the machine tool to move to a specified stroke, in order to ignore the positioning error, taking the measurement result as an initial value, and reflecting the thermal error as the difference between the measurement value of the laser interferometer and the measurement value in each thermodynamic experiment, wherein the error is called as an actually measured thermal error y.
The error measured by the laser interferometer cannot be simply equated to the thermal deformation of the screw because of the drive train between the ball screw and the stage. Therefore, the error measured by the laser interferometer is caused by the thermal deformation of the screw, but the two are not equal.
Assuming that the relationship between y and x is not a linear relationship, the algebraic relationship between the two can be fitted by a polynomial:
y＝λ0+λ1x+λ2x2+λ3x3+……+λnxn (2)
in the formula (2), y represents the measured thermal error of the feed driving system at the position of s; lambda [ alpha ]0、λ1、λ2、λ3…λnExpressing a correction coefficient, and reflecting the relation between the actually measured thermal error and the thermal deformation of the screw rod; x represents the amount of thermal deformation of the screw at position s.
λ0、λ1、λ2、λ3…λnIt can be determined by a variety of methods, such as grey theory systems, neural networks, least squares, regression analysis, multivariate regression analysis, and the like.
The application provides a composite thermal error modeling method, which specifically comprises the following steps:
initializing a network topology structure, a BP neural network weight and a threshold value to obtain a BP neural network structure;
training by utilizing the thermal deformation data under different running conditions, and calculating errors;
and (3) judging whether a termination condition is met:
when the termination condition is not met, updating the weight value and the threshold value, and repeating the step (2);
when the end condition is met, obtaining the predicted thermal deformation x according to the input parameters of the driving system*；
Step (4) of predicting the amount of thermal deformation x*And obtaining the predicted thermal error y by the variable relation obtained by polynomial interpolation fitting*；
Wherein, the polynomial interpolation fitting process is as follows:
1) inputting experimental data x and y, and determining a final fitting order by comparing polynomial fitting precision;
2) and training the multiple groups of data according to the final fitting order of the polynomial to obtain a polynomial concrete model between two errors.
The dynamic lead screw thermal deformation model is established by BP neural network modeling. The experiment is modeled based on a ball screw platform, the speed v of a workbench, the running time t and the working stroke l in the thermal error experiment are used as input quantities to change all running conditions, the thermal deformation and the temperature of the screw are measured, and a thermal error model of the ball screw is established. In the process of thermodynamic experiment, experimental data of thermal deformation change of the lead screw is detected in real time through the laser displacement sensor.
And after the thermal deformation modeling of the screw is completed, performing polynomial fitting solving on the relationship between the thermal deformation of the screw and the actually measured thermal error under different working conditions. After error data is obtained, the parameters of equation (2) are solved by using the least square method.
Firstly, a machine tool temperature rise, thermal deformation and actual measurement thermal error measurement test:
the experiment platform shown in fig. 2 is adopted in the application, namely, a ball screw feeding system, a ball screw 9 connected with a motor 11 is installed on a base 8, a nut 5 is connected on the ball screw 9, a temperature sensor T1 is installed on a near-end bearing 10 of the ball screw 9, a temperature sensor T2 is installed on a far-end bearing 6, a temperature sensor T3 is installed on the nut 5, the ambient temperature is detected by a temperature sensor T4, and the temperature sensors T1, T2, T3 and T4 sequentially pass through a signal conditioning circuit and are connected with a PC 7 through a data acquisition card.
The tail end of the ball screw 9 is provided with a micro displacement sensor W1 for measuring the thermal deformation, and the micro displacement sensor W1 is also connected to the input end of the signal conditioning circuit.
The signal conditioning circuit is also connected with a laser interferometer 1, an interference mirror 2 and a reflecting mirror 3 are sequentially arranged in front of the laser interferometer 1, and the interference mirror 2 is fixed with the laser head and used for measuring the actually measured thermal error; the reflector 3 is mounted on a magnetic base 4, the magnetic base 4 being located above the table 12.
The actual measurement thermal error measurement method comprises the following steps:
when the machine tool is started to move to a specified stroke, in order to ignore the positioning error, the measurement result is taken as an initial value, and the thermal error is reflected as the difference value between each measurement value and the thermal error. Stopping reciprocating motion every ten minutes, moving the specified stroke from the point position at the working zero point, wherein the measured value is the measured thermal error.
The method for measuring the axial thermal deformation of the ball screw comprises the following steps:
continuously acquiring data through a laser displacement sensor, a data acquisition card and a PC (personal computer) end program, and finally processing through the program to obtain a thermal deformation analysis chart and a temperature rise chart of each point.
In the experimental process, the feeding speed, the stroke and the working time of the workbench have influence on the thermal deformation of the screw, so that the influence of the working conditions is fully considered in the experimental design, and the specific experimental scheme is shown in table 1.
Table 1: experimental protocol
In the measuring stage, the machine tool is started to reach thermal balance, the movement mode is constant-speed reciprocating movement with a fixed stroke, and a group of data is measured every ten minutes of stopping. The motion starting point and the measurement starting point are both work zero points.
Secondly, training a neural network and fitting a polynomial:
the structure of the BP neural network is shown in figure 3, and for the thermal deformation part, the temperature rise and thermal deformation data obtained by the experiment I are used for training the BP neural network.
And inputting the temperature rise value of the temperature measuring point into the BP neural network as an input variable, and taking the thermal deformation of the screw rod as an output variable. The temperature rise of the fixed end of the screw rod, the temperature rise of the nut, the temperature rise of the free end of the screw rod and the environmental temperature rise are 4 input end nodes of the BP neural network, and the thermal deformation of the screw rod is used as an output node of the BP neural network. In the modeling process, the number of hidden layer nodes is 18.
In the BP neural network training process, an array (4 x 19) is formed by temperature rise values measured by 4 temperature measuring points as an input variable, and a vector (1 x 19) formed by lead screw thermal deformation quantities acquired in the period of time is used as an output variable. The network was constructed with experiment II and experiment III and continued training. And predicting and verifying the effectiveness of the BP neural network on the data of the experiment IV, and obtaining the thermal deformation of each part of the screw rod. And (4) obtaining the whole distribution of the thermal deformation of the screw through a neural network training and adding algorithm, and establishing a thermal deformation model of the screw.
And after the model of the thermal deformation of the screw rod is established, performing polynomial fitting on multiple groups of y and x measured in the experimental process. If the order is too low, the fitting accuracy is low; if the order is too high, the calculation difficulty is increased, the error implementation compensation is difficult, and the phenomenon of overfitting may occur, so that the robustness of the model is reduced.
In each experiment, through comparison of thermal error fitting accuracy of polynomials of different orders under the experimental condition, a plurality of groups of experiments are analyzed, and a proper order is selected as a final fitting order.
The evaluation index SSE is sum variance which is the sum of squares of errors of corresponding points of the fitting data and the original data; RMSE is the root mean square error, which is the square root of the ratio of the sum of the squares of the fitted data to the original data to the number of observations m.
As shown in table 2, n-3 was chosen as the final fitting order.
TABLE 2 polynomial fitting accuracy contrast
Under different operating conditions, carrying out an actual thermal error measurement experiment, and simultaneously measuring an actual thermal error and a lead screw at corresponding time in the experiment to obtain a mathematical model between the actual thermal error and the thermal deformation of the lead screw:
y＝λ0+λ1x+λ2x2+λ3x3 (3)
the parameters of the formula (3) are solved according to data measured by experiments, and a specific model between the measured thermal error and the thermal deformation of the screw can be obtained.
y＝0.0076+0.9987x+6.2×e-5x2+8.4463×e-7x3 (4)
Thirdly, analyzing a prediction result:
in the results, the thermal error predicted by directly training and testing the thermal error of the BP neural network (the direct method) is compared with a thermal error curve graph predicted by a two-step method.
Firstly, training a direct method and a two-step method through data in an experiment I; then, the accuracy of the model is verified through experiments II to IV, and the model is gradually optimized.
The temperature rise data and the measured thermal error y for experiment I are shown in fig. 4 and 5.
For prediction methodThe analyzed experimental results are five curves which are respectively the actually measured thermal error y and the thermal error y predicted by the direct method1Thermal error y predicted by two-step method2Error value between BP predicted thermal error and measured thermal error
Error value between predicted thermal error and measured thermal error of two-step process
The temperature rise data, measured thermal error and prediction model of experiment II are shown in figures 6-7,
fluctuates between-3.5 to 2.5 μm, and
the wave length fluctuates between-2.5 and 2 mu m.
Therefore, the estimation effect of the two-step method is obviously superior.
As shown in fig. 8, the measured thermal error is composed of two parts, one part is the actual thermal deformation of the screw in the experiment, and the other part is the transmission error caused by the transmission between the screw and the worktable.
Therefore, the experimental condition change only affects the thermal deformation of the screw rod actually, and the error of the polynomial fitting part is mainly affected by each transmission chain between the screw rod and the workbench and is irrelevant to the experimental operation condition.
After the thermal deformation of the lead screw and the actually measured thermal error are independently modeled and analyzed, the polynomial fitting accuracy cannot be influenced by the predicted error of the BP neural network, so that the predicted accuracy is higher than that of the previous method.
According to the temperature rise and the data of the experiment III, the actual measurement thermal error is predicted by using a direct method and a two-step method; the results are shown in figures 9-10,
is-1.5 to 1.2 μm, and
is-0.8 to 0.7 μm.
The experimental result shows that the prediction accuracy of the latter is about 80% higher than that of the former, because the model data volume is increased through two times of training of the experiment I and the experiment II, the modeling tends to be stable, and the superiority of the two-step prediction method is expressed.
For experiment IV, the operating conditions were complex and the travel was different in all three time periods. Experimental data curves for experiment IV are shown in figures 11-12,
fluctuating within the range of-5.4 to 6.6 mu m;
the fluctuation is within-3.1 to 2.2 μm.
Under the condition of complex operation, the estimated value deviation of the two models is slightly larger than that of the former model, but the prediction precision of the two-step method is about 126 percent higher than that of the first method, and is obviously better than that of the first method. The method shows that after the thermal deformation of the screw and the actually measured thermal error are subjected to polynomial fitting, the influence of the change of the running condition on the actually measured thermal error obtained by two-step prediction is lower than that of a prediction method for actually measuring the thermal error by single BP network training.
The above description is only a preferred embodiment of the present application and is not intended to limit the present application, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, improvement and the like made within the spirit and principle of the present application shall be included in the protection scope of the present application.
Claims (9)
1. A numerical control machine tool thermal error modeling method based on a two-step method is characterized in that firstly, a BP neural network is used for modeling the thermal deformation of a driving system, then the relation between the actually measured thermal error y and the actually thermal deformation x of the driving system is obtained through polynomial interpolation fitting, and a thermal error prediction model x is constructed*、y*；
The specific modeling process is as follows:
initializing a network topology structure, a BP neural network weight and a threshold value to obtain a BP neural network structure;
training by utilizing the thermal deformation data under different running conditions, and calculating errors;
and (3) judging whether a termination condition is met:
when the termination condition is not met, updating the weight value and the threshold value, and repeating the step (2);
when the end condition is met, obtaining the predicted thermal deformation x according to the input parameters of the driving system*；
Step (4) of predicting the amount of thermal deformation x*And obtaining the predicted thermal error y by the variable relation obtained by polynomial interpolation fitting*。
2. The method for modeling thermal error of numerical control machine tool based on two-step method according to claim 1, wherein in the step (1), for the thermal deformation part, the BP neural network is trained by temperature rise and thermal deformation data.
3. The numerical control machine tool thermal error modeling method based on the two-step method according to claim 2, characterized in that a thermal deformation model is established for the ball screw feeding system by using a BP neural network, a temperature rise value of a temperature measuring point is input into the BP neural network as an input variable, and a thermal deformation of the ball screw is used as an output variable.
4. The method for modeling the thermal error of the numerical control machine tool based on the two-step method according to claim 1, wherein in the step (2), the change of the operating condition is performed by using the table speed v, the operating time t and the operating stroke l in the thermal error experiment as input quantities.
5. The method for modeling the thermal error of the numerical control machine tool based on the two-step method according to claim 3, wherein in the step (3), when the termination condition is met, the thermal error is input into the workbenchThe speed, the running time, the working stroke and the nut rotating speed are used for obtaining the predicted thermal elongation x of the screw rod*。
6. The numerically-controlled machine tool thermal error modeling method based on the two-step method according to claim 1, wherein in the step (4), the polynomial interpolation fitting process is as follows:
1) inputting experimental data x and y, and determining a final fitting order by comparing polynomial fitting precision;
2) and training the multiple groups of data according to the final fitting order of the polynomial to obtain a polynomial concrete model between two errors.
7. The numerical control machine tool thermal error modeling method based on the two-step method according to claim 6, characterized in that in 1), thermal error fitting accurate comparison is performed on polynomials of different orders under the same experimental conditions, and a plurality of groups of experiments are analyzed to select a proper order as a final fitting order; wherein the evaluation indexes are sum variance SSE and root mean square error RMSE.
8. The method as claimed in claim 3, wherein in the ball screw feeding system, a laser displacement sensor is placed at the end of the screw shaft to measure the thermal deformation of the end of the screw shaft, and the positioning error of the worktable is obtained by laser interferometer measurement.
9. The numerical control machine tool thermal error modeling method based on the two-step method according to claim 1, characterized in that for the actual thermal error test, except for the measurement stage, the motion mode is constant-speed reciprocating motion with a fixed stroke from the start-up of the machine tool to the achievement of thermal equilibrium, and a set of data is measured by stopping the machine at a set time interval.
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| CN111190390B (en) * | 2020-01-14 | 2021-01-29 | 重庆大学 | Thermal error modeling method, total error modeling method and thermal error compensation system of shaft system with two-end axial constraint |
| CN111240268B (en) * | 2020-01-14 | 2021-03-16 | 重庆大学 | Axle system thermal error modeling method and thermal error compensation system based on SLSTM neural network |
| CN113211160B (en) * | 2021-04-08 | 2022-05-03 | 北京工业大学 | Ball screw pair thermal deformation compensation system and method based on extreme gradient lifting |
| CN113591339B (en) * | 2021-06-23 | 2024-03-22 | 广东智目科技有限公司 | Modeling method capable of predicting temperature rise and thermal error of ball screw |
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| CN114488945B (en) * | 2022-01-06 | 2023-11-14 | 华中科技大学 | Vertical machine tool z-axis thermal error modeling method and system under influence of ambient temperature |
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