CN116820025A - HPO-SVR-based numerical control machine tool feed shaft screw thermal error modeling method - Google Patents
HPO-SVR-based numerical control machine tool feed shaft screw thermal error modeling method Download PDFInfo
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Abstract
The invention provides a HPO-SVR-based numerical control machine tool feed shaft lead screw thermal error modeling method, which comprises the steps of measuring the temperature of temperature measuring points of feed shafts of numerical control machine tools at different times by a patch type temperature sensor and a multi-channel digital display meter, and measuring thermal errors of measuring points at different coordinate positions of a ball screw end by a laser interferometer; selecting a proper kernel function from the SVR model, optimizing a punishment parameter c of the SVR and a parameter gamma in the kernel function by using an HPO algorithm, and establishing a thermal error prediction model of a linear feed shaft of the numerical control machine according to the principle of an HPO-SVR regression optimization algorithm. The method establishes a regression model with higher precision aiming at the change relation between the temperature of the temperature measuring point of the linear feeding shaft of the numerical control machine and the thermal error of the measuring point of the screw rod end, and has the advantages of high operation speed and high accuracy.
Description
Technical Field
The invention relates to the field of numerical control machine feed shaft screw thermal error analysis, in particular to a numerical control machine feed shaft screw thermal error modeling method based on HPO-SVR.
Background
The thermal error of the numerical control machine tool is the largest error source of the numerical control machine tool and can account for 40-70% of the total error. Today, many in the manufacturing industry fields require higher machining precision and surface quality, such as machining of robot internals and turbine engine blades used in industry and medical fields, etc.; the processing of the parts is not separated from a high-precision numerical control machine tool. By establishing an accurate thermal error model, the machining precision of the numerical control machine tool can be improved by using an error compensation method.
At present, the research on the thermal error of the numerical control machine tool at home and abroad is mainly concentrated on a main shaft, the research on the feeding shaft part is less, and the feeding system screw is used as one of the precision parts of the numerical control machine tool, so that the influence of the thermal error on the whole machining precision is not neglected. The thermal error of the existing numerical control machine tool mainly depends on the modeling of the traditional neural network. The traditional neural network is easy to be fitted and difficult to debug. Because the heat sources and working conditions of different numerical control machine tools are different, the conventional modeling method also has the problems of low universality and to-be-improved modeling precision.
Therefore, in order to solve the problems of the existing modeling method, the invention provides a feeding shaft screw thermal error modeling method for effectively improving universality and modeling accuracy.
Disclosure of Invention
The invention aims to:
the invention provides a modeling method for a numerical control machine feed shaft screw rod thermal error based on HPO-SVR, and aims to provide a method capable of modeling a part of the numerical control machine feed shaft screw rod thermal error, which is improved to optimize a support vector regression algorithm (HPO-SVR) for a hunter optimization algorithm based on the original modeling, and the method is used for modeling the feed system screw rod thermal error by using a modeling method through optimizing undetermined parameters in the support vector regression model for the hunter optimization algorithm, so that the thought of how to improve the machining precision of the numerical control machine from the aspect of a feed system is provided.
The technical scheme is as follows:
in order to achieve the above purpose, the invention adopts the following technical scheme:
the invention discloses a numerical control machine tool feed shaft screw thermal error modeling method based on HPO-SVR, which comprises the following steps:
step 1: analyzing the influence factors of the thermal errors of the feeding shaft part of the numerical control machine tool and the principle of an HPO-SVR modeling method, and determining an input variable and an output variable in the modeling process;
step 2: setting a plurality of temperature test points and a lead screw thermal error test point; measuring thermal errors of a temperature test point and a lead screw thermal error test point to obtain measurement data, and dividing the measurement data into a training set and a testing set;
step 3: selecting a kernel function of the SVR model;
step 4: according to the HPO-SVR algorithm theory, utilizing an HPO algorithm to obtain optimal SVR model key parameters, namely penalty parameters c and kernel function parameters gamma;
step 5: modeling is carried out according to the obtained optimal value of the key parameter of the SVR model and based on the relation between the temperature and the thermal error, and an HPO-SVR model is created.
Step 6: and comparing the predicted value obtained by the HPO-SVR model with the data true value in the test set, and verifying the modeling result.
Further, the temperature test points in the step 2 comprise three key temperature test points of a front bearing, a nut and a rear bearing of a feeding system of the machine tool; the screw thermal error test points comprise eight screw thermal error test points distributed on the screw section; the lead screw thermal error test point is divided in the following way:
according to the stroke of the screw rod, selecting a measuring point P every 55mm a (a∈[1,8]) The position coordinates of the lead screw thermal error test points are respectively as follows: (0, 0), (55,0), (110,0), (165,0), (220,0), (275,0), (330,0), (385,0).
Further, in the step 2, three key measuring point temperatures of the temperature measuring point are measured by using a patch type temperature sensor and a multi-channel digital display meter in combination with a laser interferometerT 1 、T 2 、T 3 Measuring point thermal error E of lead screw thermal error test point a (a∈[1,8])。
Further, the input variables in step 1 are three key measurement point temperatures T 1 、T 2 、T 3 Measuring point thermal error E with output variable of screw thermal error test point a (a∈[1,8])。
Further, the kernel function selected in step 3 is a gaussian radial basis kernel function:
wherein x is y And x z Any two samples of the original space; σ represents the range of the RBF function.
Further, in step 4, according to the theory of the HPO-SVR algorithm, the optimal key parameters of the SVR model, namely, the penalty parameter c and the kernel function parameter gamma, are obtained by using the HPO algorithm, and the optimization flow is as follows:
(1) Initializing a population: creating an initial population, randomly generating a plurality of groups of c and gamma, wherein the value is defined by the following formula:
where d is the dimension, the value in this algorithm is 2; ub and lb are the upper and lower bounds of c and gamma, respectively.
(2) Fitness: the fitness in the step (1) can be used for judging the quality degree of individuals in the population, so that proper individuals can be conveniently selected. Substituting a plurality of groups of c and gamma obtained by the algorithm into the SVR model respectively, and searching for optimal values of c and gamma according to the minimum value of the sum of squares of the prediction errors, namely the minimum value of the fitness;
(3) Definition of partial parameters: mu is all of the population in one iterationAverage value of individual positions, n being individualThe total number, Z, is the adaptive parameter of the algorithm, IDX is the index defined in the algorithm, the value is 1 when the condition of P= 0 is satisfied, otherwise, the value is 0, C is the balance parameter between exploration and development, the value is reduced from 1 to 0.02 in the iterative process, and P is the Boolean vector. The definition is as follows:
IDX＝(P＝＝0)
wherein MaxIt is the set maximum number of iterations, R 2 Is [0,1 ]]The random number in the random number is used for the random number,and->Is [0,1 ]]Random vector in, dimension and +.>The same;
(4) Definition of hunters and prey in the population: setting the adjustment parameter β=0.1, r 5 Is [0,1 ]]Random numbers within. When R is satisfied in one iteration 5 <At beta, this individual is defined as hunter. The updating method of hunter position is as follows:
x i,j (t+1)＝x i,j (t)+0.5[(2CZP pos (j)-x i,j (t))+(2(1-C)Zμ(j)-x i,j (t))]
wherein x is i,j (t) is the current hunter position at the calculated jth average; x is x i,j (t+1) is the next iteration position of the hunter; p (P) pos Is the location of the current prey;
the distance of other individuals from the average μ, i.e., euclidean distance, is calculated:
where μ is the average of all individuals. In each iteration, the individual farthest from the average distance is defined as the prey;
also, when R 5 <Beta, the individual is a prey. The method for updating the position of the prey is as follows:
x i,j (t+1)＝T pos (j)+CZcos(2πR 4 )×[T pos (j)-x i,j (t)]
T pos is the global optimum position in each iteration, which will be output, i.e. the optimum c and gamma in each iteration are output, and the c and gamma values as prey will be rejected and replaced by the hunter. And iterating for a plurality of times to obtain a plurality of different values, and finally screening an optimal value by the adaptability defined by the algorithm. R is R 4 Is within the range of [ -1,1]The random number in the algorithm, the cos function and the input parameters thereof allow the next hunting position to be in the global optimal position with different radiuses and angles, and the algorithm performance is improved.
The beneficial effects are that:
the invention adopts the hunter prey optimization algorithm to optimize the support vector regression algorithm (HPO-SVR), and utilizes a modeling method to model the thermal error of the screw rod of the feeding system by optimizing undetermined parameters in the support vector regression model through the hunter prey optimization algorithm, thereby having the advantages of high modeling speed and high model prediction precision.
Drawings
FIG. 1 is a flow chart of steps in a method for modeling thermal errors of a feed shaft screw of a numerical control machine tool based on HPO-SVR;
FIG. 2 is a flowchart of an HPO-SVR algorithm in a method for modeling the thermal error of a feed shaft screw of a numerical control machine tool based on HPO-SVR;
FIG. 3 is a graph of experimental data of temperatures at three temperature measuring points measured by a patch type temperature sensor and a multi-channel digital display meter according to the present invention;
FIG. 4 is a graph of experimental data of thermal errors of eight measuring points of a screw rod section measured by a laser interferometer in the invention;
FIG. 5 is a graph showing the comparison of measured and predicted thermal errors at different positions of the feed spindle screw in the test set section of experimental data of the present invention.
Detailed Description
The invention will be better explained by the following detailed description of the embodiments with reference to the drawings.
The invention adopts a hunter prey optimization algorithm to optimize a support vector regression algorithm (HPO-SVR), and utilizes a modeling method to model a screw thermal error of a feed system by optimizing undetermined parameters in a support vector regression model through the hunter prey optimization algorithm, and referring to FIG. 1, the method comprises the following steps:
step 1: analyzing the influence factors of the thermal errors of the feeding shaft part of the numerical control machine tool and the principle of an HPO-SVR modeling method, and determining an input variable and an output variable in the modeling process;
step 2: setting a plurality of temperature test points and a lead screw thermal error test point; measuring thermal errors of a temperature test point and a lead screw thermal error test point to obtain measurement data, and dividing the measurement data into a training set and a testing set;
step 3: selecting a kernel function of the SVR model;
step 4: according to the HPO-SVR algorithm theory, utilizing an HPO algorithm to obtain optimal SVR model key parameters, namely penalty parameters c and kernel function parameters gamma;
step 5: modeling is carried out according to the obtained optimal value of the key parameter of the SVR model and based on the relation between the temperature and the thermal error, and an HPO-SVR model is created.
Step 6: and comparing the predicted value obtained by the HPO-SVR model with the data true value in the test set, and verifying the modeling result.
Because the machine tool can generate heat during working, the lead screw is caused to generate thermal deformation, and then the accuracy of the feed shaft is reduced, and the temperature is one of main influencing factors which cause the thermal error of the numerical control machine tool. Therefore, in step 1, the temperature of the input variable of the model is determined, the output variable is a thermal error, and the data of the input variable and the output variable can be measured by a patch type temperature sensor and a multi-channel digital display meter in combination with a laser interferometer.
To facilitate data measurement, we have provided a plurality of temperature test points including three critical temperature test points and eight lead screw thermal error test points P in the machine feed system a (a∈[1,8]) The three key temperature test points are respectively a front bearing, a nut and a rear bearing of a machine tool feeding system, a lead screw thermal error test point is arranged at each 55mm according to the lead screw travel, and the position coordinates of the three key temperature test points are respectively (0, 0), (55,0), (110,0), (165,0), (220,0), (275,0), (330,0) and (385,0).
In this embodiment, the input variables of the HPO-SVR model are the temperatures T of three key temperature test points 1 、T 2 、T 3 The output variable is eight lead screw thermal error test points P a (a∈[1,8]) Thermal error E in a (a∈[1,8])。
Since the errors measured by the laser interferometer at the lead screw section during the operation of the machine tool include positioning errors and thermal errors in an initial state (i.e., a stopped state), when data measurement is performed, positioning errors at different measuring points of the lead screw are measured at first in the stopped state. After the measurement is finished, the feeding shaft is made to reciprocate, the feeding speed can be set according to the machine tool parameters and the principle is moderate, in the embodiment, the Y-direction reciprocating feeding is set, the stroke of the screw rod is 0-385mm, and the speed is 10m/min. After the machine tool runs for 5 minutes, the machine tool is stopped briefly for a small meeting, and the temperatures of three key temperature test points and eight lead screw thermal error test points P are recorded a (a∈[1,8]) Thermal errors on the same. After the recording is finished, the workbench is moved, and an error value of a thermal error test point of the screw rod, which is formed by the fact that the workbench moves to the position of different test points of the screw rod, is recorded by a laser interferometer. Positioning of errors and initial conditions at this timeThe difference between the errors is the actual thermal error of the screw. And after the recording is finished, the machine tool continues to run, and the temperature of the temperature test point and the error values of the eight screw thermal error test points are repeatedly measured until the temperature is relatively stable. The measurement is stopped for 150 minutes, namely 30 times, three temperature test points are measured, and the measured values are taken as three input variables; the number of thermal error test points is eight, the measured value of each thermal error test point is taken as a single output variable, the input variable and the output variable are taken as a group of data, and the total number of the data is 240 (the data measurement results refer to fig. 3 and 4). After all the temperature and thermal error data are measured, the training set and the testing set in the data set are randomly divided according to the size ratio of the training set to the testing set of 7:3 for establishing an HPO-SVR regression model in order to improve the accuracy of the regression model. Then, the predicted value obtained by the HPO-SVR model is compared with the data true value in the test set, and the modeling result is verified, referring to FIG. 5.
Because the Gaussian radial basis function is relatively nonlinear, the kernel function selected by the SVR model in the invention is the Gaussian radial basis function:
wherein x is y And x z Any two samples of the original space; σ represents the range of the RBF function.
According to HPO-SVR algorithm theory, the HPO algorithm is utilized to obtain optimal SVR model key parameters, namely penalty parameter c and kernel function parameter gamma, and the optimization flow is as follows:
(1) Initializing a population: an initial population is created, and the objective functions are c and gamma in the RBF function. Randomly generating a plurality of groups of c and gamma, wherein the value is defined by the following formula:
where d is the dimension, and the value in this algorithm is 2; ub and lb are the upper and lower bounds of the variable, respectively.
Because c and gamma are non-negative values, and the excessive or insufficient values of the c and gamma easily cause problems of excessive fitting, excessively low accuracy and the like of the SVR model according to the related theory, the values of ub and lb are required to be in a more reasonable range;
(2) Fitness: the fitness can determine the quality degree of individuals in the population, and is convenient for selecting proper individuals. Substituting a plurality of groups of c and gamma obtained by the algorithm into the SVR model respectively, and searching the optimal values of c and gamma according to the minimum value of the sum of squares of the prediction errors, namely the minimum value of the fitness;
(3) Definition of partial parameters: μ is the average of all individual positions in the population in one iteration, n is the total number of individuals, and Z is the adaptive parameter of the algorithm. C is a balance parameter between exploration and development, the value of which decreases from 1 to 0.02 in the iterative process; p is a boolean vector, IDX is an index defined in the algorithm, and is assigned 1 when the p= =0 condition is satisfied, otherwise 0. The definition is as follows:
IDX＝(P＝0)
wherein MaxIt is the set maximum iteration number, R 2 Is [0,1 ]]The random number in the random number is used for the random number,and->Is [0,1 ]]Random vector, dimension and x in i The same;
(4) Definition of hunters and prey in the population: setting the adjustment parameter β=0.1, r 5 Is [0,1 ]]Random numbers within. When R is satisfied in one iteration 5 <At beta, this individual is defined as hunter. The updating method of hunter position is as follows:
x i,j (t+1)＝x i,j (t)+0.5[(2CZP pos (j)-x i,j (t))+(2(1-C)Zμ(j)-x i,j (t))]
wherein x is i,j (t) is the current hunter position at the calculated jth average; x is x i,j (t+1) is the next iteration position of the hunter; p (P) pos Is the location of the prey;
the distance of other individuals from the average μ, i.e., euclidean distance, is calculated:
where μ is the average of all individuals. In each iteration, the individual farthest from the average distance is defined as the prey;
also, when R 5 <Beta, the individual is a prey. The method for updating the position of the prey is as follows:
x i,j (t+1)＝T pos (j)+CZcos(2πR 4 )×[T pos (j)-x i,j (t)]
T pos is the global optimum position in each iteration, which will be output, i.e. the optimum c and gamma in each iteration are output, and the c and gamma values as prey will be rejected and replaced by the hunter. And iterating for a plurality of times to obtain a plurality of different values, and finally screening an optimal value by the adaptability defined by the algorithm. R is R 4 Is within the range of [ -1,1]The random number in the algorithm, the cos function and the input parameters thereof allow the next hunting position to be in the global optimal position with different radiuses and angles, and the algorithm performance is improved.
The foregoing has shown and described the basic principles, principal features and advantages of the invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, and that the above embodiments and descriptions are merely illustrative of the principles of the present invention, and various changes and modifications may be made without departing from the spirit and scope of the invention, which is defined in the appended claims. The scope of the invention is defined by the appended claims and equivalents thereof.
Claims (6)
1. A numerical control machine tool feed shaft lead screw thermal error modeling method based on HPO-SVR is characterized in that: the method comprises the following steps:
step 1: analyzing the influence factors of the thermal errors of the feeding shaft part of the numerical control machine tool and the principle of an HPO-SVR modeling method, and determining an input variable and an output variable in the modeling process;
step 2: setting a plurality of temperature test points and lead screw thermal error test points to measure thermal errors of the temperature test points and the lead screw thermal error test points, obtaining measurement data, and dividing the measurement data into a training set and a testing set;
step 3: selecting a kernel function of the SVR model;
step 4: according to the HPO-SVR algorithm theory, utilizing an HPO algorithm to obtain optimal SVR model key parameters, namely penalty parameters c and kernel function parameters gamma;
step 5: modeling based on the temperature and thermal error relation according to the obtained optimal value of the key parameter of the SVR model, and creating an HPO-SVR model;
step 6: and comparing the predicted value obtained by the HPO-SVR model with the data true value in the test set, and verifying the modeling result.
2. The HPO-SVR-based numerical control machine feed shaft screw thermal error modeling method is characterized by comprising the following steps of: the temperature test points in the step 2 comprise three key temperature test points of a front bearing, a nut and a rear bearing of a machine tool feeding system; the screw thermal error test points comprise eight screw thermal error test points distributed on the screw section; the lead screw thermal error test point is divided in the following way:
according to the stroke of the screw rod, selecting a measuring point P every 55mm a (a∈[1,8]) The position coordinates of the lead screw thermal error test points are respectively as follows: (0, 0), (55,0), (110,0), (165,0), (220,0), (275,0), (330,0), (385,0).
3. The modeling method for the thermal error of the feed shaft screw of the numerical control machine tool of the HPO-SVR according to claim 2 is characterized in that: in the step 2, the temperature T of three key temperature test points of the temperature test points is measured by using a patch type temperature sensor and a multichannel digital display meter and combining a laser interferometer 1 、T 2 、T 3 Measuring point thermal error E of lead screw thermal error test point a (a∈[1,8])。
4. A method for modeling thermal error of a feed shaft screw of an HPO-SVR numerical control machine tool according to claim 3, wherein: the input variables in the step 1 are three key measuring point temperatures T 1 、T 2 、T 3 Measuring point thermal error E with output variable of screw thermal error test point a (a∈[1,8])。
5. The HPO-SVR-based numerical control machine feed shaft screw thermal error modeling method is characterized by comprising the following steps of: the kernel function selected in step 3 is a gaussian radial basis function:
wherein x is y And x z Any two samples of the original space; σ represents the range of the RBF function.
6. The HPO-SVR-based numerical control machine feed shaft screw thermal error modeling method is characterized by comprising the following steps of: in the step 4, according to the HPO-SVR algorithm theory, the optimal key parameters of the SVR model, namely penalty parameter c and kernel function parameter gamma, are obtained by utilizing the HPO algorithm, and the optimization flow is as follows:
(1) Initializing a population: creating an initial population, randomly generating a plurality of groups of c and gamma, wherein the value is defined by the following formula:
where d is the dimension, the value in this algorithm is 2; ub and lb are the upper and lower bounds of c and gamma, respectively;
(2) Fitness: the fitness in the step (1) can be used for judging the quality degree of individuals in the population, so that proper individuals can be conveniently selected. Substituting a plurality of groups of c and gamma obtained by the algorithm into the SVR model respectively, and searching for optimal values of c and gamma according to the minimum value of the sum of squares of the prediction errors, namely the minimum value of the fitness;
(3) Definition of partial parameters: mu is all of the population in one iterationThe average value of individual positions, n is the total number of individuals, Z is the adaptive parameter of the algorithm, IDX is the index defined in the algorithm, the value is 1 when the condition of P= =0 is satisfied, otherwise, the value is 0, C is the balance parameter between exploration and development, the value is reduced from 1 to 0.02 in the iterative process, P is a Boolean vector, and the definition is as follows:
IDX＝(P＝0)
wherein MaxIt is the set maximum number of iterations, R 2 Is [0,1 ]]The random number in the random number is used for the random number,and->Is [0,1 ]]Random vector in, dimension and +.>The same;
(4) Definition of hunters and prey in the population: setting the adjustment parameter β=0.1, r 5 Is [0,1 ]]Random number in, when meeting R in one iteration 5 <At β, the individual is defined as hunter, and the hunter location is updated as follows:
x i,j (t+1)＝x i,j (t)+0.5[(2CZP pos (j)-x i,j (t))+(2(1-C)Zμ(j)-x i,j (t))]
wherein x is i,j (t) is the current hunter position at the calculated jth average; x is x i,j (t+1) is the next iteration position of the hunter; p (P) pos Is the location of the current prey;
the distance of other individuals from the average μ, i.e., euclidean distance, is calculated:
wherein μ is the average value of all individuals, and in each iteration, the individual with the farthest average distance is defined as the prey;
also, when R 5 <Beta, the individual is a prey. The method for updating the position of the prey is as follows:
x i,j (t+1)＝T pos (j)+CZcos(2πR 4 )×[T pos (j)-x i,j (t)]
T pos is the global optimal position in each iteration, which will be output, i.e. the optimal c and gamma in each iteration are output, while the c and gamma values as prey will be rejected and replaced by the hunter; iterating for a plurality of times to obtain a plurality of different values, and finally screening an optimal value according to the adaptability defined by the algorithm; r is R 4 Is within the range of [ -1,1]The random number in the algorithm, the cos function and the input parameters thereof allow the next hunting position to be in the global optimal position with different radiuses and angles, and the algorithm performance is improved.
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