CN110728049B - Combined prediction model establishment method for tool turning temperature change mean value - Google Patents
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Abstract
The invention relates to a combined prediction model building method of a tool turning temperature change mean value, which comprises the following steps: establishing three single prediction models containing parameters to be determined of turning temperature change mean values with respect to turning certain-direction vibration and turning parameters; processing the single prediction model established in the first step into a nonlinear function model to be optimized by using a least square method principle, and optimizing and solving undetermined parameters of the nonlinear function model based on an exponential inertia weight particle swarm algorithm; and carrying out combined prediction on the single prediction models of the three turning temperature change mean values to obtain a combined prediction model about the turning temperature change mean values. The method has the advantages that different prediction models are weighted and combined by adopting the combined prediction method, the combined prediction model is established by utilizing the useful information of each model, the influence weights of the three-way vibration in different directions on the temperature change are considered, the considered factors are more comprehensive, and the vibration and turning parameters in all directions can be comprehensively utilized to comprehensively predict the turning temperature change mean value.
Description
Technical Field
The invention relates to a combined prediction model of a tool turning temperature change mean value in a turning process and an establishment method thereof, in particular to a combined prediction method for optimizing solving parameters based on an exponential inertia weight particle swarm algorithm, and belongs to the technical field of machining and machining state monitoring informatization.
Background
It is known that during turning, the friction between the tool and the workpiece causes turning vibration, and a large amount of heat is generated at the same time, so that the temperature of the system of the tool and the workpiece is increased, the abrasion of the tool is increased, and the service life of the tool and the surface performance of the workpiece are seriously affected. At the same time, as the tool wears, the geometry of the tool and the manner in which it contacts the workpiece change. The contact area between the cutter and the workpiece is increased, so that the abrasion and turning vibration of the cutter are aggravated, and the friction and heating phenomena are more serious. Therefore, it is necessary to study the change of turning temperature change during turning, considering turning vibration in addition to the influence of turning parameters, by the mutual influence of turning vibration and turning heat during turning.
For a predicted target, there may be a plurality of influencing factors, at which time a plurality of prediction models may be built for the predicted target based on different influencing factors. Based on a plurality of single prediction models, different prediction models are weighted and combined by adopting a combined prediction method, and the combined prediction model is built by combining and utilizing information provided by each model.
For the unknown model, only a single unknown parameter exists, and when the single extremum problem is solved, the traditional algorithm is superior to the intelligent algorithm. However, the intelligent optimization algorithm performs better than the conventional algorithm in solving the global optimal solution for the multi-multipole problem in the combined prediction model of turning temperature variation. The particle swarm optimization algorithm is an artificial intelligence evolution algorithm proposed by Kennedy doctor and Eberhart doctor. Compared with other heuristic algorithms, the particle swarm algorithm has the characteristics of simple structure, simple parameter setting, short running time, strong plasticity and the like, and has wider practical application range.
When the prior art is used for predicting the problem of turning temperature change mean value, a nonlinear model established by an empirical formula in a prediction model is generally converted into a linear model, and a multi-component extremum is solved to obtain a desired multi-component model regression parameter. For example, in experimental study of turning temperature multiple regression model, a nonlinear model is converted into a linear model, but when a plurality of unknowns are solved by the method, the solved regression parameters are usually local optimal solutions, the global optimal effect cannot be achieved, and a particle swarm algorithm can be solved to obtain a global solution better than the traditional method. In addition, in experimental study of a turning temperature multiple regression model, the temperature prediction model predicts the turning temperature only according to turning parameters as variables, turning vibration is not considered, and when training data are aimed at, the model has good prediction effect, but if test data in a test are substituted, the effect is very poor, the correlation coefficient is far less than 0.8, and the prediction model obviously has the fitting phenomenon. Meanwhile, in the existing basic particle swarm algorithm, the weight is constant, and early ripening and oscillation phenomena occur in the later stage.
Disclosure of Invention
The invention aims at: aiming at the defects in the prior art, a combined prediction model establishing method of a tool turning temperature change mean value is provided, and on one hand, compared with a traditional prediction model, the correlation coefficient is higher, and the prediction is more accurate; on the other hand, the influence weights of the three-way turning vibration in different directions on the temperature change are considered, the consideration factors are more comprehensive, and the turning temperature change mean value can be comprehensively predicted by comprehensively utilizing the vibration in all directions and the turning parameters.
In order to achieve the above object, the technical scheme of the invention is as follows:
a method for establishing a combined prediction model of a tool turning temperature change mean value comprises the following steps:
firstly, acquiring temperature and three-way turning vibration signals at a tool nose of a tool in a turning test process through a turning temperature and turning three-way vibration signal acquisition system, further obtaining a change average value of temperature at each moment relative to initial temperature before turning and acceleration root mean square value of three-way vibration in each direction in each turning feeding process, and finally establishing three single prediction models containing to-be-determined parameters of turning temperature change average values relative to turning certain-direction vibration and turning parameters;
secondly, processing the single-phase prediction model established in the first step into a nonlinear function model to be optimized by using a least square method principle, and optimizing and solving undetermined parameters of the nonlinear function model based on an exponential inertia weight particle swarm algorithm to obtain three single-phase prediction models with turning temperature change mean values;
and thirdly, carrying out combined prediction on the single prediction model of the three turning temperature change mean values obtained in the second step to obtain a combined prediction model about the turning temperature change mean values.
According to the method, the root mean square value of acceleration and turning temperature variation average value of three-way turning vibration are obtained based on the collected temperature and vibration signals, and 3 single prediction models containing parameters to be determined of the turning temperature variation average value with respect to the one-way turning vibration and turning parameters are established through an empirical formula; establishing an objective function by using a least square method to obtain 3 single models to be optimized; and optimizing the model by using a particle swarm algorithm, solving to obtain 3 single turning temperature change prediction models, and comprehensively utilizing the useful information of the 3 single models by using a combined prediction method to obtain corresponding combined prediction models. Finally, verifying the combined prediction model, wherein the correlation coefficient of the combined prediction value and the measured value is higher than that of the single model and the measured value, the significance level is less than 0.05, and the effect of predicting turning temperature change by the combined prediction model method based on particle swarm optimization is demonstrated. Therefore, in the new combined model, turning vibration is added to each single model, the turning vibration has strong correlation with turning temperature change, and the overfitting effect of the model can be avoided as much as possible. The particle swarm method adopting the exponential inertia weight improvement is a particle swarm method with linearly decreasing weight, and can improve the searching capability of local and global solutions in the solving process.
The technical scheme of the invention is further optimized as follows:
preferably, the turning temperature and turning three-way vibration signal acquisition system comprises a temperature acquisition system and a vibration signal acquisition system, wherein the temperature acquisition system mainly comprises an infrared thermometer, and the infrared thermometer is connected with a computer through a data line; the vibration signal acquisition system mainly comprises a three-way acceleration sensor, and the three-way acceleration sensor is connected with a computer through a data line.
Preferably, the infrared thermometer is a portable infrared thermometer, and the handheld portable infrared thermometer is a non-contact thermometer and is used for collecting temperature signals of the tool tip of the front tool face at the contact position of the tool and the workpiece in real time.
Preferably, the three-way acceleration sensor is a piezoelectric three-way acceleration sensor, and the piezoelectric three-way acceleration sensor collects X, Y, Z three-way vibration signals at the lower surface of the cutter handle corresponding to the cutter tip of the cutter front cutter face.
Preferably, in the first step, three-way turning vibration acceleration root mean square value and turning temperature change mean value in each turning feeding process are obtained based on the collected temperature and vibration signals, and three single-way prediction models containing parameters to be determined, which are related to the unidirectional turning vibration and turning parameters, of the turning temperature change mean value are established through an empirical formula; the single prediction model of turning temperature change mean value about turning certain directional vibration and turning parameters is as follows:
where i denotes three directions of turning vibration and i=1, 2,3, v is turning speed, v f Is the feed speed, a p Is the back-to-back cutting amount,representing the root mean square value corresponding to the i-th acceleration in three-way turning vibration, <>Representing the corresponding turning temperature variation mean value obtained by fitting the ith turning vibration acceleration root mean square value with the turning parameters, C, x, y, z, w is the regression parameter to be solved.
Preferably, in the second step, the objective function ii of the multiple regression prediction model to be optimized according to the principle of least squares is as follows:
where i denotes three directions of turning vibration and i=1, 2,3, j is the number of trials,n is the number of times of turning feed tests,is the predicted value of the single turning temperature change mean value obtained by fitting the ith turning vibration and turning parameters in the jth feeding process, delta T j Is the measured value of the turning temperature change mean value in the j-th feeding test process, v j Is the turning speed v in the j-th feeding process fj Is the feed speed in the j-th feeding process, a pj Is the back cutting amount in the j-th cutting process,the method shows that the ith acceleration root mean square value corresponding to three-way turning vibration in the jth feeding process is C, x, y, z, w, and the ith acceleration root mean square value is a regression parameter to be solved.
Preferably, in the second step, the specific method for solving the undetermined parameters of the nonlinear function model is as follows:
carrying out optimization solution on the model by adopting an improved exponential inertia weight particle swarm algorithm to obtain a regression parameter, a correlation coefficient and a significance level of a turning temperature change mean value prediction model obtained by X, Y, Z vibration fitting, wherein the regression parameter of the prediction model is C, x, y, z, w, the correlation coefficient is R, and the significance level is P;
judging the reliability of the prediction effect of the prediction model according to the values of the correlation coefficient R and the significance level P, if R is more than or equal to 0.8 and P is less than 0.05, indicating that the prediction effect of the prediction model is reliable and accurate, otherwise, unreliable and accurate, and when the prediction effect is unreliable and accurate, properly changing parameter settings in a particle swarm algorithm, and optimizing the prediction result until the prediction effect of the prediction model is reliable and accurate;
when the prediction effect of the prediction model is reliable and accurate, the regression parameters C, x, y, z, w of the prediction model are substituted into the single prediction model established in the first step, so that the single prediction model with three turning temperature change mean values is obtained.
Preferably, the iterative formula for determining the particle fitness value by the exponential inertia weight particle swarm algorithm is as follows:
ω＝ω init *e^(-t/t max ) (3)
wherein ,vi Indicating the current speed, x of the ith particle i Indicating the current position of the ith particle, wherein omega is the inertia weight, the initial value of omega is 0.9, n indicates that the particle is in the nth dimension, i indicates the ith particle, t indicates the current iteration number, and c 1 and c2 Cognitive and social factors, r 1 and r2 Is [0,1 ]]Random number, p best Is the optimal solution of individual history g best Is the optimal solution of the whole particle population history omega init Represents a constant in the index inertial weight, e≡represents an exponential function based on e, t max Representing the maximum number of iterations. In addition, in the case of the optical fiber,representing the current speed of the ith particle in the nth dimension, t+1st iteration,/and ∈1,>representing the current speed of the ith particle in the nth dimension, t-th iteration, +.>An individual history optimal solution representing the t-th iteration, < >>The whole particle population history optimal solution representing the t-th iteration,>represents the ith particleCurrent position of the nth iteration in the nth dimension,/-th iteration>Representing the current position of the ith particle in the nth dimension, t+1st iteration. In formula (3), "x" represents the multiplication number.
Preferably, the specific scheme of the particle swarm optimization algorithm using the exponential inertia weight is as follows:
(6.1) initializing an initial particle swarm, and inputting actual turning parameters (turning parameters refer to turning speed, back cutting tool amount and feeding speed) and a turning vibration acceleration root mean square value;
(6.2) substituting the initialized particles into the multiple regression prediction model to be optimized, and calculating the fitness value of the particles according to the multiple regression prediction model to be optimized to obtain an individual optimal solution p of each particle best Specifically, calculating a particle fitness value through a multiple regression prediction model to be optimized, wherein the fitness value is the value of the model to be optimized, and if the fitness value is smaller than an individual extremum p best The fitness value is replaced by the individual optimal solution p of the particle best ；
(6.3) storing the individual optimal solutions of all particles to the global optimal solution g by comparing the particle fitness values best In particular for all particles, if the particle fitness value is smaller than the global extremum g best The fitness value is replaced by the global optimal solution g best (the individual optimal solution and the global optimal solution are the regression parameters which are solved);
(6.4) updating the speed and the position of each particle according to the particle fitness value iteration formula and the inertia weight formula, specifically updating the position and the speed of the particle (the position of the particle is the regression parameter of the regression model) according to the particle iteration formulas (1) and (2), wherein the weight in the particle inertia weight formula (3) is the weight omega in the speed formula for dynamically updating the particle, and obtaining the new position and the new speed of the particle according to the particle updating formula;
(6.5) updating the individual optimal solution p best And global optimal solution g best In particular if a new position of a particle is substituted into the model to be optimized if its fitness value is smaller than that of the particleSub-individual optimal solution p best It is replaced to the individual optimal solution p best If there are particles p in these particles best Less than the global optimal solution g best It is replaced by the global optimal solution g best ；
And (6.6) judging whether the iteration times meet the set requirement (the iteration times are based on the minimum error, the maximum number of particle iteration times is the number of times that the model to be optimized obtains the minimum error), stopping operation and outputting a result when the iteration times reach the set requirement, otherwise, returning to the step (6.2) until the iteration times meet the set requirement.
Preferably, in the third step, the combined prediction model building method is as follows:
wherein ,is the mean value of temperature change obtained by combining the prediction models, < >>Is a single predicted temperature change mean value, i represents three directions of turning vibration and i=1, 2,3, < ->Is the average value of the predicted temperature change obtained by fitting the axial vibration and turning parameters, +/->Is the average value of the predicted temperature change obtained by fitting radial vibration and turning parameters, +/->Is the average value alpha of the predicted temperature change obtained by fitting tangential vibration and turning parameters i Is the inertia weight of the single item i in the combined prediction, se i Is the standard error corresponding to the predicted temperature variation mean value of the single item i, m represents 3 directions of turning vibration and m=3. In the above formula "·" represents the multiplication number.
In addition, the combined prediction model is verified, and the combined prediction value is obtainedAnd comparing the measured value delta T with the measured value delta T to obtain a comparison curve of the predicted value and the measured value, and further obtaining a correlation coefficient of the combined predicted value and the measured value, wherein the correlation coefficient is higher than that of a single model and the measured value, the significance level is less than 0.05, and the effect of predicting turning temperature change by a combined prediction model method optimized based on a particle swarm algorithm is demonstrated.
The method has the advantages that when the multivariate extremum is solved, model parameters obtained by solving a single model by using a particle swarm algorithm are higher in precision than those of the traditional algorithm, and a better global solution is obtained; the combined prediction model can use the useful information of different single prediction models, adopts a combined prediction method to carry out weighted combination on different prediction models, and comprehensively utilizes the useful information provided by each model to establish the combined prediction model; the test proves that the prediction effect of the combined prediction model is better than that of a single model; the influence weights of the three-way turning vibration in different directions on the temperature change are considered, the considered factors are more comprehensive, and the turning temperature change mean value can be comprehensively predicted by comprehensively utilizing the vibration in all directions and the turning parameters.
Drawings
The invention is further described below with reference to the accompanying drawings.
FIG. 1 is a schematic diagram of the turning temperature change mean value prediction in the present invention.
FIG. 2 is a flow chart of a turning temperature variation mean combination prediction model according to the present invention.
Fig. 3 is a graph of weights of a particle swarm algorithm searched in three single prediction models in the present invention, fig. 3a is a graph of weights of a particle swarm algorithm searched in an axial vibration prediction model, fig. 3b is a graph of weights of a particle swarm algorithm searched in a radial vibration prediction model, and fig. 3c is a graph of weights of a particle swarm algorithm searched in a tangential vibration prediction model.
FIG. 4 is a graph comparing the average predicted value and the measured value of turning temperature change of each unidirectional prediction model in the present invention.
FIG. 5 is a graph showing the comparison of predicted values and measured values of a combined prediction model of turning temperature variation means in the present invention.
Detailed Description
The invention provides a method for establishing a combined prediction model of a turning temperature change mean value of a cutter, which is shown in fig. 1 and comprises the following steps:
the method comprises the steps that firstly, a turning temperature and turning three-way vibration signal acquisition system which is built by self is used, the turning temperature and turning three-way vibration signal acquisition system comprises a temperature acquisition system and a vibration signal acquisition system, the temperature acquisition system mainly comprises an infrared thermometer, the infrared thermometer is connected with a computer provided with temperature signal acquisition software through a data line, the infrared thermometer is a portable infrared thermometer, the portable infrared thermometer is a non-contact type thermometer, and the portable infrared thermometer is used for acquiring temperature signals of a tool tip of a front tool face at a contact position of a tool and a workpiece in real time. The equipment used in the temperature acquisition system is a hand-held OS523E-2 series non-contact infrared thermometer and acquisition software manufactured by OMEGA corporation of America. The vibration signal acquisition system mainly comprises a three-way acceleration sensor, wherein the three-way acceleration sensor is a piezoelectric three-way acceleration sensor which is arranged on the lower surface of the cutter handle corresponding to the cutter tip of the cutter front cutter surface and is used for acquiring X, Y, Z three-way vibration signals in the turning process through a data line and a computer provided with vibration signal acquisition software. The piezoelectric three-way acceleration sensor adopts an YD-21 piezoelectric three-way accelerometer, namely a vibration signal acquisition system consists of the YD-21 piezoelectric three-way accelerometer, a WS-2402 vibration signal acquisition instrument, DAQ signal acquisition processing software and a computer.
And acquiring temperature and three-way turning vibration signals at the tool nose of the tool in the turning test process, further obtaining a change average value of temperature at each moment relative to initial temperature before turning and acceleration root mean square value of three-way vibration in each direction in each turning feeding process through time domain analysis, and finally establishing three single prediction models containing parameters to be determined of turning temperature change average value relative to turning certain-direction vibration and turning parameters.
According to the method, three-way turning vibration acceleration root mean square value and turning temperature change average value in each turning feeding process are obtained based on collected temperature and vibration signals, three single-way prediction models containing parameters to be determined, of the turning temperature change average value, which relate to unidirectional turning vibration and turning parameters, are established through an empirical formula, and the single-way prediction models of the turning temperature change average value, which relate to certain directional turning vibration and turning parameters, are as follows:
where i denotes three directions of turning vibration and i=1, 2,3, v is turning speed, v f Is the feed speed, a p Is the back-to-back cutting amount,representing the root mean square value corresponding to the i-th acceleration in three-way turning vibration, <>Representing the corresponding turning temperature variation mean value obtained by fitting the ith turning vibration acceleration root mean square value with the turning parameters, C, x, y, z, w is the regression parameter to be solved.
And secondly, processing the single-phase prediction model established in the first step into a nonlinear function model to be optimized by using a least square method principle, and optimizing and solving undetermined parameters of the nonlinear function model based on an exponential inertia weight particle swarm algorithm to obtain the single-phase prediction model with three turning temperature change mean values.
The objective function II of the multiple regression prediction model to be optimized according to the least square method principle is as follows:
wherein i represents three directions of turning vibration and i=1, 2,3, j is the number of test times, n is the number of turning feed tests,is the predicted value of the single turning temperature change mean value obtained by fitting the ith turning vibration and turning parameters in the jth feeding process, delta T j Is the measured value of the turning temperature change mean value in the j-th feeding test process, v j Is the turning speed v in the j-th feeding process fj Is the feed speed in the j-th feeding process, a pj Is the back cutting amount in the j-th cutting process,the method shows that the ith acceleration root mean square value corresponding to three-way turning vibration in the jth feeding process is C, x, y, z, w, and the ith acceleration root mean square value is a regression parameter to be solved.
The specific method for solving the undetermined parameters of the nonlinear function model is as follows:
carrying out optimization solving on the model by adopting an improved exponential inertia weight particle swarm algorithm, namely carrying out the solving process on model parameters when the value of the model to be optimized is infinitely close to 0, wherein the solving process is as shown in the following 6.1-6.6, and finally obtaining regression parameters, correlation coefficients and significance levels of a turning temperature change mean value prediction model obtained by X, Y, Z-vibration fitting, wherein the regression parameters of the prediction model are C, x, y, z, w, the correlation coefficients are R, and the significance levels are P;
judging the reliability of the prediction effect of the three prediction models according to the values of the correlation coefficient R and the significance level P, if R is more than or equal to 0.8 and P is less than 0.01, indicating that the prediction effect of the three prediction models is reliable and accurate, otherwise, unreliable and accurate, and when the prediction effect is unreliable and accurate, properly changing parameter settings in a particle swarm algorithm, optimizing the prediction result until the prediction effect of the prediction model is reliable and accurate;
when the prediction effect of the three prediction models is reliable and accurate, the prediction model regression parameters C, x, y, z, w are substituted into the single prediction model established in the first step, so that the single prediction model with three turning temperature change mean values is obtained.
The iterative formula for determining the particle fitness value by the exponential inertia weight particle swarm algorithm is as follows:
ω＝ω init *e^(-t/t max ) (3)
wherein ,vi Indicating the current speed, x of the ith particle i Indicating the current position of the ith particle, wherein omega is the inertia weight, the initial value of omega is 0.9, n indicates that the particle is in the nth dimension, i indicates the ith particle, t indicates the current iteration number, and c 1 and c2 Cognitive and social factors, r 1 and r2 Is [0,1 ]]Random number, p best Is the optimal solution of individual history g best Is the optimal solution of the whole particle population history, t max Represents the maximum iteration step number omega init Represents a constant in the index inertial weight, e≡represents an exponential function based on e, t max Representing the maximum number of iterations. In addition, in the case of the optical fiber,representing the current speed of the ith particle in the nth dimension, t+1st iteration,/and ∈1,>representing the current speed of the ith particle in the nth dimension, t-th iteration, +.>Represents the tIndividual history optimal solution for multiple iterations, +.>The whole particle population history optimal solution representing the t-th iteration,>representing the current position of the ith particle in the nth dimension, t-th iteration, +.>Representing the current position of the ith particle in the nth dimension, t+1st iteration.
The specific scheme of the particle swarm optimization algorithm using the index inertia weight is as follows:
(6.1) initializing an initial particle swarm, and inputting actual turning parameters (turning parameters refer to turning speed, back cutting tool amount and feeding speed) and a turning vibration acceleration root mean square value;
(6.2) substituting the initialized particles into the multiple regression prediction model to be optimized, calculating the fitness value of the particles, wherein the fitness value is the value of the model to be optimized, and if the fitness value is smaller than the individual extremum p best The fitness value is replaced to the individual optimal solution p of the particle best ；
(6.3) for all particles if its fitness value is less than the global extremum g best The fitness value is replaced by the global optimal solution g best (the individual optimal solution and the global optimal solution are the regression parameters which are solved);
(6.4) updating the position and the speed of the particles (the position of the particles is the regression parameter of the regression model) according to the particle iteration formulas (1) and (2), wherein the weight in the particle inertia weight formula (3) is the weight omega in the speed formula for dynamically updating the particles, and obtaining the new position and the new speed of the particles according to the particle updating formula;
(6.5) if the new position of the particle is substituted into the model to be optimized, if the fitness value is smaller than the individual optimal solution p of the particle best It is replaced to the individual optimal solution p best If there are particles p in these particles best Less than the global optimal solution g best It is replaced by the global optimal solution g best ；
And (6.6) judging whether the iteration times meet the set requirement (the iteration times are based on the minimum error, the maximum number of particle iteration times is the number of times that the model to be optimized obtains the minimum error), stopping operation and outputting a result when the iteration times reach the set requirement, otherwise, returning to the step (6.2) until the iteration times meet the set requirement.
And thirdly, carrying out combined prediction on the single prediction model of the three turning temperature change mean values obtained in the second step to obtain a combined prediction model about the turning temperature change mean values.
The combined prediction model building method comprises the following steps:
wherein ,is the mean value of temperature change obtained by combining the prediction models, < >>Is a single predicted temperature change mean value, i represents three directions of turning vibration and i=1, 2,3, n is the number of turning feed trials, +.>Is the average value of the predicted temperature change obtained by fitting the axial vibration and turning parameters, +/->Is the average value of the predicted temperature change obtained by fitting radial vibration and turning parameters, +/->Is the average value alpha of the predicted temperature change obtained by fitting tangential vibration and turning parameters i Is the inertia weight of the single item i in the combined prediction, se i Is the standard error corresponding to the predicted temperature variation mean value of the single item i, m represents 3 directions of turning vibration and m=3.
In addition, the combined prediction model is verified, and the combined prediction value is obtainedAnd comparing the measured value delta T with the measured value delta T to obtain a comparison curve of the predicted value and the measured value, and further obtaining a correlation coefficient of the combined predicted value and the measured value, wherein the correlation coefficient is higher than that of a single model and the measured value, the significance level is less than 0.05, and the effect of predicting turning temperature change by a combined prediction model method optimized based on a particle swarm algorithm is demonstrated.
Example 1
In the aluminum alloy turning test of the embodiment, the cutter is a hard alloy cutter, and the workpiece is an aluminum bar with the diameter of 45 mm. In the turning test, the influence of three parameters, namely spindle rotation speed, feed speed and back cutting tool draft, on turning temperature is mainly considered. The spindle rotation speed is designed to be 4 levels, the feeding speed and the back cutting amount are designed to be 3 levels, and a specific test scheme is shown in table 1.
Table 1 turning test protocol
Turning tests are carried out according to the scheme shown in table 1, a turning temperature signal acquisition and cutter three-way vibration signal synchronous acquisition test system is established, and characteristic values of various data are extracted by processing the data, as shown in table 2.
Table 2 turning test data
Establishing a predictive model of turning temperature change mean value with respect to turning parameters and turning vibration:
where i is the three directions of turning vibration (i=1, 2, 3), v is the turning speed, v f Is the feed speed, a p Is the back-to-back cutting amount,is the root mean square value corresponding to the i-th acceleration in three-way turning vibration, <>The mean value of turning temperature change corresponding to the fitting of the root mean square value of the i-th turning vibration acceleration and the turning parameter is C, x, y, z, w, and the regression parameter is needed to be solved.
Obtaining a regression model target function II to be optimized as by a least square method principle
Where i is the three directions of turning vibration (i=1, 2, 3), j is the number of test times, and n is the number of turning feed tests.Is the predicted value of the single turning temperature change mean value obtained by fitting the ith turning vibration and turning parameters in the jth feeding process, delta T j Is the measured value of the turning temperature change mean value in the j-th turning test process. v j Is the turning speed v in the j-th feeding process fj Is the feed speed in the j-th feeding process, a pj Is the back cutting amount in the j-th cutting process,indicating the j-th feeding courseCorresponding to the i-th radial acceleration root mean square value in three-way turning vibration, C, x, y, z, w is a regression parameter to be solved.
The model function (2) to be optimized is a nonlinear least square function, and the embodiment improves an exponential inertia weight particle swarm algorithm to optimize and solve the model by matlab programming. Fig. 2 is a technical flow diagram of model building.
The test data in table 2 were substituted into the calculation program as follows:
/>
/>
/>
/>
after the program is run, regression parameters and correlation coefficients of the turning temperature change mean value prediction model obtained by axial vibration fitting can be obtained, and the regression parameters and the correlation coefficients of the radial and tangential turning temperature change mean value prediction model can be obtained in the same way. The specific data are shown in Table 3.
TABLE 3 regression parameters and correlation coefficients
/>
Where C, x, y, z, w are the required predictive model regression parameters, R is the correlation coefficient, and P is the significance level. The correlation coefficient is above 0.85 in all three models, and the significance level is less than 0.05. And the prediction effect of the three prediction models is reliable and accurate. Fig. 3 is a graph of the fitness evolution of the particle swarm algorithm, and fig. 4 is a graph of the comparison of the mean value predicted value and the measured value of the turning temperature change of the axial, radial and tangential vibration prediction models. The resulting axial, radial and tangential 3 single prediction models are
Three single fitting models of turning temperature change are obtained above, turning parameters in the three models are the same dependent variable, and turning vibration is different dependent variable because vibration data in different directions are adopted respectively. Thus, the results of the three model predicted turning temperatures are different for the same turning parameters. In order to obtain unified prediction results, the 3 prediction models are subjected to combined analysis, three-way vibration influencing turning temperature change and three turning parameters are comprehensively considered, and the combined prediction model based on the turning temperature change mean value weighted by the fitting goodness is researched.
The combined prediction model of the expected value method is to calculate a weighted arithmetic average value for various prediction results, and the formula is that
in the formula ,is a combined predictive model; />Is a single turning temperature change prediction model which has been established before, i represents three directions of turning vibration (i=1, 2, 3), n is the number of turning feed tests, and +.>Is the average value of the predicted temperature change obtained by fitting the axial vibration and turning parameters, +/->Is the average value of the predicted temperature change obtained by fitting radial vibration and turning parameters, +/->The average value of the predicted temperature change obtained by fitting tangential vibration and turning parameters; /> wherein ai Is the weight of each prediction model, i.e. a i Is the inertial weight of the single item i at the time of combined prediction. In formula (7) se i For standard error of prediction value of each model, i.e. se i Is the standard error corresponding to the predicted temperature variation mean value of the single item i, m represents 3 directions of turning vibration and m=3. And (3) carrying out combined prediction on the obtained three single prediction models through formulas (6) - (7). The standard error and weight data obtained are shown in table 4.
Table 4 correlation data of combined prediction model
Then the combined predictive model is
FIG. 5 is a graph comparing the mean value predicted value and the measured value of the turning temperature change of the combined prediction model.
The invention relates to a method for establishing a combined prediction model of a tool turning temperature change mean value, which is different from the method for solving a multielement extremum by utilizing a traditional algorithm according to an empirical formula in the prior literature. And by utilizing a combined prediction method, turning vibration in all directions of the single-phase model is comprehensively utilized, so that the final turning temperature change mean value prediction result is more accurate, and the finally obtained prediction model is better than the single-phase model. According to the method, the turning heat is analyzed by adopting the temperature change value, so that the influence of the difference of different environment temperatures on the turning heat can be eliminated. Different from the turning temperature change predicted by the turning parameters only, the influence factors of materials and a machine tool are considered after the turning vibration prediction is added, and the application range is wider. And turning vibration is easy to measure relative to turning temperature, and the method can alleviate the difficulty of measuring the turning temperature change average value in real time to a certain extent in a working place with a severe environment.
The foregoing is a preferred embodiment of the invention, and it should be noted that: it will be apparent to those skilled in the art that the principles of the present invention may be employed without departing from such principles. Corresponding modifications are made to the invention, which should also be regarded as the scope of protection.
Claims (7)
1. The method for establishing the combined prediction model of the turning temperature change mean value of the cutter is characterized by comprising the following steps of:
firstly, acquiring temperature and three-way turning vibration signals at a tool nose of a tool in a turning test process through a turning temperature and turning three-way vibration signal acquisition system, further obtaining a change average value of temperature at each moment relative to initial temperature before turning and acceleration root mean square value of three-way vibration in each direction in each turning feeding process, and finally establishing three single prediction models containing to-be-determined parameters of turning temperature change average values relative to turning certain-direction vibration and turning parameters;
secondly, processing the single-phase prediction model established in the first step into a nonlinear function model to be optimized by using a least square method principle, and optimizing and solving undetermined parameters of the nonlinear function model based on an exponential inertia weight particle swarm algorithm to obtain three single-phase prediction models with turning temperature change mean values; the specific scheme of the particle swarm optimization algorithm using the index inertia weight is as follows:
(6.1) initializing an initial particle swarm, and inputting actual turning parameters and a turning vibration acceleration root mean square value;
(6.2) calculating the fitness value of the particles according to the multiple regression prediction model to be optimized to obtain the individual optimal solution p of each particle best ；
(6.3) storing the individual optimal solutions of all particles to the global optimal solution g by comparing the particle fitness values best ；
(6.4) updating the speed and the position of each particle according to the particle fitness value iteration formula and the inertia weight formula;
(6.5) updating the individual optimal solution p best And global optimal solution g best ；
(6.6) judging whether the iteration times meet the set requirement, stopping running and outputting a result when the iteration times meet the set requirement, otherwise, returning to the step (6.2) until the iteration times meet the set requirement;
the iterative formula for determining the particle fitness value by the exponential inertia weight particle swarm algorithm is as follows:
ω＝ω init *e^(-t/t max )
wherein ,representing the current speed of the ith particle in the nth dimension, t+1st iteration,/and ∈1,>representing the current position of the ith particle in the nth dimension, t+1st iteration, v i Indicating the current speed, x of the ith particle i Indicating the current position of the ith particle, wherein omega is the inertia weight, the initial value of omega is 0.9, n indicates that the particle is in the nth dimension, i indicates the ith particle, t indicates the current iteration number, and c 1 and c2 Cognitive and social factors, r 1 and r2 Is [0,1 ]]Random number, p best Is the optimal solution of individual history g best Is the optimal solution of the whole particle population history omega init Represents a constant in the index inertial weight, e≡represents an exponential function based on e, t max Representing a maximum number of iterations;
thirdly, carrying out combined prediction on the single prediction model of the three turning temperature change mean values obtained in the second step to obtain a combined prediction model about the turning temperature change mean values; the combined prediction model building method comprises the following steps:
wherein ,is the mean value of temperature change obtained by combining the prediction models, < >>Is a single predicted temperature change mean value, i represents three directions of turning vibration and i=1, 2,3, a i Is the inertia weight of the single item i in the combined prediction, se i Is the standard error corresponding to the predicted temperature variation mean value of the single item i, m represents 3 directions of turning vibration and m=3.
2. The method for establishing the combined prediction model of the turning temperature change mean value of the cutter according to claim 1, wherein the turning temperature and turning three-way vibration signal acquisition system comprises a temperature acquisition system and a vibration signal acquisition system, the temperature acquisition system mainly comprises an infrared thermometer, and the infrared thermometer is connected with a computer through a data line; the vibration signal acquisition system mainly comprises a three-way acceleration sensor, and the three-way acceleration sensor is connected with a computer through a data line.
3. The method for establishing the combined prediction model of the turning temperature change mean value of the cutter according to claim 2, wherein the infrared thermometer is a portable infrared thermometer and is used for collecting temperature signals of a tool tip of a rake face at a contact position of the cutter and a workpiece in real time.
4. The method for establishing the combined prediction model of the turning temperature change mean value of the cutter according to claim 2, wherein the three-way acceleration sensor is a piezoelectric three-way acceleration sensor, and the piezoelectric three-way acceleration sensor collects X, Y, Z three-way vibration signals at the lower surface of the cutter handle corresponding to the cutter tip of the front cutter face of the cutter.
5. The method for establishing the combined prediction model of the turning temperature variation mean value of the cutter according to claim 1, wherein in the first step, three-way turning vibration acceleration root mean square value and turning temperature variation mean value in each turning feeding process are obtained based on the collected temperature and vibration signals, and three single prediction models containing parameters to be determined of the turning temperature variation mean value with respect to one-way turning vibration and turning parameters are established through an empirical formula; the single prediction model of turning temperature change mean value about turning certain directional vibration and turning parameters is as follows:
where i denotes three directions of turning vibration and i=1, 2,3, v is turning speed, v f Is the feed speed, a p Is the back-to-back cutting amount,representing the root mean square value corresponding to the i-th acceleration in three-way turning vibration, <>Representing the corresponding turning temperature variation mean value obtained by fitting the ith turning vibration acceleration root mean square value with the turning parameters, C, x, y, z, w is the regression parameter to be solved.
6. The method for building a combined prediction model of a tool turning temperature variation mean value according to claim 5, wherein in the second step, the objective function of the multiple regression prediction model to be optimized according to the least square methodThe following are provided:
wherein i represents three directions of turning vibration and i=1, 2,3, j is the number of test times, n is the number of turning feed tests,is the predicted value of the single turning temperature change mean value obtained by fitting the ith turning vibration and turning parameters in the jth feeding process, delta T j Is the measured value of the turning temperature change mean value in the j-th feeding test process, v j Is the turning speed v in the j-th feeding process fj Is the feed speed in the j-th feeding process, a pj Is the back cutting amount in the j-th feeding process>The method shows that the ith acceleration root mean square value corresponding to three-way turning vibration in the jth feeding process is C, x, y, z, w, and the ith acceleration root mean square value is a regression parameter to be solved.
7. The method for establishing a combined prediction model of a tool turning temperature variation mean value according to claim 6, wherein in the second step, the specific method for solving the parameters to be determined of the nonlinear function model is as follows:
carrying out optimization solution on the model by adopting an improved exponential inertia weight particle swarm algorithm to obtain a regression parameter, a correlation coefficient and a significance level of a turning temperature change mean value prediction model obtained by X, Y, Z vibration fitting, wherein the regression parameter of the prediction model is C, x, y, z, w, the correlation coefficient is R, and the significance level is P;
judging the reliability of the prediction effect of the prediction model according to the values of the correlation coefficient R and the significance level P, if R is more than or equal to 0.8 and P is less than 0.05, indicating that the prediction effect of the prediction model is reliable and accurate, otherwise, not reliable and accurate;
when the prediction effect of the prediction model is reliable and accurate, the regression parameters C, x, y, z, w of the prediction model are substituted into the single prediction model established in the first step, so that the single prediction model with three turning temperature change mean values is obtained.
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