CN109240204A - A kind of numerical control machining tool heat error modeling method based on two-step method - Google Patents
A kind of numerical control machining tool heat error modeling method based on two-step method Download PDFInfo
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- G—PHYSICS
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- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B19/00—Programme-control systems
- G05B19/02—Programme-control systems electric
- 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 numerical control machining tool heat error modeling method based on two-step method that the invention discloses a kind of, it solves the problems, such as not high to the precision of prediction of actual measurement Thermal Error in the prior art, predicts that obtained Thermal Error closer to actual measurement Thermal Error, has good precision of prediction；Its technical solution are as follows: drive system heat distortion amount is modeled with BP neural network first, the relationship between drive system actual measurement Thermal Error y and practical heat distortion amount x is then acquired by polynomial interopolation fitting, constructs Thermal Error prediction model x*、y*。
Description
Technical field
The present invention relates to numerical control machine tool technique field more particularly to a kind of numerical control machining tool heat error modelings based on two-step method
Method.
Background technique
As numerically-controlled machine tool gradually develops, requirement of the lathe to machining accuracy is higher and higher.Machine tool error include Thermal Error,
Error caused by geometric error and power, wherein error caused by thermal deformation accounts for the 40%~70% of machine tool error.Ball-screw
As the important transmission parts of lathe, it is widely used in servo feed system, such as numerically-controlled machine tool and feeding with high precision platform, lathe essence
Degree is directly influenced by ball-screw position error.Friction generates heat during operation for feed system, this leads to the temperature of lead screw
Degree increases, and generates biggish Thermal Error, influences machine tool accuracy.Therefore, to ball-screw Temperature Distribution, thermal deformation rule and heat
Error Compensation Technology carries out mathematical modeling research, can preferably study influence of the Thermal Error to machine finish.
For drive system Thermal Error, domestic and foreign scholars widely grind in terms of machine tool thermal error modeling and compensation
Study carefully.Main method has: neural network model method, multiple linear regression method, FInite Element and many-body theory establish Thermal Error model
Method etc..
In most of researchs, emphasis is the how motion-affecting accuracy of system temperature rise and how to reduce fuel factor,
It is all directly to replace Thermal Error caused by machine tool lead screw thermal deformation without accurate with actual measurement Thermal Error in most thermodynamics experiments
Ground indicates relationship between the two with formula.
Summary of the invention
For overcome the deficiencies in the prior art, the numerical control machining tool heat error modeling based on two-step method that the present invention provides a kind of
Method predicts that obtained Thermal Error closer to actual measurement Thermal Error, has good precision of prediction.
The present invention adopts the following technical solutions:
A kind of numerical control machining tool heat error modeling method based on two-step method, first with BP neural network to drive system thermal change
Shape amount is modeled, then acquired by polynomial interopolation fitting drive system actual measurement Thermal Error y and practical heat distortion amount x it
Between relationship, construct Thermal Error prediction model x*、y*。
Further, specific modeling process are as follows:
Step (1) initializes network topology structure, BP neural network weight and threshold value, obtains BP neural network structure；
Step (2) is trained using the thermal change graphic data under different service conditions, calculates error；
Step (3) judges whether to meet termination condition:
When being unsatisfactory for termination condition, weight and threshold value are updated, is repeated step (2)；
When meeting termination condition, parameter is inputted according to drive system and obtains prediction heat distortion amount x*；
Step (4) is according to prediction heat distortion amount x*And the variable relation that polynomial interopolation fitting obtains obtains prediction Thermal Error
y*。
Further, in the step (1), for thermal deformation part, by temperature rise and heat distortion amount data to BP nerve net
Network is trained.
Further, thermal deformation model is established to Ball-screw Drive Systems with BP neural network, with the temperature rise of temperature measuring point
Value is as in input variable input BP neural network, and ball-screw heat distortion amount is as output variable.
Further, in the step (2), with Thermal Error test in speed of table v, runing time t and working line
Journey l carries out the variation of service condition as input quantity.
Further, in the step (3), when meeting termination condition, input service platform speed, runing time, work
Stroke and nut revolving speed obtain prediction lead screw thermal expansion length x*。
Further, in the step (4), polynomial interopolation fit procedure are as follows:
1) experimental data x, y is inputted, final fitting order is determined by fitting of a polynomial accuracy comparison；
2) order is finally fitted according to multinomial to multi-group data to be trained, obtain the specific mould of multinomial between two errors
Type.
Further, it is described 1) in, it is accurate right to Thermal Error fitting of the different order multinomials under same experiment condition
Than analysis multiple groups experimental selection goes out suitable order as final fitting order；Wherein, evaluation index be and variance SSE and
Square error RMSE.
Further, in Ball-screw Drive Systems, laser displacement sensor is placed on lead screw shaft end, to measure lead screw
The heat distortion amount of shaft end obtains stage positioning errors by laser interferometer measurement.
Further, for actual measurement Thermal Error test, measuring phases are removed, reach thermal balance, movement side from lathe booting
Formula is to determine stroke uniform speed reciprocating motion, shuts down one group of data of measurement at interval of setting time.
Compared with prior art, the beneficial effects of the present invention are:
(1) present invention lead screw heat distortion amount is modeled with BP neural network, then by polynomial interopolation fitting come
The relationship between y and the practical heat distortion amount x of lead screw is acquired, Thermal Error prediction model is constructed；Have compared to direct method better
Precision of prediction, more suitable for engineer application；
(2) present invention can acquire workbench actual measurement Thermal Error and the practical thermal deformation of lead screw by polynomial interopolation fitting
Relationship between amount, high reliablity.
Detailed description of the invention
The accompanying drawings constituting a part of this application is used to provide further understanding of the present application, and the application's shows
Meaning property embodiment and its explanation are not constituted an undue limitation on the present application for explaining the application.
Fig. 1 is flow chart of the invention；
Fig. 2 is ball-screw platform measuring schematic diagram of the invention；
Fig. 3 is neural network structure figure；
Fig. 4 is the temperature rise curve figure of present invention experiment I；
Fig. 5 is the actual measurement Thermal Error curve graph of present invention experiment I；
Fig. 6 is the temperature rise curve figure of present invention experiment II；
Fig. 7 is the actual measurement Thermal Error and prediction model statistic curve figure of present invention experiment II；
Fig. 8 is measurement error composition figure；
Fig. 9 is the temperature rise curve figure of present invention experiment III；
Figure 10 is the thermal deformation errors and prediction model statistic curve figure of present invention experiment III；
Figure 11 is the temperature rise curve figure of present invention experiment IV；
Figure 12 is the actual measurement Thermal Error and prediction model statistic curve figure of present invention experiment IV；
Wherein, 1- laser interferometer, 2- interference mirror, 3- reflecting mirror, 4- magnet base, 5- nut, the distal end 6- bearing, 7-PC
Machine, 8- pedestal, 9- ball-screw, the proximal end 10- bearing, 11- motor, 12- workbench.
Specific embodiment
It is noted that following detailed description is all illustrative, it is intended to provide further instruction to the application.Unless another
It indicates, all technical and scientific terms used herein has usual with the application person of an ordinary skill in the technical field
The identical meanings of understanding.
It should be noted that term used herein above is merely to describe specific embodiment, and be not intended to restricted root
According to the illustrative embodiments of the application.As used herein, unless the context clearly indicates otherwise, otherwise singular
Also it is intended to include plural form, additionally, it should be understood that, when in the present specification using term "comprising" and/or " packet
Include " when, indicate existing characteristics, step, operation, device, component and/or their combination.
As background technique is introduced, the deficiency not high to the precision of prediction of actual measurement Thermal Error exists in the prior art,
In order to solve technical problem as above, the numerical control machining tool heat error modeling method based on two-step method that present applicant proposes a kind of.
In a kind of typical embodiment of the application, as shown in Figure 1, providing a kind of numerically-controlled machine tool based on two-step method
Thermal error modeling method, that is, drive system heat distortion amount is modeled with BP neural network first, is then inserted by multinomial
Value is fitted to acquire the relationship between drive system actual measurement Thermal Error y and practical heat distortion amount x, constructs Thermal Error prediction model
x*、y*。
The position error significant portion of feed drive system is caused by the thermal deformation of lead screw pair, with lead screw axial direction heat distortion amount
X is indicated:
X=s (t)-s (1)
In formula (1): the position of s expression lead screw pair certain point.
Lathe booting moves at specified stroke, and to ignore position error, using this measurement result as initial value, heat is accidentally
Difference is reflected as in laser interferometer measurements each in thermodynamics experiment and the difference between it, this error, which is referred to as, surveys heat accidentally
Poor y.
The error that laser interferometer measures cannot simply be equal to lead screw heat distortion amount, because in ball-screw and work
There is transmission chains between platform.So the error that laser interferometer measurement obtains is as caused by lead screw thermal deformation, but the two is simultaneously
It is unequal.
Assuming that relationship and non-linear relation between y and x, can carry out algebraic relation between the two by multinomial
Fitting:
Y=λ0+λ1x+λ2x2+λ3x3+……+λnxn (2)
In formula (2), y indicates that feed drive system is set to the actual measurement Thermal Error at s in place；λ0、λ1、λ2、λ3…λnExpression is repaired
Positive coefficient reflects the relationship of actual measurement Thermal Error and lead screw heat distortion amount；X indicates heat distortion amount of the lead screw at the s of position.
λ0、λ1、λ2、λ3…λnCan be acquired by a variety of methods, for example, Grey systemstic theory, neural network, least square method,
Regression analysis, multivariate regression analysis etc..
The application provides a kind of compound thermal error modeling method, specifically:
Step (1) initializes network topology structure, BP neural network weight and threshold value, obtains BP neural network structure；
Step (2) is trained using the thermal change graphic data under different service conditions, calculates error；
Step (3) judges whether to meet termination condition:
When being unsatisfactory for termination condition, weight and threshold value are updated, is repeated step (2)；
When meeting termination condition, parameter is inputted according to drive system and obtains prediction heat distortion amount x*；
Step (4) is according to prediction heat distortion amount x*And the variable relation that polynomial interopolation fitting obtains obtains prediction Thermal Error
y*；
Wherein, polynomial interopolation fit procedure are as follows:
1) experimental data x, y is inputted, final fitting order is determined by fitting of a polynomial accuracy comparison；
2) order is finally fitted according to multinomial to multi-group data to be trained, obtain the specific mould of multinomial between two errors
Type.
The application is modeled with BP neural network, establishes dynamic lead screw thermal deformation model.Experiment based on ball-screw platform into
Row modeling, using Thermal Error test in speed of table v, runing time t and impulse stroke l as input quantity to each service condition
It is changed, measures lead screw thermal deformation and temperature, establish the Thermal Error model of ball-screw.Process is carried out in thermodynamics experiment
In, pass through the experimental data of laser displacement sensor real-time detection lead screw thermal deformation variation.
After completing lead screw thermal deformation modeling, between the lead screw thermal deformation under different operating conditions and actual measurement Thermal Error
Relationship carries out fitting of a polynomial solution.After obtaining error information, using least square method to the parametric solution of formula (2).
One, lathe temperature rise, heat distortion amount and actual measurement Thermal Error measurement test:
The application uses experiment porch as shown in Figure 2, i.e. Ball-screw Drive Systems, is equipped on pedestal 8 and motor
11 connected ball-screws 9, attaching nut 5 on ball-screw 9, mounting temperature sensor on the proximal end bearing 10 of ball-screw 9
T1, mounting temperature sensor T2 on distal end bearing 6, mounting temperature sensor T3 on nut 5, environment temperature is by temperature sensor T4
Detection, temperature sensor T1, T2, T3, T4 pass sequentially through signal conditioning circuit, data collecting card connection PC machine 7.
The micro-displacement sensor W1 for measuring heat distortion amount is installed in 9 end of ball-screw, and micro-displacement sensor W1 is same
It is connected to signal conditioning circuit input terminal.
Signal conditioning circuit is also connected with laser interferometer 1, and 1 side sets gradually interference mirror 2, reflecting mirror 3 before laser interferometer,
Interference mirror 2 and laser head are fixed, for measuring actual measurement Thermal Error；Reflecting mirror 3 is installed on magnet base 4, and magnet base 4 is located at work
12 top of platform.
Survey method for measuring thermal error are as follows:
Lathe booting moves at specified stroke, and to ignore position error, using this measurement result as initial value, heat is accidentally
Difference is reflected as each measured value and the difference between it.It is moved back and forth every stopping in ten minutes, it is mobile from point from work zero point
Specified stroke, measured value are to measure Thermal Error.
Ball-screw axial direction heat distortion amount measurement method:
By laser displacement sensor, data collecting card and the end PC program continuous collecting data, finally by the place of program
Reason obtains thermal deformation analysis chart and each point temperature rise chart.
During the experiment, table feed speed, stroke and working time on lead screw thermal deformation all there is influence,
Therefore the influence of the above operating condition has been fully considered in experimental design, specific experiment scheme is as shown in table 1.
Table 1: experimental program
Except measuring phases, thermal balance is reached from lathe booting, motion mode is to determine stroke uniform speed reciprocating motion, Mei Geshi
Minute shuts down one group of data of measurement.Moving starting point and measurement starting point is work zero point.
Two, neural metwork training and fitting of a polynomial:
BP neural network structure is as shown in figure 3, for thermal deformation part, by testing the temperature rise and heat distortion amount number that I is obtained
According to BP neural network training.
Using the temperature rise value of temperature measuring point as in input variable input BP neural network, lead screw heat distortion amount becomes as output
Amount.The temperature rise of lead screw fixing end, nut temperature rise, the temperature rise of lead screw free end, 4 terminal input sections that environment temperature rise is BP neural network
Point, lead screw thermal deformation are then used as its output node.In modeling process, node in hidden layer is 18.
In BP neural network training process, temperature rise value composition array (4 × 19) that 4 temperature measuring points are measured becomes as input
Amount regard lead screw heat distortion amount composition vector (1 × 19) of acquisition this period as output variable.To test II and experiment III
Network is constructed, and it is continued to train.Prediction verifying BP neural network validity is carried out to the data of experiment IV, and is obtained
To the thermal deformation of lead screw everywhere.Algorithm is added by neural metwork training and obtains lead screw thermal deformation overall distribution, it is established that lead screw
Thermal deformation model.
After the model foundation for completing lead screw thermal deformation, the y and x that multiple groups experimentation is measured carry out fitting of a polynomial.
If order is too low, it is low to will lead to matching accuracy；If order is too high, difficulty in computation increases, and error implements compensation difficulty, can
The phenomenon that over-fitting can be will appear, makes the reduction of model robustness.
In each experiment, by being compared to Thermal Error fitting precision of the different order multinomials under the experiment condition,
It analyzes multiple groups experimental selection and goes out suitable order as final fitting order.
Evaluation index SSE is and variance, is the quadratic sum of the error of fitting data and initial data corresponding points；RMSE is equal
Square error is the quadratic sum of fitting data and initial data and the square root of observation frequency m ratio.
As shown in table 2, select n=3 for final fitting order.
2 fitting of a polynomial accuracy comparison of table
At different operating conditions, carry out actual measurement Thermal Error measurement experiment, in an experiment simultaneously measure actual measurement Thermal Error and
The lead screw of corresponding time, obtains the mathematical model between actual measurement Thermal Error and lead screw thermal deformation:
Y=λ0+λ1x+λ2x2+λ3x3 (3)
The data measured by experiment solve the parameter of formula (3), available actual measurement Thermal Error and lead screw thermal deformation
Between concrete model.
Y=0.0076+0.9987x+6.2 × e-5x2+8.4463×e-7x3 (4)
Three, prediction result is analyzed:
The heat that the application in the result obtains BP neural network directly training actual measurement Thermal Error (" direct method ") prediction is accidentally
The Thermal Error curve graph that difference and two-step method are predicted is compared.
Firstly, passing through data training direct method and two-step method in experiment I；Then model is verified by experiment II~IV
Accuracy, while by model successive optimization.
Temperature rise data and the actual measurement Thermal Error y for testing I are as shown in Figure 4 and Figure 5.
Totally five curves, respectively actual measurement Thermal Error y, direct method measure the experimental result analyzed prediction technique in advance
The Thermal Error y arrived1, Thermal Error y that two-step method is predicted2, Thermal Error and survey the error amount between Thermal Error that BP is predictedError amount between the Thermal Error and actual measurement Thermal Error of two-step method prediction
Temperature rise data, actual measurement Thermal Error and the prediction model for testing II are as Figure 6-Figure 7,- 3.5~2.5 μm it
Between fluctuate, andIt is fluctuated between -2.5~2 μm.
Therefore, the estimation effect of two-step method is obviously dominant.
As shown in figure 8, actual measurement Thermal Error consists of two parts, a part is the practical thermal deformation of lead screw in experiment, another
Part is driving error caused by lead screw and table drive.
Therefore, experiment condition changes practical influence lead screw thermal deformation, and the error of fitting of a polynomial part is mainly by lead screw
The influence of each transmission chain between workbench, it is unrelated with experiment service condition.
After lead screw thermal deformation and the actual measurement independent modeling analysis of Thermal Error, the error of BP neural network prediction is not interfered with
Fitting of a polynomial accuracy, therefore the accuracy of its prediction is higher than the former.
According to the temperature rise and data of experiment III, two methods of direct method and two-step method prediction actual measurement Thermal Error are utilized；As a result
As shown in Fig. 9-Figure 10,It is -1.5~1.2 μm, andIt is -0.8~0.7 μm.
According to the experimental results, the latter's precision of prediction is higher by about 80% than the former, this is because by experiment I and experiment II two
Secondary training, model data amount increase, so that modeling tends towards stability, the superiority of two-step method prediction technique is showed.
For testing IV, service condition is complex, and the stroke in three periods is all different.Test the test of IV
Data and curves as shown in Figure 11-Figure 12,It is fluctuated between -5.4~6.6 μm；It is fluctuated between -3.1~2.2 μm.
In complicated service condition, the estimated value deviation of two kinds of models is all bigger than before, but two-step method method is pre-
Survey ratio of precision first method height about 126%, hence it is evident that be better than first method.Illustrate to miss by lead screw thermal deformation and actual measurement heat
After difference carries out fitting of a polynomial, the influence that service condition variation generates the actual measurement Thermal Error that two-step method is predicted will be lower than single
Solely with the prediction technique of BP network training actual measurement Thermal Error.
The foregoing is merely preferred embodiment of the present application, are not intended to limit this application, for the skill of this field
For art personnel, various changes and changes are possible in this application.Within the spirit and principles of this application, made any to repair
Change, equivalent replacement, improvement etc., should be included within the scope of protection of this application.
Claims (10)
1. a kind of numerical control machining tool heat error modeling method based on two-step method, which is characterized in that first with BP neural network to drive
Dynamic system heat distortion amount is modeled, and drive system actual measurement Thermal Error y and reality are then acquired by polynomial interopolation fitting
Relationship between heat distortion amount x constructs Thermal Error prediction model x*、y*。
2. a kind of numerical control machining tool heat error modeling method based on two-step method according to claim 1, which is characterized in that tool
Volume modeling process are as follows:
Step (1) initializes network topology structure, BP neural network weight and threshold value, obtains BP neural network structure；
Step (2) is trained using the thermal change graphic data under different service conditions, calculates error；
Step (3) judges whether to meet termination condition:
When being unsatisfactory for termination condition, weight and threshold value are updated, is repeated step (2)；
When meeting termination condition, parameter is inputted according to drive system and obtains prediction heat distortion amount x*；
Step (4) is according to prediction heat distortion amount x*And the variable relation that polynomial interopolation fitting obtains obtains prediction Thermal Error y*。
3. a kind of numerical control machining tool heat error modeling method based on two-step method according to claim 2, which is characterized in that institute
It states in step (1), for thermal deformation part, BP neural network is trained by temperature rise and heat distortion amount data.
4. a kind of numerical control machining tool heat error modeling method based on two-step method according to claim 3, which is characterized in that with
BP neural network establishes thermal deformation model to Ball-screw Drive Systems, and BP is inputted using the temperature rise value of temperature measuring point as input variable
In neural network, ball-screw heat distortion amount is as output variable.
5. a kind of numerical control machining tool heat error modeling method based on two-step method according to claim 2, which is characterized in that institute
State in step (2), using Thermal Error test in speed of table v, runing time t and impulse stroke l transported as input quantity
The variation of row condition.
6. a kind of numerical control machining tool heat error modeling method based on two-step method according to claim 4, which is characterized in that institute
It states in step (3), when meeting termination condition, input service platform speed, runing time, impulse stroke and nut revolving speed are obtained
Predict lead screw thermal expansion length x*。
7. a kind of numerical control machining tool heat error modeling method based on two-step method according to claim 2, which is characterized in that institute
It states in step (4), polynomial interopolation fit procedure are as follows:
1) experimental data x, y is inputted, final fitting order is determined by fitting of a polynomial accuracy comparison；
2) order is finally fitted according to multinomial to multi-group data to be trained, obtain multinomial concrete model between two errors.
8. a kind of numerical control machining tool heat error modeling method based on two-step method according to claim 7, which is characterized in that institute
It states in 1), to Thermal Error fitting accurate comparison of the different order multinomials under same experiment condition, analyzes multiple groups experimental selection
Suitable order is as final fitting order out；Wherein, evaluation index is and variance SSE and root-mean-square error RMSE.
9. a kind of numerical control machining tool heat error modeling method based on two-step method according to claim 4, which is characterized in that rolling
In ballscrew feed system, laser displacement sensor is placed on lead screw shaft end, to measure the heat distortion amount of lead screw shaft end, is passed through
Laser interferometer measurement obtains stage positioning errors.
10. a kind of numerical control machining tool heat error modeling method based on two-step method according to claim 1, which is characterized in that
For actual measurement Thermal Error test, measuring phases are removed, reach thermal balance from lathe booting, motion mode is reciprocal to determine stroke uniform speed
Movement shuts down one group of data of measurement at interval of setting time.
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