CN111985149A - Convolutional network-based five-axis machine tool rotating shaft thermal error modeling method - Google Patents
Convolutional network-based five-axis machine tool rotating shaft thermal error modeling method Download PDFInfo
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Abstract
A method for modeling a thermal error of a rotating shaft of a five-axis machine tool based on a convolutional network belongs to the technical field of machining precision of numerical control machine tools and mainly comprises the following steps: firstly, determining a thermal infrared imager to shoot an object; secondly, shooting temperature rise and temperature fall images; thirdly, after the thermal image shooting is finished, measuring the rotation angle positioning error of the C axis at different temperatures by adopting a laser interferometer; fourthly, rotating the C axis at a set speed to raise the temperature, and acquiring thermal images and thermal error data for 4 hours by raising and lowering the temperature; fifthly, preprocessing a C-axis thermal image; sixthly, enhancing the thermal image; seventhly, building a multi-output classification convolutional neural network, dividing a data set into a training set, a verification set and a test set, training, stopping training and storing a model; eighth step: and inputting a test set, and checking the prediction accuracy of the model. The method overcomes the difficulty in modeling and detecting the thermal error of the rotating shaft, and can accurately predict the thermal error of the rotating shaft.
Description
Technical Field
The invention belongs to the technical field of machining precision of numerical control machines, and particularly relates to a thermal error modeling method for a rotating shaft of a five-axis machine tool based on a convolutional network.
Background
The rapid development of the manufacturing industry provides a difficult problem of how to process complex parts with high efficiency and high quality, for the problem of processing quality, thermal errors are main error sources in the processing process of a machine tool, and the total error occupation ratio of the machine tool in processing is up to 70 percent; compared with the traditional three-axis machine tool, the five-axis machine tool has the advantage that two rotating shafts in A, B, C are added on the basis of three feeding shafts of x, y and z. Thanks to the two additional rotating shafts, the five-axis machine tool can simultaneously adjust the pose of the tool relative to the workpiece, and has better processing flexibility and higher processing efficiency. Multi-axis machining is becoming a trend in the development of current machine tools. Due to the introduction of the rotating shaft, more error terms are added than a three-axis machine tool. Therefore, effective thermal error modeling of the rotating shaft of the five-axis machine tool plays a key role in controlling the machining error of the five-axis machine tool.
At present, research on modeling of the thermal error of the rotating shaft is less, and an effective scheme for predicting and compensating the thermal error of the rotating shaft is difficult to find. The reason is that the rotating shaft thermal error modeling compensation technology has the problems of data acquisition precision and temperature key point screening.
Disclosure of Invention
The invention provides a method for modeling the thermal error of a rotating shaft of a five-axis machine tool based on a convolutional network, aiming at overcoming the defects of the prior art.
The technical scheme of the invention is as follows: a rotary axis thermal error modeling method based on a convolutional neural network comprises the following steps:
firstly, determining a thermal infrared imager to shoot an object;
secondly, shooting a C-axis area heating and cooling image by using a thermal infrared imager;
thirdly, after the thermal image shooting is finished, measuring the rotation angle positioning errors of the C axis at different temperatures by using a laser interferometer, wherein in the process of measuring the rotation angle positioning errors once, the measurement starting point and the measurement end point are respectively 0 DEG and 360 DEG, and data are collected at every 10 DEG for 36 points;
fourthly, enabling the C shaft to rotate at a set speed to heat up, repeating the second step and the third step at intervals of a certain time in the heating up process to acquire thermal images and thermal error data, stopping the C shaft and cooling down after heating up for five hours, repeating the steps at intervals of a certain time in the cooling down process to acquire thermal images and thermal error data, and keeping the cooling down for 4 hours;
fifthly, preprocessing the C-axis thermal image
After converting the thermal image into an array, subtracting the initial thermal image array to obtain an image array and converting the obtained image array into an image;
sixthly, enhancing the thermal image
Turning and rotating the preprocessed thermal image, wherein the turning and rotating operations comprise up-down turning, left-right turning, and counterclockwise rotating by 90 degrees, 180 degrees and 270 degrees;
seventhly, building a thermal error prediction convolutional neural network
The built thermal error prediction convolutional neural network belongs to a multi-output classification convolutional network, a plurality of labels of an input picture can be predicted, the labels and a thermal image form a data set, the data set is divided into a training set, a verification set and a test set, training is started, the training precision reaches more than 90% of that of the verification set, the training is stopped, and a model is stored;
eighth step: inputting a test set, checking the prediction accuracy of the model, and training the model again if the prediction accuracy does not reach more than 90% until the prediction accuracy reaches more than 90%.
Compared with the prior art, the invention has the beneficial effects that:
the method adopts the thermal infrared imager to collect the temperature-rising and temperature-lowering thermal images of the rotating shaft of the five-axis machine tool; the method comprises the steps of measuring rotation axis rotation angle positioning errors at different temperatures by a laser interferometer, collecting multi-point rotation angle positioning errors, processing thermal error data obtained by measurement, fitting the thermal error data into a sine curve, using sine function parameters as labels to correspond to thermal images to form a data set, and finally designing a multi-output classified convolutional neural network model to finish training and testing to obtain accurate prediction of the rotation axis thermal errors.
The convolutional neural network has the capability of analyzing a large amount of image data information in real time, can mine the internal rules of implementation objects from complex massive image data, automatically extracts input picture characteristics and calculates the extracted characteristics through the convolutional neural network, can overcome the difficulty in a thermal error modeling detection technology, realizes thermal error robust modeling detection under complex working conditions, and can accurately predict the thermal error of a rotating shaft.
By adopting the multi-output classification convolution network model, the thermal error of the rotating shaft angle can be accurately predicted, a plurality of labels of one input picture can be predicted, the training parameters are greatly reduced, the modeling requirement is reduced, the training time is shortened, and the modeling efficiency is improved.
The technical scheme of the invention is further explained by combining the drawings and the embodiment:
drawings
FIG. 1 is a diagram of a process for modeling a thermal error of a rotating shaft of a five-axis machine tool based on a convolution network;
FIG. 2 is a schematic diagram of six geometric errors on the C-axis;
FIG. 3 is a captured rotational axis thermal map;
FIG. 4 is a schematic view of the machine C-axis and worm gear;
FIG. 5 is a diagram of a multi-output convolutional neural network architecture built by an embodiment;
FIG. 6 is a graph of a set of angular position error measurements for the C-axis of the exemplary embodiment;
FIG. 7 is a graph of the fitting result of the original error of the C axis and a set of the rotation angle positioning errors in the embodiment;
FIG. 8 is a graph showing a temperature state change in the C-axis in the embodiment;
FIG. 9 is a graph comparing predicted curves to actual thermal errors in an embodiment;
FIG. 10 is a residual error diagram of predicted values and actual values of the C-axis thermal error model in the test set of the embodiment.
Detailed Description
As shown in fig. 2, six geometric errors are generated during the rotation of the rotating shaft. Taking the C axis as an example, the position errors along the x, y and z directions are includedx(c)、y(c)、z(c) And angular error about x, y, z axesx(c)、y(c)、z(c) In that respect Wherein, the corner positioning error has the biggest influence on the precision of the rotating shaft. In order to effectively improve the machining precision of the five-axis machine tool, the influence of temperature on the positioning precision of the rotating angle is taken as a research object.
Referring to fig. 1 to 5, the method for modeling a rotational axis thermal error of a five-axis machine tool based on a convolutional network according to the present embodiment includes: firstly, determining a thermal imager to shoot an object; as shown in fig. 3 and 4, the axis C of the five-axis machine tool is driven by a motor, a gear pair and a worm gear, and compared with gear transmission, the worm gear transmission has lower transmission efficiency due to larger axial force, is easy to generate heat, and is a main research object of thermal error of the axis C, so that the worm gear area is used as a thermal image shooting object;
secondly, shooting a temperature rise and temperature reduction image of a C-axis turbine worm area by using a thermal infrared imager;
thirdly, measuring the rotation angle positioning errors of the C axis at different temperatures by adopting a laser interferometer, wherein in the process of measuring the rotation angle positioning errors once, the measurement starting point and the measurement end point are respectively 0 DEG and 360 DEG, and data are collected at every 10 DEG for 36 points; it is converted into a prediction of the three parameters of the positive (residual) curve by fitting 36 rotation angle errors. Greatly reduces training parameters, lowers modeling requirements, shortens training time and improves modeling efficiency.
The 36 corner positioning error values are instead represented by 3 function parameters. The distribution of a group of C-axis angular positioning errors, namely 36 angular positioning error points, obtained through measurement of the laser interferometer is in sine function or cosine function distribution with approximate period of 2 pi. The full closed loop control system is adopted for the machine tool, the rotation angle of the C shaft is fed back by the measuring element circular grating, and the feedback result is compared with the command rotation angle to work according to a closed loop. Circular gratings work with moire fringes, a property of which is the sinusoidality. To reduce the training parameters, the measured corner positioning error is fitted to a sinusoidal function:
y＝a·sin(π·β/180+b)+c
in the formula, a parameter is the installation eccentricity of the grating, b is the phase difference, c is the high-order small quantity, and beta is the rotation angle of the rotating shaft;
and the three parameters of a, b and C are used as labels, through fitting, the model is reduced from 36 training and prediction results to 3 training and prediction results, the direct prediction of the C-axis rotation angle positioning error is converted into the prediction of error curve parameters, and the model can be trained by only three classifiers. By the arrangement, training parameters are greatly reduced, modeling requirements are reduced, training time is shortened, and modeling efficiency is improved.
Fourthly, enabling the C axis to rotate at a set speed to heat up, repeating the second step and the third step at intervals of 6 minutes in the heating up process to acquire thermal images and thermal error data, stopping rotating and cooling after heating up for five hours, repeating the steps at intervals of 6 minutes in the cooling down process to acquire thermal images and thermal error data, and keeping cooling down for 4 hours;
fifthly, preprocessing the C-axis thermal image
Eliminating the influence of the initial temperature, converting the image into an array, subtracting the initial image array, and converting the obtained image array into the image;
sixthly, enhancing the thermal image
Turning and rotating the preprocessed image, including turning up and down, turning left and right, and rotating 90 degrees, 180 degrees and 270 degrees anticlockwise; so set up, there are 2 effects, first expand the number of heat pictures; secondly, the model is not influenced by different thermal image angles when the thermal error of the rotating shaft at the same temperature is predicted;
seventhly, as shown in fig. 5, a thermal error prediction convolutional neural network is constructed
The constructed thermal error prediction convolutional neural network belongs to a multi-output classification convolutional network, can predict a plurality of labels of an input picture, the labels and a thermal image form a data set, and the data set is divided into a training set, a verification set and a test set according to the ratio of 8:1: 1. Starting training, stopping training when the training precision reaches more than 90% on the verification set, and storing the model;
the built thermal error prediction convolutional neural network belongs to a multi-output classification convolutional network. Compared with the common multi-label output classification convolutional network, the multi-output classification convolutional network provided by the embodiment has the same convolutional layers, active layers, pooling layers and full connection layers, and a multi-label output classification model with only one group of full connection layers is different from the multi-output classification convolutional network model which has multiple groups of parallel full connection layers and can predict multiple labels of one input picture.
Optionally, the multi-output classification model built in the embodiment is composed of a convolution layer, an activation layer, a pooling layer and three parallel full-connection layers;
convolution layer for clear description of convolution calculation process, each pixel of image is numbered first, xd,i+m,j+nI + m row and j + n column pixels of a d layer representing an image; omegad,m,nRepresenting the mth row and nth column weight of the filter, wbA bias term representing a filter; numbering each element of the feature map with ai,jAn ith row and a jth column element representing the feature map; d is depth; f is the size (width or height, both equal) of the filter, denoted by F the activation function, W2Is the width of the feature map after convolution; w1Is the width of the image before convolution; f is the width of the filter; p is the number of zero padding (make several rounds of 0 around the original image), S is the stride, H2Is the height, H, of the convolved feature map1Is the width of the image before convolution, the convolution is calculated using the following formula;
W2＝(W1-F+2P)/S+ 1
H2＝(H1-F+2P)/S+ 1
an active layer: the image array introduces nonlinear characteristics through an activation layer, and by adopting a ReLU, an operational formula is as follows:
f(x)＝max(0,x)
a pooling layer: the size of the filter is 3 multiplied by 3, the step is 2, the size of the feature graph is reduced, more effective image information is extracted, after forward propagation calculation is completed, training and parameter adjustment are carried out on the model, and the optimal weight parameter and the optimal bias parameter can be obtained by the full connection layer through a back propagation algorithm by using a gradient descent method.
Furthermore, the principle of convolutional layer training is the same as that of a fully-connected layer, the convolutional layer training utilizes chain derivation to calculate the partial derivative of a loss function to each weight, then the weights are updated according to a gradient descent method, the optimal weight parameters and bias term parameters are obtained through a back propagation algorithm, and after the weight parameters and the bias term parameters are adjusted, the accuracy of the multi-output convolutional neural network model reaches the expected accuracy.
Eighth step: inputting a test set, checking the prediction accuracy of the model, and training the model again if the prediction accuracy does not reach more than 90% until the prediction accuracy reaches more than 90%.
Examples
The embodiment operates on a five-axis numerical control machining center (DMU70V type machine tool), illustrated in fig. 1-5, and in a first step and a second step, acquires thermal images of the turbine worm area; during data calibration, as shown in fig. 6, a laser interferometer is used for collecting C-axis rotation angle positioning errors in different temperature states as researched C-axis thermal errors; as shown in fig. 7, the solid black dots in the block represent the original error, the smooth curve represents the fitting curve, the collected thermal error is fitted to the sine (cosine) function, and the parameters of the a, b and c functions are set as labels; as shown in fig. 8, the experiment is divided into a heating process and a cooling process, wherein the rotating speed of the C shaft is 3200 °/min during heating, the C shaft is enabled to rotate 360 ° clockwise and anticlockwise alternately for five hours according to a set speed, and the C shaft is stopped for 4 hours and 9 hours during cooling; after data are preprocessed and expanded, a data set is manufactured and divided into a training set, a verification set and a test set. As shown in fig. 5, a multi-output classification convolutional neural network is constructed, three groups of parallel full-connected layers are provided, then a data set is input for training and prediction, an accurate thermal error is obtained and compared with an actual thermal error, and the result is shown in fig. 9.
FIG. 9 is a comparison of predicted curves versus actual thermal error for a set of data taken one revolution of the C-axis, where the curve with ■ represents the predicted fit curve, the scatter points denoted a represents the actual thermal error values measured with a laser interferometer, and the curve with ● represents the predicted residual, which is the error between the actual thermal error measurements and the model predicted values. Fig. 10 is a diagram of the predicted value of the thermal error of the C axis and the maximum residual error of 36 rotation angles of the actual thermal error value on the prediction set, and fig. 10 shows that the maximum residual error in one prediction is between 8 and 12 arcseconds, which indicates that the thermal error of the rotating axis predicted based on the convolutional network is more consistent with the actual value.
The present invention is not limited to the above embodiments, and any simple modification, equivalent change and modification made by the technical essence of the present invention by those skilled in the art can be made without departing from the scope of the present invention.
Claims (7)
1. A method for modeling the thermal error of a rotating shaft of a five-axis machine tool based on a convolutional network is characterized by comprising the following steps: it includes:
firstly, determining a thermal infrared imager to shoot an object;
secondly, shooting a C-axis area heating and cooling image by using a thermal infrared imager;
thirdly, after the thermal image shooting is finished, measuring the rotation angle positioning errors of the C axis at different temperatures by using a laser interferometer, wherein in the process of measuring the rotation angle positioning errors once, the measurement starting point and the measurement end point are respectively 0 DEG and 360 DEG, and data are collected at every 10 DEG for 36 points;
fourthly, enabling the C shaft to rotate at a set speed to heat up, repeating the second step and the third step at intervals of a certain time in the heating up process to acquire thermal images and thermal error data, stopping the C shaft and cooling down after heating up for five hours, repeating the steps at intervals of a certain time in the cooling down process to acquire thermal images and thermal error data, and keeping the cooling down for 4 hours;
fifthly, preprocessing the C-axis thermal image
After converting the thermal image into an array, subtracting the initial thermal image array to obtain an image array and converting the obtained image array into an image;
sixthly, enhancing the thermal image
Turning and rotating the preprocessed thermal image, wherein the turning and rotating operations comprise up-down turning, left-right turning, and counterclockwise rotating by 90 degrees, 180 degrees and 270 degrees;
seventhly, building a thermal error prediction convolutional neural network
The built thermal error prediction convolutional neural network belongs to a multi-output classification convolutional network, a plurality of labels of an input picture can be predicted, the labels and a thermal image form a data set, the data set is divided into a training set, a verification set and a test set, training is started, the training precision reaches more than 90% of that of the verification set, the training is stopped, and a model is stored;
eighth step: inputting a test set, checking the prediction accuracy of the model, and training the model again if the prediction accuracy does not reach more than 90% until the prediction accuracy reaches more than 90%.
2. The method for modeling the thermal error of the rotating shaft of the five-axis machine tool based on the convolutional network as claimed in claim 1, wherein the method comprises the following steps: it includes: in the third step, the distribution of 36 corner positioning error points obtained by the measurement of the laser interferometer is distributed in a sine function or cosine function with an approximate period of 2 pi.
3. The method for modeling the thermal error of the rotating shaft of the five-axis machine tool based on the convolutional network as claimed in claim 2, wherein: the sinusoidal function fitted by the corner positioning error measured in the third step is:
y＝a·sin(π·β/180+b)+c
in the formula, a parameter is the installation eccentricity of the grating, b is the phase difference, c is the high-order small quantity, and beta is the rotation angle of the rotating shaft;
and taking three parameters of a, b and c as labels. After fitting, the model is reduced from 36 training and prediction results to 3 training and prediction results, and direct prediction of the C-axis rotation angle positioning error is converted into prediction of error curve parameters.
4. The method for modeling the thermal error of the rotating shaft of the five-axis machine tool based on the convolutional network as claimed in claim 3, wherein the method comprises the following steps: the data set is divided into a training set, a validation set and a test set according to the ratio of 8:1: 1.
5. The method for modeling the thermal error of the rotating shaft of the five-axis machine tool based on the convolutional network as claimed in claim 4, wherein the method comprises the following steps: the multi-output classification convolutional network comprises a convolutional layer, an activation layer, a pooling layer and three groups of parallel full-connection layers;
convolutional layer for the sake of clarity in describing the convolution calculation process, each pixel of the image is first numbered, xd,i+m,j+nI + m row and j + n column pixels of a d layer representing an image; omegad,m,nRepresenting the mth row and nth column weight of the filter, wbA bias term representing a filter; numbering each element of the feature map with ai,jAn ith row and a jth column element representing the feature map; d is depth; f is the size of the filter, denoted by F the activation function, W2Is the width of the feature map after convolution; w1Is the width of the image before convolution; f is the width of the filter; p is the number of zero padding, S is the stride, H2Is the height, H, of the convolved feature map1Is the width of the image before convolution, the convolution is calculated using the following formula;
W2＝(W1-F+2P)/S+1
H2＝(H1-F+2P)/S+1
an active layer: the image array introduces nonlinear characteristics through an activation layer, and by adopting a ReLU, an operational formula is as follows:
f(x)＝max(0,x)
a pooling layer: filter size of 3 x 3, step size of 2
And after the forward propagation calculation is finished, training and parameter adjustment are carried out on the model, and the optimal weight parameter and the bias term parameter are obtained by the full connection layer through a back propagation algorithm by using a gradient descent method.
6. The method for modeling the thermal error of the rotating shaft of the five-axis machine tool based on the convolutional network as claimed in claim 5, wherein: the convolutional layer training utilizes chain type derivation to calculate the partial derivative of the loss function to each weight, then the weight is updated according to a gradient descent method, the optimal weight parameter and the bias term parameter are obtained through a back propagation algorithm, and after the weight parameter and the bias term parameter are adjusted, the accuracy of the multi-output convolutional neural network model reaches the expected accuracy.
7. The method for modeling the thermal error of the rotating shaft of the five-axis machine tool based on the convolutional network as claimed in claim 6, wherein: and fourthly, repeating the second step and the third step at intervals of 6 minutes in the temperature rising process to acquire thermal images and thermal error data, stopping the C axis and cooling after the temperature rises for five hours, repeating the steps at intervals of 6 minutes in the temperature lowering process to acquire the thermal images and the thermal error data, and continuing the cooling for 4 hours.
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