TWI810119B - A thermal displacement prediction method of a machine tool - Google Patents

Abstract

The present invention provides a thermal displacement prediction method of a machine tool based on a single signal time sequence. The method obtains a key signal with the highest correlation to a displacement of a main shift of the machine tool and uses a current and a past data reference of the key signal to input to a prediction model. The presentinvention then uses a convolution algorithm from a one dimensional convolutional neural network to extract a characteristic value of the input key signal. The present invention uses a fully connected layer of an artificial neural network to learn a relationship between the characteristic value of the input key signal and the displacement of a main shift of the machine tool. By tested the machine tool with different spindle speeds, the present invention shows high accuracy and stable predict result which is better than the conventional prediction model required multiple key signals.

Description

Prediction Method of Thermal Displacement of Machine Tool

A thermal displacement prediction method, in particular a thermal displacement prediction method suitable for processing machine tools.

In recent years, with the vigorous development of artificial intelligence technology, the machine tool industry has begun to introduce artificial intelligence to solve problems in related fields. Among them, the thermal error of machine tools accounts for 50% to 70% of the machining error, and the main thermal error of the spindle comes from the spindle motor and ball screw. The temperature rise of key components such as the main shaft will cause thermal expansion to cause thermal errors, resulting in thermal elongation, translation and tilt of the spindle displacement, which in turn affects the position error of the cutting point, making the workpiece unable to achieve the desired machining accuracy.

In view of this, there is an urgent need for a method that can accurately predict thermal displacement to improve machining accuracy.

In order to solve the problem that the processing accuracy caused by the thermal error of the current machine tool cannot reach expectations, the present invention provides a method for predicting the thermal displacement of a machine tool, the steps of which include: Step S1) Provide the vertical gantry three-axis processing machine, which at least includes: A spindle head sleeve, a saddle, a spindle motor and surrounding castings around one of the aforementioned components; Step S2) Evenly arrange several temperature sensors and several displacement sensors on the spindle head sleeve, the saddle, the spindle motor, and the surrounding castings; step S3) obtaining the respective values of the spindle head sleeve, the saddle, the spindle motor, and the surrounding castings sensed by several temperature sensors and several displacement sensors. A temperature point and a spindle displacement of other rotating speeds are used to receive signals and perform calculations in the following steps with a processor, a storage unit and a transceiver unit of a computer computing host; Step S4) uses the following formula (1) The Pearson product-moment correlation coefficient (PPMCC) calculates several correlation coefficients between several temperature points and the displacement of the spindle, and sorts the correlation coefficients according to the correlation from large to small; ...Formula (1), where, is the correlation coefficient between the mth temperature point and the spindle displacement, _Tm and y are the mth temperature point and the displacement data of the spindle Z direction, cov is the covariance, and Var is the variation; step S5) select the highest correlation several temperatures of the temperature as a single temperature key point; step S6) the single temperature key point, using the maximum and minimum normalization of the following formula (2) to perform data preprocessing of the single temperature key point, and obtain a one-dimensional key temperature data set , and match the corresponding spindle displacement as the thermal displacement, or preferably the training data of a prediction model of the spindle thermal displacement; ...Formula (2); wherein, T _nom is the normalized temperature value, T _min and T _max are the maximum and minimum values in the key temperature data, Tn is the nth temperature value; and step S7) establishes a single signal The prediction model of the principal axis displacement of the time series, the prediction model includes an input layer, a convolutional layer, a fully connected layer and an output layer; the one-dimensional key temperature data set and the corresponding principal axis displacement are input to The input layer learns the relationship between the key signal characteristic value of the one-dimensional key temperature data set and the spindle displacement through several different convolution kernels inside the convolution layer.

From the above description, it can be seen that the present invention proposes a machine tool thermal displacement prediction method based on a single-signal time series to establish a spindle Z-direction displacement prediction model, which is different from the traditional spindle thermal displacement prediction method, which relies on multiple key signals. Improve model accuracy.

The present invention only uses the current and past information of a single signal source as a basis, and uses the convolution operation of 1DCNN to automatically extract key feature values, and immediately and effectively predict the corresponding Z-direction spindle displacement. The test results show that the accuracy of the present invention is better than that of the four key signal sources compared with the traditional backward transfer neural modeling method under the condition of three different spindle speeds, and has high accuracy and robustness.

The present invention will be explained and described in technical detail below with several preferred embodiments, and the accompanying drawings are only some exemplary representatives or embodiments of the present invention, and for those with ordinary knowledge in the field of the present invention, it is not necessary to On the premise of paying progressive efforts, the present invention can also be applied to other similar situations according to these drawings.

"System", "device", "unit" and/or "module" as used in the present invention below is a method for distinguishing different components, elements, parts, parts or assemblies of different levels. However, the words may be replaced by other expressions if other words can achieve the same purpose. As indicated in the present application, the words "a", "an", "an" and/or "the" are not specific to the singular and may include the plural unless the context clearly suggests an exception. Generally speaking, the words "comprising" and "comprising" only suggest that the steps and elements that have been clearly stated are included, and these steps and elements do not constitute an exclusive enumeration. case, it is not excluded that other steps or elements may be included. In the present invention, a system flow chart may be used to describe the operations performed by the system according to the embodiment of the present invention. It should be understood that the preceding or following operational steps may not necessarily be performed in a precise order. On the contrary, the various steps can also be processed in reverse order or simultaneously to achieve the object of the present invention. At the same time, other operation steps can also be added to the present invention, or one or several steps of operation can be removed from it to achieve the same effect.

＜Example 1 - Thermal Displacement Prediction Method of Vertical Gantry Three-axis Machining Machine＞

Please refer to FIG. 1 , the present invention provides a first preferred embodiment, which uses a vertical gantry three-axis processing machine as the main processing tool, and executes the following steps through a computer system 100 . The computer system 100 includes at least one processor 110 , a storage unit 120 , and a sensing unit 130 connected electrically or by electrical signals. The sensing unit 130 preferably includes several temperature sensors and non-contact displacement gauges to sense the temperature and displacement data sensed from the vertical gantry three-axis processing machine, and transmit them with a general asynchronous transceiver Interfaces such as Universal Asynchronous Receiver/Transmitter (UART), Serial Peripheral Interface Bus (SPI), I2C (Inter-Integrated Circuit), Bluetooth (Bluetooth), and WIFI protocol are stored in the storage unit 120 In the process, the temperature and displacement data sensed and stored are analyzed and predicted through a thermal displacement prediction model in the processor 110, and servo compensation is performed on the processing tool in real time.

Please refer to Fig. 2, the steps of the spindle thermal displacement prediction method include:

Step S1) Provide the vertical gantry three-axis processing machine, which includes at least one passive heat-generating element; the so-called passive heat-generating element means that the vertical gantry three-axis processing machine does not generate heat independently due to mechanical transmission during processing Components such as spindle head sleeves, saddles, spindle motors, servo motors, ball screws, nuts and pulleys, and surrounding castings surrounding the aforementioned several components;

Step S2) Evenly arrange several temperature sensors and several displacement sensors on the passive heat generating element;

Step S3) Obtain a temperature point and a spindle displacement of the respective rotating speed temperature of the passive heat-generating element sensed by several temperature sensors and several displacement sensors, and use the computer to calculate the processor of the host computer . The storage unit and the sensing unit perform signal reception and perform calculations in the following steps; wherein, the spindle displacement includes at least the Z-axis spindle displacement;

Step S4) Use the Pearson product-moment correlation coefficient (PPMCC) of the following formula (1) to calculate several correlation coefficients between several temperature points and the displacement of the spindle, and each of the correlation coefficients according to Correlation is sorted from largest to smallest;

...Formula (1); where is the correlation coefficient between the mth temperature point and the spindle displacement, T _m and z are the mth temperature point and the displacement data of the spindle Z direction, Cov is the covariance, and Var is the variation;

Step S5) Select the temperature point with the highest degree of correlation with the spindle displacement as a single temperature key point; the so-called temperature point with the highest degree of correlation in this embodiment means that the absolute value of the temperature is closest to 1 as the most relevant temperature point temperature point;

Step S6) For the single temperature key point T _r , use the maximum and minimum normalization of the following formula (2) to preprocess the single temperature key point data, and obtain a one-dimensional key temperature data set, and match the corresponding spindle displacement As thermal displacement, or preferably as training data for a predictive model of spindle thermal displacement;

...Formula (2); wherein, V is the normalized temperature value, T _r,min and T _{r,max are} the maximum and minimum values in the key temperature data, and T _r,n is the nth temperature value;

Step S7) Establish the prediction model of the principal axis displacement of a single signal time series, the prediction model includes an input layer, a convolution layer, a fully connected layer and an output layer; the one-dimensional key temperature data set and the corresponding The principal axis displacement is input to the input layer, the key signal characteristic value of the temperature is captured, and the key signal characteristic value and the principal axis displacement of the one-dimensional key temperature data set are learned through several different convolution kernels inside the convolution layer The relationship between, and finally output the predicted value of the thermal displacement.

In detail, the so-called Pearson product dynamic difference correlation coefficient in the aforementioned step S4 can also use other correlation selection methods including gray correlation analysis, Spearman rank correlation coefficient, mutual information, covariance and regression analysis, etc. to calculate Z After determining the degree of correlation between the displacement of the main axis and several temperature sensing points, select the temperature point with the highest degree of correlation as the key temperature point.

Among them, the so-called preprocessing of the single temperature key point data in the aforementioned step S6 is to project the distribution of the key temperature data into the interval [0, 1]. Other preprocessing methods include maximum and minimum normalization, average value normalization, and maximum Absolute value standardization, Log function conversion, Atan function conversion, decimal scaling standardization (Decimal scaling), Z score standardization, robust scaling (RobustScaler) and scaling to unit length (Scaling to unit length), etc., and then define a single signal time series Length L, convert the normalized data V of n key temperature points into the one-dimensional key temperature data set S ={S _1, S ₁ , …, S _i } with the time series characteristics of i pen, and match the corresponding axis Z-direction displacement = {z ₁ , z ₂ , …, z _i }, used as the training data of the spindle thermal displacement prediction model; for example: if the length L of the single-signal time series is set to 3, it represents the single-signal of the current and past history The total data length is 3 data, that is, select the 3rd, 2nd, 1st single signal data of the 3rd key temperature point current and past history, or select the 4th key temperature point current and past history The 4th, 3rd, and 2nd single-signal data can reduce the number of selected temperature points, and then the current key temperature data slides to the historical data. The framed data represents a single-signal time series key data S, and finally the length of the data can be n Write one-dimensional key temperature point data, and complete the establishment of a single key temperature data set S for i pen time series characteristics.

Wherein, the training data input by the predictive model in the aforementioned step S7 is to design L input lengths with one layer of the input layer, wherein the input data formula is as shown in formula (3);

Input _i = {S _1, S ₁ , ..., S _i }…Formula (3). Among them, Input _i is the i-th input data, and S _i is the i-th time series characteristic single key temperature data set, which is the same as the one-dimensional key temperature data set S in step 6 above.

Next, in the aforementioned step S7, the key signal eigenvalues of the temperature are captured with one layer of the convolution layer, and the number of g convolution kernels is designed. The activation function uses the sigmoid function, and the output formula of each convolution is as the following formula (4 ) as shown in:

...Formula (4), where c _e is the output of the e-th convolution, S _i,j is the j-th data of the i-th input data, k _g,j is the jth data of the gth convolution kernel.

Wherein, in the aforementioned step S7, learning the relationship between the key signal eigenvalue and the spindle displacement in the one-dimensional key temperature data set is based on two hidden layers, each layer is designed with the number of e neurons, and the activation function uses the sigmoid function, Each neuron outputs a formula, as shown in the following formula (5).

...Equation (5). Among them, Neurons _e is the output of the eth neuron, w is the weight, c is the output of the previous layer, b is the partial weight, and f(.) is the activation function.

Wherein, the output of the thermal displacement prediction value in the aforementioned step S7 is to design q outputs with one layer of the output layer, wherein the output formula, as shown in the following formula (6), will use the root mean square error (Root Mean square error, RMSE) as a loss function to evaluate the difference between the actual value and the model's predicted value, and then set the maximum number of iterations to 100,000 times, through the Adam (Adam) optimization algorithm, continuously adjust the weight and partial weight of each neuron until it reaches Stop conditions, and obtain the final predicted thermal displacement prediction result of the processing machine and output the thermal displacement prediction value:

...Equation (6), where, Y _q is the qth output, Neurons _e is the output of the eth fully connected layer, and W _output is the weight of the output layer.

Preferably and optionally, according to the final predicted thermal displacement prediction value of the processing machine, the computer system 100 feeds back the result and possibly adjusts its displacement deviation.

＜Confirmation test＞

Embodiment 1 of the present invention uses a vertical gantry three-axis processing machine as a test machine, and 18 temperature sensors are evenly arranged on the main heat source such as the spindle head sleeve, the saddle, the spindle motor, and the casting around the heat source. Next, according to the ISO-230-3 international standard, install BT40 spindle test rods and self-made fixtures, arrange five non-contact displacement meters to measure the displacement of the spindle, and then collect the temperature data of different speeds of the machine and the displacement of the spindle. Experiment with three different speeds of low, medium and high speeds, namely 3000 RPM, 6000 RPM and 9000 RPM, and run for 8 hours and stop for 12 hours respectively, collect temperature and spindle displacement data every 30 seconds, and then use the Pearson correlation coefficient to calculate The correlation coefficients between the 18 temperature points and the spindle displacement in the Z direction are sorted according to the correlation from large to small. As shown in Table 1, the first five correlation points with the highest temperature are all around the spindle head sleeve, and the final selection The temperature point T ₁₇ with the highest correlation is regarded as a single temperature key point.

Table 1. temperature point number correlation coefficient T ₁₇ -0.959 T ₇ -0.957 T ₁₈ -0.956 T ₅ -0.911 T ₉ -0.890

In order to analyze the accuracy of different single-signal time series lengths and spindle thermal displacement prediction models, the present invention considers that when the length of the single-signal time series is longer, the key feature values extracted by the convolution kernel will also increase accordingly. If the fully connected layer neural If the number of elements is too small, it is easy to cause underfitting problems. Therefore, the present invention adopts a model architecture of one convolutional layer and two fully connected layers, in which the number and size of the convolution kernel are fixed, and the length of the input time series and the two layers of hidden The number of neurons in the layer, and its test parameters are shown in Table 2. A prediction model for the Z-direction displacement of the main axis with 4 different hyperparameter combinations was established.

Table 2. Example Single Signal Time Series Length Number of convolution kernels Convolution kernel size The number of neurons in the two hidden layers 1 20 6 5*1 20 2 40 60 3 60 80 4 80 100

The test results are shown in Table 3. The longer the length of the single-signal time series, the better the prediction effect of the model. When the length of the single-signal time series is set from 20 to 80, the RMSE drops from 3.219µm to 0.816µm, increasing the accuracy by 74.6%. The longer the length of the signal time series, the more time information is retained, and the thermal displacement prediction model of the main shaft can be calculated and predicted based on more historical information and current information, resulting in better prediction results of the model.

table 3. Example 3000RPM 6000RPM 9000RPM Avg. 1 4.017 3.206 2.436 3.219 2 2.712 2.286 1.441 2.146 3 1.412 1.213 0.952 1.192 4 0.859 0.809 0.78 0.816

The present invention provides a back propagation neural network (Back Propagation Neural Network, BPNN) modeling technology as a basis for comparison with the proposed method, and uses the same neural network architecture, wherein the hidden layer is designed to be 2 layers, each The number of layer neurons is 40, and the activation function is set to sigmoid function. The one-dimensional key temperature data set is the test data of three different spindle speeds collected in the aforementioned Table 1. 80% of the data set is used as training data and 20% is test data, and the prediction model of the spindle Z-direction displacement is established respectively. At the same time, RMSE is used as an evaluation index to evaluate the accuracy of different key signal sources at three different speeds. The results are shown in Table 4 below. It can be found that with the BPNN modeling method of the comparative example, as the number of key signals increases, the accuracy of the model depends on more key signal sources. When the number of key signal sources increases from 1 to 4 , the RMSE drops from 4.875 to 1.721 µm. The method provided by the present invention uses a single key signal as the basis for prediction, and its RMSE can reach 0.785µm, which improves the 83.9% accuracy of the BPNN method using the same single key signal. The displacement prediction model has good accuracy.

Table 4. method Number of key signals 3000 RPM 6000 RPM 9000 RPM Average Comparative example BPNN 1 6.399 3.563 4.648 4.976 2 6.306 3.331 4.809 4.94 3 6.081 3.444 4.697 4.838 4 5.515 3.519 4.821 4.684 5 2.785 2.217 2.559 2.528 this invention 1 0.856 0.827 0.674 0.785

In some embodiments, numbers describing the quantity of components and attributes are used, and it should be understood that such numbers used in the description of the embodiments, in some examples, use the modifiers "about", "approximately" or "substantially" to express grooming. Unless otherwise stated, "about", "approximately" or "substantially" indicates that the stated figure allows for a variation of ±20%. Accordingly, in some embodiments, the numerical parameters used in the specification and claims are approximations that may vary depending upon the desired characteristics of individual embodiments. In some embodiments, numerical parameters should take into account the specified significant digits and adopt the general digit reservation method. Although the numerical ranges and parameters used to demonstrate the breadth of scope in some embodiments of the invention are approximations, in specific embodiments such numerical values are set as precisely as practicable.

Finally, it should be understood that the embodiments described in the present invention are only used to illustrate the principles of the embodiments of the present invention. Other variations are also possible within the scope of the present invention. Accordingly, by way of illustration and not limitation, alternative configurations of the embodiments of the present invention may be considered consistent with the teachings of the present invention. Accordingly, the embodiments of the present invention are not limited to the embodiments of the present invention explicitly shown and described.

100: computer computing host 110: Processor 120: storage unit 130: sensing unit S1~S7: steps

In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings and drawings that need to be used in the description of the embodiments will be briefly introduced below. Unless it is obvious from the context or otherwise stated, the same reference numerals in the drawings represent the same structure, element, part or operation step. in: FIG. 1 is a block diagram of the structure of the computer computing host of the present invention. Fig. 2 is a flow chart of the steps of the method for predicting the thermal displacement of the spindle in the present invention.

S1~S7: steps

Claims (10)

A method for predicting thermal displacement of a machine tool, the steps of which include: step S1) a machine tool, which at least includes: a passive heat-generating element, the passive heat-generating element is that the machine tool does not generate heat independently due to mechanical transmission during processing any component; step S2) several temperature sensors and several displacement sensors are uniformly arranged on the passive heat generating element; step S3) a computer operation host obtains several temperature sensors and several displacement sensors A temperature point and a spindle displacement of the respective rotational speed temperature of the passive heat generating element are sensed, and at least one processor, a storage unit and a sensing unit of the computer computing host are used for signal reception and the following steps Operation execution; step S4) calculate several correlation coefficients between several temperature points and the displacement of the spindle, and sort the correlation coefficients according to the correlation from large to small; step S5) select several temperatures with the highest correlation As a single temperature key point; step S6) preprocessing the single temperature key point data to obtain a one-dimensional key temperature data set; and step S7) establishing a single signal time series of the spindle displacement A prediction model, the prediction model includes an input layer, a convolutional layer, a fully connected layer and an output layer; the one-dimensional key temperature data set and the corresponding spindle displacement are input to the input layer, and the The characteristic value of the key signal of temperature, and learn the relationship between the characteristic value of the key signal in the one-dimensional key temperature data set and the displacement of the main axis through several different convolution kernels inside the convolution layer, and finally output a predicted value of thermal displacement. A method for predicting thermal displacement of a machine tool as described in Claim 1, wherein: the spindle displacement at least includes the Z-axis spindle displacement; and the temperature point with the highest degree of correlation is correlated with the absolute value of the temperature closest to 1 the highest temperature point. A method for predicting thermal displacement of a machine tool as described in claim item 1, wherein: step S5) is based on Pearson product dynamic difference correlation coefficient, gray correlation analysis, Spearman rank correlation coefficient, mutual information Or covariance and regression analysis, after calculating the degree of correlation between the Z-axis spindle displacement and several temperature sensing points, select the temperature point with the highest degree of correlation as the key temperature point. A method for predicting thermal displacement of a machine tool as described in claim 3, wherein: the correlation coefficient of Pearson product dynamic difference is to use the following formula to calculate several correlation coefficients between several temperature points and the displacement of the main shaft, and each of the correlation coefficients Sort by relevance from most to least; and

,in

is the correlation coefficient between the mth temperature point and the spindle displacement, T _m and z are the mth temperature point and the displacement data of the spindle in the Z direction, Cov is the covariance, and Var is the variation. A method for predicting thermal displacement of a machine tool as described in claim 1, wherein: in step S6), the preprocessing of the single temperature key point data includes normalization by maximum and minimum, normalization by average value, normalization by maximum absolute value, and Log function conversion , Atan function conversion, decimal scaling normalization, Z-score normalization, robust scaling or scaling to unit length. A method for predicting thermal displacement of a machine tool as described in claim 5, wherein the maximum and minimum normalization of the following formula is used to perform preprocessing of the single temperature key point data;

, where V is the normalized temperature value, T _r,min and T _r,max are the maximum and minimum values in the key temperature data, T _r,n is the nth temperature value; and the maximum and minimum normalization is Project the key temperature data distribution on the [0,1] interval, then define a single signal time series length L, convert the normalized data V of n key temperature points into the one-dimensional key of i pen time series characteristics The temperature data set S={S _1, S ₁ ,...,S _i }, and the displacement in the Z direction of the corresponding spindle ={z ₁ ,z ₂ ,..., _zi }, as the displacement of the spindle One of the training data for the predictive model. A method for predicting thermal displacement of a machine tool as described in claim 1, wherein one of the training data of the prediction model in the aforementioned step S7) is the input layer of one layer, and L input lengths are designed, wherein the input data formula is as follows : Input _i ={S _1, S ₁ ,...,S _i }, where Input _i is the i-th input data, and S _i is the i-th time series characteristic single key temperature data set. A method for predicting the thermal displacement of a machine tool as described in claim 1, wherein, in the aforementioned step S7), the key signal characteristic value of the temperature is captured with one layer of the convolution layer, and the number of g convolution kernels is designed, and the activation function is used The sigmoid function, where the output formula of each convolution is as follows:

, where, c _e is the output of the e-th convolution, S _i,j is the j-th data of the i-th input data, and k _g,j is the j-th data of the g-th convolution kernel. A method for predicting thermal displacement of a machine tool as described in claim item 1, wherein: in step S7), the relationship between the key signal eigenvalue in the one-dimensional key temperature data set and the spindle displacement is learned by using two hidden layers, each The number of e neurons is designed in the layer, and the activation function uses the sigmoid function, where each neuron outputs the following formula for learning:

, where Neurons _e is the output of the eth neuron, w is the weight, c is the output of the previous layer, b is the partial weight, and f(.) is the activation function. A method for predicting thermal displacement of a machine tool as described in claim 1, wherein the output of the thermal displacement prediction value in the aforementioned step S7) is an output layer, and q outputs are designed, wherein the output formula, as shown in the following formula, model learning In this stage, the root mean square error will be used as the loss function to evaluate the difference between the actual value and the predicted value of the model, and then the maximum number of iterations will be set to 100,000, and the weight value and partial weight value of each neuron will be continuously adjusted through the Adam optimization algorithm until The stop condition is met, and the final predicted thermal displacement prediction result of the machine tool is obtained and the thermal displacement prediction value is output; and

, where Y _q is the qth output, Neurons _e is the output of the eth fully connected layer, and W _output is the weight of the output layer.

Images