CN103984287A - Numerically-controlled machine tool thermal error compensation grey neural network modeling method - Google Patents

Abstract

The invention relates to a numerically-controlled machine tool thermal error compensation grey neural network modeling method. The method mainly comprises the following steps: a. sensors are arranged; b. temperature variables are screened; c. a grey system is established and a thermal error predicted value is obtained; d. a residual sequence is solved; and e. a BP neural network model of the residual sequence is established. According to the invention, the grey system theory and the BP neural network are combined together for machine tool thermal error modeling, so the model prediction accuracy and generalization ability can be improved; accurate fitting prediction can be performed on small sample data, and advantages of simple calculation and fast response can be realized; and by using the neural network method, the system has advantages of high self-learning ability and adaptivity, the complex change of machine tool thermal error can be learned by an operator himself, the change in the machine tool machining process can be reflected, and the advantage of good reliability can be realized.

Description

A kind of numerical control machine heat error compensation grey neural network modeling method

Technical field

The present invention relates to a kind of grey neural network of applying is the method that numerical control machining tool heat error carries out mathematical modeling.Belong to precision machine tool technology or Precision Machining field

Background technology

In Modern High-Speed stock-removing machine, along with the raising of lathe rotating speed and piece surface crudy, cutting depth and feed are generally all smaller, and cutting force is also little, thus process system stress deformation on the impact of machining precision compared with thermal deformation in less important status.Along with improving constantly of manufacturing process technology level, hot error has become the main error source that affects high-speed machine tool machining precision.In the industry such as machine-building, instrument and meter, the thermal deformation being caused by temperature is the key factor that affects machine, instrument and equipment precision, and the error that thermal deformation causes can account for 1/3 of total error conventionally.In Precision Machining, the error that thermal deformation causes proportion in total machining error can reach 40%～70%.For improving the operating accuracy of machinery and equipment, conventionally can adopt two kinds of approach of temperature control and accuracy compensation to reduce the impact of temperature on precision.

With empirical modeling method set up machine tool error model be main be method, regard a black box as by machine tool system, conventionally input quantity is the variation in lathe temperature field and the variable of other correlative, output quantity is the deflection of some critical piece in machine tool system comprehensive deformation result or system, and hypothetical model structure, determine the parameters in model by the method for System Discrimination.

Because thermal deformation of machine tool is subject to the impact of a lot of Variable Factors, machine tool thermal error is a complicated problem.And the method for analyzing and modeling of machine tool thermal error prediction based on grey neural network, combine the two advantage of gray system theory and neural network, the ability that existing very strong intelligent learning and eliminating are disturbed, there are again very strong processing grey data, the ability of poor information, there is very high precision and Generalization Capability, be therefore well suited for the modeling analysis for machine tool thermal error.

Summary of the invention

Content of the present invention is to provide the new method of a kind of numerical control machining tool heat error based on grey neural network modeling.

For realizing this purpose, the technical solution used in the present invention comprises the following steps:

Step 1: placement sensor

First utilize infrared thermography to do thermograph to operation lathe after a while, the temperature cromogram showing according to thermal imaging system, temperature shows that high region is the heating region of lathe, the temperature peak of the good each heating region of mark.Shut down after cooling and place the sensor that measures ambient temperature changes on lathe side, and carry out collecting temperature delta data at all m gauge point mounting temperature sensors.X-axis, Z-direction at machine tool chief axis are respectively installed a laser displacement sensor, gather the data of thermal deformation of machine tool.In system operational process, read temperature T every phase same amount of time _iwith thermal deformation displacement X _i, the time dependent numerical value of Zi;

Step 2: screening temperature variable

According to the temperature variation sequence T having measured _i(T _i1t _i2t _i3t _ikt _i(k+1)t _is), i=1,2 ... m+1 filters out n and the high temperature variable of thermal deformation correlativity from m+1 temperature variable by grey correlation analysis;

Step 3: set up gray system and obtain hot error prediction value

Due to set up separately X to or the hot error model fitting precision of Z-direction higher, so with X to or the thermal deformation shift value of Z-direction and n temperature variable sample value that previous step filters out set up independent X to or G(1, the N of Z-direction) Grey System Model.By X _ior Z _iwith the high temperature ordered series of numbers of the n a screening degree of association composition gray system G(1, N) original data series.With the data instance of Z-direction, obtain gray system G(1, N here) original data series

$\left\{\begin{array}{cccc}{Z^{\left(0\right)}}_{\left(1\right)}& {Z^{\left(0\right)}}_{\left(2\right)}& ...& {Z^{\left(0\right)}}_{\left(s\right)}\\ T_i^{\left(0\right)}\left(1\right)& T_i^{\left(0\right)}\left(2\right)& ...& T_i^{\left(0\right)}\left(s\right)\\ ...& ...& ...& ...\\ T_n^{\left(0\right)}\left(1\right)& T_n^{\left(0\right)}\left(2\right)& ...& T_n^{\left(0\right)}\left(s\right)\end{array}\right\},i=\mathrm{1,2},...,n-1;---\left(1\right)$

Above-mentioned ordered series of numbers is made respectively to one-accumulate and generate, obtain new 1-AGO ordered series of numbers

$\left\{\begin{array}{cccc}{Z^{\left(1\right)}}_{\left(1\right)}& {Z^{\left(1\right)}}_{\left(2\right)}& ...& {Z^{\left(1\right)}}_{\left(s\right)}\\ T_i^{\left(1\right)}\left(1\right)& T_i^{\left(1\right)}\left(2\right)& ...& T_i^{\left(1\right)}\left(s\right)\\ ...& ...& ...& ...\\ T_n^{\left(1\right)}\left(1\right)& T_n^{\left(1\right)}\left(2\right)& ...& T_n^{\left(1\right)}\left(s\right)\end{array}\right\},i=\mathrm{1,2},...,n-1;---\left(2\right)$

Set up the differential equation

$d{Z}^{\left(1\right)}/\mathrm{dt}+a{Z}^{\left(1\right)}=b_1{T}_1^{\left(1\right)}+b_2{T}_2^{\left(1\right)}+...+b_n{T}_n^{\left(1\right)};---\left(3\right)$

Coefficient a, b ₁, b ₂... b _nsolve by least square method.

Solve the differential equation (3) and obtain the hot error prediction value of Z-direction

$\begin{array}{c}{{\hat{Z}}^{\left(0\right)}}_{(t+1)}={{\hat{Z}}^{\left(1\right)}}_{(t+1)}-{{\hat{Z}}^{\left(1\right)}}_{\left(t\right)}\\ =[Z^{\left(0\right)}\left(1\right)-\underset{i=2}{\overset{n}{\mathrm{\Σ}}}\frac{b_{i-1}}{a}{T}_i^{\left(1\right)}(t+1)]e^{-\mathrm{at}}+\underset{i=2}{\overset{n}{\mathrm{\Σ}}}\frac{b_{i-1}}{a}{T}_i^{\left(1\right)}(t+1)-[Z^{\left(0\right)}\left(1\right)-\underset{i=2}{\overset{n}{\mathrm{\Σ}}}\frac{b_{i-1}}{a}{T}_i^{\left(1\right)}\left(t\right)]e^{-a(t-1)}+\\ \underset{i=2}{\overset{n}{\mathrm{\Σ}}}\frac{b_{i-1}}{a}{T}_i^{\left(1\right)}\left(t\right),t=\mathrm{1,2},...,s-1;\end{array}---\left(4\right)$

Next as long as can obtain the thermal deformation displacement prediction value of lathe by Computing above formula , ,

Step 4: calculate residual values sequence

,, with true measurement Z ⁽⁰⁾(1), Z ⁽⁰⁾(2) ..., Z ⁽⁰⁾(k) subtracting each other is successively residual sequence e ⁽⁰⁾(1), e ⁽⁰⁾(2) ..., e ⁽⁰⁾(k)

$e^{\left(0\right)}\left(t\right)={{\hat{Z}}^{\left(0\right)}}_{\left(t\right)}-Z^{\left(0\right)}\left(t\right)t=\mathrm{1,2},...,k;---\left(5\right)$

Step 5: the BP neural network model of setting up residual sequence

Set up 3 layers of BP neural network, k temperature value above of the n that step 2 an is screened temperature variable is as the input sample of neural metwork training, residual sequence e ⁽⁰⁾(1), e ⁽⁰⁾(2) ..., e ⁽⁰⁾(k), as output sample, learning training BP neural network is to determine its all parameter values.After having trained, just obtain desired BP neural network model.As long as the temperature value of this temperature variable is input in the middle of neural network, just can obtain residual sequence predicted value the machine tool thermal error predicted value of artificial neural networks built-up pattern can be passed through

$\hat{Z}\left(i\right)={{\hat{Z}}^{\left(0\right)}}_{\left(i\right)}+{{\hat{e}}^{\left(0\right)}}_{\left(i\right)}---\left(5\right)$

Calculate.

As long as repeating once above step, the heat error compensation sequential value of X-direction just can obtain.

The invention has the beneficial effects as follows:

Adopt grey neural network to build that the method for error compensation model is more simple than traditional matching modeling, efficiency is high, and gray system theory and BP neural network group are combined for machine tool thermal error modeling, has improved precision of prediction and the generalization ability of model.

Even if in sample size hour, grey neural network modeling method has higher precision equally, can carry out the prediction of matching accurately to small sample data, calculate simply, be swift in response.

Use neural net method to make system have very high self-learning capability and adaptivity, the variation of the hot error complexity of energy self study lathe, can reflect the variation of machine tooling process, has good reliability.

Brief description of the drawings

Fig. 1 is workflow diagram of the present invention.

Fig. 2 is BP neural network structure figure.

Fig. 3 has provided the hot error and the hot error contrast effect figure of actual measurement that adopt Grey Neural Network Model prediction.

Fig. 4 is last 6 hot error amounts and the hot error comparison diagram of actual measurement that adopts Grey Neural Network Model and the prediction of other method.

Embodiment

Below in conjunction with accompanying drawing and implementation process, the present invention will be further described.

Hot error modeling method of the present invention realizes according to following steps, and Fig. 1 is step sketch.

First analyze the correlative factor that lathe produces hot error, first utilize infrared thermography to do thermograph to operation lathe after a while, judge the heat generating spot of lathe, the temperature peak of the good each heating region of mark.Shut down after cooling and place the sensor that measures ambient temperature changes on lathe side, and carry out collecting temperature delta data at all gauge point mounting temperature sensors.X-axis, Z-direction at machine tool chief axis are respectively installed a laser displacement sensor, gather the data of thermal deformation of machine tool.Gather a secondary data every phase same amount of time, the data that obtain will be used for modeling.

First modeling process carries out temperature variable screening.Select those and the large temperature variable of the thermal deformation degree of association by the method for grey correlation analysis, these temperature variables are for Grey Systems Modelling.

With matrix P and Z axis or X-axis thermal deformation sequential value composition GM(1, the N of the n selecting temperature variable composition) original data series of Grey System Model

$\left\{\begin{array}{cccc}{Z^{\left(0\right)}}_{\left(1\right)}& {Z^{\left(0\right)}}_{\left(2\right)}& ...& {Z^{\left(0\right)}}_{\left(s\right)}\\ T_i^{\left(0\right)}\left(1\right)& T_i^{\left(0\right)}\left(2\right)& ...& T_i^{\left(0\right)}\left(s\right)\\ ...& ...& ...& ...\\ T_n^{\left(0\right)}\left(1\right)& T_n^{\left(0\right)}\left(2\right)& ...& T_n^{\left(0\right)}\left(s\right)\end{array}\right\},i=\mathrm{1,2},...,n-1;$

Then above-mentioned ordered series of numbers is made respectively to one-accumulate and generate, obtain new 1-AGO ordered series of numbers

$\left\{\begin{array}{cccc}{Z^{\left(1\right)}}_{\left(1\right)}& {Z^{\left(1\right)}}_{\left(2\right)}& ...& {Z^{\left(1\right)}}_{\left(s\right)}\\ T_i^{\left(1\right)}\left(1\right)& T_i^{\left(1\right)}\left(2\right)& ...& T_i^{\left(1\right)}\left(s\right)\\ ...& ...& ...& ...\\ T_n^{\left(1\right)}\left(1\right)& T_n^{\left(1\right)}\left(2\right)& ...& T_n^{\left(1\right)}\left(s\right)\end{array}\right\},i=\mathrm{1,2},...,n-1;$

Set up the differential equation

$d{Z}^{\left(1\right)}/\mathrm{dt}+a{Z}^{\left(1\right)}=b_1{T}_1^{\left(1\right)}+b_2{T}_2^{\left(1\right)}+...+b_n{T}_n^{\left(1\right)}.$

Coefficient a, b ₁, b ₂... b _nsolve and obtain by least square method.

Solve the differential equation (3) and obtain the hot error prediction value of Z-direction

$\begin{array}{c}{{\hat{Z}}^{\left(0\right)}}_{(t+1)}={{\hat{Z}}^{\left(1\right)}}_{(t+1)}-{{\hat{Z}}^{\left(1\right)}}_{\left(t\right)}\\ =[Z^{\left(0\right)}\left(1\right)-\underset{i=2}{\overset{n}{\mathrm{\Σ}}}\frac{b_{i-1}}{a}{T}_i^{\left(1\right)}(t+1)]e^{-\mathrm{at}}+\underset{i=2}{\overset{n}{\mathrm{\Σ}}}\frac{b_{i-1}}{a}{T}_i^{\left(1\right)}(t+1)-[Z^{\left(0\right)}\left(1\right)-\underset{i=2}{\overset{n}{\mathrm{\Σ}}}\frac{b_{i-1}}{a}{T}_i^{\left(1\right)}\left(t\right)]e^{-a(t-1)}+\\ \underset{i=2}{\overset{n}{\mathrm{\Σ}}}\frac{b_{i-1}}{a}{T}_i^{\left(1\right)}\left(t\right),t=\mathrm{1,2},...,s-1;\end{array}---\left(4\right)$

Next obtain the thermal deformation displacement prediction value of lathe by Computing , , , with true measurement Z ⁽⁰⁾(1), Z ⁽⁰⁾(2) ..., Z ⁽⁰⁾(k) subtracting each other is successively residual sequence e ⁽⁰⁾(1), e ⁽⁰⁾(2) ..., e ⁽⁰⁾(k);

Set up 3 layers of BP neural network, the input sample using k temperature value above of matrix P as neural metwork training, residual sequence e ⁽⁰⁾(1), e ⁽⁰⁾(2) ..., e ⁽⁰⁾(k), as output sample, learning training BP neural network is to determine its all parameter values.After having trained, just obtain desired BP neural network model.As long as the temperature value of this temperature variable is input in the middle of neural network, just can obtain residual sequence predicted value (i).The machine tool thermal error predicted value of artificial neural networks built-up pattern can be passed through

$\hat{Z}\left(i\right)={{\hat{Z}}^{\left(0\right)}}_{\left(i\right)}+{{\hat{e}}^{\left(0\right)}}_{\left(i\right)}$

Calculate.

As long as repeating once above step, the heat error compensation sequential value of X-direction just can obtain.

Embodiments of the invention are below described.

Embodiment:

First a CK-6140 numerically-controlled machine is done to the hot error modeling analysis of Z-direction.

According to step 1 with Flir E50 thermal infrared imager to 1000r/min fast idle the numerically-controlled machine of 1 hour do thermal imaging; the heat generating spot of judgement the good lathe of mark; shut down cooling after; at 14 good position mounting temperature sensors of all marks, a temperature sensor measurement variation of ambient temperature is put on lathe side.A standard plug is installed on machine tool chief axis, the change in displacement with high precision laser displacement sensor difference measure-axis at X and Z axis.Every the data of temperature sensor of collection in 6 minutes and displacement sensor, gather altogether 61 groups of data, matrix A temperature data, matrix B is Z axis thermal deformation data.

A=[16.4 16.88 17.07 16.69 17.02 16.59 16.88 16.69 17.17 16.4 16.45 16.64 18.52 16.76 16.59

16.59 18.27 18.08 17.5 18.51 17.21 17.69 17.41 18.27 16.26 16.45 16.78 21.11 17.24 17.02

17.26 19.37 19.13 18.7 19.61 17.45 18.46 18.17 18.6 16.3 16.59 16.98 23.63 17.56 17.31

17.41 20.33 19.37 18.99 20.28 17.93 19.18 18.99 18.22 16.45 16.64 17.21 25.63 17.92 17.84

17.55 21.1 20.09 19.61 21.05 18.17 19.52 19.37 18.37 16.54 16.78 17.31 27.22 18.45 18.13

17.6 21.62 20.67 20.09 21.62 18.46 19.99 19.85 18.8 16.59 16.74 17.55 28.34 18.52 18.32

18.03 21.62 20.86 20.38 22.01 18.7 20.52 20.28 19.18 16.74 16.88 17.6 29.38 18.56 18.71

18.22 22.15 21.29 20.71 22.53 18.99 20.91 20.71 19.37 16.78 16.88 17.5 30.62 18.84 19.09

18.46 22.68 21.82 21.14 23.21 19.28 21.24 21 19.66 16.93 17.02 17.65 31.58 19.12 19.29

18.65 22.82 22.1 21.43 23.49 19.28 21.62 21.29 19.99 17.17 17.12 17.79 32.14 19.28 19.24

18.7 23.11 22.39 21.82 23.49 19.37 21.82 21.53 20.23 17.36 17.41 18.13 32.73 19.64 19.09

19.08 23.4 22.68 22.2 23.73 19.56 22.01 21.77 20.52 17.17 17.41 18.56 33.29 19.76 19.38

19.18 23.78 23.01 22.34 24.02 19.76 22.3 22.1 20.76 17.36 17.31 18.56 33.97 19.91 19.57

19.47 24.12 23.45 22.63 24.36 20.47 22.39 22.34 20.86 17.36 17.5 18.13 34.33 19.97 19.77

19.47 24.21 23.4 22.73 24.6 20.23 22.73 22.73 21.19 17.55 17.55 18.22 34.81 20.19 19.82

19.8 24.5 23.69 22.92 24.93 20.38 22.92 22.92 21.48 17.6 17.55 18.27 35.25 20.23 20.01

19.9 24.74 23.88 23.21 24.88 20.43 23.11 22.92 21.58 17.69 17.84 18.37 35.57 20.39 20.06

19.9 24.93 24.02 23.59 25.07 20.57 23.49 23.45 21.91 17.79 17.79 18.37 35.73 20.51 20.2

20.33 25.22 24.12 23.59 25.36 20.57 23.78 23.78 22.06 17.84 17.79 18.37 35.93 20.59 20.3

20.43 25.46 24.55 23.83 25.51 20.76 24.07 23.25 22.25 17.84 17.84 18.46 36.49 20.63 20.39

20.43 25.46 24.5 24.02 25.6 21.1 24.16 23.4 22.44 18.27 17.93 18.46 36.29 20.91 20.73

20.52 25.7 24.6 24.26 25.84 21.34 24.31 23.54 22.73 18.46 18.03 18.32 36.29 21.07 21.02

20.86 25.65 24.84 24.45 25.94 21.1 24.55 23.68 22.77 18.08 18.08 18.51 36.29 20.83 20.92

21.24 25.75 24.84 24.55 25.99 21.34 24.45 23.88 23.11 18.27 18.27 18.89 36.49 21.07 21.11

21.34 25.84 24.93 24.55 26.18 21.34 24.6 23.92 23.35 18.6 18.37 18.84 36.61 21.47 21.11

21.34 26.13 25.07 24.79 26.32 21.14 24.79 24.12 23.01 18.51 18.32 18.8 36.73 21.35 21.26

21.29 26.37 25.17 25.03 26.46 21.53 24.79 24.12 23.11 18.51 18.46 18.9 36.81 21.47 21.3

21.38 26.46 25.22 25.03 26.66 21.58 24.98 24.26 23.21 18.51 18.37 18.8 36.97 21.31 21.45

21.38 26.46 25.41 25.22 26.61 21.53 25.12 24.21 23.25 18.6 18.41 18.94 37.21 21.35 21.45

21.34 26.66 25.46 25.31 26.85 21.62 25.07 24.36 23.45 18.89 18.41 18.8 37.13 21.63 21.55

21.72 26.66 25.6 25.36 26.9 21.86 25.12 24.5 23.4 18.89 18.8 18.41 36.97 21.67 21.64

21.72 26.75 25.6 25.41 27.14 21.86 25.27 24.55 23.49 18.84 18.89 18.41 37.09 21.83 21.69

21.86 26.85 25.79 25.51 27.42 22.1 25.22 24.6 23.64 18.94 18.84 18.37 37.09 22.07 21.84

21.91 27.09 25.65 25.7 27.04 22.39 25.31 24.64 23.83 19.04 18.89 18.51 37.01 22.19 21.93

21.96 27.28 25.65 26.18 27.66 22.15 25.41 24.88 23.78 19.04 19.04 18.51 37.09 22.27 22.08

22.68 27.09 25.55 26.42 27.23 22.3 25.36 24.84 23.88 19.04 19.04 18.46 37.09 21.95 22.32

22.53 27.28 25.65 26.03 27.38 22.39 25.27 24.79 23.88 18.84 18.89 18.84 37.09 22.07 22.32

22.15 27.23 25.75 26.13 27.33 22.2 25.36 24.79 23.92 18.99 27.38 18.65 37.01 22.03 22.03

22.15 27.23 25.65 26.03 27.38 22.3 25.46 24.93 24.4 18.99 19.28 18.65 37.13 22.23 22.17

22.2 22.2 25.75 26.13 27.33 22.3 25.65 24.88 24.12 18.89 19.37 18.75 37.09 22.27 22.22

22.1 27.42 25.79 26.27 27.38 22.25 25.55 24.93 24.16 18.94 19.32 18.89 37.25 22.31 22.22

22.34 27.57 25.79 26.27 27.47 22.34 25.51 25.6 24.31 19.08 19.37 18.99 37.13 22.47 22.32

22.44 27.42 25.84 26.46 27.52 22.34 25.55 25.46 24.31 19.13 19.42 18.99 37.25 22.57 22.32

22.44 27.47 25.75 26.46 27.66 22.34 25.51 25.03 24.21 19.13 19.56 19.37 37.13 22.47 22.37

22.34 27.23 25.36 26.18 27.57 22.3 25.65 25.86 24.4 19.18 19.61 18.89 36.97 22.47 24.19

22.3 26.32 27.23 25.7 26.42 22.2 25.27 26.32 24.36 19.08 19.66 18.89 36.09 21.83 24.1

22.34 25.7 25.17 25.46 25.65 22.15 24.88 25.22 24.12 19.47 19.76 19.04 35.37 21.75 23.81

22.15 25.31 22.3 24.45 25.41 22.01 24.79 24.55 23.73 19.18 19.8 18.8 34.61 21.59 23.52

22.15 24.74 24.79 24.21 24.88 22.1 24.45 24.69 23.35 19.61 19.9 18.99 33.77 21.55 23.33

22.58 24.21 24.6 23.88 24.36 22.34 23.92 24.5 23.4 19.13 20.04 18.8 33.21 21.39 23.23

21.96 23.73 24.36 23.49 23.83 21.86 24.26 24.02 23.45 19.37 19.99 18.84 32.26 21.43 23.42

21.86 23.49 24.26 23.11 23.68 21.96 24.4 23.54 22.77 18.94 19.99 19.04 32.14 21.35 22.7

21.82 23.3 23.45 23.21 23.59 21.72 23.83 23.54 22.39 18.94 19.85 18.99 31.42 21.27 22.41

21.72 23.16 23.35 23.06 23.35 21.72 23.54 23.35 22.49 18.94 19.85 18.94 30.9 21.39 22.37

21.62 23.06 23.45 22.97 23.06 21.43 23.3 23.21 22.3 18.94 19.85 18.7 30.34 21.55 22.27

21.53 22.82 23.21 22.87 23.25 21.43 23.11 22.87 22.15 18.94 19.9 18.84 30.18 21.19 22.13

21.48 22.68 23.16 22.73 22.92 21.38 22.97 22.92 22.15 18.89 19.8 18.75 29.38 21.07 22.03

21.24 22.68 23.01 22.68 22.87 21.19 22.77 22.77 21.91 18.84 19.9 18.99 28.86 21.19 21.74

21.58 22.49 22.87 22.58 22.68 21.53 22.82 22.68 21.82 18.94 19.9 18.65 28.34 21.27 21.74

21.1 22.39 22.68 22.39 22.73 21 22.53 22.63 21.77 19.08 19.8 18.65 27.82 21.03 21.74

21.05 22.24 22.53 22.1 22.58 20.81 22.25 22.3 21.62 19.13 19.8 18.65 27.62 20.87 21.6];

B=[0 0. 14 0. 79 2.42 3.87 5.25 6.54 8.02 9.14 10.25 11.08 11.68 12.71 13.60 14.32 14.81 15.26 15.77 15.98 16.01

16.24 16.27 16.45 16.73 17.15 17.51 17.80 18.11 18.03 17.93 18.21 17.90 17.56 17.80 17.56 17.23 16.92 16.58

16.71 16.63 16.63 16.55 16.42 16.76 16.63 16.76 17.28 17.54 17.56 17.51 17.46 17.17 16.92 16.79 16.53 15.93

15.62 15.52 15.07 14.79 14.79] ^T。

To X _ithe correlation coefficient of ordering at k is

${\mathrm{\ξ}}_{0i}\left(k\right)=\frac{m+\mathrm{\θM}}{{\mathrm{\Δ}}_i\left(k\right)+\mathrm{\θM}},\mathrm{\θ}\∈\left(\mathrm{0,1}\right),k=\mathrm{1,2},...,61;i=\mathrm{1,2},...,15$

The degree of association between two sequences is calculated with the mean value of the degree of association coefficient in two each moment of sequence,

${\mathrm{\ξ}}_{0i}=\frac{1}{n}\underset{k=1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\ξ}}_{0i}\left(k\right)i=\mathrm{1,2},...,m$

The relevance degree that calculates 15 temperature sequences and Z axis thermal deformation is as follows:

ξ _z,1=0.7014 ξ _z,2=0.5881 ξ _z,3=0.6065 ξ _z,4=0.6125 ξ _z,5=0.5831 ξ _z,6=0.6947 ξ _z,7=0.6142 ξ _z,8=0.6228

ξ _z,9=0.6520 ξ _z,10=0.8065 ξ _z,11=0.7960 ξ _z,12=0.8032 ξ _z,13=0.4269 ξ _z,14=0.6994 ξ _z,15=0.6891

Visible, T ₂, T ₅, T ₁₃very little with the degree of correlation of Z axis thermal deformation, thus removed and 12 remaining temperature ordered series of numbers are formed to matrix P, as the data of grey neural network modeling.

P=[16.4 17.07 16.69 16.59 16.88 16.69 17.17 16.4 16.45 16.64 16.76 16.59

16.59 17.5 18.51 17.69 17.41 18.27 16.26 16.45 16.78 17.24 17.02

17.26 19.13 18.7 17.45 18.46 18.17 18.6 16.3 16.59 16.98 17.56 17.31

17.41 19.37 18.99 17.93 19.18 18.99 18.22 16.45 16.64 17.21 17.92 17.84

17.5520.09 19.61 18.17 19.52 19.37 18.37 16.54 16.78 17.31 18.45 18.13

17.6 20.67 20.09 18.46 19.99 19.85 18.8 16.59 16.74 17.55 18.52 18.32

18.03 20.86 20.3818.7 20.52 20.28 19.18 16.74 16.88 17.6 18.56 18.71

18.22 21.29 20.71 18.99 20.91 20.71 19.37 16.78 16.88 17.5 18.84 19.09

18.46 21.82 21.14 19.28 21.24 21 19.66 16.93 17.02 17.65 19.12 19.29

18.65 22.1 21.4319.28 21.62 21.29 19.99 17.17 17.12 17.79 19.28 19.24

18.7 22.39 21.82 19.37 21.82 21.53 20.23 17.36 17.41 18.13 19.64 19.09

19.08 22.68 22.2 19.56 22.01 21.77 20.52 17.17 17.41 18.56 19.76 19.38

19.18 23.01 22.34 19.76 22.3 22.1 20.76 17.36 17.31 18.56 19.91 19.57

19.47 23.45 22.63 20.47 22.39 22.34 20.86 17.36 17.5 18.13 19.97 19.77

19.47 23.4 22.73 20.23 22.73 22.73 21.19 17.55 17.55 18.22 20.19 19.82

19.8 23.69 22.92 20.38 22.92 22.92 21.48 17.6 17.55 18.27 20.23 20.01

19.9 23.88 23.21 20.43 23.11 22.92 21.58 17.69 17.84 18.37 20.39 20.06

19.9 24.02 23.59 20.57 23.49 23.45 21.91 17.79 17.79 18.37 20.51 20.2

20.33 24.12 23.59 20.57 23.78 23.78 22.06 17.84 17.79 18.37 20.59 20.3

20.43 24.55 23.83 20.76 24.07 23.25 22.25 17.84 17.84 18.46 20.63 20.39

20.43 24.5 24.02 21.1 24.16 23.4 22.44 18.27 17.93 18.46 20.91 20.73

20.52 24.6 24.26 21.34 24.31 23.54 22.73 18.46 18.03 18.32 21.07 21.02

20.86 24.84 24.45 21.1 24.55 23.68 22.77 18.08 18.08 18.51 20.83 20.92

21.24 24.84 24.55 21.34 24.45 23.88 23.11 18.27 18.27 18.89 21.07 21.11

21.34 24.93 24.55 21.34 24.6 23.92 23.35 18.6 18.37 18.84 21.47 21.11

21.34 25.07 24.79 21.14 24.79 24.12 23.01 18.51 18.32 18.8 21.35 21.26

21.29 25.17 25.03 21.53 24.79 24.12 23.11 18.51 18.46 18.9 21.47 21.3

21.38 25.22 25.03 21.58 24.98 24.26 23.21 18.51 18.37 18.8 21.31 21.45

21.38 25.41 25.22 21.53 25.12 24.21 23.25 18.6 18.41 18.94 21.35 21.45

21.34 25.46 25.31 21.62 25.07 24.36 23.45 18.89 18.41 18.8 21.63 21.55

21.72 25.6 25.36 21.86 25.12 24.5 23.4 18.89 18.8 18.41 21.67 21.64

21.72 25.6 25.41 21.86 25.27 24.55 23.49 18.84 18.89 18.41 21.83 21.69

21.86 25.79 25.51 22.1 25.22 24.6 23.64 18.94 18.84 18.37 22.07 21.84

21.91 25.65 25.7 2.39 25.31 24.64 23.83 19.04 18.89 18.51 22.19 21.93

21.96 25.65 26.18 22.15 25.41 24.88 23.78 19.04 19.04 18.51 22.27 22.08

22.68 25.55 26.42 22.3 25.36 24.84 23.88 19.04 19.04 18.46 21.95 22.32

22.53 25.65 26.03 22.39 25.27 24.79 23.88 18.84 18.89 18.84 22.07 22.32

22.15 25.75 26.13 22.2 25.36 24.79 23.92 18.99 27.38 18.65 22.03 22.03

22.15 25.65 26.03 22.3 25.46 24.93 24.4 18.99 19.28 18.65 22.23 22.17

22.2 25.75 26.13 22.3 25.65 24.88 24.12 18.89 19.37 18.75 22.27 22.22

22.1 25.79 26.27 22.25 25.55 24.93 24.16 18.94 19.32 18.89 22.31 22.22

22.34 25.79 26.27 22.34 25.51 25.6 24.31 19.08 19.37 18.99 22.47 22.32

22.44 25.84 26.46 22.34 25.55 25.46 24.31 19.13 19.42 18.99 22.57 22.32

22.44 25.75 26.46 22.34 25.51 25.03 24.21 19.13 19.56 19.37 22.47 22.37

22.34 25.36 26.18 22.3 25.65 25.86 24.4 19.18 19.61 18.89 22.47 24.19

22.3 27.23 25.7 22.2 25.27 26.32 24.36 19.08 19.66 18.89 21.83 24.1

22.34 25.17 25.46 22.15 24.88 25.22 24.12 19.47 19.76 19.04 21.75 23.81

22.15 22.3 24.45 22.01 24.79 24.55 23.73 19.18 19.8 18.8 21.59 23.52

22.15 24.79 24.21 22.1 24.45 24.69 23.35 19.61 19.9 18.99 21.55 23.33

22.58 24.6 23.88 22.34 23.92 24.5 23.4 19.13 20.04 18.8 21.39 23.23

21.96 24.36 23.49 21.86 24.26 24.02 23.45 19.37 19.99 18.84 21.43 23.42

21.86 24.26 23.11 21.96 24.4 23.54 22.77 18.94 19.99 19.04 21.35 22.7

21.82 23.45 23.21 21.72 23.83 23.54 22.39 18.94 19.85 18.99 21.27 22.41

21.72 23.35 23.06 21.72 23.54 23.35 22.49 18.94 19.85 18.94 21.39 22.37

21.62 23.45 22.97 21.43 23.3 23.21 22.3 18.94 19.85 18.7 21.55 22.27

21.53 23.21 22.87 21.43 23.11 22.87 22.15 18.94 19.9 18.84 21.19 22.13

21.48 23.16 22.73 21.38 22.97 22.92 22.15 18.89 19.8 18.75 21.07 22.03

21.24 23.01 22.68 21.19 22.77 22.77 21.91 18.84 19.9 18.99 21.19 21.74

21.58 22.87 22.58 21.53 22.82 22.68 21.82 18.94 19.9 18.65 21.27 21.74

21.1 22.68 22.39 21 22.53 22.63 21.77 19.08 19.8 18.65 21.03 21.74

21.05 22.53 22.1 20.81 22.25 22.3 21.62 19.13 19.8 18.65 20.87 21.6];

12 and the high variable of the Z axis thermal deformation degree of association from 15 temperature variables, are filtered out by Grey Incidence Analysis according to step 2, these 12 temperature variable composition matrix P; Utilize matrix P and Z axis thermal deformation data to set up on computers GM(1,13 according to step 3) grey forecasting model, and predict machine tool thermal error; According to step 4,6 data (15.9315.6215.5215.0714.7914.79) below that displacement sensor is obtained are predicted as validation test data, above 55 thermal deformation measured datas and Grey Model to front 55 data subtract each other successively, obtain 55 hot error residual sequences; According to the step 5 input sample of matrix P as BP neural network, the residual sequence that step 4 obtains is as output sample, neural network is carried out to learning training, re-enter temperature matrix and predict 61 residual sequence values, it is the lathe Z axis heat error compensation sequence of grey neural network prediction that the hot error amount of the sequential value of neural network prediction and grey system forecasting is added up successively, and the heat error compensation value of X-axis is as long as use above same step to obtain.Fig. 3 has provided the hot error and the hot error comparison diagram of actual measurement that adopt Grey Neural Network Model prediction, and Fig. 4 is last 6 hot error amounts and the hot error comparison diagram of actual measurement that adopts Grey Neural Network Model and the prediction of other method.Table 1 has been listed the thermal compensation value prediction comparing result at check post place.

Table 1

Claims (1)

1. a numerical control machine heat error compensation grey neural network modeling method, is characterized in that, carries out as follows:

Step 1: placement sensor

First utilize infrared thermography to do thermograph to operation lathe after a while, the temperature cromogram showing according to thermal imaging system, temperature shows that high region is the heating region of lathe, the temperature peak of the good each heating region of mark; Shut down after cooling and place the sensor that measures ambient temperature changes on lathe side, and carry out collecting temperature delta data at all m gauge point mounting temperature sensors, so one has m+1 temperature sensor; X-axis, Z-direction at machine tool chief axis are respectively installed a laser displacement sensor, gather the data of thermal deformation of machine tool; In system operational process, read the real time temperature { T of all temperature sensors every phase same amount of time _iand thermal deformation displacement { X _s, { Z _stime dependent numerical value;

Step 2: screening temperature variable

According to the temperature variation sequence T having measured _i(T _i1t _i2t _i3t _ikt _i(k+1)t _is), i=1,2 ... m+1 filters out the temperature variable that n is individual and thermal deformation correlativity is high and forms new matrix P from m+1 temperature variable by grey correlation analysis, establish P and be

P={T _i(1)T _i(2)…T _i(s)}i=1,2,…,n；

Step 3: set up gray system and obtain hot error prediction value

By X _sor Z _srespectively with matrix P composition gray system G(1, N) original data series;

By Z _swith the original data series of matrix P composition gray system be

$Q=\left\{\begin{array}{cccc}{Z^{\left(0\right)}}_{\left(1\right)}& {Z^{\left(0\right)}}_{\left(2\right)}& ...& {Z^{\left(0\right)}}_{\left(s\right)}\\ T_i^{\left(0\right)}\left(1\right)& T_i^{\left(0\right)}\left(2\right)& ...& T_i^{\left(0\right)}\left(s\right)\\ ...& ...& ...& ...\\ T_n^{\left(0\right)}\left(1\right)& T_n^{\left(0\right)}\left(2\right)& ...& T_n^{\left(0\right)}\left(s\right)\end{array}\right\},i=\mathrm{1,2},...,n-1;---\left(1\right)$

Above-mentioned ordered series of numbers is made respectively to one-accumulate and generate, obtain new 1-AGO ordered series of numbers

$Q^{\text{'}}=\left\{\begin{array}{cccc}{Z^{\left(1\right)}}_{\left(1\right)}& {Z^{\left(1\right)}}_{\left(2\right)}& ...& {Z^{\left(1\right)}}_{\left(s\right)}\\ T_i^{\left(1\right)}\left(1\right)& T_i^{\left(1\right)}\left(2\right)& ...& T_i^{\left(1\right)}\left(s\right)\\ ...& ...& ...& ...\\ T_n^{\left(1\right)}\left(1\right)& T_n^{\left(1\right)}\left(2\right)& ...& T_n^{\left(1\right)}\left(s\right)\end{array}\right\},i=\mathrm{1,2},...,n-1;---\left(2\right)$

Set up the differential equation

$d{Z}^{\left(1\right)}/\mathrm{dt}+a{Z}^{\left(1\right)}=b_1{T}_1^{\left(1\right)}+b_2{T}_2^{\left(1\right)}+...+b_n{T}_n^{\left(1\right)};---\left(3\right)$

Coefficient a, b ₁, b ₂... b _nsolve by least square method;

Solve the differential equation (3) and obtain the hot error prediction value of Z-direction

$\begin{array}{c}{{\hat{Z}}^{\left(0\right)}}_{(t+1)}={{\hat{Z}}^{\left(1\right)}}_{(t+1)}-{{\hat{Z}}^{\left(1\right)}}_{\left(t\right)}\\ =[Z^{\left(0\right)}\left(1\right)-\underset{i=2}{\overset{n}{\mathrm{\Σ}}}\frac{b_{i-1}}{a}{T}_i^{\left(1\right)}(t+1)]e^{-\mathrm{at}}+\underset{i=2}{\overset{n}{\mathrm{\Σ}}}\frac{b_{i-1}}{a}{T}_i^{\left(1\right)}(t+1)-[Z^{\left(0\right)}\left(1\right)-\underset{i=2}{\overset{n}{\mathrm{\Σ}}}\frac{b_{i-1}}{a}{T}_i^{\left(1\right)}\left(t\right)]e^{-a(t-1)}+\\ \underset{i=2}{\overset{n}{\mathrm{\Σ}}}\frac{b_{i-1}}{a}{T}_i^{\left(1\right)}\left(t\right),t=\mathrm{1,2},...,s-1;\end{array}---\left(4\right)$

Next obtain the thermal deformation predicted value of lathe Z axis by Computing ... ,

And by X _swith another gray system original data series of matrix P composition be

$W=\left\{\begin{array}{cccc}{X^{\left(0\right)}}_{\left(1\right)}& {X^{\left(0\right)}}_{\left(2\right)}& ...& {X^{\left(0\right)}}_{\left(s\right)}\\ T_i^{\left(0\right)}\left(1\right)& T_i^{\left(0\right)}\left(2\right)& ...& T_i^{\left(0\right)}\left(s\right)\\ ...& ...& ...& ...\\ T_n^{\left(0\right)}\left(1\right)& T_n^{\left(0\right)}\left(2\right)& ...& T_n^{\left(0\right)}\left(s\right)\end{array}\right\},i=\mathrm{1,2},...,n-1;---\left(5\right)$

Above-mentioned ordered series of numbers is done respectively, after one-accumulate generation, to obtain new 1-AGO ordered series of numbers

$W^{\text{'}}=\left\{\begin{array}{cccc}{X^{\left(1\right)}}_{\left(1\right)}& {X^{\left(1\right)}}_{\left(2\right)}& ...& {X^{\left(1\right)}}_{\left(s\right)}\\ T_i^{\left(1\right)}\left(1\right)& T_i^{\left(1\right)}\left(2\right)& ...& T_i^{\left(1\right)}\left(s\right)\\ ...& ...& ...& ...\\ T_n^{\left(1\right)}\left(1\right)& T_n^{\left(1\right)}\left(2\right)& ...& T_n^{\left(1\right)}\left(s\right)\end{array}\right\},i=\mathrm{1,2},...,n-1;---\left(6\right)$

Set up the differential equation

$d{X}^{\left(1\right)}/\mathrm{dt}+a{X}^{\left(1\right)}=b_1{T}_1^{\left(1\right)}+b_2{T}_2^{\left(1\right)}+...+b_n{T}_n^{\left(1\right)};---\left(7\right)$

Coefficient c, d1, d2 ... dn solves by least square method;

Solve the differential equation (7) and obtain X thermotropism error prediction value

$\begin{array}{c}{{\hat{X}}^{\left(0\right)}}_{(t+1)}={{\hat{X}}^{\left(1\right)}}_{(t+1)}-{{\hat{X}}^{\left(1\right)}}_{\left(t\right)}\\ =[X^{\left(0\right)}\left(1\right)-\underset{i=2}{\overset{n}{\mathrm{\Σ}}}\frac{d_{i-1}}{c}{T}_i^{\left(1\right)}(t+1)]e-\mathrm{ct}+\underset{i=2}{\overset{n}{\mathrm{\Σ}}}\frac{d_{i-1}}{c}{T}_i^{\left(1\right)}(t+1)-[Z^{\left(0\right)}\left(1\right)-\underset{i=2}{\overset{n}{\mathrm{\Σ}}}\frac{d_{i-1}}{c}{T}_i^{\left(1\right)}\left(t\right)]e-c(t-1)+\\ \underset{i=2}{\overset{n}{\mathrm{\Σ}}}\frac{d_{i-1}}{c}{T}_i^{\left(1\right)}\left(t\right),t=\mathrm{1,2},...,s-1;\end{array}---\left(8\right)$

Next can obtain the thermal deformation predicted value of lathe X-axis by Computing , ,

Step 4: solve residual sequence

Will , and true measurement { Z ⁽⁰⁾(1), Z ⁽⁰⁾(2) ..., Z ⁽⁰⁾(k) } subtract each other successively and obtain Z axis residual sequence e ⁽⁰⁾(1), e ⁽⁰⁾(2) ..., e ⁽⁰⁾(k), i.e. Z axis residual sequence

$e^{\left(0\right)}\left(t\right)={{\hat{Z}}^{\left(0\right)}}_{\left(t\right)}-Z^{\left(0\right)}\left(t\right)t=\mathrm{1,2},...,k;---\left(9\right)$

Will , and true measurement { X ⁽⁰⁾(1), X ⁽⁰⁾(2) ..., X ⁽⁰⁾(k) } subtract each other successively and obtain X-axis residual sequence f ⁽⁰⁾(1), f ⁽⁰⁾(2) ..., f ⁽⁰⁾(k), i.e. X-axis residual sequence

$f^{\left(0\right)}\left(t\right)={{\hat{X}}^{\left(0\right)}}_{\left(t\right)}-X^{\left(0\right)}\left(t\right)t=\mathrm{1,2},...,k;---\left(10\right)$

Step 5: the BP neural network model of setting up residual sequence

In MATLAB, set up 3 layers of BP neural network, set transport function, network training function, maximum frequency of training and convergence error; Input sample using k temperature value above of matrix P as neural metwork training, Z axis residual sequence e ⁽⁰⁾(1), e ⁽⁰⁾(2) ..., e ⁽⁰⁾or X-axis residual sequence f (k) ⁽⁰⁾(1), f ⁽⁰⁾(2) ..., f ⁽⁰⁾(k), as output sample, learning training BP neural network is to determine its all parameter values; After having trained, just obtain desired BP neural network model; As long as the temperature value of this temperature variable is input in the middle of neural network, just can obtain residual sequence predicted value or the hot error prediction value of lathe Z axis of artificial neural networks built-up pattern can be passed through

$\hat{Z}\left(t\right)={{\hat{Z}}^{\left(0\right)}}_{\left(t\right)}+{{\hat{e}}^{\left(0\right)}}_{\left(t\right)}---\left(11\right)$

Calculate;

The predicted value of the hot error of lathe X-axis of artificial neural networks built-up pattern can be passed through

$\hat{X}\left(t\right)={{\hat{X}}^{\left(0\right)}}_{\left(t\right)}+{{\hat{f}}^{\left(0\right)}}_{\left(t\right)}---\left(12\right)$

Calculate.