CN105700475A

CN105700475A - Data processing method for realizing machine tool robustness thermal error compensation of wide-range environment temperature

Info

Publication number: CN105700475A
Application number: CN201610256897.3A
Authority: CN
Inventors: 苗恩铭; 刘义; 徐建国; 刘辉
Original assignee: Hefei University of Technology
Current assignee: Hefei University of Technology
Priority date: 2016-04-20
Filing date: 2016-04-20
Publication date: 2016-06-22

Abstract

The invention discloses a data processing method for realizing thermal error compensation of machine tool robustness in a wide range of ambient temperature, comprising the steps of: 1. extracting the modeling temperature independent variable _X _k ; The variable X _k ^* is transformed to obtain the expression of the principal component Z _k ; 3. Extract the first p principal components to participate in the modeling; 4. Standardize the principal axis thermal deformation S _j , and establish the standardized thermal deformation S _j ^* and the former p Multiple linear regression equation between principal components; 5. Transform the regression equation between S _j ^* and the first p principal components into the equation of S _j ^* and X _k ^* ; 6. Convert S _j ^* and X _k ^* The regression equation of is converted into the equation of S _j and X _k , and the thermal error compensation model is established; and the prediction performance of the thermal error model is further analyzed. The invention suppresses the influence of the coupling between the independent variables of temperature on the distortion of the estimated value of the independent variables of the model, and has high prediction accuracy and robustness.

Description

A data processing method for thermal error compensation of machine tool robustness in a wide range of ambient temperatures

技术领域technical field

本发明涉及的是一种机床稳健性热误差补偿的数据处理方法，尤其是涉及一种在大范围环境温度内对机床热误差进行补偿预测的数据处理方法。The invention relates to a data processing method for machine tool robust thermal error compensation, in particular to a data processing method for compensating and predicting machine tool thermal error within a wide range of ambient temperatures.

背景技术Background technique

数控机床是制造领域的重要设备，其加工性能是一个国家制造业发展水平的主要标志之一。在数控机床加工过程中，由于机床各部件不均衡温升引起的热误差，使得刀具和工件之间的相对正确位置发生了变化，从而造成了工件的加工误差。据统计，数控机床热误差在机床总误差中占40～70％左右。通过对数控机床热误差数据进行建模处理，并通过数控系统提前给予补偿的处理方法是提高机床加工精度的一种有效而经济的手段。CNC machine tools are important equipment in the manufacturing field, and their processing performance is one of the main symbols of the development level of a country's manufacturing industry. In the process of CNC machine tool processing, due to the thermal error caused by the uneven temperature rise of various parts of the machine tool, the relative correct position between the tool and the workpiece has changed, resulting in the processing error of the workpiece. According to statistics, the thermal error of CNC machine tools accounts for about 40-70% of the total error of the machine tool. It is an effective and economical means to improve the machining accuracy of the machine tool by modeling and processing the thermal error data of the CNC machine tool and giving compensation in advance through the CNC system.

目前最常采用的机床热误差数据处理方法是基于最小二乘原理的多元线性回归。该方法基于残差平方和最小的分析原理，其所建模型具有较高的线性化拟合精度，并且算法易于实现，因此常被用来对机床热误差数据进行建模处理。但是，由于机床温度复杂的非线性和时变性特征，使得机床温度场在不同环境温度条件下具有不同特征，主要表现为机床各热源之间的耦合性差异，并且环境温度相差越大，机床温度场的耦合性差异也越大。因此，当机床所处环境温度变化较大时，各温度传感器之间的耦合程度发生较大变化，导致多元回归模型中各自变量的最小二乘估计值失真，这是多元线性回归处理方法的一个弊端。At present, the most commonly used data processing method of machine tool thermal error is multiple linear regression based on the principle of least squares. This method is based on the analysis principle of the minimum sum of squared residuals. The model built by it has high linearization fitting accuracy, and the algorithm is easy to implement. Therefore, it is often used to model the thermal error data of machine tools. However, due to the complex nonlinear and time-varying characteristics of the machine tool temperature, the temperature field of the machine tool has different characteristics under different ambient temperature conditions. The difference in field coupling is also greater. Therefore, when the ambient temperature of the machine tool changes greatly, the degree of coupling between the temperature sensors changes greatly, resulting in the distortion of the least squares estimated value of each variable in the multiple regression model, which is one of the multiple linear regression processing methods. disadvantages.

2011年，苗恩铭等人提出采用时间序列建模技术处理机床热误差数据的方法(参看文献“精密数据机床热误差时间序列建模技术研究”，来自2011年全国精密工程学术研讨会)。该方法由于将温度滞后项纳入热误差模型中，显著提高了模型的线性化拟合精度，但同样也限于小范围环境温度范围内的应用。当数控机床所处环境温度变化较大时，温度传感器间的耦合性会对时间序列模型产生比多元线性回归更严重的影响，严重降低热误差预测模型模型的预测稳健性能力。In 2011, Miao Enming and others proposed a method of processing machine tool thermal error data using time series modeling technology (see the literature "Research on Time Series Modeling Technology for Precision Data Machine Tool Thermal Error", from the 2011 National Precision Engineering Symposium). Because this method incorporates the temperature lag item into the thermal error model, it significantly improves the linearization fitting accuracy of the model, but it is also limited to applications within a small range of ambient temperatures. When the ambient temperature of the CNC machine tool changes greatly, the coupling between temperature sensors will have a more serious impact on the time series model than the multiple linear regression, which seriously reduces the prediction robustness of the thermal error prediction model.

发明内容Contents of the invention

本发明的目的在于克服现有技术中的不足，提供一种实现大范围环境温度的机床稳健性热误差补偿的数据处理方法。由于本发明中的数据处理方法为采用元自变量的主成分代替自变量建立热误差模型，且各主成分之间的协方差为零，意味着主成分之间互不相关，因此本发明提供的数据处理方法很好地抑制了温度自变量间的耦合性对模型自变量估计值失真的影响，进而保证了由本发明提供的数据处理方法建立的热误差模型在大范围环境条件下的高预测精度和预测稳健性，具有重大的实际工程应用。The purpose of the present invention is to overcome the deficiencies in the prior art, and provide a data processing method for realizing thermal error compensation of machine tool robustness in a wide range of ambient temperatures. Since the data processing method in the present invention is to use the principal components of the independent variables to replace the independent variables to establish a thermal error model, and the covariance between the principal components is zero, which means that the principal components are not correlated with each other, so the present invention provides The data processing method of the present invention suppresses the influence of the coupling between the temperature independent variables on the distortion of the estimated value of the model independent variable, and then ensures the high prediction of the thermal error model established by the data processing method provided by the present invention under a wide range of environmental conditions accuracy and predictive robustness, with significant practical engineering applications.

本发明提的对大范围环境温度内的机床稳健性热误差补偿的数据处理方法，包括以下步骤：The data processing method for the thermal error compensation of machine tool robustness within a wide range of ambient temperature proposed by the present invention comprises the following steps:

一种实现大范围环境温度的机床稳健性热误差补偿的数据处理方法，其特征在于，按如下步骤进行：A data processing method for realizing thermal error compensation of machine tool robustness in a wide range of ambient temperature, characterized in that, the steps are as follows:

步骤一：获取机床的温度变量ΔT_i和主轴热变形量S_j，其中，i＝1，2，…，m。Step 1: Obtain the temperature variable ΔT _i of the machine tool and the thermal deformation of the spindle S _j , where i=1, 2, . . . , m.

所述m是指温度变量的个数。所述j是指机床主轴的轴向，j取X、Y、和/或Z。X、Y、Z分别代表机床主轴的X轴向、主轴的Y轴向、主轴的Z轴向。The m refers to the number of temperature variables. Said j refers to the axial direction of the machine tool spindle, and j is X, Y, and/or Z. X, Y, and Z respectively represent the X axis of the machine tool spindle, the Y axis of the spindle, and the Z axis of the spindle.

由温度变量ΔT_i和主轴热变形量S_j的相关性关系获取温度自变量X_k，k＝1，2，…，n。The temperature independent variable X _k is obtained from the correlation between the temperature variable ΔT _i and the spindle thermal deformation S _j , k=1, 2, . . . , n.

所述温度自变量X_k用以建立热误差补偿模型。所述n是指温度自变量的个数，n≤m。The temperature independent variable X _k is used to establish a thermal error compensation model. The n refers to the number of temperature independent variables, n≤m.

步骤二：对由步骤一获取的的温度自变量X_k进行标准化处理，得到标准化温度自变量X_k ^*。Step 2: Standardize the temperature independent variable X _{k obtained in Step 1 to obtain a standardized temperature independent variable X k} _* ^.

并由标准化温度自变量X_k ^*转换得到主成分Z_k的表达式。And the expression of the principal component Z _k is obtained by transforming the normalized temperature independent variable X _k ^* .

所述主成分Z_k是指通过正交变换将温度自变量X_k ^*转换后得到的一组变量，该组变量线性不相关。The principal component Z _k refers to a group of variables obtained by transforming the temperature independent variable X _k ^* through orthogonal transformation, and the group of variables is linearly irrelevant.

步骤三：从由步骤二获得的主成分Z_k中提取出前p个主成分Z₁，Z₂，…，Z_p，p≤n，以用于下一步的热误差建模。Step 3: Extract the first _p principal components _Z ₁ , Z ₂ , .

步骤四：对步骤一中的主轴热变形量S_j进行标准化处理，获得标准化热变形量S_j ^*。Step 4: Standardize the spindle thermal deformation S _j in step 1 to obtain the standardized thermal deformation S _j ^* .

并对标准化热变形量S_j ^*和步骤3获得的用于热误差建模的主成分Z₁，Z₂，…，Z_p作多元线性回归分析，得到S_j ^*关于Z₁，Z₂，…，Z_p的表达式方程 And do multiple linear regression analysis on the standardized thermal deformation S _j ^* and the principal components Z ₁ , Z ₂ , ..., Z _p obtained in step 3 for thermal error modeling, and get S _j ^* about Z ₁ , Z ₂ , ..., the expression equation for Z _p

步骤五：将步骤四获得的S_j ^*关于Z₁，Z₂，…，Z_p的表达式方程转化为S_j ^*关于X_k ^*的表达式方程。Step 5: Transform the expression equation of S _j ^* about Z ₁ , Z ₂ , . . . , Z _p obtained in step 4 into the expression equation of S _j ^* about X _k ^* .

步骤六：将步骤五获得的S_j ^*关于X_k ^*的表达式方程转化为S_j关于X_k的表达式方程，该S_j关于X_k的表达式方程即为热误差模型。Step 6: Transform the expression equation of S _j ^* about X _k ^* obtained in step 5 into the expression equation of S _j about X _k , and the expression equation of S _j about X _k is the thermal error model.

进一步说，用步骤六建立的热误差模型，即S_j关于X_k的表达式方程对所述热误差模型的预测性能进行分析。Furthermore, the thermal error model established in step 6, that is, the expression equation of S _j with respect to X _k is used to analyze the prediction performance of the thermal error model.

其中，所述的第一步具体是指：Wherein, the first step specifically refers to:

1.1以温度传感器的温度值增量ΔT_i为温度变量，根据相关系数公式(1)，计算ΔT_i与主轴热变形量S_j之间的相关系数值。1.1 Take the temperature value increment ΔT _i of the temperature sensor as the temperature variable, and calculate the correlation coefficient value between ΔT _i and the spindle thermal deformation S _j according to the correlation coefficient formula (1).

式(1)中，r_ij为ΔT_i与S_j之间的相关系数值，t(ΔT_i)为ΔT_i的长度，ΔT_iq为ΔT_i序列中的第q个值，为ΔT_i序列的平均值，S_iq为S_j序列中的第q个值，为S_j序列的平均值。温度变量ΔT_i是通过温度传感器从处于运行状态的机床处采集到的。温度变量ΔT_i序列的长度与热变形量S_j序列的长度相同。In formula (1), r _ij is the correlation coefficient value between ΔT _i and S _j , t(ΔT _i ) is the length of ΔT _i , ΔT _iq is the qth value in the ΔT _i sequence, is the average value of ΔT _i sequence, S _iq is the qth value in S _j sequence, is the average value of the S _j sequence. The temperature variable ΔT _i is collected from the machine tool in running state through the temperature sensor. The length of the temperature variable ΔT _i sequence is the same as that of the thermal deformation S _j sequence.

1.2提取步骤1.1中相关系数值最大的n个温度变量，作为温度自变量X_k。所述温度自变量X_k用来建立热误差模型。n的取值不大于m。1.2 Extract the n temperature variables with the largest correlation coefficient values in step 1.1 as the temperature independent variable X _k . The temperature independent variable X _k is used to model thermal errors. The value of n is not greater than m.

其中，所述的第二步具体是指：Wherein, the second step specifically refers to:

2.1利用公式(2)，对所提取的温度自变量X_k作标准化处理，得到标准化温度自变量X_k ^*。2.1 Use the formula (2) to standardize the extracted temperature independent variable X _k to obtain the standardized temperature independent variable X _k ^* .

${X x}_{k k q q}^{* *} = = \frac{{X x}_{k k q q} - - {\overset{&OverBar; &OverBar;}{X x}}_{k k}}{\sqrt{\frac{11}{t t (({X x}_{k k}^{* *}))} {Σ Σ}_{q q = = 11}^{t t (({X x}_{k k}^{* *}))} {(({X x}_{k k q q} - - {\overset{&OverBar; &OverBar;}{X x}}_{k k}))}^{22}}},, ((k k = = 11,, 22,, ... ...,, n no,, q q = = 11,, 22,, ... ...,, t t (({X x}_{k k}^{* *})))) - - - - - - ((22))$

式(2)中，X_kq ^*为X_k ^*序列中的第q个值，X_kq为X_k序列中的第q个值，为X_k序列的平均值，t(X_k ^*)为X_k ^*序列的长度。In formula (2), X _kq ^* is the qth value in the X _k ^* sequence, X _kq is the qth value in the X _k sequence, is the average value of the X _k sequence, and t(X _k ^* ) is the length of the X _k ^* sequence.

2.2利用步骤1.1所述的相关系数公式(1)，计算任意两个标准化温度自变量之间的相关系数值，得到标准化温度自变量的相关矩阵R_n×n(3)，具体如下。2.2 Using the correlation coefficient formula (1) described in step 1.1, calculate the correlation coefficient value between any two standardized temperature independent variables, and obtain the correlation matrix R _n×n (3) of the standardized temperature independent variables, as follows.

式(3)中，r_ab表示标准化温度自变量X_a ^*和X_b ^*的相关系数值。In the formula (3), r _ab represents the correlation coefficient value of the standardized temperature independent variable X _a ^* and X _b ^* .

2.3由使关系式R_n×nu＝λu成立的u和λ分别为相关矩阵R的特征向量和特征值，求相关矩阵R_n×n的特征向量u_k和特征值λ_k，其中，k＝1，2，…，n。2.3 Since u and λ, which make the relation R _n×n u=λu established, are respectively the eigenvector and eigenvalue of the correlation matrix R, find the eigenvector u _k and eigenvalue λ _k of the correlation matrix R _n×n , where, k = 1, 2, ..., n.

2.4根据步骤2获得的标准化温度自变量X_k ^*和特征向量u_k，由公式(4)得到标准化温度自变量X_k ^*和特征向量u_k构成的主成分Z_k的表达式，具体为：2.4 According to the standardized temperature independent variable X _k ^* and eigenvector u _{k obtained in step 2, the expression of the principal component Z k} _composed of the standardized temperature independent variable X _k ^* and eigenvector u _k is obtained by formula (4), specifically:

$\{\begin{matrix} {Z Z}_{11} = = {u u}_{1111} {X x}_{11}^{* *} + + {u u}_{21 twenty one} {X x}_{22}^{* *} + + ... ... + + {u u}_{k k 11} {X x}_{k k}^{* *} + + ... ... + + {u u}_{n no 11} {X x}_{n no}^{* *} \\ {Z Z}_{22} = = {u u}_{1212} {X x}_{11}^{* *} + + {u u}_{22 twenty two} {X x}_{22}^{* *} + + ... ... + + {u u}_{k k 22} {X x}_{k k}^{* *} + + ... ... + + {u u}_{n no 22} {X x}_{n no}^{* *} \\ . . \\ . . \\ . . \\ {Z Z}_{k k} = = {u u}_{11 k k} {X x}_{11}^{* *} + + {u u}_{22 k k} {X x}_{22}^{* *} + + ... ... + + {u u}_{k k k k} {X x}_{k k}^{* *} + + ... ... + + {u u}_{n no k k} {X x}_{n no}^{* *} \\ . . \\ . . \\ . . \\ {Z Z}_{n no} = = {u u}_{11 n no} {X x}_{11}^{* *} + + {u u}_{22 n no} {X x}_{22}^{* *} + + ... ... + + {u u}_{k k n no} {X x}_{k k}^{* *} + + ... ... + + {u u}_{n no n no} {X x}_{n no}^{* *} \end{matrix} - - - - - - ((44))$

式(4)中，Var(Z_k)＝λ_k，Cov(Z_i，Z_j)＝0(i≠j)，即各主成分之间互不相关。In formula (4), Var(Z _k )=λ _k , Cov(Z _i , Z _j )=0 (i≠j), that is, the principal components are not correlated with each other.

其中，所述的第三步具体是指：Wherein, the third step specifically refers to:

设前p个主成分Z₁，Z₂，…，Z_p的累积方差贡献率为Vcc_p，p≤n，令累积方差贡献率Vcc_p不小于85％，计算出p的数值，再依据p的数值将具体的主成分Z₁，Z₂，…，Z_p提取出，以用于下一步的热误差建模。其中，前p个主成分的累积方差贡献率Vcc_p的公式为：Assume that the cumulative variance contribution rate of the first p principal components Z ₁ , Z ₂ ,..., Z _p is Vcc _p , p≤n, and make the cumulative variance contribution rate Vcc _p not less than 85%, calculate the value of p, and then base on p The specific principal components Z ₁ , _Z ₂ , . Among them, the formula of the cumulative variance contribution rate Vcc _p of the first p principal components is:

${Vcc Vcc}_{p p} = = {Σ Σ}_{i i = = 11}^{p p} {λ λ}_{i i} / / {Σ Σ}_{i i = = 11}^{n no} {λ λ}_{i i} - - - - - - ((55))$

其中，所述的第四步具体是指：Wherein, the fourth step specifically refers to:

4.1利用公式(6)，对主轴热变形量S_j作标准化处理，得到标准化热变形量S_j ^*。4.1 Use the formula (6) to standardize the thermal deformation of the spindle S _j to obtain the standardized thermal deformation S _j ^* .

${S S}_{j j q q}^{* *} = = \frac{{S S}_{j j q q} - - {\overset{&OverBar; &OverBar;}{S S}}_{j j}}{\sqrt{\frac{11}{t t (({S S}_{j j}^{* *}))} {Σ Σ}_{q q = = 11}^{t t (({S S}_{j j}^{* *}))} {(({S S}_{j j q q} - - {\overset{&OverBar; &OverBar;}{S S}}_{j j}))}^{22}}} - - - - - - ((66))$

式(6)中，S_jq ^*为S_j ^*序列中的第q个值，S_jq为S_j序列中的第q个值，为S_j序列的平均值，t(S_j ^*)为S_j ^*序列的长度。In formula (6), S _jq ^* is the qth value in the S _j ^* sequence, S _jq is the qth value in the S _j sequence, is the average value of the S _j sequence, and t(S _j ^* ) is the length of the S _j ^* sequence.

4.2对标准化热变形量S_j ^*和参与热误差建模的主成分Z₁，Z₂，…，Z_p作基于最小二乘原理的多元线性回归分析，可得到S_j ^*关于Z₁，Z₂，…，Z_p的表达式方程如式(7)。利用基于最小二乘原理的多元线性回归分析，获得模型中各元的回归系数估计值S_j ^*关于Z₁，Z₂，…，Z_p的表达式方程式与回归系数估计值分别如下：4.2 Perform multiple linear regression analysis based on the least squares principle on the standardized thermal deformation S _j ^* and the principal components Z ₁ , Z ₂ , ..., Z _p involved in thermal error modeling, and S _j ^* can be obtained for Z ₁ , Z ₂ ,..., the expression equation of Z _p is as formula (7). Using multiple linear regression analysis based on the principle of least squares to obtain the estimated value of the regression coefficient of each element in the model S _j ^* expression equation with respect to Z ₁ , Z ₂ ,…, Z _p and regression coefficient estimates They are as follows:

${\overset{^^}{S S}}_{j j}^{* *} = = {\overset{^^}{α α}}_{11} {Z Z}_{11} + + {\overset{^^}{α α}}_{22} {Z Z}_{22} + + ... ... + + {\overset{^^}{α α}}_{p p} {Z Z}_{p p} - - - - - - ((77))$

${\overset{^^}{α α}}_{p p} = = {(({Z Z}_{p p}^{T T} {Z Z}_{p p}))}^{- - 11} {Z Z}_{p p}^{T T} {S S}_{j j}^{* *} - - - - - - ((88))$

其中，所述的第五步具体是指：Wherein, the fifth step specifically refers to:

利用步骤二得到的主成分Z_k的表达式，将步骤四得到的S_j ^*关于Z₁，Z₂，…，Z_p的表达式方程转化为S_j ^*关于X_k ^*(k＝1，2，…，n)的表达式方程S_j ^*关于Xk^*的表达式方程具体如下：Using the expression of the principal component Z _k obtained in step 2, the expression equation of S _j ^* about Z ₁ , Z ₂ ,..., Z _p obtained in step 4 Transformed into the expression equation of S _j ^* about X _k ^* (k=1, 2, ..., n) Expression equation of S _j ^* with respect to Xk ^* details as follows:

$\begin{matrix} {\overset{^^}{S S}}_{j j}^{* *} = = {\overset{^^}{α α}}_{11} {Z Z}_{11} + + {\overset{^^}{α α}}_{22} {Z Z}_{22} + + ... ... + + {\overset{^^}{α α}}_{p p} {Z Z}_{p p} \\ = = {\overset{^^}{α α}}_{11} (({u u}_{1111} {X x}_{11}^{* *} + + {u u}_{21 twenty one} {X x}_{22}^{* *} + + ... ... + + {u u}_{k k 11} {X x}_{k k}^{* *} + + ... ... + + {u u}_{n no 11} {X x}_{n no}^{* *})) + + {\overset{^^}{α α}}_{22} (({u u}_{1212} {X x}_{11}^{* *} + + {u u}_{22 twenty two} {X x}_{22}^{* *} + + ... ... + + {u u}_{k k 22} {X x}_{k k}^{* *} + + ... ... + + {u u}_{n no 22} {X x}_{n no}^{* *})) \\ + + ... ... + + {\overset{^^}{α α}}_{p p} (({u u}_{11 n no} {X x}_{11}^{* *} + + {u u}_{22 n no} {X x}_{22}^{* *} + + ... ... + + {u u}_{k k p p} {X x}_{k k}^{* *} + + ... ... + + {u u}_{n no p p} {X x}_{n no}^{* *})) \\ = = {\overset{^^}{β β}}_{11} {X x}_{11}^{* *} + + {\overset{^^}{β β}}_{22} {X x}_{22}^{* *} + + ... ... + + {\overset{^^}{β β}}_{k k} {X x}_{k k}^{* *} + + ... ... + + {\overset{^^}{β β}}_{n no} {X x}_{n no}^{* *} \end{matrix} - - - - - - ((99))$

式(9)中， In formula (9),

其中，所述的第六步具体是指：Wherein, the sixth step specifically refers to:

对温度自变量X_k作标准化处理的公式X_kq ^*和对主轴热变形量S_j作标准化的公式S_jq ^*，将由步骤五得到的S_j ^*关于X_k ^*的表达式方程转化S_j关于X_k的表达式方程(10)，完成热误差预测模型的建立。其中，S_j关于X_k的表达式方程(10)为：The formula X _kq ^* for normalizing the temperature independent variable X _k and the formula S _jq ^* for standardizing the thermal deformation of the main shaft S _j are transformed into the expression equation of S _j ^* about X _k ^* obtained in step five to S _j about The expression equation (10) of X _k completes the establishment of the thermal error prediction model. Among them, the expression equation (10) of S _j with respect to X _k is:

${\overset{^^}{S S}}_{j j} = = {\overset{^^}{θ θ}}_{00} + + {\overset{^^}{θ θ}}_{11} {X x}_{11} + + {\overset{^^}{θ θ}}_{22} {X x}_{22} + + ... ... + + {\overset{^^}{θ θ}}_{k k} {X x}_{k k} + + ... ... + + {\overset{^^}{θ θ}}_{n no} {X x}_{n no} - - - - - - ((1010))$

${\overset{^^}{θ θ}}_{k k} = = \frac{{S S}_{{s the s}_{j j}}}{{S S}_{{x x}_{k k}}} {\overset{^^}{β β}}_{k k} - - - - - - ((1111))$

${θ θ}_{00} = = \overset{&OverBar; &OverBar;}{{S S}_{j j}} - - {Σ Σ}_{k k = = 11}^{n no} {\overset{^^}{θ θ}}_{k k} {\overset{&OverBar; &OverBar;}{X x}}_{k k} - - - - - - ((1212))$

式(11)中，为S_j序列的离散标准差，为X_k序列的离散标准差。In formula (11), is the discrete standard deviation of the S _j sequence, is the discrete standard deviation of the X _k sequence.

在完成步骤六后：After completing step six:

将下次实验测量得到的温度自变量值输入到热误差预测模型(10)中，获得热变形量预测值根据与热变形量测量值S_j计算得到残差值以及残余标准差值，获得预测模型(10)的预测性能，最终完成机床热误差补偿的数据处理。其中，残差是指与S_j的差值，残余标准差的计算公式如式(13)所示。Input the temperature independent variable value obtained in the next experimental measurement into the thermal error prediction model (10) to obtain the predicted value of thermal deformation according to Calculate the residual value and the residual standard deviation value with the thermal deformation measurement value S _j , obtain the prediction performance of the prediction model (10), and finally complete the data processing of the machine tool thermal error compensation. Among them, the residual is The formula for calculating the residual standard deviation of the difference with S _j is shown in formula (13).

$S S D D. = = \sqrt[22]{{Σ Σ}_{q q = = 11}^{t t (({S S}_{j j}))} \frac{{(({S S}_{j j q q} - - {\overset{^^}{S S}}_{j j q q}))}^{22}}{t t (({S S}_{j j})) - - n no - - 11}} - - - - - - ((1313))$

式(13)中，SD为残余标准差，S_jq为S_j序列中的第q个值，为序列中的第q个值，t(S_j)为S_j或序列的长度。S_j序列的长度与序列的长度相同。In formula (13), SD is the residual standard deviation, S _jq is the qth value in the S _j sequence, for The qth value in the sequence, t(S _j ) is either S _j or The length of the sequence. The length of S _j sequence and The sequences are the same length.

与现有技术相比，本发明的效益具体体现在：本发明提出的采用原始变量的主成分代替原始变量建立回归模型的方法，有效地避免了温度自变量间的耦合效应，对于大范围环境温度条件下，其所建模型均具有较好的预测精度和稳健性，为数控机床热误差补偿应用提供了一个很好的数据处理思路。Compared with the prior art, the benefits of the present invention are embodied in that the method of establishing a regression model using the principal components of the original variables instead of the original variables proposed by the present invention effectively avoids the coupling effect between the temperature independent variables, and is suitable for large-scale environments. Under the condition of temperature, the models built have good prediction accuracy and robustness, which provides a good data processing idea for the application of thermal error compensation of CNC machine tools.

附图说明Description of drawings

图1为本发明提供的一种实现大范围环境温度的机床稳健性热误差补偿的数据处理方法的流程图。FIG. 1 is a flow chart of a data processing method for implementing robust thermal error compensation of a machine tool in a wide range of ambient temperatures provided by the present invention.

图2为由Leaderway-V450数控机床实验获得的10个温度变量数据。Figure 2 shows the data of 10 temperature variables obtained from the experiment of Leaderway-V450 CNC machine tool.

图3为由Leaderway-V450数控机床实验获得的主轴Z向热变形量数据。Figure 3 shows the thermal deformation data of the spindle in the Z direction obtained from the experiment of the Leaderway-V450 CNC machine tool.

图4为为初始环境温度分别为9.19℃、19.94℃和29.19℃时、主轴转速为4000rpm时的热误差测量值、热误差预测值以及残差数据。Figure 4 shows the thermal error measurement value, thermal error prediction value and residual data when the initial ambient temperature is 9.19°C, 19.94°C and 29.19°C respectively, and the spindle speed is 4000rpm.

具体实施方式detailed description

以下结合附图和具体事例对本发明作进一步的详细描述。The present invention will be described in further detail below in conjunction with the accompanying drawings and specific examples.

参见图1，一种实现大范围环境温度的机床稳健性热误差补偿的数据处理方法，按如下步骤进行：Referring to Fig. 1, a data processing method for realizing thermal error compensation of machine tool robustness in a wide range of ambient temperature is carried out as follows:

进一步说，所述的步骤一具体是指：Further, described step one specifically refers to:

1.1获取机床的温度变量ΔT_i和主轴热变形量S_j，计算温度变量ΔT_i和主轴热变形量S_j之间的相关系数值。相关系数公式(1)如下所示：1.1 Obtain the temperature variable ΔT _i of the machine tool and the thermal deformation of the spindle S _j , and calculate the correlation coefficient value between the temperature variable ΔT _i and the thermal deformation S _j of the spindle. The correlation coefficient formula (1) is as follows:

1.2提取步骤1.1中相关系数值最大的n个温度变量，作为温度自变量X_k。所述温度自变量X_k用来建立热误差模型。所述n不大于m，优选的方案是，n取值为2～4。1.2 Extract the n temperature variables with the largest correlation coefficient values in step 1.1 as the temperature independent variable X _k . The temperature independent variable X _k is used to model thermal errors. Said n is not greater than m, and the preferred scheme is that n takes a value of 2-4.

3.根据权利要求1所述的一种实现大范围环境温度的机床稳健性热误差补偿的数据处理方法，其特征在于，所述的步骤二具体是指：3. a kind of data processing method that realizes the machine tool robustness thermal error compensation of wide range ambient temperature according to claim 1, it is characterized in that, described step 2 specifically refers to:

2.1对步骤一中获得的温度自变量X_k进行标准化处理，得到标准化温度自变量X_k ^*。对温度自变量X_k作标准化处理的公式(2)具体如下：2.1 Standardize the temperature independent variable X _{k obtained in step 1 to obtain a standardized temperature independent variable X k} _* ^. The formula (2) for standardizing the temperature independent variable X _k is as follows:

2.2利用步骤一所述的相关系数公式(1)，计算任意两个标准化温度自变量之间的相关系数值，得到标准化温度自变量的相关矩阵R_n×n(3)，具体如下。2.2 Using the correlation coefficient formula (1) described in step 1, calculate the correlation coefficient value between any two standardized temperature independent variables, and obtain the correlation matrix R _n×n (3) of the standardized temperature independent variables, as follows.

在相关矩阵R_n×n(3)中，r_ab表示标准化温度自变量X_a ^*和X_b ^*的相关系数值。In the correlation matrix R _n×n (3), r _ab represents the correlation coefficient values of the normalized temperature independent variables X _a ^* and X _b ^* .

2.3由使关系式R_n×nu＝λu成立的u和λ分别为相关矩阵R_n×n的特征向量和特征值，求相关矩阵R_n×n的特征向量u_k和特征值λ_k，其中，k＝1，2，…，n。2.3 Since u and λ which make the relation R _n×n u=λu established are the eigenvectors and eigenvalues of the correlation matrix R _n×n respectively, find the eigenvector u _k and eigenvalue λ _k of the correlation matrix R _n×n , Wherein, k=1, 2, . . . , n.

2.4根据步骤2获得的标准化温度自变量X_k ^*和特征向量u_k，得到由标准化温度自变量X_k ^*和特征向量u_k构成的主成分Z_k的表达式，具体为：2.4 According to the standardized temperature independent variable X _k ^* and eigenvector u _k obtained in step 2, the expression of the principal component Z _k composed of the standardized temperature independent variable X _k ^* and eigenvector u _k is obtained, specifically:

在主成分Z_k的表达式中，Var(Z_k)＝λ_k，Cov(Z_i，Z_j)＝0(i≠j)，即各主成分之间互不相关。In the expression of the principal component Z _k , Var(Z _k )=λ _k , Cov(Z _i , Z _j )=0 (i≠j), that is, the principal components are not correlated with each other.

进一步说，所述的步骤三具体是指：设前p个主成分Z₁，Z₂，…，Z_p的累积方差贡献率为Vcc_p，p≤n，令累积方差贡献率Vcc_p不小于85％，计算出p的数值，再依据p的数值将具体的主成分Z₁，Z₂，…，Z_p提取出，以用于下一步的热误差建模。其中，前p个主成分的累积方差贡献率Vcc_p的公式为：Furthermore, the step three specifically refers to: assuming the cumulative variance contribution rate Vcc _p of the first p principal components Z ₁ , Z ₂ , ..., Z _p , p≤n, and making the cumulative variance contribution rate Vcc _p not less than 85%, calculate the value of _p , and then extract the specific principal components Z ₁ , Z ₂ , . . . Among them, the formula of the cumulative variance contribution rate Vcc _p of the first p principal components is:

${Vcc Vcc}_{p p} = = {Σ Σ}_{i i = = 11}^{p p} {λ λ}_{i i} / / {Σ Σ}_{i i = = 11}^{n no} {λ λ}_{i i} - - - - - - ((55)) . .$

进一步说，所述的步骤四具体是指：Further, the step four specifically refers to:

4.1对步骤一中的主轴热变形量S_j作标准化处理，得到标准化热变形量S_j ^*。对主轴热变形量S_j作标准化的公式(6)为：4.1 Standardize the spindle thermal deformation S _j in step 1 to obtain the standardized thermal deformation S _j ^* . The formula (6) for standardizing the thermal deformation of the main shaft S _j is:

${S S}_{j j q q}^{* *} = = \frac{{S S}_{j j q q} - - {\overset{&OverBar; &OverBar;}{S S}}_{j j}}{\sqrt{\frac{11}{t t (({S S}_{j j}^{* *}))} {Σ Σ}_{q q = = 11}^{t t (({S S}_{j j}^{* *}))} {(({S S}_{j j q q} - - {\overset{&OverBar; &OverBar;}{S S}}_{j j}))}^{22}}} - - - - - - ((66)) . .$

4.2对标准化热变形量S_j ^*和用于热误差建模的主成分Z₁，Z₂，…，Z_p作基于最小二乘原理的多元线性回归分析，得到S_j ^*关于Z₁，Z₂，…，Z_p的表达式方程式(7)。利用基于最小二乘原理的多元线性回归分析，获得模型中各元的回归系数估计值S_j ^*关于Z₁，Z₂，…，Z_p的表达式方程式与回归系数估计值分别如下：4.2 Perform multiple linear regression analysis based on the least squares principle on the standardized thermal deformation S _j ^* and the principal components Z ₁ , Z ₂ , ..., Z _p used for thermal error modeling, and obtain S _j ^* with respect to Z ₁ , Z ₂ ,..., the expression of Z _p Equation (7). Using multiple linear regression analysis based on the principle of least squares to obtain the estimated value of the regression coefficient of each element in the model S _j ^* expression equation with respect to Z ₁ , Z ₂ ,…, Z _p and regression coefficient estimates They are as follows:

${\overset{^^}{α α}}_{p p} = = {(({Z Z}_{p p}^{T T} {Z Z}_{p p}))}^{- - 11} {Z Z}_{p p}^{T T} {S S}_{j j}^{* *} - - - - - - ((88)) . .$

进一步说，所述的步骤五具体是指：利用步骤二得到的主成分Z_k的表达式，将步骤四得到的S_j ^*关于Z₁，Z₂，…，Z_p的表达式方程转化为S_j ^*关于X_k ^*的表达式方程S_j ^*关于X_k ^*的表达式方程具体如下：Further, the step five specifically refers to: using the expression of the principal component Z _k obtained in step two, the expression equation of S _j ^* about Z ₁ , Z ₂ ,..., Z _p obtained in step four Transformed into an expression equation of S _j ^* with respect to X _k ^* Expression equation of S _j ^* with respect to X _k ^* details as follows:

式(9)中， In formula (9),

进一步说，所述的步骤六具体是指：通过对温度自变量X_k作标准化处理的公式X_kq ^*和对主轴热变形量S_j作标准化的公式S_jq ^*，将由步骤五得到的S_j ^*关于X_k ^*的表达式方程转化S_j关于X_k的表达式方程(10)，完成热误差预测模型的建立。其中，S_j关于X_k的表达式方程(10)为：Furthermore, the step six specifically refers to: through the formula X _kq ^* for normalizing the temperature independent variable X _k and the formula S _jq ^* for standardizing the thermal deformation of the main shaft S _j , the S _j obtained in step five The expression equation of ^* about X _k ^* is converted into the expression equation (10) of S _j about X _k , and the establishment of the thermal error prediction model is completed. Among them, the expression equation (10) of S _j with respect to X _k is:

参见图1，进一步说，将实时检测的温度数值代入热误差模型(10)中，对机床主轴的热误差进行预测与分析。具体为在进行预测预分析时，将实时测量得到的温度自变量值输入到所述热误差模型(10)中，得到实时的热变形量预测值根据与热变形量测量值S_j计算得到残差值以及残余标准差值，获得预测模型(10)的预测性能，最终完成机床热误差补偿的数据处理。其中，残差是指与S_j的差值，残余标准差的计算公式如式(13)所示：Referring to Fig. 1, further speaking, the temperature value detected in real time is substituted into the thermal error model (10) to predict and analyze the thermal error of the machine tool spindle. Specifically, when performing prediction pre-analysis, the temperature independent variable value obtained by real-time measurement is input into the thermal error model (10) to obtain a real-time predicted value of thermal deformation according to Calculate the residual value and the residual standard deviation value with the thermal deformation measurement value S _j , obtain the prediction performance of the prediction model (10), and finally complete the data processing of the machine tool thermal error compensation. Among them, the residual is The difference between S _j and the residual standard deviation is calculated as formula (13):

为了更清楚地理解本发明的数据处理方法，下面结合具体实施例作进一步说明。In order to understand the data processing method of the present invention more clearly, further description will be made below in conjunction with specific embodiments.

将本发明提出的数据处理方法应用于Leaderway-V450型数控机床的热误差实验数据。The data processing method proposed by the present invention is applied to the thermal error experimental data of the Leaderway-V450 CNC machine tool.

图2为由Leaderway-V450数控机床实验获得的10个温度变量数据，图3为由Leaderway-V450数控机床实验获得的主轴Z向热变形量数据。实验测量时，机床所处初始环境温度为9.25℃，主轴以恒定转速4000rpm进行空转。Figure 2 shows the data of 10 temperature variables obtained from the experiment of the Leaderway-V450 CNC machine tool, and Figure 3 shows the data of the thermal deformation of the spindle in the Z direction obtained from the experiment of the Leaderway-V450 CNC machine tool. During the experimental measurement, the initial ambient temperature of the machine tool was 9.25°C, and the spindle was idling at a constant speed of 4000rpm.

第一步：根据式(1)计算温度变量ΔT_i与主轴Z向热误差S_z之间的相关系数值。The first step: Calculate the correlation coefficient value between the temperature variable ΔT _i and the thermal error S _z of the spindle Z direction according to formula (1).

表1ΔT_i与S_z之间的相关系数值Table 1 Correlation coefficient values between ΔT _i and S _z

ΔT₁ ΔT ₁ ΔT₂ ΔT ₂ ΔT₃ ΔT ₃ ΔT₄ ΔT ₄ ΔT₅ ΔT ₅ ΔT₆ ΔT ₆ ΔT₇ ΔT ₇ ΔT₈ ΔT ₈ ΔT₉ ΔT ₉ ΔT₁₀ ΔT ₁₀ r_iz r _iz 0.900.90 0.880.88 0.850.85 0.890.89 0.960.96 0.810.81 0.860.86 0.680.68 0.810.81 0.740.74

选择相关系数最大的两个温度变量作为热误差建模的温度自变量，即X₁＝ΔT₁，X₂＝ΔT₅，即，n＝2。The two temperature variables with the largest correlation coefficients are selected as temperature independent variables for thermal error modeling, ie X ₁ =ΔT ₁ , X ₂ =ΔT ₅ , ie n=2.

第二步：对X₁，X₂进行标准化处理，得到标准化温度变量X₁ ^*，X₂ ^*的相关矩阵R_2×2和该矩阵的特征值和特征向量。The second step: standardize X ₁ and X ₂ to obtain the correlation matrix R _2×2 of the standardized temperature variables X ₁ ^* and X ₂ ^* and the eigenvalues and eigenvectors of the matrix.

${R R}_{22 \times \times 22} = = [\begin{matrix} 1.0000 1.0000 & 0.9265 0.9265 \\ 0.9265 0.9265 & 1.0000 1.0000 \end{matrix}]$

表2特征值和特征向量Table 2 Eigenvalues and Eigenvectors

特征值Eigenvalues 特征向量Feature vector λ₁＝1.9265λ ₁ =1.9265 u₁＝[0.7071 0.7071]u ₁ =[0.7071 0.7071] λ₂＝0.0735λ ₂ =0.0735 u₂＝[0.7071 -0.7071]u ₂ =[0.7071 -0.7071]

因此，得到主成分Z₁，Z₂的表达式。Therefore, the expressions of the principal components Z ₁ , Z ₂ are obtained.

$\{\begin{matrix} {Z Z}_{11} = = 0.7071 0.7071 {X x}_{11}^{* *} + + 0.7071 0.7071 {X x}_{22}^{* *} \\ {Z Z}_{22} = = 0.7071 0.7071 {X x}_{11}^{* *} - - 0.7071 0.7071 {X x}_{22}^{* *} \end{matrix}$

第三步：计算Z₁，Z₂的累积方差贡献率，可知Z₁的累积方差贡献率达到96％，因此，参与热误差建模的主成分为Z₁。Step 3: Calculate the cumulative variance contribution rate of Z ₁ and Z _2. It can be known that the cumulative variance contribution rate of Z ₁ reaches 96%. Therefore, the principal component involved in thermal error modeling is Z ₁ .

第四步：利用公式(6)对主轴热变形量S_z进行标准化处理，得到标准化热变形量S_z ^*，建立S_z ^*和Z₁的回归方程，为S_z ^*＝0.5841Z₁。Step 4: Use formula (6) to standardize the amount of thermal deformation S _z of the spindle to obtain the standardized amount of thermal deformation S _z ^* , and establish a regression equation between S _z ^* and Z ₁ , which is S _z ^* = 0.5841Z ₁ .

第五步：将S_z ^*和Z₁的方程转化为S_z ^*关于X₁ ^*和X₂ ^*的方程，为S_z ^*＝0.4130X₁ ^*+0.4130X₂ ^*。Step 5: Transform the equation of S _z ^* and Z ₁ into the equation of S _z ^* about X ₁ ^* and X ₂ ^* , which is S _z ^* = 0.4130X ₁ ^* +0.4130X ₂ ^* .

第六步：将S_z ^*关于X₁ ^*和X₂ ^*的方程转化为S_z关于X₁和X₂的方程，为S_z＝11.8384+1.5252X₁+1.9669X₂，完成热误差预测模型的建立。Step 6: Transform the equation of S _z ^* about X ₁ ^* and X ₂ ^* into the equation of S _z about X ₁ and X ₂ , which is S _z = 11.8384+1.5252X ₁ +1.9669X ₂ , and complete the thermal error prediction model of establishment.

第七步：对不同运行状态时的机床主轴Z向热误差进行预测。图4所示为初始环境温度为9.19℃、主轴转速为4000rpm时的热误差测量值1、热误差预测值1以及残差1，初始环境温度为19.94℃、主轴转速为4000rpm时的热误差测量值2、热误差预测值2以及残差2，以及初始环境温度为29.19℃、主轴转速为4000rpm时的热误差测量值3、热误差预测值3以及残差3。同时，计算得到该预测模型的残余标准差分别4.89μm、3.78μm、4.95μm。结合图4可知，无论机床所处初始环境温度多少，该模型的残差值和残余标准差均保持在较小的范围内，因此，本专利所述热误差数据处理方法具有较高的精度及稳健性。Step 7: Predict the Z-direction thermal error of the machine tool spindle in different operating states. Figure 4 shows the thermal error measurement value 1, thermal error prediction value 1 and residual error 1 when the initial ambient temperature is 9.19°C and the spindle speed is 4000rpm, and the thermal error measurement when the initial ambient temperature is 19.94°C and the spindle speed is 4000rpm Value 2, thermal error predicted value 2 and residual 2, and thermal error measured value 3, thermal error predicted value 3 and residual 3 when the initial ambient temperature is 29.19°C and the spindle speed is 4000rpm. At the same time, the residual standard deviations of the prediction model were calculated to be 4.89 μm, 3.78 μm, and 4.95 μm, respectively. Combining with Figure 4, it can be seen that regardless of the initial ambient temperature of the machine tool, the residual value and residual standard deviation of the model are kept within a small range. Therefore, the thermal error data processing method described in this patent has high accuracy and robustness.

Claims

1. a data processing method for realizing the machine tool robustness thermal error compensation of wide range ambient temperature, is characterized in that, carries out as follows:

Step 1: Obtain the temperature variable ΔT _i of the machine tool and the thermal deformation of the spindle S _j , where i=1, 2, ..., m;

The m refers to the number of temperature variables; the j refers to the axial direction of the machine tool spindle, and j is X, Y, and/or Z; X, Y, and Z represent the X axis of the machine tool spindle and the Y of the spindle respectively. Axial, the Z axis of the main shaft;

The temperature independent variable X _k is obtained from the correlation between the temperature variable ΔT _i and the thermal deformation of the spindle S _j , k=1, 2,..., n;

The temperature independent variable X _k is used to establish a thermal error compensation model; the n refers to the number of temperature independent variables, n≤m;

Step 2: Standardize the temperature independent variable X _{k obtained in step 1 to obtain the standardized temperature independent variable X k} _* ^;

And the expression of the principal component Z _k is obtained by converting the standardized temperature independent variable X _k ^* ;

The principal component Z _k refers to a group of variables obtained after the temperature independent variable X _k ^* is transformed by orthogonal transformation, and the variables of this group are linearly irrelevant;

Step 3: Extract the first p principal components Z ₁ , Z ₂ ,..., Z _p , p≤n from the principal components Z _k obtained in step 2, for the next step of thermal error modeling;

Step 4: Standardize the spindle thermal deformation S _j in step 1 to obtain the standardized thermal deformation S _j ^* ;

And do multiple linear regression analysis on the standardized thermal deformation S _j ^* and the principal components Z ₁ , Z ₂ , ..., Z _p obtained in step 3 for thermal error modeling, and get S _j ^* about Z ₁ , Z ₂ , ..., the expression equation for Z _p

Step 5: Transform the expression equation of S _j ^* about Z ₁ , Z ₂ , ..., Z _p obtained in step 4 into the expression equation of S _j ^* about X _k ^* ;

Step 6: Transform the expression equation of S _j ^* about X _k ^* obtained in step 5 into the expression equation of S _j about X _k , and the expression equation of S _j about X _k is the thermal error model.

2. a kind of data processing method that realizes the machine tool robustness thermal error compensation of wide range ambient temperature according to claim 1, it is characterized in that, described step one specifically refers to:

Step 1.1 Obtain the temperature variable ΔT _i of the machine tool and the thermal deformation of the spindle S _j , and calculate the correlation coefficient value between the temperature variable ΔT _i and the thermal deformation S _j of the spindle; the correlation coefficient formula (1) is as follows:

In formula (1), r _ij is the correlation coefficient value between ΔT _i and S _j , t(ΔT _i ) is the length of ΔT _i , ΔT _iq is the qth value in the ΔT _i sequence, is the average value of ΔT _i sequence, S _jq is the qth value in S _j sequence, is the average value of the S _j sequence; the temperature variable ΔT _i is collected from the running machine tool through the temperature sensor; the length of the temperature variable ΔT _i sequence is the same as the length of the thermal deformation S _j sequence;

Step 1.2 extracts n temperature variables with the largest correlation coefficient values in step 1.1 as temperature independent variable X _k ; said temperature independent variable X _k is used to establish a thermal error model; said n is not greater than m.

3. a kind of data processing method that realizes the machine tool robustness thermal error compensation of wide range ambient temperature according to claim 1, it is characterized in that, described step 2 specifically refers to:

Step 2.1 standardizes the temperature independent variable X _{k obtained in step 1 to obtain the standardized temperature independent variable X k} _* ^; the formula (2) for standardizing the temperature independent variable X _k is as follows:

In formula (2), X _kq ^* is the qth value in the X _k ^* sequence, X _kq is the qth value in the X _k sequence, Be the mean value of X _k sequence, t(X _k ^* ) is the length of X _k ^* sequence;

Step 2.2 uses the correlation coefficient formula (1) described in step 1 to calculate the correlation coefficient value between any two normalized temperature independent variables, and obtain the correlation matrix R _{n × n} (3) of the normalized temperature independent variable, as follows;

In the correlation matrix R _n×n (3), r _ab represents the correlation coefficient value of the standardized temperature independent variables X _a ^* and X _b ^* ;

In step 2.3, u and λ, which make the relation R _n×n u=λu established, are the eigenvectors and eigenvalues of the correlation matrix R _n×n respectively, and then find the eigenvector u _k and eigenvalue λ _k of the correlation matrix R _n×n , where k=1, 2,..., n;

Step 2.4 According to the standardized temperature independent variable X _k ^* and eigenvector u _k obtained in step 2, the expression of the principal component Z _k composed of the standardized temperature independent variable X _k ^* and eigenvector u _k is obtained, specifically:

In the expression of the principal component Z _k , Var(Z _k )=λ _k , Cov(Z _i , Z _j )=0 (i≠j), that is, the principal components are not correlated with each other.

4. A data processing method for achieving thermal error compensation of machine tool robustness in a wide range of ambient temperatures according to claim 1, wherein said step three specifically refers to: assuming the first p principal components Z ₁ , The cumulative variance contribution rate of Z ₂ ,..., Z _p is Vcc _p , p≤n, so that the cumulative variance contribution rate Vcc _p is not less than 85%, calculate the value of p, and then divide the specific principal component Z ₁ according to the value of p , Z ₂ ,..., Z _p are extracted to be used for thermal error modeling in the next step; among them, the formula of the cumulative variance contribution rate Vcc _p of the first p principal components is:

5. A kind of data processing method that realizes the thermal error compensation of machine tool robustness of wide range ambient temperature according to claim 1, is characterized in that, described step 4 specifically refers to:

Step 4.1 Standardize the spindle thermal deformation S _j in step 1 to obtain the standardized thermal deformation S _j ^* ; the formula (6) for standardizing the spindle thermal deformation S _j is:

In formula (6), S _jq ^* is the qth value in the S _j ^* sequence, S _jq is the qth value in the S _j sequence, is the average value of the S _j sequence, and t(S _j ^* ) is the length of the S _j ^* sequence.

Step 4.2 Perform a multiple linear regression analysis based on the least squares principle on the standardized thermal deformation S _j ^* and the principal components Z ₁ , Z ₂ ,..., Z _p used for thermal error modeling, and obtain S _j ^* about Z ₁ , Z ₂ ,…, Z _p expression equation (7); using multiple linear regression analysis based on the least squares principle, to obtain the estimated value of the regression coefficient of each element in the model S _j ^* expression equations with respect to Z ₁ , Z ₂ ,…, Z _p and regression coefficient estimates They are as follows:

6. A kind of data processing method that realizes the thermal error compensation of machine tool robustness of wide-range ambient temperature according to claim 1, it is characterized in that, described step five specifically refers to: utilize the principal component _Zk that step two obtains The expression of S _j ^* obtained in step 4 about Z ₁ , Z ₂ ,..., Z _p expression equation Transformed into an expression equation of S _j ^* with respect to X _k ^* Expression equation of S _j ^* with respect to X _k ^* (9) The details are as follows:

In formula (9),

7. A kind of data processing method that realizes the thermal error compensation of the machine tool robustness of wide range ambient temperature according to claim 1, it is characterized in that, described step 6 specifically refers to: by doing standardization to temperature independent variable X _k The processed formula X _kq ^* and the formula S _jq ^* for standardizing the thermal deformation of the main shaft S _j , the expression equation of S _j ^* about X _k ^* obtained in step five is converted into the expression equation of S _j about X _k (10 ), complete the establishment of the thermal error prediction model; wherein, the expression equation (10) of S _j with respect to X _k is:

In formula (11), is the discrete standard deviation of the S _j sequence, is the discrete standard deviation of the X _k sequence.

8. adopt the model operation method of the data processing method of the machine tool robust thermal error compensation of a kind of realization wide range ambient temperature of claim 1, it is characterized in that, the temperature numerical value of real-time detection is substituted in the thermal error model, to the machine tool The thermal error of the spindle is predicted and analyzed.

9. The model application method according to claim 8 that adopts a data processing method that realizes a machine tool robustness thermal error compensation for a wide range of ambient temperatures, wherein, when performing prediction and pre-analysis, the temperature obtained by real-time measurement The independent variable value is input into the thermal error model to obtain the real-time thermal deformation prediction value according to Calculate the residual value and the residual standard deviation value with the thermal deformation measurement value S _j , obtain the prediction performance of the prediction model, and finally complete the data processing of the thermal error compensation of the machine tool; where the residual error refers to The difference between S _j and the residual standard deviation is calculated as formula (13):

In formula (13), SD is the residual standard deviation, S _jq is the qth value in the S _j sequence, for The qth value in the sequence, t(S _j ) is either S _j or The length of the sequence; the length of S _j sequence and The sequences are the same length.