CN105243218A - Thermal error precision conversion and model establishing method of machine tool - Google Patents

Abstract

The invention discloses a thermal error precision conversion and model building method of a machine tool. The method comprises the following steps: 1) establishing and simplifying a machine tool CAD (Computer Aided Design) model; 2) carrying out CAE (Computer Aided Engineering) thermoanalysis on the simplified machine tool CAD model; 3) extracting the thermal deformation value of each motion axis unit through a CAE thermoanalysis postprocessing module, and converting the thermal deformation value into a basic geometrical error of a unit; and 4) on the basis of the basic geometrical error of the unit, establishing a thermal error model of a machine tool work space. Designers who adopt the method can foresee the thermal deformation of the machine tool and predict the tail end errors, the tail end precision and the like of the machine tool in a machine tool design stage, so that design reliability is increased. The method can save a great quantity of time and money on the basis of CAE software, and can provide comprehensive thermal error information.

Description

Machine tool thermal error precision transforms and method for establishing model

Technical field

The present invention relates to machine tool thermal error modeling method, particularly a kind of machine tool thermal error precision transforms and method for establishing model.

Background technology

In recent years, along with the fast development of China's manufacturing industry, also more and more higher to the requirement of the processing characteristics of high-grade, digitally controlled machine tools, synthesis precision level.Research shows, in the processing of accurate and Ultra-precision CNC Machine, the machine tool error caused by thermal effect generally accounts for about the 40%-70% of composition error.Therefore, how obtaining machine tool thermal error and to set up Thermal Error model and then obtain lathe end accuracy data, is one of key issue improving machine tool accuracy.At present, set up the method that Thermal Error model adopts usually to have: multivariate linear regression analysis model, artificial nerve network model, supporting vector machine model and gray model etc.; These models can reach certain precision, but these models have a common ground, are exactly based on experimental method.But experimental method requires a great deal of time and money usually, and limits by experiment condition, be difficult to obtain comprehensive Thermal Error information toward contact; Simultaneously also make design have hysteresis quality, just can not can control the precision of lathe end in the design phase.

Summary of the invention

The present invention provides a kind of machine tool thermal error precision to transform and method for establishing model for solving in known technology the technical matters that exists.

The technical scheme that the present invention takes for the technical matters existed in solution known technology is:

A kind of machine tool thermal error precision transforms and method for establishing model, comprises the steps:

Step one: set up Machine Tool CAD model and simplified model;

Step 2: CAE thermal analyses is carried out to the Machine Tool CAD model after simplifying;

Step 3: extract each kinematic axis unit thermal deformation value by CAE thermal analyses post-processing module, and be converted into the basic geometric error of unit;

Step 4: based on the basic geometric error of unit, sets up lathe work Space Thermal error model.

Further, in described step one, adopt Creo software, to remove in Machine Tool CAD model analysis result without the minutia of impact to simplify cad model.

Further, in described step 2, ANSYS software is adopted to read the X-T intermediate file generated by cad model, generate finite element model and machine tool structure thermal analyses is carried out to it, wherein, thermal source in lathe and radiating condition are converted into heat flow density and convection transfer rate value respectively by the heat-dissipating model of correspondence and heat dissipation model, and are loaded on finite element model with the form of thermal force.

Further, in described step 3, the concrete steps being extracted each kinematic axis unit thermal deformation value by CAE thermal analyses post-processing module are:

Step 3-1: respectively with the arbitrary axial side of the end face being arranged on each rail in the every pair of guide rails on lathe for extract path;

Step 3-2: the deflection choosing n node at the dual-side of each guide rail end face as extraction target, the X, Y, Z axis extracting all translation shaft to thermal deformation value.

In described step 3, described kinematic axis unit comprise lathe X, Y, Z axis to three pairs of translation shaft guide rails.

In described step 3, the basic geometric error of described unit comprises straightness error, Run-out error, the rolling pendulum error of the X, Y, Z axis of corresponding axle and pendulum error of running.

In described step 3, by MATLAB software, the thermal deformation value of X, Y, Z axis is converted into the basic geometric error of unit.

In described step 3, by the concrete steps that the thermal deformation value of X-axis is converted into the basic geometric error of unit be:

If:

X＝[x ₁,x ₂,x ₃,x ₄…x _n]

UUY＝[uuy ₁,uuy ₂,uuy ₃,uuy ₄…uuy _n]

UUZ＝[uuz ₁,uuz ₂,uuz ₃,uuz ₄…uuz _n](1)

DUY＝[duy ₁,duy ₂,duy ₃,duy ₄…duy _n]

DUZ＝[duz ₁,duz ₂,duz ₃,duz ₄…duz _n]

In formula:

The horizontal ordinate matrix of X for got X-axis guide rail is put;

UUY is the Y direction shift value matrix that on a guide rail in X-direction pair of guide rails, taken point is corresponding;

UUZ is the Z-direction shift value matrix that on a guide rail in X-direction pair of guide rails, taken point is corresponding;

DUY is the Y direction shift value matrix that on another guide rail in X-direction pair of guide rails, taken point is corresponding;

DUZ is the Z-direction shift value matrix that on another guide rail in X-direction pair of guide rails, taken point is corresponding; When then slide carriage is positioned at centre position, the shift value of X-direction translation shaft guide rail is

$UY=\frac{UUY+DUY}{2}=\[{\mathrm{uy}}_1,{\mathrm{uy}}_2,{\mathrm{uy}}_3,{\mathrm{uy}}_4...{\mathrm{uy}}_n\]=\[\frac{{\mathrm{uuy}}_1+{\mathrm{duy}}_1}{2},\frac{{\mathrm{uuy}}_2+{\mathrm{duy}}_2}{2},\frac{{\mathrm{uuy}}_3+{\mathrm{duy}}_3}{2},\frac{{\mathrm{uuy}}_4+{\mathrm{duy}}_4}{2}......\frac{{\mathrm{uuy}}_n+{\mathrm{duy}}_n}{2}\]---\left(2\right)$

$UZ=\frac{UUZ+DUZ}{2}=\[{\mathrm{uz}}_I,{\mathrm{uz}}_2,{\mathrm{uz}}_3,{\mathrm{uz}}_4...{\mathrm{uz}}_n\]=\[\frac{{\mathrm{uuz}}_1+{\mathrm{duz}}_1}{2},\frac{{\mathrm{uuz}}_2+{\mathrm{duz}}_2}{2},\frac{{\mathrm{uuz}}_3+{\mathrm{duz}}_3}{2},\frac{{\mathrm{uuz}}_4+{\mathrm{duz}}_4}{2}......\frac{{\mathrm{uuz}}_n+{\mathrm{duz}}_n}{2}\]$

In formula, UY is the Y direction shift value matrix of the X-direction translation shaft guide rail of slide carriage present position;

UZ is the Z-direction shift value matrix of the X-direction translation shaft guide rail of slide carriage present position;

1) two-point method asks Y, Z-direction linearity:

If ideal line is:

y＝k*x+b(3)

Then:

$k=\frac{{\mathrm{uy}}_n-{\mathrm{uy}}_1}{x_n-x_1},b={\mathrm{uy}}_n-k*x_n---\left(4\right)$

Known point (x _i, uy _i) to be h to the distance of ideal line be:

$h=\frac{\left|k*x-uy+b\right|}{\sqrt{1+k^2}}=\[h_1,h_2,h_3,h_4...h_n\]=\[\frac{\left|k*x_1-{\mathrm{uy}}_1+b\right|}{\sqrt{1+k^2}},\frac{\left|k*x_2-{\mathrm{uy}}_2+b\right|}{\sqrt{1+k^2}},\frac{\left|k*x_3-{\mathrm{uy}}_3+b\right|}{\sqrt{1+k^2}},\frac{\left|k*x_4-{\mathrm{uy}}_4+b\right|}{\sqrt{1+k^2}}...\frac{\left|k*x_n-{\mathrm{uy}}_n+b\right|}{\sqrt{1+k^2}}\]---\left(5\right)$

Y linearity is:

Δy＝h _max-h _min(6)

In formula, h _maxfor known point (x _i, uy _i) to the maximal value of ideal line distance;

H _minfor known point (x _i, uy _i) to the minimum value of ideal line distance;

2) rolling pendulum error is:

$\mathrm{\Δ}\mathrm{\α}=\frac{\left|{\mathrm{uuz}}_{mid}-{\mathrm{duz}}_{mid}\right|}{L_x}---\left(7\right)$

In formula, L _xfor Y direction distance between X-direction pair of guide rails;

Uuz _midfor the Z-direction shift value of the guide rail mid point of in X-direction pair of guide rails;

Duz _midfor the Z-direction shift value of another guide rail mid point in X-direction pair of guide rails;

3) pendulum error in top is:

$\mathrm{\Δ}\mathrm{\β}=\frac{\left|{\mathrm{uz}}_{left}-{\mathrm{uz}}_{right}\right|}{W_x}---\left(8\right)$

In formula, W _xfor X-direction pair of guide rails two slide blocks between X-direction distance;

Uz _leftfor the Z-direction shift value at X-direction guide rail left slider place;

Uz _rightfor the Z-direction shift value at the right slide block place of X-direction guide rail;

4) Run-out error is:

$\mathrm{\Δ}\mathrm{\γ}=\frac{\left|{\mathrm{uuy}}_{left}-{\mathrm{duy}}_{left}-{\mathrm{uuy}}_{right}+{\mathrm{duy}}_{right}\right|}{W_x}---\left(9\right)$

In formula, W _xfor X-direction distance between X-direction guide rail two slide block;

Uuy _leftfor the Y direction shift value at the left slider place of the guide rail of in X-direction pair of guide rails;

Duy _leftfor the Y direction shift value at the left slider place of another guide rail in X-direction pair of guide rails;

Uuy _rightfor the Y direction shift value at the right slide block place of the guide rail of in X-direction pair of guide rails;

Duy _rightfor the Y direction shift value at the right slide block place of another guide rail in X-direction pair of guide rails;

5) X, the Z axis error of perpendicularity are:

${\mathrm{\Δ\γ}}_{xz}=arctg\frac{{\mathrm{uz}}_{mid}}{L_x}-arctg\frac{{\mathrm{uy}}_{mid}}{L_z}---\left(10\right)$

In formula, L _xfor Y direction distance between X-direction pair of guide rails;

L _zfor the length of Z-direction guide rail;

Uz _midfor the Z-direction shift value of X-direction guide rail midpoint;

Uy _midfor the Y direction shift value of Z-direction guide rail midpoint.

In described step 4, utilize many-body theory, set up the mapping relations of tool-workpiece relative pose error in the thermal deformation errors at machine tool structure guide rail position place and lathe work space, thus set up lathe work Space Thermal error model.

Further, the concrete steps setting up lathe work Space Thermal error model are:

Step 4-1: the topology diagram drawing lathe according to the practical structures of lathe;

Step 4-2: the lower body array table drawing lathe according to the constraint of low sequence body sequence description method and lathe;

Step 4-3: according to the characteristic of translation motion eigenmatrix and rotary motion eigenmatrix, obtain the desired characteristics matrix between each adjacent body of lathe and error character matrix;

Step 4-4: draw machine tool error according to ideal forming function and actual shaping function.

The advantage that the present invention has and good effect are: adopt the method designer just can predict thermal deformation of machine tool, prediction lathe end error and end precision etc. in the Machine Tool design stage, designed reliability is increased; The method, based on CAE software, can save a large amount of time and money, and can provide comprehensive Thermal Error information.

Accompanying drawing explanation

Fig. 1 is method flow block diagram of the present invention;

Fig. 2 is horizontal Machining centers structural representation;

Fig. 3 is the lathe bed D1 Path Deform figure of horizontal Machining centers;

Fig. 4 is the column D1 path Y displacement deformation figure of horizontal Machining centers;

Fig. 5 is the column D1 path Z displacement deformation figure of horizontal Machining centers;

Fig. 6 is the slide carriage D1 Path Deform figure of horizontal Machining centers;

Fig. 7 is horizontal Machining centers topological structure;

Fig. 8 is that X is to error curve diagram;

Fig. 9 is Y-direction error curve diagram;

Figure 10 is Z-direction error curve diagram.

In Fig. 2: 1, column; 2, X-axis guide rail; 3, slide carriage; 4, Y-axis guide rail; 5, main spindle box; 6, main shaft; 7, worktable; 8, slide; 9, Z axis guide rail; 10, lathe bed.

Embodiment

For summary of the invention of the present invention, Characteristic can be understood further, hereby exemplify following examples, and coordinate accompanying drawing to be described in detail as follows:

Refer to Fig. 1, a kind of machine tool thermal error precision transforms and method for establishing model, comprises the steps:

Step one: set up Machine Tool CAD model and simplified model;

Step 2: CAE thermal analyses is carried out to the Machine Tool CAD model after simplifying;

Step 3: extract each kinematic axis unit thermal deformation value by CAE thermal analyses post-processing module, and be converted into the basic geometric error of unit;

Step 4: based on the basic geometric error of unit, sets up lathe work Space Thermal error model.

Further, in described step one, Creo software can be adopted, remove in Machine Tool CAD model on analysis result without impact minutia to simplify cad model.

Further, in described step 2, ANSYS software can be adopted to read the X-T intermediate file generated by cad model, generate finite element model and machine tool structure thermal analyses is carried out to it, wherein, thermal source in lathe and radiating condition can be converted into heat flow density and convection transfer rate value respectively by the heat-dissipating model of correspondence and heat dissipation model, and are loaded on finite element model with the form of thermal force.

Further, in described step 3, the concrete steps being extracted each kinematic axis unit thermal deformation value by CAE thermal analyses post-processing module be can be:

Step 3-1: can respectively with the arbitrary axial side of the end face being arranged on each rail in the every pair of guide rails on lathe for extract path;

Step 3-2: deflection n node can being chosen at the dual-side of each guide rail end face as extraction target, the X, Y, Z axis extracting all translation shaft to thermal deformation value.

In described step 3, described kinematic axis unit can comprise lathe X, Y, Z axis to three pairs of translation shaft guide rails.

In described step 3, the basic geometric error of described unit can comprise straightness error, Run-out error, the rolling pendulum error of the X, Y, Z axis of corresponding axle and pendulum error of running.

In described step 3, by MATLAB software, the thermal deformation value of X, Y, Z axis is converted into the basic geometric error of unit.

Further, in described step 3, the concrete steps that the thermal deformation value of X-axis is converted into the basic geometric error of unit be can be:

If:

X＝[x ₁,x ₂,x ₃,x ₄…x _n]

UUY＝[uuy ₁,uuy ₂,uuy ₃,uuy ₄…uuy _n]

UUZ＝[uuz ₁,uuz ₂,uuz ₃,uuz ₄…uuz _n](11)

DUY＝[duy ₁,duy ₂,duy ₃,duy ₄…duy _n]

DUZ＝[duz ₁,duz ₂,duz ₃,duz ₄…duz _n]

In formula:

The horizontal ordinate matrix of X for got X-axis guide rail is put; Wherein, x ₁, x ₂, x ₃... x _nfor the abscissa value of selected point;

UUY is the Y direction shift value matrix that on a guide rail in X-direction pair of guide rails, taken point is corresponding; Wherein, uuy ₁, uuy ₂uuy ₃uuy _nfor the Y-direction shift value of selected point;

UUZ is the Z-direction shift value matrix that on a guide rail in X-direction pair of guide rails, taken point is corresponding; Wherein, uuz ₁, uuz ₂uuz ₃uuz _nfor the Z-direction shift value of selected point;

DUY is the Y direction shift value matrix that on another guide rail in X-direction pair of guide rails, taken point is corresponding; Wherein, duy ₁, duy ₂duy ₃duy _nfor the Y-direction shift value of selected point;

DUZ is the Z-direction shift value matrix that on another guide rail in X-direction pair of guide rails, taken point is corresponding; Wherein, duz ₁, duz ₂duz ₃duz _nfor the Y-direction shift value of selected point;

When then slide carriage is positioned at centre position, the shift value of X-direction translation shaft guide rail is

$UY=\frac{UUY+DUY}{2}=\[{\mathrm{uy}}_1,{\mathrm{uy}}_2,{\mathrm{uy}}_3,{\mathrm{uy}}_4...{\mathrm{uy}}_n\]=\[\frac{{\mathrm{uuy}}_1+{\mathrm{duy}}_1}{2},\frac{{\mathrm{uuy}}_2+{\mathrm{duy}}_2}{2},\frac{{\mathrm{uuy}}_3+{\mathrm{duy}}_3}{2},\frac{{\mathrm{uuy}}_4+{\mathrm{duy}}_4}{2}......\frac{{\mathrm{uuy}}_n+{\mathrm{duy}}_n}{2}\]---\left(12\right)$

$UZ=\frac{UUZ+DUZ}{2}=\[{\mathrm{uz}}_1,{\mathrm{uz}}_2,{\mathrm{uz}}_3,{\mathrm{uz}}_4...{\mathrm{uz}}_n\]=\[\frac{{\mathrm{uuz}}_1+{\mathrm{duz}}_1}{2},\frac{{\mathrm{uuz}}_2+{\mathrm{duz}}_2}{2},\frac{{\mathrm{uuz}}_3+{\mathrm{duz}}_3}{2},\frac{{\mathrm{uuz}}_4+{\mathrm{duz}}_4}{2}......\frac{{\mathrm{uuz}}_n+{\mathrm{duz}}_n}{2}\]$

In formula, UY is the Y direction shift value matrix of the X-direction translation shaft guide rail of slide carriage present position;

UZ is the Z-direction shift value matrix of the X-direction translation shaft guide rail of slide carriage present position;

1) two-point method asks Y, Z-direction linearity:

If ideal line is:

y＝k*x+b(13)

Then:

$k=\frac{{\mathrm{uy}}_n-{\mathrm{uy}}_1}{x_n-x_1},b={\mathrm{uy}}_n-k*x_n---\left(14\right)$

Known point (x _i, uy _i) to be h to the distance of ideal line be:

$h=\frac{\left|k*x-uy+b\right|}{\sqrt{1+k^2}}=\[h_1,h_2,h_3,h_4...h_n\]=\[\frac{\left|k*x_1-{\mathrm{uy}}_1+b\right|}{\sqrt{1+k^2}},\frac{\left|k*x_2-{\mathrm{uy}}_2+b\right|}{\sqrt{1+k^2}},\frac{\left|k*x_3-{\mathrm{uy}}_3+b\right|}{\sqrt{1+k^2}},\frac{\left|k*x_4-{\mathrm{uy}}_4+b\right|}{\sqrt{1+k^2}}...\frac{\left|k*x_n-{\mathrm{uy}}_n+b\right|}{\sqrt{1+k^2}}\]---\left(15\right)$

Y linearity is:

Δy＝h _max-h _min(16)

In formula, h _maxfor known point (x _i, uy _i) to the maximal value of ideal line distance;

H _minfor known point (x _i, uy _i) to the minimum value of ideal line distance;

2) rolling pendulum error is:

$\mathrm{\Δ}\mathrm{\α}=\frac{\left|{\mathrm{uuz}}_{mid}-{\mathrm{duz}}_{mid}\right|}{L_x}---\left(17\right)$

In formula, L _xfor Y direction distance between X-direction pair of guide rails;

Uuz _midfor the Z-direction shift value of the guide rail mid point of in X-direction pair of guide rails;

Duz _midfor the Z-direction shift value of another guide rail mid point in X-direction pair of guide rails;

3) pendulum error in top is:

$\mathrm{\Δ}\mathrm{\β}=\frac{\left|{\mathrm{uz}}_{left}-{\mathrm{uz}}_{right}\right|}{W_x}---\left(18\right)$

In formula, W _xfor X-direction pair of guide rails two slide blocks between X-direction distance;

Uz _leftfor the Z-direction shift value at X-direction guide rail left slider place;

Uz _rightfor the Z-direction shift value at the right slide block place of X-direction guide rail;

4) Run-out error is:

$\mathrm{\Δ}\mathrm{\γ}=\frac{\left|{\mathrm{uuy}}_{left}-{\mathrm{duy}}_{left}-{\mathrm{uuy}}_{right}+{\mathrm{duy}}_{right}\right|}{W_x}---\left(19\right)$

In formula, W _xfor X-direction distance between X-direction guide rail two slide block;

Uuy _leftfor the Y direction shift value at the left slider place of the guide rail of in X-direction pair of guide rails;

Duy _leftfor the Y direction shift value at the left slider place of another guide rail in X-direction pair of guide rails;

Uuy _rightfor the Y direction shift value at the right slide block place of the guide rail of in X-direction pair of guide rails;

Duy _rightfor the Y direction shift value at the right slide block place of another guide rail in X-direction pair of guide rails;

5) X, the Z axis error of perpendicularity are:

${\mathrm{\Δ\γ}}_{xz}=arctg\frac{{\mathrm{uz}}_{mid}}{L_x}-arctg\frac{{\mathrm{uy}}_{mid}}{L_z}---\left(20\right)$

In formula, L _xfor Y direction distance between X-direction pair of guide rails;

L _zfor the length of Z-direction guide rail;

Uz _midfor the Z-direction shift value of X-direction guide rail midpoint;

Uy _midfor the Y direction shift value of Z-direction guide rail midpoint.

In described step 4, can many-body theory be utilized, set up the mapping relations of tool-workpiece relative pose error in the thermal deformation errors at machine tool structure guide rail position place and lathe work space, thus set up lathe work Space Thermal error model.

Further, the concrete steps setting up lathe work Space Thermal error model can be:

Step 4-1: the topology diagram that can draw lathe according to the practical structures of lathe;

Step 4-2: the lower body array table that can draw lathe according to the constraint of low sequence body sequence description method and lathe;

Step 4-3: according to the characteristic of translation motion eigenmatrix and rotary motion eigenmatrix, the desired characteristics matrix between each adjacent body of lathe and error character matrix can be obtained;

Step 4-4: machine tool error can be drawn according to ideal forming function and actual shaping function.

Please refer to Fig. 2 to Figure 10, illustrate further for certain horizontal Machining centers, this machining center is made up of structural members such as bed piece 10, worktable 7, X-axis guide rail 2, Y-axis guide rail 4, Z axis guide rail 9, column 1, slide carriage 3, slide 8, main spindle box 5, main shafts 6, adopts frame middle frame structure form.X-axis guide rail 2, Y-axis guide rail 4, Z axis guide rail 9 all adopt the parallel distribution of bilinear rolling guide, and slide 8 drives worktable 7 to move along bed piece 10 as Z-direction on guide rail; Slide carriage 3 makes X to moving along column 1 on guide rail, and main spindle box 5 moves along slide carriage 3 as Y-direction on guide rail, and Fig. 2 is shown in by its three-dimensional structure sketch; Carry out machine tool structure thermal analyses by ANSYS software to it, be loaded into thermal force on finite element model in table 1, extract guideway path in table 2, deformation curve figure is shown in Fig. 3-Fig. 6, and the error amount of gained is in table 3, and method for transformation is shown in formula 11-20.Wherein, in table 1, F1 is the pressure of column 1, slide carriage 3, main shaft 6, main spindle box 5, and unit is N; F2 is the pressure to Z axis guide rail 9 above turntable and turntable, and unit is N; M1 is the moment of torsion of slide carriage 3, main shaft 6, main spindle box 5, and unit is NM; F3 is the gravity of slide carriage 3, main shaft 6, main spindle box 5, and unit is N; M2 is the moment of torsion of main shaft 6, main spindle box 5, and unit is NM; F4 is the gravity of main shaft 6, main spindle box 5, and unit is N; The unit of temperature is DEG C, and the unit of convection current is W/m2 DEG C; In table 3, Δ x, Δ y, Δ z are each axle X, Y, Z-direction straightness error; Δ α is rolling pendulum error; Δ β is top pendulum error; Δ γ is Run-out error.

Wherein: table 1. load applying table

Table 2. extracts routing table

For X-axis, if:

X＝[x ₁,x ₂,x ₃,x ₄…x _n]

UUY＝[uuy ₁,uuy ₂,uuy ₃,uuy ₄…uuy _n]

UUZ＝[uuz ₁,uuz ₂,uuz ₃,uuz ₄…uuz _n]

DUY＝[duy ₁,duy ₂,duy ₃,duy ₄…duy _n]

DUZ＝[duz ₁,duz ₂,duz ₃,duz ₄…duz _n](21)

In formula:

The horizontal ordinate matrix of X for got X-axis guide rail is put; x ₁, x ₂, x ₃... x _nfor the abscissa value of selected point

UUY is the Y-direction shift value matrix that on X-axis upper rail, taken point is corresponding; uuy ₁, uuy ₂uuy ₃uuy _nfor the Y-direction shift value of selected point;

UUZ is the Z-direction shift value matrix that on X-axis upper rail, taken point is corresponding; uuz ₁, uuz ₂uuz ₃uuz _nfor the Z-direction shift value of selected point;

DUY is the Y-direction shift value matrix that on X-axis lower guideway, taken point is corresponding; duy ₁, duy ₂duy ₃duy _nfor the Y-direction shift value of selected point;

DUZ is the Z-direction shift value matrix that on X-axis lower guideway, taken point is corresponding; duz ₁, duz ₂duz ₃duz _nfor the Y-direction shift value of selected point;

Again during selection and withdrawal point, preferably extract at the symmetric position place of pair of guide rails, namely extract at the symmetric position place of path D1 and path D4, and the symmetric position place of path D2 and path D3 extracts.

When then slide carriage is positioned at centre position, the shift value of X-axis translation shaft guide rail is

$UY=\frac{UUY+DUY}{2}=\[{\mathrm{uy}}_1,{\mathrm{uy}}_2,{\mathrm{uy}}_3,{\mathrm{uy}}_4...{\mathrm{uy}}_n\]=\[\frac{{\mathrm{uuy}}_1+{\mathrm{duy}}_1}{2},\frac{{\mathrm{uuy}}_2+{\mathrm{duy}}_2}{2},\frac{{\mathrm{uuy}}_3+{\mathrm{duy}}_3}{2},\frac{{\mathrm{uuy}}_4+{\mathrm{duy}}_4}{2}......\frac{{\mathrm{uuy}}_n+{\mathrm{duy}}_n}{2}\]$

$UZ=\frac{UUZ+DUZ}{2}=\[{\mathrm{uz}}_1,{\mathrm{uz}}_2,{\mathrm{uz}}_3,{\mathrm{uz}}_4...{\mathrm{uz}}_n\]=\[\frac{{\mathrm{uuz}}_1+{\mathrm{duz}}_1}{2},\frac{{\mathrm{uuz}}_2+{\mathrm{duz}}_2}{2},\frac{{\mathrm{uuz}}_3+{\mathrm{duz}}_3}{2},\frac{{\mathrm{uuz}}_4+{\mathrm{duz}}_4}{2}......\frac{{\mathrm{uuz}}_n+{\mathrm{duz}}_n}{2}\]$

In formula, UY is the Y-direction shift value matrix of the X-axis translation shaft guide rail of slide carriage present position;

UZ is the Z-direction shift value matrix of the X-axis translation shaft guide rail of slide carriage present position;

Two-point method asks Y, Z-direction linearity:

If ideal line is:

y＝k*x+b(23)

Then:

$k=\frac{{\mathrm{uy}}_n-{\mathrm{uy}}_1}{x_n-x_1},b={\mathrm{uy}}_n-k*x_n---\left(24\right)$

Known point (x _i, uy _i) to be h to the distance of ideal line be:

$h=\frac{\left|k*x-uy+b\right|}{\sqrt{1+k^2}}=\[h_1,h_2,h_3,h_4...h_n\]=\[\frac{\left|k*x_1-{\mathrm{uy}}_1+b\right|}{\sqrt{1+k^2}},\frac{\left|k*x_2-{\mathrm{uy}}_2+b\right|}{\sqrt{1+k^2}},\frac{\left|k*x_3-{\mathrm{uy}}_3+b\right|}{\sqrt{1+k^2}},\frac{\left|k*x_4-{\mathrm{uy}}_4+b\right|}{\sqrt{1+k^2}}...\frac{\left|k*x_n-{\mathrm{uy}}_n+b\right|}{\sqrt{1+k^2}}\]---\left(25\right)$

Y linearity is:

Δy＝h _max-h _min(26)

In formula, h _maxfor known point (x _i, uy _i) to the maximal value of ideal line distance;

H _minfor known point (x _i, uy _i) to the minimum value of ideal line distance;

Rolling pendulum error is:

$\mathrm{\Δ}\mathrm{\α}=\frac{\left|{\mathrm{uuz}}_{mid}-{\mathrm{duz}}_{mid}\right|}{L_x}---\left(27\right)$

In formula, L _xfor Y-direction distance between X-axis upper/lower guide;

Uuz _midfor the Z-direction shift value of X-axis upper rail mid point;

Duz _midfor the Z-direction shift value of X-axis lower guideway mid point;

Top pendulum error is:

$\mathrm{\Δ}\mathrm{\β}=\frac{\left|{\mathrm{uz}}_{left}-{\mathrm{uz}}_{right}\right|}{W_x}---\left(28\right)$

In formula, W _xfor X between X-axis guide rail two slide block is to distance;

Uz _leftfor the Z-direction shift value at X-axis guide rail left slider place;

Uz _rightfor the Z-direction shift value at the right slide block place of X-axis guide rail;

Run-out error is:

$\mathrm{\Δ}\mathrm{\γ}=\frac{\left|{\mathrm{uuy}}_{left}-{\mathrm{duy}}_{left}-{\mathrm{uuy}}_{right}+{\mathrm{duy}}_{right}\right|}{W_x}---\left(29\right)$

In formula, W _xfor X between X-axis guide rail two slide block is to distance;

Uuy _leftfor the Y-direction shift value at X-axis upper rail left slider place;

Duy _leftfor the Y-direction shift value at X-axis lower guideway left slider place;

Uuy _rightfor the Y-direction shift value at the right slide block place of X-axis upper rail;

Duy _rightfor the Y-direction shift value at the right slide block place of X-axis lower guideway;

X, the Z axis error of perpendicularity are:

${\mathrm{\Δ\γ}}_{xz}=arctg\frac{{\mathrm{uz}}_{mid}}{L_x}-arctg\frac{{\mathrm{uy}}_{mid}}{L_z}---\left(30\right)$

In formula, L _xfor Y-direction distance between X-axis upper/lower guide;

L _zfor the length of Z axis guide rail;

Uz _midfor the Z-direction shift value of X-axis guide rail midpoint;

Uy _midfor the Y-direction shift value of Z axis guide rail midpoint.

The Thermal Error of table 3. horizontal Machining centers

Secondly, set up lathe work Space Thermal error model based on the basic geometric error of unit by many-body theory, described many-body theory general step is that the constraint of the practical structures according to lathe, low sequence body sequence description method and lathe draws the topology diagram of lathe, lower body array table and degree of freedom list respectively; Then desired characteristics matrix between each body of horizontal Machining centers and error character matrix is drawn respectively according to the character of translation motion eigenmatrix and rotary motion eigenmatrix; Finally calculate the position coordinates and attitude that become form point and cutter-orientation under workpiece coordinate system with cutter when having error at ideal conditions, and then obtain end error and machine tool accuracy; The work space that described lathe work space is formed with X/Y/Z tri-direction ranges for lathe.

For the horizontal Machining centers shown in Fig. 2, Fig. 7 is the topology diagram of this horizontal Machining centers, and wherein, in figure, 0 represents the earth; 1 represents lathe bed; 2 represent slide; 3 represent turntable; 4 represent workpiece; 5 represent column; 6 represent slide carriage; 7 represent main spindle box; 8 represent main shaft; 9 represent cutter; Table 4 is the lower body array table of horizontal Machining centers, table 5 is degree of freedom list, it represents the restraint condition between each unit of lathe, in table " 0 " representing can not free movement; " 1 " represent energy free movement, table 6 is horizontal Machining centers eigenmatrix table, and in table, i, j are the label of adjacent body; i gets 0-8, and j gets 2-9.

Refer to following table:

The lower body array of table 4. horizontal Machining centers

Typical body j	1	2	3	4	5	6	7	8	9
										L 0(j)	1	2	3	4	5	6	7	8	9
L 1(j)	0	1	2	3	0	5	6	7	8
										L 2(j)	0	0	1	2	0	0	5	6	7
L 3(j)	0	0	0	1	0	0	0	5	6
										L 4(j)	0	0	0	0	0	0	0	0	5
L 5(j)	0	0	0	0	0	0	0	0	0

The list of table 5. horizontal Machining centers degree of freedom

Adjacent body	X	Y	Z	α	β	γ
							0-1	0	0	0	0	0	0
1-2	0	0	1	0	0	0
							2-3	0	0	0	0	1	0
3-4	0	0	0	0	0	0
							0-5	0	0	0	0	0	0
5-6	1	0	0	0	0	0
							6-7	0	1	0	0	0	0
7-8	0	0	0	0	0	0
							8-9	0	0	0	0	0	0

Table 6. horizontal Machining centers eigenmatrix table

If cutter becomes form point, the coordinate in tool coordinate system is:

P _t＝(P _tx,P _ty,P _tz,1) ^T＝(0,0,1.75e-1,1) ^T(31)

So lathe in the ideal case, and cutter becomes form point P _tideal forming function in workpiece coordinate system is:

Lathe is having under error condition, and cutter becomes form point and the vector actual shaping function in workpiece coordinate system to be:

Error under workpiece coordinate system is:

$\begin{array}{c}{E}_P=P_{wideal}-P_w\\ =\left(\begin{array}{c}-1.3e-5+y*8.1e-6+z*3e-6\\ -x*1.28e-5+5e-7\\ x*3e-6+5.79e-6\\ 0\end{array}\right)\end{array}---\left(34\right)$

Errors is shown in Fig. 8-Figure 10.

As can be seen from error curve diagram shown in Fig. 8-Figure 10:

(1) fault in enlargement three that the fault in enlargement that caused by steady-state error, main spindle box displacement y of lathe end X-coordinate error and slide unit displacement z cause forms, the fault in enlargement that steady-state error and y, z cause presents counteracting trend, steady-state error is-13 μm, and the fault in enlargement of y, z is respectively 8.1 μm/m and 3 μm/m.

(2) fault in enlargement that lathe end Y-coordinate error is caused by steady-state error, movable workbench distance x forms, and the fault in enlargement that steady-state error and x cause presents counteracting trend, and steady-state error is 0.5 μm, and the fault in enlargement of x is 12.8 μm/m.

(3) fault in enlargement that lathe end Z error of coordinate is caused by steady-state error, movable workbench distance x forms, and the fault in enlargement that steady-state error and x cause presents superposition trend, and steady-state error is 5.79 μm, and the fault in enlargement of x is 3 μm/m.

Although be described the preferred embodiments of the present invention by reference to the accompanying drawings above; but the present invention is not limited to above-mentioned embodiment; above-mentioned embodiment is only schematic; be not restrictive; those of ordinary skill in the art is under enlightenment of the present invention; do not departing under the ambit that present inventive concept and claim protect, can also make a lot of form, these all belong within protection scope of the present invention.

Claims (10)

1. machine tool thermal error precision transforms and a method for establishing model, it is characterized in that, comprises the steps:

Step one: set up Machine Tool CAD model and simplified model;

Step 2: CAE thermal analyses is carried out to the Machine Tool CAD model after simplifying;

Step 3: extract each kinematic axis unit thermal deformation value by CAE thermal analyses post-processing module, and be converted into the basic geometric error of unit;

Step 4: based on the basic geometric error of unit, sets up lathe work Space Thermal error model.

2. machine tool thermal error precision according to claim 1 transforms and method for establishing model, it is characterized in that, in described step one, adopts Creo software, to remove in Machine Tool CAD model analysis result without the minutia of impact to simplify cad model.

3. machine tool thermal error precision according to claim 1 transforms and method for establishing model, it is characterized in that, in described step 2, ANSYS software is adopted to read the X-T intermediate file generated by cad model, generate finite element model and machine tool structure thermal analyses is carried out to it, wherein, the thermal source in lathe and radiating condition are converted into heat flow density and convection transfer rate value respectively by the heat-dissipating model of correspondence and heat dissipation model, and are loaded on finite element model with the form of thermal force.

4. machine tool thermal error precision according to claim 1 transforms and method for establishing model, and it is characterized in that, in described step 3, the concrete steps being extracted each kinematic axis unit thermal deformation value by CAE thermal analyses post-processing module are:

Step 3-1: respectively with the arbitrary axial side of the end face being arranged on each rail in the every pair of guide rails on lathe for extract path;

Step 3-2: the deflection choosing n node at the dual-side of each guide rail end face as extraction target, the X, Y, Z axis extracting all translation shaft to thermal deformation value.

5. machine tool thermal error precision according to claim 1 transforms and method for establishing model, it is characterized in that, in described step 3, described kinematic axis unit comprise lathe X, Y, Z axis to three pairs of translation shaft guide rails.

6. machine tool thermal error precision according to claim 1 transforms and method for establishing model, it is characterized in that, in described step 3, the basic geometric error of described unit comprises straightness error, Run-out error, the rolling pendulum error of the X, Y, Z axis of corresponding axle and pendulum error of running.

7. machine tool thermal error precision according to claim 1 transforms and method for establishing model, it is characterized in that, in described step 3, by MATLAB software, the thermal deformation value of X, Y, Z axis is converted into the basic geometric error of unit.

8. machine tool thermal error precision according to claim 1 transforms and method for establishing model, it is characterized in that, in described step 3, by the concrete steps that the thermal deformation value of X-axis is converted into the basic geometric error of unit is:

If:

X＝[x ₁,x ₂,x ₃,x ₄…x _n]

UUY＝[uuy ₁,uuy ₂,uuy ₃,uuy ₄…uuy _n]

UUZ＝[uuz ₁,uuz ₂,uuz ₃,uuz ₄…uuz _n]

(1)

DUY＝[duy ₁,duy ₂,duy ₃,duy ₄…duy _n]

DUZ＝[duz ₁,duz ₂,duz ₃,duz ₄…duz _n]

In formula:

The horizontal ordinate matrix of X for got X-axis guide rail is put;

UUY is the Y-direction shift value matrix that on a guide rail in X-direction pair of guide rails, taken point is corresponding;

UUZ is the Z-direction shift value matrix that on a guide rail in X-direction pair of guide rails, taken point is corresponding;

DUY is the Y-direction shift value matrix that on another guide rail in X-direction pair of guide rails, taken point is corresponding;

DUZ is the Z-direction shift value matrix that on another guide rail in X-direction pair of guide rails, taken point is corresponding;

When then slide carriage is positioned at centre position, the shift value of X-direction translation shaft guide rail is

$\begin{array}{c}UY=\frac{UUY+DUY}{2}=\[{\mathrm{uy}}_1,{\mathrm{uy}}_2,{\mathrm{uy}}_3,{\mathrm{uy}}_4\mathrm{...}{\mathrm{uy}}_n\]=\[\frac{{\mathrm{uuy}}_1+{\mathrm{duy}}_1}{2},\frac{{\mathrm{uuy}}_2+{\mathrm{duy}}_2}{2},\frac{{\mathrm{uuy}}_3+{\mathrm{duy}}_3}{2},\frac{{\mathrm{uuy}}_4+{\mathrm{duy}}_4}{2}\mathrm{......}\frac{{\mathrm{uuy}}_n+{\mathrm{duy}}_n}{2}\]\\ UZ=\frac{UUZ+DUZ}{2}=\[{\mathrm{uz}}_1,{\mathrm{uz}}_2,{\mathrm{uz}}_3,{\mathrm{uz}}_4\mathrm{...}{\mathrm{uz}}_n\]=\[\frac{{\mathrm{uuz}}_1+{\mathrm{duz}}_1}{2},\frac{{\mathrm{uuz}}_2+{\mathrm{duz}}_2}{2},\frac{{\mathrm{uuz}}_3+{\mathrm{duz}}_3}{2},\frac{{\mathrm{uuz}}_4+{\mathrm{duz}}_4}{2}\mathrm{......}\frac{{\mathrm{uuz}}_n+{\mathrm{duz}}_n}{2}\]\end{array}---\left(2\right)$

In formula, UY is the Y-direction shift value matrix of the X-direction translation shaft guide rail of slide carriage present position;

UZ is the Z-direction shift value matrix of the X-direction translation shaft guide rail of slide carriage present position;

1) two-point method asks Y, Z-direction linearity:

If ideal line is:

y＝k*x+b(3)

Then:

$k=\frac{{\mathrm{uy}}_n-{\mathrm{uy}}_1}{x_n-x_1},b={\mathrm{uy}}_n-k*x_n---\left(4\right)$

Known point (x _i, uy _i) to be h to the distance of ideal line be:

$h=\frac{|k*x-uy+b|}{\sqrt{1+k^2}}=\[h_1,h_2,h_3,h_4...h_n\]=\[\frac{|k*x_1-{\mathrm{uy}}_1+b|}{\sqrt{1+k^2}},\frac{|k*x_2-{\mathrm{uy}}_2+b|}{\sqrt{1+k^2}},\frac{|k*x_3-{\mathrm{uy}}_3+b|}{\sqrt{1+k^2}},\frac{|k*x_4-{\mathrm{uy}}_4+b|}{\sqrt{1+k^2}}...\frac{|k*x_n-{\mathrm{uy}}_n+b|}{\sqrt{1+k^2}}\]---\left(5\right)$

Y linearity is:

Δy＝h _max-h _min(6)

In formula, h _maxfor known point (x _i, uy _i) to the maximal value of ideal line distance;

H _minfor known point (x _i, uy _i) to the minimum value of ideal line distance;

2) rolling pendulum error is:

$\mathrm{\Δ}\mathrm{\α}=\frac{|{\mathrm{uuz}}_{mid}-{\mathrm{duz}}_{mid}|}{L_x}---\left(7\right)$

In formula, L _xfor Y-direction distance between X-direction pair of guide rails;

Uuz _midfor the Z-direction shift value of the guide rail mid point of in X-direction pair of guide rails;

Duz _midfor the Z-direction shift value of another guide rail mid point in X-direction pair of guide rails;

3) pendulum error in top is:

$\mathrm{\Δ}\mathrm{\β}=\frac{|{\mathrm{uz}}_{left}-{\mathrm{uz}}_{right}|}{W_x}---\left(8\right)$

In formula, W _xfor X-direction pair of guide rails two slide blocks between X-direction distance;

Uz _leftfor the Z-direction shift value at X-direction guide rail left slider place;

Uz _rightfor the Z-direction shift value at the right slide block place of X-direction guide rail;

4) Run-out error is:

$\mathrm{\Δ}\mathrm{\γ}=\frac{|{\mathrm{uuy}}_{left}-{\mathrm{duy}}_{left}-{\mathrm{uuy}}_{right}+{\mathrm{duy}}_{right}|}{W_x}---\left(9\right)$

In formula, W _xfor X-direction distance between X-direction guide rail two slide block;

Uuy _leftfor the Y-direction shift value at the left slider place of the guide rail of in X-direction pair of guide rails;

Duy _leftfor the Y-direction shift value at the left slider place of another guide rail in X-direction pair of guide rails;

Uuy _rightfor the Y-direction shift value at the right slide block place of the guide rail of in X-direction pair of guide rails;

Duy _rightfor the Y-direction shift value at the right slide block place of another guide rail in X-direction pair of guide rails;

5) X, the Z axis error of perpendicularity are:

${\mathrm{\Δ\γ}}_{xz}=arctg\frac{{\mathrm{uz}}_{mid}}{L_x}-arctg\frac{{\mathrm{uy}}_{mid}}{L_z}---\left(10\right)$

In formula, L _xfor Y-direction distance between X-direction pair of guide rails;

L _zfor the length of Z-direction guide rail;

Uz _midfor the Z-direction shift value of X-direction guide rail midpoint;

Uy _midfor the Y-direction shift value of Z-direction guide rail midpoint.

9. machine tool thermal error precision according to claim 1 transforms and method for establishing model, it is characterized in that, in described step 4, utilize many-body theory, set up the mapping relations of tool-workpiece relative pose error in the thermal deformation errors at machine tool structure guide rail position place and lathe work space, thus set up lathe work Space Thermal error model.

10. machine tool thermal error precision according to claim 9 transforms and method for establishing model, and it is characterized in that, the concrete steps setting up lathe work Space Thermal error model are:

Step 4-1: the topology diagram drawing lathe according to the practical structures of lathe;

Step 4-2: the lower body array table drawing lathe according to the constraint of low sequence body sequence description method and lathe;

Step 4-3: according to the characteristic of translation motion eigenmatrix and rotary motion eigenmatrix, obtain the desired characteristics matrix between each adjacent body of lathe and error character matrix;

Step 4-4: draw machine tool error according to ideal forming function and actual shaping function.