CN1446666A - Locating method for large size work pieces in machine work - Google Patents

Abstract

A method for searching the machining position of large workpiece includes such steps as primary fixing on machine-tool, measuring the 2D coordinates of 6 points on the workpiece by the optical reading head on the mainshaft of machine-tool and moving the numerally controlled machine-tool comparing them with theoretical 3D coordinate of said 6 points on CAD model of the workpiece, homogenizing and optimizing the errors to obtain the coordinates of the workpiece in the coordinate system of machine-tool, regulating the position of workpiece in CAD/CAM system, and generating actual machining program. Its advantage is high productivity.

Description

The machined method for position-finding of large-scale workpiece

Technical field

The invention belongs to machining manufacturing technology field, be specifically related to a kind of machined method for position-finding of large-scale workpiece.

Background technology

A product will experience many links from being designed into manufacturing in manufacturing enterprise, the particularly digital control processing of large-scale overweight workpiece, need long production time, comprise programming, transportation, measurement, installation, location and the cutter preparation etc. of workpiece, cause the manufacturing time of whole part longer like this.

The processing of large-scale overweight part is different from the processing of common parts, and traditional part processing step is that the design drawing according to part carries out industrial analysis to it earlier, determines process and processing route, designs frock clamp, carries out numerical control programming; Then frock clamp is positioned on lathe, soon workpiece is installed in the anchor clamps and clamps, and processes then.Large-scale overweight workpiece is difficult for adopting traditional handicraft, because this class workpiece is in a single day in place, because self weight and size, be difficult for carrying out the position adjustment, so adopt installation in position, measurement and positioning information, numerical control programming, the technological process of processing then is so measurement and positioning information just becomes the important step that guarantees to process qualified products.On the other hand, because the size and the weight of workpiece, make workpiece unavoidably produce distortion, there is error in the shape of workpiece blank between also may and designing a model, but must make the stressing conditions of workpiece when machining state identical in actual applications with workpiece, make troubles for so again the survey and the machining of workpiece locating information.

The machining of guide rail beam is the typical large-scale overweight processing that the distortion workpiece is arranged, and guide rail beam is built-in metal parts in cement prefab, because the distortion of large scale and cement prefab causes and adopts the general measure localization method not use.

Summary of the invention

The objective of the invention is to propose a kind of the shortening and produce time, reduce auxiliary cost of manufacture, the machined method for position-finding of the large-scale workpiece of increasing work efficiency.

The machined method for position-finding of the large-scale workpiece that the present invention proposes, its prerequisite: workpiece blank has certain allowance, and workpiece enters before the processing stations, and cad model is set up, and the coordinate in the workpiece coordinate system of the measuring point to be checked on the workpiece is known.Concrete steps of the present invention are as follows: mark 6 predefine point O in advance in the workpiece blank corresponding position ₁, O ₂, O ₃, O ₄, O ₅, O ₆, workpiece is installed the location according to the actual loading situation, the mobile lathe coordinates of motion axle of being correlated with utilizes machine tool numerical control system to measure two dimension coordinates (as shown in Figure 1) of predefine point in lathe coordinate system, promptly obtains O ₁, O ₂, O ₅, O ₆(Y, the Z) coordinate, and O of point ₃, O ₄(X, Z) coordinate of point; And and the three-dimensional coordinate comparative analysis of the theoretic measuring point to be checked of workpiece cad model, carry out the optimization process of error homogenizing, draw the relation between lathe coordinate system and the workpiece CAD coordinate system; In CAD/CAM system, determine the position of workpiece in CAD/CAM system according to resulting locating information, through the rearmounted numerical control program that generates machine tooling of handling, send into lathe and process.

Among the present invention, the optimization process of error homogenizing is the common method in the engineering.

Among the present invention, measurement mechanism adopts the ordinary optical read head as measuring stick, pack in the machine tool chief axis, measuring stick can rotate by the main shaft orientating function, the length of measuring stick compensates by the method for similar tool length compensation, so just can measure and be positioned at X-Z, two dimension coordinates of the point on the Y-Z direction.For example, for 6 predefine points, can measure O earlier among Fig. 1 ₁, O ₂(X, Z) coordinate, then, machine tool chief axis rotation 90 degree measurement O ₃, O ₄The point (X, Z) coordinate are measured O at last ₅, O ₆(X, Z) coordinate of point.As O ₄The measurement of point can obtain coordinate P from machine tool numerical control system _{M '}=(X _{M '}, Y _{M '}, Z _{M '}), the bar of measurement mechanism is long for L, so this coordinate P under lathe coordinate system _m=(X _m, Y _m, Z _m), X wherein _m=X _{M '}, Z _m=Z _{M '}+ L, Y _mCoordinate is uncertain value.Predefine point O ₁, O ₂, O ₃, O ₄, O ₅, O ₆Two coordinates of these 6 each points are definite, and another the unknown by calculating the locating information of workpiece in lathe coordinate system, thereby obtains the coordinate of workpiece in lathe coordinate system.So just can generate correct procedure.

Content of the present invention further describes as follows:

1 measuring method

1.1 the regulation of measurement point

Six measurement points are arranged on the side and end face of workpiece (as shown in Figure 1).

1.2 measuring method

This method uses gun sight to measure.Gun sight is a non-contact measurement equipment, can only record wherein two coordinates for each measurement point, and two measurement points of end face lack the y coordinate, and the four measuring point of side lacks the x coordinate, promptly

Measure period	The X coordinate	The Y coordinate	The Z coordinate
				????1	????N	????Y	????Y
????2	????N	????Y	????Y
				????3	????Y	????N	????Y
????4	????Y	????N	????Y
				????5	????N	????Y	????Y
????6	????N	????Y	????Y

Y: this coordinate that this point is corresponding can record N: this coordinate that this point is corresponding can't record

2 set up the relation between workpiece coordinate system and the design coordinate system

2.1 the setting of workpiece coordinate system

Design in the coordinate system known 6 satisfy following relation: $\stackrel{\→}{O_1{O}_2}\⊥\stackrel{\→}{O_3{O}_4}$ $\stackrel{\→}{O_5{O}_6}\⊥\stackrel{\→}{O_3{O}_4}$ Make like this and calculate simplification.

With O ₂Be initial point,

Be the y axle, Parallel vector be the x axle, be configured to the workpiece coordinate system (see figure 2).That is: $\stackrel{\→}{y_w}//\stackrel{\→}{O_1{O}_2}$ ， $\stackrel{\→}{x_w}//\stackrel{\→}{O_3{O}_4}$ ，

2.2 the setting of auxiliary work-piece coordinate system

With O ₅Be initial point,

Be the y axle,

Parallel vector be the x axle, be configured to auxiliary work-piece coordinate system (see figure 2).That is: $\stackrel{\→}{y_h}//\stackrel{\→}{O_6{O}_5}$ ， $\stackrel{\→}{x_h}//\stackrel{\→}{O_4{O}_3}$ ，

2.3 the relation between workpiece coordinate system and the design coordinate system

2.3.1 determine auxiliary work-piece coordinate system and the relation that designs coordinate system

Promptly ask O ₅, With

Expression in the design coordinate system.

If O ₃, O ₄, O ₅And O ₆Be expressed as O in design in the coordinate system _L3(x _L3, y _L3, z _L3), O _L4(x _L4, y _L4, z _L4), O _L5(x _L5, y _L5, z _L5), O _L6(x _L6, y _L6, z _L6), these parameters are all known. $\stackrel{\→}{O_{L6}{O}_{L5}}=\{x_{L5}-x_{L6},y_{L5}-y_{L6},z_{L5}-z_{L6}\}=\{{\mathrm{\Δx}}_{65L},{\mathrm{\Δy}}_{65L},{\mathrm{\Δz}}_{65L}\}$ $\stackrel{\→}{O_{L4}{O}_{L3}}=\{x_{L3}-x_{L4},y_{L3}-y_{L4},z_{L3}-z_{L4}\}=\{{\mathrm{\Δx}}_{43L},{\mathrm{\Δy}}_{43L},{\mathrm{\Δz}}_{43L}\}$

Three of the auxiliary work-piece coordinate system axial vectors being expressed as in the design coordinate system then: $\stackrel{\→}{x_{\mathrm{hl}}}=\{x_{\mathrm{hlx}},x_{\mathrm{hly}},x_{h/z}\}=\frac{1}{\left|\stackrel{\→}{O_3{O}_4}\right|}\{{\mathrm{\Δx}}_{43L},{\mathrm{\Δy}}_{43L},{\mathrm{\Δz}}_{43L}\}$ $\stackrel{\→}{y_{\mathrm{hl}}}=\{y_{\mathrm{hlx}},y_{\mathrm{hly}},y_{\mathrm{hlz}}\}=\frac{1}{\left|\stackrel{\→}{O_6{O}_5}\right|}\{{\mathrm{\Δx}}_{65L},{\mathrm{\Δy}}_{65L},{\mathrm{\Δz}}_{65L}\}$ $\frac{\{x_{\mathrm{hly}}{y}_{\mathrm{hlz}}-x_{\mathrm{hlz}}{y}_{\mathrm{hly}},x_{\mathrm{hlz}}{y}_{\mathrm{ylx}}-x_{\mathrm{hlx}}{y}_{\mathrm{hlz}},x_{\mathrm{hlx}}{y}_{\mathrm{hly}}-x_{\mathrm{hly}}{y}_{\mathrm{hlx}}\}}{\sqrt{{(x_{\mathrm{hly}}{y}_{\mathrm{hlz}}-x_{\mathrm{hlz}}{y}_{\mathrm{hly}})}^2+{(x_{\mathrm{hlz}}{y}_{\mathrm{hlx}}-x_{\mathrm{hlx}}{y}_{\mathrm{hlz}})}^2+{(x_{\mathrm{hlx}}{y}_{\mathrm{hly}}-x_{\mathrm{hly}}{y}_{\mathrm{hlx}})}^2}}$

2.3.2 determine workpiece coordinate system and the relation that designs coordinate system

Promptly ask O ₂, With Expression in the design coordinate system.

If O ₁, O ₂, O ₃And O ₄Be expressed as O in design in the coordinate system _L1(x _L1, y _L1, z _L1), O _L2(x _L2, y _L2, z _L2), O _L3(x _L3, y _L3, z _L3), O _L4(x _L4, y _L4, z _L4), these parameters are all known. $\stackrel{\→}{O_{L1}{O}_{L2}}=\{x_{L2}-x_{L1},y_{L2}-y_{L1},z_{L2}-z_{L1}\}=\{{\mathrm{\Δx}}_{12L},{\mathrm{\Δy}}_{12L},{\mathrm{\Δz}}_{12L}\}$ $\stackrel{\→}{O_{L3}{O}_{L4}}=-\stackrel{\→}{O_{L4}{O}_{L3}}=\{{\mathrm{\Δx}}_{34L},{\mathrm{\Δy}}_{34L},{\mathrm{\Δz}}_{34L}\}$

Three of workpiece coordinate system axial vectors being expressed as in the design coordinate system then: $\stackrel{\→}{x_{\mathrm{wl}}}=\{x_{\mathrm{wlx}},x_{\mathrm{wly}},x_{\mathrm{wlz}}\}=\frac{1}{\left|\stackrel{\→}{O_3{O}_4}\right|}\{{\mathrm{\Δx}}_{34L},{\mathrm{\Δy}}_{34L},{\mathrm{\Δz}}_{34L}\}=-\stackrel{\→}{x_{\mathrm{hl}}}$ $\stackrel{\→}{y_{\mathrm{wl}}}=\{y_{\mathrm{wlx}},y_{\mathrm{wly}},y_{\mathrm{wlz}}\}=\frac{1}{\left|\stackrel{\→}{O_1{O}_2}\right|}\{{\mathrm{\Δx}}_{12L},{\mathrm{\Δy}}_{12L},{\mathrm{\Δz}}_{12L}\}$

$\frac{\{x_{\mathrm{wly}}{y}_{\mathrm{wlz}}-x_{\mathrm{wlz}}{y}_{\mathrm{wly}},x_{\mathrm{wlz}}{y}_{\mathrm{wlx}}-x_{\mathrm{wlx}}{y}_{\mathrm{wlz}},x_{\mathrm{wlx}}{y}_{\mathrm{wly}}-x_{\mathrm{wly}}{y}_{\mathrm{wlx}}\}}{\sqrt{{(x_{\mathrm{wly}}{y}_{\mathrm{wlz}}-x_{\mathrm{wlz}}{y}_{\mathrm{wly}})}^2+{(x_{\mathrm{wlz}}{y}_{\mathrm{wlx}}-x_{\mathrm{wlx}}{y}_{\mathrm{wlz}})}^2+{(x_{\mathrm{wlx}}{y}_{\mathrm{wly}}-x_{\mathrm{wly}}{y}_{\mathrm{wlx}})}^2}}$

If certain a bit is expressed as O in workpiece coordinate system _Wi(x _Wi, y _Wi, z _Wi), in the design coordinate system, be expressed as O _Li(x _Li, y _Li, z _Li), following transformation relation is then arranged: $\left[\begin{array}{c}{x}_{\mathrm{Li}}\\ y_{\mathrm{Li}}\\ z_{\mathrm{Li}}\\ 1\end{array}\right]=\left[\begin{array}{cccc}{x}_{\mathrm{wlx}}& y_{\mathrm{wlx}}& z_{\mathrm{wlx}}& x_{L2}\\ x_{\mathrm{wly}}& y_{\mathrm{wly}}& z_{\mathrm{wly}}& y_{L2}\\ x_{\mathrm{wlz}}& y_{\mathrm{wlz}}& z_{\mathrm{wlz}}& z_{L2}\\ 0& 0& 0& 1\end{array}\right]\left[\begin{array}{c}{x}_{117}\\ y_{117}\\ z_{117}\\ 1\end{array}\right]$

If $A_{\mathrm{wl}}=\left[\begin{array}{cccc}{x}_{\mathrm{wlx}}& y_{\mathrm{wlx}}& z_{\mathrm{wlx}}& x_{L2}\\ x_{\mathrm{wly}}& y_{\mathrm{wly}}& z_{\mathrm{wly}}& y_{L2}\\ x_{\mathrm{wlz}}& y_{\mathrm{wlz}}& z_{\mathrm{wlz}}& z_{L2}\\ 0& 0& 0& 1\end{array}\right]$

Then use $\left[\begin{array}{c}{x}_{\mathrm{Wi}}\\ y_{\mathrm{Wi}}\\ z_{\mathrm{Wi}}\\ 1\end{array}\right]=A_{\mathrm{wl}}^{-1}\left[\begin{array}{c}{x}_{\mathrm{Li}}\\ y_{\mathrm{Li}}\\ z_{\mathrm{Li}}\\ 1\end{array}\right]$ Have a few can be converted to workpiece coordinate system from the design coordinate system.

2.3.3 determine the relation between workpiece coordinate system and the auxiliary work-piece coordinate system

Promptly determine initial point and three expressions of axial vector in workpiece coordinate system of auxiliary work-piece coordinate system.

If O ₅In workpiece coordinate system, be expressed as O _W5(x _W5, y _W5, z _W5), Being expressed as in workpiece coordinate system $\stackrel{\→}{x_{\mathrm{hw}}}(x_{\mathrm{hwx}},x_{\mathrm{hwy}},x_{\mathrm{hwz}})$ Being expressed as in workpiece coordinate system $\stackrel{\→}{y_{\mathrm{hw}}}(y_{\mathrm{hwx}},y_{\mathrm{hwy}},y_{\mathrm{hwz}})$ ,

Being expressed as in workpiece coordinate system $\stackrel{\→}{z_{\mathrm{hw}}}(z_{\mathrm{hwx}},z_{\mathrm{hwy}},z_{\mathrm{hwz}})$ 。Then have: $\left[\begin{array}{c}{x}_{L5}\\ y_{L5}\\ z_{L5}\\ 1\end{array}\right]=\left[\begin{array}{cccc}{x}_{\mathrm{wlx}}& y_{\mathrm{wlx}}& z_{\mathrm{wlx}}& x_{L2}\\ x_{\mathrm{wly}}& y_{\mathrm{wly}}& z_{\mathrm{wly}}& y_{L2}\\ x_{\mathrm{wlz}}& y_{\mathrm{wlz}}& z_{\mathrm{wlz}}& z_{L2}\\ 0& 0& 0& 1\end{array}\right]\left[\begin{array}{c}{x}_{W5}\\ y_{W5}\\ z_{W5}\\ 1\end{array}\right]=A_{\mathrm{wl}}\left[\begin{array}{c}{x}_{W5}\\ y_{W5}\\ z_{W5}\\ 1\end{array}\right]$ $\left[\begin{array}{c}{x}_{\mathrm{hlx}}\\ x_{\mathrm{hly}}\\ x_{\mathrm{hlz}}\\ 0\end{array}\right]\left[\begin{array}{cccc}{x}_{\mathrm{wlx}}& y_{\mathrm{wlx}}& z_{\mathrm{wlx}}& x_{L2}\\ x_{\mathrm{wly}}& y_{\mathrm{wly}}& z_{\mathrm{wly}}& y_{L2}\\ x_{\mathrm{wlz}}& y_{\mathrm{wlz}}& z_{\mathrm{wlz}}& z_{L2}\\ 0& 0& 0& 1\end{array}\right]\left[\begin{array}{c}{x}_{\mathrm{hwx}}\\ x_{\mathrm{hwy}}\\ x_{\mathrm{hwz}}\\ 0\end{array}\right]=A_{\mathrm{wl}}\left[\begin{array}{c}{x}_{\mathrm{hwx}}\\ x_{\mathrm{hwy}}\\ x_{\mathrm{hwz}}\\ 0\end{array}\right]$ $\left[\begin{array}{c}{y}_{\mathrm{hlx}}\\ y_{\mathrm{hly}}\\ y_{\mathrm{hlz}}\\ 0\end{array}\right]=\left[\begin{array}{cccc}{x}_{\mathrm{wlx}}& y_{\mathrm{wlx}}& z_{\mathrm{wlx}}& x_{L2}\\ x_{\mathrm{wly}}& y_{\mathrm{wly}}& z_{\mathrm{wly}}& y_{L2}\\ x_{\mathrm{wlz}}& y_{\mathrm{wlz}}& z_{\mathrm{wlz}}& z_{L2}\\ 0& 0& 0& 1\end{array}\right]\left[\begin{array}{c}{y}_{\mathrm{hwx}}\\ y_{\mathrm{hwy}}\\ y_{\mathrm{hwz}}\\ 0\end{array}\right]=A_{\mathrm{wl}}\left[\begin{array}{c}{y}_{\mathrm{hwx}}\\ y_{\mathrm{hwy}}\\ y_{\mathrm{hwz}}\\ 0\end{array}\right]$ $\left[\begin{array}{c}{z}_{\mathrm{hlx}}\\ z_{\mathrm{hly}}\\ z_{\mathrm{hlz}}\\ 0\end{array}\right]=\left[\begin{array}{cccc}{x}_{\mathrm{wlx}}& y_{\mathrm{wlx}}& z_{\mathrm{wlx}}& x_{L2}\\ x_{\mathrm{wly}}& y_{\mathrm{wly}}& z_{\mathrm{wly}}& y_{L2}\\ x_{\mathrm{wlz}}& y_{\mathrm{wlz}}& z_{\mathrm{wlz}}& z_{L2}\\ 0& 0& 0& 1\end{array}\right]\left[\begin{array}{c}{z}_{\mathrm{hwx}}\\ z_{\mathrm{hwy}}\\ z_{\mathrm{hwz}}\\ 0\end{array}\right]=A_{\mathrm{wl}}\left[\begin{array}{c}{z}_{\mathrm{hwx}}\\ z_{\mathrm{hwy}}\\ z_{\mathrm{hwz}}\\ 0\end{array}\right]$

Then $\left[\begin{array}{c}{x}_{W5}\\ y_{W5}\\ z_{W5}\\ 1\end{array}\right]=A_{\mathrm{wl}}^{-1}\left[\begin{array}{c}{x}_{L5}\\ y_{L5}\\ z_{L5}\\ 1\end{array}\right],\left[\begin{array}{c}{x}_{\mathrm{hwx}}\\ x_{\mathrm{hwy}}\\ x_{\mathrm{hwz}}\\ 0\end{array}\right]=A_{\mathrm{wl}}^{-1}\left[\begin{array}{c}{x}_{\mathrm{hlx}}\\ x_{\mathrm{hlx}}\\ x_{\mathrm{hlz}}\\ 0\end{array}\right]$ $\left[\begin{array}{c}{y}_{\mathrm{hwz}}\\ y_{\mathrm{hwy}}\\ y_{\mathrm{hwz}}\\ 0\end{array}\right]=A_{\mathrm{wl}}^{-1}\left[\begin{array}{c}{y}_{\mathrm{hlx}}\\ y_{\mathrm{hly}}\\ y_{\mathrm{hlz}}\\ 0\end{array}\right],\left[\begin{array}{c}{z}_{\mathrm{hwx}}\\ z_{\mathrm{hwy}}\\ z_{\mathrm{hwz}}\\ 0\end{array}\right]=A_{\mathrm{wl}}^{-1}\left[\begin{array}{c}{z}_{\mathrm{hlx}}\\ z_{\mathrm{hly}}\\ z_{\mathrm{hlz}}\\ 0\end{array}\right]$ If certain a bit is expressed as O in workpiece coordinate system _Wi(x _Wi, y _Wi, z _Wi), in the auxiliary work-piece coordinate system, be expressed as O _Hi(x _Hi, y _Hi, z _Hi), then have: $\left[\begin{array}{c}{x}_{\mathrm{Wi}}\\ y_{\mathrm{Wi}}\\ z_{\mathrm{Wi}}\\ 1\end{array}\right]=\left[\begin{array}{cccc}{x}_{\mathrm{hwx}}& y_{\mathrm{hwx}}& z_{\mathrm{hwx}}& x_{W5}\\ x_{\mathrm{hwy}}& y_{\mathrm{hwy}}& z_{\mathrm{hwy}}& y_{W5}\\ x_{\mathrm{hwz}}& y_{\mathrm{hwz}}& z_{\mathrm{hwz}}& z_{W5}\\ 0& 0& 0& 1\end{array}\right]\left[\begin{array}{c}{x}_{\mathrm{Hi}}\\ y_{\mathrm{Hi}}\\ z_{\mathrm{Hi}}\\ 1\end{array}\right]=A_{\mathrm{Oh}}\left[\begin{array}{c}{x}_{\mathrm{Hi}}\\ y_{\mathrm{Hi}}\\ z_{\mathrm{Hi}}\\ 1\end{array}\right]$

O ₁, O ₂And O ₄In workpiece coordinate system, be expressed as O _W1(x _W1, y _W1, z _W1), O _W2(x _W2, y _W2, z _W2) and O _W4(x _W4, y _W4, z _W4), in the auxiliary work-piece coordinate system, be expressed as O _H1(x _H1, y _H1, z _H1), O _H2(x _H2, y _H2, z _H2) and O _H4(x _H4, y _H4, z _H4), have: $\left[\begin{array}{c}{x}_{W1}\\ y_{W1}\\ z_{W1}\\ 1\end{array}\right]=\left[\begin{array}{cccc}{x}_{\mathrm{hwx}}& y_{\mathrm{hwx}}& z_{\mathrm{hwx}}& x_{W5}\\ x_{\mathrm{hwy}}& y_{\mathrm{hwy}}& z_{\mathrm{hwy}}& y_{W5}\\ x_{\mathrm{hwz}}& y_{\mathrm{hwz}}& z_{\mathrm{hwz}}& z_{W5}\\ 0& 0& 0& 1\end{array}\right]\left[\begin{array}{c}{x}_{H1}\\ y_{H1}\\ z_{H1}\\ 1\end{array}\right]=A_{\mathrm{Oh}}\left[\begin{array}{c}{x}_{H1}\\ y_{H1}\\ z_{H1}\\ 1\end{array}\right]$ $\left[\begin{array}{c}{x}_{W2}\\ y_{W2}\\ z_{W2}\\ 1\end{array}\right]=\left[\begin{array}{cccc}{x}_{\mathrm{hwx}}& y_{\mathrm{hwx}}& z_{\mathrm{hwx}}& x_{W5}\\ x_{\mathrm{hwy}}& y_{\mathrm{hwy}}& z_{\mathrm{hwy}}& y_{W5}\\ x_{\mathrm{hwz}}& y_{\mathrm{hwz}}& z_{\mathrm{hwz}}& z_{W5}\\ 0& 0& 0& 1\end{array}\right]\left[\begin{array}{c}{x}_{H2}\\ y_{H2}\\ z_{H2}\\ 1\end{array}\right]=A_{\mathrm{Oh}}\left[\begin{array}{c}{x}_{H2}\\ y_{H2}\\ z_{H2}\\ 1\end{array}\right]$ $\left[\begin{array}{c}{x}_{W4}\\ y_{W4}\\ z_{W4}\\ 1\end{array}\right]=\left[\begin{array}{cccc}{x}_{\mathrm{hwx}}& y_{\mathrm{hwx}}& z_{\mathrm{hwx}}& x_{W5}\\ x_{\mathrm{hwy}}& y_{\mathrm{hwy}}& z_{\mathrm{hwy}}& y_{W5}\\ x_{\mathrm{hwz}}& y_{\mathrm{hwz}}& z_{\mathrm{hwz}}& z_{W5}\\ 0& 0& 0& 1\end{array}\right]\left[\begin{array}{c}{x}_{H4}\\ y_{H4}\\ z_{H4}\\ 1\end{array}\right]=A_{\mathrm{Oh}}\left[\begin{array}{c}{x}_{H4}\\ y_{H4}\\ z_{H4}\\ 1\end{array}\right]$

Just can be in the hope of O ₁, O ₂And O ₄Coordinate in the auxiliary work-piece coordinate system $\left[\begin{array}{c}{x}_{H1}\\ y_{H1}\\ z_{H1}\\ 1\end{array}\right]=A_{\mathrm{Oh}}^{-1}\left[\begin{array}{c}{x}_{W1}\\ y_{W1}\\ z_{W1}\\ 1\end{array}\right],\left[\begin{array}{c}{x}_{H2}\\ y_{H2}\\ z_{H2}\\ 1\end{array}\right]=A_{\mathrm{Oh}}^{-1}\left[\begin{array}{c}{x}_{W2}\\ y_{W2}\\ z_{W2}\\ 1\end{array}\right],\left[\begin{array}{c}{x}_{H4}\\ y_{H4}\\ z_{H4}\\ 1\end{array}\right]=A_{\mathrm{Oh}}^{-1}\left[\begin{array}{c}{x}_{W4}\\ y_{W4}\\ z_{W4}\\ 1\end{array}\right]$

2.4 theory of computation angle

Ask

With

And

Angle α ₁, α ₂

With

And Angle α ₃, α ₄ $\cos {\mathrm{\α}}_1=\frac{\stackrel{\→}{O_{W2}{O}_{W2}}\·\stackrel{\→}{O_{W1}{O}_{W2}}}{\left|\stackrel{\→}{O_2{O}_5}\right|\left|\stackrel{\→}{O_1{O}_2}\right|}$ ${\cos \mathrm{\α}}_2=\frac{\stackrel{\→}{O_{W2}{O}_{W5}}\·\stackrel{\→}{O_{W6}{O}_{W5}}}{\left|\stackrel{\→}{O_2{O}_5}\right|\left|\stackrel{\→}{O_6{O}_5}\right|}$ ${\cos \mathrm{\α}}_3=\frac{\stackrel{\→}{O_{W1}{O}_{W2}}\·\stackrel{\→}{O_{W3}{O}_{W4}}}{\left|\stackrel{\→}{O_1{O}_2}\right|\left|\stackrel{\→}{O_3{O}_4}\right|}$ ${\cos \mathrm{\α}}_4=\frac{\stackrel{\→}{O_{W6}{O}_{W5}}\·\stackrel{\→}{O_{W3}{O}_{W4}}}{\left|\stackrel{\→}{O_6{O}_5}\right|\left|\stackrel{\→}{O_3{O}_4}\right|}$

The match of 3 measurement data

3.1 the location of beam in lathe coordinate system

Ask three expressions of axial vector in lathe coordinate system of workpiece coordinate system exactly according to the actual measurement coordinate figure of measurement point, and institute a bit is converted to the lathe coordinate system from workpiece coordinate system by this relation.

If certain puts the O that is expressed as in lathe coordinate system _Mi(x _Mi, y _Mi, z _Mi).

(1) asks , promptly determine the expression of y axial vector in lathe coordinate system of workpiece coordinate system

$\stackrel{\→}{O_{M1}{O}_{M2}}=\{x_{M2}-x_{M1},y_{M2}-y_{M1},z_{M2}-z_{M1}\}=\{{\mathrm{\Δx}}_{12M},{\mathrm{\Δy}}_{12M},{\mathrm{\Δz}}_{12m}\},$ Δ x wherein _12MWait to ask.Can utilize

With

Between angle restriction concern and ask Δ x _12M: $\stackrel{\→}{O_{M2}{O}_{M5}}=\{x_{M5}-x_{M2},y_{M5}-y_{M2},z_{M5}-z_{M2}\}=\{{\mathrm{\Δx}}_{25M},{\mathrm{\Δy}}_{25M},{\mathrm{\Δz}}_{25M}\}$ ${\mathrm{\Δx}}_{25M}=x_{M5}-x_{M2}=\±\sqrt{{\left|\stackrel{\→}{O_2{O}_5}\right|}^2-{(y_{M5}-y_{M2})}^2-{(z_{M5}-z_{M2})}^2}$ For lathe coordinate system, x _M5＞x _M2Be sure establishment, therefore, get $x_{M5}-x_{M2}=\sqrt{{\left|\stackrel{\→}{O_2{O}_5}\right|}^2-{(y_{M5}-y_{M2})}^2-{(z_{M5}-z_{M2})}^2}$

With

Between satisfy: $\stackrel{\→}{O_{M2}{O}_{M5}}\·\stackrel{\→}{O_{M1}{O}_{M2}}=\left|\stackrel{\→}{O_2{O}_5}\right|\left|\stackrel{\→}{O_1{O}_2}\right|{\cos \mathrm{\α}}_1$

Promptly $\{{\mathrm{\Δx}}_{25M},{\mathrm{\Δy}}_{25M},{\mathrm{\Δz}}_{25M}\}\·\{{\mathrm{\Δx}}_{12M},{\mathrm{\Δy}}_{12M},{\mathrm{\Δz}}_{12M}\}=\left|\stackrel{\→}{O_2{O}_5}\right|\left|\stackrel{\→}{O_1{O}_2}\right|{\cos \mathrm{\α}}_1$

Then ${\mathrm{\Δx}}_{12M}=\left(\right|\stackrel{\→}{O_2{O}_5}\left|\right|\stackrel{\→}{O_1{O}_2}|{\cos \mathrm{\α}}_1-{\mathrm{\Δy}}_{25M}{\mathrm{\Δy}}_{12M}-{\mathrm{\Δz}}_{25M}{\mathrm{\Δz}}_{12M})/{\mathrm{\Δx}}_{25M}$

Then $\stackrel{\→}{y_{\mathrm{wm}}}=\{y_{\mathrm{wmx}},y_{\mathrm{wmy}},y_{\mathrm{wmz}}\}=\frac{1}{\left|\stackrel{\→}{O_1{O}_2}\right|}\{{\mathrm{\Δx}}_{12M},{\mathrm{\Δy}}_{12M},{\mathrm{\Δz}}_{12M}\}$

(2) ask , promptly $\stackrel{\→}{O_{M3}{O}_{M4}}=\{x_{M4}-x_{M3},y_{M4}-y_{M3},z_{M4}-z_{M3}\}=\{{\mathrm{\Δx}}_{34M},{\mathrm{\Δy}}_{34M},{\mathrm{\Δz}}_{34M}\}$

Δ y wherein _34MWait to ask. $\stackrel{\→}{O_{M1}{O}_{M2}}\·\stackrel{\→}{O_{M3}{O}_{M4}}=\left|\stackrel{\→}{O_1{O}_2}\right|\left|\stackrel{\→}{O_3{O}_4}\right|\·{\cos \mathrm{\α}}_3$

Promptly $\{{\mathrm{\Δx}}_{34M},{\mathrm{\Δy}}_{34M},{\mathrm{\Δz}}_{34M}\}\·\{{\mathrm{\Δx}}_{12M},{\mathrm{\Δy}}_{12M},{\mathrm{\Δz}}_{12M}\}=\left|\stackrel{\→}{O_1{O}_2}\right|\left|\stackrel{\→}{O_3{O}_4}\right|\·{\cos \mathrm{\α}}_3$ ${\mathrm{\Δy}}_{34M}=\left(\right|\stackrel{\→}{O_1{O}_2}\left|\right|\stackrel{\→}{O_3{O}_4}|\·{\cos \mathrm{\α}}_3-{\mathrm{\Δx}}_{34M}{\mathrm{\Δx}}_{12M}-{\mathrm{\Δz}}_{34M}{\mathrm{\Δz}}_{12M})/{\mathrm{\Δy}}_{12M}$ $\stackrel{\→}{x_{\mathrm{wm}}}=\{x_{\mathrm{wmx}},x_{\mathrm{wmy}},x_{\mathrm{wmz}}\}=\frac{1}{\left|\stackrel{\→}{O_3{O}_4}\right|}\{{\mathrm{\Δx}}_{34M},{\mathrm{\Δy}}_{34M},{\mathrm{\Δz}}_{34M}\}$

(3) ask

(4) ask O _M2Coordinate

O _M2(x _M2, y _M2, z _M2), y wherein _M2, z _M2Record x _M2Unknown.

O ₃Coordinate O in workpiece coordinate system _W3(x _W3, y _W3, z _W3) known, the coordinate in lathe coordinate system is O _M3(x _M3, y _M3, z _M3), y wherein _M3Unknown.Pass between the two is $\left[\begin{array}{c}{x}_{M3}\\ y_{M3}\\ z_{M3}\\ 1\end{array}\right]=\left[\begin{array}{cccc}{x}_{\mathrm{wmx}}& y_{\mathrm{wmx}}& z_{\mathrm{wmx}}& x_{M2}\\ x_{\mathrm{wmy}}& y_{\mathrm{wmy}}& z_{\mathrm{wmy}}& y_{M2}\\ x_{\mathrm{wmz}}& y_{\mathrm{wmz}}& z_{\mathrm{wmz}}& z_{M2}\\ 0& 0& 0& 1\end{array}\right]\left[\begin{array}{c}{x}_{W3}\\ y_{W3}\\ z_{W3}\\ 1\end{array}\right]$

X then _M3=x _WmxX _W3+ y _WmxY _W3+ z _WmxZ _W3+ x _M2

So x _M2=x _M3-(x _WmxX _W3+ y _WmxY _W3+ z _WmxZ _W3)

Can get O _M2Coordinate (x _M2, y _M2, z _M2)

Just determined the transformation matrix between workpiece coordinate system and the lathe coordinate system this moment, is designated as A _Wml: $A_{\mathrm{wm}1}=\left[\begin{array}{cccc}{x}_{\mathrm{wmx}}& y_{\mathrm{wmx}}& z_{\mathrm{wmx}}& x_{M2}\\ x_{\mathrm{wmy}}& y_{\mathrm{wmy}}& z_{\mathrm{wmy}}& y_{M2}\\ x_{\mathrm{wmz}}& y_{\mathrm{wmz}}& z_{\mathrm{wmz}}& z_{M2}\\ 0& 0& 0& 1\end{array}\right]$

x _M1=x _M2-Δ x _12M, be designated as x _{M1 (2)}

y _M3=x _WmyX _W3+ y _WmxY _W3+ z _WmxZ _W3+ y _M2, be designated as y _{M3 (2)}

y _M4=y _M3+ Δ y _34M, be designated as y _{M4 (2)}

With transformation matrix thus push away O _M5, O _M6Be designated as O _{M5 (2)}(x _{M5 (2)}, y _{M5 (2)}, z _{M5 (2)}) and O _{M6 (2)}(x _{M6 (2)}, y _{M6 (2)}, z _{M6 (2)}). $\left[\begin{array}{c}{x}_{M5\left(2\right)}\\ y_{M5\left(2\right)}\\ z_{M5\left(2\right)}\\ 1\end{array}\right]=\left[\begin{array}{cccc}{x}_{\mathrm{wmx}}& y_{\mathrm{wmx}}& z_{\mathrm{wmx}}& x_{M2}\\ x_{\mathrm{wmy}}& y_{\mathrm{wmy}}& z_{\mathrm{wmy}}& y_{M2}\\ x_{\mathrm{wmz}}& y_{\mathrm{wmz}}& z_{\mathrm{wmz}}& z_{M2}\\ 0& 0& 0& 1\end{array}\right]\left[\begin{array}{c}{x}_{W5}\\ y_{W5}\\ z_{W5}\\ 1\end{array}\right]=A_{\mathrm{wm}1}\left[\begin{array}{c}{x}_{W5}\\ y_{W5}\\ z_{W5}\\ 1\end{array}\right]$ $\left[\begin{array}{c}{x}_{M6\left(2\right)}\\ y_{M6\left(2\right)}\\ z_{M6\left(2\right)}\\ 1\end{array}\right]=\left[\begin{array}{cccc}{x}_{\mathrm{wmx}}& y_{\mathrm{wmx}}& z_{\mathrm{wmx}}& x_{M2}\\ x_{\mathrm{wmy}}& y_{\mathrm{wmy}}& z_{\mathrm{wmy}}& y_{M2}\\ x_{\mathrm{wmz}}& y_{\mathrm{wmz}}& z_{\mathrm{wmz}}& z_{M2}\\ 0& 0& 0& 1\end{array}\right]\left[\begin{array}{c}{x}_{W6}\\ y_{W6}\\ z_{W6}\\ 1\end{array}\right]=A_{\mathrm{wm}1}\left[\begin{array}{c}{x}_{W6}\\ y_{W6}\\ z_{W6}\\ 1\end{array}\right]$

(5) comparison of deviation

Be the actual O that records _M5Be O _{M5 (1)}(x _{M5 (1)}, y _{M5 (1)}, z _{M5 (1)}) and the comparison of the value of obtaining of deriving, wherein x _{M5 (1)}Unknown.

With (y _{M5 (1)}, z _{M5 (1)}) and (y _{M5 (2)}, z _{M5 (2)}) relatively:

d ₁＝(y _M5(2)-y _M5(1)) ²+(z _M5(2)-z _M5(1)) ²

3.2 homogenizing is handled

3.2.1 ask

, i.e. the expression of y coordinate vector in lathe coordinate system of auxiliary work-piece coordinate system

(1) O _M5, O _M6Y, z coordinate get O respectively _{M5 (1)}, O _{M5 (2)}And O _{M6 (1)}, O _{M6 (2)}Average, be designated as

O _M5(x _M5，y _M5，z _M5)，O _M6(x _M6，y _M6，z _M6)

y _M5＝(y _M5(1)+y _M5(2))/2，z _M5＝(z _M5(1)+z _M5(2))/2

y _M6＝(y _M6(1)+y _M6(2))/2，z _M6＝(z _M6(1)+z _M6(2))/2

x _M5And x _M6Uncertain.This moment O _M5, O _M6Y, z coordinate passed through homogenizing, use as exact value.

(2) ask

, promptly determine $\stackrel{\→}{O_{M6}{O}_{M5}}=\{x_{M5}-x_{M6},y_{M5}-y_{M6},z_{M5}-z_{M6}\}=\{{\mathrm{\Δx}}_{65M},{\mathrm{\Δy}}_{65M},{\mathrm{\Δz}}_{65M}\}$

Δ x wherein _65MUnknown.

Known $\stackrel{\→}{O_{M2}{O}_{M5}}\·\stackrel{\→}{O_{M6}{O}_{M5}}=\left|\stackrel{\→}{O_2{O}_5}\right|\left|\stackrel{\→}{O_6{O}_5}\right|{\cos \mathrm{\α}}_2$ Promptly $\{{\mathrm{\Δx}}_{25M},{\mathrm{\Δy}}_{25M},{\mathrm{\Δz}}_{25M}\}\·\{{\mathrm{\Δx}}_{65M},{\mathrm{\Δy}}_{65M},{\mathrm{\Δz}}_{65M}\}=\left|\stackrel{\→}{O_2{O}_5}\right|\left|\stackrel{\→}{O_6{O}_5}\right|{\cos \mathrm{\α}}_2$ ${\mathrm{\Δx}}_{65M}=\left(\right|\stackrel{\→}{O_2{O}_5}\left|\right|\stackrel{\→}{O_6{O}_5}|{\cos \mathrm{\α}}_2-{\mathrm{\Δy}}_{25M}{\mathrm{\Δy}}_{65M}-{\mathrm{\Δz}}_{25M}{\mathrm{\Δz}}_{65M})/{\mathrm{\Δx}}_{25M}$ $\stackrel{\→}{y_{\mathrm{hm}}}=\{y_{\mathrm{hmx}},y_{\mathrm{hmy}},y_{\mathrm{hmz}}\}=\frac{1}{\left|\stackrel{\→}{O_6{O}_5}\right|}\{{\mathrm{\Δx}}_{65M},{\mathrm{\Δy}}_{65M},{\mathrm{\Δz}}_{65M}\}$

3.2.2 ask

, i.e. the expression of x coordinate vector in lathe coordinate system of auxiliary work-piece coordinate system

Because O ₃, O ₄Apart from each other, error are less relatively, so its measured value is as exact value. $\stackrel{\→}{O_{M4}{O}_{M3}}=\{x_{M3}-x_{M4},y_{M3}-y_{M4},z_{M3}-z_{M4}\}=\{{\mathrm{\Δx}}_{43M},{\mathrm{\Δy}}_{43M},{\mathrm{\Δz}}_{43M}\}$

Δ y wherein _43MWait to ask. $\stackrel{\→}{O_{6M}{O}_{5M}}\·\stackrel{\→}{O_{3M}{O}_{4M}}=\left|\stackrel{\→}{O_6{O}_5}\right|\left|\stackrel{\→}{O_3{O}_4}\right|\·{\cos \mathrm{\α}}_4$

Just $\stackrel{\→}{O_{6M}{O}_{5M}}\·(-\stackrel{\→}{O_{4M}{O}_{3M}})=\left|\stackrel{\→}{O_6{O}_5}\right|\left|\stackrel{\→}{O_3{O}_4}\right|\·{\cos \mathrm{\α}}_4$

Promptly $\{{\mathrm{\Δx}}_{65M},{\mathrm{\Δy}}_{65M},{\mathrm{\Δz}}_{65M}\}\·\{-{\mathrm{\Δx}}_{43M},-{\mathrm{\Δy}}_{43M},-{\mathrm{\Δz}}_{43M}\}=\left|\stackrel{\→}{O_6{O}_5}\right|\left|\stackrel{\→}{O_3{O}_4}\right|\·\cos {\mathrm{\α}}_4$ ${\mathrm{\Δy}}_{43M}=-\left(\right|\stackrel{\→}{O_6{O}_5}\left|\right|\stackrel{\→}{O_3{O}_4}|\·\cos {\mathrm{\α}}_4+{\mathrm{\Δx}}_{65M}\·{\mathrm{\Δx}}_{43M}+{\mathrm{\Δz}}_{65M}\·{\mathrm{\Δz}}_{43M})/{\mathrm{\Δy}}_{65M}$ $\stackrel{\→}{x_{\mathrm{hm}}}=\{x_{\mathrm{hmx}},x_{\mathrm{hmy}},x_{\mathrm{hmz}}\}=\frac{1}{\left|\stackrel{\→}{O_4{O}_3}\right|}\{{\mathrm{\Δx}}_{43M},{\mathrm{\Δy}}_{43M},{\mathrm{\Δz}}_{43M}\}$

3.2.3 ask the expression of z coordinate vector in lathe coordinate system of auxiliary work-piece coordinate system

3.2.4 ask O _M5Coordinate (x _M5, y _M5, z _M5)

Y wherein _M5, z _M5Known, x _M5Wait to ask.

O ₄Coordinate (x in the auxiliary work-piece coordinate system _H4, y _H4, z _H4) known, the coordinates table in lathe coordinate system is shown (x _M4, y _M4, z _M4), y wherein _M4Unknown.Pass between the two is $\left[\begin{array}{c}{x}_{M4}\\ y_{M4}\\ z_{M4}\\ 1\end{array}\right]=\left[\begin{array}{cccc}{x}_{\mathrm{hmx}}& y_{\mathrm{hmx}}& z_{\mathrm{hmx}}& x_{M5}\\ x_{\mathrm{hmy}}& y_{\mathrm{hmy}}& z_{\mathrm{hmy}}& y_{M5}\\ x_{\mathrm{hmz}}& y_{\mathrm{hmz}}& z_{\mathrm{hmz}}& z_{M5}\\ 0& 0& 0& 1\end{array}\right]\left[\begin{array}{c}{x}_{H4}\\ y_{H4}\\ z_{H4}\\ 1\end{array}\right]$

X then _M4=x _HmxX _H4+ y _HmxY _H4+ z _HmxZ _M4+ x _M5,

So x _M5=x _M4-(x _HmxX _H4+ y _HmxY _H4+ z _HmxZ _H4),

Can determine O _M5(x _M5, y _M5, z _M5).

3.2.5 with the auxiliary work-piece coordinate is the frame of reference, asks O ₁, O ₂Expression O in lathe coordinate system _M1' (x _M1', y _M1', z _M1'), O _M2' (x _M2', y _M2', z _M2') $\left[\begin{array}{c}{x_{M1}}^{\′}\\ {y_{M1}}^{\′}\\ {z_{M1}}^{\′}\\ 1\end{array}\right]=\left[\begin{array}{cccc}{x}_{\mathrm{hmx}}& y_{\mathrm{hmx}}& z_{\mathrm{hmx}}& x_{M5}\\ x_{\mathrm{hmy}}& y_{\mathrm{hmy}}& z_{\mathrm{hmy}}& y_{M5}\\ x_{\mathrm{hmz}}& y_{\mathrm{hmz}}& z_{\mathrm{hmz}}& z_{M5}\\ 0& 0& 0& 1\end{array}\right]\left[\begin{array}{c}{x}_{H1}\\ y_{H1}\\ z_{H1}\\ 1\end{array}\right]=A_{\mathrm{hm}}\left[\begin{array}{c}{x}_{H1}\\ y_{H1}\\ z_{H1}\\ 1\end{array}\right]=A_{\mathrm{hm}}{A}_{\mathrm{Oh}}^{-1}\left[\begin{array}{c}{x}_{W1}\\ y_{W1}\\ z_{W1}\\ 1\end{array}\right]$ $\left[\begin{array}{c}{x_{M2}}^{\′}\\ {y_{M2}}^{\′}\\ {z_{M2}}^{\′}\\ 1\end{array}\right]=\left[\begin{array}{cccc}{x}_{\mathrm{hmx}}& y_{\mathrm{hmx}}& z_{\mathrm{hmx}}& x_{M5}\\ x_{\mathrm{hmy}}& y_{\mathrm{hmy}}& z_{\mathrm{hmy}}& y_{M5}\\ x_{\mathrm{hmz}}& y_{\mathrm{hmz}}& z_{\mathrm{hmz}}& z_{M5}\\ 0& 0& 0& 1\end{array}\right]\left[\begin{array}{c}{x}_{H2}\\ y_{H2}\\ z_{H2}\\ 1\end{array}\right]=A_{\mathrm{hm}}\left[\begin{array}{c}{x}_{H2}\\ y_{H2}\\ z_{H2}\\ 1\end{array}\right]=A_{\mathrm{hm}}{A}_{\mathrm{Oh}}^{-1}\left[\begin{array}{c}{x}_{W2}\\ y_{W2}\\ z_{W2}\\ 1\end{array}\right]$

Tie up to expression in the lathe coordinate system 3.2.6 recomputate workpiece coordinate

With O ₂The actual measurement coordinate be kept at O _{M2 (1)}In, be designated as O _{M2 (1)}(x _{M2 (1)}, y _{M2 (1)}, z _{M2 (1)}), O _M2Get O _M2' (x _M2', y _M2', z _M2) value,

Be O _M2(x _M2, y _M2, z _M2)=O _M2' (x _M2', y _M2', z _M2') $\stackrel{\→}{x_{\mathrm{wm}}}=-\stackrel{\→}{x_{\mathrm{hm}}}$

3.2.7 determine transformation matrix $A_{\mathrm{WM}2}=\left[\begin{array}{cccc}{x}_{\mathrm{wmx}}& y_{\mathrm{wmx}}& z_{\mathrm{wmz}}& x_{M2}\\ x_{\mathrm{wmy}}& y_{\mathrm{wmy}}& z_{\mathrm{wmy}}& y_{M2}\\ x_{\mathrm{wmz}}& y_{\mathrm{wmz}}& z_{\mathrm{wmz}}& z_{M2}\\ 0& 0& 0& 1\end{array}\right]$

3.2.8 with (y _{5 (1)}, z _{5 (1)}) and (y _{2 (1)}, z _{2 (1)}) and (y ₅, z ₅) and (y ₂, z ₂) comparison deviation d ₂₁=(y ₅-y _{5 (1)}) ²+ (z ₅-z _{5 (1)}) ²d ₂₂=(y ₂-y _{2 (1)}) ²+ (z ₂-z _{2 (1)}) ²Get d ₂=max{d ₂₁, d ₂₂}

3.2.9 determine the transition matrix A between workpiece coordinate system and the lathe coordinate system _Wm

With the deviate d that obtains before the homogenizing ₁With the deviate d that obtains after the homogenizing ₂Compare, if d ₂＜d ₁, illustrate that then this homogenization process has played the effect of homogenizing really, otherwise then do not have homo-effect.That is to say:

If d ₁≤ d ₂, then get A _Wm=A _Wm1, otherwise get A _Wm=A _Wm2The coordinate of i point in workpiece coordinate system is O _Wi(x _Wi, y _Wi, z _Wi), the coordinate in lathe coordinate system is O _Mi(x _Mi, y _Mi, z _Mi), then have: $\left[\begin{array}{c}{x}_{\mathrm{Mi}}\\ y_{\mathrm{Mi}}\\ z_{\mathrm{Mi}}\\ 1\end{array}\right]=A_{\mathrm{wm}}\left[\begin{array}{c}{x}_{\mathrm{Wi}}\\ y_{\mathrm{Wi}}\\ z_{\mathrm{Wi}}\\ 1\end{array}\right]$ 4 determine total transformation matrix

Determine to be tied to total transition matrix between the lathe coordinate system from geodetic coordinates

Above step is done one sum up, with the O of i point from earth coordinates _Ei(x _Ei, y _Ei, z _Ei) be converted to the O under the lathe coordinate system _Mi(x _Mi, y _Mi, z _Mi), its total transition matrix A _EmFor:

A _Em=A _WmA _Wl ^-1A _ErlA _EerPromptly $\left[\begin{array}{c}{x}_{\mathrm{Mi}}\\ y_{\mathrm{Mi}}\\ z_{\mathrm{Mi}}\\ 1\end{array}\right]=A_{\mathrm{em}}\left[\begin{array}{c}{x}_{\mathrm{Ei}}\\ y_{\mathrm{Ei}}\\ z_{\mathrm{Ei}}\\ 1\end{array}\right]$

The present invention be directed to the processing of large-scale overweight workpiece and propose, but its basic principle all has practicality to the processing of all workpiece, its advantage mainly shows the following aspects:

1, simplified the requirement that workpiece steps up to locate:, just can obtain the coordinate of workpiece in lathe coordinate system by two dimension coordinates of the tested point on the measuring workpieces.Thereby clamping and centering location, the shortening of simplifying workpiece are produced time, are optimized the establishment of numerical control program.Workpiece does not need accurate location, particularly large-scale workpiece through simple location and clamping, adjusts very difficulty of position, adopts this method greatly to shorten difficulty and time that the location is adjusted.

2, simplified measurement work reduces the cost of measurement mechanism: the present invention adopts optical readings, by coordinate points on the measuring workpieces, obtains the coordinate of workpiece under machine coordinates.Measurement mechanism is installed on the machine tool chief axis, and by it move of machine tool numerical control system control, the data of measurement are read by digital control system or passed through file transfers.

3, the precision of Ce Lianging does not directly influence machining accuracy: method of the present invention, be adapted to clamping No. one time, finish all manufacturing procedures, because there is allowance in blank, so workpiece deformation and certainty of measurement are in allowed limits, can both finish processing qualified workpiece.

4, guarantee machining accuracy and reduction cutting output: because the size and the weight of workpiece, inevitably there is distortion in workpiece, the coordinate of these tested points also changes thereupon, adopt algorithm of the present invention, the matching degree of measurement model and cad model will be optimized, thereby guarantee final Working position precision, reduce cutting output.

Description of drawings

Fig. 1 is a measurement markers point diagram of the present invention.

Fig. 2 is the setting of workpiece coordinate system of the present invention and auxiliary work-piece coordinate system.

Fig. 3 is a measurement mechanism schematic diagram of the present invention.

Fig. 4 is a production line vertical view of the present invention.

The specific embodiment

Embodiment: the present invention is applied in the processing of Shanghai magnetic suspension train guide rail beam, the layout of system of processing as shown in Figure 4, two lathes are five coordinate lathes, workpiece is positioned in the middle of two lathes, lathe directions X stroke is about 30 meters, adopt the control of grating chi full cut-off ring, machine pillar can rotate around Y-axis, and main shaft rotates around X-axis.Relation between two lathe coordinate systems is known, and the coordinate of arbitrary lathe mid point all can be transformed in another lathe through translation easily.

Measure by using gun sight.Gun sight is a non-contact measurement equipment, and to 6 measurement on the workpiece, the workpiece locating information that adopts computational methods of the present invention to obtain is worked out corresponding procedure then, finishes processing to part by Digit Control Machine Tool.Measurement point design coordinate (unit: rice)

1?????????????8408.6321???????????????13.3726???????????????16730.7227

2?????????????8408.6321???????????????13.9726???????????????16730.7229

3?????????????8408.6587???????????????14.2227???????????????16730.4222

4?????????????8410.7813???????????????14.2307???????????????16706.4379

5?????????????8410.8079???????????????13.9808???????????????16706.137

6 8410.8079 13.3808 16706.1368 measurement point measured values (unit: millimeter, lathe coordinate system)

Claims (3)

1, a kind of machined method for position-finding of large-scale workpiece is characterized in that marking predefine point O in the workpiece blank corresponding position in advance ₁, O ₂, O ₃, O ₄, O ₅, O ₆Workpiece is installed the location according to the actual loading situation, utilize the measurement mechanism on the lathe to measure two dimension coordinates of predefine point in lathe coordinate system, and and the three-dimensional coordinate of the theoretic measuring point to be checked of workpiece cad model compare analysis, carry out the optimization process of error homogenizing, draw the relation between lathe coordinate system and the workpiece CAD coordinate system; In CAD/CAM system, determine the position of workpiece in CAD/CAM system according to resulting locating information, through the rearmounted numerical control program that generates machine tooling of handling, send into lathe and process.

2, the machined method for position-finding of large-scale workpiece according to claim 1, it is characterized in that measurement mechanism adopts the ordinary optical read head as measuring stick, pack in the machine tool chief axis, measuring stick can rotate by the main shaft orientating function, the length of measuring stick compensates by the method for similar tool length compensation, can obtain coordinate P from machine tool numerical control system _{M '}=(X _{M '}, Y _{M '}, Z _{M '}), the bar of measurement mechanism is long to be L, this coordinate P under lathe coordinate system _m=(X _m, Y _m, Z _m), X wherein _m=X _{M '}, Z _m=Z _{M '}+ L, Y _mCoordinate is uncertain value.

3, the machined method for position-finding of large-scale workpiece according to claim 1 is characterized in that in the design coordinate system predefined 6 some O ₁, O ₂, O ₃, O ₄, O ₅, O ₆, satisfy following relation: $\stackrel{\→}{O_1{O}_2}\⊥\stackrel{\→}{O_3{O}_4}$ $\stackrel{\→}{O_5{O}_6}\⊥\stackrel{\→}{O_3{O}_4}$ O ₂Be coordinate origin.

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