CN103206932A - Assessment method for geometric errors of five-axis tool machine - Google Patents

Abstract

The invention discloses an assessment method for geometric errors of a five-axis tool machine, and the assessment method can be applied to a five-axis processing machine. The assessment method includes the steps that an R-test measuring tool with a probe and a standard ball is arranged on the five-axis machining machine, the sphere center of the standard ball serves as the original point of a reference coordinate system, a five-axis synchronous movement path serves as a measuring path to measure the assembly error of the five-axis tool machine, the assembly error obtained through measuring and a known mechanism parameter of the five-axis tool machine are substituted in a geometric error model, and values of 11 items of geometric errors of the five-axis tool machine are obtained through solving by using a method of least square. The assessment method has the advantages of being fast and accurate.

Description

The geometric error appraisal procedure of five instrument machineries

Technical field

The present invention is relevant with instrument machinery, particularly about a kind of appraisal procedure that can measure and calculate five instrument machinery geometric errors, has the advantage that makes up easy and pinpoint accuracy.

Background technology

The source of error of instrument machinery is mainly divided into structural failure (Structurally-induced Errors), is driven error (Driven-induced Errors) and static error (Quasi-static Errors), wherein static error accounts for 70% of the instrument machinery margin of error, the main source of static error then is geometric error (Geometric Errors), in other words, the geometric error that accurately measures instrument machinery is the key step of improvement instrument machining accuracy.

Because the complex structure of five instrument machineries itself, the accurate measurement of partial geometry error term is very difficult, therefore, the measurement standard program of five instrument machineries, as ISO/10791-6, be to utilize measurer earlier, R-Test measurer for example, carry out after the measurement of assembly geometric error, the partial geometry error term of rotation axis estimated in summary again, and overall process is consuming time, and its estimation result is accurate inadequately, be unfavorable for five follow-up error compensation and precision improvements of instrument machinery, be necessary further improvement.

Summary of the invention

Because above-mentioned defective, fundamental purpose of the present invention is to provide a kind of geometric error appraisal procedure of five instrument machineries, thereby can finish the evaluates calculation of geometric error item fast and accurately.

The geometric error appraisal procedure of a kind of five instrument machineries provided by the present invention can be applicable to the First Five-Year Plan axis processing machine, and its step includes:

(a) utilize the R-test measurer with probe and standard ball, this probe is installed in the main shaft of this five axis processing machine, and this standard ball is installed in the board of this five axis processing machine, and with the centre of sphere of this standard ball initial point as the reference coordinate system;

(b) move the path together as measuring route according to the First Five-Year Plan axle, use the assembly error of these these five instrument machineries of R-test gage measuring;

(c) with five known mechanism parameter substitution one geometric error model of instruments machinery of the measured assembly error that obtains of preceding step and this, utilize least square method to find the solution and obtain the value of listed 11 the geometric error items of this geometric error model.

Therefore, the present invention utilizes the R-test measurer to measure three dimensions assembly error fast and accurately with five together moving paths of K4, and application only comprises the simple and easy geometric error model of 11 geometric error items, cooperate least square method can estimate 11 geometric error items accurately, can be made for the operation that improves that five instrument machineries carry out follow-up precision.

In addition, the applied five together moving paths of the present invention are good with the K4 path of ISO/CD10791-6 institute standard.

Description of drawings

Fig. 1 is the model definition synoptic diagram of X linear movement axle geometric error of the present invention.

The model definition synoptic diagram of Fig. 2 C rotational motion of the present invention axle geometric error.

Fig. 3 is located at the coordinate system synoptic diagram that five instrument machineries constitute for the present invention with the R-test Measuring instrument rack.

Fig. 4 utilizes the synoptic diagram of the measured geometric error of R-test measurer for the present invention.

Fig. 5 utilizes the K4 path for one embodiment of the present invention and measures and the error amount comparison diagram that passes through after calculating.

[main element symbol description]

Xr, Yr, Zr:R reference frame axially;

The mechanism parameter of Xx, Yx, Zx:X axle;

The mechanism parameter of Xy, Yy, Zy:Y axle;

The mechanism parameter of Xz, Yz, Zz:Z axle;

The mechanism parameter of Zc:C axle;

The mechanism parameter of Xa, Ya, Za:A axle;

Xw, Yw, Zw: the standard ball center is at the coordinate figure of C axis coordinate system;

The component error amount of EXX, EYX, EZX, EAX, EBX, ECX:X axle;

The component error amount of EXY, EYY, EZY, EAY, EBY, ECY:Y axle;

The component error amount of EXZ, EYZ, EZZ, EAZ, EBZ, ECZ:Z axle;

The component error amount of EXC, EYC, EZC, EAC, EBC, ECC:C axle;

The component error amount of EXA, EYA, EZA, EAA, EBA, ECA:A axle;

The Xm:X axle is with respect to the displacement of its initial point;

The Ym:Y axle is with respect to the displacement of its initial point;

The Zm:Z axle is with respect to the displacement of its initial point;

The mechanism parameter of Xx, Yx, Zx:X axle;

The mechanism parameter of Xy, Yy, Zy:Y axle;

The mechanism parameter of Xz, Yz, Zz:Z axle;

The orientation angle of Cm:C axle;

The orientation angle of Am:A axle;

XOC, YOC:C axle are in the installation side-play amount of X, Y-direction;

YOA, ZOA:A axle are in the installation side-play amount of Y, Z direction;

The verticality site error of AOZ, the relative X of BOZ:Z axle and Y-axis;

The verticality site error of AOC, the relative X of BOC:C axle, Y-axis;

The verticality site error of BOA, the relative Y of COA:A axle, Z axle;

The upright position error of the relative C axle of COX:X axle;

The verticality site error of Y, Z axle in COA, the relative X-axis reference frame of BOC:A axle;

Xh, Zh: main shaft is with respect to the original displacement of Z axle;

Zp: pop one's head in the side-play amount of main shaft coordinate system Z-direction;

XOW, YOW, ZOW: standard ball is in the position offset error of C axis coordinate system X, Y and Z-direction;

The assembly error of Δ Xp, Δ Yp, Δ Zp:X, Y, Z direction;

P _{E, r}: the relative object of tool ends end coordinate system is sat up straight the site error that mark ties up to reference frame.

Embodiment

Below will cooperate the accompanying drawing of enclosing by cited embodiment, describe technology contents of the present invention and feature in detail, wherein:

Fig. 1 is the model definition synoptic diagram of X linear movement axle geometric error of the present invention;

Fig. 2 is the model definition synoptic diagram of C rotational motion axle geometric error of the present invention;

Fig. 3 is located at the coordinate system synoptic diagram that five instrument machineries constitute for the present invention with the R-test Measuring instrument rack;

Fig. 4 utilizes the synoptic diagram of R-test gage measuring gained assembly error for the present invention;

Fig. 5 utilizes the K4 path for one embodiment of the present invention and measures and the error amount comparison diagram that passes through after calculating.

See also Fig. 1, the geometric error of instrument machinery can define the single linear kinematic axis six component error items (Component Errors), comprise three linear error items (Translational Error) and three rotation error items, per two crossing linear axes then have the site error (Location Errors) of verticality, X linear movement axle with instrument machinery is example, the geometric error model of the relative R reference frame of X coordinate system can with 4 * 4 homogeneous transition matrixes (Homogeneous Transformation Matrix HTM) is expressed as follows:

$T_x^r=\left[\begin{array}{cccc}1& 0& 0& X_x\\ 0& 1& 0& \mathrm{<figure-callout\; id="0"\; label="Yx"\; filenames="HDA0000130018350000051.png"\; state="\{\{state\}\}">Yx</figure-callout>}\\ 0& 0& 1& \mathrm{<figure-callout\; id="0"\; label="Zx"\; filenames="HDA0000130018350000051.png"\; state="\{\{state\}\}">Zx</figure-callout>}\\ 0& 0& 0& 1\end{array}\right]\left[\begin{array}{cccc}1& -\mathrm{<figure-callout\; id="0"\; label="COX"\; filenames="HDA0000130018350000051.png"\; state="\{\{state\}\}">COX</figure-callout>}& 0& 0\\ \mathrm{<figure-callout\; id="1"\; label="COX"\; filenames="HDA0000130018350000051.png"\; state="\{\{state\}\}">COX</figure-callout>}& 1& 0& 0\\ 0& 0& 1& 0\\ 0& 0& 0& 1\end{array}\right]\left[\begin{array}{cccc}1& -\mathrm{ECX}& \mathrm{EBX}& \mathrm{Xm}+\mathrm{EXX}\\ \mathrm{ECX}& 1& -\mathrm{EAX}& \mathrm{EYX}\\ -\mathrm{EBX}& \mathrm{EAX}& 1& \mathrm{EZX}\\ 0& 0& 0& 0\end{array}\right].$

Wherein, Xx, Yx, Zx be X-axis initial point (Home) with respect to the coordinate figure of R reference frame, i.e. mechanism parameter (Kinematic Parameter);

COX then is the site error of verticality between Y-axis in X linear movement axle and the R reference frame (namely being the little amount of spin of this two coordinate system at the Z axle);

EXX, EYX, EZX, EAX, EBX and ECX then are 6 component error amounts of X linear movement axle;

Xm represents that X linear movement axle is with respect to the displacement of its initial point.

Then have 6 component error items and 4 position error term as for single rotational motion axle, see also Fig. 2, be example with C rotational motion axle, the geometric error model of the relative R reference frame of C axis coordinate system can be expressed as follows with 4 * 4 homogeneous transition matrixes (HTM) equally:

$T_c^r=\left[\begin{array}{cccc}1& 0& 0& \mathrm{<figure-callout\; id="0"\; label="Xc"\; filenames="HDA0000130018350000051.png"\; state="\{\{state\}\}">Xc</figure-callout>}\\ 0& 1& 0& \mathrm{<figure-callout\; id="0"\; label="Yc"\; filenames="HDA0000130018350000051.png"\; state="\{\{state\}\}">Yc</figure-callout>}\\ 0& 0& 1& \mathrm{<figure-callout\; id="0"\; label="Zc"\; filenames="HDA0000130018350000051.png"\; state="\{\{state\}\}">Zc</figure-callout>}\\ 0& 0& 0& 1\end{array}\right]\left[\begin{array}{cccc}1& 0& \mathrm{<figure-callout\; id="0"\; label="BOC\; XOC"\; filenames="HDA0000130018350000051.png"\; state="\{\{state\}\}">BOC</figure-callout>}& \mathrm{XOC}\\ 0& 1& -\mathrm{AOC}& \mathrm{YOC}\\ -\mathrm{<figure-callout\; id="1"\; label="BOC\; AOC"\; filenames="HDA0000130018350000051.png"\; state="\{\{state\}\}">BOC</figure-callout>}& \mathrm{AOC}& 1& 0\\ 0& 0& 0& 1\end{array}\right]$

$\left[\begin{array}{cccc}\mathrm{Cce}& -\mathrm{Sce}& \mathrm{EBC}& \mathrm{EXC}\\ \mathrm{Sce}& \mathrm{Cce}& -\mathrm{EAC}& \mathrm{EYC}\\ \mathrm{EAC}\&times;\mathrm{Sce}-\mathrm{EBC}\&times;\mathrm{Cce}& \mathrm{EAC}\&times;\mathrm{Cce}+\mathrm{EBC}\&times;\mathrm{<figure-callout\; id="1"\; label="Sce"\; filenames="HDA0000130018350000051.png"\; state="\{\{state\}\}">Sce</figure-callout>}& 1& \mathrm{<figure-callout\; id="0"\; label="EZC"\; filenames="HDA0000130018350000051.png"\; state="\{\{state\}\}">EZC</figure-callout>}\\ 0& 0& 0& 0\end{array}\right]$

Wherein, Xc, Yc, Zc be C axle initial point (Home) with respect to the coordinate figure of R reference frame, i.e. mechanism parameter (Kinematic Parameter);

XOC and YOC are that C rotation axis actual installation center and desired center are in the linear deflection amount of X, Y-direction;

AOC and BOC install the verticality site error (namely being that this two coordinate system is at little amount of spin of X, Y-axis) between X, Y-axis in axis and the R reference frame for the C rotation axis;

EXC, EYC, EZC, EAC, EBC and ECC then are 6 component error amounts of C rotation axis;

Sce=sin (Cm+ECC), Cce=cos (Cm+ECC), and Cm represents the orientation angle of C rotation axis.

Five instrument machineries of tradition have three linear movement axles and two rotational motion axles, therefore, the geometric error of three linear movement axles has 21 geometric error items, the geometric error of two rotational motion axles then has 20 geometric errors, add up to 41 geometric error items, and the geometric error model of all the other linear movement axles and rotational motion axle can be represented all with aforementioned 4 * 4 homogeneous transition matrixes (HTM).

A preferred embodiment provided by the present invention is to adopt the R-test measurer that the error of five instrument machineries is measured, aforementioned R-test measurer comprises that 3D probe (including three perpendicular position transducers) is arranged on the instrument mechanical main shaft, and one standard ball (Master Ball) be arranged on the board of instrument machinery, with the centre of sphere of the standard ball initial point as the R reference frame, make the motion process of five instrument machineries form the mechanism's chain that seals, as shown in Figure 3, the error of five instrument machineries will be reflected on the aforementioned 3D probe.

The present invention is installed in five instruments coordinate systems that machinery constitutes with the R-test measurer, the geometric error model of X linear movement axle formula as described above wherein, and the geometric error model of the relative R reference frame of Y linear movement axle is as follows:

$T_y^r=\left[\begin{array}{cccc}1& -\mathrm{ECY}& \mathrm{EBY}& \mathrm{EXY}\\ \mathrm{ECY}& 1& -\mathrm{EAY}& \mathrm{Ym}+\mathrm{EYY}\\ -\mathrm{<figure-callout\; id="1"\; label="EBY\; EAY"\; filenames="HDA0000130018350000051.png"\; state="\{\{state\}\}">EBY</figure-callout>}& \mathrm{EAY}& 1& \mathrm{<figure-callout\; id="0"\; label="EZY"\; filenames="HDA0000130018350000051.png"\; state="\{\{state\}\}">EZY</figure-callout>}\\ 0& 0& 0& 1\end{array}\right]$

Wherein, EXY, EYY, EZY, EAY, EBY and ECY are 6 component error amounts of Y linear movement axle, and Ym represents Y linear movement axle with respect to the displacement of its initial point, and do not exist between this model hypothesis Y-axis and the reference frame C axle perpendicular axially.

Geometric error model as for the relative R reference frame of Z linear movement axle then is:

$T_z^r=\left[\begin{array}{cccc}1& 0& 0& \mathrm{<figure-callout\; id="0"\; label="Xz"\; filenames="HDA0000130018350000051.png"\; state="\{\{state\}\}">Xz</figure-callout>}\\ 0& 1& 0& \mathrm{<figure-callout\; id="0"\; label="Yz"\; filenames="HDA0000130018350000051.png"\; state="\{\{state\}\}">Yz</figure-callout>}\\ 0& 0& 1& \mathrm{<figure-callout\; id="0"\; label="Zz"\; filenames="HDA0000130018350000051.png"\; state="\{\{state\}\}">Zz</figure-callout>}\\ 0& 0& 0& 1\end{array}\right]\left[\begin{array}{cccc}1& 0& \mathrm{<figure-callout\; id="0"\; label="BOZ"\; filenames="HDA0000130018350000051.png"\; state="\{\{state\}\}">BOZ</figure-callout>}& 0\\ 0& 1& -\mathrm{AOZ}& 0\\ -\mathrm{<figure-callout\; id="1"\; label="BOZ\; AOZ"\; filenames="HDA0000130018350000051.png"\; state="\{\{state\}\}">BOZ</figure-callout>}& \mathrm{AOZ}& 1& 0\\ 0& 0& 0& 1\end{array}\right]\left[\begin{array}{cccc}1& -\mathrm{ECZ}& \mathrm{EBZ}& \mathrm{EXZ}\\ \mathrm{ECZ}& 1& -\mathrm{EAZ}& \mathrm{EYZ}\\ -\mathrm{<figure-callout\; id="1"\; label="EBZ\; EAZ"\; filenames="HDA0000130018350000051.png"\; state="\{\{state\}\}">EBZ</figure-callout>}& \mathrm{EAZ}& 1& \mathrm{Zm}+\mathrm{<figure-callout\; id="0"\; label="EZZ"\; filenames="HDA0000130018350000051.png"\; state="\{\{state\}\}">EZZ</figure-callout>}\\ 0& 0& 0& 0\end{array}\right].$

Wherein, Xz, Yz, Zz are that Z axle initial point is with respect to the coordinate figure of R reference frame;

AOZ and BOZ then are the site error of verticality between Y and X-axis in the relative R reference frame of Z axle;

EXZ, EYZ, EZZ, EAZ, EBZ and ECZ then are 6 component error amounts of Z linear movement axle, and Zm represents that Z linear movement axle is with respect to the displacement of its initial point.

In addition, the main shaft of five instrument machineries (Holder) coordinate system, and be folded in the probe (Probe) of main shaft with respect to the geometric error model of Z axis coordinate system, then be respectively:

$T_h^z=\left[\begin{array}{cccc}1& 0& 0& \mathrm{<figure-callout\; id="0"\; label="Xh"\; filenames="HDA0000130018350000051.png"\; state="\{\{state\}\}">Xh</figure-callout>}\\ 0& 1& 0& 0\\ 0& 0& 1& \mathrm{<figure-callout\; id="0"\; label="Zh"\; filenames="HDA0000130018350000051.png"\; state="\{\{state\}\}">Zh</figure-callout>}\\ 0& 0& 0& 1\end{array}\right],$

$T_p^h=\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& 1& 0& 0\\ 0& 0& 1& \mathrm{<figure-callout\; id="0"\; label="Zp"\; filenames="HDA0000130018350000051.png"\; state="\{\{state\}\}">Zp</figure-callout>}\\ 0& 0& 0& 1\end{array}\right],$

Wherein Xh is the original displacement of the relative Z axis coordinate system of main shaft with Zh, and Zp then lies in the side-play amount of Z-direction for the relative main shaft coordinate of probe.

In the embodiment of the invention five instrument machinery wherein an A rotation axis can be expressed as with respect to the geometric error model of X-axis coordinate system:

$T_a^x=\left[\begin{array}{cccc}1& 0& 0& \mathrm{<figure-callout\; id="0"\; label="Xa"\; filenames="HDA0000130018350000051.png"\; state="\{\{state\}\}">Xa</figure-callout>}\\ 0& 1& 0& \mathrm{<figure-callout\; id="0"\; label="Ya"\; filenames="HDA0000130018350000051.png"\; state="\{\{state\}\}">Ya</figure-callout>}\\ 0& 0& 1& \mathrm{<figure-callout\; id="0"\; label="Za"\; filenames="HDA0000130018350000051.png"\; state="\{\{state\}\}">Za</figure-callout>}\\ 0& 0& 0& 1\end{array}\right]\left[\begin{array}{cccc}1& \mathrm{<figure-callout\; id="0"\; label="COA\; BOA"\; filenames="HDA0000130018350000051.png"\; state="\{\{state\}\}">COA</figure-callout>}& \mathrm{BOA}& 0\\ \mathrm{<figure-callout\; id="1"\; label="COA"\; filenames="HDA0000130018350000051.png"\; state="\{\{state\}\}">COA</figure-callout>}& 1& 0& \mathrm{YOA}\\ -\mathrm{<figure-callout\; id="0"\; label="BOA"\; filenames="HDA0000130018350000051.png"\; state="\{\{state\}\}">BOA</figure-callout>}& 0& 1& \mathrm{<figure-callout\; id="0"\; label="ZOA"\; filenames="HDA0000130018350000051.png"\; state="\{\{state\}\}">ZOA</figure-callout>}\\ 0& 0& 0& 1\end{array}\right]$

$\left[\begin{array}{cccc}1& \mathrm{EBA}\&times;\mathrm{Sae}-\mathrm{ECA}\&times;\mathrm{Cae}& \mathrm{ECA}\&times;\mathrm{Sae}+\mathrm{Eba}\&times;\mathrm{Cae}& \mathrm{EXA}\\ \mathrm{ECA}& \mathrm{Cae}& -\mathrm{Sae}& \mathrm{EYA}\\ -\mathrm{EBA}& \mathrm{<figure-callout\; id="0"\; label="Sae\; Cae\; EZA"\; filenames="HDA0000130018350000051.png"\; state="\{\{state\}\}">Sae</figure-callout>}& \mathrm{Cae}& \mathrm{EZA}\\ 0& 0& 0& 0\end{array}\right]$

Wherein, Xa, Ya, Za are that A axle initial point is with respect to the coordinate figure of X-axis reference frame;

YOA and ZOA are that A rotation axis actual installation center and desired center are in the linear deflection amount of Y, Z direction;

COA and BOC install Y, Z between centers verticality site error in axis and the X-axis reference frame for the A rotation axis;

BOA and COA install the verticality site error of Y, Z axle in axis and the X-axis reference frame for the A rotation axis

EXA, EYA, EZA, EAA, EBA and ECA then are 6 component error amounts of A rotation axis;

Sae=sin (Am+EAA), Cae=cos (Am+EAA), and Am represents the orientation angle of A rotation axis.

As for another C rotation axis of instrument machinery, its coordinate origin is arranged on the intersection point of C rotation axis and instrument machinery spindle axis line, and its geometric error model can be expressed as:

$T_c^a=\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& 1& 0& 0\\ 0& 0& 1& \mathrm{<figure-callout\; id="0"\; label="Zc"\; filenames="HDA0000130018350000051.png"\; state="\{\{state\}\}">Zc</figure-callout>}\\ 0& 0& 0& 1\end{array}\right]\left[\begin{array}{cccc}1& 0& \mathrm{<figure-callout\; id="0"\; label="BOC\; XOC"\; filenames="HDA0000130018350000051.png"\; state="\{\{state\}\}">BOC</figure-callout>}& \mathrm{XOC}\\ 0& 1& -\mathrm{AOC}& \mathrm{YOC}\\ -\mathrm{<figure-callout\; id="1"\; label="BOC\; AOC"\; filenames="HDA0000130018350000051.png"\; state="\{\{state\}\}">BOC</figure-callout>}& \mathrm{AOC}& 1& 0\\ 0& 0& 0& 1\end{array}\right]$

$\left[\begin{array}{cccc}\mathrm{Cce}& -\mathrm{Sce}& \mathrm{EBC}& \mathrm{EXC}\\ \mathrm{Sce}& \mathrm{Cce}& -\mathrm{EAC}& \mathrm{EYC}\\ \mathrm{EAC}\&times;\mathrm{Sce}-\mathrm{EBC}\&times;\mathrm{Cce}& \mathrm{EAC}\&times;\mathrm{Cce}+\mathrm{EBC}\&times;\mathrm{<figure-callout\; id="1"\; label="Sce"\; filenames="HDA0000130018350000051.png"\; state="\{\{state\}\}">Sce</figure-callout>}& 1& \mathrm{<figure-callout\; id="0"\; label="EZC"\; filenames="HDA0000130018350000051.png"\; state="\{\{state\}\}">EZC</figure-callout>}\\ 0& 0& 0& 0\end{array}\right]$

Wherein, Zc is that C axle initial point is with respect to the coordinate figure of A axis coordinate system;

XOC and YOC are that C rotation axis actual installation center and desired center are in the linear deflection amount of X, Y-direction;

AOC and BOC install in axis and the A axis coordinate system site error of verticality between X, Y-axis for the C rotation axis;

EXC, EYC, EZC, EAC, EBC and ECC then are 6 component error amounts of C rotation axis;

Sce=sin (Cm+ECC), Cce=cos (Cm+ECC), and Cm represents the orientation angle of C rotation axis.

Because the present invention is positioned at the R-test measurer on the default location that passes through the C rotation axis on the board, just the absolute workpiece coordinate with instrument machinery is located on the intersection point of C rotation axis and instrument machinery spindle axis line zero point, but this intersection point is not the null position of the absolute workpiece coordinate of instrument machinery itself, therefore arranging of R-test measurer can be introduced standard ball site error (Ball Position Errors) in addition, and its geometric error model is as follows:

$T_w^c=\left[\begin{array}{cccc}1& 0& 0& \mathrm{Xw}+\mathrm{<figure-callout\; id="0"\; label="XOW"\; filenames="HDA0000130018350000051.png"\; state="\{\{state\}\}">XOW</figure-callout>}\\ 0& 1& 0& \mathrm{Yw}+\mathrm{<figure-callout\; id="0"\; label="YOW"\; filenames="HDA0000130018350000051.png"\; state="\{\{state\}\}">YOW</figure-callout>}\\ 0& 0& 1& \mathrm{Zw}+\mathrm{<figure-callout\; id="0"\; label="ZOW"\; filenames="HDA0000130018350000051.png"\; state="\{\{state\}\}">ZOW</figure-callout>}\\ 0& 0& 0& 1\end{array}\right],$

Wherein Xw, Yw, with Zw be the standard ball center at the coordinate figure of C axis coordinate system, XOW, YOW and ZOW then are that standard ball is in the position offset error of C axis coordinate system X, Y and Z-direction.

Set via aforesaid geometric error model, illustrated embodiment of the present invention always has 44 error terms, and workpiece (Workpiece) coordinate system and probe (Prode) coordinate system can be expressed as respectively with respect to the relativeness of R reference frame:

^rT _w＝ ^rT _x ^xT _a ^aT _c ^cT _w

^rT _p＝ ^rT _y ^yT _z ^zT _h ^hT _p

In theory, the spindle end coordinate system of five instrument machineries should be identical on hypothetical machine with the work end coordinate system, yet, on actual machine, can have geometric error between the two, as shown in Figure 5, the sphere centre coordinate of the standard ball of R-test measurer is the object end P of representative instrument machinery _w=[X _wY _wZ _w], and represent the tool ends end P of instrument machinery with the probe coordinate system _p=[X _tY _tZ _t] can represent with following formula respectively:

[P _w?1] ^T＝ ^rT _w[0?0?0?1] ^T

[P _p?1] ^T＝ ^rT _p[0?0?0?1] ^T

And the relative object of tool ends end coordinate system is sat up straight the site error P that mark ties up to the R reference frame _{E, r}(Δ Xp Δ Yp Δ Zp) is: P _{E, r}=P _w-P _p

Aforementioned location potential difference P _{E, r}(Δ Xp Δ Yp Δ Zp) also can be converted to the probe coordinate system with following formula:

[P _e，p?0] ^T＝( ^rT _p) ^-1[P _e，r?0]＝[ΔX _p?ΔX _p?XΔ _p?0] ^T

Simultaneously, the sphere centre coordinate of aforementioned R-test measurer is P _wVector of unit length [0 0 1] can be converted to the vectorial O of R reference frame _w, probe coordinate system P _pVector of unit length [0 0 1] can be converted to the vectorial O of R reference frame equally _p,

[O _w?0] ^T＝( ^rT _w- ^rT _w，ideal)[0?0?1?0] ^T

[O _p?0] ^T＝( ^rT _p- ^rT _p，ideal)[0?0?1?0] ^T

Wherein, ^rT _{W, ideal}With ^rT _{P, ideal}Be respectively ^rT _wWith ^rT _pCoordinate conversion matrix is (under the situation of hypothetical machine) when not considering geometric error, the indivedual transition matrixes with respect to reference frame of hypothetical machine workpiece coordinate system and tool coordinates system.

Therefore, tool coordinates system ties up to cutter error in pointing O under the reference frame with respect to workpiece coordinate _{E, r}(Δ Ip Δ Jp Δ Kp) is:

O _e，r＝O _w-O _p

By aforementioned setting, the geometric error model of five instrument machineries can be set up as following table listed, wherein, assembly error (Overall Error) at directions X is Δ Xp, equal each error term and multiply by its dilution of precision (Error Gain, EG) summation is example with the ECX of directions X, and its error contribution to directions X (Error Contribution) is ECX * (Y _h-Y _z); In addition, following table also can be considered as the sensitivity analysis table (Sensitivity Analysis Table) of geometric error.

Finish after the geometric error model of five instrument machineries, the present invention uses the R-test measurer to measure data necessary, comprise site error and the ball position error (Ball Postion Error) of X, Y and Z-direction, just can use least square method (Least Square Method) afterwards and calculate site error and the ball position error that assessment can't directly measure.

Because each error term all has its error contribution for the site error of X, Y and Z-direction, least square method is the data q that learns by measuring, and the unknown parameter a of linear dependence shows its relation with following formula:

q＝Ha+e，

Make its correlation parameter quantity be respectively m and n, then q is the measurement vector of m * 1, and a is the unknown errors vector of n * 1, and e is the noise vector of m * 1, and H is the error contribution matrix of m * n, can be expressed as follows respectively:

q＝[q _1，x…q _m，x?q _1，y…q _m，y?q _1，z…q _m，z] ^T

a＝[a ₁…a _n] ^T

Error contribution function (Error Gain Functions) f in the middle of the error contribution matrix H _{I, x}(p _j), f _{I, y}(p _j) and f _{I, z}(p _j) represent that each error term is for the influence of ad-hoc location Pj.

Parameter vector to be found the solution

Be the summation of each side-play amount least square, so its cost function (Cost Function) is:

$E\left(\tilde{a}\right)=e^{T}e={(q-H\tilde{a})}^T(q-H\tilde{a}).$

An ideal solution can occur in the minimum value of cost function, just

$\frac{\&PartialD;E\left(\tilde{a}\right)}{\&PartialD;\tilde{a}}=2H^{T}H\tilde{a}-2H^{T}q=0,$

Therefore can try to achieve parameter vector to be found the solution

For

$\tilde{a}={\left(H^{T}H\right)}^{-1}{H}^{T}q,$

Because least square method can only be used for estimating the constant error item irrelevant with the kinematic axis movement position, the error term that the present invention is less with the error contribution amount, 21 error terms that comprise three linear movement axles, and 12 error terms of two rotation axiss, amount to 33 error terms and ignore, and the geometric error model of five instrument machineries can be simplified as following table:

Through after simplifying procedures, 8 alignment error items of the geometric error Xiang Yousan of required estimation ball position error term and two rotation axiss, amount to 11 geometric error items, can utilize least square method to find the solution equally, because the computing of least square method generally as described above, and be present The common calculation methods, intend not giving unnecessary details detailed solution procedure at this.

A preferred embodiment provided by the present invention, its concrete steps comprise:

Utilize the assembly error that the R-test measurer can actual measurement First Five-Year Plan axle instrument machinery, present embodiment is example with Heidenhain iTNC, the mechanism parameter of aforementioned five instrument machineries, comprise that the standard ball center is at coordinate figure Xw, Yw and the Zw of C axis coordinate system, C axle initial point is with respect to the coordinate figure Zc of reference frame, and probe and main shaft coordinate lie in the side-play amount Zp of Z-direction, its actual measurement or known numerical value such as following table:

Assembly error measure as for aforementioned five instrument machineries, the present invention carries out according to the specifications of surveys of ISO/CD10791-6 that ISO (International Standards Organization) is formulated, wherein, the K4 path of measuring route to put down in writing in the aforementioned standard: tilt and rotate two rotation axiss angle changing simultaneously, and with five moving together moving paths, the most suitable the present invention is as the measuring route of assembly error thereupon for three linear axes.

Finish the formula that can utilize least square method after the abovementioned steps, to find the solution each geometric error item, just will measure the assembly error of gained and the geometric error model of known mechanism parameter substitution aforementioned simplified and calculate assembly error delta X _p, Δ Y _pWith Δ Z _pAnd obtain measuring vectorial q, and set an ad-hoc location Pj (X, Y, Z, A, C) _mTo calculate each error contribution function (Error Gain Functions) f _{I, x}(p _j), f _{I, y}(p _j) and f _{I, z}(p _j), the contribute matrix of the substitution error of calculation afterwards H.

Aforementioned this process also can be by means of operational software, as MATLAB, and with rapid solving, the result of calculation of present embodiment such as following table:

Actual measurement is compared with the result who utilizes abovementioned steps of the present invention to estimate, its result as shown in Figure 5, all within 12 microns (μ m), precision is quite high for the deviation range of X, Y and Z axle.

If by the ISO/CD10791-6 standard defined path K1 and K2 as measuring route with checking the present invention, its deviation range will be greater than 15 microns (μ m), demonstration the present invention adopts the K4 path to measure to help to improve the precision of estimating the result really; Certainly, the present invention also be suitable for other five with moving paths as two side paths.

Comprehensively aforementioned, the present invention sets up easy geometric error model, with the defined K4 of ISO/CD10791-6 path, and after adopting the R-test measurer to accurately measure, use the geometric error item that least square method comes quick estimation to measure, be conducive to follow-up precision of carrying out five instrument machineries and improve operation.

Above-described specific embodiment; purpose of the present invention, technical scheme and beneficial effect are further described; institute is understood that; the above only is specific embodiments of the invention; be not limited to the present invention; within the spirit and principles in the present invention all, any modification of making, be equal to replacement, improvement etc., all should be included within protection scope of the present invention.

Claims (4)

1. the geometric error appraisal procedure of five instrument machineries is characterized in that, can be applicable to the First Five-Year Plan axis processing machine, and its step includes:

A, utilize one to have a probe and the R-test measurer of a standard ball, this probe is installed in a main shaft of this five axis processing machine, and this standard ball is installed in a board of this five axis processing machine, and with the centre of sphere of this standard ball initial point as a reference frame;

B, according to the First Five-Year Plan axle with moving path as measuring route, use the assembly error of these these five instrument machineries of R-test gage measuring;

C, with the measured assembly error that obtains of preceding step, and these five known mechanism parameter substitution one geometric error model of instrument machinery, utilize least square method to find the solution and obtain the value of listed 11 the geometric error items of this geometric error model, wherein, this geometric error model such as following table:

Wherein, Δ Xp, Δ Yp, Δ Zp is X, Y, the assembly error of Z direction, equal the summation that each error term multiply by its dilution of precision, XOW, YOW, ZOW for this standard ball arrange the position with respect to a workpiece actual zero point position of these five instrument machineries at X, the site error of Y and the skew of Z direction, YOA and ZOA are that a rotation axis of these five instrument machineries is at Y, the installation side-play amount of Z direction, BOA is the relative Y of this rotation axis with COA, the verticality site error of Z axle, XOC and YOC are that another rotation axiss of this five instrument machineries is at X, the installation side-play amount of Y-direction, BOA is the relative Y of this another rotation axis with COA, the verticality site error of Z axle, and C _a=cos (A _m), C _c=cos (C _m), S _a=sin (A _m), S _c=sin (C _m), Am and Cm are the orientation angle of this rotation axis and this another rotation axis.

2. the geometric error appraisal procedure of five instrument machineries according to claim 1 is characterized in that, these five is the K4 path of ISO/CD10791-6 institute standard with moving path among the step b.

3. the geometric error appraisal procedure of five instrument machineries according to claim 1, it is characterized in that, the least square method of steps d comprises calculates the assembly error, be that each error term multiply by the summation of its dilution of precision and obtains measuring vector, and set an ad-hoc location calculating each error contribution function, the contribute matrix of the substitution error of calculation afterwards and finding the solution.

4. the geometric error appraisal procedure of five instrument machineries according to claim 1 is characterized in that, these five instrument machineries have three linear axes and two rotation axiss.

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