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

Geometric error evaluation method of five-axis tool machine

Technical Field

The invention relates to a tool machine, in particular to an evaluation method capable of measuring and calculating the geometric error of a five-axis tool machine, which has the advantages of simple construction and high accuracy.

Background

The error sources of the tool machine are mainly classified into structural-induced Errors (structural-induced Errors), driving-induced Errors (driving-induced Errors), and static Errors (Quasi-static Errors), wherein the static Errors account for about 70% of the mechanical error amount of the tool machine, and the main source of the static Errors is Geometric Errors (geometrical Errors), in other words, accurately measuring the Geometric Errors of the tool machine is a critical step for improving the machining accuracy of the tool machine.

Since the five-axis tool machine has a complex structure and it is very difficult to accurately measure the partial geometric error term, the measurement standard program of the five-axis tool machine, such as ISO/10791-6, first measures the assembly geometric error by using a measuring tool, such as an R-Test measuring tool, and then roughly estimates the partial geometric error term of the rotating shaft, which is time-consuming in the overall process and not accurate enough in the estimation result, thus it is not beneficial to the subsequent error compensation and accuracy improvement of the five-axis tool machine, and further improvement is necessary.

Disclosure of Invention

In view of the above-mentioned drawbacks, a primary object of the present invention is to provide a method for evaluating geometric errors of a five-axis machine tool, so that evaluation calculations of geometric error terms can be performed quickly and accurately.

The invention provides a geometric error evaluation method of a five-axis tool machine, which can be applied to a five-axis processing machine and comprises the following steps:

(a) utilizing an R-test measuring tool with a probe and a standard ball, wherein the probe is arranged on a main shaft of the five-shaft processing machine, the standard ball is arranged on a machine table of the five-shaft processing machine, and the center of the standard ball is used as the origin of a reference coordinate system;

(b) measuring the assembly error of the five-axis tool machine by using the R-test measuring tool according to a five-axis same path as a measuring path;

(c) and substituting the assembly error measured in the previous step and the known mechanism parameters of the five-axis tool machine into a geometric error model, and solving by using a least squares method to obtain the values of 11 geometric error terms listed in the geometric error model.

Therefore, the invention utilizes the R-test measuring tool to quickly and accurately measure the three-dimensional space assembly error by using the K4 five-axis same path, and applies the simple geometric error model only comprising 11 geometric error terms, and can accurately estimate the 11 geometric error terms by matching with the least squares method, thereby being used as a five-axis tool machine to carry out subsequent precision improvement operation.

In addition, the five-axis same path applied by the invention is preferably the K4 path specified in ISO/CD 10791-6.

Drawings

FIG. 1 is a schematic diagram of the model definition of the geometric error of the X-axis linear motion according to the present invention.

FIG. 2 is a schematic diagram of the model definition of the geometric error of the rotational motion axis of the present invention C.

FIG. 3 is a schematic view of a coordinate system formed by erecting an R-test measuring tool on a five-axis tool machine according to the present invention.

FIG. 4 is a schematic representation of the geometric error measured by the R-test gauge of the present invention.

FIG. 5 is a graph comparing measured and calculated error values using the K4 path in accordance with a preferred embodiment of the present invention.

[ description of main element symbols ]

Xr, Yr, Zr: r axial of the reference coordinate system;

xx, Yx, Zx: mechanical parameters of the X-axis;

xy, Yy, Zy: mechanical parameters of the Y axis;

xz, Yz, Zz: mechanical parameters of the Z axis;

and Zc: mechanical parameters of the C axis;

xa, Ya, Za: mechanism parameters of the A axis;

xw, Yw, Zw: the center of the standard ball is in the coordinate value of the C-axis coordinate system;

EXX, EYX, EZX, EAX, EBX, ECX: the component error amount on the X-axis;

EXY, EYY, EZY, EAY, EBY, ECY: the component error amount of the Y axis;

EXZ, EYZ, EZZ, EAZ, EBZ, ECZ: the component error amount of the Z axis;

EXC, EYC, EZC, EAC, EBC, ECC: the component error amount of the C axis;

EXA, EYA, EZA, EAA, EBA, ECA: the component error amount of the a axis;

xm: the displacement of the X-axis relative to its origin;

ym: displacement of the Y-axis relative to its origin;

and Zm: the displacement of the Z-axis relative to its origin;

xx, Yx, Zx: mechanical parameters of the X-axis;

xy, Yy, Zy: mechanical parameters of the Y axis;

xz, Yz, Zz: mechanical parameters of the Z axis;

cm: the positioning angle of the C axis;

am, and (2): the positioning angle of the A axis;

XOC, YOC: the mounting offset of the C axis in the direction X, Y;

YOA, ZOA: the installation offset of the A axis in the direction of Y, Z;

AOZ, BOZ: the perpendicularity position error of the Z axis relative to the X axis and the Y axis;

AOC, BOC: perpendicularity position error of the C axis relative to the X, Y axis;

BOA, COA: perpendicularity position error of the A axis relative to the Y, Z axis;

COX: vertical position error of the X axis relative to the C axis;

COA, BOC: the perpendicularity position error of the axis A relative to the axis Y, Z in the X-axis reference coordinate system;

xh, Zh: the original displacement of the principal axis relative to the Z axis;

and (4) Zp: the offset of the probe in the Z-axis direction of the main axis coordinate system;

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

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

P_e，r: the position error of the tool end coordinate system relative to the object end coordinate system in the reference coordinate system.

Detailed Description

The technical content and the characteristics of the invention will be described in detail by the listed embodiments and the attached drawings, wherein:

FIG. 1 is a schematic diagram of the model definition of the geometric error of the X-axis linear motion according to the present invention;

FIG. 2 is a schematic diagram of the model definition of the geometric error of the rotational axis of motion according to the present invention C;

FIG. 3 is a schematic view of a coordinate system formed by erecting an R-test measuring tool on a five-axis tool machine according to the present invention;

FIG. 4 is a schematic view of the assembly error measured by the R-test gauge of the present invention;

FIG. 5 is a graph comparing measured and calculated error values using the K4 path in accordance with a preferred embodiment of the present invention.

Referring to fig. 1, the geometric Error of the machine tool may define six Component Error terms (Component Errors) from a single linear motion axis, including three linear Error terms (Translational Error) and three rotational Error terms, where each two intersecting linear axes have a vertical position Error (locational Error), and taking the X linear motion axis of the machine tool as an example, the geometric Error model of the X coordinate system relative to the R reference coordinate system may be represented by a 4 × 4 Homogeneity Transformation Matrix (HTM) 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 and Zx are coordinate values of an X-axis origin (Home) relative to an R reference coordinate system, namely a mechanical Parameter (Kinematic Parameter);

COX is the position error of the perpendicularity between the X linear motion axis and the Y axis in the R reference coordinate system (i.e. the micro-rotation quantity of the two coordinate systems in the Z axis);

EXX, EYX, EZX, EAX, EBX and ECX are the error quantities of 6 elements of the X linear motion axis;

xm represents the displacement amount of the X linear motion axis with respect to its origin.

Referring to fig. 2, for a single rotational axis having 6 component error terms and 4 position error terms, the geometric error model of the C-axis coordinate system with respect to the R-reference coordinate system can be represented by a 4 × 4 Homogeneity Transform Matrix (HTM) as follows:

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

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

wherein Xc, Yc and Zc are coordinate values of a C-axis origin (Home) relative to an R reference coordinate system, namely a mechanical Parameter (Kinematic Parameter);

XOC and YOC are linear offsets of the actual installation center and the ideal center of the C rotating shaft in the X, Y direction;

the AOC and the BOC are perpendicularity position errors between the mounting axis of the C rotating shaft and X, Y shafts in an R reference coordinate system (namely, the micro-rotation quantity of the two coordinate systems in X, Y shafts);

EXC, EYC, EZC, EAC, EBC and ECC are 6 element error quantities of the C rotating shaft;

sce is sin (Cm + ECC), cco is cos (Cm + ECC), and Cm denotes a positioning angle of the C rotation axis.

The conventional five-axis tool machine has three linear motion axes and two rotational motion axes, so that the geometric errors of the three linear motion axes have 21 geometric error terms, the geometric errors of the two rotational motion axes have 20 geometric errors, which are 41 geometric error terms in total, and the geometric error models of the remaining linear motion axes and rotational motion axes can be represented by the 4 × 4 Homogeneity Transform Matrix (HTM).

In a preferred embodiment of the present invention, the R-test measuring tool is used to measure the error of the five-axis tool machine, and the R-test measuring tool includes a 3D probe (including three vertical position sensors) disposed on the spindle of the tool machine, and a Master Ball (Master Ball) disposed on the stage of the tool machine, and the center of the Master Ball is used as the origin of the R reference coordinate system, so that the motion process of the five-axis tool machine forms a closed mechanical chain, as shown in fig. 3, the error of the five-axis tool machine will be reflected on the 3D probe.

The invention installs the R-test measuring tool in the coordinate system formed by the five-axis tool machine, wherein the geometric error model of the X linear motion axis is as the formula, and the geometric error model of the Y linear motion axis relative to the R reference coordinate system is as follows:

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

where EXY, EYY, EZY, EAY, EBY and ECY are the 6 element error quantities for the Y linear motion axis, Ym represents the displacement of the Y linear motion axis from its origin, and the model assumes that there is no perpendicular axis between the Y axis and the C axis of the reference coordinate system.

For the geometric error model of the Z linear motion axis with respect to the R reference frame, then:

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

wherein Xz, Yz and Zz are coordinate values of a Z-axis origin relative to an R reference coordinate system;

the AOZ and the BOZ are position errors of the Z axis relative to the perpendicularity between the Y axis and the X axis in the R reference coordinate system;

EXZ, EYZ, EZZ, EAZ, EBZ and ECZ are the 6 element error amounts of the Z linear motion axis, Zm represents the displacement amount of the Z linear motion axis with respect to its origin.

In addition, the geometric error models of the spindle (Holder) coordinate system of the five-axis tool machine and the Probe (Probe) interposed between the spindles with respect to the Z-axis coordinate system are:

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

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

wherein Xh and Zh are the original displacement of the main shaft relative to the Z-axis coordinate system, and Zp is the offset of the probe relative to the Z-axis coordinate system in the Z-axis direction.

In the embodiment of the invention, a geometric error model of one A rotating shaft of the five-axis tool machine relative to an X-axis coordinate system can be expressed as follows:

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

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

wherein Xa, Ya and Za are coordinate values of the origin of the A axis relative to the reference coordinate system of the X axis;

YOA and ZOA are linear offset of the actual installation center and the ideal center of the A rotating shaft in the Y, Z direction;

COA and BOC are perpendicularity position errors between the mounting axis of the A rotating shaft and Y, Z axes in the X-axis reference coordinate system;

BOA and COA are perpendicularity position errors of the A rotating shaft installation axis and Y, Z axes in an X-axis reference coordinate system

EXA, EYA, EZA, EAA, EBA and ECA are the error amounts of 6 elements of the rotating shaft A;

sae-sin (Am + EAA), Cae-cos (Am + EAA), and Am denotes the positioning angle of the a rotation axis.

Regarding another C-axis of rotation of the tool machine, the origin of the coordinate system is set at the intersection point of the C-axis of rotation and the axis of the spindle of the tool machine, and the 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 a coordinate value of the C-axis origin relative to the A-axis coordinate system;

XOC and YOC are linear offsets of the actual installation center and the ideal center of the C rotating shaft in the X, Y direction;

the AOC and the BOC are position errors of perpendicularity between the mounting axis of the C rotating shaft and the X, Y shaft in the A shaft coordinate system;

EXC, EYC, EZC, EAC, EBC and ECC are 6 element error quantities of the C rotating shaft;

sce is sin (Cm + ECC), cco is cos (Cm + ECC), and Cm denotes a positioning angle of the C rotation axis.

Because the R-test measuring tool is positioned at the default Position of the machine platform passing through the C rotating shaft, namely the zero point of the absolute workpiece coordinate of the tool machine is arranged on the intersection point of the C rotating shaft and the axial lead of the main shaft of the tool machine, but the intersection point is not the zero point Position of the absolute workpiece coordinate of the tool machine, the setting of the R-test measuring tool can additionally introduce the standard Ball Position Errors (Ball Position Errors), and the 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, and Zw are coordinate values of the center of the standard sphere in the C-axis coordinate system, and XOW, YOW, and ZOW are position deviation errors of the standard sphere in the C-axis coordinate system X, Y and the Z-axis direction.

Through the aforementioned geometric error model setting, the illustrated embodiment of the present invention has a total of 44 error terms, and the relative relationship between the Workpiece (Workpiece) coordinate system and the probe (Prode) coordinate system with respect to the R-reference coordinate system can be respectively expressed as:

^rT_w＝^rT_x ^xT_a ^aT_c ^cT_w

^rT_p＝^rT_y ^yT_z ^zT_h ^hT_p

theoretically, the spindle end coordinate system and the workpiece end coordinate system of a five-axis tool machine should be identical on an ideal machine, however, there will be geometric errors between them on an actual machine, as shown in fig. 5, and the center coordinate system of the reference sphere of the R-test gauge represents the target end P of the tool machine_w＝[X_wY_wZ_w]And the coordinate system of the probeTool end P of watch tool machine_p＝[X_tY_tZ_t]Can be expressed by the following formulas, 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 position error P of the tool end coordinate system relative to the object end coordinate system in the R reference coordinate system_e，r(Δ Xp Δ Yp Δ Zp) is: p_e，r＝P_w-P_p。

The position difference P_e，r(Δ Xp Δ Yp Δ Zp) can also be converted to the probe coordinate system using the following equation:

[P_e，p 0]^T＝(^rT_p)^-1[P_e，r 0]＝[ΔX_p ΔX_p XΔ_p 0]^T

meanwhile, the sphere center coordinate system P of the R-test measuring tool_wUnit vector of [ 001]Vector O convertible to R reference coordinate system_wProbe coordinate system P_pUnit vector of [ 001]Vector O which can likewise be converted into the R reference coordinate system_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，idealand^rT_p，idealare respectively as^rT_wAnd^rT_pcoordinate transformation matrix when geometric errors are not taken into account (i.e. in the case of an ideal machine), the ideal machine workpiece coordinate system and the tool coordinate system are individually transformed matrices relative to the reference coordinate system.

Thus, the tool coordinate system is related to the tool pointing error O in the reference coordinate system of the workpiece coordinate system_e，r(Δ Ip Δ Jp Δ Kp) is:

O_e，r＝O_w-O_p

with the foregoing settings, a geometric Error model of a five-axis tool machine can be constructed as set forth in the following table, where the total Error (over Error) in the X-direction is Δ Xp, which is equal to the sum of each Error term multiplied by its Error Gain (EG), and the Error Contribution (Error Contribution) to the X-direction is ECX × (-Y) for the X-direction ECX as an example_h-Y_z) (ii) a In addition, the following Table can also be regarded as a Sensitivity Analysis Table (Sensitivity Analysis Table) of geometric errors.

After completing the geometric Error model of the five-axis tool machine, the present invention uses the R-test measuring tool to measure necessary data, including X, Y and the position Error and the ball position Error (ballpoint Error) in the Z-axis direction, and then a Least squares Method (Least Square Method) can be applied to calculate and evaluate the position Error and the ball position Error that cannot be directly measured.

Since each error term contributes to the position error of X, Y with respect to the Z-axis direction, the least squares method is to measure the known data q and to show the relationship with the linearly dependent unknown parameter a by the following formula:

q＝Ha+e，

let the number of relevant parameters be m and n, respectively, q is a m × 1 measurement vector, a is an n × 1 unknown error vector, e is an m × 1 noise vector, and H is an m × n error contribution matrix, which can be respectively expressed as follows:

q＝[q_1，x…q_m，x q_1，y…q_m，y q_1，z…q_m，z]^T

a＝[a₁…a_n]^T

error contribution function (Error Gain Functions) f among Error contribution matrix H_i，x(p_j)、f_i，y(p_j) And f_i，z(p_j) Indicating the effect of each error term on a particular location Pj.

Parameter vector to be solved

Is the sum of the least squares of the offsets, so the 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 will occur at the minimum of the cost function, i.e. at

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

Thus, the parameter vector to be solved can be obtained

Is composed of

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

Because the least squares method can only be used for estimating the constant error term which is irrelevant to the movement position of the movement axis, the invention ignores 33 error terms with smaller error contribution, including 21 error terms of three linear movement axes and 12 error terms of two rotation axes, and can simplify the geometric error model of the five-axis tool machine as the following table:

after the procedure is simplified, the geometric error terms to be estimated include three ball position error terms and 8 installation error terms of two rotation axes, and the total number of the geometric error terms is 11, and the geometric error terms can be solved by using the least squares method, and since the operation of the least squares method is already outlined as above and is a currently common calculation method, detailed solving processes are not repeated here.

The invention provides a preferred embodiment, which comprises the following specific steps:

the R-test measuring tool can be used to actually measure the assembly error of a five-axis machine tool, in this embodiment, taking Heidenhain iTNC as an example, the mechanical parameters of the five-axis machine tool include the coordinate values Xw, Yw and Zw of the standard sphere center in the C-axis coordinate system, the coordinate value Zc of the C-axis origin with respect to the reference coordinate system, and the offset Zp of the probe and the main axis coordinate system in the Z-axis direction, and the actual measured or known values are as follows:

as for the measurement of the assembly error of the five-axis machine tool, the measurement is performed according to the measurement specification of ISO/CD10791-6, which is set by the international organization for standardization, wherein the measurement path is defined by the K4 path described in the specification: the five-axis co-motion path that the two rotating shafts are inclined and rotated to change the angle simultaneously and the trilinear shaft co-moves with the rotating shafts is most suitable for being used as the measuring path of the assembly error.

After the above steps are completed, the formula of the least squares method can be used to solve each geometric error term, that is, the measured assembly error and the known mechanism parameters are substituted into the simplified geometric error model to calculate the assembly error Δ X_p、ΔY_pAnd Δ Z_pObtaining a measurement vector q and setting a specific position 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) And then substituted into the calculated error contribution matrix H.

The foregoing process can also be solved quickly by using computing software, such as MATLAB, and the calculation results of this embodiment are as follows:

comparing the actual measurement with the result estimated by the previous steps of the present invention, the deviation of X, Y from the Z axis is within 12 microns (μm), as shown in FIG. 5, and the accuracy is quite high.

If the paths K1 and K2 defined by the ISO/CD10791-6 specification are used as the measurement paths to verify the present invention, the deviation range will be larger than 15 micrometers (μm), which shows that the measurement using the K4 path in the present invention is indeed helpful to improve the accuracy of the estimation result; of course, the present invention is also applicable to other five-axis same path as the two-sided path.

In summary, the invention establishes a simple geometric error model, uses the K4 path defined by ISO/CD10791-6, and uses the R-test measuring tool to perform accurate measurement, and then uses the least square method to quickly estimate the geometric error item which can not be obtained by measurement, thereby being beneficial to the subsequent precision improvement operation of five-axis tool machinery.

The above-mentioned embodiments are intended to illustrate the objects, technical solutions and advantages of the present invention in further detail, and it should be understood that the above-mentioned embodiments are only exemplary embodiments of the present invention, and are not intended to limit the present invention, and any modifications, equivalents, improvements and the like made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (4)

1. A method for evaluating geometric errors of a five-axis machine tool, which is applicable to a five-axis machine tool, comprises the following steps:

a. utilizing an R-test measuring tool with a probe and a standard ball, wherein the probe is arranged on a main shaft of the five-shaft processing machine, the standard ball is arranged on a machine table of the five-shaft processing machine, and a sphere center of the standard ball is used as an origin of a reference coordinate system;

b. measuring the assembly error of the five-axis tool machine by using the R-test measuring tool according to a five-axis same path as a measuring path;

c. substituting the assembly error measured in the previous step and the known mechanism parameters of the five-axis tool machine into a geometric error model, and solving by using a least squares method to obtain the values of 11 geometric error terms listed in the geometric error model, wherein the geometric error model is as follows:

wherein Δ Xp, Δ Yp, Δ Zp are total errors in X, Y, Z directions, which are equal to the sum of error terms multiplied by error amplification factors thereof, XOW, YOW, and ZOW are position errors in which the standard ball is disposed at a position shifted in X, Y and Z directions with respect to an absolute zero position of a workpiece of the five-axis tool machine, YOA and ZOA are installation shift amounts in a Y, Z direction of a rotational axis of the five-axis tool machine, BOA and COA are perpendicularity position errors of the rotational axis with respect to Y, Z axes, XOC and YOC are installation shift amounts in a X, Y direction of another rotational axis of the five-axis tool machine, BOA and COA are perpendicularity position errors of the another rotational axis with respect to Y, Z axes, and C and_a＝cos(A_m)，C_c＝cos(C_m)，S_a＝sin(A_m)，S_c＝sin(C_m) And Am and Cm are the positioning angles of the rotating shaft and the other rotating shaft.

2. The five-axis tool machine geometric error evaluation method according to claim 1, wherein the five-axis common path in step b is a K4 path specified in ISO/CD 10791-6.

3. The method of claim 1, wherein the least squares method of step d includes calculating the total error, i.e. the sum of each error term multiplied by its error magnification factor to obtain a measurement vector, and setting a specific position to calculate each error contribution function, and then substituting into the calculated error contribution matrix to solve.

4. The five-axis tool machine geometric error evaluation method according to claim 1, wherein the five-axis tool machine has three linear axes and two rotational axes.

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