CN103809513A - Error verification method of CA oscillating structure five-axis machine tool - Google Patents

Abstract

The invention relates to the technical field of numerical control, and specifically relates to an error verification method of a CA oscillating structure five-axis machine tool. The error verification of a CA oscillating five-axis machine tool is finished in a high-efficient manner by use of a simple measuring device, the deviation direction of the measuring device, and a meter checking mode. The structure of a five-axis machine tool is analyzed through an error-free kinematic model and an error-containing kinematic model, by combining with the motion interval and the motion direction of a turning shaft, the mobile direction of a measuring point is analyzed, and the mobile direction of each compensation amount needed by actual machine tool error correction is solved so as to finish correction of machine tool structure error parameters. According to the invention, simple measuring devices such as a verification rod and the like are utilized, and the method provided by the invention can be applied to obtaining the deviation of each error item through effective and accurate measuring.

Description

A kind of method of calibration of CA yaw structure five-axis machine tool error

Technical field

The present invention relates to fields of numeric control technique, specifically a kind of method of calibration of CA yaw structure five-axis machine tool error.

Background technology

To have processing precise degree high due to it for 5-shaft linkage numerical control lathe, and soon and larger dirigibility, the plurality of advantages such as economic benefit height, all have a wide range of applications in each fields such as electric power, boats and ships, Aero-Space speed.High precision Double swing head is as the critical component in five-axis linkage machine tools, and its development level has become an important indicator weighing five-axis machine tool performance.

In the time carrying out the assembling of high precision CA yaw five-axis machine tool, guarantee that two rotating shaft center are on the position of design, it is very difficult making in addition main shaft rotation centerline overlap completely with C axle rotation centerline, can have deviation.This five-axis machine tool accuracy error can cause the biasing of cutter heart point position, affects processing effect.For guaranteeing five axle machining precisioies, must complete these errors are compensated by digital control system.In general existing system all can complete above compensation of error, but existing measuring method complicated operation, time-consuming and efficiency is low.For example, the CYCLE996 function of Siemens system can have been popped one's head in the measurement of error and the check and correction of structural parameters by high precision 3D, but the measurement scheme based on 3D probe, cost costliness, test period is long.

Summary of the invention

For the weak point of existing verification and optimization method, the invention provides a kind of for thering is the method for calibration of CA yaw structure five-axis machine tool, utilize the simple machine tool measuring equipment such as check bar, clock gauge, according to provided method, can whether there is error by verification five-axis machine tool, and have which kind of error, and the direction departing to shaft, to instruct the adjustment to lathe, eliminate machine tool error.

The technical scheme that the present invention adopted is for achieving the above object: a kind of method of calibration of CA yaw structure five-axis machine tool error, comprises the following steps:

Keeping C shaft angle degree is that 0, A axle forwards 90 degree to from 0 degree, keeps cutter heart point motionless, records the offset direction of cutter heart point; Keeping C shaft angle degree is that 0, A axle forwards-90 degree to from 0 degree, keeps cutter heart point motionless, records the offset direction of cutter heart point;

According to the offset direction of the above-mentioned cutter heart point of record, by searching offset direction and the δ l of cutter heart point at y, z axle _ywith δ l _zthe corresponding relation of offset direction, obtains δ l _ywith δ l _zoffset direction; Described δ l _yfor A axle rotation center to cutter shaft rotation center the error in y direction, described δ l _zfor A axle rotation center to cutter shaft rotation center the error in z direction;

According to δ l _y, δ l _zoffset direction, reconditioner bed structure in the other direction, eliminates error delta l _y, δ l _z;

Keeping A shaft angle degree is that 0, C axle forwards 360 degree to from 0 degree, keeps cutter heart point motionless, records the offset direction of cutter heart point; According to the situation that departs from of this cutter heart point of record, by searching offset direction and the δ h of cutter heart point at x, y axle _x+ δ l _xwith δ h _ythe corresponding relation of offset direction, obtains δ h _x+ δ l _x, δ h _yoffset direction; Described δ h _x+ δ l _xfor C axle rotation center to cutter shaft rotation center the error in x direction, described δ h _yfor C axle rotation center to A axle rotation center the error in y direction;

According to δ h _x+ δ l _x, δ h _yoffset direction, reconditioner bed structure in the other direction, eliminates error delta h _x+ δ l _x, δ h _y.

The described maintenance cutter heart is put in motionless situation, and the analog value of the linear axes amount of feeding is:

$\left[\begin{array}{c}X\\ Y\\ Z\end{array}\right]=\left[\begin{array}{c}{Q}_{x0}+(l_x+h_x)-(h_x+l_x)\cos {\mathrm{\θ}}_c+h_y{\sin \mathrm{\θ}}_c+l_y{\cos \mathrm{\θ}}_a\sin {\mathrm{\θ}}_c-({-L}_t+l_z){\sin \mathrm{\θ}}_a{\sin \mathrm{\θ}}_c\\ Q_{y0}+l_y+h_y-(h_x+l_x)\sin {\mathrm{\θ}}_c-h_y\cos {\mathrm{\θ}}_c-l_y{\cos \mathrm{\θ}}_a\cos {\mathrm{\θ}}_c+({-L}_t+l_z)\cos {\mathrm{\θ}}_c{\sin \mathrm{\θ}}_a\\ Q_{z0}-L_t+l_z-l_y\sin {\mathrm{\θ}}_a-({-L}_t+l_z)\cos {\mathrm{\θ}}_a\end{array}\right]---\left(9\right)$

Wherein, (h _x, h _y, h _z) be the offset vector of C axle rotation center to A axle rotation center, (l _x, l _y, l _z) be the offset vector of A axle rotation center to main shaft rotation center, (Q _x0, Q _y0, Q _z0) be ideally initial cutter heart point coordinate, L _tfor actual tool length.θ _c, θ _abe respectively the anglec of rotation of C axle, A axle.

The offset direction of described cutter heart point obtains by cutter heart point measurement equipment.

Described offset direction and the δ l of cutter heart point at y, z axle that search _ywith δ l _zthe corresponding relation of offset direction is:

In the situation that A axle forwards 90 degree to from 0 degree, if cutter heart point at the offset direction of y axle by just becoming negative, and cutter heart point at the offset direction of z axle always for just, in addition, in the situation that A axle forwards-90 degree to from 0 degree, cutter heart point at the offset direction of y axle always for negative, and cutter heart point at the offset direction of z axle by just bearing change, A axle rotation center departs from δ l to the Y-direction of cutter heart point _zfor on the occasion of, Z-direction departs from δ l _zfor negative value;

In the situation that A axle forwards 90 degree to from 0 degree, if cutter heart point is negative at the offset direction of y axle always, and cutter heart point at the offset direction of z axle by just becoming negative, in addition, in the situation that A axle forwards-90 degree to from 0 degree, cutter heart point at the offset direction of y axle by just becoming negative, and cutter heart point at the offset direction of z axle always for negative, A axle rotation center departs from δ l to the Y-direction of cutter heart point _yfor on the occasion of, Z-direction departs from δ l _zfor on the occasion of;

In the situation that A axle forwards 90 degree to from 0 degree, if cutter heart point at the offset direction of y axle by just bearing change, and cutter heart point is negative at the offset direction of z axle always, in addition, in the situation that A axle forwards-90 degree to from 0 degree, cutter heart point at the offset direction of y axle always for just, and cutter heart point at the offset direction of z axle by just becoming negative, A axle rotation center departs from δ l to the Y-direction of cutter heart point _zfor negative value, Z-direction departs from δ l _zfor on the occasion of;

In the situation that A axle forwards 90 degree to from 0 degree, if cutter heart point at the offset direction of y axle always for just, and cutter heart point at the offset direction of z axle by just bearing change, in addition, in the situation that A axle forwards-90 degree to from 0 degree, cutter heart point at the offset direction of y axle by just bearing change, and cutter heart point at the offset direction of z axle always for just, A axle rotation center departs from δ l to the Y-direction of cutter heart point _zfor negative value, Z-direction departs from δ l _zfor negative value.

Described cutter heart point is at offset direction and the δ h of x, y axle _x+ δ l _xwith δ h _ythe corresponding relation of offset direction is:

In the situation that C axle forwards 360 degree to from 0 degree, if cutter heart point at the offset direction of x axle by just becoming negative, and cutter heart point at the offset direction of y axle by just becoming negative, C axle departs from δ h to cutter heart point directions X _x+ δ l _xfor on the occasion of, and C axle rotation center is to the biasing δ h of A axle rotation center Y-direction _yfor negative value;

In the situation that C axle forwards 360 degree to from 0 degree, if cutter heart point at the offset direction of x axle by just bearing change, and cutter heart point at the offset direction of y axle by just becoming negative, C axle departs from δ h to cutter heart point directions X _x+ δ l _xfor on the occasion of, and C axle rotation center is to the biasing δ h of A axle rotation center Y-direction _yfor on the occasion of;

In the situation that C axle forwards 360 degree to from 0 degree, if cutter heart point at the offset direction of x axle by just bearing change, and cutter heart point at the offset direction of y axle by just bearing change, C axle departs from δ h to cutter heart point directions X _x+ δ l _xfor negative value, and C axle rotation center is to the biasing δ h of A axle rotation center Y-direction _yfor on the occasion of;

In the situation that C axle forwards 360 degree to from 0 degree, if cutter heart point at the offset direction of x axle by just becoming negative, and cutter heart point at the offset direction of y axle by just bearing change, C axle departs from δ h to cutter heart point directions X _x+ δ l _xfor negative value, and C axle rotation center is to the biasing δ h of A axle rotation center Y-direction _yfor negative value.

The present invention has following beneficial effect and advantage:

1. the present invention has set up CA yaw five-axis machine tool ideal model and the kinematics model with error simultaneously, supports for the research of lathe being provided to theoretical, makes the analysis of lathe science, effective more;

2. effectively whether verification CA yaw five-axis machine tool there is kinematics error;

3. the numerical relation while setting up machine tool motion between cutter heart point position deviation and each error term;

4. use the easy measuring equipments such as check bar, can apply the inventive method, effectively measure accurately the situation that departs from of each error term.

Accompanying drawing explanation

Fig. 1 is overview flow chart of the present invention;

Fig. 2 is CA yaw five-axis machine tool schematic diagram;

Fig. 3 is the CA yaw five-axis machine tool schematic diagram with error term;

Fig. 4 is that lathe has, motion state comparison diagram when error free;

Fig. 5 is that measuring equipment is measured cutter heart point offset direction schematic diagram.

Embodiment

Below in conjunction with drawings and Examples, the present invention is described in further detail.

1. error free kinematics model

As shown in Figure 2, the type lathe has C axle, two turning axles of A axle to error free CA yaw five-axis machine tool structure, respectively around Z axis linear axes, the rotation of X-axis linear axes.

Wherein, for C axle rotation center is to the offset vector of A axle rotation center, for A axle rotation center is to the offset vector of main shaft rotation center, be actual tool length.

According to CA swinging machine bed structure, utilize homogeneous coordinate transformation and five-axis machine tool Kinematic Model theory, set up following kinematics model:

Wherein, Rot is rotation matrix, and Trans is translation matrix, (Q _x, Q _y, Q _z) represent the cutter heart point position vector with respect to workpiece coordinate system, P _zfor the translatory distance of z direction, and the pass of itself and X, Y, the Z linear axes amount of feeding is:

$\left[\begin{array}{c}X\\ Y\\ Z\end{array}\right]=\left[\begin{array}{c}{P}_x+h_x+l_x\\ P_y+h_y+l_y\\ P_z+h_z+l_z-L_t\end{array}\right]---\left(2\right)$

Solving this model by direct kinematics obtains:

$\left[\begin{array}{c}{Q}_x\\ Q_y\\ Q_z\end{array}\right]=\left[\begin{array}{c}X-(l_x+h_x)+(h_x+l_x)\cos {\mathrm{\θ}}_c-h_y{\sin \mathrm{\θ}}_c-l_y{\cos \mathrm{\θ}}_a\sin {\mathrm{\θ}}_c+({-L}_t+l_z){\sin \mathrm{\θ}}_a{\sin \mathrm{\θ}}_c\\ Y-l_y-h_y+(h_x+l_x)\sin {\mathrm{\θ}}_c+h_y\cos {\mathrm{\θ}}_c+l_y{\cos \mathrm{\θ}}_a\cos {\mathrm{\θ}}_c-({-L}_t+l_z)\cos {\mathrm{\θ}}_c{\sin \mathrm{\θ}}_a\\ Z+L_t-l_z+l_y\sin {\mathrm{\θ}}_a+({-L}_t+l_z)\cos {\mathrm{\θ}}_a\end{array}\right]---\left(3\right)$

$\left[\begin{array}{c}X\\ Y\\ Z\end{array}\right]=\left[\begin{array}{c}{Q}_x+(l_x+h_x)-(h_x+l_x)\cos {\mathrm{\θ}}_c+h_y{\sin \mathrm{\θ}}_c+l_y{\cos \mathrm{\θ}}_a\sin {\mathrm{\θ}}_c-({-L}_t+l_z){\sin \mathrm{\θ}}_a{\sin \mathrm{\θ}}_c\\ Q_y+l_y+h_y-(h_x+l_x)\sin {\mathrm{\θ}}_c-h_y\cos {\mathrm{\θ}}_c-l_y{\cos \mathrm{\θ}}_a\cos {\mathrm{\θ}}_c+({-L}_t+l_z)\cos {\mathrm{\θ}}_c{\sin \mathrm{\θ}}_a\\ Q_z-L_t+l_z-l_y\sin {\mathrm{\θ}}_a-({-L}_t+l_z)\cos {\mathrm{\θ}}_a\end{array}\right]---\left(4\right)$

2. there is error kinematics model

Due to factors such as lathe assembling and lathe long-plays, can make each axle depart from original position, establishing C axle rotation center is (δ h to the error vector of A axle rotation center _x, δ h _y, δ h _z), A axle rotation center is (δ lx, δ ly, δ lz) to the error vector of main shaft rotation center.

According to CA swinging machine bed structure (accompanying drawing 3) and Kinematic Model theory with error, set up the kinematics model with error term as follows.

$\left[\begin{array}{c}{Q}_x\\ Q_y\\ Q_z\\ 1\end{array}\right]=\mathrm{Trans}(P_x,P_y,P_z)\×\mathrm{Rot}(Z,{\mathrm{\θ}}_c)\×\mathrm{Trans}(h_x+\mathrm{\δ}{h}_x,h_y+{\mathrm{\δh}}_y,h_z+\mathrm{\δ}{h}_z)\×\mathrm{Rot}(X,{\mathrm{\θ}}_a)\mathrm{Trans}(l_x+{\mathrm{\δl}}_x,\mathrm{ly}+{\mathrm{\δl}}_y,\mathrm{lz}+{\mathrm{\δl}}_z)\left[\begin{array}{c}0\\ 0\\ -L_t\\ 1\end{array}\right]---\left(5\right)$

Solve and obtain by direct kinematics:

$\left[\begin{array}{c}{Q}_x\\ Q_y\\ Q_z\end{array}\right]=\left[\begin{array}{c}X-(l_x+h_x+{\mathrm{\δl}}_x+{\mathrm{\δh}}_x)+(h_x+l_x+{\mathrm{\δh}}_x+{\mathrm{\δl}}_x)\cos {\mathrm{\θ}}_c-(h_y+{\mathrm{\δh}}_y)\sin {\mathrm{\θ}}_c-(l_y+{\mathrm{\δl}}_y)\cos {\mathrm{\θ}}_a\sin {\mathrm{\θ}}_c+({-L}_t+l_z+{\mathrm{\δl}}_z)\sin {\mathrm{\θ}}_a{\sin \mathrm{\θ}}_c\\ Y-(l_y+{\mathrm{\δl}}_y)-(h_y+{\mathrm{\δh}}_y)+(h_x+l_x+{\mathrm{\δl}}_x+{\mathrm{\δh}}_x)\sin {\mathrm{\θ}}_c+(h_y+{\mathrm{\δh}}_y)\cos {\mathrm{\θ}}_c+(l_y+{\mathrm{\δl}}_y)\cos {\mathrm{\θ}}_a\cos {\mathrm{\θ}}_c-({-L}_t+l_z+{\mathrm{\δl}}_z)\cos {\mathrm{\θ}}_c\sin {\mathrm{\θ}}_a\\ Z+L_t-(l_z+{\mathrm{\δl}}_z)+(l_y+{\mathrm{\δl}}_y)\sin {\mathrm{\θ}}_a+({-L}_t+l_z+{\mathrm{\δl}}_z)\cos {\mathrm{\θ}}_a\end{array}\right]---\left(6\right)$

Analyze this kinematics model, can draw, the CA yaw five-axis machine tool kinematics transformational relation with error and error parameter item δ h _zirrelevant, with single δ h _xwith δ l _xirrelevant, and with δ h _x+ δ l _xrelevant, in addition with δ h _y, δ l _y, δ l _zrelevant, the error parameter that affects CA yaw five-axis machine tool kinematics transformational relation is δ h _x+ δ l _x, δ h _y, δ l _y, δ l _z.Therefore, δ l can be set _x=0, δ h _z=0, only need measure all the other four error terms in addition, can determine the CA yaw five-axis machine tool kinematics transformational relation with error, lathe is proofreaied and correct, realize high precision processing.

3. measuring method

For CA yaw five-axis machine tool, in free from error situation, make C axle, A axle rotate corresponding angle θ _c, θ _a, calculate X, Y, the corresponding amount of feeding of the each linear axes of Z according to formula (4) formula, according to this kind of operation, the position vector of cutter heart point is constant.And if lathe is while existing error, the each linear axes of XYZ is still by (4) formula feeding, the position of cutter heart point has certain departing from, as shown in Figure 4.

If lathe reference position: the feeding of each linear axes is x _s, y _s, z _s, the feeding of C axle is θ _cs, the feeding of A axle is θ _as, the ideal coordinates that obtain under cutter heart point original state according to (3) formula are:

$\left[\begin{array}{c}{Q}_{x0}\\ Q_{y0}\\ Q_{z0}\end{array}\right]=\left[\begin{array}{c}{x}_s-(l_x+h_x)+(h_x+l_x)\cos {\mathrm{\θ}}_{\mathrm{cs}}-h_y{\sin \mathrm{\θ}}_{\mathrm{cs}}-l_y{\cos \mathrm{\θ}}_{\mathrm{as}}\sin {\mathrm{\θ}}_{\mathrm{cs}}+({-L}_t+l_z){\sin \mathrm{\θ}}_{\mathrm{as}}{\sin \mathrm{\θ}}_{\mathrm{cs}}\\ y_s-l_y-h_y+(h_x+l_x)\sin {\mathrm{\θ}}_{\mathrm{cs}}+h_y\cos {\mathrm{\θ}}_{\mathrm{cs}}+l_y{\cos \mathrm{\θ}}_{\mathrm{as}}\cos {\mathrm{\θ}}_{\mathrm{cs}}-({-L}_t+l_z)\cos {\mathrm{\θ}}_{\mathrm{cs}}{\sin \mathrm{\θ}}_{\mathrm{as}}\\ z_s+L_t-l_z+l_y\sin {\mathrm{\θ}}_{\mathrm{as}}+({-L}_t+l_z)\cos {\mathrm{\θ}}_{\mathrm{as}}\end{array}\right]---\left(7\right)$

According to (6) formula, the actual coordinate that obtains initial cutter heart point is:

$\left[\begin{array}{c}{Q}_{x0}^{\′}\\ Q_{y0}^{\′}\\ Q_{z0}^{\′}\end{array}\right]=\left[\begin{array}{c}{Q}_{x0}-({\mathrm{\δl}}_x+{\mathrm{\δh}}_x)+({\mathrm{\δh}}_x+{\mathrm{\δl}}_x)\cos {\mathrm{\θ}}_{\mathrm{cs}}-{\mathrm{\δh}}_y\sin {\mathrm{\θ}}_{\mathrm{cs}}-{\mathrm{\δl}}_y\cos {\mathrm{\θ}}_{\mathrm{as}}\sin {\mathrm{\θ}}_{\mathrm{cs}}+{\mathrm{\δl}}_z\sin {\mathrm{\θ}}_{\mathrm{as}}{\sin \mathrm{\θ}}_{\mathrm{cs}}\\ Q_{y0}-{\mathrm{\δl}}_y-{\mathrm{\δh}}_y+({\mathrm{\δl}}_x+{\mathrm{\δh}}_x){\sin \mathrm{\θ}}_{\mathrm{cs}}+{\mathrm{\δh}}_y\cos {\mathrm{\θ}}_{\mathrm{cs}}+{\mathrm{\δl}}_y\cos {\mathrm{\θ}}_{\mathrm{as}}\cos {\mathrm{\θ}}_{\mathrm{cs}}-{\mathrm{\δl}}_z\cos {\mathrm{\θ}}_{\mathrm{cs}}{\sin \mathrm{\θ}}_{\mathrm{as}}\\ Q_{z0}-{\mathrm{\δl}}_z+{\mathrm{\δl}}_y\sin {\mathrm{\θ}}_{\mathrm{as}}+{\mathrm{\δl}}_z\cos {\mathrm{\θ}}_{\mathrm{as}}\end{array}\right]---\left(8\right)$

Ideally, keep cutter heart point (Q _x0, Q _y0, Q _z0) motionless, CA two turning axles turn to angle θ _c, θ _a, linear axes need to be done corresponding feeding, and by (4) formula, the analog value of trying to achieve each linear axes amount of feeding is:

$\left[\begin{array}{c}X\\ Y\\ Z\end{array}\right]=\left[\begin{array}{c}{Q}_{x0}+(l_x+h_x)-(h_x+l_x)\cos {\mathrm{\θ}}_c+h_y{\sin \mathrm{\θ}}_c+l_y{\cos \mathrm{\θ}}_a\sin {\mathrm{\θ}}_c-({-L}_t+l_z){\sin \mathrm{\θ}}_a{\sin \mathrm{\θ}}_c\\ Q_{y0}+l_y+h_y-(h_x+l_x)\sin {\mathrm{\θ}}_c-h_y\cos {\mathrm{\θ}}_c-l_y{\cos \mathrm{\θ}}_a\cos {\mathrm{\θ}}_c+({-L}_t+l_z)\cos {\mathrm{\θ}}_c{\sin \mathrm{\θ}}_a\\ Q_{z0}-L_t+l_z-l_y\sin {\mathrm{\θ}}_a-({-L}_t+l_z)\cos {\mathrm{\θ}}_a\end{array}\right]---\left(9\right)$

If lathe is error free, CA turning axle forwards respectively angle θ to _c, θ _a, linear axes is pressed above formula feeding, ideally cutter heart point is motionless, and if there is error in lathe, still press above formula feeding, can there is certain deviation in cutter heart point, below, this kind of deviation analyzed.

Press above formula to linear axes feeding, in conjunction with CA yaw five-axis machine tool kinematics model (6) formula with error, obtain CA turning axle and forward respectively angle θ to _c, θ _atime, the physical location of cutter heart point is:

$\left[\begin{array}{c}{Q}_x\\ Q_y\\ Q_z\end{array}\right]=\left[\begin{array}{c}{Q}_{x0}-(\mathrm{\δ}{l}_x+{\mathrm{\δh}}_x)+({\mathrm{\δh}}_x+{\mathrm{\δl}}_x)\cos {\mathrm{\θ}}_c-\mathrm{\δ}{h}_y{\sin \mathrm{\θ}}_c-\mathrm{\δ}{l}_y{\cos \mathrm{\θ}}_a\sin {\mathrm{\θ}}_c+\mathrm{\δ}{l}_z{\sin \mathrm{\θ}}_a{\sin \mathrm{\θ}}_c\\ Q_{y0}-\mathrm{\δ}{l}_y-\mathrm{\δ}{h}_y+({\mathrm{\δl}}_x+{\mathrm{\δh}}_x)\sin {\mathrm{\θ}}_c+\mathrm{\δ}{h}_y\cos {\mathrm{\θ}}_c+\mathrm{\δ}{l}_y{\cos \mathrm{\θ}}_a\cos {\mathrm{\θ}}_c-{\mathrm{\δl}}_z\cos {\mathrm{\θ}}_c{\sin \mathrm{\θ}}_a\\ Q_{z0}-{\mathrm{\δl}}_z+\mathrm{\δ}{l}_y\sin {\mathrm{\θ}}_a+\mathrm{\δ}{l}_z\cos {\mathrm{\θ}}_a\end{array}\right]---\left(10\right)$

CA is rotated to θ _c, θ _atime cutter heart point position (10) formula, deduct initial cutter heart point physical location (8) formula, obtain cutter heart point depart from for:

$\left[\begin{array}{c}{\mathrm{\δ}}_x\\ {\mathrm{\δ}}_y\\ {\mathrm{\δ}}_z\end{array}\right]=\left[\begin{array}{c}{Q}_x-Q_{x0}^{\′}\\ Q_y-Q_{y0}^{\′}\\ Q_z-Q_{z0}^{\′}\end{array}\right]$

$=\left[\begin{array}{c}({\mathrm{\δh}}_x+{\mathrm{\δl}}_x)({\cos \mathrm{\θ}}_c-\cos {\mathrm{\θ}}_{\mathrm{cs}})-{\mathrm{\δh}}_y({\sin \mathrm{\θ}}_c-\sin {\mathrm{\θ}}_{\mathrm{cs}})-{\mathrm{\δl}}_y({\cos \mathrm{\θ}}_a\sin {\mathrm{\θ}}_c-\cos {\mathrm{\θ}}_{\mathrm{as}}\sin {\mathrm{\θ}}_{\mathrm{cs}})+{\mathrm{\δl}}_z(s{\mathrm{in\θ}}_a{\sin \mathrm{\θ}}_c-\sin {\mathrm{\θ}}_{\mathrm{as}}{\sin \mathrm{\θ}}_{\mathrm{cs}})\\ ({\mathrm{\δh}}_x+\mathrm{\δ}{l}_x)({\sin \mathrm{\θ}}_c-\sin {\mathrm{\θ}}_{\mathrm{cs}})+{\mathrm{\δh}}_y({\cos \mathrm{\θ}}_c-\cos {\mathrm{\θ}}_{\mathrm{cs}})+{\mathrm{\δl}}_y({\cos \mathrm{\θ}}_a\cos {\mathrm{\θ}}_c-\cos {\mathrm{\θ}}_{\mathrm{as}}\cos {\mathrm{\θ}}_{\mathrm{cs}})-{\mathrm{\δl}}_z(\cos {\mathrm{\θ}}_{c}s{\mathrm{in\θ}}_a-\cos {\mathrm{\θ}}_{\mathrm{cs}}\sin {\mathrm{\θ}}_{\mathrm{as}})\\ {\mathrm{\δl}}_y({\sin \mathrm{\θ}}_a-\sin {\mathrm{\θ}}_{\mathrm{as}})+{\mathrm{\δl}}_z({\cos \mathrm{\θ}}_a-\cos {\mathrm{\θ}}_{\mathrm{as}})\end{array}\right]---\left(11\right)$

4. measuring method analysis

(1) getting reference position is: θ _cs=0, θ _as=0.It is 0 constant keeping C turning axle angle, makes A axle forward angle θ to _a, linear axes is done corresponding feeding by (9) formula, and through type (11) obtains:

$\left[\begin{array}{c}{\mathrm{\δ}}_{x1}\\ {\mathrm{\δ}}_{y1}\\ {\mathrm{\δ}}_{z1}\end{array}\right]=\left[\begin{array}{c}0\\ {\mathrm{\δl}}_y({\cos \mathrm{\θ}}_a-1)-{\mathrm{\δl}}_z\sin {\mathrm{\θ}}_a\\ {\mathrm{\δl}}_y\sin {\mathrm{\θ}}_a+{\mathrm{\δl}}_z({\cos \mathrm{\θ}}_a-1)\end{array}\right]---\left(12\right)$

Obtain thus following two equatioies:

δ _y1=δ l _y(cos θ _a-1)-δ l _zsin θ _aequation 1

δ _z1=δ l _ysin θ _a+ δ l _z(cos θ _a-1) equation 2

These two equatioies represent respectively variable δ _y1, δ _z1about independent variable θ _afunction, below the zero point of these two functions is analyzed.

Make function 1 the right equal 0, obtain the zero point independent variable θ of function 1 _avalue:

${\mathrm{\θ}}_a=2\mathrm{k\π}+2\arctan \left(\frac{{-\mathrm{\δl}}_z}{{\mathrm{\δl}}_y}\right)$ (k=0,1,2 and $-\frac{\mathrm{\π}}{2}\≤{\mathrm{\θ}}_a\≤\frac{\mathrm{\π}}{2})$

Make function 2 the right equal 0, obtain the zero point independent variable θ of function 2 _avalue:

${\mathrm{\θ}}_a=2\mathrm{k\π}+2\mathrm{arccot}\left(\frac{{\mathrm{\δl}}_z}{{\mathrm{\δl}}_y}\right)$ (k=0,1,2 ... and $-\frac{\mathrm{\π}}{2}\≤{\mathrm{\θ}}_a\≤\frac{\mathrm{\π}}{2})$

By the interval of function 1 function 2 independents variable, according to zero point, be divided into several intervals, in each interval, as given δ l _y, δ l _zsign time, to δ _y1, δ _z1corresponding sign is analyzed, and obtains the value relation as shown in table 1,2,3,4:

Table 1 is as δ l _y>0 and δ l _zwhen <0, δ _y1, δ _z1value condition

Table 2 is as δ l _y>0 and δ l _zwhen >0, δ _y1, δ _z1value condition

Table 3 is as δ l _y<0 and δ l _zwhen >0, δ _y1, δ _z1value condition

Table 4 is as δ l _y<0 and δ l _zwhen <0, δ _y1, δ _z1value condition

By above analysis, obtain in the time that A axle rotates δ _y1δ _z1the measuring method of offset direction.

Table 5 check bar departs from situation and δ l _y, δ l _zthe corresponding table of the situation that departs from

According to δ l _y, δ l _zthe situation that departs from, lathe is adjusted, if δ l _yfor forward bias from, just by main shaft to Y-axis negative sense adjust, if δ l _yfor negative sense departs from, just main shaft is adjusted to Y-axis forward.If δ is l _zfor forward bias from, just by main shaft to Z axis negative sense adjust, if δ l _zfor negative sense departs from, just main shaft is adjusted to Z axis forward.

(2) getting reference position is: θ _cs=0, θ _as=0.It is 0 constant keeping A turning axle angle, makes C axle forward angle θ to _c, linear axes is done corresponding feeding by (9) formula, and through type (11) obtains:

$\left[\begin{array}{c}{\mathrm{\&delta;}}_{x2}\\ {\mathrm{\&delta;}}_{y2}\\ {\mathrm{\&delta;}}_{z2}\end{array}\right]=\left[\begin{array}{c}({\mathrm{\&delta;h}}_x+{\mathrm{\&delta;l}}_x)({\cos \mathrm{\&theta;}}_c-1)-({\mathrm{\&delta;h}}_y+{\mathrm{\&delta;l}}_y)\sin {\mathrm{\&theta;}}_c\\ ({\mathrm{\&delta;h}}_x+{\mathrm{\&delta;l}}_x)\sin {\mathrm{\&theta;}}_c+({\mathrm{\&delta;h}}_y+{\mathrm{\&delta;l}}_y)({\cos \mathrm{\&theta;}}_c-1)\\ 0\end{array}\right]---\left(14\right)$

Can try to achieve according to (14) formula: (δ h _x+ δ l _x), (δ h _y+ δ l _y) value as follows:

$\left[\begin{array}{c}{\mathrm{\&delta;h}}_x+{\mathrm{\&delta;l}}_x\\ {\mathrm{\&delta;h}}_y+{\mathrm{\&delta;l}}_y\end{array}\right]=\left[\begin{array}{c}\frac{{\mathrm{\&delta;}}_{x2}({\cos \mathrm{\&theta;}}_c-1)+{\mathrm{\&delta;}}_{y2}\sin {\mathrm{\&theta;}}_c}{{({\cos \mathrm{\&theta;}}_c-1)}^2+{\sin }^2{\mathrm{\&theta;}}_c}\\ \frac{{\mathrm{\&delta;}}_{y2}({\cos \mathrm{\&theta;}}_c-1)-{\mathrm{\&delta;}}_{x2}\sin {\mathrm{\&theta;}}_c}{{({\cos \mathrm{\&theta;}}_c-1)}^2+{\sin }^2{\mathrm{\&theta;}}_c}\end{array}\right]---\left(15\right)$

Obtain following equation:

δ _x2=(δ h _x+ δ l _x) (cos θ _c-1)-(δ h _y+ δ l _y) sin θ _cequation 3

δ _y2=(δ h _x+ δ l _x) sin θ _c+ (δ h _y+ δ l _y) (cos θ _c-1) equation 4

Equation 3, equation 4 are respectively variable δ _x2, δ _y2about θ _cfunction, below the zero point of these two functions is analyzed.

Make function 3 right-hand members equal 0, obtain the zero point θ of function 3 _cvalue be:

${\mathrm{\&theta;}}_c=2\mathrm{k\&pi;}+2\arctan \left(\frac{-({\mathrm{\&delta;h}}_y+{\mathrm{\&delta;l}}_y)}{{\mathrm{\&delta;h}}_x+{\mathrm{\&delta;l}}_x}\right)$ (k=0,1,2 ... and 0≤θ _c≤ 2)

Make function 4 formula right-hand members equal 0, obtain the zero point θ of function 4 _cvalue be:

${\mathrm{\&theta;}}_c=2\mathrm{k\&pi;}+2\mathrm{arccot}\left(\frac{{\mathrm{\&delta;h}}_y+{\mathrm{\&delta;l}}_y}{{\mathrm{\&delta;h}}_x+{\mathrm{\&delta;l}}_x}\right)$ (k=0,1,2 ... and 0≤θ _c≤ 2)

By function 3,4 independent variable θ _cinterval, divide according to zero point, be divided into several intervals, in each interval, as given δ h _x+ δ l _x, δ h _y+ δ l _ysign time, to δ _x2, δ _y2corresponding sign is analyzed, and obtains the value relation as shown in table 6,7,8,9:

Table 6 is as δ h _x+ δ l _x>0 and δ h _y+ δ l _ywhen <0, δ _x2, δ _y2value condition

Table 7 is as δ h _x+ δ l _x>0 and δ h _y+ δ l _ywhen >0, δ _x2, δ _y2value condition

Table 8 is as δ h _x+ δ l _x<0 and δ h _y+ δ l _ywhen >0, δ _x2, δ _y2value condition

Table 9 is as δ h _x+ δ l _x<0 and δ h _y+ δ l _ywhen <0, δ _x2, δ _y2value condition

By above theoretical analysis, adjust after lathe according to step 1, can be by δ l _yvalue be adjusted into 0, δ h _y+ δ l _ypositive negativity, be δ l _ypositive negativity, obtain thus as shown in table 10, C axle rotate time, check bar departs from situation and δ h _x+ δ l _x, δ h _ydepart from the corresponding relation of situation.

Table 10 check bar departs from situation and δ h _x+ δ l _x, δ h _ythe corresponding table of the situation that departs from

According to δ h _x+ δ l _x, δ h _ythe situation that departs from, lathe is adjusted, if δ h _x+ δ l _xfor forward bias from, just axial A X-axis negative sense is adjusted, if δ h _x+ δ l _xfor negative sense departs from, just A is adjusted to X-axis forward.If δ is h _yfor forward bias from, just axial A Y-axis negative sense is adjusted, if δ h _yfor negative sense departs from, just axial A Y-axis forward is adjusted.

5. measuring method and flow process

Depart from by the tool setting heart point corresponding relation that situation and error term departs from situation and analyze (table 5, table 10), obtain a kind of method that estimation error item departs from situation, the idiographic flow of an embodiment of the method is as follows:

(1) check bar is stuck in to main shaft cutter heart point place, keeping C shaft angle degree is that 0, A axle forwards 90 degree to from 0 degree, keeps cutter heart point motionless (X, Y, the Z linear axes amount of feeding are by the calculating of (9) formula), records check bar and departs from situation (forward bias from, negative sense depart from).

(2) check bar is stuck in to main shaft cutter heart point place, keeping C shaft angle degree is 0, A axle forwards-90 degree to from 0 degree, keeps cutter heart point motionless (X, Y, the Z linear axes amount of feeding are by the calculating of (9) formula), records check bar and departs from situation (forward bias from, negative sense depart from).

(3) according to the situation that departs from of the check bar of record, by the corresponding relation shown in look-up table 5, obtain δ l _y, δ l _zthe situation that departs from (forward bias from or negative sense depart from).

(4), according to the situation that departs from of δ ly, δ lz, reconditioner bed structure, eliminates error delta l _y, δ l _z.

(5) check bar is stuck in to main shaft cutter heart point place, keeping A shaft angle degree is 0, C axle forwards 360 degree to from 0 degree, keeps cutter heart point motionless (X, Y, the Z linear axes amount of feeding are by formula (9) calculating), records check bar and departs from situation (forward bias from, negative sense depart from).

(6) according to the situation that departs from of the check bar of record, by the corresponding relation shown in look-up table 10, obtain δ h _x+ δ l _x, δ h _ythe situation that departs from (forward bias from or negative sense depart from).

(7) according to δ h _x+ δ l _x, δ h _ythe situation that departs from, reconditioner bed structure, eliminates error delta h _x+ δ l _x, δ h _y.

In actual enforcement, measuring equipment comprises check bar, clock gauge etc.

Claims (5)

1. a method of calibration for CA yaw structure five-axis machine tool error, is characterized in that: comprise the following steps:

Keeping C shaft angle degree is that 0, A axle forwards 90 degree to from 0 degree, keeps cutter heart point motionless, records the offset direction of cutter heart point; Keeping C shaft angle degree is that 0, A axle forwards-90 degree to from 0 degree, keeps cutter heart point motionless, records the offset direction of cutter heart point;

According to the offset direction of the above-mentioned cutter heart point of record, by searching offset direction and the δ l of cutter heart point at y, z axle _ywith δ l _zthe corresponding relation of offset direction, obtains δ l _ywith δ l _zoffset direction; Described δ l _yfor A axle rotation center to cutter shaft rotation center the error in y direction, described δ l _zfor A axle rotation center to cutter shaft rotation center the error in z direction;

According to δ l _y, δ l _zoffset direction, reconditioner bed structure in the other direction, eliminates error delta l _y, δ l _z;

Keeping A shaft angle degree is that 0, C axle forwards 360 degree to from 0 degree, keeps cutter heart point motionless, records the offset direction of cutter heart point; According to the situation that departs from of this cutter heart point of record, by searching offset direction and the δ h of cutter heart point at x, y axle _x+ δ l _xwith δ h _ythe corresponding relation of offset direction, obtains δ h _x+ δ l _x, δ h _yoffset direction; Described δ h _x+ δ l _xfor C axle rotation center to cutter shaft rotation center the error in x direction, described δ h _yfor C axle rotation center to A axle rotation center the error in y direction;

According to δ h _x+ δ l _x, δ h _yoffset direction, reconditioner bed structure in the other direction, eliminates error delta h _x+ δ l _x, δ h _y.

2. the method for calibration of a kind of CA yaw structure five-axis machine tool error according to claim 1, is characterized in that: the described maintenance cutter heart is put in motionless situation, and the analog value of the linear axes amount of feeding is:

$\left[\begin{array}{c}X\\ Y\\ Z\end{array}\right]=\left[\begin{array}{c}{Q}_{x0}+(l_x+h_x)-(h_x+l_x)\cos {\mathrm{\&theta;}}_c+h_y{\sin \mathrm{\&theta;}}_c+l_y{\cos \mathrm{\&theta;}}_a\sin {\mathrm{\&theta;}}_c-({-L}_t+l_z){\sin \mathrm{\&theta;}}_a{\sin \mathrm{\&theta;}}_c\\ Q_{y0}+l_y+h_y-(h_x+l_x)\sin {\mathrm{\&theta;}}_c-h_y\cos {\mathrm{\&theta;}}_c-l_y{\cos \mathrm{\&theta;}}_a\cos {\mathrm{\&theta;}}_c+({-L}_t+l_z)\cos {\mathrm{\&theta;}}_c{\sin \mathrm{\&theta;}}_a\\ Q_{z0}-L_t+l_z-l_y\sin {\mathrm{\&theta;}}_a-({-L}_t+l_z)\cos {\mathrm{\&theta;}}_a\end{array}\right]---\left(9\right)$

Wherein, (h _x, h _y, h _z) be the offset vector of C axle rotation center to A axle rotation center, (l _x, l _y, l _z) be the offset vector of A axle rotation center to main shaft rotation center, (Q _x0, Q _y0, Q _z0) be ideally initial cutter heart point coordinate, L _tfor actual tool length.θ _c, θ _abe respectively the anglec of rotation of C axle, A axle.

3. the method for calibration of a kind of CA yaw structure five-axis machine tool error according to claim 1, is characterized in that: the offset direction of described cutter heart point obtains by cutter heart point measurement equipment.

4. the method for calibration of a kind of CA yaw structure five-axis machine tool error according to claim 1, is characterized in that: described in search offset direction and the δ l of cutter heart point at y, z axle _ywith δ l _zthe corresponding relation of offset direction is:

In the situation that A axle forwards 90 degree to from 0 degree, if cutter heart point at the offset direction of y axle by just becoming negative, and cutter heart point at the offset direction of z axle always for just, in addition, in the situation that A axle forwards-90 degree to from 0 degree, cutter heart point at the offset direction of y axle always for negative, and cutter heart point at the offset direction of z axle by just bearing change, A axle rotation center departs from δ l to the Y-direction of cutter heart point _zfor on the occasion of, Z-direction departs from δ l _zfor negative value;

In the situation that A axle forwards 90 degree to from 0 degree, if cutter heart point is negative at the offset direction of y axle always, and cutter heart point at the offset direction of z axle by just becoming negative, in addition, in the situation that A axle forwards-90 degree to from 0 degree, cutter heart point at the offset direction of y axle by just becoming negative, and cutter heart point at the offset direction of z axle always for negative, A axle rotation center departs from δ l to the Y-direction of cutter heart point _yfor on the occasion of, Z-direction departs from δ l _zfor on the occasion of;

In the situation that A axle forwards 90 degree to from 0 degree, if cutter heart point at the offset direction of y axle by just bearing change, and cutter heart point is negative at the offset direction of z axle always, in addition, in the situation that A axle forwards-90 degree to from 0 degree, cutter heart point at the offset direction of y axle always for just, and cutter heart point at the offset direction of z axle by just becoming negative, A axle rotation center departs from δ l to the Y-direction of cutter heart point _zfor negative value, Z-direction departs from δ l _zfor on the occasion of;

In the situation that A axle forwards 90 degree to from 0 degree, if cutter heart point at the offset direction of y axle always for just, and cutter heart point at the offset direction of z axle by just bearing change, in addition, in the situation that A axle forwards-90 degree to from 0 degree, cutter heart point at the offset direction of y axle by just bearing change, and cutter heart point at the offset direction of z axle always for just, A axle rotation center departs from δ l to the Y-direction of cutter heart point _zfor negative value, Z-direction departs from δ l _zfor negative value.

5. the method for calibration of a kind of CA yaw structure five-axis machine tool error according to claim 1, is characterized in that: described cutter heart point is at offset direction and the δ h of x, y axle _x+ δ l _xwith δ h _ythe corresponding relation of offset direction is:

In the situation that C axle forwards 360 degree to from 0 degree, if cutter heart point at the offset direction of x axle by just becoming negative, and cutter heart point at the offset direction of y axle by just becoming negative, C axle departs from δ h to cutter heart point directions X _x+ δ l _xfor on the occasion of, and C axle rotation center is to the biasing δ h of A axle rotation center Y-direction _yfor negative value;

In the situation that C axle forwards 360 degree to from 0 degree, if cutter heart point at the offset direction of x axle by just bearing change, and cutter heart point at the offset direction of y axle by just becoming negative, C axle departs from δ h to cutter heart point directions X _x+ δ l _xfor on the occasion of, and C axle rotation center is to the biasing δ h of A axle rotation center Y-direction _yfor on the occasion of;

In the situation that C axle forwards 360 degree to from 0 degree, if cutter heart point at the offset direction of x axle by just bearing change, and cutter heart point at the offset direction of y axle by just bearing change, C axle departs from δ h to cutter heart point directions X _x+ δ l _xfor negative value, and C axle rotation center is to the biasing δ h of A axle rotation center Y-direction _yfor on the occasion of;

In the situation that C axle forwards 360 degree to from 0 degree, if cutter heart point at the offset direction of x axle by just becoming negative, and cutter heart point at the offset direction of y axle by just bearing change, C axle departs from δ h to cutter heart point directions X _x+ δ l _xfor negative value, and C axle rotation center is to the biasing δ h of A axle rotation center Y-direction _yfor negative value.

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