CN113741342A - Five-axis linkage track error tracing method - Google Patents

Five-axis linkage track error tracing method Download PDF

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CN113741342A
CN113741342A CN202111017159.0A CN202111017159A CN113741342A CN 113741342 A CN113741342 A CN 113741342A CN 202111017159 A CN202111017159 A CN 202111017159A CN 113741342 A CN113741342 A CN 113741342A
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axis
error
formula
track
tool
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CN113741342B (en
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吕盾
叶欣欣
刘辉
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Xian Jiaotong University
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B19/00—Programme-control systems
    • G05B19/02—Programme-control systems electric
    • G05B19/18—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form
    • G05B19/404—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form characterised by control arrangements for compensation, e.g. for backlash, overshoot, tool offset, tool wear, temperature, machine construction errors, load, inertia
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B2219/00—Program-control systems
    • G05B2219/30—Nc systems
    • G05B2219/31—From computer integrated manufacturing till monitoring
    • G05B2219/31434—Zone supervisor, collects error signals from, and diagnoses different zone
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02P—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN THE PRODUCTION OR PROCESSING OF GOODS
    • Y02P90/00—Enabling technologies with a potential contribution to greenhouse gas [GHG] emissions mitigation
    • Y02P90/02—Total factory control, e.g. smart factories, flexible manufacturing systems [FMS] or integrated manufacturing systems [IMS]

Abstract

A five-axis linkage track error tracing method comprises the steps of firstly establishing a positive kinematic transformation model of a five-axis machine tool, respectively inputting and calculating an ideal cutter center pose under a workpiece coordinate system and an actual cutter center pose under the workpiece coordinate system by a command position sequence and a grating feedback position sequence, and respectively synthesizing an ideal cutter center position and an actual cutter center position into a command track and an actual track; solving a five-axis linkage track error, and projecting a tool nose position error vector between the actual track and the instruction track to the normal direction of the instruction track to solve the five-axis linkage track error; then, reconstructing a track error solving model by using a Jacobian matrix, rewriting track errors into a full differential form, representing each axis following error and five-axis linkage track errors into a linear relation, and obtaining the influence degree and action effect of each axis following error on the linkage track errors by using an error contribution degree model; the invention realizes the quantitative tracing of the five-axis linkage track error.

Description

Five-axis linkage track error tracing method
Technical Field
The invention belongs to the technical field of five-axis numerical control machines, and particularly relates to a five-axis linkage track error tracing method.
Technical Field
The five-axis numerical control machine tool is key processing equipment for processing complex curved surface parts such as aviation structural parts, engine blade discs/impellers and gas turbine blades, and the five-axis linkage track error determines the contour error of the complex curved surface parts. In the high-speed high-precision cutting process, the following error is a main influence factor causing the linkage track error of the numerical control machine tool, so that the influence of the tracing single-axis following error on the five-axis linkage track error plays an important role in controlling the five-axis linkage track error, ensuring the machining precision and improving the machining efficiency.
At present, a certain research is lacked for a five-axis linkage track error tracing method caused by following errors, and the existing tracing research mainly aims at the influence of dynamic factors such as acceleration, jerk, position loop gain and the like under different parameter values on a single-axis following error so as to map the single-axis linkage track error to the five-axis linkage track error. The existing method cannot directly reveal the quantitative relation between the following error of each axis and the five-axis linkage track error, and cannot reduce the linkage track error from the angle of controlling the single-axis following error.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention aims to provide a five-axis linkage track error tracing method, which can directly obtain the quantity relation between a five-axis following error and a linkage track error and quantitatively realize the tracing of the five-axis linkage track error caused by a single-axis following error.
In order to achieve the purpose, the invention adopts the technical scheme that:
a five-axis linkage track error tracing method comprises the following steps:
1) establishing a positive kinematic transformation matrix: establishing a positive kinematic transformation matrix [ g ] based on a rotation theory according to a kinematic structure of a machine toolwt](ii) a The AC double-turntable five-axis machine tool has two open-loop kinematic chains which are respectively a cutter kinematic chain [ g ]bt]And workpiece kinematic chain [ g ]bw]Cutter kinematic chain [ g ]bt]As shown in formula (1), the workpiece kinematic chain [ g ]bw]As shown in equation (2); two open-loop kinematic chains constitute a global kinematic chain [ g ] from the workpiece to the toolwt]As shown in formula (3);
Figure BDA0003240298710000021
[gwt]＝[gbw]-1·[gbt] (3)
wherein (x, y, z, theta)A,θC) The motion amounts of the X axis, the Y axis, the Z axis, the A axis and the C axis under a machine tool coordinate system (L)CAx,LCAy,LCAz) In the numerical control system, the coordinates of the positions of the fourth axis to the fifth axis in RTCP are reversed, (G54)x,G54y,G54z) Is the offset value, L, of the workpiece coordinate system relative to the machine coordinate systemtoolIs the length of the cutter;
2) synthesizing an instruction track and an actual track: the instruction position sequence (x, y, z, theta)A,θC) And raster feedback position sequence
Figure BDA0003240298710000036
Respectively input into the formula (4) to calculate the ideal tool center pose (P) under the workpiece coordinate systemx,Py,Pz,Vx,Vy,Vz) And the actual tool center pose under the workpiece coordinate system
Figure BDA0003240298710000037
Synthesizing the ideal cutter center position and the actual cutter center position into an instruction track and an actual track respectively;
Figure BDA0003240298710000031
3) solving the five-axis linkage track error:
from step 2) a sequence of tool center positions (P) on the command trajectory can be obtainedx,Py,Pz) And the center sequence of the tool positions on the actual path
Figure BDA0003240298710000032
Calculating the error vector of the center position of the cutter by using a formula (5), and setting the pose of the cutter at any point on the instruction track as Pi(Pi,x,Pi,y,Pi,z,Vi,x,Vi,y,Vi,z) And P isiThe position and posture of the next adjacent point are Pi+1(Pi+1,x,Pi+1,y,Pi+1,z,Vi+1,x,Vi+1,y,Vi+1,z) Then P is calculated according to equation (6)iUnit normal vector n of pointiProjecting the error vector of the center position of the tool to the normal direction of the command track according to the formula (7) to calculate the track error epsilonP；
Figure BDA0003240298710000033
Figure BDA0003240298710000034
Figure BDA0003240298710000035
4) Rewriting five-axis linkage track error: substituting the positive kinematic transformation model formula (4) into the tool center position error vector calculation formula (5) to obtain formula (8), and rewriting the formula (8) into a differential form of formula (9) by using a Jacobian matrix, wherein the command position sequence (x, y, z, theta)A,θC) And raster feedback position sequence
Figure BDA0003240298710000041
Satisfies the formula (10), and rewrites the Jacobian matrix in the formula (9) into a column vector MiRewriting the tool center position error vector E according to equation (11)PCalculating a five-axis linkage track error value epsilon according to the formula (12)P；
Figure BDA0003240298710000042
Figure BDA0003240298710000043
Figure BDA0003240298710000044
Figure 1
Figure BDA0003240298710000046
In the formula (epsilon)X,εY,εZ,εA,εC) Five-axis following error;
5) tracing five-axis linkage track error: calculating the contribution value of each axis following error to the five-axis linkage track error according to a formula (13), calculating the contribution proportion of each axis following error to the five-axis linkage track error according to a formula (14), and determining the influence degree and action effect of each axis following error to the five-axis linkage track error, wherein a negative value/proportion indicates that the axis following error has a counteraction effect on the linkage track error;
Ui＝(Mi·n)εi (i＝X,Y,Z,A,C) (13)
Figure BDA0003240298710000051
the five-axis linkage track error tracing method is also applicable to a three-axis machine tool.
The five-axis linkage track error tracing method is also applicable to five-axis linkage cutter attitude errors.
The invention has the following beneficial effects:
the invention can trace the source and lead the contribution proportion and contribution value and action effect of each axis following error of the five-axis linkage track error in the part processing or after the part processing, and combines the tracing result to control each axis following error by properly adjusting the dynamic parameters of the position where the part processing error exceeds the standard so as to ensure that the linkage track error is in the standard range, thereby ensuring the processing precision of the part. The invention provides thinking and direction for adjusting dynamic parameters of the machine tool and controlling following errors.
Drawings
Fig. 1 is a five-axis machine tool structure according to an embodiment of the present invention.
Fig. 2 is a schematic diagram of a kinematic structure of a machine tool according to an embodiment of the invention.
FIG. 3 is a flow chart of the synthetic trace of the present invention.
FIG. 4 shows a synthetic command trajectory and an actual trajectory of an S-shaped test piece according to an embodiment of the present invention.
FIG. 5 is a diagram illustrating a normal direction of a track according to an embodiment of the present invention.
FIG. 6 is a schematic diagram of five-axis linkage trajectory error solution.
FIG. 7 is a five axis linkage trajectory error.
FIG. 8 is a schematic diagram showing the relationship between the error vector of the center position of the tool and the following error of each axis.
FIG. 9 is a schematic diagram showing the relationship between the five-axis linkage trajectory error and the following error of each axis.
FIG. 10 is a graph showing the contribution of the tracking error to the axis following error in the embodiment.
FIG. 11 is a graph showing the ratio of the contribution of the axis following errors to the tracking error in the embodiment.
Detailed Description
The invention is described in detail below with reference to the figures and examples.
A five-axis linkage track error tracing method comprises the following steps:
1) establishing a positive kinematic transformation matrix:
the present embodiment adopts an AC double-turntable five-axis machine tool shown in fig. 1, the kinematic structure of which is shown in fig. 2, and the machine tool has two open-loop kinematic chains, namely a tool kinematic chain [ g ]bt]And workpiece kinematic chain [ g ]bw]Cutter kinematic chain [ g ]bt]As shown in formula (1), the workpiece kinematic chain [ g ]bw]As shown in equation (2); two open-loop kinematic chains constitute a global kinematic chain [ g ] from the workpiece to the toolwt]As shown in formula (3); the cutter moving chain starts from a machine tool coordinate system to a Y axis, an X axis and a Z axis, and the cutter is finally fixed on the Z axis; the workpiece moving chain is started from a machine tool coordinate system and sequentially goes to an axis A and an axis C, and the workpiece is finally fixed on a workbench of the axis C; the whole motion chain starts from the workpiece,sequentially moving to a C axis, an A axis, a machine tool coordinate system, a Y axis, an X axis and finally moving to a cutter from a Z axis;
Figure BDA0003240298710000061
Figure BDA0003240298710000071
[gwt]＝[gbw]-1·[gbt] (3)
wherein (x, y, z, theta)A,θC) The motion amounts of the X axis, the Y axis, the Z axis, the A axis and the C axis under a machine tool coordinate system (L)CAx,LCAy,LCAz) In the numerical control system, the coordinates of the positions of the fourth axis to the fifth axis in RTCP are reversed, (G54)x,G54y,G54z) Is the offset value, L, of the workpiece coordinate system relative to the machine coordinate systemtoolIs the length of the cutter;
2) synthesizing an instruction track and an actual track:
referring to fig. 3, a positive kinematic transformation model from a command position to a cutter center position is established, and interpolation command position sequences (x, y, z, theta) of an ISO10791-7 standard S-shaped test piece are collected from a numerical control system respectivelyA,θC) And raster feedback position sequence
Figure BDA0003240298710000072
Respectively inputting the collected instruction position sequence and the grating feedback position sequence into a formula (4), and calculating the ideal tool center pose (P) under the workpiece coordinate systemx,Py,Pz,Vx,Vy,Vz) And the actual tool center pose under the workpiece coordinate system
Figure BDA0003240298710000073
Synthesizing the ideal cutter center position and the actual cutter center position into an instruction track and an actual track respectively, as shown in fig. 4;
Figure BDA0003240298710000074
3) solving the five-axis linkage track error:
the cutter center position sequence on the instruction track can be obtained from the step 2) as (P)x,Py,Pz) The center sequence of the tool positions on the actual track is
Figure BDA0003240298710000086
Calculating the error vector of the center position of the cutter by using a formula (5), and setting the pose of the cutter at any point on the instruction track as Pi(Pi,x,Pi,y,Pi,z,Vi,x,Vi,y,Vi,z) And P isiThe position and posture of the next adjacent point are Pi+1(Pi+1,x,Pi+1,y,Pi+1,z,Vi+1,x,Vi+1,y,Vi+1,z) And the acquisition period of the numerical control system is 2ms, and the instruction position sequence is dense, so that P can be takeniTangential vector Q ofiIs composed of
Figure BDA0003240298710000081
PiThe knife axis vector of (A) is marked as ViThen P isiThe normal direction of (A) is as shown in FIG. 5, and P is calculated according to equation (6)iUnit normal vector n of pointiFor clearly reflecting the quantitative relationship between the single-axis following error and the five-axis linkage trajectory error, as shown in fig. 6, the error vector of the center position of the tool is projected to the normal direction of the command trajectory to obtain a trajectory error vector, and a trajectory error value epsilon is calculated according to the formula (7)PThe results are shown in FIG. 7;
Figure BDA0003240298710000082
Figure BDA0003240298710000083
Figure BDA0003240298710000084
4) rewriting five-axis linkage track error:
substituting a positive kinematic transformation model formula (4) into a cutter center position error vector calculation formula (5) to obtain a formula (8), and in order to express the five-axis linkage track error and the following errors among all axes as a linear relation, rewriting the formula (8) into a differential form of a formula (9) by utilizing a Jacobian matrix, wherein a command position sequence (x, y, z, theta) isA,θC) And raster feedback position sequence
Figure BDA0003240298710000085
Satisfies the formula (10), and rewrites the Jacobian matrix in the formula (9) into a column vector MiRewriting the tool center position error vector E according to equation (11)PAt this time, the error vector of the center position of the tool can be expressed as the vector superposition sum of the following errors of each axis, as shown in fig. 8, each vector is projected onto a normal vector n of the command trajectory to obtain a reconstructed five-axis linkage trajectory error, as shown in fig. 9, and a five-axis linkage trajectory error value epsilon is calculated according to a formula (12)P；
Figure BDA0003240298710000091
Figure BDA0003240298710000092
Figure BDA0003240298710000093
Figure 2
Figure BDA0003240298710000095
In the formula (epsilon)X,εY,εZ,εA,εC) A following error of five axes;
5) tracing the five-axis linkage track error:
in order to quantitatively analyze the influence of each axis following error on the five-axis linkage track error, researching the contribution amount of each single axis following error in the track error, calculating the contribution value of each axis following error on the five-axis linkage track error according to a formula (13), calculating the contribution proportion of each axis following error on the five-axis linkage track error according to a formula (14), and determining the influence degree and action effect of different axis following errors on the five-axis linkage track error, wherein a negative value/proportion indicates that the axis following error has a counteraction effect on the linkage track error; FIG. 10 is the contribution value of each axis following error to the five-axis linkage trajectory error, FIG. 11 is the proportion of each axis following error in the five-axis linkage trajectory error, negative values and negative ratios of FIGS. 10 and 11 show that the axis following error has a function of counteracting the final five-axis linkage trajectory error, and the two graphs show the contribution value and proportion of each axis following to the five-axis linkage trajectory error at different machining positions, wherein the contribution value and proportion of the X-axis, the Y-axis and the C-axis to the five-axis linkage trajectory error are large, the change of the magnitude, proportion and positive and negative changes are severe along with the machining position, and the contribution value, proportion and positive and negative changes of the Z-axis and the A-axis are relatively small, thereby realizing the tracing to the five-axis linkage trajectory error,
Ui＝(Mi·n)εi (i＝X,Y,Z,A,C) (13)
Figure BDA0003240298710000101
。

Claims (3)

1. a five-axis linkage track error tracing method is characterized by comprising the following steps:
1) establishing a positive kinematic transformation matrix: establishing a positive kinematic transformation matrix [ g ] based on a rotation theory according to a kinematic structure of a machine toolwt](ii) a AC double-turntable five-axis machine tool has two open-loop motions in totalChains, each being a cutter-moving chain [ g ]bt]And workpiece kinematic chain [ g ]bw]Cutter kinematic chain [ g ]bt]As shown in formula (1), the workpiece kinematic chain [ g ]bw]As shown in equation (2); two open-loop kinematic chains constitute a global kinematic chain [ g ] from the workpiece to the toolwt]As shown in formula (3);
Figure FDA0003240298700000011
Figure 3
Figure FDA0003240298700000022
wherein (x, y, z, theta)A,θC) The motion amounts of the X axis, the Y axis, the Z axis, the A axis and the C axis under a machine tool coordinate system (L)CAx,LCAy,LCAz) In the numerical control system, the coordinates of the positions of the fourth axis to the fifth axis in RTCP are reversed, (G54)x,G54y,G54z) Is the offset value, L, of the workpiece coordinate system relative to the machine coordinate systemtoolIs the length of the cutter;
2) synthesizing an instruction track and an actual track: the instruction position sequence (x, y, z, theta)A,θC) And raster feedback position sequence
Figure FDA0003240298700000023
Respectively input into the formula (4) to calculate the ideal tool center pose (P) under the workpiece coordinate systemx,Py,Pz,Vx,Vy,Vz) And the actual tool center pose under the workpiece coordinate system
Figure FDA0003240298700000024
Respectively synthesizing the ideal cutter center position and the actual cutter center position into an instruction track and an actualA boundary trajectory;
Figure FDA0003240298700000025
3) solving the five-axis linkage track error:
from step 2) a sequence of tool center positions (P) on the command trajectory can be obtainedx,Py,Pz) And the center sequence of the tool positions on the actual path
Figure FDA0003240298700000026
Calculating the error vector of the center position of the cutter by using a formula (5), and setting the pose of the cutter at any point on the instruction track as Pi(Pi,x,Pi,y,Pi,z,Vi,x,Vi,y,Vi,z) And P isiThe position and posture of the next adjacent point are Pi+1(Pi+1,x,Pi+1,y,Pi+1,z,Vi+1,x,Vi+1,y,Vi+1,z) Then P is calculated according to equation (6)iUnit normal vector n of pointiProjecting the error vector of the center position of the tool to the normal direction of the command track according to the formula (7) to calculate the track error epsilonP；
Figure FDA0003240298700000031
Figure FDA0003240298700000032
Figure FDA0003240298700000033
4) Rewriting five-axis linkage track error: substituting the positive kinematic transformation model formula (4) into the tool center position error vector calculation formula (5) to obtain a formula (8), and rewriting the formula (8) into a differential form of a formula (9) by using a Jacobian matrixWherein the sequence of instruction locations (x, y, z, θ)A,θC) And raster feedback position sequence
Figure FDA0003240298700000034
Satisfies the formula (10), and rewrites the Jacobian matrix in the formula (9) into a column vector MiRewriting the tool center position error vector E according to equation (11)PCalculating a five-axis linkage track error value epsilon according to a formula (12)P；
Figure FDA0003240298700000035
Figure FDA0003240298700000036
Figure FDA0003240298700000037
Figure 4
Figure FDA0003240298700000042
In the formula (epsilon)X,εY,εZ,εA,εC) Five-axis following error;
5) tracing five-axis linkage track error: calculating the contribution value of each axis following error to the five-axis linkage track error according to a formula (13), calculating the contribution proportion of each axis following error to the five-axis linkage track error according to a formula (14), and determining the influence degree and action effect of each axis following error to the five-axis linkage track error, wherein a negative value/proportion indicates that the axis following error has a counteraction effect on the linkage track error;
Ui＝(Mi·n)εi (i＝X,Y,Z,A,C) (13)
Figure FDA0003240298700000043
。
2. the method of claim 1, wherein: the five-axis linkage track error tracing method is also applicable to a three-axis machine tool.
3. The method of claim 1, wherein: the five-axis linkage track error tracing method is also applicable to five-axis linkage cutter attitude errors.
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CN117434889A (en) * 2023-11-28 2024-01-23 清华大学 Five-axis linkage numerical control machine tool linkage error prediction method, device, equipment and medium

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CN117434889A (en) * 2023-11-28 2024-01-23 清华大学 Five-axis linkage numerical control machine tool linkage error prediction method, device, equipment and medium

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