Procedia CIRP 8 ( 2013 ) 135 – 140
2212-8271 © 2013 The Authors. Published by Elsevier B.V.
Selection and peer-review under responsibility of The International Scientifi c Committee of the “14th CIRP Conference on Modeling of Machining Operations” in the person of the Conference Chair Prof. Luca Settineri
doi: 10.1016/j.procir.2013.06.078
14
thCIRP Conference on Modeling of Machining Operations (CIRP CMMO)
Integrated geometric error compensation of machining processes on
CNC machine tool
Xiaoyan Zuo, Beizhi Li*, Jianguo Yang, Xiaohui Jiang
College of Mechanical Engineering, Donghua University, Shanghai, 20060, China * Corresponding author. Tel.:+86-18971483300; fax: +86-021-67792439.E-mail address: [email protected]. AbstractKinematic errors due to geometric inaccuracies in machining system cause deviations of tool positions and orientation from being machined point on the workpiece, which consequently affect geometric accuracy of the machined surface. This paper presents an integrated geometric error model of machining system and compensation method on machine tools. Regarding a machine tool, fixtures, workpiece and tool as an assembly, an integrated geometric error model has been established. The integrated error is modeled by the propagation and the accumulation of errors based on Jacobian-Torsor theory. It is different with previous model, in this model, all the geometric errors of machining system are converted into the machine tool instead of the workpiece machining surface. As is well known in the machine tool, there are 21 geometric error of a 3-axis milling machine tool, which can be measured by laser interferometer. Based on this integrated model and machine tool error, the combination of geometric errors of machining system reflect on the machine tool can be predicted. Finally, a new compensation method is proposed to realize the error compensation, NC program is corrected corresponding NC codes according to the predicted errors during virtual machining before it is fed to the actual machining. A case demonstrates the application of how the method could be used in error compensation for machining processes.
© 2013 The Authors. Published by Elsevier B.V.
Selection and/or peer-review under responsibility of The International Scientific Committee of the 14th CIRP Conference on Modeling of Machining Operations" in the person of the Conference Chair Prof. Luca Settineri
Keywords: CNC milling machine tool, Geometric error, Machining error, Error compensation, Jacobian-Torsor Theory;
1. Introduction
Error compensation plays a significant role in ensuring the overall product quality. Many researchers have done a lot of work on error compensation that take into account the tool/workpiece deflection during machining. Based on the assumption of rigid body, various optimization and compensation techniques [1-4] were used to improve product quality. Law[5]studied the cavity deformation based on Arbor slot machining process and error compensation method, but the model did not consider the error of the workpiece. Bandy et al.[6]obtained the information and error vectors of measured points using a probe, and then modified the tool path according to the error vectors. Cho et al [7] studied the error compensation method of the simple parts based on the experimental statistics. Yang and Menq [8] presented a scheme that can compensate the
machining error using the discrete measured data from a coordinate measuring machine. However, the coordinate measuring machine is an off-line method, which will cause relocation errors and longer production cycles when machining again. From the previous literature review, it is shown that the compensation method is complex for practical.
Despite the significant developments in prediction and compensation, there are still exiting a relatively small percentage of machining error. The decision on how to accurately compare the machined workpiece to the initial CAD model is critical importance in achieving high-quality machining product. This paper introduces an advanced error compensation strategy integrating geometric errors in machining. The machining errors are predicted by Jacobian-Torsor Theory[9]. The error compensation is achieved by optimizing the tool path according to the predicted milling error.
© 2013 The Authors. Published by Elsevier B.V.
Selection and peer-review under responsibility of The International Scientifi c Committee of the “14th CIRP Conference on Modeling of Machining Operations” in the person of the Conference Chair Prof. Luca Settineri
Open access under CC BY-NC-ND license.
Fig.1. analysis of errors source in a generic machining system
2. Geometric error propagation model
2.1. .Modeling geometric error transfer process
The error sources and propagation method can be ascertained from a study of the operational cycle in a machining process (see Fig.1). In the setup 1 operation, specific fixtures are fixed on the machine worktable. On the one hand, because of the manufacturing error and wear, the machine tool and fixtures may have a lower precision than they should be. Hence the manufacturing system introduces machine error and fixtures errors. On the other hand, the operator may also introduce errors due to a wrong setup of fixtures on the worktable. In the setup 2 operation, when the blank is installed in the fixtures, an error is induced due to the datum errors. In the setup 3 operation, tool is installed in the machine spindle, there is an error caused by tool wear and setup. These errors are known as geometric errors, which have already existed prior to machining, and will reflect onto the part during machining.
2.2. Machining features and its expression
In this study, the workpiece is composed of a set of features, and each feature is discrete to a series of points. The example of the workpiece in Fig.2 has two main features X1(k) (lower surface) and X2(k) (upper surface).
The coordinates of points in a nominal feature can be represented as:
;
N
3
N
3
N
3
N
LQ L L L Where:3
N
[
N
\
N
]
N
LM LM LM LMThe matrix represents the homogenous coordinates of a point (j) of a feature (i) in Workpiece Coordinate
(WCS). Then the nominal clouds points' model of the workpiece is constructed as follows:
:
;
N
;
N
;
N
Q :&6For each surface, the deviations are expressed as:
]
\
[
'
R[\ ] SODQH^
`
(1) Where]
\
[
'
: Translational vectors of thesurface in direction X, Y and Z;
: Rotating vectors aroundX, Y and Z.
Fig.2. example of the workpiece
2.3. Geometric error propagation model based on Jacobian-Torsor theory
In this study, the new method of error propagation analysis is based on the Jacobian-Torsor model which is related in details in [9]. Focusing on a specific process plan, mechanical manufacturing process collects the errors propagated in successive machining operations.
There are two main error propagation relations chain in the entire processing system (see Fig.3).
The following error propagation model is yielded for the machine and tool focus on Fig.3.
@
>
)( )( )( )( WRRO PDFKLQHT
T
-)5
(2)Error propagation formula of machine tool, fixtures and workpiece is:
@ > )( )( )( )( ZRUNSLHFH PDFKLQH
T
T
-)5
(3) Where: 7 )(L )(LG[
G\
G]
U[
U\
U]
T
: Variation of six freedom degrees associates with the it components (machine worktable, machine spindle, tool, fixtures and workpiece) relative to reference coordinate system;
)(L
-
: Jacobian matrix.(a)
(b)
Fig.3. error propagation relations in the machine process 2.4. Overall geometric error vector
Simple summation of geometric error values (tool, workpiece, fixture and machine tool) results in the overall error vector. the final output error of comprehensive error propagation in the process system based on the following equation:
ZRUNSLHFH PDFKLQH WRRO PDFKLQH
)5
)5
)5
(4)3. Compensation and Control Strategy
The compensation strategy proposed for geometric error correction on the CNC machine tool is based on Eq. (2) and (3) above. Geometric error associated with any position in machining system is calculated using the error model and corrected in software to the actual position value of the machine. Fig.4 represents this compensation strategy.
The forward kinematics based error model is used to produce error vectors corresponding to sets of input positions. So the compensation of these errors could be suggested as the following. The nominal tool path or initial G-Code (G1) is modified by the tool deflection error compensation algorithm, which yields to new tool path (G2). Then G2 could be modified by the geometric error compensation algorithm, which leads to G3. G3 is the final modified tool path. Therefore, by implying only two compensation algorithms after each other in the described order, it is possible to compensate the combination of two errors (see Fig.5).
Fig.4. compensation strategy
Fig.5. two steps for compensation.
4. Case Study
To describe the error compensation method, a finishing machining operation is implemented on a thin-walled structure workpiece made from LY12 aluminum with size (250mmx200mmx8mm) as shown in Fig. 6. There are seven cavities in the block, the wall thickness
is 2mm. Note that the thin-walled structure is located by one plane, three locators and three clamping elements.
(a) (b)
Fig.6. geometric error propagation model
Table 1. Example-coefficient matrices and functional elements torsor with vertex
Functional Elements Torsor Parameters Jacobian Matrix Torsor
No. Name Setup 1 machine 1 Work-table FE1 , 6 Spindle FE6 , Setup 2 fixture 2 Below plane FE2 , 3 Upper plane FE3 , Setup 3 Fixture link 8 Pin
9 Pin 10 Pin Setup 4 workpiece 4 Datum surface FE4 , 5 Machine feature FE5 , Setup 5
tool 7 Tool FE7 ,
Because all the error propagation analysis expands in the reference coordinate system (see Fig.7). We obtain the Jacobian Matrix and Torsor values of each Functional Elements shown in the last two columns of Table 1. In this example, according the Eq. (2), (3) and (4), final error vector is the overall effect of all geometrical errors and kinematical deviations of
path: ZRUNSLHFH Z PDFKLQH WRRO W PDFKLQH
)5
)5
)5
The results are calculated using the MATLAB tool box. According to error values, it is able to adjust process or carry out error compensation.
5. Conclusion
This paper proposed an integrated geometric error modeling, identification and compensation method. Especially, the method can be introduced to any assembly of Milling. Compared with previous methods [10, 11], this new approach has the following advantages: (1) all geometric error components inherent to each propagation chain can be recognized; (2) it is suitable for any type of assembly; and (3) no special measurement instruments need to be developed.
Acknowledgements
This project was supported by National nature science founding (50975046) and shanghai leading academic discipline project (No. B 602).
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