Research on Geometric Error Model for Multi-Axis CNC Machines Based on Differential Transform

2012 ◽  
Vol 522 ◽  
pp. 359-363
Author(s):  
Jian Xiong Chen ◽  
Shu Wen Lin
Keyword(s):  
Differential Operator ◽  
Geometric Error ◽  
Error Model ◽  
Geometric Errors ◽  
Cnc Machines ◽  
Ideal Position ◽  
Closed Chain ◽  
Differential Movement ◽  
Differential Transform ◽  
Series Type

The geometric error of machine axis can be equivalent to the differential movement, regarded as a differential operator based on its ideal position. Thus, a new modeling method for multi-axis CNC machines based on differential transform theory is proposed in this paper. Firstly, the workpiece coordinate system is selected to observe the error of tools cutter location and orientation. Then, the kinematics chain of the machine will be consolidated into one, and the closed chain can be changed to open series type. The transform matrix is adopted to convert the differential operator between the different basis, because of the geometric errors have a different basis between measurement and modeling. Eventually, the general geometric error model for multi-axis machines is established after a XYFZ type three-axis machine is studied in detail.

Research on Geometric Error Compensating Technique of CNC P3G Grinding Machine

2012 ◽  
Vol 462 ◽  
pp. 287-294 ◽  
Author(s):  
Yi Jian ◽  
Qian Qian Li ◽  
Hong Cheng ◽  
Bin Wu Lai ◽  
Jian Fei Zhang
Keyword(s):  
Machine Tools ◽  
Geometric Error ◽  
Error Model ◽  
Error Modeling ◽  
Numerical Control ◽  
Geometric Errors ◽  
Real Time Control ◽  
Time Control ◽  
Applied Software ◽  
Grinding Machine

Kinematic accuracy is a key reason which influence workpiece's geometric error precision on traditional working process of precisely CNC（Computerized Numerical Control）P3G（polygon profile with 3 lobes） grinding machine. A systematic geometric error model has been presented for CNC P3G grinding machine， proposed multi-body system theory integrate with the structure of CNC P3G grinding machine tools, researched on the machine's space geometric errors. By means of separate geometric errors from the machine tools, build geometric mathematical error model. Then, identify 21 error parameters through method of 9 lines, analysis and calculate the total space geometric errors of the workpiece and wheel. Finally, formed a parameter-list and applied software error compensational technique ， achieved real-time control to the motions of workpiece and wheel. Experimental results shown that the geometrical error modeling technique is accurate and efficient, and the precision of CNC P3G grinding machine is highly raised 70%.

Interpolation and Extrapolation of Optimally-Fitted Kinematic Error Model for Five-Axis Machine Tools

2021 ◽  
pp. 1-25
Author(s):  
Le Ma ◽  
Douglas Bristow ◽  
Robert Landers
Keyword(s):  
Machine Tool ◽  
Interpolation Space ◽  
Geometric Error ◽  
Error Model ◽  
Geometric Errors ◽  
Model Errors ◽  
Volumetric Error ◽  
Extrapolation Space ◽  
The Mean ◽  
Five Axis

Abstract Machine tool geometric errors are frequently corrected by populating compensation tables that contain position-dependent offsets to each commanded axis position. While each offset can be determined by directly measuring the individual geometric error at that location, it is often more efficient to compute the compensation using a volumetric error model derived from measurements across the entire workspace. However, interpolation and extrapolation of measurements, once explicit in direct measurement methods, become implicit and obfuscated in the curve fitting process of volumetric error methods. The drive to maximize model accuracy while minimizing measurement sets can lead to significant model errors in workspace regions at or beyond the range of the metrology equipment. In this paper, a novel method of constructing machine tool volumetric error models is presented in which the characteristics of the interpolation and extrapolation errors are constrained. Using a typical five-axis machine tool compensation methodology, a constraint bounding the tool tip modeled error slope is added to the error model identification process. By including this constraint over the entire space, the geometric errors over the interpolation space are still well-identified. Also, the model performance over the extrapolation space is consistent with the behavior of the geometric error model over the interpolation space. The methodology is applied to an industrial five-axis machine tool. In the experimental implementation, for measurements outside of the measured region, an unconstrained model increases the mean residual by 40% while the constrained model reduces the mean residual by 40%.

Modeling and Identification of Geometric Error Based on Screw Theory

2014 ◽  
Vol 941-944 ◽  
pp. 2219-2223 ◽  
Author(s):  
Guo Juan Zhao ◽  
Lei Zhang ◽  
Shi Jun Ji ◽  
Xin Wang
Keyword(s):  
Machine Tool ◽  
Laser Interferometer ◽  
Screw Theory ◽  
Geometric Error ◽  
New Method ◽  
Geometric Errors ◽  
Volumetric Error ◽  
B Spline ◽  
The Individual

In this paper, a new method is presented for the identification of machine tool component errors. Firstly, the Non-Uniform Rational B-spline (NURBS) is established to represent the geometric component errors. The individual geometric errors of the motion parts are measured by laser interferometer. Then, the volumetric error for a machine tool with three motion parts is modeled based on the screw theory. Finally, the simulations and experiments are conducted to confirm the validity of the proposed method.

Sensitivity Analysis of Geometric Errors for Five-Axis CNC Machine Tool Based on Multi-Body System Theory

2012 ◽  
Vol 271-272 ◽  
pp. 493-497
Author(s):  
Wei Qing Wang ◽  
Huan Qin Wu
Keyword(s):  
System Theory ◽  
Sensitivity Analysis ◽  
Machine Tool ◽  
Geometric Error ◽  
Machining Accuracy ◽  
Geometric Errors ◽  
Body System ◽  
Cnc Machine ◽  
Multi Body ◽  
Five Axis

Abstract: In order to determine that the effect of geometric error to the machining accuracy is an important premise for the error compensation, a sensitivity analysis method of geometric error is presented based on multi-body system theory in this paper. An accuracy model of five-axis machine tool is established based on multi-body system theory, and with 37 geometric errors obtained through experimental verification, key error sources affecting the machining accuracy are finally identified by sensitivity analysis. The analysis result shows that the presented method can identify the important geometric errors having large influence on volumetric error of machine tool and is of help to improve the accuracy of machine tool economically.

Kinematic calibration of a laser tracker based on nonlinear optimization of a refined geometric error model

Measurement ◽  
2022 ◽  
pp. 110672
Author(s):  
Xiaopeng Chen ◽  
Yanyang Liu ◽  
Yang Xu ◽  
Siyuan Gou ◽  
Siyan Ma ◽  
...  
Keyword(s):  
Nonlinear Optimization ◽  
Geometric Error ◽  
Error Model ◽  
Laser Tracker ◽  
Kinematic Calibration

Precise geometric error model based on z-axis motion platform of micro v-groove machine tools

2017 ◽  
Vol 92 (9-12) ◽  
pp. 3219-3224 ◽  
Author(s):  
Huabing Zou ◽  
Yuejiao Ding ◽  
Jing Zhang ◽  
Anhui Cai ◽  
Xiaohong Zhang ◽  
...  
Keyword(s):  
Machine Tools ◽  
Geometric Error ◽  
Error Model ◽  
Motion Platform ◽  
Model Based

Table-Based Volumetric Error Compensation of Large Five-Axis Machine Tools

2016 ◽  
Vol 139 (2) ◽  
Author(s):  
Jennifer Creamer ◽  
Patrick M. Sammons ◽  
Douglas A. Bristow ◽  
Robert G. Landers ◽  
Philip L. Freeman ◽  
...  
Keyword(s):  
Machine Tool ◽  
Error Compensation ◽  
Machine Tools ◽  
Data Gathering ◽  
Measurement Data ◽  
Geometric Error ◽  
Compensation Method ◽  
Geometric Errors ◽  
Simultaneous Generation ◽  
Five Axis

This paper presents a geometric error compensation method for large five-axis machine tools. Compared to smaller machine tools, the longer axis travels and bigger structures of a large machine tool make them more susceptible to complicated, position-dependent geometric errors. The compensation method presented in this paper uses tool tip measurements recorded throughout the axis space to construct an explicit model of a machine tool's geometric errors from which a corresponding set of compensation tables are constructed. The measurements are taken using a laser tracker, permitting rapid error data gathering at most locations in the axis space. Two position-dependent geometric error models are considered in this paper. The first model utilizes a six degree-of-freedom kinematic error description at each axis. The second model is motivated by the structure of table compensation solutions and describes geometric errors as small perturbations to the axis commands. The parameters of both models are identified from the measurement data using a maximum likelihood estimator. Compensation tables are generated by projecting the error model onto the compensation space created by the compensation tables available in the machine tool controller. The first model provides a more intuitive accounting of simple geometric errors than the second; however, it also increases the complexity of projecting the errors onto compensation tables. Experimental results on a commercial five-axis machine tool are presented and analyzed. Despite significant differences in the machine tool error descriptions, both methods produce similar results, within the repeatability of the machine tool. Reasons for this result are discussed. Analysis of the models and compensation tables reveals significant complicated, and unexpected kinematic behavior in the experimental machine tool. A particular strength of the proposed methodology is the simultaneous generation of a complete set of compensation tables that accurately captures complicated kinematic errors independent of whether they arise from expected and unexpected sources.

Error Sensitivity Analysis for Optimal Calibration of Parallel Kinematic Machines

2002 ◽  
Author(s):  
Fengfeng Xi ◽  
Marcel Verner ◽  
Chris Mechefske
Keyword(s):  
Sensitivity Analysis ◽  
Error Model ◽  
Condition Numbers ◽  
Geometric Errors ◽  
Error Sensitivity ◽  
Parallel Kinematic Machines ◽  
Parallel Kinematic ◽  
Error Sensitivity Analysis ◽  
Jacobian Inverse ◽  
Optimal Calibration

In this paper, error sensitivity analysis is discussed for the purpose of optimal calibration of parallel kinematic machines (PKMs). The idea is to find a less error sensitive area in the workspace for calibration. To do so, an error model is developed that takes into consideration all the geometric errors due to imprecision in manufacturing and assembly. Based on this error model, it is shown that the error mapping from the geometric errors to the pose error of the PKM depends on the Jacobian inverse. The Jacobian inverse would introduce spurious errors that would affect the calibration results, if used without proper care. Hence, it is suggested to select the areas in the workspace with smaller condition numbers for calibration. A case study is presented to illustrate the proposed method.

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