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.

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.

scholarly journals Modelling and characterisation of geometric errors on 5-axis machine-tool

2019 ◽  
Vol 20 (6) ◽  
pp. 605
Author(s):  
Fabien Viprey ◽  
Hichem Nouira ◽  
Sylvain Lavernhe ◽  
Christophe Tournier
Keyword(s):  
Machine Tool ◽  
Research Work ◽  
Metrological Traceability ◽  
Measurement Procedure ◽  
Geometric Errors ◽  
Volumetric Error ◽  
Identification Procedure ◽  
Time Drift ◽  
The Mean ◽  
Structural Loop

This research work deals with the geometric modelling of 5-axis machine tool based on a standardised parameterisation of geometric errors with the aim to decrease the volumetric error in the workspace. The identification of the model’s parameters is based on the development of a new standard thermo-invariant material namely the Multi-Feature Bar. Thanks to its calibration and a European intercomparison, it now provides a direct metrological traceability to the SI metre for dimensional measurement on machine tool in a hostile environment. The identification of three intrinsic parameters of this standard, coupled with a measurement procedure ensures a complete and traceable identification of motion errors of linear axes. An identification procedure of location and orientation errors of axes is proposed by probing a datum sphere in the workspace and minimising the time drift of the structural loop and the effects of the previously identified motion errors. Finally, the developed model partially identified, allows the characterisation of 95% of the measured volumetric error. Therefore, the mean volumetric error not characterised by the model only amounts to 8 μm.

Geometric accuracy allocation for multi-axis CNC machine tools based on sensitivity analysis and reliability theory

2014 ◽  
Vol 229 (6) ◽  
pp. 1134-1149 ◽  
Author(s):  
Qiang Cheng ◽  
Ziling Zhang ◽  
Guojun Zhang ◽  
Peihua Gu ◽  
Ligang Cai
Keyword(s):  
Sensitivity Analysis ◽  
Machine Tool ◽  
Operating Conditions ◽  
Numerical Control ◽  
Cnc Machine Tools ◽  
Machining Accuracy ◽  
Geometric Errors ◽  
Volumetric Error ◽  
The Cost ◽  
Five Axis

Machining accuracy of a machine tool is influenced by geometric errors produced by each part and component. Different errors have varying influence on the machining accuracy of a tool. The aim of this study is to optimize errors to get a desired performance for a numerical control machine tool. Applying multi-body system theory, a volumetric error model was constructed to track and compensate effects of errors during operation of the machine, and to relate the functional specifications on volumetric accuracy to the permissible errors on the joints and links of the machine. Error sensitivity analysis was used to identify the influence of different errors (especially the errors which have large influences) on volumetric error. Based on First Order and Second Moment theory, an error allocation approach was developed to optimize allocation of manufacturing and assembly tolerances along with specifying the operating conditions to determine the optimal level of these errors so that the cost of controlling them and the cost of failure to meet the specifications is minimized. The approach developed was implemented in software and an example of the geometric errors budgeting for a five-axis machine was discussed. It is identified that the different optimal standard deviations reflect the cost-weighted influences of the respective parameters in the equations of the functional requirements. This study suggests that it is possible to determine the coupling relationships between these errors and optimize the allowable error budgeting between these sources.

Machine-Tool Error Observer Design With Application to Thermal Error Tracking

2019 ◽  
Vol 141 (12) ◽  
Author(s):  
Hua-Wei Ko ◽  
Patrick Bazzoli ◽  
J. Adam Nisbett ◽  
Douglas Bristow ◽  
Yujie Chen ◽  
...  
Keyword(s):  
Machine Tool ◽  
Parameter Identification ◽  
Thermal Error ◽  
Error Model ◽  
Optimal Designs ◽  
Model Parameters ◽  
Volumetric Error ◽  
Identification Procedure ◽  
Five Axis ◽  
Large Machine

Abstract A parameter identification procedure for identifying the parameters of a volumetric error model of a large machine tool requires hundreds of random volumetric error components in its workspace and thus takes hours of measurement time. It causes thermal errors of a large machine difficult to be tracked and compensated periodically. This paper demonstrates the application of the optimal observation design theories to volumetric error model parameter identification of a large five-axis machine. Optimal designs maximize the amount of information carried in the observations. In this paper, K-optimal designs are applied for the construction of machine-tool error observers by determining locations in the workspace at which 80 components of volumetric errors to be measured so that the model parameters can be identified in 5% of an 8-h shift. Many of optimal designs tend to localize observations at the boundary of the workspace. This leaves large volumes of the workspace inadequately represented, making the identified model inadequate. Therefore, the constrained optimization algorithms that force the distribution of observation points in the machine’s workspace are developed. Optimal designs reduce the number of observations in the identification procedure. This opens up the possibility of tracking thermal variations of the volumetric error model with periodic measurements. The design, implementation, and performance of a constrained K-optimal in tracking the thermal variations of the volumetric error over a 400-min period of operation are also reported. About 70–80% of machine-tool error can be explained using the proposed thermal error modeling methodology.

Fluctuation prediction of machining accuracy for multi-axis machine tool based on stochastic process theory

2014 ◽  
Vol 229 (14) ◽  
pp. 2534-2550 ◽  
Author(s):  
Qiang Cheng ◽  
Qiunan Feng ◽  
Zhifeng Liu ◽  
Peihua Gu ◽  
Ligang Cai
Keyword(s):  
Stochastic Process ◽  
Machine Tool ◽  
Significant Influence ◽  
Geometric Error ◽  
Error Modeling ◽  
Precision Machining ◽  
Machining Accuracy ◽  
Geometric Errors ◽  
Volumetric Error ◽  
Ultra Precision

Geometric error has significant influence on the processing results and reduces machining accuracy. Machine tool geometric errors can be interpreted as a deterministic value with an uncertain fluctuation of probabilistic distribution. Although, the uncertain fluctuation can not be compensated, it has extremely profound significance on the precision and ultra-precision machining to reduce the fluctuation range of machining accuracy as far as possible. In this paper, a typical 3-axis machine tool with high precision is selected and the fluctuations in machining accuracy are studied. The volumetric error modeling of machine tool is established by multi-body system (MBS) theory, which describes the topological structure of MBS in a simple and convenient matrix form. Based on the volumetric error model, the equivalent components of the errors for the three axes are established by reducing error terms. Then, the fluctuations of equivalent errors and the machining accuracy in working planes are depicted and predicted using the theory of stochastic process, whose range should be controlled within a certain confidence interval. Furthermore, the critical geometric errors that have significant influence on the machining accuracy fluctuation are identified. Based on the analysis results, some improvement in the machine tool parts introduced and the results for the modified machine show that the prediction allow for reduction in errors for the precision and ultra-precision machining.

scholarly journals An Analysis Methodology for Stochastic Characteristic of Volumetric Error in Multiaxis CNC Machine Tool

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Qiang Cheng ◽  
Can Wu ◽  
Peihua Gu ◽  
Wenfen Chang ◽  
Dongsheng Xuan
Keyword(s):  
Machine Tool ◽  
Geometric Error ◽  
Error Modeling ◽  
Machining Accuracy ◽  
Geometric Errors ◽  
Cnc Machine ◽  
Analysis Model ◽  
Volumetric Error ◽  
Value Analysis ◽  
Stochastic Characteristic

Traditional approaches about error modeling and analysis of machine tool few consider the probability characteristics of the geometric error and volumetric error systematically. However, the individual geometric error measured at different points is variational and stochastic, and therefore the resultant volumetric error is aslo stochastic and uncertain. In order to address the stochastic characteristic of the volumetric error for multiaxis machine tool, a new probability analysis mathematical model of volumetric error is proposed in this paper. According to multibody system theory, a mean value analysis model for volumetric error is established with consideration of geometric errors. The probability characteristics of geometric errors are obtained by statistical analysis to the measured sample data. Based on probability statistics and stochastic process theory, the variance analysis model of volumetric error is established in matrix, which can avoid the complex mathematics operations during the direct differential. A four-axis horizontal machining center is selected as an illustration example. The analysis results can reveal the stochastic characteristic of volumetric error and are also helpful to make full use of the best workspace to reduce the random uncertainty of the volumetric error and improve the machining accuracy.

Modeling Quasi-Static Errors in a Five-Axis Gantry Machine Tool

2012 ◽  
Vol 152-154 ◽  
pp. 781-787
Author(s):  
Jian Yin ◽  
Ming Li ◽  
Fang Yu Pan
Keyword(s):  
Machine Tool ◽  
Thermal Error ◽  
Geometric Error ◽  
Error Model ◽  
Error Modeling ◽  
Compensation Scheme ◽  
Homogeneous Transformation Matrix ◽  
Body Kinematic ◽  
Five Axis ◽  
Gantry Machine Tool

Enhancing the accuracy of machine tool is a key goal of machine tool manufactures and users. To characterize the Quasi-static errors and then use software compensation is an important step for accuracy enhancement. The effectiveness of an error compensation scheme relies heavily on the error model. The model must be concise and roust which can be applied to any machine tool. The total Quasi-static errors within the workspace of a five-axis gantry machine tool is composed of geometric error, kinematic error, thermal error. This paper presents an error model which can be used for practical compensation scheme. Homogeneous transformation matrix, rigid body kinematic and small angle approximations are used in this paper for error modeling.

Tool path error prediction of a five-axis machine tool with geometric errors

2002 ◽  
Vol 216 (5) ◽  
pp. 697-712 ◽  
Author(s):  
Y A Mir ◽  
J R R Mayer ◽  
C Fortin
Keyword(s):  
Machine Tool ◽  
Computer Aided Design ◽  
Tool Path ◽  
Kinematic Model ◽  
Dimensional Accuracy ◽  
Geometric Error ◽  
Geometric Errors ◽  
Computer Aided Process Planning ◽  
Computer Aided ◽  
Five Axis

Predicting the actual tool path of a machine tool prior to machining a part provides useful data in order to ensure or improve the dimensional accuracy of the part. The actual tool path can be estimated by accounting for the effect of the machine tool geometric error parameters. In computer aided design/computer aided manufacture (CAD/CAM) systems, the nominal tool path [or CL (cutter location) data] is directly generated from the curves and surfaces to be machined and the errors of the machine tool are not considered. In order to take these errors into consideration, they must first be identified and then used in the machine tool forward kinematic model. In this paper a method is presented to identify the geometric errors of machine tools and predict their effect on the tool-tip position. Both the link errors (position-independent geometric error parameters) and the motion errors (position-dependent geometric error parameters) are considered. The nominal and predicted tool paths are compared and an assessment is made of the resulting surfaces with respect to the desired part profile tolerance. A methodology is also suggested to integrate this tool within a CAD/CAPP (computer aided process planning)/CAM environment.

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