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.

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

2018 ◽  
Author(s):  
Hua-Wei Ko ◽  
Shiv G. Kapoor ◽  
Placid M. Ferreira ◽  
Patrick Bazzoli ◽  
J. Adam Nisbett ◽  
...  
Keyword(s):  
Machine Tool ◽  
Parameter Identification ◽  
Thermal Error ◽  
Error Model ◽  
Observer Design ◽  
Optimal Designs ◽  
Model Parameters ◽  
Volumetric Error ◽  
Identification Procedure ◽  
Volumetric Errors

A parameter identification procedure for identifying the parameters of a volumetric error model of a large and complex machine tool usually requires a large number of observations of volumetric error components in its workspace. This paper demonstrates the possibility of applying optimal observation/experimental design theories to volumetric error model parameter identification of a large 5-axis machine with one redundant axis. Several designs such as A-, D- and K-optimal designs seek to maximize the amount of information carried in the observations made in an experiment. In this paper, we adapt these design approaches in the construction of machine-tool error observers by determining locations in the workspace at which components of volumetric errors must be measured so that the underlying error model parameters can be identified. Many of optimal designs tend to localize observations at either the center or the boundary of the workspace. This can leave large volumes of the workspace inadequately represented, making the identified model parameters particularly susceptible to model inadequacy issues. Therefore, we develop constrained optimization algorithms that force the distribution of observation points in the machine’s workspace. Optimal designs provide the possibility of efficiency (reduced number of observations and hence reduced measurement time) in the identification procedure. This opens up the possibility of tracking thermal variations of the volumetric error model with periodic quick measurements. We report on the design, implementation and performance of a constrained K-optimal in tracking the thermal variations of the volumetric error over a 5.5 hour period of operations with measurements being made each hour.

scholarly journals Impact of Model Complexity in the Monitoring of Machine Tools Condition Using Volumetric Errors

2020 ◽  
Vol 14 (3) ◽  
pp. 369-379
Author(s):  
Kanglin Xing ◽  
◽  
J. R. R. Mayer ◽  
Sofiane Achiche
Keyword(s):  
Machine Tool ◽  
Recognition Rate ◽  
Error Model ◽  
Model Complexity ◽  
Model Parameters ◽  
Machine Error ◽  
Error Models ◽  
Tool Condition ◽  
Volumetric Errors ◽  
Five Axis

The scale and master ball artefact (SAMBA) method allows estimating the inter- and intra-axis error parameters as well as volumetric errors (VEs) of a five-axis machine tool by using simple ball artefacts and the machine tool’s own touch-trigger probe. The SAMBA method can use two different machine error models named after the number of model parameters, i.e., the “13” and “84” machine error models, to estimate the VEs. In this study, we compare these two machine error models when using VE vector directions and values for monitoring the machine tool condition for three cases of machine malfunctions: 1) a C-axis encoder fault, 2) an induced X-axis linear positioning error, and 3) an induced straightness error simulated fault. The results show that the “13” machine error model produces more focused concentrated VE directions but smaller VE values when compared with the “84” machine error model; furthermore, although both models can recognize the three faults and are effective in monitoring the machine tool condition, the “13” machine error model achieves a better recognition rate of the machine condition. This paper provides guidelines for selecting machine error models for the SAMBA method when using VEs to monitor the machine tool condition.

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.

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%.

A sensitivity method to analyze the volumetric error of five-axis machine tool

2018 ◽  
Vol 98 (5-8) ◽  
pp. 1791-1805 ◽  
Author(s):  
Qingzhao Li ◽  
Wei Wang ◽  
Yunfeng Jiang ◽  
Hai Li ◽  
Jing Zhang ◽  
...  
Keyword(s):  
Machine Tool ◽  
Volumetric Error ◽  
Sensitivity Method ◽  
Five Axis

A kinematic approach for error modelling in drilling

2019 ◽  
Vol 36 (4) ◽  
pp. 1364-1383 ◽  
Author(s):  
Wilma Polini ◽  
Andrea Corrado
Keyword(s):  
Machine Tool ◽  
Reference Frame ◽  
Kinematic Model ◽  
Model Parameters ◽  
Geometric Errors ◽  
Volumetric Error ◽  
Machined Surface ◽  
Content Type ◽  
Practical Applications ◽  
Source Errors

Purpose The purpose of this paper is to model how geometric errors of a machined surface (or manufacturing errors) are related to locators’ error, workpiece form error and machine tool volumetric error. A kinematic model is presented that puts into relationship the locator error, the workpiece form deviations and the machine tool volumetric error. Design/methodology/approach The paper presents a general and systematic approach for geometric error modelling in drilling because of the geometric errors of locators positioning, of workpiece datum surface and of machine tool. The model can be implemented in four steps: (1) calculation of the deviation in the workpiece reference frame because of deviations of locator positions; (2) evaluation of the deviation in the workpiece reference frame owing to form deviations in the datum surfaces of the workpiece; (3) formulation of the volumetric error of the machine tool; and (4) combination of those three models. Findings The advantage of this approach lies in that it enables the source errors affecting the drilling accuracy to be explicitly separated, thereby providing designers and/or field engineers with an informative guideline for accuracy improvement through suitable measures, i.e. component tolerancing in design, machining and so on. Two typical drilling operations are taken as examples to illustrate the generality and effectiveness of this approach. Research limitations/implications Some source errors, such as the dynamic behaviour of the machine tool, are not taken into consideration, which will be modelled in practical applications. Practical implications The proposed kinematic model may be set by means of experimental tests, concerning the industrial specific application, to identify the values of the model parameters, such as standard deviation of the machine tool axes positioning and rotational errors. Then, it may be easily used to foresee the location deviation of a single or a pattern of holes. Originality/value The approaches present in the literature aim to model only one or at most two sources of machining error, such as fixturing, machine tool or workpiece datum. This paper goes beyond the state of the art because it considers the locator errors together with the form deviation on the datum surface into contact with the locators and, then, the volumetric error of the machine tool.

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.

A Complete, Continuous, and Minimal Product of Exponentials-Based Model for Five-Axis Machine Tools Calibration With a Single Laser Tracker, an R-Test, or a Double Ball-Bar

2019 ◽  
Vol 141 (4) ◽  
Author(s):  
Peng Xu ◽  
Benny C. F. Cheung ◽  
Bing Li
Keyword(s):  
Machine Tool ◽  
Machine Tools ◽  
Rigid Bodies ◽  
Error Model ◽  
Laser Tracker ◽  
Calibration Model ◽  
Transformation Matrices ◽  
Double Ball Bar ◽  
Ball Bar ◽  
Five Axis

Calibration is an important way to improve and guarantee the accuracy of machine tools. This paper presents a systematic approach for position independent geometric errors (PIGEs) calibration of five-axis machine tools based on the product of exponentials (POE) formula. Instead of using 4 × 4 homogeneous transformation matrices (HTMs), it establishes the error model by transforming the 6 × 1 error vectors of rigid bodies between different frames resorting to 6 × 6 adjoint transformation matrices. A stable and efficient error model for the iterative identification of PIGEs should satisfy the requirements of completeness, continuity, and minimality. Since the POE-based error models for five-axis machine tools calibration are naturally complete and continuous, the key issue is to ensure the minimality by eliminating the redundant parameters. Three kinds of redundant parameters, which are caused by joint symmetry information, tool-workpiece metrology, and incomplete measuring data, are illustrated and explained in a geometrically intuitive way. Hence, a straightforward process is presented to select the complete and minimal set of PIGEs for five-axis machine tools. Based on the established unified and compact error Jacobian matrices, observability analyses which quantitatively describe the identification efficiency are conducted and compared for different kinds of tool tip deviations obtained from several commonly used measuring devices, including the laser tracker, R-test, and double ball-bar. Simulations are conducted on a five-axis machine tool to illustrate the application of the calibration model. The effectiveness of the model is also verified by experiments on a five-axis machine tool by using a double ball-bar.

Spindle Thermal Error Optimization Modeling of a Five-axis Machine Tool

2017 ◽  
Vol 30 (3) ◽  
pp. 746-753 ◽  
Author(s):  
Qianjian GUO ◽  
Shuo FAN ◽  
Rufeng XU ◽  
Xiang CHENG ◽  
Guoyong ZHAO ◽  
...  
Keyword(s):  
Machine Tool ◽  
Thermal Error ◽  
Optimization Modeling ◽  
Five Axis ◽  
Error Optimization

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.

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