Modeling Errors in Coordinate Measuring Machines and Machine Tools Using Homogeneous Transformation Matrices (HTM)

Coordinate Measuring Machines (CMM's) have attributes to provide results with accuracy and repeatability in measurements, so they are considered equipment with potential for application in industrial environments, specifically in inspection processes. However, as in a machine tools the knowledge of the errors in CMM is needed and allows applying techniques of error compensation. This study aimed to develop a mathematical model of the kinematic errors of a bridge type CMM in "X", "Y" and "Z" directions. Modeling of the errors was accomplished using coordinate transformations applied to the rigid body kinematics; the method of the homogeneous transformation was used for the development of the model. The position and angular errors for the three axes of CMM, in addition to errors related to the absence of orthogonality between them were equated. This study allowed to conclude that modeling of errors applied to CMM allied to calibration is able to evaluate the metrological performance of equipment with displacement on guides, thus is possible to use this technique as error budget analysis in machines.

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Calibration of Positional Errors in Coordinate Measuring Machines and Machine Tools Using a Laser Interferometer System

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.798.303 ◽

2015 ◽

Vol 798 ◽

pp. 303-307 ◽

Cited By ~ 2

Author(s):

Benedito di Giacomo ◽

César Augusto Galvão de Morais

Keyword(s):

Machine Tools ◽

Coordinate Measuring Machine ◽

Laser Interferometry ◽

Dynamic Mode ◽

Coordinate Measuring Machines ◽

Measurement Systems ◽

Volumetric Errors ◽

Bridge Type ◽

Measuring Machine

Dimensional inspections in manufactured workpieces allow assess the quality of the manufacturing process, in this context the quality and development of measurement systems are issues addressed by many researchers. The coordinate measuring machines (CMMs) are versatile systems, can measure complex geometries quickly and accurately. Positional errors are parts of volumetric error and affect the correct positioning of probe in CMMs or of the tool in machine tools. Faced with this, the purpose this investigation is show a method to calibrate the positional errors in a bridge-type coordinate measuring machine, this method collects data in dynamic mode and reduces cyclic errors. The calibration of positional errors was performed using laser interferometry in the “on-the-fly” mode and a method to reduce cyclic errors was applied. The highest value of position error occurred in x axis with value positive of 10μm in the position of 220mm, while in the y and z axis the higher absolute values were 2μm and 6μm respectively. From calibration and compensating of positional errors it is possible to reduce the effects of the volumetric errors in machines with axis of linear displacements as the CMMs and machine tools.

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Machine tools. Test conditions for bridge-type milling machines. Testing of the accuracy

10.3403/30141130 ◽

2008 ◽

Keyword(s):

Machine Tools ◽

Test Conditions ◽

Milling Machines ◽

Bridge Type

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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

Journal of Manufacturing Science and Engineering ◽

10.1115/1.4042582 ◽

2019 ◽

Vol 141 (4) ◽

Cited By ~ 2

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.

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Mathematical Approach for Geometric Error Modeling of Three Axis CNC Vertical Milling Machine

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.842.303 ◽

2016 ◽

Vol 842 ◽

pp. 303-310 ◽

Cited By ~ 1

Author(s):

Widyanti Kwintarini ◽

Agung Wibowo ◽

Yatna Yuwana Martawirya

Keyword(s):

Machine Tool ◽

Machine Tools ◽

Machining Process ◽

Cnc Machine Tools ◽

Milling Machine ◽

Cnc Machine ◽

Geometrical Errors ◽

Vertical Milling ◽

Vertical Milling Machine ◽

Accuracy And Repeatability

The aim of this paper overviews about to find out the errors that come from three axis CNC vertical milling machine. The errors come from, the CNC milling machine can be modelled into mathematical models and later on these error models will be used to analyse the errors in the measured data. Many errors from CNC machine tools have given significant effects toward the accuracy and repeatability of manufacturing process. There are two error sources come from CNC machine tools such as tool deflection and thermal distortions of machine tool structure. These errors later on will contribute to result in the geometrical deviations of moving axis in CNC vertical milling machine. Geometrical deviations of moving axis such as linear positioning errors, roll, pitch and yaw can be designated as volumetric errors in three axis machine tool. Geometrical deviations of moving axises happen at every axis in three axis CNC vertical milling machine. Geometrical deviations of moving axises in linear and angular movement has the amount of errors up to twenty one errors. Moreover, this geometrical errors play the major role in the total amount of errors and for that particular reason extra attention towards the geometrical deviation errors will be needed along machining process. Each of geometrical error of three axes vertical machining center is modeled using a homogeneous transformation matrix (HTM). The developed mathematical model is used to calculate geometrical errors at each axis and to predict the resultant error vector at the interface of machine tool and workpiece for error compensation.

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Prediction of Machining Accuracy of 5-Axis Machine Tools with Kinematic Errors

Proceedings of the 35th International MATADOR Conference ◽

10.1007/978-1-84628-988-0_64 ◽

2007 ◽

pp. 285-288

Author(s):

M. Sharif Uddin ◽

S. Ibaraki ◽

A. Matsubara ◽

T. Matsushita

Keyword(s):

Machine Tools ◽

Machining Accuracy ◽

Kinematic Errors

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Uncertainty analysis of a laser calibration system for evaluating the positioning accuracy of a numerically controlled axis of coordinate measuring machines and machine tools

Precision Engineering ◽

10.1016/j.precisioneng.2007.05.001 ◽

2008 ◽

Vol 32 (2) ◽

pp. 106-113 ◽

Cited By ~ 14

Author(s):

H.F.F. Castro

Keyword(s):

Uncertainty Analysis ◽

Machine Tools ◽

Coordinate Measuring Machines ◽

Calibration System ◽

Positioning Accuracy ◽

Laser Calibration

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Volumetric Positioning Errors of CNC Machining Tools and Laser Sequential Step Diagonal Measurement

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.315-316.98 ◽

2006 ◽

Vol 315-316 ◽

pp. 98-102 ◽

Cited By ~ 5

Author(s):

J.H. Shen ◽

H.T. Zhang ◽

Hong Tao Cao ◽

Jian Guo Yang ◽

C. Wang

Keyword(s):

Machine Tools ◽

Measurement Method ◽

Measurement Data ◽

Cnc Machining ◽

Cnc Machine Tools ◽

Cnc Machine ◽

Transformation Matrices ◽

Positioning Errors ◽

Analysis Measurement ◽

Key Factor

The volumetric positioning precision of CNC machine tools is the key factor to get high machining precision, so the analysis, measurement and compensation of the volumetric error is becoming more and more important. In this paper, the modeling results of 3-axes CNC machine tools with four different configurations are given based on rigid body theory and homogeneous coordination transformation matrices. An improved sequential step diagonal measurement method is proposed and analyzed because the current laser measurement methods are complex and time cost. At the final section of the paper, the measurement data was applied into the error compensation and the sequential step diagonal measurement method was validated efficient and convenient.

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