Efficient uncertainty estimation of indirectly measured geometric errors of five-axis machine tools via Monte-Carlo validated GUM framework

Sepahi-Boroujeni, Saeid; Mayer, Josef; Khameneifar, Farbod

doi:10.1016/j.precisioneng.2020.09.027

Cited by 26 publications

(10 citation statements)

References 21 publications

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“…Where By decoupling equation ( 6), all PDGEs of the Aaxis can be obtained, as shown in equation (7). It is noticed here that there are two solutions for e xa in equation 7(a).…”

Section: Pdges Identification Based On Ballbarmentioning

confidence: 99%

“…6 The GUM method calculates the estimated value and uncertainty of the output quantity based on the uncertainty propagation law, so the GUM method based on the uncertainty propagation law cannot evaluate the uncertainty of the geometric error, and an appropriate method is needed to evaluate the uncertainty, such as MCM. 7 The MCM computes the probability density function (PDF) of the output by measuring the PDF of the model propagation input. Since MCM allows the uncertainty to be evaluated without calculating the partial derivatives of the measurement model, 8 this study uses MCM to analyze the measurement uncertainty of the ballbar.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Geometric error measurement uncertainty analysis of rotary axis based on Monte Carlo method

Sun

Xiang

et al. 2023

Proceedings of the Institution of Mechanical Engineers, Part C:

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Ballbar is widely used for geometric error measurement of the rotary axis, and the uncertainty analysis is of great significance to ensure the reliability of error identification. This study analyzes the measurement uncertainty based on the Monte Carlo method. First, this study clarifies the uncertainty mechanisms caused by tool setting error, translational axis motion error, and ballbar installation error, and proposes a measurement model comprehensively considering the uncertainty sources. In this study, the same ballbar measurement experiments were carried out 10 times in three measurement modes, and the standard deviation of the ballbar length change under different rotation angles was analyzed to ensure that the uncertainty of the geometric error can be effectively analyzed. Furthermore, the uncertainty of each error at different angles of the rotary axis is evaluated based on the measurement model. The results show that the translational axis motion error and tool setting error are important sources of uncertainty. The measurement uncertainty of the angle positioning error is the largest in A- and C-axis, and its standard uncertainty reaches 9.38″ and 2.81″. After optimizing the sine and cosine terms in the identification model, the standard uncertainties of the angular positioning errors are reduced to 6.43″ and 2.26″, and also the estimated errors are close to the actual values, which verifies the validity of the uncertainty analysis method.

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“…Where By decoupling equation ( 6), all PDGEs of the Aaxis can be obtained, as shown in equation (7). It is noticed here that there are two solutions for e xa in equation 7(a).…”

Section: Pdges Identification Based On Ballbarmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Geometric error measurement uncertainty analysis of rotary axis based on Monte Carlo method

Sun

Xiang

et al. 2023

Proceedings of the Institution of Mechanical Engineers, Part C:

View full text Add to dashboard Cite

show abstract

“…The approximate model (7) could itself be the result of a numerical procedure, or an analytic expression taken as a proxy for the measurement model.…”

Section: Nonlinear Modelmentioning

confidence: 99%

“…It produces virtual data whose properties reflect those of the data observed in the corresponding real experiment. Virtual experiments have become increasingly important in modern metrology and industrial applications [2][3][4][5][6][7]. They are utilized, for example, to explore the accuracy of a measurement device, or to specify machine tolerances needed to reach a required accuracy [8].…”

Section: Introductionmentioning

confidence: 99%

GUM-Compliant Uncertainty Evaluation Using Virtual Experiments

et al. 2022

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A virtual experiment simulates a real measurement process by means of a numerical model. The numerical model produces virtual data whose properties reflect those of the data observed in the real experiment. In this work, we explore how the results of a virtual experiment can be employed in the context of uncertainty evaluation for a corresponding real experiment. The uncertainty evaluation was based on the Guide to the Expression of Uncertainty in Measurement (GUM), which defines the de facto standard for uncertainty evaluation in metrology. We show that, under specific assumptions about model structure and variance of the data, virtual experiments in combination with a Monte Carlo method lead to an uncertainty evaluation for the real experiment that is in line with Supplement 1 to the GUM. In the general case, a GUM-compliant uncertainty evaluation in the context of a real experiment can no longer be based on a corresponding virtual experiment in a simple way. Nevertheless, virtual experiments are still useful in order to increase the reliability of an uncertainty analysis. Simple generic examples as well the case study of a virtual coordinate measuring machine are presented to illustrate the treatment.

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“…Published in 2008, the Propagation of Distributions Using a Monte Carlo Method, Supplement 1 to the guide, discusses the propagation of probability distributions through a mathematical measurement model [22,23]. The GUM method and Monte Carlo method (MCM) have been widely used in numerous fields to evaluate measurement uncertainties [24][25][26][27][28][29][30][31].…”

Section: Introductionmentioning

confidence: 99%

Uncertainty analysis of two-dimensional self-calibration with hybrid position using the GUM and MCM methods

Qiao¹,

Fan²,

Chen³

et al. 2021

Meas. Sci. Technol.

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Two-dimensional (2D) self-calibration is more suitable for ultra-precision engineering than conventional calibration, as it does not require higher-precision device calibration. A grid plate is translated or rotated in various positions on a stage, and the translation and rotation can be combined into a hybrid position. Using 2D self-calibration, the stage and plate errors are separated from the overall measurement errors obtained by measuring the grid plate on the stage. During this process, random noise propagates to the separated stage errors through the self-calibration model, causing propagation of the uncertainty of the errors. Accordingly, in this study, least squares-based 2D self-calibration was investigated. An overdetermined linear equation system was established based on the relationships among the variables for self-calibration. The Guide to the Expression of Uncertainty in Measurement was used to calculate the uncertainty propagation ratio after obtaining the least squares solutions for the self-calibration model, and the uncertainty was further analyzed using the Monte Carlo method. The uncertainty propagation ratios were less than 1, indicating that the self-calibration model had a favourable noise-suppression ability. The robustness of this self-calibration approach was mathematically determined. The effects of various position schemes (with and without a hybrid position) on the uncertainty propagation ratio were examined to support the design optimisation of the self-calibration program. The experiments revealed that the use of hybrid position schemes was advantageous over not using such schemes, although the self-calibration performance was comparable under both types of schemes.

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Efficient uncertainty estimation of indirectly measured geometric errors of five-axis machine tools via Monte-Carlo validated GUM framework

Cited by 26 publications

References 21 publications

Geometric error measurement uncertainty analysis of rotary axis based on Monte Carlo method

Geometric error measurement uncertainty analysis of rotary axis based on Monte Carlo method

GUM-Compliant Uncertainty Evaluation Using Virtual Experiments

Uncertainty analysis of two-dimensional self-calibration with hybrid position using the GUM and MCM methods

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