## Abstract

The authors regret making an error in simulation code used to produce the data for the original paper. Due to errors in seeding the random number generator and handling the probe angles, the original simulations correspond to a situation with a reduced amount of data and calculation of the roundness profiles with exact information of the probe angles in the frame. A more realistic situation, as we originally intended it to be, would be the calculation of the roundness profiles with the nominal probe angles with the actual angles having some deviations. When reading the observations made in the results and discussion sections of the original paper should, it should be considered that the deviating angles were used in the calculation of the roundness profile. The updated results show that the using the incorrect angles in calculation with the selected deviation results in an error greater than with the other applied sources of error. The errors have been corrected and the simulations have been re-run. Results presented in Tables 2, 3 and 4 and Figs. 7, 8 and 10–15 have been updated. Please note that the following sentences have been corrected: Correction The reference profile was simulated as a circular polygon constructed from 2500 points. Original The reference profile was simulated as a circular polygon constructed from 1024 points. Correction The slower convergence when considering the whole range of harmonics is due to larger errors in the higher order components. Original The slower convergence when considering the whole range of harmonics is due to larger errors in the higher order components, especially in the least squares four-point method, which produced very large errors for some harmonic components in some of the cases. Correction For single components, the three point method yielded the largest standard deviations. Original For single components, the least squares minimization yielded the largest standard deviations. This can be explained by the probe angles having been optimized for the three-point method based on a smallest total error propagation rate for the lower order components. Correction Angular misalignment errors of the probes are a dominating source of error in multi-probe measurement, and they lead to a large phase errors. Unlike in diameter sampling, in the other methods, the errors were more spread between the phase and the amplitude of the components. Original Angular misalignment errors of the probes are especially harmful for diameter sampling, and lead to a large phase errors. In the other methods, these errors were spread between the phase and the amplitude of the component. Correction In this research, one particularly large source of uncertainty was the angular misalignment error of the probes, which caused major errors especially in all of the methods. The effects of the angular errors can be well seen in the figures and tables with all of the errors combined. Original In this research, one particularly large source of uncertainty was the angular misalignment error of the probes, which caused major errors especially in the methods using four probes. Their effects can be well seen in the figures and tables with all of the errors combined. Correction When all errors were applied (Fig. 15), the means of the four-point methods where more accurate than in the three point-method when considering the full range of harmonics. Original When all errors were applied (Fig. 15), although there were observable differences between the methods in the standard deviations of the amplitudes and phases of the harmonic components, the means re approximately as accurate. Correction Whitehouse [15] has suggested that adding more probes will incur limited benefits, since additional probes will also give rise to additional tilts and shifts to the system. The results support this claim when only considering the low order harmonic components. Zhang [12] claims that generally speaking the measurement errors are caused by angular misalignment of the probes are not as great as the errors introduced by the accuracy of the probes. The results obtained here conflict with this statement, given that the selected distribution was selected to resemble the error of tactile probes. Original Whitehouse [15] has suggested that adding more probes will incur limited benefits, since additional probes will also give rise to additional tilts and shifts to the system. The results support this claim. Zhang [12] claims that generally speaking the measurement errors are caused by angular misalignment of the probes are. The results obtained here conflict with this statement, given that the selected distribution was selected to resemble the error of tactile probes.

Original language | English |
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Article number | 107495 |

Number of pages | 6 |

Journal | Mechanical Systems and Signal Processing |

Volume | 158 |

Early online date | 13 Mar 2021 |

DOIs | |

Publication status | Published - Sep 2021 |

MoE publication type | Not Eligible |