Investigation and modeling of the uncertainty in laser-Doppler-velocimeter-based radius measurement

Research output: Contribution to journalResearch articleContributedpeer-review

Contributors

Abstract

Abstract Laser Doppler velocimeter (LDV) allows for measurement of the lateral velocity of rotating cylindrical workpiece, thus, enabling the absolute radius measurement, showing great application prospects. However, there exist adverse factors that decrease the measurement accuracy, for example, variation of fringe spacing, fluctuation of rotating speed, spindle error motions, and Doppler frequency estimation. In this context, this paper comprehensively investigates the uncertainty in the LDV-based radius measurement. First, an LDV sensor was constructed and calibrated. Then, a primary model of the LDV-based radius measurement is presented: r = f d ⋅ D 2 π ⋅ f n , which suggests that the measurand is indirectly calculated from three input quantities: the Doppler frequency f d , the fringe spacing D , and the rotation frequency f n , each of which owns an estimation uncertainty, propagating into the measurement result. Based on this, uncertainty propagation in LDV-based radius measurement is investigated: (1) By calculating the partial derivative of the measurement model, uncertainty propagation of the rotational frequency fluctuation is derived and the resulting uncertainty is 2.2 μ m . (2) Random uncertainty in Doppler frequency estimation leads to stochastic dispersion in radius estimates. The resulting uncertainty is statistically derived to be 11.4 μ m . (3) Measurement procedure is numerically simulated to verify that a sinusoidal systematic uncertainty can be caused by the fringe spacing variation and the workpiece runout. The resulting uncertainty is 10 .6 μ m . (4) Spectral analysis reveals that spindle error motions introduce a significant uncertainty, accounting for 74% of the total uncertainty. For a comprehensive modeling of uncertainty, the spindle error motions δ ( t ) is incorporated into the measurement model: r = f d ⋅ D − δ ˙ ( t ) 2 π ⋅ f n . (5) Taking the roundness error ρ ( θ ) as an input uncertainty, the measurement model is further revised to: r = f d ⋅ D − δ ˙ ( t ) 2 π ⋅ f n + ρ ( θ ) .

Details

Original languageEnglish
Article number095204
JournalMeasurement Science and Technology
Volume36
Issue number9
Publication statusPublished - 30 Sept 2025
Peer-reviewedYes

External IDs

ORCID /0000-0002-8321-7488/work/214455710

Keywords

Keywords

  • laser Doppler velocimeter, radius measurement, uncertainty evaluation