Error interval evaluation method for gear tooth surface waviness fourier analysis based on forward calculation

Abstract

This invention discloses a method for evaluating the error interval of Fourier analysis of gear tooth surface waviness based on forward modeling. First, a homogeneous evaluation dataset is constructed, and the distribution characteristics of the actual sampling interval are statistically analyzed to determine the frequency domain confidence range. The core of this method lies in introducing Monte Carlo forward modeling to quantify the systematic deviation and random fluctuations caused by sampling interval fluctuations to the spectrum. Based on this, a heteroscedastic normal distribution model of the measured amplitude is established, and the true amplitude value is inversely derived using maximum likelihood estimation. The pivot method is then used to calculate the error interval of the amplitude at key frequency points under a predetermined confidence level. Further forward modeling is used to optimize and determine the optimal sampling length and resampling interval. This invention overcomes the limitation of traditional measurements that can only provide a single spectrum result, achieving quantitative calibration of the error introduced by the measurement system itself, providing reliability evaluation results with confidence intervals, and providing a closed-loop optimization decision-making basis for the selection of measuring instruments and parameter settings.

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