Abstract

The early detection of gear faults remains a major problem, especially when the gears are subjected to non stationary phenomena due to defects. In industrial applications, the crack of tooth is a default very difficult to detect whether using the time descriptors or the frequency analysis. In this work and based on a numerical model, we prove that the crack default affects directly the phase of the frequency component of the defective wheel (frequency modulation). To properly estimate the phases, we suggest two high-resolution techniques (Estimation of Signal Parameters via Rotational Invariance Techniques ESPRIT with a sliding window and Weighted Least Squares Estimator WLSE). The results of both methods are compared to the phase obtained by Hilbert transform. The three techniques are then applied on a multiplicative signal with a frequency modulation to show the influence of the amplitude modulation on the quality of phase estimation. We note that the ESPRIT method is much better in the estimation of frequencies while WLSE shows much efficiency in the estimation of phases if we keep the frequencies almost stables.

Highlights

  • This paper is aimed to the improvement of signal processing methods to perform an early diagnosis of faults in mechanical systems using vibration signals

  • The techniques of high-resolution ESPRIT [10] and Weighted Least Square Estimator (WLSE) [11] which allow for estimating the frequency components and their energies from vibratory signals are used in this paper

  • Since amplitude and frequency modulations appear in a breathing crack, a multiplicative signal with frequency-modulation is first used to analyze the influence of the amplitude modulation phenomenon on the quality of phase estimation

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Summary

Introduction

This paper is aimed to the improvement of signal processing methods to perform an early diagnosis of faults in mechanical systems using vibration signals. The techniques of high-resolution ESPRIT [10] and WLSE [11] which allow for estimating the frequency components and their energies from vibratory signals are used in this paper. A sliding window is introduced into the ESPRIT method for monitoring the instantaneous phase variation due to cracks.

Tooth crack modeling
Data model formulation
ESPRIT approach
WLSE approach
The Hilbert transform
Numerical analysis
Phase analysis of a cracked tooth model
Conclusion

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