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Control of phases by ESPRIT and WLSE methods for the early detection of gear cracks

Published online by Cambridge University Press:  16 September 2014

Thameur Kidar ,
Marc Thomas ,
Mohamed El Badaoui  and
Raynald Guilbault
Thameur Kidar
Affiliation:
Department of Mechanical Engineering, École de Technologie Supérieure, 1100, Notre-Dame street West, Montreal, H3C 1K3, Quebec, Canada University of Lyon, University of Saint-Etienne, LASPI EA-3059, 20 Avenue de Paris, 42334 Roanne Cedex, France
Marc Thomas*
Affiliation:
Department of Mechanical Engineering, École de Technologie Supérieure, 1100, Notre-Dame street West, Montreal, H3C 1K3, Quebec, Canada
Mohamed El Badaoui
Affiliation:
University of Lyon, University of Saint-Etienne, LASPI EA-3059, 20 Avenue de Paris, 42334 Roanne Cedex, France
Raynald Guilbault
Affiliation:
Department of Mechanical Engineering, École de Technologie Supérieure, 1100, Notre-Dame street West, Montreal, H3C 1K3, Quebec, Canada
*
a Corresponding author: marc.thomas@etsmtl.ca
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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.

Keywords

Gear crackphase measurementsamplitude and frequency modulationsHilbert transformESPRIT and WLSE methods
Type
Research Article
Information
Mechanics & Industry , Volume 15 , Issue 6 , 2014 , pp. 487 - 495
Copyright
© AFM, EDP Sciences 2014

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