A New Analytical Method for Modeling the Effect of Assembly Errors on a Motor-Gearbox System

Bilal El Yousfi,François Guillet,Abdenour Soualhi,Kamal Medjaher

doi:10.3390/en14164993

Abstract

The well-known gear tooth defects such as root cracks and flank spalls have been widely investigated in previous studies to model their effects on the time varying mesh stiffness (TVMS) and consequently the dynamic response of motor-gearbox systems. Nevertheless, the effect of assembly errors such as the center distance and the eccentricity has been less considered in past works. Determining the signature of these errors on the system response can help for their early detection and diagnostic to avoid overloading and failure of gears. An original geometric-based method combined with the potential energy method is proposed in this paper to accurately model the effect of these assembly errors on the TVMS of mating spur gear pairs. This is achieved by updating the line of action equation (LOA) at each meshing step using the actual coordinates of gear centers and employing a contact detection algorithm (CDA) to determine the actual contact points coordinates. An electrical model of a three-phase induction machine was then coupled with a dynamic model of a one-stage spur gear system to simulate the effect of assembly errors on the electromechanical response of the motor-gearbox system. The simulation results showed that the center distance error induces a reduction in the TVMS magnitude and the contact ratio, whereas the eccentricity error causes a double modulation of the TVMS magnitude and frequency. In addition, the results showed that assembly errors can be detected and diagnosed by analyzing the system vibration and the motor phase-current.

Highlights

Thanks to their robustness and good efficiency–cost ratio, induction motors and gearboxes are widely adopted in modern power transmission applications
Two types of mounting errors were considered in this study, namely the center distance error and the eccentricity error
The gear teeth geometry has a direct impact on the gear mesh stiffness curve and modifying the gear teeth width causes a deformation of the time varying mesh stiffness (TVMS) magnitude;

Summary

Introduction

Thanks to their robustness and good efficiency–cost ratio, induction motors and gearboxes are widely adopted in modern power transmission applications. Two frequent problems are almost inevitable when assembling gear systems: the center distance and the eccentricity errors. The center distance error occurs when the distance separating the two mating gear centers is not adjusted properly, whereas the eccentricity error appears when a shift exists between the geometric center of the gear and its rotation center. These anomalies should be avoided in gear systems because they affect the transmission efficiency of gearboxes and reduce their practical useful life by increasing the tooth surface contact stress and the tooth root bending stress [2]. Understanding the effect of the center distance and eccentricity errors on the system’s observable quantities such as the vibration and the electrical response could help enormously in the early detection and reparation of them in order to avoid system failure [3,4]

Methods

Results

Conclusion