Damage Detection of Localized Defects in Spur Gear Pairs and Geared Transmissions Using Damage-Induced Dynamic Response

Abstract

Geared transmissions are important systems, especially in the aerospace and rotorcraft industry. Loss of power from gearbox failure due to damaged tooth poses reliability and safety issues. Health and Usage Monitoring Systems (HUMS) are used in rotorcraft vehicles to monitor the performance of their transmissions and other critical components. Condition monitoring systems use measured vibrations from geared transmissions to detect damage to the gears and other components inside them. A major challenge for damage detection systems is identifying damage from otherwise normal changes in vibrations that may occur. In this dissertation, the analysis of the damage-induced dynamic response of geared transmission is carried out by understanding the dynamic response on the spur gear pair and applying it to the geared transmission accelerations. For the accurate damage-induced dynamic response of the spur gear pair, accurate tooth mesh interface parameters are derived utilizing the finite element/contact mechanics (FE/CM) method. Tooth mesh characterization involves determining the static transmission error and the mesh stiffnesses when the teeth have either root cracks or surface pitting damage. The damage cases considered include tooth root cracks or surface pits localized to a single gear tooth. The FE/CM method accurately predicts the tooth mesh stiffnesses of the unity-ratio gear pair when it is healthy without damage, and when the teeth have root cracks and surface pitting. The static transmission error increases and the tooth mesh stiffness decreases with increasing size of pits and increasing lengths of cracks. The distinct differences in duration observed between tooth surface pit and root cracks may permit their detection from static transmission error measurements. Dynamic transmission error is calculated using the lumped-parameter model and shown to compare well with dynamic response calculations from the FE/CM gear pair model. Larger damage on the gear pair generally causes higher vibrations to result. Quasi-static responses are observed at speeds less than one-third of the natural frequency, while above that, the damage-induced dynamic response shows impulse-like behavior. The damage-induced dynamic response of high-speed spur gear pairs with localized defects shows that the response is oscillatory with decaying amplitudes, a linear oscillator, and based on these, a phenomenon-based model is proposed for approximating the damage-induced dynamic response which is determined solely by an amplitude (dependent on damage severity), damping ratio, and natural frequency (properties of gear pair). The simplicity of the phenomenon-based model permits analytical closed-form expressions of several condition indicators used in damage detection and the ability to predict condition indicators for varying gear pair properties. Geared transmission vibrations are determined using the FE/CM model to detect damage. When damage (i.e., tooth root cracks or tooth surface pits) occurs on the individual gears of the planetary stage, additional transient vibrations occur that meaningfully alter the resulting vibrations and their spectrum. The ability to calculate condition indicators (CI) for detecting damage is explored and and it appears to be sensitive to the input vibration signal used in the CI calculation. Tooth root cracks with lengths less than 50 percent through the tooth thickness generally do not lead to substantial increases in the individual CIs. Calculating the damage-induced dynamic response or the exact difference signal effectively detects even smaller crack length damages in the space-fixed or rotating gears of the planetary stage, utilizing the calculations of CIs. These will enable reliable damage detection techniques for geared transmissions, improving safety, reliability, vehicle readiness, and vehicle performance