Modeling the Transmission Path Effect in a Planetary Gearbox

In such mechanical systems, as helicopters and self-propelled cranes, designers need to use gearboxes which have an important reduction ratio within compact space. Hence, planetary gearboxes are widely used. Consequently, its monitoring presents an important task for researchers and engineers either in healthy or damaged case. Many researchers are interested on the investigation of the modulation phenomenon in planetary gearbox. It is presented in a frequency representation as side-band activity near to the gear-mesh frequency component and its harmonics. In a healthy case, the origin of this phenomenon in a planetary gearbox (stationary ring) is that the transducer, which is mounted on the external housing of the ring gear, perceived signals from all components including sun-gear, ring-gear, carrier and planet-gears which can occupy different position in one carrier period rotation. Hence, when the planet comes closer to the sensor, the vibration signal increases and vice-versa. In this work, a two dimensional linear lumped parameter model is proposed to model vibration sources. A mathematical formulation of the transmission path is introduced in order to model only the amplitude modulation phenomenon due to the change of the planet-gear position since the speed of the sun is constant. A frequency representation of numerical results is presented and analyzed.