Aircraft transmissions have the peculiar characteristics of light structures and high operating speeds, therefore relatively low flexural natural frequencies and high excitation frequencies due to rotation and meshing. Resonance vibrations can create serious problems of malfunctions and even catastrophic failures. A reliable numerical model is surely a convenient means to perform preliminary simulations to identify the most critical resonance conditions and evaluate the effect of structural modifications on the dynamic behaviour of the component in the design development phase. Most numerical investigations found in the literature are carried out on simplified models of the rotating bodies likened to discs to reduce the computational effort. In this work a novel approach based on the application of Duhamel’s integral for the determination of the dynamic behaviour of a rotating gear subject to meshing forces has been developed to obtain more reliable results with a realistic model at an affordable computational cost. The gear response to dynamic excitation is obtained by the determination of its response to impulse using a single 3D finite element transient analysis taking afterwards into account the effect of the gear rotation. Subsequently, the Duhamel’s integral is applied using the tooth load time history in order to simulate as realistically as possible the gear load conditions. This paper presents the case of a real bi-helicoidal gear. A test bench was simulated measuring the displacement observed by some non-rotating virtual displacement sensors, located near the gear rim and disc. The signal was processed identifying the most critical rotating speeds on the basis of its RMS value. The numerical Campbell speed/frequency diagrams are in good agreement with experimental results.

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