Several modal analysis techniques are widely used to study the dynamic characteristics of a structure byidentifying the modal parameters. This paper presented a comparison between anExperimental Modal Analysis (EMA) test and an Operational Modal Analysis (OMA) test and an Order Based Modal Analysis (OBMA) applied on a recirculating energy planetary gear. TheOMA and OBMA offer a test of the planetary gear under its realboundary conditions, whereas the EMA is based on the frequency response function estimation. Using the different techniques, the back to back planetary gearmodal parameterswereidentified. In afirst step, the experimental results determined by EMA and OMA were correlated to the numerical results model obtained by athreedimensional lumped parameter model. In asecond step,the OBMA estimated modal parameters were compared to those of the EMA. According to the obtained results, OMA cannot excite all the modes. However,it was noticed that there is no significant differencebetween the modal parameters obtained by the EMA and theOBMA.The natural frequencies and damping ratios were deviating by 11% and 2.43%, respectively.
Highlights Planetary gear natural frequencies and damping ratios wereidentified with three different modal analysis techniques. FRF, Cross Power Spectral Density, Order Function, Mode shapes,modal assurance criterion and stability diagram were presented. Modal analysis under rotating excitation is different from the conventional modal analysis. Validation by three-dimensional lumped parameter model.
The nonlinear effects in gearboxes are a key concern to describe accurately their dynamic behavior. This task is difficult for complex gear systems such as planetary gearboxes. The main aim of this work is to provide responses to overcome this difficulty especially in nonstationary operating regimes by investigating a back-to-back planetary gearbox in steady conditions and in the run-up regime. The nonlinear Hertzian contact of teeth pair is modeled in stationary and nonstationary run-up regime. Then it is incorporated in to a torsional model of the planetary gearbox through different mesh stiffness functions. In addition, motor torque and external load variation are taken into account. The nonlinear equations of motion of the back-to-back planetary gearbox are computed through the Newmark- β algorithm combined with the method of Newton–Raphson. An experimental validation of the proposed numerical model is done through a test bench for both stationary and run-up regimes. The vibration characteristics are extracted and correlated to speed and torque. Time–frequency analysis is implemented to characterize the transient regime during the run-up.
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