Variable loads to which gearboxes are subjected are considered as one of the main sources of nonstationarity in these transmissions. In order to characterise their dynamic behaviour in such conditions, a torsional lumped parameter model of a planetary gear with power recirculation was developed. The model included time varying loading conditions and took into account the non-linearity of contact between teeth. The meshing stiffness functions were modelled using Finite Element Method and Hertzian contact theory in these conditions. Series of numerical simulations was conducted in stationary conditions, with different loading conditions. Equation of motion was solved using Newmark algorithm. Numerical results agreed with experimental results obtained from a planetary gear test bench. This test bench is composed of two similar planetary gears called test planetary gear set and reaction planetary gear set which are mounted back-to-back so that the power recirculates through the transmission. The external load was applied through an arm attached to the free reaction ring. Data Acquisition System acquired signals from accelerometers mounted on the rings and tachometer which measured instantaneous angular velocity of the carrier's shaft. The signal processing was achieved using LMS Test.Lab software. Modulation sidebands were obtained from the ring acceleration measurements as well as a non-linear behaviour in case of variable loading resulted by a transfer of the spectral density from the fundamental mesh stiffness to its second harmonic.
Abstract. The objective of this paper is to study the effects of meshing phase between planets, the effects of the gravity of carrier and the planet position error on the load sharing behavior in planetary gear set. These effects will be studied numerically under the stationary condition and will be validated experimentally by a back-to-back planetary gear test bench. In this test bench, strain gauges are installed on each planet's pin hole in order to compare strains in the pinhole of each planet.
Gear transmissions in general and spur gears in particular exhibit a different dynamic behavior depending on the level of the transmitted load. This fact justifies the interest in the study of the role of the load in gear dynamics not only in the context of design, vibration and noise control but also for condition monitoring. This task requires the development of advanced models achieving a compromise between accuracy and computation time. In this work, gear and bearing non-linearities associated with the contact among teeth and roller elements have been included, taking into account the flexibility of gears, shafts and bearings. Besides, parametric excitations coming both from gear and bearing supports, as well as clearance, were also considered. Gear contact force calculations are carried out following a hybrid approach which combines both analytical and numerical tools. This lets to achieve accurate results with an acceptable computational effort and thus dynamic analysis becomes feasible. This approach was improved and the calculation speeded up from the point of view of computational time. This was performed by using a pre-calculated value for gear tooth stiffness as a function of load and the angular position when it operates under stationary conditions. On the other hand, bearings were formulated just as deflections of Hertzian type. This means that bending and shearing of races and rolling elements are neglected. However, the variation in the number of loaded rolling elements as a function of the load and the angular position was taken into account. Shaft flexibilities were added to gear and bearing models to define a simple transmission that was used to study the vibratory behavior under different levels of applied torque. In a preliminary study, this model was linearized for several loads, obtaining the corresponding frequencies and mode-shapes in order to assess their variation with this parameter. Finally, dynamic simulations were carried out, showing the modifications undergone by the orbits, meshing contact forces and transmitted bearing forces.
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