Dynamic behavior of the nonlinear planetary gear model in nonstationary conditions

Abstract

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.

Operational modal analysis using order-based analysis in a two-stage planetary gear with mechanical power recirculation

“…The increase in torque has effects on the MSF amplitude. In fact, the contact area between the teeth increases, producing a variation in both fillet stiffness and the Hertzian one [33]. In addition, the entire system matrices change.…”

Modal sensitivity of three-dimensional planetary geared rotor systems to planet gear parameters

“…These research papers show that the stiffnesses of shafts, bearings and gear teeth can directly affect the modal behaviour and dynamic response of geared rotors. Numerous linear and nonlinear dynamic analyses have been undertaken to understand the time-varying mesh stiffness effect on the dynamic behaviour of a gear pair since the gear mesh stiffness fluctuates during a contact period in reality [52][53][54][55] . A few parameter studies have investigated the constant gear mesh stiffness effect on the dynamic behaviour of planetary gearboxes and geared rotor systems, which is a valid assumption for heavily loaded gears [53] .…”

Research on dynamic load sharing characteristics of double input face gear split-parallel transmission system

“…Hammami A et al. 5 studied the dynamic behaviors of the nonlinear planetary gear model in nonstationary operating regimes. Wang YZ et al.…”

“…Liu SY et al 4 established the corresponding relationship between the drive error and the gear geometry. Hammami A et al 5 studied the dynamic behaviors of the nonlinear planetary gear model in nonstationary operating regimes. Wang YZ et al 6 researched the effects of tooth deformation on the error and contact stress of gears by a parametric finite element modeling method.…”