Nonlinear dynamic analysis for bevel-gear system under nonlinear suspension-bifurcation and chaos

Abstract

a b s t r a c tThis study aims to analyze the dynamic behavior of bevel-geared rotor system supported on a thrust bearing and journal bearings under nonlinear suspension. The dynamic orbits of the system are observed using bifurcation diagrams plotted with both the dimensionless unbalance coefficient and the dimensionless rotational speed ratio as control parameters. The onset of chaotic motion is identified from the phase diagrams, power spectra, Poincaré maps, Lyapunov exponents, and fractal dimensions of the gear-bearing system. The numerical results reveal that the system exhibits a diverse range of periodic, sub-harmonic, and chaotic behaviors. The results presented in this study provide an understanding of the operating conditions under which undesirable dynamic motion takes place in a gear-bearing system and therefore serves as a useful source of reference for engineers in designing and controlling such systems.

Nonlinear torsional vibrations of a wind turbine gearbox

“…They found that twisting vibrations separate the edges of mating gear teeth causing contact loss. Chang-Jian [34] studied the dynamic behaviour of a bevelgeared rotor system ,and found that the system exhibits a diverse range of periodic, sub-harmonic and chaotic behaviours. Chang-Jian and Hsu [35] also presented a numerical analysis of the nonlinear dynamic response of a gear-bearing system.…”

Spiral Bevel Gears Nonlinear Vibration Having Radial and Axial Misalignments Effects

“…Furthermore, some assumptions are considered: pure involute profile, dry and frictionless contact; moreover, thermal effects are not considered. To investigate the effect of misalignments on dynamic behavior, three cases are considered as follows [1] The dynamic equations of motion of this system (Figure 2) are given by [20][21][22][23][24][25]: The dynamic equations of motion of this system (Figure 2) are given by [20][21][22][23][24][25]: The dynamic equations of motion of this system (Figure 2) are given by [20][21][22][23][24][25]: Due to mounting and manufacturing error or teeth profile modifications, the backlash between mating teeth varies; it is called geometric transmission error, or e(t). The linear dynamic transmission error (DTE) along the line of action is defined as = − .…”

Pitchfork and Hopf bifurcations of geared systems with nonlinear suspension in permanent contact regime

“…Where, the clearance between the gears are considered as the main source of the nonlinearity [11,14]. This is while, there are some works that analyzed the performance of the geared system by including the nonlinear effect of the supporting shaft [2,13] or the clearance of the bearing [6,3] along with the nonlinearity due to the backlash, which lead into occurrence of free play mode, and impact phases [8]. But not many attempts have been made to investigate the effect of the nonlinear suspension on the performance of the gears under the assumption that the gears in mesh do not separate and the nonlinearity due to free play mode and impact phases do not participate in system's response.…”