Abstract
Considering time-varying meshing stiffness, comprehensive errors, and piecewise backlash nonlinearities of gear and spline, a torsional nonlinear dynamic model of star gear-rotor coupling transmission system of (Geared Turbofan Engine) GTF aeroengine is established. By using the Runge–Kutta numerical integration method, the dynamic responses are solved, analyzed, and illustrated with the bifurcation parameters including input rotational speed, gear backlash, damping ratio, and comprehensive meshing errors. The motions of the star gearing system and diverse nonlinear dynamic characteristics are identified through global bifurcation, FFT spectra, Poincaré map, and the phase diagram. The results reveal that the star gear-rotor system exhibits abundant torsional nonlinear behaviors, including multiperiodic, quasi-periodic, and chaotic motions. Furthermore, the roads to chaos via quasi-periodicity, period-doubling scenario, and mutation are demonstrated. These results provide an understanding of undesirable torsional dynamic motion for the GTF transmission system and provide a reference for the design and control of gear system.
Highlights
Piecewise linear–α α x (t) ηα Figure 2: Schematic diagram of the spline joint model. (a) Spline connection model, (b) piecewise linear function of clearance
Introduction e most advancedGTF aeroengine currently uses a star gearing system as the main decelerator for fan, allowing the low-pressure rotor to operate at high efficiency and high speed to match the optimum speed of the fan. e star gearing drive is shared by multiple fixed-axis star gears
Siyu et al [13] established a nonlinear gear rotor transmission model and investigated the effect of gear friction and backlash on the system; the results indicated that the vibration magnitude enlarged with the dynamic backlash, which may bring the system into chaotic motion
Summary
–α α x (t) ηα Figure 2: Schematic diagram of the spline joint model. (a) Spline connection model, (b) piecewise linear function of clearance. In the dynamic model of star gearing system, ksp, csp, krp, crp represent the meshing stiffness and damping of sun-star meshing pair and star-ring meshing pair. X ωs kspbsp esp Figure 3: Dynamic model of star gearing system GTF gearbox. For the meshing damping of gear pair, we can use formula (2) to calculate. For the torsional damping of gear pair, we can use formula (3) to calculate.
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