Symmetry breaking and chaos-induced imbalance in planetary gears

Abstract

The goal of the present paper was a com- plete analysis of the dynamic scenario of planetary gears. A lumped mass two-dimensional model is adopted; the model takes into account: time-varying stiffness; nonsmooth nonlinearity due to the backlash, i.e., teeth contact loosing; and bearing compliance. The time-varying meshing stiffness is evaluated by means of a nonlinear finite element model, which allows an accurate evaluation of global and local teeth defor- mation. The dynamic model is validated by compar- isons with the most authoritative literature: linear nat- ural frequencies and nonlinear response. The dynamic scenario is analyzed over a reasonable engineering range in terms of rotation speed and torque. The clas- sical amplitude–frequency diagrams are accompanied by bifurcation diagrams, and for specific regimes, the spectral and topological properties of the response are discussed. Periodic, quasiperiodic and chaotic regimes are found; nonsmooth bifurcations lead period one to period two trajectories. It is found that the bearing com- pliance can influence the natural frequencies combina- tion magnifying the modal interactions due to internal resonances and greatly enlarging the chaotic regions. It is evidenced that the chaotic response indices a sym- metry breaking in the dynamical systems. The physical consequence is that the planetary gearbox under inves- tigation, which is perfectly balanced for each position, can suffer of a big dynamic imbalance when chaotic regimes take place; such imbalance gives rise to alter- nate and unexpected high-level stresses on bearings

Study of the influence mechanism of pitch deviation on cylindrical helical gear meshing stiffness and vibration noise

“…where k m (t) is the time-varying meshing stiffness of helical gear and c m is the meshing damping of helical gear. [19][20][21] The simulation data from Figures 11 and 12 show that the vibration noise of helical gear with pitch deviation is obviously bigger than that with standard pitch under the given conditions. The RMS value of meshing vibration acceleration in Figure 11 is 72.71 m/s 2 under the influence of pitch deviation, which is bigger than the value of 68.51 m/s 2 under the standard pitch.…”

Research Progress in Dynamics of Planetary Gear Transmission System

“…In 2012, Zhang [77] analyzed the meshing mechanism of single pair gear pairs, studied the influence of friction excitation, error excitation and slapping excitation on the non-linear vibration characteristics of the system, and carried out experimental verification. In 2015, Masoumi et al [78] analyzed the contact of planetary gear pairs based on finite element method and obtained the time-varying meshing stiffness. Based on this, a translation-torsion dynamic model considering friction effect was established, and its solution results were compared with the classical literature to verify the correctness and reliability of the model.…”

Framework of mechanical symmetry breaking theory and its application to innovative design

“…However, they did not mention the necessity of the existence of symmetry breaking, i.e., asymmetrical structures within PGT. Masoumi et al (2015) made a complete analysis of the dynamics of planetary gears and verified that the chaotic response indicates symmetry breaking in the dynamic systems. In the design for assembly (DFA) field, Boothroyd (2009) analyzed the effect of the symmetry of parts on their assembly efficiency, and two design rules were proposed: (1) try to design parts as symmetrical structures to save orienting manipulation; (2) increase asymmetry features of parts to assist orienting manipulation when parts cannot be designed as symmetrical structures.…”