The nonlinear dynamical model including piecewise backlash was created for combining spiral gear train

the governing equations of motion was solved by employing variant-step Gills numerical algorithm. The cell-mapping technique was put forward to investigate the two dimensional basins of dynamic parameters. Parametric excitations covering the backlash

transmission error

time-varying mesh stiffness and damping ratio

were considered in basin planes in terms of steady solutions. The dynamical bifurcation behavior under the excitation of various parameters was performed by means of the phase portrait

Lyapunov exponent (LE)

Poincaré section and fast Fourier transform (FFT). It is validated that Cell-mapping approach is effective in gear dynamic parameter design. The result shows that the system leads to chaos via period-doubling cascades under the backlash and transmission error while large damping ratio within the range ξ∈［0.025

0.225］ is beneficial to periodic states of the system. Under the excitation of time-varying mesh stiffness

significant transition between periodic response and chaotic motion was exhibited

small changes nearby parametric domain boundary guided the attracter into another basin of attraction.