A Planetary Gear Train (PGT) can be used in series-parallel transmission to redistribute powers. Selectable one-way clutches (SOWCs), compared with traditional friction clutches, can simplify controls and diversify patterns especially for hybrid transmissions. In this paper, a nonlinear torsional model of a power-split PGT coupled with three SOWCs is proposed. Piecewise nonlinearities of SOWCs as well as clearance, time-varying mesh stiffness, and synthetic transmission error of the PGT are considered. With a specified group of comprehensive evaluation indices, influences of piecewise nonlinearities of SOWCs are explored. Simulation results show that the piecewise nonlinearities of SOWCs can diminish collision range and reduce resonances of the PGT. Further research studies on parameter configurations of each SOWC reveal that of the three SOWCs, stiffness and radius of the SOWC connected to the sun gear of the PGT are dominant factors. Large stiffness and effective radius of the SOWC render the PGT fall into chaos on lower meshing frequencies; however, enormous impact vibrations occur to the SOWC if it gets too soft. Additionally, the increase of the damping ratio of the SOWC connected to sun gear can distinctly reduce the vibration and maximum dynamic load of the system on the entire working range.
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