Post-grazing dynamics of a vibro-impacting energy generator

•Grazing bifurcations induce asymmetric motion of a vibro-impact energy harvester.•The asymmetric behavior includes less efficient low-velocity impacts.•Nonlinear maps provide analytical expressions of periodic asymmetric motion.•Numerical and analytical results for this motion are in excellent agreement.•Additional grazing, studied numerically, yields more asymmetry and reduces efficiency.