This article presents a novel stability analysis of plunge centerless grinding. The analysis considers the nonlinearity associated to wheel-workpiece detachment under large waviness. The loss of contact is approximated by a harmonic linearization, in the frequency domain, by a double input describing function (DIDF). The stability analysis shows the effects of clipping and structural compliance: both clearly produce a waviness with a quasi-integer number of lobes. Our approach removes the need of additional hypotheses, sometime found in the literature. Under increasing lobes amplitude, clipping reduces waviness growth rate until a limit cycle is reached. Numerical and experimental verifications are provided.