The dynamics associated with bouncing-type partial contact cycles are considered for a 2 degree-of-freedom unbalanced rotor in the rigid-stator limit. Specifically, analytical explanation is provided for a previously proposed criterion for the onset upon increasing the rotor speed
Ω
of single-bounce-per-period periodic motion, namely internal resonance between forward and backward whirling modes. Focusing on the cases of 2 : 1 and 3 : 2 resonances, detailed numerical results for small rotor damping reveal that stable bouncing periodic orbits, which coexist with non-contacting motion, arise just beyond the resonance speed
Ω
p
:
q
. The theory of discontinuity maps is used to analyse the problem as a codimension-two degenerate grazing bifurcation in the limit of zero rotor damping and
Ω
=
Ω
p
:
q
. An analytic unfolding of the map explains all the features of the bouncing orbits locally. In particular, for non-zero damping
ζ
, stable bouncing motion bifurcates in the direction of increasing
Ω
speed in a smooth fold bifurcation point that is at rotor speed
O
(
ζ
)
beyond
Ω
p
:
q
. The results provide the first analytic explanation of partial-contact bouncing orbits and has implications for prediction and avoidance of unwanted machine vibrations in a number of different industrial settings.
Explanation of the onset of bouncing cycles in isotropic rotor dynamics; a grazing bifurcation analysis