  High-speed machinery is often designed to pass several $"$critical$"$ speeds,
where vibration levels can be very high. To reduce vibrations, rotors usually
undergo a mass balancing process, where the machine is rotated at its full
speed range, during which the dynamic response near critical speeds can be
measured. High sensitivity, which is required for a successful balancing
process, is achieved near the critical speeds, where a single deflection mode
shape becomes dominant, and is excited by the projection of the imbalance on
it. The requirement to rotate the machine at high speeds is an obstacle in many
cases, where it is impossible to perform measurements at high speeds, due to
harsh conditions such as high temperatures and inaccessibility (e.g., jet
engines). $\\$ This paper proposes a novel balancing method of flexible rotors,
which does not require the machine to be rotated at high speeds. With this
method, the rotor is spun at low speeds, while subjecting it to a set of
externally controlled forces. The external forces comprise a set of tuned,
response dependent, parametric excitations, and nonlinear stiffness terms. The
parametric excitation can isolate any desired mode, while keeping the response
directly linked to the imbalance. A software controlled nonlinear stiffness
term limits the response, hence preventing the rotor to become unstable. These
forces warrant sufficient sensitivity required to detect the projection of the
imbalance on any desired mode without rotating the machine at high speeds.
Analytical, numerical and experimental results are shown to validate and
demonstrate the method.
