  Active control of friction by ultrasonic vibration is a well-known effect
with numerous technical applications ranging from press forming to
micromechanical actuators. Reduction of friction is observed with vibration
applied in any of the three possible directions (normal to the contact plane,
in the direction of motion and in-plane transverse). In this work, we consider
the multi-mode active control of sliding friction, where phase-shifted
oscillations in two or more directions act at the same time. Our analysis is
based on a macroscopic contact-mechanical model that was recently shown to be
well-suited for describing dynamic frictional processes. For simplicity, we
limit our analysis to a constant, load-independent normal and tangential
stiffness and two superimposed phase-shifted harmonic oscillations, one of them
being normal to the plane and the other in the direction of motion. As in
previous works utilizing the present model, we assume a constant local
coefficient of friction, with reduction of the observed force of friction
arising entirely from the macroscopic dynamics of the system. Our numerical
simulations show that the resulting law of friction is determined by just three
dimensionless parameters. Depending on the values of these parameters, three
qualitatively different types of behavior are observed: (a) symmetric
velocity-dependence of the coefficient of friction (same for positive and
negative velocities), (b) asymmetric dependence with respect to the sign of the
velocity, but with zero force at zero velocity, and (c) asymmetric dependence
with non-zero force at zero velocity. The latter two cases can be interpreted
as a "dynamic ratchet" (b) and an actuator (c).
