When an imbalanced rotor is sped up to pass through the critical speed with a constant acceleration, sustainable rubbing can be induced if the maximum vibration amplitude of the rotor exceeds the gap. This is the so-called stiffness increase or stiffening phenomenon. The maximum vibration amplitude is dependent on the magnitude of the rotor’s acceleration: the smaller the acceleration, the larger the maximum amplitude. Thus, there exists a critical acceleration: for accelerations smaller than the critical one, the sustainable rubbing will be induced. To prevent such unwanted rubbing, the rotor acceleration or the gap must be large enough. Since the acceleration is limited by the power/torque of driving system while large gap decreases the efficiency of some rotating machines, smaller driving power and higher efficiency have to be content with the second best. In this paper, the phase modulation method is applied to reduce the critical acceleration, and experiments are conducted on a setup designed to test the phase of the imbalanced force. The method is to operate the rotor with a scheduled, not continuously increased speed: when accelerated to a given speed, the rotor is decelerated to an assigned speed, and then accelerated again. Numerical and experimental results show that the critical acceleration is reduced about 50% by this technique. A prerequisite for this method is that the rotor’s speed is controllable.