Gyroscopic Systems

Gyroscopic systems experience Coriolis and centripetal acceleration components as a result of rotation. They are abundant in engineered systems. Example gyroscopic systems are given below.

Spinning rotor

A rotor supported on an elastic shaft is an example of a gyroscopic system. A lumped-parameter model of this system is shown below (right). The rotor is represented by a mass that translates in the plane. The discrete stiffnesses represent the elastic shafting. The system's natural frequencies (left) depend on the system's rotation speed. The decreasing natural frequency represents an orbit of the mass in the direction of rotation. This is called a forward orbit mode, which is shown in the movie below (right). The mass orbits in the direction opposite of the rotation in the mode corresponding to the increasing natural frequency. This mode is called a backward orbit mode and is shown in the left movie.

Planetary gears

Planetary gears with rotating carriers experience gyroscopic effects. Planetary gears have specific mode types called planet, rotational, and translational modes. In planet modes (shown below, left) only the planets vibrate. The sun, carrier, and ring have no motion. For rotational modes (shown below, middle) the sun, carrier, and ring have purely rotational motion with no translation. Each planet has identical radial, tangential, and rotational vibration. Translational modes (shown below, right) have purely translational motion of the sun, carrier, and ring gear. These gears have no rotational vibration.

Planetary gear model

A lumped-parameter planetary gear model is shown to the right. In this model all gears are modeled as rigid bodies that have planar motion. The contact between the sun and planet, and the ring and planet, are modeled as discrete stiffnesses.

Planetary Gear Structured Vibration Modes