Practical Solutions to Machinery and Maintenance Vibration Problems
Chapter 3, Detuning and Proving Resonance
Section 9, Understanding the Orbit of a Rotor's Centerline Due to Unbalance (when Running Above Resonance)
In Fig. 1 there is the usual shaft centerline or geometric center for the round rotor shaft. It is assumed that a rotor rotates about that center, and it does if the rotor is perfectly balanced, perfectly aligned and so on. However, such perfection rarely exists, and the rotor actually rotates around another axis called the "axis of rotation." When balance and alignment are theoretically perfect, the axis of rotation and the geometric center coincide. When not perfect, there is a small distance between them. It is easier to explain this through the example of an unbalanced rotor (although any vibration source such as shaft-to-shaft misalignment results in a distance between the actual axis of rotation and the geometric centerline). For simplicity, Fig. 1 shows a disc-shaped rotor with basic single plane unbalance.
For an unbalanced rotor, the point about which all is balanced is called the "center-of-mass." There is some distance between the rotor's geometric center or centerline and the rotor's center-of-mass. That distance is called the "eccentricity," represented by the symbol "e."
When a rotor runs at an rpm above the first resonant frequency range of some part of the rotor or machine's support system, it acts like it is running "free-in-space." When running free-in-space, the rotor rotates about its axis of rotation, which is at the center-of-mass. Notice that this means the rotor's geometric center is tracing a circular orbit around the axis of rotation. The diameter of that orbit is 2e (the shaft's displacement vibration).
Although rotors running "above resonance" are considered to be running free-in-space, the actual machine conditions, such as unequal rigidity in the vertical direction relative to the horizontal direction, cause the orbit to be elliptical in shape, rather than round. (Other orbit shapes can also result but from other vibration sources such as shaft-to-shaft misalignment, rubs, etc.)
The vibration displacement is determined by 2e and expected to remain relatively constant at all speeds above the 1st critical range until another critical speed range is reached. However, displacement amplitude does decrease slightly as the speed increases through the non-resonance range.
This textbook contains only part of the information in our Practical Vibration Analysis seminar.