# Design Basis for Rotating Compressors – Dynamic Forces

The dynamic force generated by the rotor(s) of rotary and dynamic compressors is related to the running speed and the vibration of the rotor. Because of the complexity of the subject, it is impossible to accurately predict the behavior of a rotor system with one or two simple equations.

Fortunately, however, standards have been developed for allowable limits of vibration for new machinery. One of the most widely used standards is the API limit for dynamic and rotary machines: where:
Av = Peak-to-peak amplitude (displacement) of vibration in mils (0.001 inches)
N = Rated speed in RPM

Note This equation is valid for speeds down to about 3000 RPM. Below 3000 RPM the limit is 2 mils.

The following equation may be used for calculating the force used in foundation design. This equation is based on a vibration three times the amplitude calculated from Equation 200-17. A safety factor of three is recommended because that is about the maximum vibration level where you would ever allow a compressor to continue to operate. where:
F = Dynamic force, lbs
N = RPM
WR = Weight of rotor, lbs

The force calculated is actually a rotating vector, and it should be assumed that it is acting perpendicularly at the center of the rotor. It should also be assumed that there will be a 50% reaction at each bearing from the unbalanced rotating force. The reactions at the machine’s hold-down bolts can then be resolved.

Figure 200-72 shows the resolution of these forces to bearing reactions. The latter reactions are transmitted to the foundation via soleplates or baseplate and anchor bolts. Note that Equation200-18 can also be applied to the rotors of turbine drivers and gearboxes.

Occasionally the foundation designer may want to add a factor above the dynamic force determined by Equation200-18, although Equation 200-18 is quite conservative. Five times the API vibration limit has been used as a design criterion in some cases where there were special concerns about the design. This would provide a safety factor of 1.67 beyond Equation200-18. To make the calculation, substitute 7.1 for 4.3 in Equation200-18. 