Air Compressor System
Air Compressor System
Resonance in a Mechanical System
Resonance in a Mechanical System
Mechanical systems are in resonance when a forcing frequency produced by or applied to a system matches a natural frequency of the system; this condition is important to understand, as operating near or at resonance greatly magnifies the response of the system, and this increased response can lead to noise, component failure or other undesirable outcomes.
June 23, 2017—Les Grundman
The sketch below shows an air compressor mounted on a beam; this is a realistic configuration, as air compressors are sometimes mounted on ceiling beams in manufacturing plants or shop installations to save floor space.
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Conceptual Model
Conceptual Model
The conceptual model of the above air compressor system is shown below; the spring represents the vertical stiffness of the horizontal beam, the dash pot represents energy absorption in the system, the mass represents the effective mass of the air compressor and the applied force represents a periodic force arising from imbalance in the motor/compressor system, which is spinning at some frequency .
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The free-body diagram for this conceptual model is created by imagining the mass being displaced in the positive direction of the x coordinate system and drawing the forces on the mass that result from movement in this direction.
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Newton’s second law is applied by summing all forces acting on the mass and equating this summation to the mass times the acceleration; this yields the equation of motion (EOM) for the system.
mx’’+cx’+kx=Fosin(ωt)
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)The following sections demonstrate the solution to the above equation and allow exploration of this system using nondimensionalized parameters.
Solution to the Homogeneous Equation
Solution to the Homogeneous Equation
Free Vibration in an Underdamped System
Free Vibration in an Underdamped System
Forced Vibration
Forced Vibration
Interpretation
Interpretation
AUTHORSHIP INFORMATION
Les Grundman
6/23/2017