A Brief Introduction to Vibration Analysis of Process Plant Machinery (III)

Basic Concepts III

Forced Vibration

•          Exciting Force = Stiffness Force + Damping Force + Inertial Force

•          Stiffness

–        Stiffness is the spring like quality of mechanical elements to deform under load

–        A certain force of Kgs produces a certain deflection of mm

–        Shaft, bearing, casing, foundation all have stiffness 

•          Viscous Damping

–        Encountered by solid bodies moving through a viscous fluid

–        Force is proportional to the velocity of the moving object

–        Consider the difference between stirring water versus stirring molasses

•          Inertial Forces

–        Inertia is the property of a body to resist acceleration

–        Mainly weight 

Physical Concept of Vibration Forces

•          Stiffness determines the deflection of a rotor by centrifugal forces of unbalance

–        Determined by the strength of the shaft

•          Damping force is proportional to velocity of the moving body and viscosity of the fluid

–        Damping is provided by lube oil

•          Inertial forces are similar to those caused by an earthquake when acceleration can be very high.

–        Acceleration is related to the weight of the rotor

–        It can cause distortion of structures

Physical Concept of Vibration Parameters

•          Displacement

–        Displacement is independent of frequency

–        Displacement is related to clearances in machine

–        If displacement exceeds available clearances, rubbing occurs.

•          Velocity

–        Velocity is proportional to frequency

–        Velocity is related to wear

–        In machines higher the velocity, higher the wear

•          Acceleration

–        Proportional to square of frequency

–        Acceleration is related to force

–        Excessive acceleration at the starting block can strain an athlete’s leg muscle

–        Acceleration is important for structural strength

Stiffness Influence

•          Stiffness is measured by the force in Kgs required to produce a deflection of one mm.

•          Stiffness of a shaft is

–        Directly proportional Diameter⁴ and Modulus of Elasticity

–        Directly proportional to Modulus of Elasticity

–        Inversely proportional to Length³

•          Typical Stiffness values in pounds / inch

–        Oil film bearings – 300,000 to 2,000,000

–        Rolling element bearings – 1,000,000 to 4,000,000

–        Bearing Housing, horizontal – 300,000 to 4,000,000

–        Bearing housing, vertical – 400,000 to 6,000,000

–        Shaft 1’ to 4” diameter – 100,000 to 4,000,000

–        Shaft 6” to 15” diameter – 400,000 to 20,000,000

Damping Influence

•          Damping dissipates energy

•          Rotor instability can be related to lack of damping

•          System Damping controls the amplitude of vibration at critical speed.

•           With low damping there is poor dissipation of energy and amplitude is high

Amplification factor Q through resonance is an indicator of damping

Relationship between Displacement, Velocity and Acceleration (For British Units)

Acceleration Varies as the Square of Frequency

 •          Acceleration is negligible at low frequencies.

•           It predominates the high frequency spectrum

•           Measure displacement at low frequency, velocity at medium frequencies and acceleration at high frequencies