Introduction to vibration

R.Narasimha SwamySenior consultant

narasimhaswamy@yahoo.com

What is vibration?

• Vibration can be defined as simply the cyclic or oscillating motion of a machine or machine component from its position of rest.

• An important class of dynamics concerning the linear and angular motions of bodies that respond to the applied disturbances in the presence of restoring forces.

• Examples are response of building structure to an earthquake, unbalanced axle rotation, flow induced vibrations of a car body, and the rattling of tree leaves etc

Basic concepts

• Vibration sources are characterized by their time and frequency domain properties.

• Categorized principally as: – Periodic

• originate from the HVAC, DG, fans etc• simplest form of periodic disturbance is harmonic. • In the time domain, this is represented as a sinusoid

and in the frequency domain by a single line spectrum.

– Random disturbances • originate from footsteps sound, conversation etc• only statistical representations are possible. • generally represented by its power spectrum.

What causes vibration? [1/2]

• Repeating forces

• Looseness

• Resonance

What causes vibration? [2/2]

• Change in direction with time, such as the force generated by a rotating unbalance.

• Change in amplitude or intensity with time, such as the unbalanced magnetic forces generated in a motor due to unequal air gap between the armature and stator.

• Friction between rotating and stationary machine components like between bow and the violin string to vibrate.

• Impacts, such as gear tooth contacts or the impacts generated by the rolling elements of a bearing passing over flaws in the bearing raceways.

• Randomly generated turbulence force devices such as fans, blowers, pumps, gas turbines or boilers.

• Improper installation without proper or improper mounts, isolators etc.

• Flanking transmission path in piping, building etc

Hazards of vibration

• Quality problems• Severe machine damage• High power consumption• Machine unavailability due to

breakdown• Unnecessary maintenance• Occupational hazards

Statistical model of vibration • All mass-elastic systems have natural frequencies

– For linear system these frequencies are constant • related only to the mass and stiffness distribution

– Non-linear effects require special treatment

• A few of the lower order frequencies are of interest because the higher ones are more highly damped.

• For a frequency, a system vibrates in a particular way, depicted by the relative amplitude and phase at various locations - mode of vibration.

Statistical model of vibration Contd.,

If there is no external force applied on the system, the system will experience un-damped free vibration. Motion of the system will be established by an initial disturbance (i.e. initial conditions).

Furthermore, if there is no resistance or damping in the system, the oscillatory motion will continue forever with a constant amplitude. Such a system is termed un-damped and is shown in the following figure,

The exponential term defines how quickly the system “damps” down. The larger the damping ratio, the quicker it damps to zero.

The cosine function is the oscillating portion of the solution, but the frequency of the oscillations is different from the un-damped case.

Damped and un-damped natural frequencies

Characterization of vibration

• Displacement is represented as amplitude. This important factor can also be represented as velocity or acceleration to make this factor qualified with reference to time.

• Frequency

• FFT (spectrum)

Measurement types

• Vibration displacement: deviation of measured point from rest position in mm or mil.

• Vibration velocity. Velocity with which measured point moves about rest position in mm/s or ips.

• Vibration acceleration. Acceleration with which measured point moves about rest position in m/s2 or “g” force.

Vibration measurement devices• Transducers based on seismic mass displacement

measurement, capacitive, linear variable differential transformer (LVDT), piezo-resistive, strain-gauges etc

• Frequency compensated electro-dynamic sensor, specially designed for measuring low intensity, low frequency acceleration.

• Servo accelerometers, working on force compensation principle.

• Today, all these devices are neatly integrated in the form of MEMS - a revolutionary semiconductor based technology.

Impact sound

Impact insulation class (or IIC)• IIC is an integer number rating of how well a building

floor attenuates impact sounds, such as footsteps.

• A larger number means more attenuation and better for human comfort. It uses decibel scale.

• The IIC is derived from ASTM method E989, which in turn uses a tapping machine specified in ASTM method E492. This machine incorporates five steel-faced hammers that strike the test floor and generate noise in a room below.

• The IIC number is derived from sound attenuation values tested at sixteen standard octave bands from 100 to 3150 Hz.

• IIC strength: Helps to rate structure-borne noise such as footfall, a chair dragging on the floor, or other realistic sounds in a single number.

• IIC weakness: Due to the nature of the testing procedure, almost any assembly with carpet will meet the IIC requirement. Meeting the IIC requirement does not ensure the control of footfall noise. Conversely, if an assembly does not meet the IIC requirement, it does not necessarily mean that there will be a footfall noise issue. 

• The tapping machine frequently used for this test is not designed to simulate any one type of impact, such as a male or female footsteps, nor to simulate the weight of a human walker. Thus the subjectively annoying creak or boom generated by human footfalls on a limber floor assembly may not be adequately evaluated by this method (ASTM, E 1007, 5.2).

Structure borne soundSound travelling by means of structure vibration is usually unnoticed but can become audible and a problem.

Thank you