Vibration Control

Vibration Control

Consequences• Excessive wear of bearings• Formation of cracks• Loosening of fastener• Structural failure• Mechanical failure• Frequent and costly maintenance• Electronic malfunction – fractures of solder joints andabrasion of insulation• Humans – pain, discomfort and reduce efficiency

Vibration control• Vibration can be eliminated on the basis of theoreticalanalysis, however, the manufacturing cost involved ineliminating may be too high• A designer must compromise between acceptableamount of vibration and reasonable manufacturingcost• Objective of the lecture is to consider varioustechniques of vibration control – elimination orreduction

Vibration Nomograph & Criteria• The acceptable levels of vibration are often specified interms of the response of an undamped single degree offreedom system undergoing harmonic vibration• Vibration Nomograph• Displays the variation of displacement, velocity andacceleration amplitudes with respect to the frequencyof vibrationx( t) X sin tv( t) Xcos t2fXcos t2a(t) X2sint 4f2Xsint

v max2fXaln v2 2max f X 2ln v max lnmax4 fv lna2fln X ln2maxmaxf

Usual Ranges of Vibrations• Atomic vibrations• Frequency = 10 12 Hz• Displacement amplitude =10 -8 to 10 -16 mm• Microseism or minor tremor of earth’s crust• Frequency = 0.1 to 1 Hz• Displacement=10 -5 to 10 -3 mm• Human perception threshold• Frequency = 1 to 8 Hz

• Machinery and building• Frequency=10 to 100 Hz• Displacement=0.01 to 1 mm• Swaying of tall building• Frequency=0.1 to 5 Hz• Displacement = 10 to 1000 mm

Reduction of Vibration at the Source• The first thing to be explored to control vibrations is totry to alter the source of vibration• It not always feasible (earthquakes, atmosphericturbulence, road roughness, engine combustioninstability)• Other sources of vibrations such as unbalance inrotating or reciprocating machine can be reduce byeither internal balancing or an increase in theprecision of machine elements• Tolerance• Surface finishing

Balancing of Rotating Machines• The presence of an eccentric or unbalanced mass in arotating disc causes vibration, which may beacceptable up to a certain level• Can be eliminated by removing the eccentric mass oradding an equal mass in such a position that it cancelthe effect of the unbalance• Causes• Machining errors• Variations in sizes of bolts, nuts, rivets, and welds• Types• Single –plane• Two - plane

Whirling of Rotating Shaft• “Çritical Speed”• Modeling• Equation Motion• Critical Speed• Response• Stability

Balancing of Reciprocating Engines• Vibrations inreciprocating enginesarise due to;• Periodic variations of thegas pressure in thecylinder• Inertia forces associatedwith the moving parts• Balancing

Control of Vibration• In many practical situations, it is possible to reducebut not eliminate the dynamic forces that causesvibrations• Method used to control vibrations;• 1)Controlling the natural frequencies of the system andavoiding resonance under external excitations• Mass, m• Stiffness, k

Control of Vibration• 2)Preventing excessive response of the system, even atresonance by introducing a damping or energydissipatingmechanism• Structural material having high internal damping• Viscoelastic materials• Bolted and riveted joints• 3)Reducing the transmission of the excitation forcesfrom one part of the machine to another, by the use ofvibration isolator• Involve the insertion of a resilient member between thevibrating mass and the source of vibration• Passive/Active

• Types• Vibration Isolation with Rigid Foundation• Reduction of the force transmitted to foundationm x cx kxF0cos t• Reduction of the force transmitted to the massmz cz kz my

• Types• Vibration Isolation with Flexible Foundationm x11 km x22x1 kx2 F0x x 021cos t

• Types• Vibration Isolation with Partially Flexible Foundationm 1x1 kx1 x2 F0cos tk x x xZ 212

• Types• Active Vibration Control

Control of Vibration• 4)Reducing the response of the system, by the additionof an auxiliary mass neutralizer or vibration absorberm x11 k21m x2x1 kk2x1 x2x x 021F0sin t

m x11 k21m x2x1 kk2x1 x2c2x1 x2x x c x x 021212F0sin t

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