VIBRATION ANALYSIS FOR CBMBASIC CONCEPTS – UNIT 3

BY DIBYENDU DE

VIBRATION MONITORING

Forced Vibration?

Exciting Force = Stiffness + Damping + Inertia

Oscillating Patterns

STIFFNESS

STIFFNESS (K)

• Stiffness is the quality of an element to deform/deflect under load

• Shaft, bearing, casing, foundation all have different stiffness

• Different directions can have different stiffness

• Stiffness is also connected to shape and size of the body

• The reason why resonant frequencies are infinite for a body

• Stiffness can also vary – variable stiffness

• It has a non-linear relationship with shaft diameter & length

WHAT ARE THE PRINCIPLES THAT MAKES STRUCTURES & SEA SHELLS STIFF ENOUGH TO RESIST FAILURE BY DEFORMATION?

WHAT ABOUT A BIRD’S NEST AND A TREE?

WHAT ABOUT A TEMPLE & A MACHINE?

EXERCISE

• A motor and a helical gear box are coupled together. For the same exciting force which sub-assembly is expected to have higher amplitudes of vibration?

• Which parameter of vibration would best show that?

• Would it affect the life of the anti-friction bearings fitted on the motor and the gearbox?

• What might be the likely cause if the horizontal direction vibrates more than the vertical direction?

• Observe that the machine is like a tall column pitching effect.

• The width at the base (c to c of cushy foot) = 0.7 m. Length is 1 m

• Note the sensitive directions shown by the red arrows.

0.7 m

Principles of Sensitive Direction,

Proportions & Structures See

E M E

Nemetics

N

• The paper reel unit, the stair case are attached to the main unit. (Left hand side of the red line)

• It shifts the centre of mass and induces vibration which is amplified by the low stiffness of the staircase

• The yellow line more-or-less shows the centre of mass

• Note that the machine has two regions of stiffness. One the left hand side of the red line it is the region of low stiffness and on the right is the region of high stiffness.

1 M

Low Stiff region

High Stiff region

Principles of Centre of Mass &

Stiffness See

E M E

Nemetics

N

• The shampoo feed pipe is attached to the machine. Hence pipe vibrations are easily transferred to the machine.

• Solution: Detach the pipe to isolate pipe vibration. And pipe hangers should be at unequal distance

Principle of PipesSee

E M E

Nemetics

N

STRUCTURE AND PROPORTION

Vibration reduced from 65 microns to 5 microns

Productivity went up by 33%

Failures reduced to 0

Quality loss reduced to 0

DAMPING

DAMPING – BASICS

• Friction (dry or Coulomb friction)

• Bodies moving through fluids (viscous damping)

• Damping is proportional to speed (at lower speeds)

• Damping is proportional to square of speed (at higher speeds) – non-linearity

• Damping is proportional to cube of speed (at very high speeds) – non-linearity

• Positive damping reduces amplitude of vibration. Negative damping enhances the amplitude of vibration.

CARNOT WAS RIGHT!

• Carnot was right - avoid friction of all types -- avoid heat transfer across finite temperature differences, heat leaks, shocks and mixing (all connected to damping)

• This slider mechanism is

critical for the operation.

• Here the linear bearing

can’t be lubricated by any

means.

• Moreover, the L/D ratio of

the bearing is also not

ideal. This would lead to

accelerated wear &

misalignment

Linear Bearings

Principle of centre of friction &

proportion – damping See

E M E

Nemetics

N

EXERCISE: IDENTIFY THE DAMPING ISSUES IN THIS CONTEXT

EXERCISE – CLASS DISCUSSION

• Slightly over lubricating an anti-friction bearing is a good idea.

• Turbulence is a form of damping

• Temperature has a relationship with damping

• Lubricant acts as a damper

• A damper can also have stiffness

• More the damping lesser would be the amplitude of vibration

• Can we estimate the amount of damping from vibration (time waveforms and from spectrums)

• Would humidity have any effect on damping?

INERTIA

INERTIA

• Mass

• Ability to resist acceleration

• Momentum

• Angular momentum

• Change of momentum

• Connected to forces and therefore measured in acceleration

• Experienced as forces and flows and turbulence

GAME – THE ETERNAL DANCE

GAME

• Play between Inertia, Forces, Stiffness and Damping

• Both in linear and in non-linear zones.

• So long things are in equilibrium and linear – no problem

• But unfortunately, systems always operate Out of Equilibrium. In Non-Linear zones following the Arrow of Time – the cause of all failures.

• That is the game – identify the key actors in the game and correct situation.

• Infinite possibilities

• Exhibited as dynamic pattern

• Our job is to understand such dynamic pattern through vibration and other techniques.

THANK YOU FOR COMPLETING UNIT 3 CONTACT: FOR FACILITATED TRAINING

DIBYENDU DE, EMAIL ID: DDE337@GMAIL.COM