Unit 3 which is a part of a continuing series on education in vibration analysis of live engineering systems operating in both linear and non-linear out of equilibrium zones.

1. VIBRATION ANALYSIS FOR CBM
BASIC CONCEPTS – UNIT 3
BY DIBYENDU DE

2. VIBRATION MONITORING
Forced Vibration?
Exciting Force = Stiffness + Damping + Inertia
Oscillating Patterns

3. STIFFNESS

4. 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

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

6. WHAT ABOUT A BIRD’S NEST AND A TREE?

7. WHAT ABOUT A TEMPLE & A MACHINE?

8. 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?

9. • 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

10. • 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

11. • 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 Pipes
See
E M E
Nemetics
N

12. 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

13. DAMPING

14. 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.

15. 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)

16. • 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

17. EXERCISE: IDENTIFY THE DAMPING ISSUES IN THIS
CONTEXT

18. 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?

19. INERTIA

20. 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

21. GAME – THE ETERNAL DANCE

22. 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.

23. THANK YOU FOR COMPLETING UNIT 3
CONTACT: FOR FACILITATED TRAINING
DIBYENDU DE, EMAIL ID: DDE337@GMAIL.COM