Dr' S' K' Kudari, Professor, BVB College of Engg'

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CHAPTER-5
VIBRATION MEASURING INSTRUMENTS
Topics covered Theory of Vibration measuring
instruments Displacement measuring instrument
(Vibrometer) Velocity measuring instrument
(Velometer) Acceleration measuring instrument
(Accelerometer) Numerical Problems/Discussions
03/04/07
04/04/07
Dr. S. K. Kudari, Professor, BVB College of Engg.
Tech., Hubli
2
Recap
Theory of Vibration measuring instruments
(Seismic instruments)
An instrument, which is used to measure
displacement, velocity and acceleration
components of a system, is referred as vibration
measuring instrument or seismic instrument
Machine
Dr. S. K. Kudari, Professor, BVB College of Engg.
Tech., Hubli
3
Recap
Theory of Vibration measuring instruments
(Seismic instruments)
Dynamic
Static
Dr. S. K. Kudari, Professor, BVB College of Engg.
Tech., Hubli
4
Recap
Theory of Vibration measuring instruments
(Seismic instruments)
The seismic response is
Phase angle
Dr. S. K. Kudari, Professor, BVB College of Engg.
Tech., Hubli
5
Recap
Theory of Vibration measuring instruments
(Seismic instruments)
0.707
Is more suited for seismic instruments
Dr. S. K. Kudari, Professor, BVB College of Engg.
Tech., Hubli
6
Condition for Displacement measuring instrument
(Vibrometer)
Frequency ratio, r, should be more than 3 Damping
ratio, ? , should be less than 0.707
Dr. S. K. Kudari, Professor, BVB College of Engg.
Tech., Hubli
7
Condition for Velocity measuring instrument
(Velometer)
Frequency ratio, r should be more than 3 Damping
ratio, ? , should be less than 0.707
Dr. S. K. Kudari, Professor, BVB College of Engg.
Tech., Hubli
8
Condition for Acceleration measuring instrument
(Accelerometer)
Frequency ratio, r should be between 0 and
0.6 Damping ratio, ? , should be less than 0.707
Dr. S. K. Kudari, Professor, BVB College of Engg.
Tech., Hubli
9
Numerical problems
Problem-1
A seismic instrument is mounted on a machine
running at 1000 rpm. The natural frequency of the
seismic instrument is 20 rad/sec. the instrument
records a relative amplitude of 0.5 mm. Compute
the displacement, velocity and acceleration of
the machine. Neglect the damping in seismic
instrument.
Dr. S. K. Kudari, Professor, BVB College of Engg.
Tech., Hubli
10
Numerical problems
Problem-1
Given data
20 rad/s, ?0
Speed of the machine 1000 rpm
104.72 rad/s
Frequency ratio
Dr. S. K. Kudari, Professor, BVB College of Engg.
Tech., Hubli
11
Numerical problems
Problem-1
For seismic instrument
Damping is neglected for given system
Dr. S. K. Kudari, Professor, BVB College of Engg.
Tech., Hubli
12
Numerical problems
Problem-1
Displacement of the machine
Velocity of the machine
?.Y (104.72) 13.36 1399.04 mm/s 1.4 m/s
Velocity of the machine
?2.Y (104.72)2 13.36 146506.68 mm/s2 1.46
m/s2
Dr. S. K. Kudari, Professor, BVB College of Engg.
Tech., Hubli
13
Numerical problems
Problem-2
A seismic instrument has natural frequency of 6
Hz. What is the lowest frequency beyond which the
amplitude can be measured within 2 error.
Neglect damping
Dr. S. K. Kudari, Professor, BVB College of Engg.
Tech., Hubli
14
Numerical problems
Problem-2
Z Y0.02 Y 1.02 Y
Dr. S. K. Kudari, Professor, BVB College of Engg.
Tech., Hubli
15
Numerical problems
Problem-2
r 0.7034
The lowest frequency beyond which the amplitude
can be measured within 2 error is
? r. ?n
? (0.7034) 6
? 4.22 Hz
Dr. S. K. Kudari, Professor, BVB College of Engg.
Tech., Hubli
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Numerical problems
Problem-3
A seismic instrument is found to have 2 error in
its measurement. Its natural frequency is 8 Hz.
If the lower natural frequency that can be
measured with the instrument is 40 Hz, find the
magnitude of damping factor.
Dr. S. K. Kudari, Professor, BVB College of Engg.
Tech., Hubli
17
Numerical problems
Problem-3
Considering error is ve
Solve the above equation to find ?
Dr. S. K. Kudari, Professor, BVB College of Engg.
Tech., Hubli
18
Numerical problems
Problem-4
A seismic instrument has natural frequency of 6
Hz and damping factor of 0.25. What is the lowest
frequency beyond which the amplitude can be
measured within 2 error.
Dr. S. K. Kudari, Professor, BVB College of Engg.
Tech., Hubli
19
Numerical problems
Problem-4
Solve for r in the above equation. Find frequency
Dr. S. K. Kudari, Professor, BVB College of Engg.
Tech., Hubli
20
Numerical problems
Problem-5
Design a vibrometer for the range of frequency
0-10 Hz.
Dr. S. K. Kudari, Professor, BVB College of Engg.
Tech., Hubli
21
Numerical problems
Problem-5
It is required to design stiffness of spring (K),
value of damping coefficient (c) and the
magnitude of seismic mass (m) for the given
requirements
Dr. S. K. Kudari, Professor, BVB College of Engg.
Tech., Hubli
22
Numerical problems
Problem-5
From theory, it is known that for vibrometer the
frequency ratio should be more than 3
Dr. S. K. Kudari, Professor, BVB College of Engg.
Tech., Hubli
23
Numerical problems
Problem-5
Consider minimum r 3 for the design
r ? /?n
For the given frequency, natural frequency of the
instrument should be
?n ? /r
?n 10 /3 3.33 Hz 20.92 rad/sec
Dr. S. K. Kudari, Professor, BVB College of Engg.
Tech., Hubli
24
Numerical problems
Problem-5
where, K stiffness of spring and m seismic mass
For the fixed value of K magnitude of m can be
obtained
We know, ? c/cc
and cc 2 m ?n
From above equations, for a particular value of ?
one can estimate the magnitude of damping factor c
Dr. S. K. Kudari, Professor, BVB College of Engg.
Tech., Hubli
25
Theory questions
Explain with a neat sketch, a seismic
instrument. What is the difference between
vibrometer and accelerometer (VTU Jan/Feb 2004)
for 10 marks
Explain the seismic instrument and how it can be
used to measure displacement and acceleration
(VTU , Aug 2001, Jan/Feb 2003) for 10 marks
Dr. S. K. Kudari, Professor, BVB College of Engg.
Tech., Hubli
26
Theory questions
Write detailed note on Vibration measuring
instruments (VTU July/Aug 2004) for 06 marks
Discuss general theory of seismic instruments and
obtain the conditions for using it as (i)
Vibrometer and (ii) Accelerometer (VTU Jan/Feb
2005) for 10 marks
Dr. S. K. Kudari, Professor, BVB College of Engg.
Tech., Hubli
27
Theory questions
What do you understand by seismic instrument.
Explain the theory of seismic instruments giving
the conditions under which the instrument can be
used as accelerometer and vibrometer (VTU
July/Aug 2003) for 10 marks
Explain the working principle of Vibrometer (VTU
July/Aug 2005) for 10 marks
Dr. S. K. Kudari, Professor, BVB College of Engg.
Tech., Hubli
28
Theory questions
Discuss the basic principles on which vibration
measuring instruments are designed. What are the
practical limitations (VTU Jan/Feb 2006) for 08
marks
Explain the principles of vibration measuring
instrument and indicate the conditions for using
it as a vibrometer and an accelerometer (VTU
Dec/Jan 2007) for 08 marks
Dr. S. K. Kudari, Professor, BVB College of Engg.
Tech., Hubli
29
Theory questions
Sketch the dimensional less amplitude Vs.
frequency ratio characteristics (curves) of a
vibration measuring instrument. Explain in what
region it can be used as accelerometer. (VTU July
2006) for 10 marks
Dr. S. K. Kudari, Professor, BVB College of Engg.
Tech., Hubli
30
Dr. S. K. Kudari, Professor, BVB College of Engg.
Tech., Hubli
31
Summary
Seismic instruments are used to measure the
displacement, velocity and acceleration
components of a vibratory system
Basic theory of Seismic instruments can used to
design the seismic instruments depending the
requirements
Dr. S. K. Kudari, Professor, BVB College of Engg.
Tech., Hubli
32
Thank You
Dr. S. K. Kudari, Professor, BVB College of Engg.
Tech., Hubli