IX. THE VELOCITY DECIBEL –
A USEFUL WAY TO MEASURE VIBRATION LEVELS
IN ROTATING MACHINERY
A primary requirement for any
instrument or system used in periodic
vibration monitoring is simplicity. It
must be easy for the operator to
understand what he is measuring,
to know what’s normal and to know
when a change signifies trouble.
Perhaps the most convenient way to
measure vibration is to use the decibel
(dB). Already accepted for sound
level measurement, the advantages
of the “dB” for vibration measurement
are now becoming known.
The Major Advantages Are:
1. An extremely wide range of
vibration levels is covered by
a few easy to use numbers.
2. A doubling or tripling of vibration
is represented by the same “dB”
number, regardless of the level at
which the change occurs.
3. No decimal points are required—
whole numbers are used.
BIG CHANGES =
SMALL “DB” NUMBERS
Think of “dB” as a means to express
“relative” changes of 2 to 1, 5 to 1,
or “N” to 1 in a consistent way.
For example: 20 dB = 10 to 1
If a quantity increases by a factor
of 10, it increased +20 dB; if it
decreases to one-tenth its value,
it decreases –20 dB. The words
‘increase’ or ‘decrease’ are
unnecessary because, by definition,
‘plus’ means increase and ‘minus’
means decrease. Note that any 10
to 1 change corresponds to 20 dB,
regardless of the level of vibration
being measured. Thus:
1 to 10 = +20 dB
10 to 100 = +20 dB
.5 to 5 = +20 dB
.02 to .002 = –20 dB
Some convenient dB/ratio numbers
are as follows:
Relative Change
1 to 1 (no change)
—
√ 2 to 1
2 to 1
3 to 1
10 to 1
30 to 1
100 to 1
1000 to 1
10,000 to 1
100,000 to 1
dB
0
3
6
10
20
30
40
60
80
100
Note that, to multiply ratios, simply
add dB values. Thus, a 1000 to 1
change (10 times 100) is 20 dB plus
40 dB, or 60 dB total.
Measuring Actual
Vibration Levels
dB values conveniently measure
changes in vibration levels: a level
which doubles from .01 in/sec to .02
in/sec increases +6 dB. Just as
important, dB can be used to
conveniently measure absolute levels.
Since “dB” expresses a ratio of one
number to another, it is possible to
indicate specific absolute levels by
setting a 0 dB reference value. For
example, if a vibration velocity
amplitude of 10–6 cm/sec is made the
0 dB reference, then the level of
10–5 cm/sec has a value of +20 VdB
(10 x reference) and so forth. The
term “VdB” is used to indicate
velocity decibel values. The
corresponding VdB values of in/sec
(rms) and in/sec (peak) using a
0 VdB reference value of 1 x 10–6
cm/sec (rms) (equal to .394 x 10–6
in/sec (rms)) are shown in Figure 1.
A Convenient Warning Alert
VdB simply specifies absolute values
of vibration velocity relative to a
chosen reference level. A vibration
level of .1 in/sec (rms) is 108 VdB;
.04 in/sec is 100 VdB. It is easy to
convert from in/sec to VdB and back.
Most important, changes in absolute
values are more easily expressed in
VdB units. For example, a normal
vibration level of .1 in/sec (rms) that
increases to .2 in/sec (rms) has
changed by a factor of two. The
corresponding VdB levels would be
108 VdB increasing to 114 VdB.
Note that adding 6 VdB defined the
change. This is quite important in
machinery vibration monitoring
because a doubling of vibration
levels is a widely accepted “red flag”
alert indicating possible problems.
This “6 VdB” increase is an effective
warning alert regardless of the
level of vibration measured, the
problem(s) causing it, the frequency
involved or the RPM of the machine.
This makes a decibel extremely
useful for Predictive Maintenance
Programs. Any reading that
Nominal Conversion Chart
VdB
50
56
60
63
66
70
71
72
73
74
75
76
77
78
79
80
81
82
reference: 0 VdB = .394 x 10–6 in./sec (rms)
= 1 x 10–6 cm sec (rms)
in/sec (rms) in/sec (pk) VdB in/sec (rms) in/sec (pk)
.125 x 10–3
.177 x 10–3
83
5.56 x 10–3
7.86 x 10–3
.25
"
.35
"
84
6.24
"
8.82
"
.394
"
.557
"
85
7.0
"
9.90
"
.556
"
.786
"
86
7.86
"
1.11 x 10–2
.786
"
1.11
"
87
8.8
"
1.24
"
1.25
"
1.77
"
88
9.9
"
1.40
"
1.4
"
1.98
"
89
1.11 x 10–2
1.57
"
1.57
"
2.22
"
90
1.25
"
1.77
"
1.76
"
2.49
"
91
1.4
"
1.98
"
1.97
"
2.79
"
92
1.57
"
2.22
"
2.2
"
3.11
"
93
1.76
"
2.49
"
2.5
"
3.54
"
94
1.97
"
2.79
"
2.8
"
3.96
"
95
2.2
"
3.11
"
3.13
"
4.43
"
96
2.48
"
3.50
"
3.5
"
4.95
"
97
2.8
"
3.96
"
3.94
"
5.57
"
98
3.13
"
4.43
"
4.4
"
6.22
"
99
3.5
"
4.95
"
4.96
"
7.01
"
100
3.94
"
5.57
"
VdB
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
Figure 1
Z-164
Velocity decibel (VdB) to in/sec (rms).
in sec (peak)
in/sec (rms) in/sec (pk) VdB in/sec (rms)
4.4 x 10–3
6.22 x 10–3 119
3.5 x 10–1
4.96 "
7.01
"
120
3.94 "
5.56 "
7.86
"
121
4.4
"
6.24 "
8.82
"
122
4.96 "
7.00 "
9.90
"
123
5.56 "
7.86 "
1.11 x 10–1 124
6.24 "
8.8
"
1.24
"
125
7.00 "
9.9
"
1.40
"
126
7.86 "
1.11 x 10–1
1.57
"
127
8.8
"
1.25 "
1.77
"
128
9.9
"
1.4
"
1.98
"
129
1.11 x 103
1.57 "
2.22
"
130
1.25 "
1.76 "
2.49
"
133
1.76 "
1.97 "
2.79
"
136
2.48 "
2.2
"
3.11
"
140
3.94 "
2.48 "
3.50
"
142
4.96 "
2.8
"
3.96
"
148
9.9
3.13 "
4.43
"
150
12.5 "
in/sec (pk)
4.95 x 10–1
5.57
"
6.22
"
7.01
"
7.86
"
8.82
"
9.90
"
1.11 x 109
1.24
"
1.40
"
1.57
"
1.77
"
2.49
"
3.5
"
5.57
"
7.01
"
1,4 x 108
1.77
"
increases 6 VdB is cause for alarm.
If last month’s reading was 80 and
now it is 86 (or 95/101, or 110/116),
the technician knows immediately
that he has a potential problem.
This also makes the dB ideal for
“computerized” monitoring systems,
because it simplifies analysis and
can reduce operator error.
Summary
The VdB is a simple and useful way
of measuring and comparing vibration
levels in rotating machinery. Widely
different levels are covered by a
small range of whole numbers. This
reduces errors in recording and
promises confidence and
understanding.
Note that if the measured quantity
were “acceleration,” AdB would be
the units and 1x 10 –6 g (rms) would
be the reference (see below).
The decibel as used in vibration
measurement is defined as follows:
N 
dB = 20 log10  1 
 N2 
An example of using VdB best
illustrates its advantages: most
periodic monitoring programs have
the technician make initial readings
on selected machines to establish
norms. By using an instrument
reading VdB, such as the NOVA
100 Machinery Defect Analyzer,
these initial levels are given in VdB
numbers. For example, in starting
a program, the technician measures
the level 100 VdB. His chart
indicates this is normal, and several
rechecks indicate 100 again, so 100
is entered into his chart. Each
month, the same point is checked
and the numbers recorded:
Critical changes (i.e., 6 VdB
increases) in machinery vibration
levels are easily identified by
“unskilled” technicians. Problems
are easier to detect and define,
resulting in a more profitable,
effective program.
where:
N1 = measured vibration level 1
N2 = reference vibration level 2
Example of Actual Problem
Detection
Example:
Start (Sept.)...100 VdB
Oct............101
Nov............100 (Normal readings)
Dec..............99
Jan............101
Feb............104 (Starting to get worse)
March...........106 (Alert)
September Vibration Level N2
= 0.2 in/sec (rms) reference level
Log 400 = 4 x 102
Log 400 = 2.6
Expressed in dB, this change would
be:
Mantissa (Log of 4)
Characteristic (Power of 10)
August
Vibration Level N1
= .02 in/sec (rms)
 0.2 
dB = 20 log10 
 = 20 [log (10)]
 0.02 
Referring to the table: Log of 10 = 1.0
Therefore, dB = 20 x 1 = 20
a + 20 dB change!
When measuring vibration in velocity
relative to a chosen reference level,
use the term VdB.
 Vm 
VdB = 20 Log10 

 Vr 
where:
Vm = measured vibration velocity
Vr = international reference 1 x
10–6 cm/sec (rms)
or .394 x 10–6 in/sec( rms)
Example:
Measured vibration = 1 cm/sec (rms)
VdB = 20 Log 1 x 10 –1
1 x 10 –6
= 20 Log (2 x 10 5) = 20 [5] = 100
Z-165
10 = 101
1 = 10 0
5 = 10 .6
100 = 102
Log 10 = 1
Log 1 = 0
Log 5 = .6
Log 100 = 2
A log consists of a characteristic
and the mantissa
Example:
Reproduced with permission of
Vibra-Metrics.
DYNAMIC MEASUREMENT
The technician knows that a 6 VdB
increase indicates trouble. He
reports the problem and schedules
the blower for maintenance. A
fatigued bearing housing is found
and replaced. After replacement and
balancing, the bearing reading is
repeated and is now 98 VdB. He
knows that things are back to
normal. Using VdB is as simple as
that. At no time did the technician
have to worry about “mils” or “in/sec,”
RPM’s, or the specific problem
involved. For ongoing programs
already taking in/sec readings, the
measurements can be converted to
VdB and the program continued.
A technician measures the vibration
level at a motor bearing in August at
0.02 in/sec (rms). In September, the
level measure is 0.2 in/sec (rms).
The log10 of a number X is the
exponential power to which 10 must
be raised to equal that number.
K