2012 1 theory of vibration
TRANSCRIPT
Vibration Control
ISO 2631.1 (1997)
Micro-Vibration Level
ONE-DOF Vibration
Active isolation1
Machines are normally mounted on metal springs or by blocks and mouldings of rubber-like materials in order to isolate vibration.
Active isolation2
The system can be viewed as a simple mass-spring system as shown in here.
Transmissibility of the force TF is given by
2
n
0
TF
1
1FF
T
Active isolation3
There are three regions.
(1) < n,
(2) = n, and
(3) > n .
FT/F0
/n
Active isolation4(1) When < n, the base experiences the same force as if the
mass is fixed to it. The forces are in phase.
(2) When = n, Force at base goes to infinity and this must be
avoided.
(3) When > n, TF decrease towards 1. For /n >2, TF
becomes less than unity and enter the isolation zone.
Isolation improves as (/n) increases. The fall-off rate is
approximately equal to 12 dB/octave. The forces are 180o out of phase.
Td behaves the same.
Active isolation5
Another useful equation is
where is the static deflection. This can be used to estimate the natural frequency of the system.
g
21
mgkg
21
21
f nn
Active isolation6
For a system with damping, TF is given by
Graphically it can be represented as
ux
21
21
FF
T2
n
22
n
2
n
0
TF
Active isolation7
The peak now has finite amplitude. Criteria for effective isolation remains as
2n
Active isolation8 Peak response shifted towards lower
frequency with increased damping and reduced transmissibility.
TF is not decaying as far as the case when = 0. Decay rate can be as low as 6dB/oct.A technique known as “clearance viscous damping” can be used to overcome this problem. In this arrangement, damping comes in when amplitude is high i.e. at resonance. At low amplitudes, the system is undamped. This gives good high frequency isolation.
Factors affecting Vibration
REDUCTION AT SOURCE ISOLATION
ux
21
21
FF
T2
n
22
n
2
n
0
TF
REDUCTION AT SOURCE
Balancing of moving mass Balancing of magnetic forces
Control of clearances Smoothen the flow
Reduce self-excitation
(1) Unbalancing of rotating machines
For a well balanced
Rotating machine, the
axis of rotation coincides
with the principle axis of
the rotor. No force is
generated.
F
e
Response of a unbalanced rotor
Response X of the mass M due to the eccentric mass m is:
It starts at zero.
2
n
22
n
2
n
21me
MX
Eccentric masses
Eccentric masses arise because of: Manufacturing Tolerance Assembly Tolerances
Non-homogenous Material Assembly Non-symmetry Distortion at service speed
Hydraulic unbalance Aerodynamic unbalance
Thermal gradient
Types of unbalancing
ISO Recommendation 1925 Balancing terminology
Static Unbalance Couple unbalance
Quasi-static unbalance Dynamic unbalance
(a) Static Balancing
Also known as
“Single Plane Balancing”. Principle Axis of Inertia
C.G.
Axis of rotation
Auto balancing
Some system such as washing drum has shifting unbalanced mass. To properly counter this, automatic balancing technique has to be used.
F
e
counter force
counter force
(b) Couple balancing
C.G.
Axis of rotation
Principle axis of Inertia
Correction mass
Unbalanced mass
(c) Quasi-static balancing
Principle axis of Inertia
Axis of rotation
Correction masses
Unbalanced masses
C.G.
When the two axes intersect at a point other than the C.G., quasi-static unbalance occurs.
(d) Dynamic unbalance
Principle axis of Inertia
Unbalanced mass
Unbalanced mass
Correction mass
Correction mass
C.G.
Axis of rotation
When both axes do not intersect dynamic unbalance occurs. The correction masses will not be placed diametrically opposite to each other to correct this defect.
(2) Balancing of rotating machines
The set-up for single plane balancing is shown here . Only one pickup is required.
Procedures
i) Reference marks are placed on the rotor (wheel) and the stator as shown
The reference mark on the rotor will move to a different position under operating condition.
Simultaneously, the amplitude of vibration is picked up by the sensor placed at the bearing. This unbalance vector can be plotted as.
Now attach a trial mass, mt is placed at the reference mark on the rotor. If the rotor is running again at the same rotational speed, the reference mark will be shifted to a new position.
The vector diagram now becomes
C
The trial mass introduces the vector C
The vector diagram now becomes
C
The trial mass introduces the vector C
D
C’
Two-plane balancing
Flexible Unbalance
The rotor considered in the previous sections are assumed to be rigid. If this is not true then the balancing becomes much more complicated because many deformation shapes can occur.
Utilizing unbalanced force
Unbalanced can sometime be used usefully. The vibrator in handphone and the shaker shown here are both example of harnessing unbalncced force.