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.