3.Static and Dynamic Balancing

Static and dynamic balancing AIM: 1.To understand the principles of static and dynamic balancing 2.To perform static and dynamic balancing of given unbalanced shaft. APPARATUS REQUIRED: Static and dynamic balancing machine TM170. THEORY: Any rotating system (rotor) should have uniformly distributed mass about its rotating axis. If the mass is uniformly distributed about the rotational axis the inertia forces, ie. Centrifugal forces, which arise due to the spinning, would cancel each other. Then the rotor is said to be balanced. If the mass of the rotor is not uniformly distributed about its rotating axis (i.e., the center gravity is out of rotating axis) the inertial forces would not be balanced and would create reactions at the bearings. The unbalanced rotor will create severe vibrations and noise at the rotating frequency. Unbalance of a rotor is divided into two types 1.Static unbalance 2.Dynamic unbalance. 1.STATIC UNBALANCE: If the center of gravity of a rotor is outside the axis of rotation and the principle inertial axis is parallel to the axis of rotation, the rotor is statically unbalanced.

The static unbalance can be determined by way of oscillation. The rotor is turned few turns and allowed to rest. The rest position is noted against a reference point. The rotor is turned again and allowed to rest by itself freely. The rest position is noted again. The procedure is repeated number of times. If the rotor rests at same position, then the rotor is statically unbalanced. The principle involved in above procedure is that the rotor will rest with the center of gravity point at the lowest position. The bearing supports will move in same direction while rotating the rotor with static unbalance . 2.DYNAMIC UNBALANCE: If the center of gravity of a rotor is on the axis of rotation and the rotors principle inertial axis is inclined to the axis of rotation, the rotor is

dynamically unbalanced. The dynamic unbalance exerts a couple, if the rotor is rotated. The bearings will move in opposite direction at particular instance.

. EXPERIMENT: The unbalance is simulated using four unbalance masses, mounted on a shaft. Two unbalance masses are with out additional masses and two unbalance masses with additional masses. 1.Determination of unbalances: The first step is to determine the unbalance value of the unbalance masses. Two different types of unbalance can be configured. - Unbalance mass with no additional mass (minor unbalanced graphic symbol: white dot) - Unbalance mass with additional mass (major unbalanced graphic symbol: black dot) For the following experiments it is appropriate to position two unbalance masses without additional mass on the sides of the rotor and the two remaining masses with additional mass in the center.

To determine the unbalance, the rotor is first allowed to naturally come to rest. The unbalance masses become positioned at the bottom. An external moment is then applied with the rope pulley and weight basket. The rotor turns through a certain angle into a new equilibrium position. The unbalance can be calculated by way of equilibrium of moments:

ΣM= 0 =mass of balls* g* r – unbalance mass* g* e* sinα Where r the radius of the cable pulley, e the eccentricity and α angle of deflection. The mass of the unbalance and the eccentricity are combined to give the unbalance value U in cm-gms.

U= unbalance mass * e

The unbalance being sought is thus U= mass of the balls* r/2*sin

TABLE: UNBALNCE U1 Radius of pulley(r) No. Of balls (n) Angle turned () Mass of balls (m) U1=m*r/2sin

(cmg)

=3.33cm = = = nx3 grms

UNBALANCE UA Radius of pulley(r) No. Of balls (n) Angle turned () Mass of balls (m)

=

UA=m*r/2sin

=3.33cm = = = nx3 grms (cmg)

=

Static balance:

Angle of U1 Angle of UA Angle of UA

=  1 =+180-acos (U1/UA)  2 =+180+ acos (U1/UA)

If the angle 1 and 2 are greater than 360 subtract 360 from the value.

Dynamic unbalance:

Distance between U1 Distance between UA

a= b=(U1/UA )* a

Combination of static and dynamic unbalance: General unbalance is a combination of static and dynamic unbalance. It can be easily illustrated as follows. 1.Clamp the two unbalance masses U1 to the ends of the shaft with 90o offset. 2.The two large unbalance masses UA remain in the same position as per the preceding experiment. Without belt, the rotor has a pronounced rest position. It is statically not balanced.

Set the unbalance U1 at 90 First balance the static unbalance.

Angle between unbalance U1

2=

Angle of unbalance UA1

1=+180- acos(U1cos/UA)

Angle of unbalance UA2

1=+180- acos(U1cos/UA)

Balance the dynamic component:

Distance between U1

a=

Distance between UA

b=(U1*sin/UA*sin)* a where =acos(U1*cos/UA)

After balancing the rotor, run the rotor at 1000 r/min and check for vibration of the base. If the system is balanced the vibrations would not be present. Result: