balancing of rotating masses-final.docx

BALANCING OF ROTATING MASSES

Dept. of Mechanical Engineering

INTRODUCTION In machines rotating parts are very common. Because of the non-homogeneity of the material used and deflections of the shafts, the center of gravity of most of them, do not coincide with the axis of  rotation. In such a situation the rotor is said to be in a state of unbalance. As a result of this the rotor will undergo a centrifugal acceleration, which would need a force. This force is proportional to the square of the speed of the rotation. This will produce undesirable vibrations which will cause to high internal stresses in parts and the reactions in bearings will go high. And also the shaft which involves in rotation! could get bend or could be get fractured in high speed rotation. Therefore balancing of rotating items is very essential in machines.

THEORY  If a set of masses had to be balanced, then the inertia forces acting on the rotor must be in equilibrium. "or a set of forces in equilibrium, the vector sum of the forces should be #ero and as well as the vector sum of couples. This phenomenon implies that the force polygon and the couple polygon engaged with the force system should be closed. "or a closed force polygon ∑mrω ∑ mr

=

2

= !

0

"a#

where , m $ mass , r $ radius ,

ω

 $ angular velocity

ω  i# a con#tant for the concerne$ in#tance an$ co%%on

for all force#& for a closed couple polygon ∑mrω

2

l

=  !

'here , m $ mass , r $ radius , l

∑mrl = 

"a#

co%%on for all force#&

ω

ω

 $ angular velocity

 $ %istance from the reference point.

i# a con#tant for the concerne$ in#tance an$

PROCEDURE Force polygon %raw the first two lines using the given data. %raw the first line hori#ontally and magnitude &'mm mr ta(e the scale as)  product, * unit + * mm!. ar( it as AB. Then draw the second line B with the angle of ' anticloc(wise! to AB and the length is /0mm.T hen by using compass draw an arc with the distance of // mm from the point . draw another arc from the point A with the distance of 12 mm. mar( the intersecting point as %.

Couple polygon 3imilarly use the given data and draw the first line of the couple polygon .The distance of the first rotor is #ero. That means it is a point and the initial point of the polygon.4oint it as A. %raw the first line with the product of

mrl

scale is product

mrl

) 2 units + * mm! and the angle relative to

hori#ontal is '. 5ou can obtain the other two angles of the 6 rd and 0th rotors from the force polygon. 7sing those angles complete the couple polygon. 5ou can obtain the distances of the 6rd and 0th rotors relative to the rotor *, using the co uple polygon. Then by using the ruler and the other necessary equipment arrange the system and observe the system when rotating and when it is not rotating. 5ou can inspect the balancing of dynamic and static respectively.

DISCUSSION Balancing of rotating masses is very essential in mechanical applications. Because, most of the wastages of energy in machines are occurred due to vibration.ost of the times the vibrations occurred due to the unbalance of the rotating parts. 4reventing unnecessary vibration as much as possible is very essential in machines. Because, the energy wastages are no t very healthy in economic aspects.  8ot only the energy wastages but also the inefficiency of the machine will go high due to these unbalances. And also because of the unbalance forces there will be wearing of the parts at the 9oints. And there will be a high reaction forces at the bearing 9oints and it will cause to damage the bearings. That means all the machining process could get bloc(ed. These effects are not good for the machine and as well as the manufacturing process where the machine is involved. By balancing the masses and get the vibration in to an acceptable level, we could prevent those unnecessary effects. Therefore balancing is a very important in industry. :owever balancing is not always necessary in industry. That does depend on the situation. As an example when the cost of the balancing is much higher than the maintenance cost, balancing is not a good decision. And also it is not necessary to balance all the vibrations li(e small vibrations. In present there exists a conventional percentage of vibration which is acceptable in machines. Another fact is if  the life time of the machine is about to expire, attempts to balance is 9ust a money wastage. Also when comparing with the cost of balancing and the profit gain, if the profit is comparatively not going considerably high the balancing is not much useful. Those are some examples for the situations which are not necessary to balance the rotating parts. ;ngineers have to concern about those facts also when  planning to balance the rotating parts. nce we rotate the shaft and stop somewhere the system should be in balance at that position. = %ynamic balance