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# Balancing masses on a shaft supported by two bearings

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1. A shaft 2m long 1500 rev min-1 between the bearing shown in figure below. Bearing have forces 5kN and 3kN acting in same plane as shown. A single mass is to be used to balance the shaft so that reactions are zero. The mass is to be placed at a radius of 200mm from the shaft centre 180° from the direction of bearing reactions. Determine the size and position ( a and b) of the mass.

Diagram attached.

2. The shaft in Q1 is to be balanced using two masses, m1 and m2 placed 0.5m and 1.5m from A and 180° from the direction of bearing reactions, each with a radius arm 100mm long. What are the sizes of m1 and m2.

Diagram attached.

https://brainmass.com/engineering/mechanical-engineering/balancing-masses-shaft-supported-two-bearings-593575

#### Solution Preview

1. A shaft 2m long 1500 rev min-1 between the bearing shown in figure below. Bearing have forces 5kN and 3kN acting in same plane as shown. A single mass is to be used to balance the shaft so that reactions are zero. The mass is to be placed at a radius of 200mm from the shaft centre 180° from the direction of bearing reactions. Determine the size and position ( a and b) of the mass.

Solution: First of all, the figure was changed to show that the centrifugal force acting on the balancing mass is oriented in opposite direction against the reactions.
From the equation of forces balance it follows that:
( 1)
where Fc = centrifugal ...

#### Solution Summary

Based on the size of the shaft and the values of the bearing reactions, the values of the necessary balancing masses are found, knowing the position where these masses are placed.

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