MTE

1. MANSOURA UNIVERSITY 2014-2015
Faculty Of Engineering
Machines Mechatronics
department
Prod. Eng. & Mech. Design
Dept.
Sheet (3) Balance
Problem (1)
The weights of four masses A, B, C and D are 200 kg, 300 kg, 240 kg and 260 kg
respectively.
The corresponding radii of rotation are 20 cm, 15cm, 25 cm and 30 cm respectively
and the angles between successive masses are 450
, 750
, and 1350
.
Find the position and magnitude of the balance weight required if its radius of
rotation is 20 cm.
Problem (2)
A shaft carries three rotating masses A, B and C of weights 10, 12 and 15 kg and
their radii of rotation are 6, 5 and 8 cm from the axis of the shaft.
The planes of rotation of B and C are 50 and 80 cm from A and on the same side
of it .
The angular position of the masses B and C with respect to the mass A is 750
and
1400
respectively.
Determine the weight of the balancing masses in planes L and M and their angular
positions with respect to A.
The plane L is 20 cm to the left of the plane A and the plane M is 100 cm to the right
of plane A.
The radii of rotation of the balancing weights is 8 cm .

2. Problem (3)
A shaft carries four masses A, B, C and D placed in parallel planes perpendicular to
the shaft axis along the shaft .
The masses B and C are 40 Kg and 30 kg respectively and both are assumed to be
concentrated at a radius of 15 cm, while the masses in planes A and D are both at a
radius of 20 cm.
The angle between the radii of B and C is 900
and that between B and A is 2100
, both
angles are measured in the same sense.
The planes containing A and B are 25 cm apart and those containing B and C are
50 cm apart.
If the shaft is to be in completely dynamic balance, determine:
(a) The masses of A and D.
(b)The distance between the planes containing C and D .
(c) The angular position of the mass D .
Problem (4)
A, B, C, and D are four masses carried by a rotating shaft at radii 10 cm, 12.5 cm, 20
cm, and 15 cm respectively. The four planes in which the masses revolve are spaced
60 cm apart and the weights of B, C, and D are 10 kg, 5 kg, and 4 kg respectively.
Find the required mass A and the relative angular setting of the masses so that the
shaft is in complete balance.

3. Problem (5)
A shaft carries four masses A, B, C and D placed in parallel planes perpendicular to
the shaft axis along the shaft.
The masses B and C are 46 Kg and 35 kg respectively and both are assumed to be
concentrated at a radius of 20 cm, while the masses in planes A and D are both at a
radius of 15 cm.
The angle between the radii of B and C is 1200
and that between B and A is 2100
,
both angles are measured in the same sense.
The planes containing A and B are 25 cm apart and those containing B and C are 50
cm apart.
If the shaft is to be in completely dynamic balance, determine:
(d)The masses of A and D.
(e) The distance between the planes containing C and D.
(f) The angular position of the mass D.
With Best Wishes