Unit II Balancing Single Rotating mass by a single mass rotating in the same plane and two masses rotating in different planes.

Balancing of rotating mass Balancing- Definition The process of providing secondary mass in order to counteract the effect of first mass is called as balancing of mass. The following cases are important from the subject point of view: 1. Balancing of a single rotating mass by a single mass rotating in the same plane. 2. Balancing of a single rotating mass by two masses rotating in different planes. 3. Balancing of different masses rotating in the same plane. 4. Balancing of different masses rotating in different planes.

Balancing of a Single Rotating Mass By a Single Mass Rotating in the Same Plane

Balancing of a Single Rotating Mass By Two Masses Rotating in Different Planes The net dynamic force acting on the shaft is equal to zero. This requires that the line of action of three centrifugal forces must be the same. In other words, the centre of the masses of the system must lie on the axis of rotation. This is the condition for static balancing. The net couple due to the dynamic forces acting on the shaft is equal to zero. In other words, the algebraic sum of the moments about any point in the plane must be zero. The following two possibilities may arise while attaching the two balancing masses

1. When the plane of the disturbing mass lies in between the planes of the two balancing masses

2. When the plane of the disturbing mass lies on one end of the planes of the balancing masses

1. Four masses m1, m2, m3 and m4 are 200 kg, 300 kg, 240 kg and 260 kg respectively. The corresponding radii of rotation are 0.2 m, 0.15 m, 0.25 m and 0.3 m respectively and the angles between successive masses are 45°, 75° and 135°. Find the position and magnitude of the balance mass required, if its radius of rotation is 0.2 m. Given : m1 = 200 kg ; m2 = 300 kg ; m3 = 240 kg ; m4 = 260 kg ; r1 = 0.2 m ; r2 = 0.15 m ; r3 = 0.25 m ; r4 = 0.3 m ; 1 θ = 0° ; 2 θ = 45° ; 3 θ = 45° + 75° = 120° ; 4 θ = 45° + 75°+ 135° = 255° ; r = 0.2 m

2. A shaft carries four masses A, B, C and D of magnitude 200 kg, 300 kg, 400 kg and 200 kg respectively and revolving at radii 80 mm, 70 mm, 60 mm and 80 mm in planes measured from A at 300 mm, 400 mm and 700 mm. The angles between the cranks measured anticlockwise are A to B 45°, B to C 70° and C to D 120°. The balancing masses are to be placed in planes X and Y. The distance between the planes A and X is 100 mm, between X and Y is 400 mm and between Y and D is 200 mm. If the balancing masses revolve at a radius of 100 mm, find their magnitudes and angular positions. mA = 200 kg ; mB = 300 kg ; mC = 400 kg ; mD = 200 kg ; rA = 80 mm = 0.08m ; rB = 70 mm = 0.07 m ; rC = 60 mm = 0.06 m ; rD = 80 mm = 0.08 m ; rX = rY = 100 mm = 0.1 m

3. Four masses A, B, C and D as shown below are to be completely balanced. The planes containing masses B and C are 300 mm apart. The angle between planes containing B and C is 90°. B and C make angles of 210° and 120° respectively with D in the same sense. Find : 1. The magnitude and the angular position of mass A ; and 2. The position of planes A and D.

Step 1:Write the Given Data Step 2: Finding Suitable Formula Step 3: Apply Condition If Any Step 4: Evaluate Required Data Step 5: Evaluate the Result

The balancing of rotating and reciprocating parts of an engine is necessary when it runs at slow speed (b) medium speed (c) high speed 2. A disturbing mass m1 attached to a rotating shaft may be balanced by a single mass m2 attached in the same plane of rotation as that of m1 such that m1.r2 = m2.r1 (b) m1.r1 = m2.r2 (c) m1. m2 = r1.r2 3. For static balancing of a shaft, (a) the net dynamic force acting on the shaft is equal to zero (b) the net couple due to the dynamic forces acting on the shaft is equal to zero (c) both (a) and (b) (d) none of the above

HOQ Discuss how a single revolving mass is balanced by two masses revolving in different planes HW 1. Four masses A, B, C and D revolve at equal radii and are equally spaced along a shaft. The mass B is 7 kg and the radii of C and D make angles of 90° and 240° respectively with the radius of B. Find the magnitude of the masses A, C and D and the angular position of A so that the system may be completely balanced. [Ans. 5 kg ; 6 kg ; 4.67 kg ; 205° from mass B in anticlockwise direction]