TOPIC : 8 : Balancing --------------------------------------------------------------- Q.1. What is balancing? What are its objectives? What are types of balancing? BALANCING: Balancing is the technique of correcting or eliminating unwanted inertia forces or moments in rotating or reciprocating masses and is achieved by changing the location of the mass centers. The objectives of balancing an engine are to ensure: 1. That the centre of gravity of the system remains stationary during a complete revolution of the crankshaft and. That the couples involved in acceleration of the different moving parts balance each other. Types of balancing: a) Static Balancing: i) Static balancing is a balance of forces due to action of gravity. ii) A body is said to be in static balance when its centre of gravity is in the axis of rotation. b) Dynamic balancing: i) Dynamic balance is a balance due to the action of inertia forces. ii) A body is said to be in dynamic balance when the resultant moments or couples, which involved in the acceleration of different moving parts is equal to zero. iii) The conditions of dynamic balance are met, the conditions of static balance are also met. Q.. State the adverse effect of Imbalance force in rotating machine? Or Why balancing is necessary? If a machine is not balanced properly it will have following Adverse effect of imbalance in rotating elements: i) Vibrations are caused ii) Machine accuracy gets disturbed iii) Life of machine decreases iv) Friction increases v) Noise level increases Q.3.State any two adverse effects of imbalance. All the rotating and reciprocating parts should be completely balanced as far as possible. If these parts are not properly balanced, 1) The dynamic forces are set up. ) These forces increase the loads on bearings and stresses in the various members. 3) Also produce unpleasant and even dangerous vibrations.
Q.4.State the procedure of balancing single rotating mass when its balancing mass is rotating in the same plane as that of disturbing mass. Balancing of a single Rotating Mass By a Single Mass Rotating in the same Plane Consider a disturbing mass m 1 attached to a shaft rotating at a rad/s as shown in fig Let r 1 be the radius of rotation of the mass m 1 (i.e. distance between the axis of rotation of the shaft and the centre of gravity of the mass m 1 ). We know that the centrifugal force exerted by the mass m 1 on the shaft, F C 1 = m 1. ω. η (i) This centrifugal force acts radially outwards and this produces bending moment on the shaft. In order to counteract the effect of the force, a balancing mass ( m ) may be attached in the same plane of rotation as that of disturbing mass ( m 1 ) such that the centrifugal forces due to the two masses are equal and opposite. Let r = Radius of rotation of the balancing mass m (i.e. distance between the axis of rotation of the shaft and the centre of gravity of mass m ). Therefore Centrifugal force due to mass m, F C 1 = m. ω. r..(ii) Equation (i) and (ii), m 1.ω. r 1 = m. ω.r or m 1. r 1 = m. r
Q.5.State the procedure of balancing single rotating mass when its balancing mass is rotating in the different plane as that of disturbing mass. ANS: When the plane of the disturbing mass lies in the between the planes of the two balancing masses Let l 1 = Distance between the planes A and L. l = Distance between the planes A and M, and. l 1 = Distance between the planes L and M.. Balancing of a single rotating mass by two rotating masses in different planes when the plane of single rotating mass lies in between the planes of two balancing masses. We know that the centrifugal force exerted by the mass m in the plane A, F C = m.ω. r Similarly, the centrifugal force exerted by the mass m 1 in the plane L, F C 1 = m 1.ω. n and, the centrifugal force exerted by the mass m in the plane M. F C = m.ω. r Since the net force acting on the shaft must be equal to zero, therefore the centrifugal force on the disturbing mass must be equal to the sum of the centrifugal force on the balancing masses, therefore F C = F C 1 + F C or m. ω. r = m 1.ω.r 1 + m.ω.r therefore m.r = m 1.r 1 + m.r..(i) Now in order to find the magnitude of balancing force in the plane L (or the dynamic force at the bearing Q of a shaft), take moments about P which is the point of intersection of the plane M and the axis of rotation. Therefore F C 1 l = F C l or m 1.ω.r 1 l = m.ω.r l Therefore m.r. l = m. r. l 1 or m.r = m. r. l 1 l..(ii) Similarly, in order to find the balancing force in plane M (or the dynamic force at the bearing P of a shaft), take moments about Q which is the point of intersection of the plane L and the axis of rotation. Therefore therefore F C 1 l = F C l or m 1.ω.r l m 1.r1 = m. r. l 1 or m.r = m. r.. l 1 l (iii)
Q.6.State the procedure of balancing SEVERAL rotating mass when its balancing mass is rotating in the same plane as that of disturbing mass.
Numerical Problems 1) Three masses 10 kg, 0 kg and 15 kg are attached at a point at radii of 0 cm, 0 0 cm and 15 cm respectively. if the angle between successive 60 and 90. Determine analytically the balancing mass to be attached at radius of 30 cm.. WInter 014 3. Four masses m1,m,m3 and m4 are 00 kg, 300 kg,40 kg and 60 kg respectively. The corresponding radii or rotation are 0.m,0.15m,0.5m and 0.3m respectively and the angles between successive masses are 45 0, 75 0 and 135 0. Find the position and magnitude of the balance mass required, if the radius of rotation is 0.m. using, 1) 1)Analytical method ) Graphical method 4. 5. Four masses A,B,C and D are attached to a shaft and revolve in the same plane. The masses are 1 kg,10 kg,18 kg and 15 kg respectively and their radii of rotation are 40 mm,50mm,60mm and 30 mm respectively. The angular position of the masses B, C and D are 60 0, 135 0, and 70 0 from mass A. Find the magnitude and position of the balancing mass at a radius of rotation 100mm using, 1) Analytical method ) Graphical method