DOM.pdf

DOM.pdf

• 1. @Need of balancing-(1) In comparison with the static forces are very large in magnitude.(2) Example of high dynamic force: Consider rotor of steam turbine with mass (m) = 1 tonne, speed (n) = 3000 r.p.m., and distance of C.G. of rotor from axis (r) = 2 mm. Resultant dynamic force (centrifugal force) is,Fc= 197.39*103N(3)Effect of high dynamic force need of balancing : Such high dynamic force produces hammering action and sets up vibrations. It has a tendency to lift the machine from the foundation. No foundation will normally be able to withstand force of such high magnitude and frequency. Hence, to avoid such effects, precise balancing is essential. Thus, the purpose of balancing is to avoid the vibration of the machine by balancing the resultant inertia forces and couples. The balancing is highly essential, especially in high speed applications such as electric motors, generators, turbines, pumps, aircrafts, machine tools, etc.(4)Balancing is the process of correcting or eliminating, either partially or completely, the effects due to resultant inertia forces and couples acting on the machine parts or components.@static & dynamic Static balancing dynamic balancing Static balancing is a balance of forces due to action of gravity Dynamic balance is a balance due to the action of inertia forces Static balance is done with the object which are balanced at rest Dynamic balancing is done with the object being balanced in motion A body is said to be in static balance when its centre of gravity is in the axis of rotation. A body is said to be in dynamic balance when the resultant forces and couples, which involved in the inertia or acceleration of different moving parts is equal to zero In static balancing, only the forces are balanced In dynamic balancing, both the forces and the couples are balanced. Condition for static balancing: For the system to be statically balanced, the resultant of all the dynamic forces (centrifugal forces) acting on the system must be zero. Conditions for dynamic (complete) balancing :The system is said to be dynamically balanced if The resultant of all the dynamic forces acting on the system during rotation must be zero. For statically unbalanced system, the axis of C.G of rotor is offset and parallel with the axis of rotation. For dynamically unbalance system, the axis of C.G of rotor is offset and non-parallel with the axis of rotation. Ex.: Thisoccurs when there is unequal or heavy weight at one side of the tire and which causing the tyre and wheel to move up-and- down motion called shaking of wheel. This occurs when there is unequal or heavy weight at one or both side of the tire and which causing the tyre and wheel to move side-to-side wobble motion called shimmy of wheel. @Need of Balancing of Reciprocating Masses: In applications like I.C. engines, reciprocating compressors and reciprocating pumps, reciprocating parts are subjected to continuous acceleration and retardation. Due to this continuous acceleration and retardation, the inertia force acts on the reciprocating parts which is in a direction opposite to the direction of acceleration. This inertia force is a disturbing force or unbalanced dynamic force acting on the reciprocating parts. Hence, the balancing of the reciprocating parts or masses means eliminating, partially or completely the effect of inertia force by using suitable balancing masses. @Direct & Reverse cranks method - The method of direct and reverse cranks is used for balancing of the radial engines or V-engines. In a radial engines and Vengines all the connecting rods are connected to a common crank and this crank revolves in one plane. Hence, there is no primary or secondary couple. Only the primary and secondary forces are required to be balanced. Let,ὠ = uniform angular speed of crank, rad/s Ө = angle made by crank with i.d.c. position, rad r = length of crank, m, n = obliquity ratio, m = mass of reciprocating parts, kg. Primary Direct and Reverse Cranks :The arrangement shown in Fig. can be replaced by another arrangement, shown in Fig. in which OC is called as the actual crank or primary direct crank and OC' is called as the indirect crank or primary reverse crank. Primary direct crank: The primary direct crank OC makes an angle with i.d.c. position and is rotating uniformly at 'w' rad/s in clockwise direction. Primary reverse crank : The primary reverse crank OC' makes an angle → with i.d.c. position and is rotating uniformly at 'w' rad/s in anticlockwise direction as shown in Fig. Thus the primary reverse crank is mirror image of the primary direct crank.

• 2. @What is steering, pitching and rolling with respect to navel ship? The terms used in connection with ships are as follows: (1) Bow or fore end: It is the front end of the ship.ii) Stern or aft or rear end: It is rear end of the ship. (iii) Starboard: It is the right hand side of the ship when seen from the stern. (rear end)(iv) Port: It is the left hand side of the ship when seen from the stern. (rear end) (v) Steering of ship: Steering is the turning of a complete ship in a curve towards the left or right.(vi) Pitching of ship : Pitching is the cyclic up and down motion of the bow and stern in a vertical plane about the (vii) Rolling of ship : Rolling is the cyclic up and down motion of the port and the starboard about the longitudinal. @dynamic Balancing Machines :- (1)In case of parts, having considerable width, such as turbine rotors, motor armature etc, the unbalanced centrifugal force results into the unbalance couple. The purpose of dynamic balancing is to measure the unbalanced couple and introduce a new couple with same magnitude but opposite in direction.(2)Fig shows pivoted cradle type dynamic balancing machine. The part which is to be balanced is mounted on cradle with the help of half-bearings or supporting rollers. The one end of the part is connected to a motor through a universal or Hook's coupling.(3) The cradle can be allowed to rock, or oscillate about either of two pivot points. The pivot points can be adjusted to coincide with the correction planes on the part to be balanced. (4) Fig shows the left pivot in released position and right pivot is in locked position so as to rock or oscillate the cradle and part about right pivot(5)At both the ends of cradle, the springs and dashpots. are attached which are adjustable so that the natural frequency can be adjusted and made equal to the motor speed. two amplitude indicators are attached at each end of the cradle. These are also called velocity-type vibration pickups. The permanent magnet is mounted on the cradle, which moves relative to a stationary coil and generates a voltage which is proportional to the unbalance couple. This voltage is amplified and read from a voltmeter which is calibrated in kg-cm or kgm.When the right hand pivot is locked, the unbalance in the left correction plane will cause vibration whose amplitude is measured by left amplitude indicator.When the left pivot is locked, another set of measurement is made for right hand correction plane using the amplitude indicator of the right hand side. ` @Concept of Gyroscopic couple- Consider a disc spinning (rotating) with an angular velocity '' about spin axis OX in an anticlockwise direction, as shown in Fig. The plane in which the disc is spinning (rotating) Le. plane YOZ is called as plane of spin. The axis of spin is precessing in a horizontal plane XOZ about an axis OY with an angular velocity '00, The horizontal plane XOZ is called as plane of precession and axis OY is called as precession axis.Let I = Mass moment of inertia of the disc about OX, kg-m²; ὠ= angular velocity of the disc, rad/s;ὠp= angular velocity of precession of axis of spin, rad/s; The initial position of the spin axis is OX. Let the spin axis OX is turned through a small angle '80' in time '8t' in the horizontal plane XOZ about the precession axis OY