Answer Happy

Balancing Objectives After completing this experiment, the student should be able to: • understand the static and dynamic balancing of a rotating system; • reduce the out of balance forces and moments of a rotating system. Equipment The balancing machine comprises :- 1. A rigid frame from which is suspended on a cradle. 2. A variable speed motor. 3. A transducer to measure the amplitude of oscillation of the cradle. 4. A five disc rotor with slots and holes for the attachment of balancing weights. 5. A control box which provides a low voltage power supply for the drive motor, an oscillator for the stroboscope and an analogue readout of the cradle amplitude of oscillation 6. A set of masses, steel rule, allen keys, pointer with magnetic base and drive belt. The rotor to be balanced rests between end stops on two pairs of ball races clamped to a supporting cradle, and is driven by a variable speed motor through a light flat belt. The cradle is attached to the base of the machine by a cross-spring pivot at one end and two suspension cables at the other. Thus the cradle and rotor assembly is free to rotate in a horizontal plane about the axis of the cross-spring pivot, this motion being opposed by the elastic moment of the pivot. The amplitude of movement of the cradle is measured by a L.V.D.T. transducer which contains the necessary electronics to provide a voltage output which is proportional to the displacement of the core which is fastened to the cradle. The voltage output is displayed on the meter as an out of balance amplitude.
Part A - Background ms my mi ty ms ma o 14 m 12 T Om mi ms mi Figure 1: The static and dynamic balancing of a rotating system. mer: ms Is Xs mX X2מית Figure 2 : Moment Vector Polygon MA mars mut mit mer Figure 3 : Force Vector Polygon
Refer to Figure 1, when the mass system is rotating at an angular velocity ca, Centrifugal force caused by individual mass m mre Total force mrw MF When the masses are not lying on the same plane then the vectors mr will form moments about the pivot plane Let x be the distances between the pivot plane and the masses. Moment of one mass Total moment mor «Σrx mirzes mrx mix can be found by drawing the moment vector polygon as shown in Figure 2. For moment balance, omrx = 0, i.e. the moment vector polygon must be closed. X mr can be found by drawing the force vector polygon as shown in Figure 3. For static force balance, wmr = 0, i.e. the force vector polygon must be closed. Part B - Procedures 1. Switch on the motor and slowly increase the rotor speed to = 300 rpm and record the actual rotor speed 2 Record meter reading of vibration amplitude. 3. Decrease the rotor speed back to 0 rpm and switch off the motor. 4 Clamp out-of-balancing masses to the corresponding discs as shown 4 3 2 ומוח 100 100 mm 100 mm 100 mm
Disc m, (g) e. (deg) r. (mm) 65 2 ㅑ ㅑ ㅏ 를 3 65 9 4 65 5. Run the rotor to the speed as in step(1) and repeat steps (2) and (3). 6. Construct the moment vector polygon and force vector polygon to determine the balancing masses to be added to disc 1 and 5 to give completely balance. 7 Add balancing masses to the rotor discs according to the results obtained in step (6). 8. Repeat step (5) to check the validity of your graphical results for static and dynamic balancing Plane m E60 х mm deg mr g mm mrx g mm 0 1 2 3 4 5 mm 0 100 200 300 400 Speed of Rotor (t.p.m.) Vibration Amplitude Reading Rotor with no mass 300 0.2 Rotor with out-of-balance masses only Rotor with balancing masses added to disc 1 and 5 300 17.0
Part C - Discussions 1. Compare the vibration amplitude before and after adding balancing masses to rotor discs. 2. Comment on the amount of vibration observed after the rotor is 'balanced' 3. Is the solution obtained unique (.e. is there any other possible solution)? 4. Does the out of balance amplitude increase with the rotating speed? Why?
5. Comment on whether dynamic balancing will also fulfil static balancing. Is it reversible? Summary Write briefly what you have learnt in this experiment.