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  Determination of Critical Speed of Whirling of Shaft 1.   Objective 1.   To Study the phenomenon of whirling of shafts. 2.   To Study the effect of different sizes and end conditions on whirling speeds. 2.   Aim 1.   To determine experimentally critical speed of whirling of shaft with different end conditions. 2.   To calculate the theoretical whirling speeds of shaft and compare with experimental speeds. 3.   Theory Refer the following study material for theory related to whirling of shafts. 1.   Theory of Machines 14E, R.S.Khurmi and J.K.Gupta, S.Chand Publishers, 930-937. 2.   Ballaney, P.L. (2003). Theory of Machines & Mechanisms. 23rd Ed. ED: Khanna Publishers, pp xxx-xxx. 4.   Description of Apparatus This apparatus is to study the whirling phenomenon. The shaft may have any type of end conditions i.e., one end fixed and other simply supported or both ends fixed. The apparatus consists of a frame to support its driving motor and fixing blocks etc. A special design is provided to clear out the effects of bearings of motor spindle from those of testing shafts. a.   KINEMATIC COUPLING: This coupling C is specially designed to eliminate the side effect on motor spindle bearings on those of the rotating shafts. b.   BALL BEARING FIXING ENDS (a and b): These ends fix the shafts while it rotates with easy shaft replace system. The fixing ends provide change of end fixing condition of the rotating shaft as per the requirement. c.   END FIXING ARRANGEMENTS: The end supporting block (motor side) may be used with conditions of fixed end of the rotating shaft. To make the end fixed, both all bearings support the rotating sleeve. To provide fixed end and directionally free end, the separate sleeves are provided. Each sleeve may be easily fitted in the end supporting block. d.   SHAFT GUARD The shaft guards are fixed in position on the supporting base frame. Rotating shafts are to be fitted in the end blocks. The driving motor 220 volts, AC/DC ¼ HP 5000 RPM 50 c/s motor, with speed control unit. e.   MEASUREMENT OF SPEED: To measure the speed a digital rpm indicator with sensor is provided.  5.   Experimental procedure a.   Take the 3mm dia. Shaft and put the sleeve having Φ3mm bore. Keep the sleeve loose for a while on the shaft. b.   Mount the hinged/fixed support bearing at the right hand side depending upon the end conditions required and tighten using provided Allen screw firmly. c.   Put the end of the shaft which is opposite to sleeve end in the fixed support at the left side and tighten firmly with Allen screws. d.   Now at the right side, insert the sleeve end of the shaft along with the sleeve into the hinged/fixed bearing socket and hold firmly so that shaft comes out from the other end of the bearing. Tighten firmly using the Allen screw provided. e.   Check all the screws and nuts for the loose assembly. If found loose tighten firmly. f.   Now instrument is ready for experimentation. Switch on the power supply of the dimmer stat and see for the rpm indicator. g.   Slowly increase the speed of the motor so that shaft starts rotating. Observe the shaft motion as the speed increases slowly. h.   As you go on increasing the speed of motor, you can observe the whirling of the shaft about its central axis. You may observe the loops which are called as bow or node shape. i.   If the revolution of a shaft is gradually increased it is found that after a certain speed reaches at which violent instability will occur, the shaft deflects into a single bow whirling round like a skipping rope.  j.   If this speed is maintained the deflection will become so large that the shaft may break, but if this speed is quickly run through, the shaft will become so true until at another higher speed the same phenomenon will occur, the deflection now, however, being a double bow and so on. Such speeds are called critical speeds of whirling. k.   Note down the speeds when the first bow starts and ends. Also note down the speed at which two bow i.e. two loops will be observed clearly. l.   After noting down the whirling speeds for mode 1 and 2, slowly reduce the motor speed and bring it to halt. m.   Switch off the power supply and change the shaft following the same procedure and observe the whirling speeds for different size shafts if needed. 6.   Precaution to be observed in experiments It is advisable to increase the speed of shaft rapidly and pass through the critical speeds first rather than observing the 1 st  critical speed which increases the speed of rotation slowly. In this process there is a possibility that the amplitude of vibration will increase suddenly bringing the failure of the shaft. If, however, the shaft speed is taken to maximum first and then slowly reduced, (thus not allowing time to build-up the amplitude of vibration at resources) higher mode will be observed first and the corresponding speed noted by using a stroboscope and then by reducing the speed further the next mode of lower frequency can be observed without any danger of rise in amplitude as the speed is being decreased and the inertial forces are smaller in comparison with the bending spring forces. Hence possibility of building up of dangerous amplitudes at resources or near resource is avoided.  7.   Typical test observations    Both ends of shaft free (hinged): 1 st  and 2 nd  mode of vibration can be observed on shafts with 3mm dia and 4mm dia.    One end of shaft fixed and the other free: 1 st  and 2 nd  mode of vibration can be observed on shaft with 3mm dia.    Both ends of shaft fixed: 2nd mode of vibration cannot be observed on 5mm dia shaft as the speeds are very high and hence beyond the range of the apparatus.    There is a difference between theoretical speed of whirl and actual speed observed, due to following reasons :    The end conditions are not as exact as assumed in theory.    Pressure of damping at the end bearings.    Assumption made in theoretical predictions.    Lack of knowledge of exact properties of shaft material. 8.   Experimental Observations Young’s modulus of the shaft (E)  : 2.06E11 N/m 2   Density of the Shaft material (ρ)  : 7991.8 Kg/m 3   Observation Table Note down the whirling speeds in rpm  as per the end conditions and nodes observed in following table. Node No. Dia. 3mm shaft Dia. 4mm shaft Dia. 5mm shaft Fixed-Fixed Fixed-Hinged Fixed-Fixed Fixed-Hinged Fixed-Fixed Fixed-Hinged Node I Node II 9.   Theoretical Calculations of whirling speeds The theoretical frequency of vibration of uniform shafts for various nodes is given by,     =  2 √     Where, f  n =Natural frequency (cycle/sec) E=Young’s modulus for shaft material. (N/m 2 ) I =second moment of area of rod c/s. (m 4 ) A=Cross-section area of rod (m 2 ) ρ=Mass density of rod material (Kg/m 3 ) L=length of rod (m) α=Numerical co -efficient depending upon mode and support.  The various value of α:  End Fixings Value of α  First Node Second Node Hinged-Fixed 2.45 7.96 Fixed-Fixed 3.38 9.82 Calculation table Sr.No Shaft Dia. Area Moment of Area End Conditions Theoretical critical speed Experimental critical speed Units (mm) X 10 -5  m 2  X 10 -11  m 4  -- RPM RPM 1 3 Hinged-Fixed Fixed-Fixed 2 4 Hinged-Fixed Fixed-Fixed 3 5 Hinged-Fixed Fixed-Fixed 10.Results and conclusions Students should write appropriate conclusions based on the comparison of experimental and theoretical values of critical whirling speed. Viva Questions- Determination of Critical Speed of Whirling of Shaft 1.   What do you mean by mechanical vibrations? What are the three types of free vibrations generally observed? 2.   Differentiate between longitudinal and transverse vibrations. 3.   What do you mean by natural frequency of vibrations? What are material and geometry parameters that affect the natural frequency of vibrations? 4.   What are the different end fixity conditions observed generally for a rotating shaft? 5.   How do you achieve the hinged end conditions for a rotating shaft? 6.   What is whirling speed of rotation for a shaft? 7.   Why does the whirling of shaft occurs? 8.   What are the nodes observed while studying whirling phenomenon? 9.   Why it is necessary to pass the first node speed range quickly and increase the speed further to observe the second node? 10.   What is the effect of end conditions, size (length and dia.) of the shaft on whirling speed of the shaft? 11.   How does the material of shaft affects the whirling speed? 12.   How to prevent the whirling of shaft in operation?
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