Whirling of shaft - Technical symposium

By Sylvia Torres,2014-12-26 03:54
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Whirling of shaft - Technical symposiumWhirli


    Class : V Semester Mechanical Sections : A & B


    1. Free Transverse Vibration I Determination of Natural Frequency 2. Cam Analysis Cam Profile and Jump-speed Characteristics 3. Free Transverse Vibration II Determination of Natural Frequency 4. Free Vibration of Spring Mass System Determination of Natural Frequency 5. Compound Pendulum Determination of Radius of Gyration and Moment of Inertia 6. Bifilar Suspension Determination of Radius of Gyration and Moment of Inertia 7. Trifilar Suspension Determination of Radius of Gyration and Moment of Inertia 8. Whirling of Shaft Determination of Critical Speed

    9. Balancing of Rotating Masses

    10. Determination of Gyroscopic Couple

    11. Turn Table

    12. Hartnell Governor

    13. Free Vibration of Spring Mass System Determination of Natural Frequency

Beyond the Syllabus

14. Speed Ratio of Epi-cyclic Gear Train

    15. Speed Ratio of Worm and Worm Wheel


Aim: To find the natural frequency of transverse vibration of the cantilever beam.

    Apparatus required: Displacement measuring system (strain gauge) and Weights


    Strain gauge is bound on the beam in the form of a bridge. One end of the beam is fixed and the

    other end is hanging free for keeping the weights to find the natural frequency while applying

    the load on the beam. This displacement causes strain gauge bridge to give the output in milli-

    volts. Reading of the digital indicator will be in mm.

Formulae used:

    1. Natural frequency = 1/2;?(g/;) Hz 2 where g= acceleration due to gravity in m/sand ; = deflection in m.

     32. Theoretical deflection ;= Wl/3EI

    Where, W= applied load in Newton, L= length of the beam in mm 24 3 E= young‟s modules of material in N/mm, I= moment of inertia in mm=bh/1233. Experimental stiffness = W/; N-mm and Theoretical stiffness = W/; =3EI/l N/mm


    1. Connect the sensors to instrument using connection cable.

    2. Plug the main cord to 230v/ 50hz supply

    3. Switch on the instrument

    4. Keep the switch in the read position and turn the potentiometer till displays reads “0”

    5. Keep the switch at cal position and turn the potentiometer till display reads 5

    6. Keep the switch again in read position and ensure at the display shows “0”

    7. Apply the load gradually in grams

    8. Read the deflection in mm


    Draw the characteristics curves of load vs displacement, natural frequency

    Draw the characteristics curves of displacement vs natural frequency Result:

    Observation: Cantilever beam dimensions: Length=30cm, Breadth=6.5cm and Height=0.4cm


Sl. Applied Deflection Theoretical Experimental Theoretical Natural

    No. mass deflection Stiffness Stiffness frequency ; (mm)

    m (kg) k (N/mm) k (N/mm) fn (Hz) ; (mm) T



    To study the profile of given can using cam analysis system and to draw the displacement diagram for the follower and the cam profile. Also to study the jump-speed characteristics of the cam & follower mechanism.

    Apparatus required: Cam analysis system and Dial gauge


    A cam is a machine element such as a cylinder or any other solid with a surface of contact so designed as to give a predetermined motion to another element called the follower.A cam is a rotating body importing oscillating motor to the follower. All cam mechanisms are composed of at least there links viz: 1.Cam, 2. Follower and 3. Frame which guides follower and cam.

Specification :

    Diameter of base circle =150mm, Lift = 18mm, Diameter of cam shaft = 25mm

    Diameter of follower shaft = 20 mm, Diameter of roller = 32mm, Dwell period = 180

    Type of follower motion = SHM (during ascent & descent)


    Cam analysis system consists of cam roller follower, pull rod and guide of pull rod.

    1. Set the cam at 0? and note down the projected length of the pull rod

    2. Rotate the can through 10? and note down the projected length of the pull rod above the


    3. Calculate the lift by subtracting each reading with the initial reading. Jump-speed:

    1. The cam is run at gradually increasing speeds, and the speed at which the follower jumps off

    is observed.

    2. This jump-speed is observed for different loads on the follower.


    Displacement diagram and also the cam profile is drawn using a polar graph chart.

    The Force Vs Jump-speed curve is drawn.



    1.Cam profile

    Sl. Angle of Lift in mm Lift + base circle radius (mm)

    No. rotation


2. Jump-speed.

    Sl. Load on the Jump-speed

    No. Follower, F (N) N (RPM)


Aim: To study the transverse vibrations of a simply supported beam subjected to central or offset

    concentrated load or uniformly distributed load.

    Apparatus Required: Trunnion bearings, beams, weights.



    1. Fix the beam into the slots of trunnion bearings and tighten.

    2. Add the concentrated load centrally or offset, or uniformly distributed.

    3. Determine the deflection of the beam for various weights added.

Formulae used: 3Defection at the center, ;= Wl/48EI for central concentrated load. T22Defection at the load point, ;= Wab/3EIl for offset concentrated load. T4Defection at the center, ;= 5wl/384EI for uniformly distributed load. T

     3I = bd/12; b = width of the beam, d = depth of the beam, l = length of the beam. Natural frequency of transverse vibrations, f= 1/2;?(g/;) Hz n2 where g= acceleration due to gravity in m/sand ; = deflection in m.

Observations: b = , d = , l = , E =

Tabular column:

    Sl. Mass added Experimental Theoretical Theoretical Experimental Theoretical

    No. m , kg Deflection Deflection Nat. freq. Stiffness Stiffness

     , Hz K, N/m K, N/m f;, m ;, m nT


    1. Deflection Vs. load (N) from this get stiffness (graph) 2. Deflection Vs. Natural frequency

    3. Load in N Vs. natural frequency

Stiffness experimental, K = load/deflec