OBJECTIVE STUDY OF EPICYCLIC GEAR TRAIN & HOLDING TORQUE APPARATUS by pptfiles

VIEWS: 250 PAGES: 44

									V Semester                                                        Dynamics of Machine Lab




       DYNAMICS OF MACHINES LAB (TME – 553)
                                        MANUAL
                                       V Semester




Department of Mechanical Engineering                Ideal Institute Of Technology, Ghaziabad
V Semester                                                         Dynamics of Machine Lab




    IDEAL INSTITUTE OF TECHNOLOGY
             MECHANICAL ENGINEERING DEPARTMENT
             MECHANICAL ENGINEERING DEPARTMENT




             DYNAMICS OF MACHINES LAB
                                       (TME – 553)
                                        V Semester



NAME
NAME
UNIIVERSIITY ROLL NO
UN VERS TY ROLL NO
CLASS ROLL NO
CLASS ROLL NO
BRANCH
BRANCH
BATCH
BATCH




Department of Mechanical Engineering                 Ideal Institute Of Technology, Ghaziabad
V Semester                                                     Dynamics of Machine Lab


    IIDEAL IINSTIITUTE OF TECHNOLOGY GHAZIIABAD
      DEAL NST TUTE OF TECHNOLOGY GHAZ ABAD
          DEPARTMENT OF MECHANIICAL ENGIINEERIING
          DEPARTMENT OF MECHAN CAL ENG NEER NG

                                       INDEX
EXP..
EXP
                      OBJECTIIVE
                      OBJECT VE           DATE
                                          DATE       GRADE
                                                     GRADE           REMARKS
                                                                     REMARKS
 NO
 NO

  1
  1


  2
  2


  3
  3


  4
  4


  5
  5


  6
  6


  7
  7


  8
  8


  9
  9


  10
  10



Department of Mechanical Engineering             Ideal Institute Of Technology, Ghaziabad
V Semester                                                      Dynamics of Machine Lab




                                       CONTENTS

Exp.No         Name of the Experiment                                Page No

1.             Slider Crank Mechanism                                        1

2.             Cam                                                           4

3.             Governor                                                      9

4.             Gyroscope                                                   14

5.             Whirling Speed of Shaft                                     99

6.             Balancing (Static & Dynamic)                                19

7.             Vibration (Longitudinal)                                    24

8.             Vibration (Torsional)                                       29

9.             Gear Train                                                  77

10.            Gears                                                      88




Department of Mechanical Engineering              Ideal Institute Of Technology, Ghaziabad
V Semester                                                                   Dynamics of Machine Lab

                 Experiment. No: 1 Slider Crank Mechanism

1.1 Objective, 1.2 Apparatus, 1.3 Theory, 1.4 Description of Apparatus, 1.5 Procedure, 1.6
Specification, 1.7 Observation Table 1.8 Calculation, 1.9 Graph, 1.10 Result & Discussion, 1.11
Precautions, 1.12 Sources of error, 1.13 Viva-voce questions



1.1 Objective: To draw the slider displacement versus crank angle and time
versus velocity curve for a slider crank mechanism (reciprocating engine
mechanism) and compare the results with theoretical values.
1.2 Apparatus: Slider crank mechanism, graph sheet.
1.3 Theory: Fig. 1.1 shows the line diagram of a slider crank mechanism.




                               Fig.1.1, Slider Crank Mechanism
When the crank OC has moved through an angle θ from IDC ( Inner Dead
Centre), slider has moved from G to F so that the displacement of the slider
FG = x
Let, crank radius = OC = r,
Length of connecting rod = CS = l

Department of Mechanical Engineering                           Ideal Institute Of Technology, Ghaziabad
V Semester                                                           Dynamics of Machine Lab

If ω is the angular speed of the crank, it is found that:-
Displacement, x= r. [ (1-cos θ) + n - √ (n2 - sin2 θ)] --- --- --- (1)
Velocity of slider or piston, vpo= vp = dx / dt = (dx / dθ)*( dθ / dt) = (dx /dθ).ω
vp = ωr [ sinθ + sin 2θ/ 2 √ (n2 - sin2 θ)]
Acceleration of slider or piston ,
ap = d2x / dt2 = dv / dt = (dv / dθ)*( dθ / dt) = ω.(dv / dθ)
= ω2 r [ cos θ + (cos 2θ) / n ]


1.4 Description of Apparatus:
The apparatus consists of a slider, which reciprocates inside the cylinder as
the crank rotates. A graduated scale is provided to read the displacement of
the slider corresponding to the crank rotation. When crank is rotated the slider
slides to and fro in a linear motion. The motion of the slider can be read on a
scale attached to the frame. A graduated wheel is provided to read the crank
rotation.


1.5 Procedure:-
   1.        Bring the wheel and the slider to respective reference marks.
   2.        For a given angle of rotation of the crank note down the displacement
             of the slider.
   3.        Plot a graph between the slider displacement and the crank rotation.
   4.        Assume that crank is rotating with a uniform angular speed of one rad
             per sec (1 rad /sec).
   5.        Convert the crank rotation angle into time and plot the slider
             displacement versus time.
   6.        By graphical differentiation determine the velocity time graph.
   7.        By differentiation twice determine the acceleration graph.
   8.        Calculate values of displacement, velocity and acceleration from
             equation.
   9.        Compare the results.




Department of Mechanical Engineering                   Ideal Institute Of Technology, Ghaziabad
V Semester                                                                       Dynamics of Machine Lab



1.6 Specification:
                                Length of connecting rod, l = 120 mm.
                                Crank radius, r = 50 mm.

1.7 Observation table:
                                 Slider
                                                 Slider        Slider Acceleration
           Crank     Time     displacement                                                Remark
S.No.                                         Velocity (m/s)            (m/s2)
           rotation ( Sec.)       (mm)
                              Theor.   Pract. Theor. Pract.    Theor.        Pract.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.

1.8 Calculations:

1.9 Graph: Plot a graph between the slider displacement and the crank rotation

1.10 Result & Discussion:

1.11 Precautions:
      1.      Displacement of slider should be measured at equal interval of crank rotation.
      2.      Smooth curves should be drawn in plotting the graph.
1.12 Sources of Errors:
      1. Clearances in the joints.
      2. Inaccurate graduation.
      3. Inaccuracy in performing experiments.
Department of Mechanical Engineering                             Ideal Institute Of Technology, Ghaziabad
V Semester                                                                     Dynamics of Machine Lab

1.13 Viva-voce questions




                                 Experiment No: 2 Cam

1.1 Objective, 1.2 Apparatus, 1.3 Theory, 1.4 Description of Apparatus, 1.5 Procedure, 1.6 Observation
Table 1.7 Calculation, 1.8 Graph, 1.9 Result & Discussion, 1.10 Precautions, 1.11 Sources of error, 1.12
Viva-voce questions.



1.1 Objective: To study motion of the follower with the given profile of the cam
and to determine displacement , velocity & acceleration.
1.2 Apparatus: Cam and follower apparatus , graph sheet.
1.3 Theory: Cam may be defined as a rotating & reciprocating element of a
mechanism which imparts a reciprocating or oscillating motion to another
element called follower. The cam are of the disc or cylindrical types and the
follower are of knife edge, roller or flat faced. The usual motions for the
follower are :
   A. S.H.M:
   Let         S= lift of the follower
               X= displacement of the follower when crank has turned
Then X= S / 2{I-Cos θ]
      V= ω S / 2
V max   = π ωS/2θ
      A= ω2 S cos θ / 2                   during ascent
      amax = π2 ω2 S / 2 θ2               during decent

B. Uniform acceleration or deceleration:



Department of Mechanical Engineering                             Ideal Institute Of Technology, Ghaziabad
V Semester                                                            Dynamics of Machine Lab

Then displacement
Y=½ a t2
V average = S / t
V max     =2S/t
          = 2 ω S / θo                 during ascent
          =V ω2 S/ θ2                  during descent




                             Fig.2.1, Cam & Follower Apparatus


1.4 Description of Apparatus:
The apparatus is shown fig. 2.1. It consists of a cam with flat-faced follower.
The angle of rotation of the cam and follower displacement can be read from
the graduation marked on cam and follower scale.


1.5 Procedure:-
   1.        Bring the cam & following to zero position.



Department of Mechanical Engineering                    Ideal Institute Of Technology, Ghaziabad
V Semester                                                            Dynamics of Machine Lab

   2.        Rotate cam slowly and note down the angle of rotation of the cam at
             regular interval and the corresponding displacement of the follower.
   3.        Plot a graph between displacement of the follower and the angle of
             rotation of the cam.
   4.        Plot the velocity and acceleration diagram.
   5.        Determine the maximum velocity and acceleration during ascent and
             descent.

1.6 Observation table:

     S.NO.                 Angle of rotation       Displacement of follower
                                       ( 0)                    (cm)
        1.
        2.
        3.
        4.
        5.

1.7 Calculations:

1.8 Graph:
   Plot a graph between displacement of the follower and the angle of rotation
   of the cam. Plot the velocity and acceleration diagram

1.9 Result & Discussion:

1.10 Precautions:
   1.        Cam should be rotate lowly and continuously.
   2.        Lubricant the can the roller bearing to decrease friction.
1.11 Sources of Errors:
   1.        Effect of clearance in the roller and cam spindle.

Department of Mechanical Engineering                    Ideal Institute Of Technology, Ghaziabad
V Semester                                                             Dynamics of Machine Lab

   2.        Effect of the elasticity of the links.
   3.        Lateral shift in the roller follower and cam.




Department of Mechanical Engineering                     Ideal Institute Of Technology, Ghaziabad
V Semester                                           Dynamics of Machine Lab




Department of Mechanical Engineering   Ideal Institute Of Technology, Ghaziabad
V Semester                                                               Dynamics of Machine Lab

                              Experiment No: 3 Governor

1.1 Objective, 1.2 Apparatus, 1.3 Theory, 1.4 Description of Apparatus, 1.5 Procedure, 1.6
Specification, 1.7 Observation Table 1.8 Calculation, 1.9 Graph, 1.10 Result & Discussion, 1.11
Precautions, 1.12 Viva-voce questions.



1.1 Objective: To find the controlling force (Fc) for porter governor and proell
  governor.
1.2 Apparatus: Governor Arrangements, vary volt, tachometer,
1.3 Theory: Definitions of
Sensitivity:




Stability:




Hunting:




Isochronisms:




Effort & power:




Insensitiveness:




Department of Mechanical Engineering                       Ideal Institute Of Technology, Ghaziabad
V Semester                                                                Dynamics of Machine Lab

1.4 Description of Apparatus:




                                       Fig.3.1 Porter Governor




                                       Fig.3.2 Proell Governor




Department of Mechanical Engineering                        Ideal Institute Of Technology, Ghaziabad
V Semester                                                                Dynamics of Machine Lab



1.5 Procedure:-
   1.        Check the instrument for the proper connections.
   2.        Place the governor assembly in position along with balls and arms.
   3.        Tighten the screws, nut and bolt gently.
   4.        Measure the initial height of the governor.
   5.        Switch on the supply.
   6.        Vary the height of the governor and corresponding speed with the
             help of vary-volt.
   7.        Bring back the governor to initial position and switch off the supply.
   8.        Measure the weight of the ball, sleeve and length of the links.
1.6 Specification:

Weight of the sleeve                    =-----------------------Kg
Mass of the ball                        =-----------------------Kg
Length of the link                      =-----------------------mm
Initial height of the governor, hi      =-----------------------mm
Weight placed on the sleeve             =-------------------------Kg
Proell Governor:
Weight of the sleeve                    =---------------------------Kg
Mass of the ball                        =---------------------------Kg
Length of the link                      =---------------------------mm
Initial height of the governor, hi      =---------------------------mm
Weight placed on the sleeve             =----------------------------Kg




Department of Mechanical Engineering                      Ideal Institute Of Technology, Ghaziabad
V Semester                                                                          Dynamics of Machine Lab

1.7 Observation table:
Porter Governor:

Weight placed on the sleeve-----------------Kg.

S. No.   Speed, N      Angular         Sleeve          Height of      Radius of      Controlling     Remark
                                                                      rotation
         (rpm)         speed (rad      displacement,   Governor             2   2    Force,
                                                                      r= √1 - h
                                                                                              2
                       /sec)           x in mm         h=hi-x/2                      Fc=m ω r

1.
2.
3.
4.
5.


Proell Governor:
Weight placed on the sleeve-----------------Kg.


S. No.   Speed, N      Angular         Sleeve          Height of      Radius of      Controlling     Remark
                                                                      rotation
         (rpm)         speed (rad      displacement,   Governor             2   2    Force,
                                                                      r= √1 - h
                                                                                              2
                       /sec)           x in mm         h=hi-x/2                      Fc=m ω r

1.
2.
3.
4.
5.


1.8 Calculations:

1.9 Graph:
Plot a graph between the angular speed and sleeve displacement for both the
governors.


Department of Mechanical Engineering                               Ideal Institute Of Technology, Ghaziabad
V Semester                                                            Dynamics of Machine Lab

Plot a graph between the controlling force and radius of rotation for both the
governors.

1.10 Result & Discussion:

1.11 Precautions:
   1.        Reading should be taken carefully.
   2.        Speed should be increased gradually and slowly noting that sleeve may not
             come out.




Department of Mechanical Engineering                    Ideal Institute Of Technology, Ghaziabad
V Semester                                                                    Dynamics of Machine Lab




                            Experiment No.: 4 Gyroscope

1.1 Objective, 1.2 Apparatus, 1.3 Theory, 1.4 Description of Apparatus, 1.5 Procedure, 1.6
Specification, 1.7 Observation Table 1.8 Calculation, 1.9 Graph, 1.10 Result & Discussion, 1.11
Precautions, 1.12 Sources of error, 1.13 Viva-voce questions.



1.1 Objective: To verify the law of gyroscopic couple, C=I ω ωp with the help
of motorized Gyroscope.
1.2 Apparatus: Motorized Gyroscope, weights, stopwatch & tachometer
1.3 Theory: Fig. 4.1 shows motorized gyroscope.




                                        Fig.4.1 Gyroscope
   The various terms involved are:
   GYROSCOPE: It is rotating body, which processes perpendicular to plate of
   rotation, i.e. axis of rotation also changes its direction under the action of
   external forces.
   Axis of Spin: Is the axis about which a disc/rotor rotates as shown in figure

Department of Mechanical Engineering                            Ideal Institute Of Technology, Ghaziabad
V Semester                                                         Dynamics of Machine Lab

   Precession: It means the rotation of axes in other plane or about other axis
   (axis of precession) which is perpendicular to both the axis i.e. axis of spin
   and axis of couple.
   Gyroscopic Couple: it is applied couple needed to change the angular
   momentum vector of rotating disc/Gyroscope when it processes. It acts in
   the plane of coupe which is perpendicular to both the other planes (plane of
   spin and plane of precession) it is given as:-
                                         C= I ω ωp
   Where,
   I   = Moment of inertia of rotor.
   ω = Angular velocity of rotor.
   ωp= Angular velocity of precession.
1.4 Description of Apparatus:
1.5 Procedure:-
   1. Balance the initial horizontal position of the rotor.
   2. Start the motor by increasing the voltage with the transformer & watch
       until it attains a constant speed.
   3. Process the yoke frame no.2 about vertical axis by applying necessary
       force by hand to the same.
   4. It will be observed that the rotor frame swing about the horizontal axis Y-
       Y. Motor side is seen coming upward and the weight pan side doing
       downwards.
   5. Rotate the vertical Yoke axis in the anti-clock wise direction seen from
       above & observe that the rotor frame swing in opposite sense.
   6. Balance the rotor position on the horizontal frame.
   7. Start the motor by measuring the voltage with the autotransformer & wait
       till it attains constant speed.

Department of Mechanical Engineering                 Ideal Institute Of Technology, Ghaziabad
V Semester                                                               Dynamics of Machine Lab

     8. Put weight in the weight pan & start the stopwatch to note the time in sec
          required
     9. Speed may be measured by the tachometer provided on control panel.
     10 Enter the observation in the table.

1.6 Specification:

1.        Weight of rotor      - 6.25 kg
2.        Rotor diameter       - 301 mm
3.        Rotor thickness      - 100.45 mm

1.7 Observation table:

            Speed     of
            disc
            C for 90o 0.5               1          1.5            2               2.5
            precession
            Load
            Time


1.8 Calculations:
   1.   I=
     2.      ω=
     3.      ωp= d θ / dt = π/2/E 2 S / 2 2
1.9 Graph:
1.10 Result & Discussion:

1.11 Precautions:
     1.      At starting the pointer should be at zero mark.



Department of Mechanical Engineering                       Ideal Institute Of Technology, Ghaziabad
V Semester                                                             Dynamics of Machine Lab

   2.        For comparison of Gyroscopic couple angular displacement for different
             loads should be insured before conducting the experiment.
   3.      Proper lubrication should be placed gently and without impact.
1.12 Sources of Errors:
   1. Rotor should run at a steady speed.
   2. Rotor should rotate in a vertical plane.




Department of Mechanical Engineering                     Ideal Institute Of Technology, Ghaziabad
V Semester                                                               Dynamics of Machine Lab

                  Experiment No: 5 Whirling Speed of Shaft

1.1 Objective, 1.2 Apparatus, 1.3 Theory, 1.4 Description of Apparatus, 1.5 Procedure, 1.6
Specification, 1.7 Observation Table 1.8 Calculation, 1.9 Graph, 1.10 Result & Discussion, 1.11
Precautions, 1.12 Viva-voce questions.



1.1 Objective: Determine the whirling speed of various shafts
1.2 Apparatus: Whirling of shaft apparatus, auto-transformer, various shafts,
tachometer.
1.3 Theory: Describe whirling of shaft and effects of whirling.
     Deflection due to mass of shaft.
     5 w L4
δ=
     384 E I
     Critical speed or whirling of speed
Nc= (1/2 )π      ( √g / δ) rps.

     Where,
     L= Length of the shaft
     W= weight of the shaft= mass of the shaft x 9.81
     I=Moment of inertia in mm4
     E= Young’s modulus of elasticity= 210 N/M2


1.4 Description of Apparatus:
Fig. 5.1 shows whirling of shaft apparatus.




Department of Mechanical Engineering                       Ideal Institute Of Technology, Ghaziabad
V Semester                                                              Dynamics of Machine Lab




                                   Fig.4.1 whirling of shaft apparatus


1.5 Procedure: -
   1. Fix the shaft properly at both the ends.
   2. Check the whole apparatus for tightening of screws etc.
   3. First increases the voltage slowly for maximum level and then start
        slowing down step by step.
   4. Observe the loops appearing on the shaft and note down the number of
        loops and the speed at which they are appearing.
   5. Slowly bring the shaft to rest and switch off the supply.
   6. Repeat the same procedure for different shaft.



1.6 Specification:
   L=
   W=
   I=
   E= Young’s modulus of elasticity= 210 N/M2

Department of Mechanical Engineering                      Ideal Institute Of Technology, Ghaziabad
V Semester                                                             Dynamics of Machine Lab

1.7 Observation table:

    S.No           Shaft diameter      Moment of            Weight                 Length
                         (cm)          inertia (cm4)       (Kg./cm)                 (cm)
1
2
3

Critical speed
                             Shaft-1           Shaft-2              Shaft-3
First Node
Second Node
Third Node

1.8 Calculations:

1.9 Graph:

1.10 Result & Discussion:

1.11 Precautions:
    1. The shaft should be straight
    2. The shaft should be properly tightened.
    3. Voltage should not be very high.
    4. Reading should be taken properly.
1.12 Sources of Errors:
    3. Rotor should run at a steady speed.
    4. Rotor should rotate in a vertical plane.




Department of Mechanical Engineering                     Ideal Institute Of Technology, Ghaziabad
V Semester                                                                       Dynamics of Machine Lab

             Experiment No: 6 Balancing (Static & Dynamic)

1.1 Objective, 1.2 Apparatus, 1.3 Theory, 1.4 Description of Apparatus, 1.5 Procedure, 1.6
Specification, 1.7 Result & Discussion, 1.8 Viva-voce questions.



1.1 Objective: To verify the fundamental laws of balancing by using rotating
masses.
1.2 Apparatus: Balancing apparatus, steel shaft, weights etc.
1.3 Theory: Fig. 6.1 shows balancing apparatus.




                                 Fig.6.1 Balancing Apparatus
   When a disc is rotating along its centre of gravity with uniform speed, inertia
   forces and torques will be zero if the matter is uniformly distributed about its
   C.G. but if the centre of rotation and the geometrical centre of G are
   different the inertia force and inertia torque will have some finite values.
   The inertia force in this case will be balanced by the input torque but inertia
   force will cause deformation of the shaft in radial direction i.e. along the line
   joining the center of rotation and C.G. if the disc is allowed to move in one

Department of Mechanical Engineering                               Ideal Institute Of Technology, Ghaziabad
V Semester                                                         Dynamics of Machine Lab

   plane and is suspended by a spring to provide a restoring force the disc will
   oscillate due to the fact that a force of type Fsinwt, Fcoswt will act upon it.
   In the apparatus the C.G. is made to change from C.G. of rotation by adding
   some weight at a certain distance from the C.G. of rotation of disc. The
   unbalance added will depend upon the product weight added and the
   distance at which at which it is added.
   The balancing law can be written by applying condition of equilibrium to the
   system.
1.4 Description of Apparatus:
   The apparatus basically consists of a steel shaft mounted in ball bearing in
   a stiff rectangular main frame. A set of six blocks of different weights is
   provided & may by clamped in any position on the shaft, and also be easily
   detached from the shaft.
   The disc caring circular protector scale is fitted in the side of the rectangular
   frame. Shaft carried a disc & rim of this disc is grooved to take a tight hold
   provided with two cylinder metal containers of exactly the same weight. The
   scale is fitted to the lower member of the main frame and when used in
   conjunction with the circular protractor scale, allows the exact longitudinal &
   angular position of each angular block to be determined.
   A 230 V drives the shaft, single phase 50 cycles electric motor, mounted
   under the main frame through a belt. For static balancing of individual
   weights, the main frame is suspended to the support frame by chain & in
   this position motor driving belt is removed.
   For dynamic balancing of the rotating mass system the main frame is
   suspended from the support frame by two short links such as that the main
   frame & the supporting frame are in the same frame.



Department of Mechanical Engineering                 Ideal Institute Of Technology, Ghaziabad
V Semester                                                           Dynamics of Machine Lab

1.5 Procedure:-
Static Balancing: Remove the drive belt, the value of wrN for each block is
determined by clamping each block in turn on the shaft & with a cord &
container system suspended over the protector disc, the no. of steel balls,
which are of equal weights, are placed into one of the container to exactly
balance the block on the shaft. When the block becomes horizontal, the no. of
balls “N” will give the value of weight for the block.
For finding our “wr” during static balancing proceed as follows:
   1.        Remove the belt.
   2.        Screw the combine hook to the pulley with the groove (this pulley is
             different than the belt pulley)
   3.        Attach the cord ends of the pass to the above combined hooks.
   4.        Attach the block no.1 to the shaft at any convenient position & in
             vertical downward direction.
   5.        Put steel balls in one of the pan till the block starts moving up. (upto
             horizontal position)
   6.        No. of balls gives the “wr” value of block 1 repeat this for 2-3 times &
             find the avg. no. of balls.
   7.        Repeat the procedure for the other blocks.
Dynamic Balancing :
It is necessary to leave the machine before the experiment. Using the value of
“wr” obtained as above & if the angular position & planes of rotation of three of
four blocks are known, the students can calculate the position of other blocks,
(s) for balancing of the complete system, from the calculations, the students
finally clamps all the blocks on the haft in their appropriate position & then by
running the one can verify that these calculations are correct & the blocks are
perfectly balanced.


Department of Mechanical Engineering                   Ideal Institute Of Technology, Ghaziabad
V Semester                                           Dynamics of Machine Lab




1.6 Specification:


1.7 Result & Discussion:




Department of Mechanical Engineering   Ideal Institute Of Technology, Ghaziabad
V Semester                                                                     Dynamics of Machine Lab



                  Experiment No: 7 Vibration (Longitudinal)

1.1 Objective, 1.2 Apparatus, 1.3 Theory, 1.4 Description of Apparatus, 1.5 Procedure, 1.6
Specification, 1.7 Observation Table 1.8 Calculation, 1.9 Result & Discussion, 1.10 Precautions.



1.1 Objective: To study the longitudinal vibration of helical spring and to
determine the frequency of period of vibrator theoretically & actually by
experiment.

1.2 Apparatus: Vibration apparatus, stopwatch, weights, stand scale etc.
1.3 Theory:
    Longitudinal vibration:
    Spring stiffness:
1.4 Description of Apparatus:
    Fig. 7.1 shows the line diagram of vibration apparatus.




                                  Fig.7.1, Vibration apparatus




Department of Mechanical Engineering                             Ideal Institute Of Technology, Ghaziabad
V Semester                                                                Dynamics of Machine Lab



1.5 Procedure:-
1.     Fix one end of helical spring by upper screw.
2.     Determine the free length.
3.     Put some weight on platform & note down the deflection.
4.     Stretch spring length some distance & release.
5.     Count the time required in sec. for say 10,20 oscillations.
6.     Determine the actual period.
7.     Repeat the procedure for different weights.



1.6 Specification:

Axial length of spring =
Mean diameter of spring =
Wire diameter =

1.7 Observation table:
                                       For Mean Stiffness

          S.No.              Wt. attached            Deflection of             Stiffness (k)
                            W= (m x 9.81) N          spring (cm)                  (N/cm)
         1.

         2.

         3.

         4.




Department of Mechanical Engineering                        Ideal Institute Of Technology, Ghaziabad
V Semester                                                             Dynamics of Machine Lab



                                       For Mean Period

             S.No.   Wt. attached          No.of        Time for             Period (t/n)
                     W= (m x 9.81)      oscillations   oscillations
                           N                (n)             (t)
          1.

          2.

          3.

          4.



1.8 Calculations:

1.9 Result & Discussion:

1.10 Precautions:
   1.        Note down the time correctly.
   2.        Note down the oscillations properly.
   3.        Don’t stretch spring very much.




Department of Mechanical Engineering                     Ideal Institute Of Technology, Ghaziabad
V Semester                                                                     Dynamics of Machine Lab

                    Experiment No: 8 Vibration (Torsional)

1.1 Objective, 1.2 Apparatus, 1.3 Theory, 1.4 Description of Apparatus, 1.5 Procedure, 1.6
Specification, 1.7 Observation Table 1.8 Calculation, 1.9 Result & Discussion, 1.10 Precautions.



1.1 Objective: To study the torsional vibration (undamped) of single rotor shaft
system.

1.2 Apparatus: Torsional vibration apparatus, stopwatch etc.

1.3 Theory:
Torsional vibration:
Modulus of rigidity:
Polar moment of inertia:
Fig. 8.1 shows the line diagram of a torsional vibration apparatus.




                           Fig.8.1, Torsional vibration apparatus




Department of Mechanical Engineering                             Ideal Institute Of Technology, Ghaziabad
V Semester                                                            Dynamics of Machine Lab

1.4 Description of Apparatus:
     One end of the shaft is gripped in the chuck and heavy flywheel free to
     rotate in ball bearing is fixed at the other end of the haft. The bracket with
     fixed end of the shaft can be clamped at any convenient position along
     lower beam. Thus length of the shaft can be varied during the
     experiments.The ball bearing housing is fixed to side member of the main
     frame.



1.5 Procedure:-
     1.   Fix the bracket at convenient position along the lower beam.
     2.   Grip one end of the shaft at bracket by chuck.
     3.   Fix the rotor on other end of the shaft.
     4.   Twist the rotor through some angle and release.
     5.   Note down the time required for 10,20 oscillation.
     6.   Repeat the procedure in different length of the shaft.



1.6 Specification:
   (a) Shaft diameter=
   (b) Diameter of disc=
   (c) Weight if the disc=
   (d) Modulus of rigidity for shaft= 0.8*106 Kg/cm2


1.7 Observation table:

     S.No.       Length of shaft (L)       No. of       Time taken for Periodic
                                       Oscillations (n) n oscillations time
                                                              (t)      (T=t/n)
1.
2.
3.
4.
5.




Department of Mechanical Engineering                    Ideal Institute Of Technology, Ghaziabad
V Semester                                                                Dynamics of Machine Lab

1.8 Calculations:
        i. Find the torsional stiffness Kt

             Kt= GIP/L Where L= length of shaft
                            D= Diameter of shaft
                            Ip= P.I. of shaft
                            G= Modulus of rigidity

             ii Theoretical

                        T=2 π √I/kt

                     Where, I= M.I. of disc=

             iii Experimental

                        Time of oscillating
                T=
                        No. of oscillation



1.9 Result & Discussion:

1.10 Precautions:
   1.        The chuck should properly tighten the shaft.
   2.        Note down the time correctly .




Department of Mechanical Engineering                        Ideal Institute Of Technology, Ghaziabad
V Semester                                                             Dynamics of Machine Lab




                               Experiment No: 9 Gear Train

Aim: To study the different types of gear train.

Gear Train:
Sometime two or more gears are made to mesh with each other to transmit
power from one shaft to another such combination is called gear train.
Following are the different types of gear train, depending upon the
arrangement of wheels.

   1.          Simple gear train.
   2.          Compound gear train.
   3.          Reverted gear train
   4.          Epicyclic gear train.

   1. Simple gear Train:- When there is only one gear on each shaft is Known
      as simple gear train.


Since circumferential velocity of meshing gear are same. (fig. a)

      1   N1             2    N2
                 =
      60                               60

  d1 N1              =   d2 N2

N1              Z2
…..….      =    ……….
 N2             Z1             Where: d1 = P.C.D. of driver gear
                             d2 = P.C.D of driven gear                      Z1 = no. of
Teeth on Driver
     m = module                                 Z2 = no. of Teeth on Driven
         = P.C.D./ z                            Z = no. of Teeth on gear
      N1 = Speed of driver ( r.p.m.)
      N2 = Speed of drive ( r.p.m.)

The ratio of N1 and N2 is known as speed ratio.


Department of Mechanical Engineering                     Ideal Institute Of Technology, Ghaziabad
V Semester                                                                    Dynamics of Machine Lab

Train value is reciprocal of speed ratio i.e. speed ratio of driven gear to driver
gear.

         N2                 Z1
                  =
             N1                 Z2

It may be noted (from fig. ) that when the number of intermediate gear are odd
the motion of driven and driver are same and if number of intermediate gear
are even the motion of driver & driven is opposite direction from fig. (b)

Let N1= Speed of driver gear 1      Z1 = No. of teeth on driver gear
    N2= Speed of intermediate gear2 Z2 = No of teeth on intermediate gear
    N3= Speed of driven gear           Z3 = No. of teeth on driven gear

Since gear 1 and gear 2 are in meshing.

     N1                     Z2
             =                   --- --- --- (i) and similarly gear 2,3 are in meshing .
     N2                     Z1

     N2                Z3
             =              --- --- --- (ii)
     N3                Z2

Multiply both equations

    N1                     N2         Z2 Z3
         ×         =             ×
    N2            N3             Z1 Z2

                  N1                 Z3
                            =
                      N3             Z1

                  Speed of driver                      No. of teeth on driven
i .e. speed ratio              =
                      Speed of driven                       No. of teeth on driver




Department of Mechanical Engineering                            Ideal Institute Of Technology, Ghaziabad
V Semester                                                                      Dynamics of Machine Lab

                          Speed of driven                      No. of teeth driver
and train value                         =
                          Speed of driver                      No. of teeth on driven


From above we see that the speed ratio and train value in a simple train of
gear is independent of the size and no. of intermediates gears. These
intermediates gears are called Idler gear.
Idler gear does not effect on the train value and speed ratio.

COMPUND GEAR TRAIN: In compound gear train there are more then one
gear on a shaft.




Let N1= Speed of the driving gear,                   N2, N3, N4, N5, N6 speed of respective
gears.
Z1= No. of teeth on driving gear                     Z2, Z3, Z4, Z5, Z6 no. of teeth on
respective gears.

Since gear 1 in mesh with gear 2.
               N1      Z2
Speed ratio =         =           --- --- ---                  (i) similarly
               N2      Z1

                    N3          Z4
                =           =                ---- --- ---      (ii)
                    N4          Z3

                    N5          Z6
               =            =               --- --- --- (iii)
               N6         Z5
Speed ratio of compound gear train.
Multiplying equation (i), (ii) and (iii) we get.

     N1              N3         N5             Z2         Z4          Z6
 =        ×     ×           =          ×      ×
     N2              N4                N6            Z1        Z3          Z5


Department of Mechanical Engineering                             Ideal Institute Of Technology, Ghaziabad
V Semester                                                                    Dynamics of Machine Lab

N2 = N3, N5 = N4

     N1                Z2 ×Z4 ×Z6
          =
     N6            Z2 ×Z4 ×Z6

          Speed of the first driver                    Product of the no. of teeth on driven
Speed ratio: = ----------------------------            = -----------------------------------
              Speed of the last driven                  product of the no. of teeth on drivers




         Speed of the last driven            Product of the no. of teeth on drivers
Train ratio: = ---------------------------- =     ---------------------------------
          Speed of the first driven product of the no. of teeth on driven

The advantage of compound train over a simple gear train is that a much
larger speed reduction from first shaft to the last shaft can be obtain with small
gears.
Reverted Gear Train: When the axis of the first gear and last gear are co-axial
, then the gear train is known as reverted gear train. In reverted gear motion of
first and last gear is in same direction.

 Let Z1 = no. of teeth on gear1       Z2, Z3, Z4, no. of teeth on respective gears.
      d1 = P.C.D. of gear            d2, d3, d4 P.C.D. of respective gears
      N1= speed of gear 1 in (r. p .m).
If a is the distance between the centre of shaft. (It is assume module of all
gears are same)

           d1+d2       d3+d4
a=                 =
              2           2


or               mZ1 + mZ2                mZ3 + mZ3
          a = --------------- =        -----------------
                   2                              2

a = Z1 +Z2 = Z3 +Z4


Department of Mechanical Engineering                            Ideal Institute Of Technology, Ghaziabad
V Semester                                                         Dynamics of Machine Lab

or    Z1 + Z2=Z3 + Z4

Epicyclic Gear Train:

In an epicyelic gear train, the axis of the shaft, over which the gear are
mounted , may move relative to a fixed axis. A simple epicyclic gear train is
shown in fig. where gear A and the arm C have a common axis at O1 about
which they can rotate. Gear B meshes with gear A and has its axis on the arm
at O2, about which the gear B can rotate, if the arm is fixed , the gear train is
simple and gear a can drive gear B or vice versa, but if gear A is fixed and the
arm is rotated about the axis of gear A ( i.e. O1).then the gear B is forced to
rotate upon and around gear A . Such a motion is called epicyclic and the gear
trains arranged in such a manner that one or ore of their members move upon
and around another member are known as epicyclic gear trains (epi. Means
upon and cyclic mean around). The epicyclic gear trains my be simple or
compound.
The epicyclic gear trains are useful for transmitting high velocity ratio with
gears of moderate size in a comparatively lesser space. The epicyclic gear
trains are used in the back gear of lathe, differential gears of the automobiles.
Hoists, pulley blocks. Wrist watches etc.

 Velocity Ratio of Epicyclic Gear Train:
The following two methods may be used for finding out the velocity ratio of an
epicyclic gear train.

     1.      Tabular method, 2. Algebraic method

      Tabular method Consider and epicyclic gear train as shown in Fig. 13.6
     Let TA=no. of teeth on gear A , and TB= no. of teeth on gear B
     First of all, let us suppose that the arm is fixed. Therefore the axis of both
     the gear are also fixed relative to each other. When gear A makes one
     revolution anticlockwise, the gear B will make TA/TB revolution clockwise.
     Assuming the anticlockwise rotation as positive and clockwise as negative,
     we may say that when gear A makes +1 revolution, then gear B will makes
     (-TA/TB) revolution. This statement of relative motion is entered in the first
     row of table .
     Secondly, if the gear A makes +x revolution, then the gear B will make -x.
     TA/TB revolutions. This statement is entered in second row of table. In other
     words, multiply the each motion (entered in the first row) by x.



Department of Mechanical Engineering                 Ideal Institute Of Technology, Ghaziabad
      V Semester                                                       Dynamics of Machine Lab

         Thirdly , each element of an epicyclic train is given +y revolution and
         entered in the third row. Finally, the motion of each element of a gear train
         is added up and entered in the fourth row.
         A little consideration will show that when two conditions about the motion of
         rotation of two elements are known, then unknown speed of third element
         may be obtained by substituting the given data in third column of the forth
         row
                                         Table of motion

Step                  Condition of motion                   Revolution of elements

no.                                                 Arm C    Gear A              Gear B

01.           Arm fixed gear A rotates through +1 0          +1                  -TA/TB

              revolution i.e.1 rev. anticlockwise

02.           Arm fixed gear A rotates through +x 0          +x                  -x. TA/TB

              revolutions

03.           Add +y revolution to all elements     +y       +y                  +y

04.           Total motion                                   x +y                y-x. TA/TB




      Department of Mechanical Engineering               Ideal Institute Of Technology, Ghaziabad
V Semester                                                       Dynamics of Machine Lab

                               Experiment No: 10 Gears

Aim : To study the Gears.

Gear : Gear are defined as toothed wheels or multilobed cams which transmit
power and motion from one shaft to another by means of successive
engagement of teeth .

The motion and power transmitted by gears is kinematically equivalent to that
transmitted by friction wheels or discs. In order to understand how the motion
can be transmitted by two toothed wheels, consider two plain circular wheels
A and B mounted on shafts, having sufficient rough surfaces and pressing
against each other as shown in fig. 10.1 (a).
Let the wheel A be keyed to the rotating shaft and the wheel B to the shaft, to
be rotated. A little consideration will show, that when the wheel A is rotated by
a rotating shaft, it will rotate the wheel B in the opposite direction as shown in
Fig. 10.1 (a).
If P>F sleeping will takes place, P= is tangential force
If P< F sleeping not occurs,              F= is frictional force

In order to avoid sleeping a number of projection (called teeth) are provided on
the periphery of wheel.

TERMINOLOGY:


Pitch Circle: - It is an imaginary circle which by pure rolling action would give
the same motion as actual gear.

Pitch circle diameter (P.C.D.): It is the diameter of pitch circle. The size of
gear is usually specified by the P.C.D.

Pitch Point: It is common point of contact between two pitch circles.

Pressure angle or angle of obliquity: it is the angle between common
normal to two gear teeth at a point of contact and the common tangent at the
pitch point . Slandered pressure angle are 14½, 20o .

Addendum: It is a radial distance of a tooth from pitch circle to the top of the
tooth .


Department of Mechanical Engineering               Ideal Institute Of Technology, Ghaziabad
V Semester                                                                Dynamics of Machine Lab

Dedendum: It is a radical distance of a tooth from pitch circle. to the bottom of
tooth .

Clearance: Dedendum-Addendum.

Circular Pitch:- Circular pitch is the distance measured along the pitch circle
between two similar point on adjacent teeth .
             π × P.C.D.
  Pc =                        Z = no. of teeth on wheel
                       Z
Module:- is the ratio of P.C.D. to the no of teeth.
           P. C. D.
  m=       --------
              Z

Diametral Pitch: it is the ratio no of teeth to pitch circle diameter.
                                    Z
                           Pd=    --------
                                  P.C.D

                π × P.C.D.         Z
         Pc×Pd = -----------     × ---------              Pc×Pd= π
                    Z                P.C.D

Addendum (ha) =m
Dedendum ( Hf ) = 1.25 m.
Clearance =( hf ) = (hf -ha) = 0.25 m
Tooth thickness = 1.5708 m

                               TYPES OF GEAR
Gears are broadly classified in to four groups.
-Spur gear
-Helical gear
-Bevel gear
-Worm gear




Department of Mechanical Engineering                        Ideal Institute Of Technology, Ghaziabad
V Semester                                                       Dynamics of Machine Lab



Spur Gear:-Teeth are cut parallel to the axis of the shaft. Profile of the gear
tooth is in the shape of involute curve and remains identical along entire width
of gear wheel. As the teeth are parallel to the axis of the shaft spur gear are
used only when the shaft are parallel. Spur gear impose radical load on the
shafts.

Helical Gear:-The teeth of these gears are cut at an angle with the axis of the
shaft. Helical gear have an involute profile similar to that of spur gear. However
this involute profile is in a plane which is perpendicular to the tooth elements
.The magnitude of helix angle of pinion and gear is same, however the hand of
helix is opposite. A right hand pinion meshes with left hand gear and vice
versa. Helical gear impose radical and thrust load on the shaft.

There is a special types of helical gear consisting a double helical gear with
small grove between two helices. The grove is required for hobbing and
grinding operation. These gears are called herringbone gear. The
construction results in equal and opposite thrust reaction balancing each other
and imposing no thrust load on the shaft .Herringbone gear are used only for
parallel shafts.

Bevel gear: - Bevel gear have a shape of truncated cone. The size of gear
tooth, including the thickness and height, decreases towards the apex of the
cone. Bevel gear are normally used for shafts which are right angles to
each other. This however is not rigid condition and the angle can be slightly
more or less then 90 degrees. The tooth of the bevel gears can be cut straight
or spiral (4) Bevel gear impose radical and thrust load on the shafts.

Worm gear:-The warm gears consist of a warm and a warm wheel. The warm
is in the form of a threaded screw, which meshes with the matching wheel. The
threads on the warms can be single or multi start and usually have a small
lead. Warm gear drives are used for the shafts, the axis of which do not
intersect and are perpendicular or to each other. The warm impose high thrust
load while worm wheel impose high radical load on the shaft. Worm gear drive
are characterized by high speed reduction ratio.

Law of gearing:- The common normal at the point of contact between a
pair of teeth must always pass through a fixed point in order to obtained
constant velocity ratio. Fixed point is called pitch point.

Forms of Teeth:- Two types of teeth commonly used.
Department of Mechanical Engineering               Ideal Institute Of Technology, Ghaziabad
V Semester                                                         Dynamics of Machine Lab



                     (i)      Cycloidal Teeth
                     (ii)     Involute Teeth

Interference :- The phenomenon when tip of tooth undercut the root on its
mating gear is known as interference .
Only Involute and cycloidal curves satisfy the fundamental law of gearing. In
case of involute profile the common normal at the point of contact always
passes through the pitch point (p) and maintains a constant inclination (α ) with
common tangent to the pitch circle. The α is called pressure angle . In case of
cycloid curves the pitch point is fixed but inclination α various , it is due to this
reason cycloidal carves become obsolete . Some time combination of
involutes and cycloid carves is used for gear tooth in order to avoid
interference . In this case middle third of the tooth profile has an involute
shape while the remaining profile is cycloidal.
The disadvantage of the involute teeth is that the interference occurs with
pinion having smaller no. of teeth . This may be avoided by altering the
heights of addendum and dedendum of mating teeth or angle of ablightly.
Envolute teeth are easy to manufacturer then cycloid teeth .

Cycloidal gears are stronger then the involute gear for the same pitch. Less
wear in cycloidal gear as compared to involute gears. In cycloidal gear
interference does not occur.




Department of Mechanical Engineering                 Ideal Institute Of Technology, Ghaziabad

								
To top