1. V Semester Dynamics of Machine Lab DYNAMICS OF MACHINES LAB (TME – 553) MANUAL V SemesterDepartment of Mechanical Engineering Ideal Institute Of Technology, Ghaziabad
2. V Semester Dynamics of Machine Lab IDEAL INSTITUTE OF TECHNOLOGY MECHANICAL ENGINEERING DEPARTMENT DYNAMICS OF MACHINES LAB (TME – 553) V SemesterNAMEUNIVERSITY ROLL NOCLASS ROLL NOBRANCHBATCHDepartment of Mechanical Engineering Ideal Institute Of Technology, Ghaziabad
3. V Semester Dynamics of Machine Lab IDEAL INSTITUTE OF TECHNOLOGY GHAZIABAD DEPARTMENT OF MECHANICAL ENGINEERING INDEXEXP. OBJECTIVE DATE GRADE REMARKS NO 1 2 3 4 5 6 7 8 9 10 CONTENTSDepartment of Mechanical Engineering Ideal Institute Of Technology, Ghaziabad
4. V Semester Dynamics of Machine LabExp.No Name of the Experiment Page No1. Slider Crank Mechanism 12. Cam 43. Governor 94. Gyroscope 145. Whirling Speed of Shaft 996. Balancing (Static & Dynamic) 197. Vibration (Longitudinal) 248. Vibration (Torsional) 299. Gear Train 7710. Gears 88 Experiment. No: 1 Slider Crank MechanismDepartment of Mechanical Engineering Ideal Institute Of Technology, Ghaziabad
5. V Semester Dynamics of Machine Lab1.1 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, 1.12Sources of error, 1.13 Viva-voce questions1.1 Objective: To draw the slider displacement versus crank angle and timeversus velocity curve for a slider crank mechanism (reciprocating enginemechanism) 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 MechanismWhen the crank OC has moved through an angle θ from IDC ( Inner DeadCentre), slider has moved from G to F so that the displacement of the sliderFG = xLet, crank radius = OC = r,Length of connecting rod = CS = lIf ω is the angular speed of the crank, it is found that:-Displacement, x= r. [ (1-cos θ) + n - √ (n2 sin2 θ)] --- --- --- (1)Department of Mechanical Engineering Ideal Institute Of Technology, Ghaziabad
6. V Semester Dynamics of Machine LabVelocity of slider or piston, vpo= vp = dx / dt = (dx / dθ)*( dθ / dt) = (dx /dθ).ωvp = 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 asthe crank rotates. A graduated scale is provided to read the displacement ofthe slider corresponding to the crank rotation. When crank is rotated the sliderslides to and fro in a linear motion. The motion of the slider can be read on ascale attached to the frame. A graduated wheel is provided to read the crankrotation.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.1.6 Specification: Length of connecting rod, l = 120 mm.Department of Mechanical Engineering Ideal Institute Of Technology, Ghaziabad
7. V Semester Dynamics of Machine Lab Crank radius, r = 50 mm.1.7 Observation table: Slider Slider Slider Acceleration Crank Time displacement RemarkS.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 rotation1.10 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.1.13 Viva-voce questionsDepartment of Mechanical Engineering Ideal Institute Of Technology, Ghaziabad
8. V Semester Dynamics of Machine Lab Experiment No: 2 Cam1.1 Objective, 1.2 Apparatus, 1.3 Theory, 1.4 Description of Apparatus, 1.5 Procedure, 1.6 ObservationTable 1.7 Calculation, 1.8 Graph, 1.9 Result & Discussion, 1.10 Precautions, 1.11 Sources of error, 1.12Viva-voce questions.1.1 Objective: To study motion of the follower with the given profile of the camand 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 amechanism which imparts a reciprocating or oscillating motion to anotherelement called follower. The cam are of the disc or cylindrical types and thefollower are of knife edge, roller or flat faced. The usual motions for thefollower are : A. S.H.M: Let S= lift of the follower X= displacement of the follower when crank has turnedThen X= S / 2{I-Cos θ] V= ω S / 2V max = π ωS/2θ A= ω2 S cos θ / 2 during ascent amax = π2 ω2 S / 2 θ2 during decentB. Uniform acceleration or deceleration:Then displacementY=½ a t2V average = S / tDepartment of Mechanical Engineering Ideal Institute Of Technology, Ghaziabad
9. V Semester Dynamics of Machine LabV max =2S/t = 2 ω S / θo during ascent =V ω2 S/ θ2 during descent Fig.2.1, Cam & Follower Apparatus1.4 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 fromthe graduation marked on cam and follower scale.1.5 Procedure:- 1. Bring the cam & following to zero position. 2. Rotate cam slowly and note down the angle of rotation of the cam at regular interval and the corresponding displacement of the follower.Department of Mechanical Engineering Ideal Institute Of Technology, Ghaziabad
10. V Semester Dynamics of Machine Lab 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 diagram1.9 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. 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
11. V Semester Dynamics of Machine LabDepartment of Mechanical Engineering Ideal Institute Of Technology, Ghaziabad
12. V Semester Dynamics of Machine LabDepartment of Mechanical Engineering Ideal Institute Of Technology, Ghaziabad
13. V Semester Dynamics of Machine Lab Experiment No: 3 Governor1.1 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, 1.12Viva-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 ofSensitivity:Stability:Hunting:Isochronisms:Effort & power:Insensitiveness:Department of Mechanical Engineering Ideal Institute Of Technology, Ghaziabad
14. V Semester Dynamics of Machine Lab1.4 Description of Apparatus: Fig.3.1 Porter Governor Fig.3.2 Proell GovernorDepartment of Mechanical Engineering Ideal Institute Of Technology, Ghaziabad
15. V Semester Dynamics of Machine Lab1.5 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 =-----------------------KgMass of the ball =-----------------------KgLength of the link =-----------------------mmInitial height of the governor, hi =-----------------------mmWeight placed on the sleeve =-------------------------KgProell Governor:Weight of the sleeve =---------------------------KgMass of the ball =---------------------------KgLength of the link =---------------------------mmInitial height of the governor, hi =---------------------------mmWeight placed on the sleeve =----------------------------KgDepartment of Mechanical Engineering Ideal Institute Of Technology, Ghaziabad
16. V Semester Dynamics of Machine Lab1.7 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 Force, r= √12- h2 /sec) x in mm h=hi-x/2 Fc=m ω2r1.2.3.4.5.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 Force, r= √12- h2 /sec) x in mm h=hi-x/2 Fc=m ω2r1.2.3.4.5.1.8 Calculations:1.9 Graph:Plot a graph between the angular speed and sleeve displacement for both thegovernors.Plot a graph between the controlling force and radius of rotation for both thegovernors.1.10 Result & Discussion:1.11 Precautions:Department of Mechanical Engineering Ideal Institute Of Technology, Ghaziabad
17. V Semester Dynamics of Machine Lab 1. Reading should be taken carefully. 2. Speed should be increased gradually and slowly noting that sleeve may not come out. Experiment No.: 4 GyroscopeDepartment of Mechanical Engineering Ideal Institute Of Technology, Ghaziabad
18. V Semester Dynamics of Machine Lab1.1 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, 1.12Sources of error, 1.13 Viva-voce questions.1.1 Objective: To verify the law of gyroscopic couple, C=I ω ωp with the helpof motorized Gyroscope.1.2 Apparatus: Motorized Gyroscope, weights, stopwatch & tachometer1.3 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 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.Department of Mechanical Engineering Ideal Institute Of Technology, Ghaziabad
19. V Semester Dynamics of Machine Lab 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. 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.Department of Mechanical Engineering Ideal Institute Of Technology, Ghaziabad
20. V Semester Dynamics of Machine Lab 10 Enter the observation in the table.1.6 Specification:1. Weight of rotor - 6.25 kg2. Rotor diameter - 301 mm3. Rotor thickness - 100.45 mm1.7 Observation table: Speed of disc C for 90o 0.5 1 1.5 2 2.5 precession Load Time1.8 Calculations: 1. I= 2. ω= 3. ωp= d θ / dt = π/2/E 2 S / 2 21.9 Graph:1.10 Result & Discussion:1.11 Precautions: 1. At starting the pointer should be at zero mark. 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.Department of Mechanical Engineering Ideal Institute Of Technology, Ghaziabad
21. V Semester Dynamics of Machine Lab 2. Rotor should rotate in a vertical plane. Experiment No: 5 Whirling Speed of Shaft1.1 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, 1.12Viva-voce questions.Department of Mechanical Engineering Ideal Institute Of Technology, Ghaziabad
22. V Semester Dynamics of Machine Lab1.1 Objective: Determine the whirling speed of various shafts1.2 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 L4δ= 384 E I Critical speed or whirling of speedNc= (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/M21.4 Description of Apparatus:Fig. 5.1 shows whirling of shaft apparatus.Department of Mechanical Engineering Ideal Institute Of Technology, Ghaziabad
23. V Semester Dynamics of Machine Lab Fig.4.1 whirling of shaft apparatus1.5 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/M21.7 Observation table: S.No Shaft diameter Moment of Weight Length (cm) inertia (cm4) (Kg./cm) (cm)123Department of Mechanical Engineering Ideal Institute Of Technology, Ghaziabad
24. V Semester Dynamics of Machine LabCritical speed Shaft-1 Shaft-2 Shaft-3First NodeSecond NodeThird Node1.8 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. 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 rotatingmasses.1.2 Apparatus: Balancing apparatus, steel shaft, weights etc.1.3 Theory: Fig. 6.1 shows balancing apparatus.Department of Mechanical Engineering Ideal Institute Of Technology, Ghaziabad
25. V Semester Dynamics of Machine Lab 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 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.Department of Mechanical Engineering Ideal Institute Of Technology, Ghaziabad
26. V Semester Dynamics of Machine Lab1.4 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.1.5 Procedure:-Static Balancing: Remove the drive belt, the value of wrN for each block isdetermined 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 exactlybalance the block on the shaft. When the block becomes horizontal, the no. ofballs “N” will give the value of weight for the block.For finding our “wr” during static balancing proceed as follows:Department of Mechanical Engineering Ideal Institute Of Technology, Ghaziabad
27. V Semester Dynamics of Machine Lab 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 offour blocks are known, the students can calculate the position of other blocks,(s) for balancing of the complete system, from the calculations, the studentsfinally clamps all the blocks on the haft in their appropriate position & then byrunning the one can verify that these calculations are correct & the blocks areperfectly balanced.1.6 Specification:1.7 Result & Discussion:Department of Mechanical Engineering Ideal Institute Of Technology, Ghaziabad
28. 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 todetermine the frequency of period of vibrator theoretically & actually byexperiment.1.2 Apparatus: Vibration apparatus, stopwatch, weights, stand scale etc.Department of Mechanical Engineering Ideal Institute Of Technology, Ghaziabad
29. V Semester Dynamics of Machine Lab1.3 Theory: Longitudinal vibration: Spring stiffness:1.4 Description of Apparatus: Fig. 7.1 shows the line diagram of vibration apparatus. Fig.7.1, Vibration apparatus1.5 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:Department of Mechanical Engineering Ideal Institute Of Technology, Ghaziabad
30. V Semester Dynamics of Machine LabAxial 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. 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.Department of Mechanical Engineering Ideal Institute Of Technology, Ghaziabad
31. V Semester Dynamics of Machine Lab 2. Note down the oscillations properly. 3. Don’t stretch spring very much. 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 shaftsystem.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.Department of Mechanical Engineering Ideal Institute Of Technology, Ghaziabad
32. V Semester Dynamics of Machine Lab Fig.8.1, Torsional vibration apparatus1.4 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=Department of Mechanical Engineering Ideal Institute Of Technology, Ghaziabad
33. V Semester Dynamics of Machine Lab (b) Diameter of disc= (c) Weight if the disc= (d) Modulus of rigidity for shaft= 0.8*106 Kg/cm21.7 Observation table: S.No. Length of shaft (L) No. of Time taken for Periodic Oscillations (n) n oscillations time (t) (T=t/n)1.2.3.4.5.1.8 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 oscillation1.9 Result & Discussion:Department of Mechanical Engineering Ideal Institute Of Technology, Ghaziabad
34. V Semester Dynamics of Machine Lab1.10 Precautions: 1. The chuck should properly tighten the shaft. 2. Note down the time correctly . Experiment No: 9 Gear TrainAim: To study the different types of gear train.Gear Train:Sometime two or more gears are made to mesh with each other to transmitpower from one shaft to another such combination is called gear train.Following are the different types of gear train, depending upon thearrangement 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)Department of Mechanical Engineering Ideal Institute Of Technology, Ghaziabad
35. V Semester Dynamics of Machine Lab  d1 N1  d2 N2 = 60 60 d1 N1 = d2 N2N1 Z2…..…. = ………. N2 Z1 Where: d1 = P.C.D. of driver gear d2 = P.C.D of driven gear Z1 = no. ofTeeth 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.Train value is reciprocal of speed ratio i.e. speed ratio of driven gear to drivergear. N2 Z1 = N1 Z2It may be noted (from fig. ) that when the number of intermediate gear are oddthe motion of driven and driver are same and if number of intermediate gearare 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 gearSince 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 Z2Department of Mechanical Engineering Ideal Institute Of Technology, Ghaziabad
36. V Semester Dynamics of Machine LabMultiply both equations N1 N2 Z2 Z3 × = × N2 N3 Z1 Z2 N1 Z3 = N3 Z1 Speed of driver No. of teeth on driveni .e. speed ratio = Speed of driven No. of teeth on driver Speed of driven No. of teeth driverand train value = Speed of driver No. of teeth on drivenFrom above we see that the speed ratio and train value in a simple train ofgear is independent of the size and no. of intermediates gears. Theseintermediates 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 onegear on a shaft.Let N1= Speed of the driving gear, N2, N3, N4, N5, N6 speed of respectivegears.Z1= No. of teeth on driving gear Z2, Z3, Z4, Z5, Z6 no. of teeth onrespective gears.Since gear 1 in mesh with gear 2. N1 Z2Department of Mechanical Engineering Ideal Institute Of Technology, Ghaziabad
37. V Semester Dynamics of Machine LabSpeed ratio = = --- --- --- (i) similarly N2 Z1 N3 Z4 = = ---- --- --- (ii) N4 Z3 N5 Z6 = = --- --- --- (iii) N6 Z5Speed ratio of compound gear train.Multiplying equation (i), (ii) and (iii) we get. N1 N3 N5 Z2 Z4 Z6 = × × = × × N2 N4 N6 Z1 Z3 Z5N2 = N3, N5 = N4 N1 Z2 ×Z4 ×Z6 = N6 Z2 ×Z4 ×Z6 Speed of the first driver Product of the no. of teeth on drivenSpeed 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 driversTrain ratio: = ---------------------------- = --------------------------------- Speed of the first driven product of the no. of teeth on drivenThe advantage of compound train over a simple gear train is that a muchlarger speed reduction from first shaft to the last shaft can be obtain with smallgears.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 offirst and last gear is in same direction.Department of Mechanical Engineering Ideal Institute Of Technology, Ghaziabad
38. V Semester Dynamics of Machine Lab 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 allgears are same) d1+d2 d3+d4a= = 2 2or mZ1 + mZ2 mZ3 + mZ3 a = --------------- = ----------------- 2 2a = Z1 +Z2 = Z3 +Z4or Z1 + Z2=Z3 + Z4Epicyclic Gear Train:In an epicyelic gear train, the axis of the shaft, over which the gear aremounted , may move relative to a fixed axis. A simple epicyclic gear train isshown in fig. where gear A and the arm C have a common axis at O1 aboutwhich they can rotate. Gear B meshes with gear A and has its axis on the armat O2, about which the gear B can rotate, if the arm is fixed , the gear train issimple and gear a can drive gear B or vice versa, but if gear A is fixed and thearm is rotated about the axis of gear A ( i.e. O1).then the gear B is forced torotate upon and around gear A . Such a motion is called epicyclic and the geartrains arranged in such a manner that one or ore of their members move uponand around another member are known as epicyclic gear trains (epi. Meansupon and cyclic mean around). The epicyclic gear trains my be simple orcompound.The epicyclic gear trains are useful for transmitting high velocity ratio withgears of moderate size in a comparatively lesser space. The epicyclic geartrains 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 anepicyclic gear train.Department of Mechanical Engineering Ideal Institute Of Technology, Ghaziabad
39. V Semester Dynamics of Machine Lab 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. 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 motionStep Condition of motion Revolution of elements Arm C Gear A Gear Bno.01. Arm fixed gear A rotates through +1 0 +1 -TA/TB revolution i.e.1 rev. anticlockwise02. Arm fixed gear A rotates through +x 0 +x -x. TA/TB revolutions03. Add +y revolution to all elements +y +y +y04. Total motion x +y y-x. TA/TB Department of Mechanical Engineering Ideal Institute Of Technology, Ghaziabad
40. V Semester Dynamics of Machine Lab Experiment No: 10 GearsAim : To study the Gears.Gear : Gear are defined as toothed wheels or multilobed cams which transmitpower and motion from one shaft to another by means of successiveengagement of teeth .The motion and power transmitted by gears is kinematically equivalent to thattransmitted by friction wheels or discs. In order to understand how the motioncan be transmitted by two toothed wheels, consider two plain circular wheelsA and B mounted on shafts, having sufficient rough surfaces and pressingagainst 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, tobe rotated. A little consideration will show, that when the wheel A is rotated bya rotating shaft, it will rotate the wheel B in the opposite direction as shown inFig. 10.1 (a).If P>F sleeping will takes place, P= is tangential forceIf P< F sleeping not occurs, F= is frictional forceIn order to avoid sleeping a number of projection (called teeth) are provided onthe periphery of wheel.TERMINOLOGY:Pitch Circle: - It is an imaginary circle which by pure rolling action would givethe same motion as actual gear.Department of Mechanical Engineering Ideal Institute Of Technology, Ghaziabad
41. V Semester Dynamics of Machine LabPitch circle diameter (P.C.D.): It is the diameter of pitch circle. The size ofgear 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 commonnormal to two gear teeth at a point of contact and the common tangent at thepitch point . Slandered pressure angle are 14½, 20o .Addendum: It is a radial distance of a tooth from pitch circle to the top of thetooth .Dedendum: It is a radical distance of a tooth from pitch circle. to the bottom oftooth .Clearance: Dedendum-Addendum.Circular Pitch:- Circular pitch is the distance measured along the pitch circlebetween two similar point on adjacent teeth . π × P.C.D. Pc = Z = no. of teeth on wheel ZModule:- is the ratio of P.C.D. to the no of teeth. P. C. D. m= -------- ZDiametral 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.DAddendum (ha) =mDedendum ( Hf ) = 1.25 m.Clearance =( hf ) = (hf -ha) = 0.25 mTooth thickness = 1.5708 mDepartment of Mechanical Engineering Ideal Institute Of Technology, Ghaziabad
42. V Semester Dynamics of Machine Lab TYPES OF GEARGears are broadly classified in to four groups.-Spur gear-Helical gear-Bevel gear-Worm gearSpur Gear:-Teeth are cut parallel to the axis of the shaft. Profile of the geartooth is in the shape of involute curve and remains identical along entire widthof gear wheel. As the teeth are parallel to the axis of the shaft spur gear areused only when the shaft are parallel. Spur gear impose radical load on theshafts.Helical Gear:-The teeth of these gears are cut at an angle with the axis of theshaft. Helical gear have an involute profile similar to that of spur gear. Howeverthis 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 ofhelix is opposite. A right hand pinion meshes with left hand gear and viceversa. Helical gear impose radical and thrust load on the shaft.There is a special types of helical gear consisting a double helical gear withsmall grove between two helices. The grove is required for hobbing andgrinding operation. These gears are called herringbone gear. Theconstruction results in equal and opposite thrust reaction balancing each otherand imposing no thrust load on the shaft .Herringbone gear are used only forparallel shafts.Bevel gear: - Bevel gear have a shape of truncated cone. The size of geartooth, including the thickness and height, decreases towards the apex of thecone. Bevel gear are normally used for shafts which are right angles toeach other. This however is not rigid condition and the angle can be slightlymore or less then 90 degrees. The tooth of the bevel gears can be cut straightor spiral (4) Bevel gear impose radical and thrust load on the shafts.Department of Mechanical Engineering Ideal Institute Of Technology, Ghaziabad
43. V Semester Dynamics of Machine LabWorm gear:-The warm gears consist of a warm and a warm wheel. The warmis in the form of a threaded screw, which meshes with the matching wheel. Thethreads on the warms can be single or multi start and usually have a smalllead. Warm gear drives are used for the shafts, the axis of which do notintersect and are perpendicular or to each other. The warm impose high thrustload while worm wheel impose high radical load on the shaft. Worm gear driveare characterized by high speed reduction ratio.Law of gearing:- The common normal at the point of contact between apair of teeth must always pass through a fixed point in order to obtainedconstant velocity ratio. Fixed point is called pitch point.Forms of Teeth:- Two types of teeth commonly used. (i)Cycloidal Teeth (ii)Involute TeethInterference :- The phenomenon when tip of tooth undercut the root on itsmating gear is known as interference .Only Involute and cycloidal curves satisfy the fundamental law of gearing. Incase of involute profile the common normal at the point of contact alwayspasses through the pitch point (p) and maintains a constant inclination (α ) withcommon tangent to the pitch circle. The α is called pressure angle . In case ofcycloid curves the pitch point is fixed but inclination α various , it is due to thisreason cycloidal carves become obsolete . Some time combination ofinvolutes and cycloid carves is used for gear tooth in order to avoidinterference . In this case middle third of the tooth profile has an involuteshape while the remaining profile is cycloidal.The disadvantage of the involute teeth is that the interference occurs withpinion having smaller no. of teeth . This may be avoided by altering theheights 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. Lesswear in cycloidal gear as compared to involute gears. In cycloidal gearinterference does not occur.Department of Mechanical Engineering Ideal Institute Of Technology, Ghaziabad
44. V Semester Dynamics of Machine LabDepartment of Mechanical Engineering Ideal Institute Of Technology, Ghaziabad