Marwadi Education Foundation Group of Institutions Department of Mechanical Engineering EXPERIMENT NO. 1: – Flywheel AIM Study about working of flywheel in power press. Theory:A flywheel used in machines serves as a reservoir, which stores energy during the period when the supply of energy is more than the requirement, and releases it during the period when the requirement of energy is more than the supply. In case of steam engines, internal combustion engines, reciprocating compressors and pumps, the energy is developed during one stroke and the engine is to run for the whole cycle on the energy produced during this one stroke. For example, in internal combustion engines, the energy is developed only during expansion or power stroke which is much more than the engine load and no energy is being developed during suction, compression and exhaust strokes in case of four stroke engines and during compression in case of two stroke engines. The excess energy developed during power stroke is absorbed by the flywheel and releases it to the crankshaft during other strokes in which no energy is developed, thus rotating the crankshaft at a uniform speed. A little consideration will show that when the flywheel absorbs energy, its speed increases and when it releases energy, the speed decreases. Hence a flywheel does not maintain a constant speed; it simply reduces the fluctuation of speed. In other words, a flywheel controls the speed variations caused by the fluctuation of the engine turning moment during each cycle of operation. In machines where the operation is intermittent like punching machines, shearing machines, riveting machines, crushers, etc., the flywheel stores energy from the power source during the greater portion of the operating cycle and gives it up during a small period of the cycle. Thus, the energy from the power source to the machines is supplied practically at a constant rate throughout the operation. Energy Stored in a Flywheel A flywheel is shown in Fig. that when a flywheel absorbs energy, its speed increases and when it gives up energy, its speed decreases. Let m = Mass of the flywheel in kg, k = Radius of gyration of the flywheel in metres, Marwadi Education Foundation Group of Institutions Department of Mechanical Engineering I = Mass moment of inertia of the flywheel about its axis of rotationin kg-m2 = m*k2, N1 and N2 = Maximum and minimum speeds during the cycle in r.p.m., ω1 and ω2 = Maximum and minimum angular speeds during the cycle in rad/s, We know that the mean kinetic energy of the flywheel, 1 1 πΈ = ∗ πΌ ∗ π2 = ∗ π ∗ π 2 ∗ π2 … … … . ππ π − π ππ π½ππ’πππ 2 2 As the speed of the flywheel changes from ω1 to ω2 the maximum fluctuation of energy. β³ πΈ = πππ₯πππ’π πΎ. πΈ. −ππππππ’π πΎ. πΈ. 1 1 1 = ∗ πΌ(π1 )2 − ∗ πΌ(π2 )2 = ∗ πΌ[(π)2 − (π)2 ] 2 2 2 = 1 ∗ πΌ(π1 + π2 )(π1 − π2 ) = πΌ(π1 − π2 ) 2 ∴π= π1 + π2 2 π1 − π2 ) … … … … … … … … … . (ππ’ππ‘ππππ¦πππ & π·ππ£πππππ ππ¦ π π = πΌ ∗ π2 πΆπ = π ∗ π 2 π2 πΆπ ∴ πΌ = π ∗ π2 1 = 2πΈπΆπ (ππ π − π ππ π½ππ’πππ ) ∴ πΈ = ∗ πΌπ2 … … . (1) 2 The radius of gyration (k) may be taken equal to the mean radius of the rim (R), because the thickness of the rim is very small as compared to the diameter of the rim. Therefore, submitting k = R, in equation (1), we have β³ πΈ = π ∗ π 2 ∗ π2 πΆπ = ππ£ 2 πΆπ Where, v = Mean linear velocity (i.e. at the mean radius) in m/s = ω*R = πΌ ∗ π2 ( Conclusion:- Marwadi Education Foundation Group of Institutions Department of Mechanical Engineering Example:1. The mass of flywheel of an engine is 6.5 tonnes and the radius of gyration is 1.8 meters. It is found from the turning moment diagram that the fluctuation of energy is N-m. If the mean speed of the engine is 120 r.p.m., find the maximum and minimum speeds. Marwadi Education Foundation Group of Institutions Department of Mechanical Engineering Experiment 2 :- UNIVERSAL GOVERNOR APPARATUS DESCRIPTION The apparatus is designed to exhibit the characteristics of the spring-loaded governor and dead weight governor. The apparatus is driven by a D.C. Motor with variable speed control unit. The Apparatus can perform following experiments. A. Watt Governor B. Porter Governor C. Proell Governor D. Hartnell type Governors. Separate linkages for governor arrangements mentioned above are provided using same motor and base. Speed measurement is to be done directly by digital RPM meter. Sleeve displacement is to be noted on scale provided. Variable control unit is provided with the apparatus i.e. for watt governor, porter governor and also on spring loaded governor INTRODUCTION The drive unit consists of a small electric motor connected through 'V' belt to drive shaft. Motor and main shaft are mounted on a rigid M.S. Base plate in vertical fashion. The spindle is supported in ball bearings. The optional governor mechanism can be mounted on spindle. Precise speed control is afforded by the speed control unit and counter hole over the spindle shaft and the speed is directly indicated on digital RPM meter. A graduated scale is fixed to the sleeve and guided in vertical direction. The center sleeve of the porter and Proell governors incorporates a weight sleeve to which weights may be added. The Hartnell Governor provided means of varying spring rate and initial compression level and mass of rotating weight. This enables the Hartnell Governor, to be operated as a stable or unstable governor. Marwadi Education Foundation Group of Institutions Department of Mechanical Engineering EXPERIMENTATION ο· ο· ο· ο· Determination of characteristics of sleeve position against controlling force and speed. Plotting of characteristic of radius of rotation against force. Obtaining the graph of governor speed V/s sleeve displacement. Obtaining the governor characteristics i.e. the graph of controlling force v/s radius of the ball center. PROCEDURE The governor mechanism under test is fitted with the chosen rotating weights and spring, where applicable and inserted into the drive unit. The following procedure may then be followed. The control unit is switched on and the speed control slowly rotated, increasing the governor speed until the center sleeve rises off the lower stop and aligns with the first division on the graduated scale. The governor speed is then increased in steps to give suitable sleeve movements, and readings repeated at each stage through out the range of sleeve movement possible. The result may be plotted as curves of speed against sleeve position. Further tests are carried out changing the value of variable at a time to draw curves. SPECIFICATIONS ο· Toggle switch : 15 Amp, DPST, Qty:1 No. ο· Diode : 4 Amp, bridge type, Qty:1 No. ο· Speed indicator ο· Dimmer :Type – RC2100, Range – 4.00 to 9999rpm, Relay rating – 5A @ 230VAC/24VDC, Sensor supply – 12VDC, 30mA, Accuracy – 0.05%, Qty: 1 No. ο· Proximity Switch Max load – 300 mA, 8mm, 10 – 30VDC, Qty:1 No. : 2Amp – open type, 230 VAC, Qty:1 No. : M – 12, PNP/NO, Marwadi Education Foundation Group of Institutions Department of Mechanical Engineering ο· Motor PMDC, Flandge mounted, 0 – 180 VDC, Qty:1 No. :1/4th HP, 1500rpm, Service Required: A.C. Single Phase 5 Amp Electrical Supply 230 V, 50 Hz standard Supply. OPERATING INSTRUCTIONS ο· Arrange the set up as a watt, proell governor. This can be done by removing the upper sleeve on the vertical spindle of the governor and using proper linkages provided. ο· Make proper connections of the motor. ο· Increase the motor speed gradually. ο· Note the sleeve displacement on the scale provided and speed on digital RPM meter. ο· Plot the graph of speed v/s sleeve displacement for watt, porter and proell ο· Plot the graph of speed v/s governor height for watt governor. ο· Plot the governor characteristics after doing the necessary calculations. governor. PRECAUTIONS ο· ο· ο· ο· ο· Do not keep the mains ‘ON’ when the trial is complete. Increase the speed gradually. Take the sleeve displacement reading when the pointer remains steady. See that at higher speed the load on sleeve does not hit the upper sleeve of the governor. While closing the test bring the dimmer to zero position and then switch 'OFF' the motor. Marwadi Education Foundation Group of Institutions Department of Mechanical Engineering A. WATT GOVERNOR AIM Evaluate the performance of watt governer. INTRODUCTION The simplest form of a centrifugal governor is a Watt governor as shown in figure. It is basically a conical pendulum with links attached to a sleeve of negligible weight. OBSERVATION ο· ο· ο· ο· Length of each link (L) Initial height of governor (ho) Initial radius of rotation (ro) Weight of each ball (W) = 0.125 m = 0.95 m = 0.132 m = 0.298 Kg. Go on increasing the speed gradually and take the readings of speed of rotation 'N' and corresponding sleeve displacement 'X', radius of rotation 'r,' at any position. OBSERVATION TABLE Sr.No. N (rpm) X (m) 1 2 3 4 5 Where, x = Sleeve Displacement in m N = Speed of Governor in RPM ο· = Angular velocity in rad / sec FC = Centrifugal Force in kg. W = Weight of each ball in Kg r = Radius of rotation in m Marwadi Education Foundation Group of Institutions Department of Mechanical Engineering CALCULATION ο· h = Height of the Governor in meter h = ho - x/2 ο· ο‘ = Angle of inclination of the arm (or upper link) to the vertical Cos ο‘ = h / L = (ho - x/2) / L ο· r = Radius of Rotation in meter r = 50 + L Sin ο‘ or ο± ο· ο· = Angular Velocity in rad /sec ο· = (2 ο° N) /60 ο· Fc = Centrifugal force in Kg Fc= (W/g) ο·2 x r GRAPH: ο· Force V/s radius of rotation. ο· Speed V/s sleeve displacement Marwadi Education Foundation Group of Institutions Department of Mechanical Engineering B. PORTER GOVERNOR AIM Evaluate the performance of porter governor. INTRODUCTION The porter governor is a modification of a Watt’s governor. With the center load attached to the sleeve as shown in figure. The load moves up and down the central spindle. This additional down word force increase the speed of revolution required to enable the balls to rise to any predetermine level. OBSERVATION ο· ο· ο· ο· Length of each link (L) Initial height of governor (ho) Initial radius of rotation (ro) Weight of each ball (W) = 0.125 m = 0.95 m = 0.132 m = 0.298 Kg. Go on increasing the speed gradually and take the readings of speed of rotation 'N' and corresponding sleeve displacement 'X', radius of rotation 'r,' at any position. OBSERVATION TABLE Sr. No. N (rpm) X (m) W (Kg) 1 2 3 4 5 Where, X = Sleeve Displacement in m N = Speed of Governor in RPM ο· = Angular velocity in rad / sec FC =Centrifugal Force in kg. W = weight of each ball in Kg r = Radius of rotation in m Marwadi Education Foundation Group of Institutions Department of Mechanical Engineering CALCULATION ο· h = Height of the Governor in meter h = ho - x/2 ο· ο‘ = Angle of inclination of the arm (or upper link) to the vertical Cos ο‘ = h / L = (ho - x/2) / L ο· r = Radius of Rotation in meter r = 50 + L Sin ο‘ or ο± ο· ο· = Angular Velocity in rad /sec ο· = (2 ο° N) /60 ο· Fc = Centrifugal force in Kg Fc= (W/g) ο·2 x r GRAPH : ο· Force V/s radius of rotation. ο· Speed V/s sleeve displacement Marwadi Education Foundation Group of Institutions Department of Mechanical Engineering C. PROELL GOVERNOR AIM Evaluate the performance of proell governor. INTRODUCTION In the Proell Governor, with the use of flyweights (Forming full ball) the governor becomes highly sensitive. Under these conditions large sleeve displacement is observed for very small change in speed. In order to make it suitable, it is necessary to carry out the experiments by using half ball flyweight on each side. OBSERVATION ο· ο· ο· ο· ο· Length of each link = 0.125 m Initial height of governor ho = 0.95 m Initial radius of rotation ro = 0.140 m Weight on sleeve = 0.458 Kg. each Weight of each ball = 0.228 Kg Go on increasing the speed gradually and take the readings of speed of rotation 'N' and corresponding sleeve displacement 'X' complete the following table draws the following graphs. ο· Speed Vs sleeve displacement ‘X’. ο· Then for any displacement 'X' of the sleeve it is possible to find 'r' and 'N'. Force 'F' any be found by knowing 'r' and 'N' OBSERVATION TABLE Sr. No. 1 2 3 4 5 N (rpm) X (m) W (Kg) Marwadi Education Foundation Group of Institutions Department of Mechanical Engineering CALCULATION ο· h = Height of the Governor in meter h = ho - x/2 ο· ο‘ = Angle of inclination of the arm (or upper link) to the vertical Cos ο‘ = h / L = (ho - x/2) / L ο· r = Radius of Rotation in meter r = 50 + L Sin ο‘ or ο± ο· ο· = Angular Velocity in rad /sec ο· = (2 ο° N) /60 ο· Fc = Centrifugal force in Kg Fc= (W/g) ο·2 x r Where, x = Sleeve Displacement in m N = Speed of Governor in RPM ο· = Angular velocity in rad / sec FC = Centrifugal Force in kg. W = Weight of each ball in Kg r = Radius of rotation in m GRAPH : ο· Force V/s radius of rotation. ο· Speed V/s sleeve displacement Marwadi Education Foundation Group of Institutions Department of Mechanical Engineering D. HARTNELL GOVERNOR AIM Explore the working of Hartnell Governor. INTRODUCTION A hartnell governor is a spring loaded governor as shown in figure. It consists of two bell crank levers pivoted at the points O, O to the frame. The frame is attached to the governor spindle and therefore rotates with it. Each lever carries a ball at the end of the vertical arm OB and a roller at the end of the horizontal arm OR. A helical spring in compression provides equal downward forces on the two rollers through a collar on the sleeve. OBSERVATION ο· ο· ο· ο· ο· ο· Length of the vertical (a) = 0.075 m Length of the horizontal (b) = 0.121 m Initial radius of rotation (ro) = 0.160 m Free height of spring = 0.132 m Weight of sliding sleeve = 0.712 kg. Weight of sliding sleeve = 0.226 kg Measure initial compression of the spring. Go on increasing the speed gradually and take the readings of speed of rotation ‘N’ and corresponding sleeve displacement 'x' radius of rotation r at any position could be found as follows: OBSERVATION TABLE Sr. No. 1 2 3 4 5 N (rpm) X (m) W (Kg) Marwadi Education Foundation Group of Institutions Department of Mechanical Engineering CALCULATION ο· r = Radius of Rotation in meter r = ro + x (a) / (b). ο· ο· = Angular Velocity in rad /sec ο· = (2 ο° N) /60 ο· Fc = Centrifugal force in Kg Fc= (W/g) ο·2 x r Where, x = Sleeve Displacement in m N = Speed of Governor in RPM ο· = Angular velocity in rad / sec FC = Centrifugal Force in kg. W = Weight of each ball in Kg r = Radius of rotation in m GRAPHS : ο· Force V/s radius of rotation. ο· Speed V/s sleeve displacement Marwadi Education Foundation Group of Institutions Department of Mechanical Engineering EXPERIMENT NO. :3 – Clutch and Break AIM Study of different clutches and breaks EXPERIMENT NO. :4 – Dynamo-meter AIM Study of dynamo-meters EXPERIMENT NO. :5 – Dynamics AIM Static force analysis of 4-bar mechanism and slider crank mechanism Dynamics force analysis of 4-bar mechanism and slider crank mechanism Marwadi Education Foundation Group of Institutions Department of Mechanical Engineering EXPERIMENT NO. 6: – MOTORISED GYROSCOP AIM Study of Gyroscopic couple on Motorised Gyroscope. INTRODUCTION Gyroscope: It is a body while spinning about an axis is free to rotate in other directions under the action of external forces. Examples: Locomotive, automobile and aeroplane making a turn. In certain cases, the gyroscopic forces are undesirable whereas in other cases the gyroscopic effect may be utilized in developing desirable torque. See fig. no. 1 Motorized Gyroscope: The reaction couple exerted by the body on its frame is equal in magnitude to that of C but opposite in direction. DESCRIPTION AND WORKING INSTRUCTIONS The motor is coupled to the disc rotor, which is balanced. The disc shaft rotates about XX axis in two ball bearings housed in the frame No.1. This frame can swing about YY axis in bearing provided in the yoke type frame No.2. In steady position, Frame No.1 is balanced by providing a weight pan on the opposite side of the motor. The yoke frame is free to rotate about vertical axis ZZ. Thus, freedom of rotation about three perpendicular axes is given to the rotor. SPECIFICATION ο· Toggle Switch : 15 amp, DPST, Qty:1 No. ο· Diode : 4 Amp, Bridge type, Qty: 1 No. ο· Universal Motor 6500 rpm - AC/DC, : 1/6 H.P. single phase, Marwadi Education Foundation Group of Institutions Department of Mechanical Engineering Qty:1 No. ο· Speed Indicator :Type – RC2100, Range – 4.00 to 9999rpm, Relay rating –5A @ 230VAC/24VDC, Sensor supply – 12VDC, 30mA, Accuracy – 0.05%, Qty: 1 No. ο· : M – 12, PNP/NO, Proximity Switch Max load – 300mA, 8mm, 10 - 30VDC, Qty: 1 No. ο· Dimmer : 2Amp – open type, 230VAC : 4 Amp, 5mmο¦,20mmL, Qty: 1 No. ο· Glass Fuse Qty:1No. Marwadi Education Foundation Group of Institutions Department of Mechanical Engineering THEORY A) Axis of Spin : If a body is revolving about an axis, the latter is known as axis of spin, where OC is the axis of spin) B) Precession : Precession means the rotation of axis of spin about the axis OY which is perpendicular to the both axis of spin OX and that of couple OZ. C) Axis of Precision : The third axis OZ is perpendicular to both the axis of spin OX and that of precession OY is known as axis of precession. D) Gyroscopic Effect : To a body revolving (or spinning) about an axis say OX (refer Fig. 1) if a couple represented by a vector OZ perpendicular to OX is applied, then the body tries to process about an axis OY which is perpendicular both to OX and OZ. Thus, the plane of spin, plane of precession and plane of gyroscopic couple are mutually perpendicular. The above combined effect is known as precessional or gyroscopic effect. GYROSCOPIC COUPLE OF A PLANE DISC: Let a disc of weight 'W' having of inertia I be spinning at an angular velocity about axis OX in anticlockwise direction viewing from front. (Refer Fig. 2) Therefore the angular momentum of disc is Iw. Applying right hand, screw rule, the sense of vector representing the angular momentum of disc which is also a vector quantity will be in the direction OX as shown. A couple, whose axis is OZ perpendicular to OX and is in the plane perpendicular to OZ, is now applied to process the axis OX. Let axis OX turn through a small angular displacement from OX to OX' in time ο€t. The couple applied produces a change in the direction of angular velocity, and the magnitude remaining constant. This change is due to the velocity of precession. Therefore OX' represents the angular momentum after time ο€t. Marwadi Education Foundation Group of Institutions Department of Mechanical Engineering Change of angular momentum = OX' - OX = XX OR Angular Displacement Rate of change of angular momentum = ---------------------------------Time ο€t. OX x ο€ο± -------------------- XX' -------------- = ο€t. As XX’ = OX x ο€ο± in direction of XX'. Now, as rate of change of angular momentum = Couple applied = C = T We get, OX x ο€ο± T = -----------------ο€t. But OX = I.ο· Where, I = Moment of Inertia of disc. ω = Angular Velocity of disc. And in the limit when ο± is very small. We have ο± dο± -------- = ----------t dt And, dο± ------- = ο·p = Angular velocity of precession of yoke @ vertical axis. dt Thus, we get, T = I x ο·xο·p The direction of the couple applied on the body is clockwise when looking in direction OZ and in the limit this is perpendicular to the axis of ο· and of ο·p. RULE No.1: "The spinning body exerts a torque or couple in such a direction which tends to make the axis of spin coincides with that of the precession". RULE NO. 2: '' The spinning body processes in such a way as to make the axis of spin Coincide with that of the couple applied, through 900 turn axis." Marwadi Education Foundation Group of Institutions Department of Mechanical Engineering EXPERIMENTAL DETAILS: – MOTORISED GYROSCOP AIM Evaluate the Gyroscopic couple on Motorised Gyroscope. EXPERIMENT: ο· To observe gyroscopic behaviouer ο· To measure torque applied & gyro-torque ο· To apply torque and measure developed precession. PROCEDURE To study the rule of gyroscopic behavior following procedure may be adopted. ο· Balance the rotor position on the horizontal frame. ο· Start the motor by increasing the voltage with the autotransformer and wait till the disc attains constant speed. ο· Put weight (1 Kg., 2 Kg. or 1/2 Kg.) in the weight pan, and start the stop watch to note the time in seconds required for precession, through 300, 600, 900 etc. ο· The vertical yoke processes about OZ axis as per the rule No. 2 ο· Speed may be measured by the tachometer provided on control panel. ο· Enter the observations in the table. OBSERVATION ο· ο· ο· Weight of Disc (W) Diameter of Disc Distance betn center of the disc And center of the weight pan of Weight = 6.216 kg. = 0.300 m = 0.150 m Marwadi Education Foundation Group of Institutions Department of Mechanical Engineering OBSERVATION TABLE Speed of Disc N = 2000 RPM Sr. No. Weight on Pan Kg - w Angle of Rotation ο± Time in t sec. T CALCULATION A) The Gyroscopic Torque Relation: T = I x ο·xο·p (Kg.m) 1) I = Moment of Inertia of disc in Kg.m.sec2 I = W/g x r2/2 Where, W = weight of disc in Kg r = radius of Disc in meter 2) ο· = Angular Velocity In rad / Sec 2ο°N ο· = -----------60 Where, N =Speed of Disc in RPM 3) ο·P = Angular velocity of precession of yoke @ vertical in rad / sec dο± ο·P = -------dt Where, dο± = Angle of Precession = (ο± x ο°) /180 rad dt = Time required for this precession in sec N = Motor speed in RPM Marwadi Education Foundation Group of Institutions Department of Mechanical Engineering 4) Ttheo. = Theroetical torque relation in Kg.m T = W x L. Where, W = Weight on pan in Kg L = Distance betn center of the disc And center of the weight pan of Weight Precession is to be calculated for short duration of time, as the balance of rotation of disc about the horizontal axis YY due to application to torque, because of which p goes on reducing gradually.
