ABHISHEK GOYAL

12-MES-05

MACHINE DYNAMICS FILE

INDEX

Sno. Topic Date Remarks1 To study different types of cam and

followers.

2 To study the profile and stroke of a cam and follower mechanism.

3 To study the phenomenon of jump in a cam and follower mechanism.

4 To study the performance characteristics of a simple Watt governor.

5 To study the performance characteristics of a Porter governor.

6 To study the performance characteristics of a Proell governor.

7 To study the performance characteristics of a Hartnell governor.

8 To study the Gyroscopic effects on a disc and verification of relation, C = I.ω.ωp.

9 To study the dynamic balancing machines for rotor.

EXPERIMENT 1

OBJECTIVE: To study different types of cam and followers.

THEORY:

A cam is a rotating or sliding piece in a mechanical linkage used especially in transforming rotary motion into linear motion or vice versa. It is often a part of a rotating wheel or shaft that strikes a lever at one or more points on its circular path. The cam can be a simple tooth, as is used to deliver pulses of power to a steam hammer, for example, or an eccentric disc or other shape that produces a smooth reciprocating (back and forth) motion in the follower, which is a lever making contact with the cam.

Types of cams-

Cams can be classified according to

Shape Follower movement Manner of constraint of the follower

According to shape

1. Wedge and flat cams: Here the cam is in the form of a wedge and has translational motion. The follower can either translate or oscillate. A spring is generally used to maintain the contact between the cam and the follower.

Instead of using a wedge, a flat plate with a groove can also be used. In the groove the follower is held. Thus a positive drive is achieved without the use of a spring.

2. Radial or disc cams: In the radial cams, the working surface of the cam is designed such that follower moves in a plane perpendicular to the axis of the cam performing a reciprocating or oscillating motion.

3. Spiral cams: A spiral cam is a face cam in which a groove is cut in the form of a spiral. The spiral groove consists of teeth which mesh with a pin gear follower. The velocity of the follower is proportional to the radial distance of the groove from the axis of the cam.

The use of such cam is limited as the can has to reverse the direction to reset the position of the follower. It finds its use in computers.

4. Cylindrical cams: In this type of cam, the follower either reciprocates or oscillates in a plane parallel to the axis of the cam. In this a circumferential contour is cut in the surface of the cylinder which rotates about its own axis. The follower rides in the groove of the cylinder surface and it reciprocates in the plane parallel to the axis of rotation.

5. Conjugate cams: A conjugate cam is a double-disc cam in which the two discs are keyed together and are in contact touch with the two rollers of a follower. Thus the follower has a positive contact. Such a type of cam is preferred when the requirements are low wear, low noise, better control of the follower, high speed, high dynamic loads etc.

6. Globoidal cams: A globoidal cam can have two types of surfaces, convex or concave. A circumferential contour is cut on the surface of rotation of the cam to impart motion to the follower which has an oscillatory motion. The application of such cams is limited to moderate speeds and where the angle of oscillation of the follower is large.

7. Spherical cams: In a spherical cam, the follower oscillates about an axis perpendicular to the axis of rotation of the cam. Note that in a disc cam, the follower oscillates about an axis parallel to the axis of rotation of the cam.

A spherical cam is in the form of a spherical surface which transmits motion to the follower.

According to follower movement

The motion of the followers is distinguished from each other by the dwells they have. A dwell is the zero displacement or the absence of motion of the follower during the motion of the cam.

Cams are classified according to the motions of the follower in the following ways:

1. Rise-Return-Rise: In this, there is alternate rise and return of the follower with no periods of dwells. Its use is very limited in the industry. The follower has a linear or an angular displacement.

2. Dwell-Rise-Return-Dwell: In such a type of cam, there is rise and return of the follower after a dwell. This type is used more frequently than the R-R-R type of cam.

3. Dwell-Rise-Dwell-Return-Dwell: It is the most widely used type of cam. The dwelling of the cam is followed by rise and dwell and subsequently by return and dwell. In case, the return of the follower is by a fall, the motion may be known as dwell-rise-dwell.

According to manner of constraint of the follower

A pre loaded compression spring is used for the purpose of keeping the contact between the cam and the follower

1. Pre loaded spring cam: A pre-loaded compression spring is used for the purpose of keeping the contact between the cam and the follower.

2. Positive drive cam: In this type, contact touch between the cam and follower is maintained by a roller follower operating in the groove of a cam. The follower cannot go out of this groove under the normal working operations. A constrained or positive is also obtained by the use of a conjugate cam.

3. Gravity cam: If the rise of the cam is achieved by the rising surface of the cam and the return by the force of gravity or due to the weight of the cam, the cam is known as gravity cam.

Classification of Cam Followers:

According to the Surface Contact:

1. Knife edged followers: These are simple in construction. The contacting end of the follower with the cam has a sharp knife edged hence it is called so. The motion between the cam and follower is sliding. It is not used in practice because small area of contact surface results in high rate of wear at the edges due to which the transmission of motion may not be accurate as desired.

2. Roller follower: The contact end of the follower is roller and the rolling motion exists between the cam and follower. Compared to knife edge followers, the rate of wear and tear is less due to less friction. These are used in aircraft engines and oil engines.

3. Flat face or mushroom follower: These are used where space is limited to operate valve of automobile engine. The contact surface is perfectly flat. The side thrust between guide and follower is much reduced. It is called a mushroom follower when the flat face is circular.

4. Spherical follower: When the contact end of the follower is of spherical shape.

According to the Path of the Motion of the Follower:

1. Radial follower: In a radial follower, the follower translates along an axis passing through the center of the cam.

2. Offset follower: The axis movement of the follower is away from the axis of the centre of rotation of the cam.

DISCUSSION:

A cam is a mechanical member used to impart desired motion to follower by direct contact. The cam may be rotating or reciprocating whereas the follower may be rotating, oscillating or reciprocating. Cams are widely used in machines, Internal Combustion engines, machine tools, printing control mechanisms, etc.

EXPERIMENT 2

OBJECTIVE: To study the profile and stroke of a cam and follower mechanism.

THEORY:

Motion of the follower

Though the follower can be made to have any desired motion, knowledge of the existing motion programs saves time and labor while designing the cam. The generally known types of motions are:

1. Constant Velocity motion2. Simple Harmonic motion3. Constant Acceleration motion4. Cycloidal motion

OBSERVATION TABLE:

Sno. Angle (θ) Lift (mm)

1 00 02 200 03 400 04 600 05 800 3.56 1000 5.07 1200 10.08 1400 20.09 1600 30.010 1800 37.011 2000 30.012 2200 20.013 2400 10.014 2600 5015 2800 3.516 3000 0

17 3200 018 3400 019 3600 0

RESULT:

Angle of ascent = 1200

Angle of descent = 1200

Angle of dwell = 1200

Length of rise = 37 mm

DISCUSSION:

From the performed experiments, it can be concluded that as a cam rotates about its axis, it imparts a specific motion to the follower which is repeated with each revolution of the cam. During rotation of the cam through one revolution, the follower is made to execute a series of events such as rises, dwells and return.

EXPERIMENT 3

OBJECT: To study the phenomenon of jump in a cam and follower mechanism.

APPARATUS USED:

Cam and follower mechanism setup Stethoscope Tachometer (Contact Type)

THEORY:

Jump phenomenon:

The jump phenomenon occurs in case of cam and follower operating under the action of compression spring load. This is a transient condition that occurs only with high speed, highly flexible cam follower system. With jump the cam and follower separate swing to successively unbalanced force exceeding the spring force acting during the period of negative acceleration. This is indelible since the fundamental function of cam-follower system the constraint and control of follower motion are not maintained. Also it relates to the short life of the cam flank surface, high noise, vibrations and poor action. To observe the phenomenon of jump, use of stethoscope is necessary. When jump occurs the following points on the cam surface give a good thumping sound.

OBSERVATION TABLE:

Sno. Weight RPM Spring Length (cm)

1 0 498 3.02 0.5 410 3.03 1.0 400 3.04 1.5 380 3.05 2.0 347 3.06 2.5 439 3.57 0 472 3.08 0 486 2.79 0 515 2.5

10 0 640 2.4

RESULT:

As can be observed from the graphs; the RPM of the cam decreases with the increase in weight on the follower for a constant spring length. Also, the RPM of the cam decreases with the increase in spring length without any load on the follower.

DISCUSSION:

Jump phenomenon is an important phenomenon used extensively while designing a cam follower system for a specific purpose. This helps in rating the RPM of the machines to avoid jump and ultimately failure of the cam follower assembly in both imparting the required motion and catastrophic failure.

EXPERIMENT 4

OBJECT:

To study the performance characteristics of a simple Watt governor and plot

1. Force vs radius of rotation2. Speed vs sleeve displacement

THEORY:

In simple centrifugal or Watt governor, a pair of ball (masses) is attached to the spindle with the help of links. The upper links are pinned at point O. The lower link fixed to the sleeve free to move on the vertical spindle.

As the spindle rotates, the balls take up a position depending upon the speed of the spindle. If it lowers, they move near the axis due to reduction in the centrifugal force on the ball and the ability of the sleeve to slide on the spindle. The movement of the sleeve is further taken to the throttle of the engine, by means of a suitable linkage to decrease or increase the fuel supply.

OBSERVATIONS:

ro = 140 mm

ho = 85 mm

Length of arm, l = 125 mm

Weight of each ball, W = 160 gm = 0.16 Kg

OBSERVATION TABLE:

Sno. N (RPM) Sleeve Disp (x)

h = ho – x/2

α = cos-

1(h/l)r=

50+l.sin(α)Fc (N)

1 211.2 6.8 5.1 65.92 16.41 12.842 236 10.0 3.5 73.74 17.00 16.613 276 12.3 2.35 79.16 17.28 23.104 221 7.9 4.55 68.65 16.64 14.265 244 9.8 3.6 73.26 19.95 17.736 264 11.3 2.85 76.82 17.17 21.00

RESULT:

From force vs radius of rotation graph, we can conclude that for a very small change in radius of rotation there is a huge change in force. From speed vs sleeve displacement graph we can conclude that there is a little increase in sleeve displacement with increase in speed.

DISCUSSION:

With slight change i.e. increase in RPM, centrifugal force on the masses (balls) increase, increasing the radius of rotation resulting in increased sleeve displacement. As the speed decreases, the radius of rotation decreases slightly resulting in lowering of the sleeve. This phenomenon is used to regulate the fuel supply into an engine, which ultimately regulates the running speed of the engine.

EXPERIMENT 5

OBJECT:

To study the performance characteristics of a simple porter governor and plot

1. Force vs Radius of rotation2. Speed vs Sleeve displacement

THEORY:

If the sleeve of a Watt governor is loaded with a heavy mass, it becomes a porter governor. The force of friction always acts in a direction opposite to that of the motion. Thus when the sleeve moves up, the force of friction acts in the downward direction and the downward force acting on the sleeve is Mg + f. Similarly, when the sleeve moves down, the force on the sleeve will me (Mg – f).

If the speed of the engine increases, the balls would tend to move away from the axis, but now as the friction has to act in the downward direction, the resistance to the motion would be Mg + f. In the same way, when the sleeve has moved up and the speed decreases, the resistance to the sleeve movement would be Mg – f.

OBSERVATIONS:

ro = 140 mm

ho = 85 mm

L = 125 mm

W = 0.16 Kg

OBSERVATION TABLE:

Sno. M (Kg)

N ( RPM)

Sleeve Disp (mm)

h=ho – x/2

α=cos-1(h/l)

r=50+l.sin(α)

1 1 180.5 34 68 57.04 154.882 1 208.1 80 45 68.89 166.613 1 229 89 40.5 71.09 168.254 2 212.8 50 60 61.31 159.655 2 230.3 75 47.5 67.66 165.626 2 206.5 38 66 58.13 156.167 3 229.5 40 65 58.67 156.778 3 241.8 43 63.5 59.47 157.679 3 292 58 56 63.38 161.75

RESULT:

From force vs radius of rotation graph, we can conclude that for a very small change in radius of rotation there is a huge change in force. From speed vs sleeve displacement graph we can conclude that there is a little increase in sleeve displacement with increase in speed.

EXPERIMENT 6

OBJECT:

To study the performance characteristics of a simple Proell governor and plot

1. Force vs Radius of rotation2. Speed vs Sleeve displacement

THEORY:

If the two balls (masses) of a porter governor are fixed on the upward extensions of the lower links which are in the form of bent links, it becomes a Proell governor.

As the spindle rotates with the variation of speed, the ball takes up a position depending upon the speed of the spindle. If the speed is low i.e. load is very high, then the arms move near the axis due to reduction in centrifugal force on the ball and the ability of sleeve to slide on the spindle. The movement of sleeve is further taken to the throttle of the engine, by means of a suitable linkage to decrease or increase the fuel supply.

OBSERVATIONS:

ro = 140 mm

x = 15 mm

ho = 95 mm

L = 125 mm

W = 0.16 Kg

OBSERVATION TABLE:

Sno. M (Kg)

N ( RPM)

Sleeve Disp (mm)

h=ho – x/2

F (N) α r (mm) e (mm)

1 1 202 15 87.5 162.39 45.5 238.26 162.52 1 224 34 78 172.48 51.3 347.68 1533 1 260 54 68 184.54 57.0 154.88 143

4 2 247 32 79 235.06 50.08 146.8 1545 2 297 78 56 276.33 63.3 161.75 1326 2 338 94 48 294.3 67.4 165.42 123

7 3 263 36 77 302.69 51.9 148.47 1528 3 310 63 60.5 339.55 61 159.38 135.59 3 266 88 51 369.15 65.9 164.12 126

RESULT:

The graph between the force and radius of rotation is a straight line, representing a linear relation between the force and radius of rotation. Also, the graph between speed and sleeve displacement is observed to be curved, representing a parabolic relation between the speed and the sleeve displacement.

DISCUSSION:

With slight change i.e. increase in RPM, centrifugal force on the masses (balls) increase, increasing the radius of rotation resulting in increased sleeve displacement. As the speed decreases, the radius of rotation decreases slightly resulting in lowering of the sleeve. This phenomenon is used to regulate the fuel supply into an engine, which ultimately regulates the running speed of the engine.

EXPERIMENT 7

OBJECT:

To study the performance characteristics of a Hartnell governor and plot

1. Force vs Radius of rotation2. Speed vs Sleeve displacement

THEORY:

In this type of governor, the balls are controlled by a spring. Initially, the spring is fitted in compression so that a force is applied to the sleeve. Two bell crank levers, each carrying a mass at one end and/or roller at the other, are pivoted to a pair of arms which rotate with the spindle. The rollers fit into a groove in the spindle.

As the speed increases and the balls move away from the spindle axis, the bell crank levers moves on the pivot and lifts the sleeve against the spring force. If the speed decreases, the sleeve moves downwards. The movement of the sleeve is communicated to the throttle of the engine. The spring force can be adjusted with the help of a screw cap.

OBSERVATIONS:

Length, a = 78 mm (Ball Arm)

Length, b = 125 mm (Sleeve Arm)

Mass of each ball = 160 gm

Initial radius of rotation, ro = 155 mm

Weight of sleeve = 1.53 Kg

OBSERVATION TABLE:

Sno. N ( RPM) Sleeve Disp (mm)

r = ro + x(a/b) F (N)

1 454 20 167.48 60.542 330 5 158.12 30.213 362 9 160.62 36.934 395 15 164.36 44.995 506 23 169.35 76.08

CALCULATION:

r = ro + x(a/b)

Taking 1st observation

r = 155 + 20 x (78/125)

= 167.48 mm

F = mrw2 = 0.16 x 167.4 x 10-3 x ( 2 x π x 454/60 )2

= 60.54 N

RESULT:

The graph between the sleeve displacement and speed and between the force and radius of rotation came out to be straight line, representing a linear variation of speed and sleeve displacement with radius of rotation.

DISCUSSION:

With slight change i.e. increase in RPM, centrifugal force on the masses (balls) increase, increasing the radius of rotation resulting in increased sleeve displacement. As the speed decreases, the radius of rotation decreases slightly resulting in lowering of the sleeve. This phenomenon is used to regulate the fuel supply into an engine, which ultimately regulates the running speed of the engine.

EXPERIMENT 8

OBJECT:

To study the Gyroscopic effects on a disc and verification of relation, C = I.ω.ωp.

EQUIPMENT USED:

Tachometer (Contact Type) Gyroscope Stopwatch Weights

THEORY:

A gyroscope is a device for measuring or maintaining orientation, based on the principle of preserving angular momentum of the moving body. Mechanical gyroscopes typically comprise a spinning wheel or disc in which the axle is free to assume any orientation. Although the orientation of the spin axis changes in response to an external torque, the amount of change and the direction of the change is less and in a different direction than it would be if the disk were not spinning. When mounted in a gimbal (which minimizes external torque), the orientation of the spin axis remains nearly fixed, regardless of the mounting platform's motion.

Description and working instructions:

The motor is coupled to the disc rotor, which is statistically and dynamically balanced. This disc shaft rotates about x-x axis in two ball bearings housed in the frame. This frame can swing about y-y axis in bearings provided in the yoke type frame. The yoke frame is free to rotate about vertical axis z-z. The freedom of rotation about the three perpendicular axes is given to the rotor.

OBSERVATION TABLE:

Sno. N (RPM)

W (Kg) Time (sec) θp

1 6000 1 11.31 902 6000 2 5.39 903 6000 3 4.76 904 6000 4 2.85 90

CALCULATIONS:

Length, l = 197 mm

M = 6.5 Kg

R = 150 mm

Moment of inertia of flywheel = MD2/8

= 0.073 Kg m2

T = F.r = c = I.ω.ωpTaking 1st observation

T = 12.31 sec

mw = 1 Kg = ωp = dp/dtw = (2.π.N)/60 = 628.318 m/s

c = I.ω.ωp

= 0.073 x 628.32 x 0.08

= 1.92 N-m

CONCLUSION:

It is thus concluded that the equation T = I.ω.ωp holds valid for gyroscopic action. The slight error might be due to parallax and gyroscopic speed.

EXPERIMENT 9

OBJECT:

To study the dynamic balancing machines for rotor.

THEORY:

A balancing machine is used to measure an unbalancing in a part if any, both static or dynamic and indicate its magnitude and location. This out of balance may exist in the material density or in accuracies in asting or machining.

Since the centrifugal force and couple may vary as the square of the speed, even the small errors may lead to serious troubles at high speeds of rotation. Thus effort is used to measure this unknown unbalance so that suitable corrections can be made to the part to reduce the final errors.

There are two types of balancing machines, hard bearing and soft bearing. In hard bering machines, balancing is done at a frequency lower than the resonance frequency of the rotating part. In the soft bearing machines, balancing is done at a frequency higher than that of the resonance frequency.

Static Balancing: Static balance occurs when the centre of gravity of an object is on the axis of rotation. The object can therefore remain stationary, with the axis horizontal, without the application of any braking force. It has no tendency to rotate due to the force of gravity.

Dynamic Balancing: Rotating shaft unbalanced by two identical attached weights, which causes a counterclockwise centrifugal couple Cd that must be resisted by a clockwise couple Fℓ = Cd exerted by the bearings. The figure is drawn from the viewpoint of a frame rotating with the shaft, hence the centrifugal forces.

A rotating system of mass is in dynamic balance when the rotation does not produce any resultant centrifugal force or couple. The system rotates without requiring the application of any external force or couple, other than that required to support its weight. If a system is initially unbalanced, to avoid the stress upon the bearings caused by the centrifugal couple, counterbalancing weights must be added. This is commonly done, for example: in the case of an automobile tire, where the imbalance is due to imperfections of manufacture that make the tire composition inhomogeneous

Unbalanced Systems: When an unbalanced system is rotating, periodic linear and/or torsional forces are generated which are perpendicular to the axis of rotation. The periodic nature of these forces is commonly experienced as vibration. These off-axis vibration forces may exceed the design limits of individual machine elements, reducing the service life of these parts. For instance, a bearing may be subjected to perpendicular torsion forces that would not occur in a nominally balanced system, or the instantaneous linear forces may exceed the limits of the bearing. Such excessive forces will cause failure in bearings in short time periods. Shafts with unbalanced masses can be bent by the forces and experience fatigue failure.

Under conditions where rotating speed is very high even though the mass is low, as in gas turbines or jet engines, or under conditions where rotating speed is low but the mass is high, as in ship propellers, balance of the rotating system should be highly considered, because it may generate large vibrations and cause failure of the whole system.

CONSTRUCTION:

For dynamic balancing of a rotor, two balancing or counter masses are used in any two conventional planes. Balancing is achieved by addition and removal of masses on these two planes, whichever is convinient.

Pivoted Cradle Balancing Machine

In this type of machine, thr rotor to be balanced is mounted on half bearings in a rigid carriage and is rotated by a drive motor through a universal joint.

Field Balancing

It is essentially, a method and not the machine used to balance heavy machines like turbines, generators, where it is not possible to balance the rotors by mounting.

OBSERVATION TABLE:

Sno Weight (gms) No. of balls

1 226 1182 260 983 264 1164 270 120

WORKING:

With the rotating blades resting on the bearing a vibration sensor is attached to the rotors. In the most soften bearing machines, a velocity sensor is used. This sensor works by moving a magnet voltage proportional to the velocity of vibrations.

Accelerometer, which measures accelerations of the vibrations, can also be used. A photocell sometimes called a phaser is a proximity sensor or encoder used to determine the rotational speed as well as the relative phase of the rotating part. This phase information is then used to filter the vibrations to determine the amount of movement or force in one rotation of the rotor.

Calibration is performed by adding a known weight at a known angle. In a soft bearing machine, the trial weights must be added in correction planes along the rotational axis.