Best Mechanical engineering tutorials MECHANICS OF MACHINES ~ Mech Universe

MECHANICS OF MACHINES

Plane Motion:

When the motion may be confined to one plane then it is called as plane motion. There are two types

rectilinear motion - In rectilinear the motion is along a straight path.
curvilinear motion - It is in circular path.

Simple Harmonic Motion ( SHM ):

For a body to execute SHM, it should satisfy the following two conditions.

Its acceleration is always directed towards the center called as the mean position.
The acceleration is proportional to the distance from that point.

            The following are the basic concepts to be worth noting.

Amplitude: Maximum displacement of a body from its mean position.
Time Period: Is the time taken for the complete revolution. Tp = 2
Frequency: Number of cycles per second.

Center of Percussion:

Also called as the center of oscillation. It is the point at which a blow may be struck on a suspended body so that the reaction at the support is zero.

Simple Mechanisms:

Types of Links: There are three types of links. They are

- Rigid link
- Flexible link and
- Fluid link.

Structure:

            It is an assemblage of a number of members having no relative motion between them and are meant for carrying loads. E.g.. Bridge, Truss and Machine Frames.

Difference Between a Machine and Structure:

* In machines, the parts move relative to one another, but in structure, it is not so.
* Machine transforms energy to useful work, but in structure there is no such things.
* Links in machines transmit power and motion. But links of structure transmit force.

Types of Motion

1. Completely Constrained Motion: In this the motion is limited to a definite direction, irrespective of direction of force. E.g.. Piston and cylinder
2. Incompletely Constrained Motion: Here the motion between a pair takes place in more than one direction.
3. Successfully Constrained Motion: When the motion between the elements is such that the completed constrained motion is not completed by itself, but a external source. E.g.: Shaft in a foot bearing.

Kinematics Pair:

Two elements in contact in a machine is called a pair. If the relative motion between them is completely constrained, then it is called kinematic pair.

Classification of Kinematic Pairs:

a. Sliding Pair :- Piston and cylinder ( Example of CCM )
b. Turning Pair :- Two elements of a pair are such that one element turns about the fixed axis of another element.
c. Rolling Pair :- One element rolls over another fixed element. E.g.. Roller and Ball bearing.
d. Screw Pair :- One element can turn about the other by means of screw threads E.g.. Bold and nut.
e. Spherical Pair :- One element is spherical in shape, turns or swivels about another fixed element. E.g.. Car mirror attachment.

Lower Pair:- When two elements of a pair have surface contact during relative motion, then it is called as lower pair. E.g.. Sliding, shaft in bearings, turning and Screw pairs.

Higher Pair:- When two elements in the pair have line or point contact when relative motion takes place and the relative motion between them is partly turning and sliding then it is a higher pair.

E.g..     - Belt and rope drives.
            - Cam and
            - Ball and roller Bearings.

Kinematic Chain: When the kinematic pairs are coupled in such a way that the last link is joined to the first link to transmit definite motion. It is a combination of kinematic pairs, joined in such a way that each link forms a part of the pair and the relative motion between the links is in CCM or SCM.

Mechanism:

            When one link in a kinematic pair is fixed then the chain is called a mechanism. It is used for transmitting or transforming motion. A simple mechanism contains around four links and a complex mechanism contains more than 4 links.

Friction:

Laws of Dynamic Friction:

Force of friction always acts opposite to direction of motion.
For moderate speed, force of friction is constant but decreases slightly at higher speeds.

Laws of Fluid Friction:

Friction force reduces with increase in temperature.
The force of friction is different for different lubrication substance.

Screw friction:

Threads are of two types. They are V-Threads and Square threads. V threads are stronger and offer more frictional resistance to motion. V-Threads are used in nuts and bolts. Square threads are used in Screw jacks.

Simple Pendulum:

In its simples form this type of pendulum has a heavy bob, suspended at the end of a light inextensible, flexible string and the other end of the string is rigidly fixed to wall. 'm' is the mass of the bob and 'l' is the length of string. Following laws of simple pendulum are important.

Law of isochronism: It states that the time period (t) of simple pendulum does not depend on its amplitude of vibrations, and remain the same provided the angular acceleration does not exceed 4.
Law of mass: States that the time period of a simple pendulum does not depend upon the mass of the body suspended at the free end of the string.
Law of length: states that the time period of a simple pendulum is proportional to Ö l, where l is the length of the string.
Law of gravity: states that the time period of simple pendulum is inversely proportional to Ö g.

Hence the time period t = 2 pÖ l / g

Belt Drives:

Belts are used to transmit power from one shaft to another by means of a pulley. When the driver rotates, it carries the belt due to grip between its surface and the belt. The belt in turn carries, the driven pulley which starts rotating. The grip between the pulley and the belt is obtained by friction. This friction grip if required is increased by tightening the belt. The amount of power transmitted depends upon

Tension under the belt.
Velocity of belt. and
Arc of contact.

Leather, Rubber, cotton and Balata are the materials used for belt. Flat belt, V-Belt and round belt are the different types of belt. The following are the common terms used in belts.

Slip: This is caused because of less friction. The effect is that, it educes the overall velocity ratio.

S₁ - % Slip in driver belt.
S₂ - % Slip in driven belt.

The speed ratio is given by

N₂ / N₁ = ( d₁+ t ) / ( d₂ + t ) x ( 1 - S / 100 )

Creep: When the belt passes from slack side to the tight side, a certain portion of belt extends and contracts again when moving from tight to slack side. Because of this, there is a relative motion between belt and pulley called creep.

V- Belts:

These belts are used when two pulleys are nearby each other. The included angle is usually 30^o -40^o. In order to have good grip the V-Belt is in contact with side faces of the groove.

Chain Drives:

            The advantage of chain drive are that it prevents slipping. Steel chains are used. The chains are made of rigid links, which are hinged together. They wrap around the driving and driven wheels. The wheels are also called sprocket and resemble spur gears.

Pitch of Chain: It is the distance between the hinge center of one link and the hinge center of the adjacent link.

Gears:

Following are the different types of gears.

Parallel Gears:  The shafts are parallel. Spur gears are where the teeth is parallel to axis of wheel. But in helical gears the teeth are inclined at an angle to the axis. A double helical gear is called as herringbone gears.

Non Parallel and Intersecting Gears: Bevel and Helical bevel gears are the examples.

Non Parallel and Non Intersecting Gears:  Spiral Gearing.

Terms Used in Gears:

S. No	Terms	Definition
1	Pitch Circle	A imaginary circle which by pure rolling action would give the same motion as the actual gear.
2	Pitch Circle Diameter	The diameter of Pitch circle. Gears are specified by this PCD.
3	Addendum	The radial distance between the PCD and top of tooth. Addendum circle is drawn through the top of teeth and concentric to PC.
4	Deddendum	The radial distance been the PC and bottom of teeth.
5	Circular Pitch	The distance measured from the circumference of the pitch circle from a point in one tooth, to the corresponding point in next tooth.
6	Module	it is the ratio of PCD to the number of teeth.
7	Diametrical pitch	Inverse of Module.
8	Total depth	Addendum + Deddendum
9	Tooth Thickness	Width of the tooth measured along pitch circle.
10	Face of Tooth	Surface of gear above the pitch surface.
11	Flank of Tooth	Surface of gear above the pitch surface.

System of Gear Teeth:

14.5^o Composite System.
14.5^o Full depth involute system.
20^o Full depth involute system.
20^o Stub involute system.

Gear ratio = T / t = Teeth on Wheel / Teeth on pinion.

Gear Trains:
Two or more gears are made to mesh with each other to transmit power from one shaft to another shaft. Such a combination is called as gear train.

Simple gear train
compound gear train
Reverted gear train
Epicyclic gear train.

Flywheel:

It acts as a reservoir which stores energy when the energy supply is more than requirement and releases it during the period when required energy is less than supply.

Coefficient of Fluctuation of Speed in Flywheel :

The difference between Max. and Min speeds is called as Maximum fluctuation of speed. The ratio between max. fluctuation of speed and mean speed is called as Coefficient of Fluctuation of Speed.

            Cs = 2 ( N₂ - N₁ ) / ( N₂ + N₁ )

            1 / Cs = m =Coefficient of steadiness.

            Energy stored in a fly wheel = mk²w²Cs

Governors :

The function is to regulate the mean speed of the engine with changes in load. The governor automatically controls the supply of working fluid to the engine with the varying load conditions and keeps the mean speed with the certain limits. Governors are broadly classified into Centrifugal governors and Inertia governors.

Centrifugal governors :

The main principle of working of the centrifugal governor is based upon the balancing of centrifugal force on the rotating balls by an equal and opposite radial force, known as the controlling force.

Pendulum Type - Watt governor

Load type

Dead weight governors - Proel and portel governors.

Spring controlled governors - Hartnell, hartung governors, Wilson-hartnell and Pickering governors.

Inertial governors :

They operate on different principle .Governor balls are arranged that the inertia forces caused by an angular acceleration & retardation of the governor shaft tend to alter their position. The obvious advantage of this type of governor is quick response to load variation .This advantage is offset however by the practical difficulty of arranging for complete balance of the revolving parts of the governor.

Equilibrium speed: Is the speed at which the governor balls are at complete equilibrium and the sleeve does not tend to move up or down.

Sensitiveness: If there is more displacement in sleeve for the same speed then the governor is said to be sensitive. It is equal to

2 ( N₂ - N₁ ) / ( N₂ + N₁ )

Hunting: In this the governor switches between the maximum and minimum position.

Lubrication :

The different types of lubrication between two surfaces having relative motion can be classified as

Fluid film lubrication
Boundary lubrication
Extreme boundary lubrication
Surface contact of the sliding members

Fluid film lubrication:

In this the moving or sliding surfaces are separated from each other by a thick film of fluid which is at least 1000 angstrom thick so that direct surface-to-surface contact and welding of junctions rarely occurs. This is also called as hydrodynamic lubrication.

Fluid friction is considerably less than metallic friction and under such circumstances, the viscosity of the fluid plays an important role in the design parameters of the bearing. It is very clear that the lubricant chosen should have the minimum viscosity under the working conditions. At the same time it should remain in place and separate the surfaces. The co-efficient of friction in such cases should be as low as 0.001 to 0.03. Fluid film lubrication prevails when there is high relative velocity between sliding surfaces. In a journal bearing the lubricating oil covers the irregularities of shaft as well as the bearing surfaces and the metal surfaces do not come into direct contact with each other.

Boundary lubrication:

This is also called as thin film lubrication. when t he relative velocity between the two sliding surfaces is very low, the fluid film will not be able to support the total load and under such circumstances boundary lubrication is done.

The clearance space between the moving surface is lubricated with a lubricating oil., a thin layer of which is adsorbed, on both the metallic surfaces. These layers avoids direct metal-to-metal contact. The value of co-efficient of friction is usually, 0.05 to 0.15.

The friction phenomena in this case is complicated and no exact theory is available for boundary lubricated bearings. However it has been found that certain metals and lubricants with less friction compared to others have the same viscosity improve the performance of such bearings.

Extreme boundary lubrication:

When the moving surfaces are under very high pressure and speed, a high local temperature is attained and under such condition the fluid film is completely broken because of decomposition or vapoursation and there is direct metal to metal contact at that high spots of the sliding materials. High load and speed in turn generates heat with the following mentioned effects.

Welded junction and metal tearing.
Deformation and seizure of surfaces.
Change in physical and chemical properties of metals and lubricants that renders lubricants ineffective.

The mechanism of this type of lubrication is given below. Special additives that are capable of withstanding very high load and temperatures are added to the lubricants. These additives react with metallic surfaces at prevailing high temperatures to form metallic chlorides, sulphides or phosphides. These metallic compound posses high melting points and serve as good lubricant under high temperature and pressure conditions. If by chances, the low shear strength films are broken by the rubbing action of moving parts, they are immediately replenished. Since a chemical reaction takes place in this lubrication, the metal surface under goes certain wear.

The function of lubricant is to reduce the loss of energy, to reduce surface deformation, war and tear, to increase the efficiency of engine, to reduce the frictional heat and thus prevents the expansion of metals, to reduce the maintenance cost of a machine etc.

Application of Liquid Lubricants:

Mechanical devices to supply lubricants are called lubricators. A simple form of lubricator is a container mounted over a bearing or other part and provided with a hole or an adjustable valve through which the lubricant is gravity-fed at the desired rate of flow. Wick-feed oilers are placed under moving parts, and by pressing against them they feed oil by capillary action. Horizontal bearings are frequently oiled by a rotating ring or chain that carries oil from a reservoir in the bearing housing and distributes it along the bearing through grooves or channels. Bath oiling is useful where an oil-tight reservoir can be provided in which the bearing journal may be submerged; the pool of oil helps to carry away heat from contact surfaces. Splash-oiling devices are used where gears, bearings, or other parts contained in housings have moving parts that dip into the lubricant and splash it on the bearings or into distribution channels. Centralized oiling systems usually consist of a reservoir, pump, and tubes through which oil is circulated, while heaters or coolers may be introduced to change the viscosity of the lubricant for various parts of the system. Many oiling operations are automatically synchronized to start and stop with the machinery.

Application of Semisolid and Solid Lubricants:

Grease lubricants are semisolid and have several important advantages. They resist being squeezed out, they are useful under heavy load conditions and in inaccessible parts where the supply of lubricant cannot easily be renewed, and they tend to form a crust that prevents the entry of dirt or grit between contact surfaces. Grease is a mixture of a lubricant and a thickener; often it is made from a mineral oil and a soap. It may be applied in various ways: by packing enclosed parts with it, by pressing it onto moving parts from an adjacent well, by forcing it through grease cups by a spring device, and by pumping it through pressure guns. Solid lubricants are especially useful at high and low temperatures, in high vacuums, and in other applications where oil is not suitable; common solid lubricants are graphite and molybdenum disulfide.

CAM:

Is a rotating machine element which transmits oscillating or reciprocating motion to the follower. They have line contact and constitutes higher pair. According to the type of follower they are classified as