Theory of Machines and Machine Design
Category : Railways
Theory of Machines and Machine Design
THEORY OF MACHINES
It is the branch of Engineering Science, which deals with the study of relative motion between the various parts of machine along with the forces acting on the parts is known as the Theory of Machines (TOM).
Kinematic Link: Each resistant body in a machine which moves relative to another resistant body is called kinematic link or element.
A resistant body is which do not go under deformation while transmitting the force.
Kinematic Pair: If the relative motion between the two elements of a machine in contact with each other is completely or successfully constrained then these elements together is known as kinematic pair.
CONSTRAINED MOTIONS
Constrained motion (or relative motion) can be broadly classified is to three types.
TYPES OF KINEMATIC PAIRS OR CHAINS
Usaually, A kinematic chain has a one degree of freedom. The kinematic chains having number of lower fairs are tour are considered to be the most important kinematic chains in which each pair act as a sliding pair or turning pair.
Some of them are given as:
(a) Four bar chain
(b) Single slider crank chain
(c) Double slider crank chain
The classified of kinematic pairs is listed as below:
(a) Lower Pair: Links in the pair have surface or area contact between them. The surface of one element slides over the surface of the other. For example: a piston along with cylinder.
(b) Higher Pair: In which the links have point or line contact and motions are partly luring and partly sliding.
For example: ball bearings, can and follower.
(a) Self Closed Pair: If the links in the pair have direct mechanical contact, even without the application of external force.
(b) Force Closed Pair: If the links in the pair are kept in contact by the application of external forces.
(a) Sliding Pair: A kinematic pair in which each element has sliding contact with respect to the other element.
(b) Rolling Pair: In a rolling pair, one element undergoes rolling motion with respect to the other.
(c) Turning Pair: In a turning pair, one link undergoes turning motion relative to the other link.
(d) Screw Pair: It consists of links that have both turning and sliding motion relative to each other.
(e) Cylindrical Pair: A kinematic pair in which the links undergo both rotational and translational motion relative to one another.
(f) Spherical Pair: In a spherical pair, a spherical link turns inside a fixed link. It has three degrees of freedom.
DEFINITION OF KINEMATIC CHAIN
Combination of kinematic pairs joined in such a way that the last link is joined to the first link and the relative motion between them is definite. There are two equations to find out. Whether the chain is kinematic or not.
\[l=2p-4\]
where l= number of links
p= number of pairs also
also
\[j=\frac{3}{2}\,\,l-2\]
where
j = number of joints
To determine the nature of chain we use equation
\[j+\frac{h}{2}=\frac{3}{2}l-2\]
where h = No. of higher pairs
If L.H.S > R.H. S. then it is a locked chain
L.H.S. = R.H.S. then it is a kinematic chain
L.H.S. < R.H.S. then it is an unconstrained chain
MECHANISM
A mechanism is obtained by fixing one of the links of a kinematic chain, for example a typewriter. Basically there are two types of a mechanism.
Inversion of a Mechanism
We can obtain different mechanisms by fixing different links in a kinematic chain, this method is known as inversion of a mechanism.
Inversions of mechanisms:
(a) Four bar mechanism
Types: (i) Beam engine
(ii) Locomotive coupling rod
(iii) Watts indicator mechanism
(b) Single slider crank chain
Types: (i) Pendulum pump
(ii) Oscillating cylinder engine
(iii) Rotary internal combustion engine
(iv) Crank and slotted liver quick return mechanism
(v) Whitworth quick return mechanism
(c) Double Slider crank chain
Types:
(i) Elliptical trammel
(ii) Scotch-yoke mechanism
(iii) Old ham's coupling
BELT DRIVE
The transmission of power from one rotating shaft to another lying at a considerable distance, is achieved using belts and ropes. Two parallel shafts may be connected by open belt or by cross belt. In the open belt system, the rotation of both the pulleys is in the same direction. If a crossed belt system is used, the rotation of pulleys will be in the opposite direction.
Types of Belts
There are three types of belts
(a) Flat belts: Cross section of a flat belt is shown in Fig. 14. Flat belts are easier to use and are subjected to minimum bending stress. The load carrying capacity of a flat belt depends on its width.
(b) V-belts: Fig. shows the cross section of the V-belts. V-belts are available in five sections designed A, B, C, D, and E and there are used in order of increasing loads. Section A is used for light loads only and section E is used for heavy duty machines. The angle of V-belt for all sections is about 40°. In order to increase the power output, several V-belts may be operated side by side. In multiple V-belt drive, all the belts should stretch at the same rate so that the load is equally divided between them.
(c) Circular belts: The cross section of a circular belt is shown in Fig. The circular belts are also known as round belts. These are employed when low power is to be transmitted, for example in house hold appliances, table top tools and machinery of the clothing. Round belts are made of leather, canvas and rubber.
GEARS AND GEAR DRIVE
A wheel with teeth on its periphery is known as gear. The gears are used to transmit power from one shaft to another when the shafts are at a small distance apart.
Types of Gears
Commonly used gear are as below:
(a) Spur gear: A cylindrical gear whose tooth traces are straight lines parallel to the gear axis. These are used for transmitting motion between two shafts whose axis are parallel and coplanar.
(b) Helical gear: A cylindrical gear whose tooth traces are straight helices, teeth are inclined at an angle to the gear axis. Double helical gears called herringbone gears. The helical gears are used in automobile gear boxes and in steam and gas turbines for speed reduction. The herringbone gears are used in machinery where large power is transmitted at low speeds.
(c) Bevel gear: The bevel gear wheels conform to the frusta of cones having a common vertex, tooth traces are straight line generators of the cone. Bevel gears are used to connect two shafts whose axis are coplanar but intersecting when the shafts are at right angles and the wheels equal in size, the bevel gears are called mitre gears. When the bevel gears have their teeth inclined to the face of the bevel, they are known as helical bevel gears.
(d) Spiral gear: These are identical to helical gears with the difference that these gears have a point contact rather than a line contact. These gears are used to connect intersecting and coplanar shafts.
(e) Worm gear: The system consists of a worm basically part of a screw. The warm meshes with the teeth on a gear wheel called worm wheel. It is used for connecting two non-parallel, non-intersecting shafts which are usually at right angles.
(f) Rack and pinion: Rack is a straight line spur gear of infinite diameter. It meshes. both internally and externally, with a circular wheel called pinion. Rack and pinion is used to convert linear motion into rotary motion and vice versa.
(g) Internal and external gearing: Two gears on parallel shaft may gear either externally or internally.
Gear Terminology
Terms associated with profile of a gear tooth are illustrated in Fig.
Pitch circle: Essentially an imaginary circle which by pure, rolling action gives the same motion as the actual gear.
Dedendum: Radial distance of a tooth from 103m the pitch circle to the bottom of the tooth.
Addendum circle: Circle drawn through the top of the teeth and is concentric with the pitch circle.
Circular pitch: Distance measured on the circumference of the pitch circle from a point of one tooth to the corresponding point on the next tooth. It is denoted by Pc,.
Total depth: Radial distance between the addendum and the dedendum circles of gear.
Tooth depth = Addendum + dedendum
Path of contact: Path traced by the point of contact of two teeth from the begining to the end of engagement.
Length of the path of contact: Length of the common normal cut-off by the addendum circle & of the wheel and pinion.
Law of gearing: According to the law of gearing, the common normal at the point of contact between a pair of teeth must always pass through the pitch point.
FLYWHEEL
A wheel used in machines to control the speed variations caused by the fluctuation of the engine turning moment during each cycle of operation. These wheels are known as flywheel. It absorbs energy when crank turning moment is greater than resisting moment and gives energy when turning moment is less than resisting moment. The speed of a flywheel increases during it absorbs energy and decreases when it gives up energy. This way flywheel supplies energy from the power source to the machine at a constant rate throughout the operation.
GOVERNORS
The function of a governor is to regulate the mean speed of an engine within mentioned speed limits for varying type of load condition.
Terms Used in Governors
(1) Height of Governor: Vertical distance from the centre of the ball to a point where arms intersect on the spindle axis.
(2) Equilibrium Speed: The speed at which the governor balls, arms etc. are in complete equilibrium and the sleeve does not tend to move upwards or downwards.
(3) Sleeve Lift: Vertical distance with the sleeve travels because of change in equilibrium speed.
(4) Mean Equilibrium Speed: The speed at the mean position of the balls or sleeve.
(5) Sensitiveness: A governor is said to be sensitive, if its change of speed is from no load to full load may be small a fraction of the mean equilibrium speed as possible and the corresponding sleeve lift may be as large as possible.
(6) Stability: If for every speed within the working range there is a configuration of governor balls, then it is said that governor is stable. For a stable governor, the radius of governor balls must increase with increase in the equilibrium speed.
(7) Hunting: Fluctuation in the speed engine continuously above and below the mean speed is called hunting.
(8) Isochronism: A governor is isochronous provided the equilibrium speed is constant for all radii of rotation of the balls upto the working range.
(9) Governor Effort: The average force required on the sleeve to make it rise or come down for a given change in speed.
(10) Power of Governor: The work done at sleeve for a given percentage change in speed. Mathematically
Power = Mean effort \[\times \] Lift of sleeve
Types of Governors
Different types of Governors are:
(1) Simple governor-Watt type:
(2) Porter governor:
(3) Hartnell governor:
CAMS
A rotating machine element which gives reciprocating or oscillating motion to another element called follower is known as cam. These are mainly used for inlet and exhaust values of I.C. engines, lathes etc.
Types of Cams
(a) Reciprocating cam
(b) Tangent cam
(c) Circular cam
CAMS TERMINOLOGY
MACHINE DESIGN
A machine which is more economical in the overall cost of production and operation is called a new or better machine. Machine design deals with the creation of new and better machine and also improving the existing machines. Metal' selected to design an element of a machine has some mechanic— properties associated with the ability of the material to res-? mechanical forces and load.
BASIS OF LIMIT SYSTEM
In order to control the size of finished part with due allowance are error for interchangeable parts is called limit system. There are generally two basis of limit system.
(a) Hole basis system: In this system the hole is kept as a member and different fits are obtained by varying size.
(b) Shaft basis system: In this system the shaft is k" constant member and different fits are obtained by the hole size.
STATIC LOADING AND DYNAMIC LOADING
(a) Static loading: A type of loading in which the load is app'- slowly or increases from nil to a higher value at a slow
There are no acceleration produced in the static loading
(b) Dynamic loading: At type of loading which varies in magnitude as well as direction, very frequently, such type of loading is called dynamic loading or fluctuating or alternating loads.
STRESS AND STRAIN
(a) Stress: Resistive force per unit area to the external force on a body, set up within the body is called stress on that body.
(b) Strain: Deformation produced per unit length of a body is called strain.
Types of stresses
Stresses are classified as
(i) Tensile stress: If a body is subjected to two equal and opposite external pulls, then the stress developed inside the body is called tensile stress
(ii) Compressive stress: If the body is subjected to two equal and opposite pushes then the stress developed is called compressive stress.
(ii) Direct shear stress: When a body is subjected to two equal and opposite forces, acting tangentially across the resisting section, as a result of which the body tends to shear off the section, then the stress induced is called shear stress. The strain occured due to the shear stress is called shear strain.
(iii) Torsional shear stress: When a body is subjected to two equal and opposite torques or torsional moments acting in parallel planes, the body is said to be in torsion, and the stress produced due to torsion is called torsional shear stress.
(iv) Bending stress: When a body is subjected to a transverse load, it produces tensile as well as compressive stresse, then stress is called. Bending stress.
(v) Bearing stress or crushing stress: A localised compressive stress at the surface of contact between two members that are relatively at rest is known as bearing stress or crushing stress.
The bearing stress is taken into account in case of riveted joints, cotter joints, knuckle joints etc.
RIVET JOINTS
A rivet is made of a short cylindrical bar with a head integral toil. Reveting is common method of joining and fastening because of low cost, simple operation and high production rates. Based on the way in which the plates are connected, rivet joints can be classified into two types of joints listed below.
Important Terms used in Riveting
(i) Gage line: A line passing through the centres of row of rivets which is parallel to the plate edge.
(ii) Pitch: It is the distance from the centre of one rivet to the centre of the next rivet measured parallel to the seam.
(iii) Back pitch: The perpendicular distance between the centre lines of the successive rows is known as back pitch.
(iv) Diagonal pitch: The distance between the centres of the rivets in adjacent rows of zig-zag riveted joints is called diagonal pitch.
(v) Marginal pitch: The distance between the centre of rivet hole to the nearest edge of the plate is called marginal pitch.
(vi) Caulking: A process in which, the edges of the plates are given blows to facilitate the forcing down of the edge.
Blowing the plate with the help of caulking tool forms a metal to metal contact point.
(vii) Fullering: A process in which a more satisfactory joint is made by using a tool which has its thickness near the end equal to the thickness of plate. This gives better joint with clean finish.
WELDED JOINTS
A permanent joint obtained by the fusion of the edges of the two parts to be joined together, with or withiout the application of pressure and-a filler material. There are two types of welded joints commonly used listed below:
(a) Lap joint or Filler joint: In this joint the plates are overlapped and then welded along the edges. The weld filled is traingular. There are various types of lap joints like single transverse, double transverse and parallel fillet joints.
The transverse fillet welded joints are designed for tensile strength whereas the parallel fillet welded joints are designed for shear strength.
(b) Butt Joint: In this joint plates are placed edge to edge order and then welded. Plates are bevelled to V-shape or U-shape if thickness of plate is more than 5 nun. The but joints are designed for tension or compression.
KEYS
To prevent the relative motion of the shaft and the machinery part connected to it we use a piece of mild steel called key. Keys are temporary fastenings and are subjected to considerable crushing and shearing stresses. Different types of keys are listed below.
(a) Sunk keys: These keys are designed in such a way that they are halfway in the key way of the hub of pulley and half in the key way of the shaft.
(b) Tangent keys: These keys are fitted in pair at right angles, each key is to withstand torsion in one direction only. Tangent keys are used for heavy duty applications.
(c) Saddle keys: These are taper keys fitted in key way and designed such that it is flat on the shaft.
(d) Wood ruff keys: This key is made of apiece from a cylindrical disc of segmental cross-section.
(e) Round keys: These keys are circular in cross-section and are fitted partly into the shaft and partly into the hub.
(f) Splines: When splines are integrated with the shaft which finally fits into the keyways of the hub. These are stronger than a single keyway.
SHAFTS
Shafts are used to transmit power from one place to another, these are normally of circular cross-section. Mild steels are hot rolled and then finished to actual size by turning, grinding or cold drawing to manufacture shafts. Alloy steels with composition of but with higher residual stresses.
Types of Shafts
There can be two types of shafts
(a) Transmission shaft such as counter shafts, line shafts, overhead shafts, etc.
(b) Machine shaft such as crank shaft
BEARINGS
A machine element which permits a relative motion between the contact surfaces of the members while carrying the load. It supports journal. The bearings are mainly classified as
(a) Sliding contact bearings
(b) Rolling contact bearings
Sliding Contact Bearings
In these bearings, the sliding takes place along the surfaces of contact between the moving element and the fixed element. These are also known as plain bearings.
According to the thickness of layer of the lubricant between the bearing and the journal, sliding contact bearings can be classified as
(a) Thick film bearings: Bearings in which the working surfaces are completely separated from each other by the lubricant.
These are also called a hydrodynamic lubricated bearings.
(b) Thin film bearings: In these bearings although lubricant is present, the working surfaces partially contact each other at least part of the time. Such type of bearings are also called boundary lubricated bearings.
(c) Zero film bearings: Bearings which operate without any lubricant are known as zero film bearings.
(d) Hydrostatic bearings: Bearings which can support steady loads without any relative motion between the journal and the bearings because there is externally pressurized lubricant between the members.
Rolling Contact Bearings
Bearing which operate on the basis of principle of rolling, Le. The contact between the bearing surfaces is rolling are known as rolling contact bearings. These are also called antifriction bearings as they offer low friction. Mainly there are two types of rolling contact bearings.
(i) Ball bearing
(ii) Roller bearing
Average life (Median life) of a bearing: It is the number of revolutions or number of hours at a constant speed that 50% o: batch of ball bearing will complete or maybe exceed and 50% fail before the rated life is achieved. It is denoted by\[{{L}_{50}}\]
\[Life\,\,\alpha \frac{1}{{{(Load)}^{3}}}\]
Dynamic load rating: Value of radial load which bearing can suffer for 1 million revolutions of inner ring with only 10% failure i-' known as dynamic load rating or basic dynamic capacity or specific dynamic capacity.
Rating .Life L \[={{\left( \frac{C}{P} \right)}^{3}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(\therefore P=load)\]
(C = dynamic basic load rating)
CLUTCHES
Clutch is a connection between the driving and driven shafts with the provision to disconnect the driven shaft instantaneously without stopping the driving shaft. Main functions of clutches are to stop and start the driven member without stopping the driving member, to maintain torque, power and speed, and to eradicate the effects of shocks while transmitting power.
Clutches are classified into two types:
Positive clutches: These are used where there is requirement of positive drive for example jaw or claw clutch.
Friction clutches: Friction clutch transmits the power by friction without shock. It is used where sudden and complete disconnection of two rotating shafts are necessary, and the shafts are in axial alignment. The power transmission takes place due to two or more concentric rotating frictional surfaces in contact. Due to friction heat is generated which should be dissipated rapidly. Friction clutches are further classified into (a) Disc or plate clutch
(b) Cone clutch
(c) Centrifugal clutch
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