In this article we will discuss about:- 1. Strength of Materials Used in Farm Machinery 2. Bending Stress of Materials Used in Farm Machinery 3. Testing 4. Bearing.
Strength of Materials Used in Farm Machinery:
The strength, durability of implements and machines depend upon material used in their fabrication. The strength of the material is measured by the amount of stress it can bear. When some force is applied over a body, it tends to change its shape or dimensions. But at the same time, some internal forces develop within the body which tends to prevent the change of shape or dimensions.
Stress:
When a force is applied on a body there will be relative displacement of the particles and due to the property of elasticity, the particles tend to regain their original position. Stress is defined as the restoring force per unit area.
There are three kinds of stresses:
1. Tensile stress due to tension,
2. Compressive stress due to compression and
3. Shear stress due to a tendency to prevent sliding of one body over the other.
1. Tensile Stress:
When a pulling force is applied over a body, it tends to increase longitudinally i.e. when the tendency of the load is to pull a portion of a body; the stress produced in the body is called tensile stress.
2. Compressive Stress:
When a portion of a body is compressed or forced together, some internal stresses develop within the body to prevent compression. These stresses are called compressive stresses. Compressive stresses are determined by dividing the compressive force by the area over which it is acting.
In the Fig. 11.2, consider a bar AB is being pulled by a force F and a bar CD is being pushed or compressed by a force F. In each case, the bar is in equilibrium. At any point O of the bar, across sectional area, perpendicular to the direction of F the force F is ‘a’ then the tensile stress in AB and the compressive stress in CD is F/a.
3. Shear Stress:
When a body slides over another body, an internal force tends to prevent sliding. These internal forces per unit area are called shear stresses. Shearing stress occurs when the tendency of the load is to cause one portion of a body to slide over another body.
Strain:
The ratio of the change in shape to the original shape is called Strain. Strain refers to the change of form or dimensions of a body which occurs when a body is loaded or subjected to a stress. A bar tends to become longer when subjected to tensile stress and shorter when stress is compressive.
Strain = Change in Length/Original Length = l/L
Where,
I = Change in Length, and
L = Original Length
Strains are of three types:
i. Longitudinal Strain,
ii. Volumetric Strain, and
iii. Shear Strain
i. Longitudinal Strain:
The ratio of change in length to original length is called longitudinal strain.
Longitudinal strain = l/L.
ii. Volumetric Strain:
It is the ratio of change in volume to original volume. Volumetric strain occurs when a body is subjected to uniform fluid pressure over the whole of its exposed surfaces. The volume changes somewhat under these conditions.
Volumetric strain = v/V
Let,
v = Change in Volume
V = Original Volume
iii. Shear Strain:
Shear strain is defined as the angle of shear, measured in radians. Shear occurs when a body is subjected to shear stresses. Such stresses produce a change in the shape of the body. In shear, the strain is measured by the angle Ɵ through which the body is distorted by the applied forces. In the Fig. 11.3, the block ABDC is distorted through an angle Ɵ by the force F, so that the face AB moves to the position A’ B’.
Shear Strain = F/θ
Where, θ is given in radian.
Strain is simply a ratio and hence a dimensionless quantity.
Stress-Strain Diagram:
If the strain and the corresponding stresses on a loaded bar be plotted on a graph (Fig. 11.4), it is found that stress/strain is constant up to a point A. This point A is called elastic limit.
Any elastic material is found to recover its original shape and dimensions when the load is removed, provided the material is not stressed beyond that limit i.e., elastic limit. Beyond this elastic limit, the strain increases more rapidly than stress and the results are represented by a more or less irregular curved line.
Important Terms:
There are few important terms related to stresses and strains.
1. Elastic Limit:
The maximum stress up to which a body exhibits the property of elasticity is called Elastic limit. It is the point, up to which the material remains elastic in nature. During this range, the bar returns to its original length if the load is removed. The elastic limit is expressed in terms of stress, which is obtained by dividing the load by the original cross sectional area of the bar.
It can be said that when there is some changes in shape of a body due to the action of some externally applied force, the rate of change of shape is proportional to the applied force up to a limit. If we go on increasing the load, a stage comes after which the change of shape would not be proportional to the applied force, that stage is elastic limit.
2. Yield Point:
The stage, at which the change of shape becomes more rapid than the increase of force, is called Yield point. Up to the elastic limit the change of shape is temporary and the body comes back to its original shape as soon as the force is removed.
But after the yield point is reached, the change of shape becomes permanent i.e. the body does not come back to its original form even after the force is removed.
3. Ultimate Strength:
The maximum force, which a body can resist, is called ultimate strength of the material. It is obtained by dividing the maximum load by the original cross sectional area.
Ultimate Stress = Maximum load, the body can resist /Original cross sectional area.
4. Working Load:
The force required for the working of a body or a machine is called working load of the machine.
5. Breaking Load:
The amount of force which breaks the body or the machine is called Breaking load.
Factor of Safety = Breaking load / Working load
6. Poisson’s Ratio:
When a body is pulled, it becomes longer and thinner. If the body is compressed, it becomes shorter and thicker. Therefore, tensile stress acting in any direction produces a tensile strain in that direction and also it produces a compressive strain in every other direction, perpendicular to the first.
Similarly a compressive stress produces compressive strain in its own direction and tensile strain in every lateral direction. Poisson’s ratio is given by the ratio of lateral strain find longitudinal strain.
Poisson’s Ratio = Lateral strain/Longitudinal strain
7. Hooke’s Law:
It states that within elastic limit, stress is proportional to strain. Robert Hooke discovered that so long as elastic limit is not passed, the strain is proportional to stress producing it. The strain may be due to tension, compression or shear stresses.
8. Modulus of Elasticity:
The ratio of stress and strain is called modulus of elasticity or coefficient of elasticity.
Modulus of elasticity is of three types:
i. Young’s Modulus,
ii. Bulk Modulus, and
iii. Modulus of Rigidity
i. Young’s Modulus (Y):
It is defined as the ratio of normal stress to longitudinal strain. When a body is subjected to simple tension or simple compression, it is called coefficient of direct elasticity or Young’s modulus and is denoted by the symbol Y.
Where,
P = total pull applied,
A = area of cross section,
I = change of length, and
L = original length.
ii. Bulk Modulus (K):
It is defined as the ratio of normal stress to volume strain. When a pressure is applied all over surface of body, a volumetric strain is produced which is denoted by symbol K.
Where,
p = pressure applied over body,
v = change in volume, and
V = original volume.
iii. Modulus of Rigidity (ƞ):
It is defined as the ratio of tangential stress to shear strain. When a shearing stress is applied to a body, the change in shape is due to shearing strain.
ƞ = Tangential Stress/Shear Strain
Bending Stress of Materials Used in Farm Machinery:
Stresses produced in a body or a beam due to bending action is known as bending stress.
In analysing the bending stresses in a beam, it is usual to make the following assumptions:
1. The effect of shear stresses in the beam may be neglected and plane section of the beam which is perpendicular to the axis, remains plane.
2. The material is elastic and obeys Hooke’s law i.e. the stress is proportional to strain.
3. The beam is straight before it is loaded.
Suppose a beam AB is supported and loaded (Fig. 11.5). The lower part is stretched, the upper part is compressed and that there is an intermediate surface which does not change in length. This surface is called Neutral surface. The neutral surface is perpendicular to the plane of the paper and is represented by NS.
If the curve NS is very short, it may be regarded as circular arc with its centre known as centre of curvature. The radius of the arc is called Radius of curvature and is denoted by R.
The whole beam is not usually bent to a circular arc, but the centre line of the neutral surface has a different radius of curvature at every point. Consider a thin layer DF at a distance Y from the neutral surface and its length be D’ F after bending.
Testing of Materials Used in Farm Machinery:
The main tests of a material for agricultural purpose are hardness testing and impact testing. For agricultural implements, the hardness testing is usually done by Brinell hardness testing machine.
Brinell Hardness Test:
In this test, an indentation is made in the material under test by a hardened steel ball, to which a static load is applied gradually and maintained for a definite time. This time is usually taken as 15 seconds. Brinell hardness number is equal to the applied load in kilogram divided by the spherical area of the indentation in square millimeter.
If P is load in kg (Fig. 11.6), D is ball diameter in mm, d is diameter of indentation in mm, y is the depth of indentation below the top of the ridge in mm and A is the spherical area of indentation in sq. mm, it can be written as-
A micrometer microscope is used to measure the diameters of indentation and the value of d is taken as the mean of two mutually perpendicular diameters.
Impact Test:
Izod impact testing machine is used for impact testing. The machine consists of a pendulum arranged to swing freely between two ‘A’ shaped frames attached to a heavy base casting (Fig. 11.7).
The base is bolted on a concrete foundation. The pendulum mounted on ball bearings consists of a tube braced by Tee rods and fitted with a hammer ‘H’ in which there is hardened steel precision knife edge or striker ‘S’ is represented by an arrow head.
When a test is to be done, the pendulum is raised by a handle to the predetermined position and supported by a catch operated by a trigger T. The specimen which is notched is held vertically in a vice V operated by a small hand-wheel W, the notch is positioned by a gauge so that it is in level with the top of the die in the vice and facing the pendulum.
When the trigger T is pulled, the pendulum falls, the striker S hits the specimen and breaks it. The hammer which is hollow cleans the vice and the pendulum continues its journey until it comes to rest.
The energy used in breaking the specimen is equal to the difference between the height of the centre of gravity of the pendulum before the test and the height at the end of the swing, multiplied by the height of the pendulum but the value of this product is shown by a pointer or a scale attached to a quadrant. The pointer moves freely and is carried round by the pendulum.
Bearing Used in Farm Machinery:
Bearing is a support in which a journal or other moving parts rotate. A journal is that portion of a rotating shaft which turns in bearing. Farm machines have many rotating shafts, spindles, axles and pins which require bearings. There are various types of bearings depending upon the speed and load.
Bearing is commonly classified into two groups:
1. Plain Bearing, and
2. Antifriction Bearing
1. Plain Bearing:
It is the simplest type of bearing, used for agricultural machines. It is used where the load is applied perpendicular or radial to a revolving shaft.
Plain bearings are made of:
(a) Bronze:
Bronze bearings are extensively used for small bearings, subjected to high speeds and excessive pressure, viz. piston pin bearings.
(b) Babbitt:
Babbitt is an alloy containing copper, tin, lead and antimony. Bearings made of babbitt metal are mostly used for line shaft, crankshaft and connecting rods. It is hard enough to withstand excessive pressure. It retains the lubricants well in position.
(c) Wood:
Wooden bearings are used where the bearing is exposed to dirt and grit. It is subjected to rapid wear and frequent replacement. It is used in agricultural machines such as disc harrows and many other agricultural machines.
2. Antifriction Bearing:
Antifriction bearing causes less power loss due to less friction because rolling friction is less than sliding friction. This bearing contains balls or rollers, placed between the shaft and the supporting bearing, thus reducing friction. The lubrication keeps the bearing cooled and protects the rubbing surfaces.
Antifriction bearings are of two types:
(i) Roller Bearing and
(ii) Ball Bearing
(i) Roller Bearing:
Roller bearings are of four types:
(a) Plain Roller:
Such bearing consists of a number of solid cylindrical steel rollers. It is very common bearing used in agricultural machinery.
(b) Tapered Roller:
Such bearing is made of a number of conical rollers, assembled in a cage. It revolves about the outer and inner races, whose bearing surfaces are also conical. The rollers and races are made of high carbon steel. This bearing carries radial and side thrust as well as angular thrust. It is very useful for agricultural equipments.
(c) Spiral Roller:
Such bearing consists of a number of hollow steel rollers. Each roller is made in form of a helix. It is used for heavy duty, light duty and high speed work.
(d) Needle Roller:
It consists of an outer shell containing a number of hardened rollers with pointed ends. It has got the capacity to carry high radial load. It is easily used where the bearing space is small.
(ii) Ball Bearing:
It consists of one or more rows of hardened steel balls held in a cage. The balls roll between inner and outer races. The balls are separated and held in position by a retainer. It may carry radial load, thrust load, as well as radial and thrust load combined. The contact surface between the balls and shaft is small hence friction is very less.
Care and Maintenance of Bearings:
For longer life to bearing, there are a few common precautions to be taken:
1. It must be properly installed to have normal strains.
2. It must be well enclosed to prevent dust and dirt.
3. It should be adjusted if it is adjustable and
4. It should be properly lubricated.