FRICTIONAL PROPERTIES
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FRICTIONAL PROPERTIES
• The knowledge about frictional properties is essential for selection of sowing, harvesting,
transport, cleaning, sorting, storage and processing parameters of biological materials.
it is important for analyzing and modeling various handling processes
• The frictional properties of biological materials can differ significantly due to their morphological
variation.
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FRICTIONAL PROPERTIES Cont..
Frictional parameters of plant materials are determined by;
• Species (variety), ripeness, moisture content,
• Friction surface, material porosity,
• Orientation relative to the direction of motion,
• Normal pressure exerted on particles,
• Variations in particle shape and
• Time of material storage
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FRICTIONAL PROPERTIES Cont..
• The need for knowledge of coefficient of friction of agricultural materials on various
surfaces has long been recognised by engineers concerned with rational design of
grain bins, silos and other bulk storage structures.
• Static and dynamic coefficient of friction of grain, forage and other agricultural
materials on wood, metal, plastic and other materials are needed by design
engineers for rational design and prediction of motion and power required to move
or handle materials during harvesting, handling and processing.
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FRICTIONAL PROPERTIES CONT..
• Frictional properties such as angle of repose and coefficient of friction are
important in designing equipment for solid flow and storage structures and the
angle of internal friction between seed and wall in the prediction of seed pressure
on walls.
• The coefficient of static friction plays also an important role in transports (load
and unload) of goods and storage facilities.
• It is important in filling flat storage facility when grain is not piled at a uniform
bed depth but rather is peaked
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FRICTIONAL PROPERTIES CONT….
• The coefficient of friction is also important in determining the pressure exerted by
grain or any other free flowing commodity against retaining walls, storage bins and silo
walls.
• Before agricultural materials such as grain can slide down a chute or discharge from a
bulk bin, the forces of static friction due to inter particle friction and particle – wall
friction must be overcome.
• Coefficient of friction is important in designing storage bins, hoppers, chutes, screw conveyors,
forage harvesters, and threshers.
• Once the material begins to flow the coefficient of dynamic friction must be exceeded
in order that flow should continue. All these must be known before designing
discharge hoppers and chutes.
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FRICTIONAL PROPERTIES CONT….
• In design of material handling equipment, such as mechanical and pneumatic
conveying machines, the material comes in direct contact with the trough, casing or
other components of the machine over which it must slide.
• The total power required to drive these machines is composed of several components,
of which power consumed to overcome friction is one of the important component.
• Its rational estimate requires knowledge of frictional properties of the material to be
handled.
• In design of silos, bins and retaining walls, friction is an important factor in determining
the pressure exerted by the material against the walls. It is therefore a very useful
design data in the construction of these structures.
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ANGLE OF REPOSE
• When bulk granular materials are poured onto a horizontal surface, a conical pile
will form.
The internal angle between surface of the pile and a horizontal surface is known as
the angle of repose.
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ANGLE OF REPOSE Cont..
Angle of repose is defined as the angle with the horizontal at which a granular
material (such as grain flour, sugar, salt etc.) will stand when piled freely.
There are two angles of repose, i.e. static and dynamic angles of repose.
• The static angle of repose is the angle taken up by a granular material about
to slide upon itself.
• The dynamic angle of repose is more important as it arises in all cases where
bulk of material in motion such as movement of grain discharging from a bin
or a hopper come to rest. This is very important in the design of gravity
discharge hoppers and self-emptying bins
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Angle of repose Cont..
• The angle of repose can range from 0° to 90°
• It is affected by the morphology of a material.
• It is related to the density, surface area and shapes of the particles
and the coefficient of friction of the material.
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Angle of repose Cont..
• The angle of repose is used in design of equipment for the processing of
particulate solids.
• It may be used to;
• design an appropriate hopper or silo to store the material
• size a conveyor belt for transporting the material.
• determine whether or not a slope of a stockpile will likely collapse.
• Calculate correctly the vessels’ stability.
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Methods applied to determine the angle of repose
1. Tilting box method.
 This method is appropriate for fine-grained, non-cohesive materials, with individual
particle size less than 10 mm eg. Maize, rice, sorghum etc. can be determined using a
wooden box full of grain mounted on a tilting top drafting table.
 The table is tilted until the grain began to move leaving an inclined surface.
 The angle of inclination of the table is then measured as the angle of repose of that
particular grain sample
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2. Fixed funnel method
 The material is poured through a funnel to form a conical shape.
 The tip of the funnel should be held close to the growing cone and slowly raised as the pile grows, to minimize the
impact of falling particles.
 Stop pouring the material when the pile reaches a predetermined height or the base reaches a predetermined
width.
 Rather than attempt to measure the angle of the resulting cone directly, divide the height by half the width of the
base of the cone.
 The inverse tangent of this ratio is the angle of repose.
A  tan
1
 H 


 D 
Where A = Angle of repose
H = height of the pile and
D = Diameter of the pile
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3. Use of glass box Method
 Using of a glass box with a lifting door on one side is another method for determining the angle of
repose.
 The box with the door closed, is filled with the material whose angle of repose is to be measured.
 The door is then opened to allow the material to flow out of the box freely leaving a small quantity of
the material at the bottom with inclined surface.
 Then measure the angle between the horizontal surface and the surface of grain left on the box.
NOTE:
Angle of repose varies widely with moisture content and the type of material
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The angle of repose for some of the grains is given in Table
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Angle of internal friction/coefficient of internal friction
• In predicting the lateral pressure on retaining wall in storage bins or design of bins and
hoppers for gravity discharge the coefficients of friction between particles of the
granular materials is needed as a design parameter.
• For example in design of shallow bins the Rankine equation is used, this require
knowledge of angle of internal friction of the material

3
 wy tan
2
i 

 45 

2 

• Where
3 = lateral pressure against the wall at point
Y = depth of grain, below the top of the wall
w = density of the material (kg/m3) and
i = angle of internal friction
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Angle of internal friction/coefficient of internal friction Cont..
• In designing of deep bins and other similar storage structures such as
silos, the pressure ratio k, which is the ratio of the lateral pressure 3 to
the vertical pressure 1 at a given point in the material is needed
k
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

3

1
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Angle of internal friction/coefficient of internal friction Cont..
• The pressure ratio k can also be found from the angle of internal friction as follows:
k 
1  sin 
i
1  sin 
i
• Knowing the value of k the horizontal pressure against the wall can be estimated for
any given vertical pressure.
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• The vertical pressure causes a column action while the lateral pressure
causes a bending action on the wall (bursting force).
• The value of k varies with the type of material, geometry of the bin,
depth and moisture content of the material, friction and cohesion
properties of the material.
• In designing of deep bins, Janssen’s equation for lateral pressure is used;

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
wR 
1  

f s 
kf s h
R




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• Where: R = the hydraulic radius (=cross-sectional area /circumference),
w = bulk density of the material,
fs = static coefficient of friction against the wall,
h = the depth of material in the bin
• Vertical pressure 1 can be calculated from:

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

1  
k 

wR
f
s

kf
s
R
h




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Definition of shallow and deep bins.
• A grain bin is referred to as a shallow bin when the depth of the granular material in the
bin is less than or equal to the equivalent diameter of the bin.
• In a deep bin, the depth of the grain is greater than the equivalent diameter.
• The equivalent diameter is taken as four times the hydraulic radius of the bin.
• Another method of determining the deepness of a bin is to draw a line at an angle equal
to the angle of repose of the granular material from the intersection of the bin wall and
floor to the opposite bin wall.
• In a deep bin, this line intersects the opposite wall before passing through the upper
surface of the granular material.
• In a shallow bin, the line meets the opposite wall at or above the surface of the granular
material.
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Measurement of static and dynamic coefficient of friction
• The usual methods for determination of coefficient of friction
include,
1. The use of inclined plane method or moving of a given surface
against the material.
• The inclined plane method can be used for cereal grains, coffee
fruits and coffee beans, and different types of fruits.
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• The object whose coefficient of friction is to be measured is placed on the
inclined plane and the inclined plane is slowly raised by cranking the handle
(see figure) until the object begin to slide down the inclined plane.
• The ratio between the force of friction F, and the force normal to the
surface of contact, N is given by the well-known relationship:
 
F
N
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• The coefficient of friction can also be given by the tangent of the angle of
the inclined surface upon which the friction force tangent to the surface
and the component of the weight normal to the surface are acting.
  tan 
• Where Ø is the angle of inclination
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Incline plane Apparatus
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2. Another method is the one, which places the material in contact with a positively
driven surface; the surface is either mounted on a revolving circular disc or horizontal
table. This method can be used with chopped forage, straw, silage, or grains.
• The surface is driven at known velocity against the material that is held in a container
(usually loaded with dead weights).
• The horizontal force required to move the surface is equal to the friction force (F) and
can be measured with a spring scale.
F  N
• where F = friction force,
N = Normal force (weight of material in container plus dead weights) and
 = Dynamic coefficient of friction
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Rotating disc apparatus for friction determination
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3. Another method, which can be used, for measuring the coefficient
of friction of things like a single fibre of wool, cotton, sisal or a stalk
of straw or grass is shown on the diagram below.
• The fibre is placed on the rotating drum B that is covered with the
friction surface under study.
• The force F2 for a given F1 at a given drum speed is determined.
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• The coefficient of friction can be calculated from the following
equation:
 
1

ln
F2
F1
• where  = angle of contact of material with the friction drum and
 = coefficient of friction
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Apparatus for determination of coefficient of friction
of a single fiber
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Aerodynamic and hydrodynamic properties
• Aerodynamic and hydrodynamic properties of agricultural products are essential
for air and water conveying and separation of foreign matter.
• Aero and /or hydrodynamic properties are very important characters in hydraulic
transport and handling as well as hydraulic sorting of agricultural products.
• To provide basic data for the development of equipment for sorting and sizing of
agricultural commodities, several properties such as physical characteristics and
terminal velocity are needed.
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Aerodynamic and hydrodynamic properties
cont…
• When air stream is used for separation of products such as grain from its
associated foreign matter such as straw and chaff, a knowledge of terminal
velocity of all the particles involved would define the range of air velocities which
will affect good separation of the grain from the foreign materials.
• For this reason terminal velocity is an important aerodynamic characteristic of
materials in such applications as pneumatic conveying and separation from
foreign materials.
• Density, size, shape and the drag coefficient are the physical properties needed in
calculating the terminal velocity of an object in the fluid
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Terminal Velocity
• The terminal velocity of a particle may be defined as equal to the air
velocity at which a particle remains in suspended state in a vertical pipe.
• In free fall, the object will attain a constant terminal velocity Vt at which,
where acceleration will be zero.
• Net gravitational accelerating net upward equals to the sum of buoyant
force and drag force
• Gravitational force acting downward = buoyant force exerted by the fluid
on the body in upward direction + drag force (frictional resistance due to
motion of the body in the fluid medium)
Measurement of terminal velocity
• Most scientists and researchers employ air column to find out the terminal
velocity of grains.
• The set up usually consists of a vertical air column, which is blown from the
bottom and passes through the screen. The screen uniformly distributes the air
velocity.
• The air column is also attached with velocity measuring device. The blower
maintains variable speed.
• When grains are allowed to drop into the column, initially they attains
acceleration, once the velocity is adjusted they fall to the bottom with a constant
velocity. This constant velocity is termed as terminal velocity
Terminal Velocity cont..
• In air conveying or pneumatic separation, an air velocity greater than the terminal
velocity will lift the particle
• While an air velocity lower than the terminal velocity will allow the particle to fall.
• To allow the particle to fall gently, the air velocity is adjusted to a point just below
the terminal velocity
• while to lift the particle gently the air velocity is adjusted to air velocity just above
the terminal velocity of the particle.
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Terminal Velocity cont..
• Terminal velocity can be determined from the following equation:
 2 mg   p  
Vt  
  p  f A p C
f

1
2


• Where;
m = Mass of the particle,
g = Acceleration due to gravity,
p = Mass density of the particle,
f = Mass density of the fluid,
Ap = Projected area of the particle normal to the direction of motion and
C = Drag coefficient
• This principle has been employed in design of Aspirators for cleaning of agricultural produce ( fig
below)
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Aspirator for cleaning of agricultural materials
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Working principle of Aspirator
• Under steady state condition, where terminal velocity has been
achieved, if the particles density is greater than fluid density, the
particles motion will be downward.
• If particles density is smaller than the fluid density, the particle will be
rise.
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Application to Agricultural products
1. Separation of foreign materials from seeds, grains potato, blue
berry
2. Conveying and handling of grains, chopped forage small & large
fruits
3. Hydraulic handling of apples, cherries, mango& potatoes etc.
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Table 1. Air velocity requirement for air borne of some of the
agricultural materials
Grain
Unit density, kg/m3
Terminal velocity, m/s
Wheat
998-1238
9-11.5
Rye
1158-1218
8.5-10
Oats
738-968
8-9
Corn
1138-1198
34.9
Soybean
1029-1152
44.3
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Table 2. Terminal velocity and drag coefficient for groundnut and
soybean
Grain
Terminal velocity m/s
Drag Coefficient
Range
Mean
Range
Mean
Groundnut kernel
12.31-13.78
13.23
0.52-0.64
0.58
Soybean
12.30-13.92
13.40
0.38-0.62
0.47
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Drag Coefficient
• It is used to quantify drag or resistance of an object is a fluid environment such as
air or water. It is a dimensionless quantity.
• Drag coefficient is always associated with surface area:
• When fluid flow occurs about immersed objects, the action of the forces involved
can be illustrated as follows.
• The pressure of the upper side of the object is less than that of lower side is great
than that of and that of lower side is greater than the pressure p in the
undisturbed fluid stream.
• In addition to these force normal to the surface of the object, there are shear
stresses, C acting tangential to the surfaces in the direction of flow and resulting
from frictional effects.
ELECTRICAL PROPERTIES
• Electrical properties are important when processing foods involving
electric fields, electric current conduction, or heating through
electromagnetic waves.
• The electrical properties of agricultural products, which are
important in handling and processing, are:
• Electrical conductance and capacitance, dielectric properties, and reaction
to electromagnetic radiation.
• Electrical conductance and capacitance are used in moisture content
determination of products such as cereal grains.
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Electrical properties cont..
• The principle of electrostatic separation is used in separation and
cleaning of agricultural seeds.
• With small seeds, it has been found that electrostatic separation is
essentially independent of size, shape, weight, and surface texture.
• When devices depending upon these physical characteristics fail to
separate similar seed varieties, the seed’s ability to hold electrostatic
charge can be used for separation.
• Conductivity of the seed is the property, which would determine,
basically the ability of the seed to hold surface charge.
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Electrostatic separation/cleaning
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Electrical properties cont..
• These properties are also useful in the detection of processing
conditions or the quality of foods.
• Electrical conductivity is a measure of how well electric current flows
through a food of unit cross-sectional area A, unit length L, and
resistance R.
• It is the inverse value of electrical resistivity (measure of resistance to
electric flow) and is expressed in SI units S/m in the following relation:
ƒÐ = L /(AR)
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Electrical properties cont..
• Electrical permittivity is a dielectric property used to explain
interactions of foods with electric fields.
• It determines the interaction of electromagnetic waves with matter
and defines the charge density under an electric field.
• In solids, liquid, and gases the permittivity depends on two values:
a. The dielectric constant; related to the capacitance of a substance and its
ability to store electrical energy.
b. The dielectric loss factor; related to energy losses when the food is
subjected to an alternating electrical field (i.e., dielectric relaxation and
ionic conduction)
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Dielectric properties
• Dielectric properties of agricultural materials and foods provide
information about their behavior during electromagnetic heating.
• These properties of materials need to be known in order to understand the
microwave heating mechanism, and hence for simulating, modeling, and
applying microwave heating successfully, and for designing microwave
heating systems.
• The dielectric constant (ε′) and dielectric loss factor (ε″), which are the real
and the imaginary parts of the relative complex permittivity (εr),
respectively, are the major dielectric parameters, and the relationship
between them is given by the following equation:
• Ɛr = έ - Ɛ″
• The dielectric constant is the ability of a material to store microwave
energy, whereas the dielectric loss factor is the ability of a material to
dissipate microwave energy as heat.
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Optical properties
• Light transmittance and reflectance properties of agricultural products have been
exploited in recent years for electronic sorting and grading, maturity and surface
colour determinations, and in the study of the interior characteristics of fruits and
vegetables.
• An instrument has been developed which allows the transmittance and measurement
of monochromatic light through intact biological specimens.
• The technique, which is based on light transmittance characteristics and absorption
spectra of the material has been exploited to determine internal colour of fruits like
• tomatoes, smut content of wheat, fruit maturity, internal discoloration of potatoes,
blood spots and green rot in eggs, water core in apples, insect infestation in grain
and moisture content of seeds.
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Detection of water core in apples
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Optical properties cont…
• Light reflectance characteristics of agricultural products are also exploited in
sorting ,grading and cleaning or separation of desirable products from foreign
materials.
• The use of this principle has been explored in the design of a colour-sorting
machine (see fig 17).
• It is also used in sorting potatoes from soil clods and stones.
• The reflectance properties of potatoes are sufficiently different from those of
soil clods to allow reflectance to be used to differentiate between the two
materials electronically.
• Light reflectance curves of different fruits have shown distinct variation in
various stages of fruit maturity.
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Color sorting machine
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Firmness and hardness
• Firmness is an important textural attribute in fruits and vegetables in connection
with readiness of the crop for harvest, quality evaluation during storage for fresh
market, as well as prior to processing, and
• its influence on the correlation between the quality of the raw material and
that of the processed or manufactured product.
• Such correlations are due to the fact that many changes in physical, chemical and
structural properties of fruits and vegetables are reflected in changes in firmness
of the material.
• Hardness of grain is important in evaluating their feeding values as well as their
size reduction and milling characteristics.
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Determination of firmness and hardness
• Hardness of several agronomic crops as well as some manufactured food products
is also important in ascertaining other physical and chemical properties during and
after processing
• Numerous devices have been proposed and used in measurement of firmness and
hardness of food materials.
• Results obtained are however, usually expressed in arbitrary units which makes it
practically impossible to compare samples tested by means of different and
sometimes even same instrument.
• A good example is the difficulty involved in trying to convert the readings from a
Magness-Taylor pressure tester using a 7/16-inch tip to those using a 5/16-inch tip.
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Magness – Taylor fruit pressure tester
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Firmness determination
• Firmness of fruits and vegetables
• To imitate the pressing of a fruit with the ball of the thumb to determine its
ripeness,
• the amount of force required to press a marble into the side of an apple
was noted on a dial of a spring scale.
• This development was followed by the Magness-Taylor fruit pressure tester.
• This instrument, which is still widely used, consist of a plunger either 7/16-inch
or 5/16-inch in diameter attached to a calibrated spring.
• The round tip of the plunger is pressed into the fruit to the depth of 5/16-inch,
marked on the plunger, and the penetrating force is read on the scale.
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Firmness determination cont…
• The Magnes-tylor pressure tester has been modified recently to reduce the
depth of penetration of the tip to 0.055-inch indicated by means of a small
bulb connected to a battery and to eliminate the ‘human element’ from the
reading of this instrument mechanical press and automatic recording has been
employed.
• Another instrument employed in measurement of firmness of fruits and
vegetables is the firmness meter (figure 12).
• It is designed to pre-stress the specimen, apply load, and measure
deformation of the specimen during a given time.
• The right weight pre-stresses the sample and ensures good contact.
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Firmness determination cont..
• The left weight deforms the sample for a given time.
• After this time, a solenoid sets the brake and stops the deforming
force.
• The force is applied through a selection of roller chains, flat surfaces,
and fibreglass tape to products such as apples, onions, tomatoes etc.
• the force is applied uniformly around the circumference of the
object simulating firmness measurement of fruits and vegetables
when held in hand.
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Firmness meter
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Hardness Determination
• Hardness can be defined as the resistance of a material to permanent
deformation.
• A number of tests have been made to provide quantitative measure
of hardness of individual seeds and grain or of the average hardness
of bulk samples.
• Determination of percent of “floury” portion in the kernel of cereal grains,
• crushing the grain between the jaws of a force-measuring device, and
• measuring the torque required for crushing a sample of grain between
two crushing wheels are among the methods used to determine the
hardness of agricultural materials.
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Hardness Determination cont…
• A common method used for determination of hardness under
dynamic loading of agricultural material is the pendulum impacter.
• This apparatus employ the principle of a simple pendulum (figure
13).
• The pendulum can be a small steel ball used as an indenter,
impacting the fixed test specimen, or the specimen itself hung by a
string striking a rigid surface.
• In the latter case, the dynamic hardness Pd can be expressed as a
function of the rebound height h2 and height of fall h1 according to
the following equation:
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Hardness Determination cont…
Pd 


 3 
mg  h 1    h 2 
 8 


Va
• where
Pd =dynamic hardness,
m =mass of the indenter,
g = acceleration due to gravity,
Va = apparent volume of the indentation (obtained by assuming
that the indentation has the same radius of curvature as the
indenter),
h1 and h2 = height of drop and height of rebound respectively
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Pendulum Impacter
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