conveyor belt related equations2010
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Conveyor belt related equations
MODULUS OF ELASTICITY
The modulus of elasticity () is calculated by dividing the stress by the strain:
where is the modulus of elasticity (or Young's modulus), in Pascals
F is the force, in Newtons
A is the cross-sectional area through which the force is applied, in square meters
x is the extension, in meters
l is the natural length, in meters
Example: A typical for rubber would be 6,9 MPa (1000 psi). For an average strength steel cord
conveyor belt the modulus of elasticity would be 200 kN/mm and for an average textile conveyor beltaround 7 kN/mm.
In other words: The higher the modulus the lower the elastic elongation per unit stress
TENSION FORCE
The modulus of elasticity of a material can be used to calculate the tension force it exerts under a specifi
extension:
where T is the tension force
is the modulus of elasticity
A is the cross-sectional area
x is the extension
l is the length in m
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EYTELWEIN EQUATION
The minimum belt tensions for transmitting the pulley peripheral forces are calculated as follows:
where is the length (circular measure) that the belt is wrapped around the pulley (arc of
contact)
is the coefficient of friction between belt and pulley
TAKE-UP LENGTH
where SSp is take-up length in m
L is centre distance in m
is belt elongation in % (elastic and permanent)
As a rough guideline, use 1,5% elongation for textile belts and 0,25% for steel cord conveyor belts.
COEFFICIENT C
The coefficient C is a function of the length of the installation.The total resistances without slope and special resistances are divided by the main resistances.
ARRHENIUS EQUATION
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where kis the rate constant of chemical reactions on the temperature
EA is the activation energy
T is the temperature in Kelvin
Ris the gas constant
A is the prefactor (frequency factor)
The Arrhenius equation describes the quantitative relation between reaction velocity and temperature (asyou know, the speed of chemical reactions increase with rising temperature)
STRESS IN RUBBER
where s is the stress
v is the period of strain oscillation
d is the phase lag between stress and strain
STRAIN IN RUBBER
where e is the strain
v is the period of strain oscillation
t is time
to
STORAGE MODULUS
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where E' is the storage modulus
s is the stress
e is the strain
d is the phase lag between stress and strain
LOSS MODULUS
where E'' is the loss modulus
s is the stress
e is the strain
d is the phase lag between stress and strain
INTERNAL FRICTION
where tan d is the internal friction of a rubber
E' is the storage modulus
E'' is the loss modulus
The tan d is sometimes used to determine the indentation loss of a conveyor belt cover (cf. Energy SavinBelts). E' and E'' should be as low as possible. However, there are a number of misconceptions related to
specifiying E' and E''.
http://www.conveyorbeltguide.com/EnergySavingBelts.htmlhttp://www.conveyorbeltguide.com/EnergySavingBelts.htmlhttp://www.conveyorbeltguide.com/EnergySavingBelts.htmlhttp://www.conveyorbeltguide.com/EnergySavingBelts.html -
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LENGTH RELATED MASS FLOW (m/h)
where v is the belt velocity in m/s
lvth is the theoretical volume flow in m/h
r is the bulk density of the conveyed material in t/m
jSt is the coefficient for determination of the volume flow
BRAKING FACTOR
where rB0 is the braking factor related to the rated torque of all drive motors
hges is the overall efficiency of all transmission elements between motor and pulley shaft
PMerf is the total capacity of the drive motors required in a steady operating state
PMinst is the total installed capacity of the drive motors in N
MINIMUM BELT TENSION FOR BELT SAG LIMITATION (top side, loaded)
where g is gravity (9,81 m/s)
m'Li is the mass of the conveyed material, uniformly distributed across a section of theconveyor in kg/m
m'G is the length related mass of the conveyor belt in kg/m
IRo is the idler spacing in top run in m
hrel is the maximum belt sag related to the spacing between the carry idlers in %
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MINIMUM BELT TENSION FOR BELT SAG LIMITATION (bottom side, unloaded)
where g is the gravity (9,81 m/s)
m'G is the length related mass of the conveyor belt in kg/m
IRu is the idler spacing in bottom run in m
hrel is the maximum belt sag related to the spcing between the carry idlers in %
PRIMARY RESISTANCES IN AN EVENLY TILTED CONVEYOR
where fis the friction factor in top and bottom run
L is the conveyor length in m
g is the gravity acceleration in m/s
m'R is the mass of the idlers in kg/m
m'L is the mass of the conveyor belt with an evenly distributed load in kg/m
d is the even inclination of the conveyor in
MAXWELL MODEL
where e is strain
s is stress
VOIGT MODEL
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where e is strain
s is stress
Used to express the relaxation behavior of polymers.