formulas used in conveyor

8/12/2019 formulas used in conveyor

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TECHNICAL / EQUATIONS Please

Please scroll for equations keywords (This chapter is still being improved. Sorry for inconveniences.)

MODULUS OF ELASTICITY

The modulus of elasticity is calculated by dividing the stress by the strain:

where M is the modulus of elasticity (ISO 9856)

F is the force (N)

elast is the elastic elongation at the end of the specified number of cycles in N/mm

In other words: The higher the modulus the lower the elastic elongation per unit stress. See definition h

TENSION FORCE

The modulus of elasticity of a material can be used to calculate the tension force it exerts under a speci

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 (m)

MINIMUM PERIPHERAL FORCE

The minimum belt tensions for transmitting the pulley peripheral forces are calculated as follows:

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where FU Minimum peripheral force,

C Coefficient C,

f artificial friction coefficient,

L conveyor length (m),

g acceleration (m/s),

q Ro mass of revolving idler parts of top strand (kg/m),

q Ru mass of revolving idler parts of bottom strand (kg/m),

q B mass of the belt on top strand (kg/m),

q G mass of the belt in bottom strand (kg/m),

H lift of the conveyor between discharge and loading area (m),

FS1 special main resistances,

FS2 special secondary resistances.

TAKE-UP LENGTH

where S Sp is take-up length (m)

L is centre distance (m)

is belt elongation, elastic and permanent (%)

As a rough guideline, use 1,5% elongation for textile belts and 0,25% for steel cord conveyor belts.

Note: For long-distance conveyors, dynamic start-up calculations may be required, because not all elesimultaneously, due to the elastic properties of the conveyor belt.




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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

where k is the temperature dependence of the rate constant (of a chemical reaction)

EA is the activation energy

T is the temperature

R is the gas constant

A is the prefactor (frequency factor)

The Arrhenius equation describes the quantitative relation between reaction velocity and temperature (chemical reactions increase with rising temperature).

STRESS IN RUBBER

where is the stress

is the period of strain oscillation

is the phase lag between stress and strain

STRAIN IN RUBBER

where is the strain




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is the period of strain oscillation

t is time

STORAGE MODULUS

where E' is the storage modulus

is the stress

is the strain

is the phase lag between stress and strain

INTERNAL FRICTION

where tan is the internal friction of a rubber

E' is the storage modulus (N/mm)

E'' is the loss modulus (N/mm)

The tan is sometimes used to determine the indentation loss of a conveyor belt cover (cf. Energy Savias low as possible. However, there are a number of misconceptions related to specifiying E' and E''.

LENGTH RELATED MASS FLOW (m/h)

where v is the belt velocity (m/s),

lvth is the theoretical volume flow (m/h),

is the bulk density of the conveyed material (t/m),




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St is the coefficient for determination of the volume flow.

BRAKING FACTOR

where 0 is the braking factor related to the rated torque of all drive motors,

ges is the overall efficiency of all transmission elements between motor and pulley sh

P Merf is the total capacity of the drive motors required in a steady operating state,

P Minst is the total installed capacity of the drive motors (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 the c

m' G is the length related mass of the conveyor belt (kg/m)

IRo is the idler spacing in top run (m)

h re l is the maximum belt sag related to the spacing between the carry idlers (%)

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 (kg/m)

IRu is the idler spacing in bottom run (m)

h rel is the maximum belt sag related to the spcing between the carry idlers (%)

PRIMARY RESISTANCES IN AN EVENLY TILTED CONVEYOR

where f is the friction factor in top and bottom run

L is the conveyor length (m)

g is the gravity acceleration (m/s)

m' R is the mass of the idlers (kg/m) m' L is the mass of the conveyor belt with an evenly distributed load (kg/m)




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is the even inclination of the conveyor ()

MAXWELL MODEL

where is strain

is stress

VOIGT MODEL

where is dynamic viscosity is total stress

is total deformation

D is shear rate

G is shear modulus

Used to express the relaxation behavior of polymers.

ROLLING RESISTANCE

where F is resistance force

C rr is the dimensionless rolling resistance coefficient

Nf is the normal force

or

where E' is the storage modulus (N/mm)

tan is the internal friction

MINIMUM TRANSITION LENGTH (m)

where B is belt width (mm)




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is troughing angle ()

S is the safety factor

KG is the belt parameter

Kf1 is the troughing parameter

PERIPHERAL FORCE (N)

where FH is the main resistance

FN is the secondary resistance

FS1 are the special main resistances

FS2 are the special secondary resistances

FSt are the resistances due to slope

where P Tr is the drive power (pulley)

v is speed (m/s)

where C is the coefficient (main resistance factor)

f is the resistance coefficient

L is belt length (m)

g is acceleration (m/s)

q RO is the mass of the idlers on top side (kg/m)

q RU is the mass of the idlers on bottom side (kg/m) q B is the belt mass (kg/m)

q G is the mass of the conveyed material (kg/m)

H is the lift (m)

FS1 are the special main resistances

FS2 are the special secondary resistances

SLOPE RESISTANCE




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where q G is the conveying mass (kg/m)

H is the lift (m)


TRANSITION CURVES (m)

where m' G is the length related mass of the conveyor belt (kg/m)


b is width (mm)

is troughing angle

l is idler length (mm)

B is belt width (mm)

Tx is drive traction

ELASTIC ELONGATION (ISO 9856)

where le is the elastic elongation (mm),

Io is the initial length of the test piece(mm).

PERMANENT (PLASTIC) ELONGATION (ISO 9856)

where lp is the permanent elongation (mm),

Io is the initial length of the test piece (mm).

For the drawing: FU is 10% force of the belt breaking strength multiplied by the test piece width (

FL is 2% force of the belt breaking strength multiplied by the test piece width (N

F is the test force range.

YOUNG'S MODULUS

where L is the amount by which the length changes (mm)




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F is the force

Ao is the original cross-sectional area

Lo is the original length (mm)

DRIVE POWER

where F are the resistances to motion

v is belt speed

RESISTANCES TO MOTION

-

where FH are the primary resistances (idlers, belt indentation, etc.)

FN are the secondary resistances (feeding, scrapers etc.)

FS are extraordinary resistances

FSt are gradient resistances

DOWNHILL FORCE

where FGH is the downhill force

FG is the weight force

Gravity acts straight down (= the weight of the conveyor belt) and the support force acts away from thesloped, there is a net force acting down the slope.See also Clamping Force

EYTELWEIN'S FORMULA

where e is 2,7183




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ROOT MEAN SQUARE

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formulas used in conveyor

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