(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) 

εelast 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 here 
TENSION FORCE 
The modulus of elasticity of a material can be used to calculate the tension force it exerts under a specific extension: 

where 
T is the tension force 

λ is the modulus of elasticity 

A is the crosssectional 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: 

where 
FU 
Minimum peripheral force, 

C 
Coefficient C, 

f 
artificial friction coefficient, 

L 
conveyor length (m), 

g 
acceleration (m/s²), 

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

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

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

qG 
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. 
TAKEUP LENGTH 

where

SSp is takeup length (m) 

L is centre distance (m) 

ε 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 longdistance conveyors, dynamic startup calculations may be required, because not all elements are set in motion simultaneously, due to the elastic properties of the conveyor belt. 
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 (as you know, the speed of chemical reactions increase with rising temperature). 
STRESS IN RUBBER 

where

σ is the stress 

v is the period of strain oscillation 

δ is the phase lag between stress and strain 
STRAIN IN RUBBER 

where

ε is the strain 

ω is the period of strain oscillation 

t is time 


where 
E' is the storage modulus 

σ is the stress 

ε is the strain 

δ is the phase lag between stress and strain 
INTERNAL FRICTION 

where 
tan δ is the internal friction of a rubber 

E' is the storage modulus (N/mm²) 

E'' is the loss modulus (N/mm²) 
The tan d is sometimes used to determine the indentation loss of a conveyor belt cover (cf. Energy Saving Belts). E' and E'' should be as low as possible. However, there are a number of misconceptions related to specifiying E' and E''. 
LENGTH RELATED MASS FLOW (m³/h) 

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

lvth 
is the theoretical volume flow (m³/h), 

ρ 
is the bulk density of the conveyed material (t/m³), 

φSt 
is the coefficient for determination of the volume flow. 


where 
ΡB0 
is the braking factor related to the rated torque of all drive motors, 

ηges 
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 (N). 
MINIMUM BELT TENSION FOR BELT SAG LIMITATION (top side, loaded) 

where 
g is gravity (9,81 m/s²) 

m'Li is the mass of the conveyed material, uniformly distributed across a section of the conveyor (kg/m) 

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

IRo is the idler spacing in top run (m) 

hrel 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/s²) 

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

IRu 
is the idler spacing in bottom run (m) 

hrel 
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/s²) 

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) 

δ is the even inclination of the conveyor (°) 
MAXWELL MODEL 

where 
ε is strain 

σ is stress 
VOIGT MODEL 

where 
η is dynamic viscosity 

τ is total stress 

γ 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 

Crr is the dimensionless rolling resistance coefficient 

Nf is the normal force 
or 


where 
E' is the storage modulus (N/mm²) 

tanδ is the internal friction 
MINIMUM TRANSITION LENGTH (m) 

where 
B is belt width (mm) 

λ 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 
PTr 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/s²) 

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

qRU is the mass of the idlers on bottom side (kg/m) 

qB is the belt mass (kg/m) 

qG 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 


where 
qG is the conveying mass (kg/m) 

H is the lift (m) 

g is acceleration (m/s²) 


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

g is acceleration (m/s²) 

b is width (mm) 

δ is troughing angle 

l is idler length (mm) 

B is belt width (mm) 

Tx is drive traction 
ELASTIC ELONGATION (ISO 9856) 

where 
Δle is the elastic elongation (mm), 

Io is the initial length of the test piece(mm). 
PERMANENT (PLASTIC) ELONGATION (ISO 9856) 



where 
Δ 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 (N), 

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

ΔF is the test force range. 


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

F is the force 

Ao is the original crosssectional area 

Lo is the original length (mm) 


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 


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 the conveyor. Since the conveyor is sloped, there is a net force acting down the slope.
See also Clamping Force 


where 
e is 2,7183 

ROOT MEAN SQUARE 



