Please scroll for equations keywords Arrhenius equation Belt elongation Braking factor Coefficient C Coefficient of friction Downhill force Elastic elongation Elongation Eytelwein's formula Internal friction Length mass flow Length related mass flow Maxwell model Minimum belt tension bottom run Minimum belt tension top run Minimum peripheral force Minimum transition length Modulus of elasticity Peripheral force Permanent elongation Reference elongation Rolling resistance Slope resistance Strain in rubber Stress in rubber Storage modulus Take-up length Tension force Transition curves Turnover length Voigt model Young's modulus (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 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:
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.

TAKE-UP LENGTH
where	SSp is take-up 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 long-distance conveyors, dynamic start-up 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

STORAGE MODULUS
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.

BRAKING FACTOR
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

SLOPE RESISTANCE
where	qG is the conveying mass (kg/m)
	H is the lift (m)
	g is acceleration (m/s²)

TRANSITION CURVES (m)
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.

YOUNG'S MODULUS
where	ΔL is the amount by which the length changes (mm)
	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 the conveyor. Since the conveyor is sloped, there is a net force acting down the slope. See also Clamping Force

EYTELWEIN'S FORMULA
where	e is 2,7183

ROOT MEAN SQUARE

Please see here for reference!