DESIGN PROCEDURE Calculations for Belt Width: Width of belt is depends upon the lump size which depends upon the following factors, 1. Volume of material to be conveyed 2. Angle of repose of material to be conveyed 3. Density of material to be conveyed 4. Troughing angle of belt 5. Maximum allowable belt speed Let, Mass of material conveyed per unit length of belt = Volume to be conveyed per meter length of belt, ∴V= ∴V= Area of cross section of lump on troughed belt of width ‘w’ is shown in figure. Hence area of cross section of lump can be calculated as, A = ½(0.6w + 0.6w + 2 × 0.2w cosӨ) × 0.2w sinӨ + ½(0.6w + 0.4w cosӨ) × ½(0.6w + 0.4w cosӨ) cotФ ∴Volume/ meter length of belt (V) = A × 1 This must be equal to volume to be conveyed per meter length of belt,
∴
= ½(0.6w + 0.6w + 2 × 0.2w cosӨ) × 0.2w sinӨ + ½(0.6w + 0.4w cosӨ) × ½(0.6w + 0.4w cosӨ) cotФ
Knowing
, Ө, Ф, belt width w can be calculated and selected from standard range available.
Calculations for Motor Power: Work is required to raise the material against gravity and to overcome the rolling resistance between the idler rollers and belt. Resistance to move the material horizontally, =
× g (m +
)
Where, = coefficient of rolling resistance (for this application it lies between 0.15 to 0.3) g
= gravitational acceleration
m
= total load over whole length =
length of conveyor
= mass of belt = mass of belt per unit length
length of belt
Resistance to raise the material against gravity, = g × m × L × sinα Where, g
= Gravitational acceleration
m
= Total load over whole length
L
= Total length of conveyer
α
= Angle of elevation
Maximum resistance, =( + For lagged pulley
)× is 1.3………. from table
Motor power: Power required (P) = total force × speed of belt P=
×v
Motor Power, = Where, = transmission efficiency
Calculations for Minimum Pulley Diameter: The minimum drive pulley diameter
can be calculated as,
= Where, = 25…………………. from table β = Angle of contact The next standard diameter of pulley available in the market should be used.
The length of driving pulley rollers should be slightly more than that of width of belt. The standard clearances on both sides of belt for different belt widths have been given in the table.
Rotational speed of roller: Rotational speed of the roller is the function of diameter of roller and belt speed. Rotational speed of pulley (N) can be given as, N= Calculations for Belt Selection: Drive side tensions
and
are related by,
= Total force ∴
=
where, = Tight side Tension = Slack side Tension Also,
= Where, µ = Coefficient of friction between belt and pulley β = Angle of Wrap Now, Belt Stress =
= Belt safety factor = The recommended maximum belt tension (RMBT) is provided by the belt manufacturer for the belts of different widths. The belt safety factor should be more than one, if not, select next belt of higher ply rating. Calculations for Design of Drive Shaft: Motor Torque, = Where, = Motor Power = Motor Speed Gear Box Reduction Ratio, G=
G= Torque at drive shaft, = Motor torque =
gear box reduction
G
According to maximum shear stress theory for shaft design, =
∴d= where, d = diameter of drive shaft
= maximum shear stress = torque at drive shaft = bending moment The next standard diameter of shaft should be used. Selection of Bearings: The general equation for equivalent dynamic load is given by, =X
+Y
where, = equivalent dynamic load
= axial or thrust load (N) In our case the load is pure radial and there no axial load or thrust hence, =
=(
)
The dynamic load capacity is given by, = where, = dynamic load capacity (N)
= rated bearing life (in million revolution) p = 3(for all ball bearings) p = 10/3 (for roller bearings) Bearing life can also be given in working hours. The relationship between life in million revolutions and life in the working hours is given by, = where, = rated bearing life (hours) n = speed of rotation (rpm) According to the value of dynamic load capacity ‘c’, select the suitable bearing from the manufacturer’s catalog for the given shaft diameter.
