Calculations

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Calculations

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Belt conveyor capacity

Theoretical mass flow rate of a belt conveyor with known area and material density.

Mass flow rate

$$ Q_{conv_m} = {{A \over 10 ^ 6} \cdot v_{conv} \cdot 3600 \cdot \rho_{bm}} \; \; , {{kg \over h}} $$

Base of triangle

Calculates base of isosceles triangle for given area and base angle.

Base length

$$ c_{isos} = {\sqrt{ {( 2 \cdot A ) \over \tan( \alpha_{rad} )} }} \; \; , {mm} $$

Area of triangle

Calculates area of isosceles triangle by given base and base angle

Area

$$ A_{isos_{\alpha}} = {{c ^ 2 \over 2} \cdot \tan( \alpha_{rad} )} \; \; , {mm ^ 2} $$

Angle

Convert angle from degrees to radians

Angle in radians

$$ \alpha_{rad} = {\alpha_{deg} \cdot {\pi \over 180}} \; \; , {rad} $$

Electrical motor power

Electrical motor power from nominal torque and rotational speed.

Motor power

$$ P_n = {{( T_n \cdot n_n ) \over 9550}} \; \; , {kW} $$

Gearbox reduction ratio

Reduction ratio of 4 stage gearbox

Four stage gearbox ratio

$$ i_{gb4} = {i_{gr1} \cdot i_{gr2} \cdot i_{gr3} \cdot i_{gr4}} \; \; $$

Gear reduction ratio

Reduction ratio of two gear wheels using number of teeth

Fourth stage ratio

$$ i_{gr4} = {z_8 \over z_7} \; \; $$

Gear reduction ratio

Reduction ratio of two gear wheels using number of teeth

Second stage ratio

$$ i_{gr2} = {z_4 \over z_3} \; \; $$

Gear reduction ratio

Reduction ratio of two gear wheels using number of teeth

Third stage ratio

$$ i_{gr3} = {z_6 \over z_5} \; \; $$

Gearbox reduction ratio

Reduction ratio of 3 stage gearbox

Three stage gearbox ratio

$$ i_{gb3} = {i_{gr1} \cdot i_{gr2} \cdot i_{gr3}} \; \; $$

Travel drive gearbox ratio

Calculate travel drive reduction ratio for known traveling velocity in m/min and wheel diameter in m.

Gearbox ratio

$$ n_{gb_{req}} = {{n_{motor} \over n_{wheel}}} \; \; $$

Travel wheel revolutions

Calculate travel wheel rpm from linear speed in m/min.

$$ n_{wheel} = {{v_{mm} \over \left({ \pi \cdot D_{wheel} }\right)}} \; \; , {rpm} $$

Velocity

Traveling velocity in m/min.

Traveling velocity

$$ v_{mm} = {10} \; \; , {{m \over min}} $$

Efficiency

Efficiency measured in %.

$$ \eta = {90} \; \; , {\%} $$

Velocity

Traveling velocity in m/s.

Traveling velocity

$$ v_{ms} = {{v_{mm} \over 60}} \; \; , {{m \over s}} $$

Total travel power required

Combined bower for travel and acceleration.

Total power

$$ P_{tr} = {{( P_{v} + P_{a} ) \over T_{r}}} \; \; , {kW} $$

Motor power requirement

Calculate motor power required to accelerate.

Power required

$$ P_{a} = {{( C \cdot v_{ms} ^ 2 ) \over \left({ \eta \cdot t_a }\right)}} \; \; , {kW} $$

Motor power requirement

Calculate motor power required to maintain traveling speed.

Power required

$$ P_{v} = {{( C \cdot g \cdot v_{ms} \cdot w_t ) \over \eta}} \; \; , {kW} $$

Capacity

Mass to be lifted or travel.

$$ C = {10000} \; \; , {kg} $$

Horizontal reaction in support

Horizontal reaction force in support due to point load when support is at an angle

Horizontal reaction

$$ Ah_{angled} = {P \cdot \tan( \alpha_{rad} )} \; \; , {N} $$