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Calculation No.: Calc-001
Revision: A
Description:
Created By: Engineer Name
Project: Project Name
Project No.: P001
Client: Client Name

Input Parameters

The following design parameters were considered for this belt conveyor calculation (ISO 5048 / DIN 22101):
Parameter Symbol Value Notes
Design Capacity Q 200 t/h Required throughput
Bulk Density ρ 1.6 kkg/m³ General aggregate
Conveyor Length L 120 m Centre-to-centre
Inclination Angle φ 0 ° Positive = uphill
Belt Speed v 3 m/s
Troughing Angle θ 35 ° Idler troughing
Rolling Resistance Coefficient f 0.02 DIN 22101 Table
Belt-Pulley Friction μ 300 m Lagged drum
Drive Drum Diameter Ddrum 500 mm
Wrap Angle α 210 ° Belt on drive drum
Motor Speed nmotor 1.45 krpm Nominal
Service Factor SF 1.3
Gearbox Efficiency ηgb 0.95
Coupling Efficiency ηc 0.99
Motor Efficiency ηm 0.95
Impact Factor Kimp 1

Calculations

All calculations performed in accordance with ISO 5048, DIN 22101, and CEMA standards.

Step 1: Required Cross-Sectional Area

From capacity formula: Q = \u03c1 \u00d7 v \u00d7 A \u00d7 3600, where Q is in t/h, \u03c1 in t/m\u00b3, v in m/s, A in m\u00b2.

Formula: $$ \begin{align*} A &= \frac{Q}{\rho \cdot v \cdot 3600} \\[0.1em] \\ &= \frac{200}{1.6 \cdot 3 \cdot 3600} \\[0.1em] \\ &= 0.0116 \; \text{m}^2 \end{align*} $$

Step 2: Belt Width Selection

K(35°) = 0.197. Selected standard width: 300 mm.

Formula: $$ \begin{align*} B &= \sqrt{\frac{A}{K(\theta)}} \\[0.1em] \\ &= \sqrt{\frac{0.0116}{0.197}} \\[0.1em] \\ &= 0.3 \; \text{m} \end{align*} $$

Actual area A = K \u00d7 B\u00b2 = 0.017730 m\u00b2.

Formula: $$ \begin{align*} Q_{\text{actual}} &= \rho \cdot v \cdot A_{\text{actual}} \cdot 3600 \\[0.1em] \\ &= 1.6 \cdot 3 \cdot 0.0177 \cdot 3600 \\[0.1em] \\ &= 306 \; \text{t/h} \end{align*} $$

Step 3: Linear Masses

ISO 5048 / DIN 22101: material mass per metre at the design throughput (not a full trough).

Formula: $$ \begin{align*} q_G &= \frac{Q}{3.6 \cdot v} \\[0.1em] \\ &= \frac{200}{3.6 \times 3} \\[0.1em] \\ &= 18.5 \; \text{kg/m} \end{align*} $$

Belt mass estimated from width (≈15 kg/m per m width). Idler rotating mass (carry and return) estimated as set mass / pitch for typical 500 mm sets (Rulmeca Tab. 11; 1.2 m carrying, 3.0 m return pitch).

Formula: $$ \begin{align*} q_B &= 4.5 \; \text{kg/m}, \quad q_{RO} = 4.25 \; \text{kg/m}, \quad q_{RU} = 1.23 \; \text{kg/m} \end{align*} $$

Step 4: Motional Resistances

Idler rotation, belt indentation and flexing on both strands (ISO 5048 / DIN 22101).

Formula: $$ \begin{align*} F_H &= f \cdot L \cdot g \cdot [q_{RO} + q_{RU} + (2 q_B + q_G) \cos\delta] \\[0.1em] \\ &= 0.02 \times 120 \times 9.81 \times [4.25 + 1.23 + (2 \times 4.5 + 18.5) \cos(0^\circ)] \\[0.1em] \\ &= 777 \; \text{N} \end{align*} $$

C = 1.700 for L = 120 m (DIN 22101 Table 5 from 80 m; shorter conveyors approximate). Covers feed acceleration, feed skirts, pulley bearings and belt bending.

Formula: $$ \begin{align*} F_N &= (C - 1) \cdot F_H \\[0.1em] \\ &= (1.7 - 1) \times 777 \\[0.1em] \\ &= 544 \; \text{N} \end{align*} $$

Step 5: Total Traction Force

Base force (before impact factor): 1320.89 N. Drive mode loaded: motoring (a negative force means the belt overhauls the drive).

Formula: $$ \begin{align*} F_{\text{total}} &= (F_H + F_N + F_{St} + F_S) \times K_{\text{imp}} \\[0.1em] \\ &= (777 + 544 + 0 + 0) \times 1 \\[0.1em] \\ &= 1321 \; \text{N} \end{align*} $$

No material on the belt: no material main-resistance or lift term and no loading impact (CEMA 7th ed. / DIN 22101: check the empty and loaded operating cases; part-loaded belts lie between the two on a single slope). Drive mode empty: motoring.

Formula: $$ \begin{align*} F_{\text{empty}} &= C \cdot f \cdot L \cdot g \cdot [q_{RO} + q_{RU} + 2 q_B \cos\delta] + F_S \\[0.1em] \\ &= 341 + 239 + 0 \\[0.1em] \\ &= 580 \; \text{N} \end{align*} $$

Governed by the loaded belt. Basis for belt tensions, drum torque and take-up.

Formula: $$ \begin{align*} F_{\text{design}} &= \max(|F_{\text{total}}|, |F_{\text{empty}}|) \\[0.1em] \\ &= 1321 \; \text{N} \end{align*} $$

Step 6: Drive Power Calculation

Formula: $$ \begin{align*} P_{\text{drum}} &= F_{\text{total}} \times v \\[0.1em] \\ &= 1321 \times 3 \\[0.1em] \\ &= 3963 \; \text{W} \\[0.1em] \\ &= 3.96 \; \text{kW} \end{align*} $$

Motoring.

Formula: $$ \begin{align*} P_{\text{motor,loaded}} &= \frac{P \times SF}{\eta_{\text{gb}} \eta_{\text{c}} \eta_{\text{m}}} \\[0.1em] \\ &= \frac{3.96 \times 1.3}{0.893} \\[0.1em] \\ &= 5.77 \; \text{kW} \end{align*} $$
Formula: $$ \begin{align*} P_{\text{empty}} &= F_{\text{empty}} \times v \\[0.1em] \\ &= 580 \times 3 / 1000 \\[0.1em] \\ &= 1.74 \; \text{kW} \end{align*} $$

Motoring.

Formula: $$ \begin{align*} P_{\text{motor,empty}} &= \frac{P \times SF}{\eta_{\text{gb}} \eta_{\text{c}} \eta_{\text{m}}} \\[0.1em] \\ &= \frac{1.74 \times 1.3}{0.893} \\[0.1em] \\ &= 2.53 \; \text{kW} \end{align*} $$

Combined efficiency: 0.8935. Governed by the loaded belt. Selected standard motor: 7.5 kW.

Formula: $$ \begin{align*} P_{\text{motor}} &= \max(P_{\text{motor,loaded}}, P_{\text{motor,empty}}) \\[0.1em] \\ &= 5.77 \; \text{kW} \end{align*} $$

Step 7: Belt Tensions (Eytelwein Equation)

Eytelwein ratio: e^(\u03bc\u00b7\u03b1) = 3.0028, where \u03bc = 0.3 and \u03b1 = 210\u00b0.

Formula: $$ \begin{align*} T_2 &= \frac{F_{\text{design}}}{e^{\mu \cdot \alpha} - 1} \\[0.1em] \\ &= \frac{1321}{3 - 1} \\[0.1em] \\ &= 660 \; \text{N} \end{align*} $$

Tension per mm width: 6.60 N/mm.

Formula: $$ \begin{align*} T_1 &= T_2 + F_{\text{design}} \\[0.1em] \\ &= 660 + 1321 \\[0.1em] \\ &= 1980 \; \text{N} \end{align*} $$

Step 8: Drum Torque and Gearbox Ratio

Formula: $$ \begin{align*} T_{\text{drum}} &= F_{\text{design}} \times \frac{D_{\text{drum}}}{2} \\[0.1em] \\ &= 1321 \times \frac{0.5}{2} \\[0.1em] \\ &= 330 \; \text{N{\cdot}m} \end{align*} $$
Formula: $$ \begin{align*} n_{\text{drum}} &= \frac{v}{\pi \cdot D_{\text{drum}}} \times 60 \\[0.1em] \\ &= \frac{3}{\pi \times 0.5} \times 60 \\[0.1em] \\ &= 115 \; \text{rpm} \end{align*} $$
Formula: $$ \begin{align*} GR &= \frac{n_{\text{motor}}}{n_{\text{drum}}} \\[0.1em] \\ &= \frac{1450}{115} \\[0.1em] \\ &= 12.7 \text{:1} \end{align*} $$

Take-Up Requirements

Take-up travel: 3.000 m (2% thermal + 0.5% elastic elongation). Take-up force: 989.27 N (1.5 x T2, design load case). Recommended type: Gravity.

Belt Conveyor Profile Diagram

Belt Conveyor Profile Tail Head (Drive) M T1 T2 L = 120.0 m Capacity: 200.0 t/h Belt Speed: 3.00 m/s Belt Width: 300 mm Motor: 7.50 kW T1: 1980 N T2: 660 N

The profile diagram shows the conveyor layout with head (drive) and tail pulleys, belt tensions T1 and T2, inclination angle, and key design parameters.

Figure 1: Belt conveyor profile with key dimensions and tensions

Summary of Results

Below is the summary of calculated values for ease of reference:
Parameter Symbol Value Notes
Selected Belt Width B 300 mm Standard width
Actual Capacity Qactual 306 t/h Margin: 53.2%
Total Traction Force Ftotal 1.32 kN Including impact factor
Empty Belt Traction Force Fempty 580 N Drive mode: motoring
Power at Drum Pdrum 3.96 kW Loaded; drive mode: motoring
Regenerative Power Pregen 0 kW Not regenerative
Selected Motor Power Pmotor 7.5 kW Loading: 76.9%; loaded belt governs
Tight Side Tension T1 1.98 kN
Slack Side Tension T2 660 N
Drum Torque Tdrum 330 N·m
Drum Speed ndrum 115 rpm
Gearbox Ratio GR 12.7 :1

Recommendations

- Idler rotating mass (carry and return) estimated from typical 500 mm idler sets at 1.2 m carrying / 3 m return pitch: enter the selected idlers' values. - Use VFD for soft start and torque limiting. - Install belt speed sensor and load cells for monitoring. - Use impact beds at loading points and proper skirtboard seals. - Install belt misalignment switches and emergency pull cords.

Approval:

This calculation has been reviewed and approved by:
Created By
Engineer Name
Date: ..........................
Checked
By: .............................
Date: ..........................
Approved
By: .............................
Date: ..........................
Client Approved
By: .............................
Date: ..........................

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