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How to Calculate Motor Power and Torque for a Belt Conveyor (Preliminary Sizing Guide)

How to Calculate Motor Power and Torque for a Belt Conveyor (Preliminary Sizing Guide)

Free Body Diagram of Conveyor Belt Forces showing Friction and Gravity
Figure 1: The Free Body Diagram (FBD) is the first step in sizing a drive. It visualizes the formula: Te = Friction + Gravity.

The most expensive mistake a mechanical designer can make is undersizing the drive motor. If you guess, you risk burning out the winding or stalling the load during startup. If you oversize, you waste thousands of dollars on electricity and larger gearboxes.

This guide covers the physics of Effective Tension (Te), Torque, and Horsepower, and includes a real-world selection example and an Excel VBA script to automate your calculations (in both Imperial and SI units).

Method Selection: Quick Calc vs. CEMA

Method Best Used For Accuracy
Quick Calc (This Guide) Short transfer conveyors (< 15m / 50ft), Unit handling. Good for sizing. Typically over-estimates slightly (Safe).
CEMA / ISO 5048 Long overland bulk conveyors, High-speed systems. Precise. Accounts for belt sag, idler bearing drag, and skirting friction.
Engineering Scope Note:
The method below is for preliminary sizing. For high-inertia systems or frequent start/stop cycling, you must calculate Acceleration Torque (F=ma) separately or apply a generous Service Factor (typically 1.5 to 2.0).

1. The Physics: Calculate Effective Tension (Te)

Before you can pick a motor, you need to know how hard the belt pulls. This is called Effective Tension (Te). It is the sum of all resistance forces.

The Formula:

Te = Ffriction + Fgravity

A. Friction (Ffriction)

This is the force needed to slide the belt over the slider bed or rollers. Note that on an incline, friction applies only to the Normal Force (W × cosθ).

Ffriction = μ × Wtotal × cos(θ)
  • μ (Friction Coefficient):
    • 0.20 – 0.30: Rubber Belt on Steel Slider Bed.
    • 0.02 – 0.05: Belt on Precision Rollers (e.g., Interroll).
  • Wtotal: Total weight of the product + the belt itself.
    Imperial: Pounds-Force (lbf) | SI: Newtons (N)

B. Gravity (Fgravity)

If your conveyor is inclined, you must lift the load against gravity.

Fgravity = Wtotal × sin(θ)
Engineering Tip:
Don't have the friction data? Use a Digital Force Gauge to physically pull a sample box across your material. This "Empirical Testing" is always more accurate than a textbook guess.

2. The Drive Train: Gearbox Efficiency

Mechanical engineers often forget that the motor does not drive the belt directly. It goes through a gearbox. This means we must divide our required power by the Gearbox Efficiency (η).

  • 0.95: Helical / Bevel Gearbox (High Efficiency).
  • 0.60 - 0.70: Worm Gearbox (Low Efficiency - Beware of this!).

Note on Torque: While we calculate Power below, remember that the Gear Ratio multiplies motor torque but does not change the Power requirement (conservation of energy).

NEMA B Motor Torque Speed Curve showing Locked Rotor and Breakdown Torque
Figure 2: Understanding Starting Torque (Locked Rotor) is critical for inclined conveyors. If your load requires 200% torque to start, a standard motor (150%) will stall.

3. Calculate Running Power

We calculate power directly from tension and speed. This bypasses intermediate torque steps, reducing calculation errors.

Imperial (Horsepower):

HPrequired = (Te × Velocity) / (33000 × Î·gearbox)

*Where Te is in lbf and Velocity is in ft/min.

SI Metric (Kilowatts):

Power (kW) = (Te × Velocity) / (1000 × Î·gearbox)

*Where Te is in Newtons and Velocity is in m/s.

Note: Motor selection must also satisfy Starting and Pull-Up Torque requirements. Ideally, select a motor where the running power is 75-80% of rated power.

4. Real-World Selection Examples

Below are two examples of sizing the same conveyor: one in Imperial units and one in SI Metric.

4A. Imperial Calculation

  • Load (Wtotal): 500 lbs (Product + Belt)
  • Speed: 60 FPM
  • Incline: 10 Degrees
  • Friction (μ): 0.25 (Slider Bed)
  • Gearbox: Worm Gear (η = 0.70)

Step 1: Calculate Forces
Ffriction = 500 × cos(10°) × 0.25 = 123 lbf
Fgravity = 500 × sin(10°) = 87 lbf
Te = 123 + 87 = 210 lbf

Step 2: Calculate Power
HP = (210 lbf × 60 FPM) / (33000 × 0.70) = 0.54 HP

Step 3: Select Motor & Gear Ratio
Motor: The calculated requirement is 0.54 HP. Select the next NEMA size up: 0.75 HP or 1.0 HP.
Gear Ratio: Using a 4-pole motor (1750 RPM) and 6-inch drive pulley:
Target RPM = 38 RPM.
Ratio = 1750 / 38 ≈ 45:1.

4B. SI Metric Calculation

  • Load (Mass): 230 kg (Product + Belt)
  • Speed: 0.3 m/s
  • Incline: 10 Degrees
  • Friction (μ): 0.25
  • Gearbox: Worm Gear (η = 0.70)

Step 1: Calculate Forces (Newtons)
First, convert Mass to Weight: W = 230 kg × 9.81 m/s² = 2,256 N
Ffriction = 2,256 × cos(10°) × 0.25 = 555 N
Fgravity = 2,256 × sin(10°) = 392 N
Te = 555 + 392 = 947 N

Step 2: Calculate Power (kW)
Power = (947 N × 0.3 m/s) / (1000 × 0.70) = 0.41 kW

Step 3: Select Motor & Gear Ratio
Motor: The calculated requirement is 0.41 kW. Select the next standard IEC size: 0.55 kW.
Gear Ratio: Using a 4-pole motor (1450 RPM at 50Hz) and 150mm drive pulley:
Target RPM ≈ 38 RPM.
Ratio = 1450 / 38 ≈ 38:1 (Select standard 40:1).

5. Automated Excel VBA Calculation Tool

Why do this by hand every time? Below are two custom VBA functions (one for Imperial, one for SI Metric) that you can paste into Excel.
They use your preferred lowerCamelCase variable naming convention. 

' ==========================================
' OPTION 1: IMPERIAL UNITS (HP, lbf, ft/min)
' ==========================================
Function calculateConveyorRunningHP(totalLoadLbs As Double, frictionCoeff As Double, velocityFPM As Double, inclineDeg As Double, driveEfficiency As Double) As Double
    ' Inputs:
    ' totalLoadLbs   = Weight (lbf)
    ' frictionCoeff  = 0.25 (slider) or 0.05 (roller)
    ' velocityFPM    = Speed (ft/min)
    ' inclineDeg     = Angle (0 for horizontal)
    ' driveEfficiency= 0.95 (Helical) or 0.70 (Worm)
    
    Dim effectiveTension As Double
    Dim forceFriction As Double
    Dim forceGravity As Double
    Dim radians As Double
    
    radians = inclineDeg * (3.14159 / 180)
    
    forceFriction = (totalLoadLbs * Cos(radians)) * frictionCoeff
    forceGravity = totalLoadLbs * Sin(radians)
    effectiveTension = forceFriction + forceGravity
    
    ' Calculate HP: (Force * Velocity / 33000) / Efficiency
    calculateConveyorRunningHP = ((effectiveTension * velocityFPM) / 33000) / driveEfficiency
End Function

' ==========================================
' OPTION 2: SI METRIC UNITS (kW, Newtons, m/s)
' ==========================================
Function calculateConveyorRunningKW(totalLoadNewtons As Double, frictionCoeff As Double, velocityMPS As Double, inclineDeg As Double, driveEfficiency As Double) As Double
    ' Inputs:
    ' totalLoadNewtons = Weight (N) [Mass kg * 9.81]
    ' frictionCoeff    = 0.25 (slider) or 0.05 (roller)
    ' velocityMPS      = Speed (m/s)
    ' inclineDeg       = Angle (0 for horizontal)
    ' driveEfficiency  = 0.95 (Helical) or 0.70 (Worm)
    
    Dim effectiveTension As Double
    Dim forceFriction As Double
    Dim forceGravity As Double
    Dim radians As Double
    
    radians = inclineDeg * (3.14159 / 180)
    
    forceFriction = (totalLoadNewtons * Cos(radians)) * frictionCoeff
    forceGravity = totalLoadNewtons * Sin(radians)
    effectiveTension = forceFriction + forceGravity
    
    ' Calculate kW: (Force * Velocity / 1000) / Efficiency
    calculateConveyorRunningKW = ((effectiveTension * velocityMPS) / 1000) / driveEfficiency
End Function

How to use it:
1. Open Excel and press ALT + F11.
2. Insert a new Module and paste the code.
3. For Imperial: Type =calculateConveyorRunningHP(500, 0.25, 60, 10, 0.70)
4. For Metric: Type =calculateConveyorRunningKW(2256, 0.25, 0.3, 10, 0.70)

Conclusion

Sizing a motor is not a guessing game. By accounting for Incline Gravity and Gearbox Efficiency, you ensure your design will work in the real world.
Once you have your motor selected, the next step is controlling it. Check out our Engineer's Guide to VFDs for speed control tips.

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