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Conveyor Belt Tension Calculation: T1, T2 & Take-Up Design

In any friction-driven conveyor system, the most fundamental concept is the relationship between the Tight Side Tension (T 1 ) and the Slack Side Tension (T 2 ) . If you get this ratio wrong, your drive pulley will slip, your belt will wear out prematurely, or your take-up counterweight will be too light to maintain traction. In this guide, we will use CEMA standard calculations to determine the correct tensions and take-up weight. Table of Contents 1. The Basics: T1 vs T2 2. Euler’s Equation (The Grip Formula) 3. Worked Example: Calculating Tensions 4. Take-Up Units: Gravity vs Screw 5. Common Failure Modes Advertisement 1. The Basics: T1 vs T2 Imagine a conveyor belt running over a drive pulley. The motor pulls the belt, creating a tension differential: T 1 (Tight Side): The tension pulling the loaded belt toward the drive pulley. This is the highest tension point in the system. ...
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Conveyor Belt Tension Calculation: T1, T2 & Take-Up Design

In any friction-driven conveyor system, the most fundamental concept is the relationship between the Tight Side Tension (T1) and the Slack Side Tension (T2).

If you get this ratio wrong, your drive pulley will slip, your belt will wear out prematurely, or your take-up counterweight will be too light to maintain traction. In this guide, we will use CEMA standard calculations to determine the correct tensions and take-up weight.

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1. The Basics: T1 vs T2

Imagine a conveyor belt running over a drive pulley. The motor pulls the belt, creating a tension differential:

  • T1 (Tight Side): The tension pulling the loaded belt toward the drive pulley. This is the highest tension point in the system.
  • T2 (Slack Side): The tension leaving the drive pulley. This tension is maintained by the Take-Up system to prevent slippage.

The difference between these two is the Effective Pull (Te), which does the actual work of moving the load.

The Fundamental Link:

Te = T1 - T2

(Recall that we calculated Te in our previous guide on Conveyor Motor Sizing.)
Engineering diagram of conveyor belt drive pulley showing T1 entering and T2 leaving
Figure 1: The drive arrangement and friction determine the relationship between T1 and T2.

2. Euler’s Equation (The Grip Formula)

How much tension do you need on the slack side (T2) to prevent the pulley from just spinning inside the belt? This is governed by Euler’s Capstan Equation:

T1 / T2 ≤ eμθ

Where:

  • e: Base of natural logarithms (2.718).
  • μ (Mu): Coefficient of friction between belt and pulley (typically 0.25 bare, 0.35 lagged).
  • θ (Theta): Angle of wrap in radians (e.g., 180° = 3.14 radians).

To simplify this for industrial design, we often use a Drive Factor (Cw).

The drive factor (Cw) is a practical simplification derived from Euler’s equation and published CEMA design tables.

T2 = Te × Cw

Common Drive Factors (Cw)

Drive Arrangement Wrap Angle Lagging Type Drive Factor (Cw)
Single Drive 180° Bare Steel 0.84
Single Drive 180° Rubber Lagged 0.50
Single Drive (Snubbed) 210° Rubber Lagged 0.38
Dual Drive 380° Rubber Lagged 0.11
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3. Worked Example: Calculating Tensions

Let's continue with the example from our Motor Sizing Guide.

📝 Engineering Scenario

  • Effective Pull (Te): 3,200 N
  • Drive Type: Single Pulley, Rubber Lagged (180° Wrap)
  • Drive Factor (Cw): 0.50 (from table above)

Step 1: Calculate Slack Side Tension (T2)
T2 = Te × Cw
T2 = 3200 N × 0.50 = 1,600 N

Step 2: Calculate Tight Side Tension (T1)
T1 = Te + T2
T1 = 3200 + 1600 = 4,800 N

Result: Your belt must be rated for at least 4,800 N of working tension.

4. Take-Up Units: Gravity vs Screw

The T2 tension doesn't just appear by magic; it must be applied by a Take-Up Unit. There are two main types used in industry.

1. Gravity Take-Up (Constant Tension)

Best for long conveyors. A counterweight hangs freely, ensuring T2 remains constant even as the belt stretches over time.

Rule of Thumb: The counterweight force is typically set to 2 × T2 to account for both belt strands.

Note: Counterweight mass must be calculated from force using gravity (Mass = Force / 9.81).

2. Screw Take-Up (Fixed Distance)

Best for short conveyors (under 50m). The operator manually tightens a screw to set the tension. The downside is that as the belt stretches, tension drops, leading to slippage.

Industrial conveyor screw take-up unit bearing housing
Figure 2: A manual Screw Take-Up is simple but requires regular adjustment.

5. Common Failure Modes

Diagnosing belt issues often comes down to analyzing the T1/T2 relationship.

  • Slippage at Startup: Usually caused by insufficient T2 (Take-up weight too light) or worn lagging (low friction coefficient μ).
  • Glazing on Drive Pulley: A shiny, smooth pulley surface indicates chronic slippage. Apply Belt Dressing temporarily, but re-lagging is the real fix.
  • Bearing Failure: Often caused by over-tensioning a screw take-up to compensate for a lack of wrap angle.
About the Author:
This article is written by a mechanical design engineer specializing in material handling, conveyor system design, and power transmission analysis.

As an Amazon Associate, I earn from qualifying purchases.

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