For engineers who already know the math—but still lose projects. For the last few years, I’ve been sharing technical guides here on Mechanical Design Handbook —how to size a motor, how to calculate fits, and (as you recently read) how to choose between timing belts and ball screws. But after 25 years in industrial automation, I realized something uncomfortable: Projects rarely fail because the math was wrong. They fail because: The client changed the scope three times in one week. A critical vendor lied about a shipping date (and no one verified it). The installation technician couldn’t fit a wrench into the gap we designed. University taught us the physics. It didn’t teach us the reality. That gap is why I wrote my new book, The Sheet Mechanic . This is not a textbook. It is a field manual for the messy, political, and chaotic space between the CAD model and the factory floor. It captures the systems I’ve used to survive industrial projec...
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.
Table of Contents
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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.)
Te = T1 - T2
(Recall that we calculated Te in our previous guide on Conveyor Motor Sizing.)
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.
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.
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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