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...
The Failure Scenario: You specify a 50 HP AC induction motor for an industrial shredder. To achieve the required reduction ratio, you mount a very small diameter roller chain sprocket directly onto the motor shaft. Six months later, the solid steel motor shaft snaps completely off, flush with the bearing housing.
The Cause: You exceeded the motor's maximum Overhung Load (OHL). The motor was perfectly sized for the torsional load (the twisting force), but the mechanical geometry created a massive radial load (a bending force) that destroyed the shaft through high-cycle fatigue.
Power transmission is not just about matching horsepower. The physical connection method (chains, V-belts, or gears) drastically alters the stress applied to the motor bearings. This guide explains the physics of OHL, how to calculate it, and how to engineer your way out of radial failure.
Table of Contents
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1. The Physics: Torsion vs. Bending Moment
When a motor spins a load, the shaft experiences two completely different types of stress simultaneously:
- Torsional Stress: The twisting force required to turn the load. This is a function of Horsepower and RPM.
- Radial Bending Stress: The side-pulling force exerted by the belt or chain pulling against the shaft. This acts as a cantilevered beam.
An inline flexible coupling (like a jaw or grid coupling) transfers pure torsion. However, any time you mount a pulley, sheave, or sprocket on a shaft, you introduce a radial force. Because this component "hangs over" the motor bearing, it creates an Overhung Load. A small radial force applied far away from the bearing acts as a powerful lever, creating a massive bending moment.
Figure 1: The OHL creates a bending moment. The farther the sprocket is from the bearing (Distance X), the greater the bending stress on the shaft base.
2. The OHL Calculation Formula
Motor and gearbox manufacturers list a "Maximum Allowable OHL" in their catalogs. If you exceed this number, you void the warranty and guarantee failure. You must calculate your actual OHL to compare against their limit.
Imperial Calculation:
OHL (lbs) = (126,050 × HP × K) / (RPM × Pitch Diameter in inches)
*Note: 126,050 is derived from the standard torque constant (63,025) doubled to convert torque on a radius into tangential force on a diameter.
Metric Calculation:
OHL (Newtons) = (19,100,000 × kW × K) / (RPM × Pitch Diameter in mm)
OHL (lbs) = (126,050 × HP × K) / (RPM × Pitch Diameter in inches)
*Note: 126,050 is derived from the standard torque constant (63,025) doubled to convert torque on a radius into tangential force on a diameter.
Metric Calculation:
OHL (Newtons) = (19,100,000 × kW × K) / (RPM × Pitch Diameter in mm)
Engineering Reality Check: Most NEMA and IEC frame motors list their maximum allowable OHL at a specific distance from the shaft shoulder (typically 1 inch or 25mm). If your sprocket sits further out, the bending moment increases, and the allowable OHL must be derated. Always verify the manufacturer's catalog conditions.
Where:
- HP: Motor Horsepower
- RPM: Speed of the shaft
- Pitch Diameter (inches): The effective diameter of your sprocket, gear, or sheave.
- K (Load Factor): A multiplier based on the transmission type.
The "Small Sprocket" Trap
Look at the denominator of the equation: Pitch Diameter. Because diameter is in the denominator, decreasing the size of the sprocket increases the Overhung Load exponentially. A 2-inch sprocket exerts twice the side-loading force on the motor bearings as a 4-inch sprocket transmitting the exact same horsepower.
3. The Load Connection Factor (K)
Not all drive components pull on the shaft equally. A roller chain relies entirely on mechanical engagement (teeth), so it requires very little pre-tension. A flat belt relies entirely on friction, so it must be stretched tightly across the pulleys to prevent slipping, creating a massive static radial load even when the motor is turned off.
| Drive Connection Type | Load Factor (K) | Physics Rationale |
|---|---|---|
| Chain Drive (Roller Chain) | 1.00 | Positive engagement; zero static pre-tension required. |
| Gear Drive (Spur/Helical) | 1.25 | Pressure angle forces teeth apart, adding radial thrust. |
| V-Belt Drive | 1.50 | Requires moderate static pre-tension to wedge into the groove. |
| Flat Belt Drive | 2.50 | Requires extreme static tension to maintain surface friction. |
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4. Failure Modes: Shaft Fatigue & Bearing Spalling
When OHL limits are exceeded, the system fails in one of two distinct ways:
1. Bearing Spalling (Flaking)
The motor's drive-end bearing takes the brunt of the radial load. The Hertzian contact stress between the ball bearings and the raceway becomes too high. The microscopic layer of lubrication collapses, and steel grinds on steel. This causes "spalling"—where flakes of steel break off the raceway, leading to a catastrophic seizure.
2. Shaft Fatigue Fracture
As the motor spins, the bending moment forces the shaft to flex downward. After 180 degrees of rotation, the top of the shaft is now on the bottom, flexing in the opposite direction. At 1750 RPM, the shaft is being bent back and forth millions of times per day. This causes micro-cracks to form at the stress concentrator (usually the step where the shaft meets the bearing). The crack propagates inward until the shaft suddenly snaps, leaving a classic "beach mark" pattern on the broken face.
Figure 2: A snapped shaft caused by high-cycle fatigue. The Overhung Load created a continuous bending moment that propagated a crack through the steel.
5. Engineering Solutions: Fixing High OHL
If your calculated OHL exceeds the motor manufacturer's limit, you must alter the mechanical architecture. Do not simply specify a bigger motor.
Design Mitigation Strategies:
1. Increase Pitch Diameter: Swap a 3-inch sheave for a 6-inch sheave (and adjust the driven sheave to maintain the ratio). This instantly cuts OHL in half.
2. Change Transmission Type: Switch from a Flat Belt (K=2.5) to a Roller Chain (K=1.0) to eliminate pre-tension radial loads.
3. Mount Closer to the Bearing: Slide the sprocket as far down the shaft as possible. Decreasing the lever arm distance drastically reduces the bending moment.
4. Add an Outboard Bearing: Support the free end of the motor shaft with a pillow block bearing. This changes the physics from a "cantilevered beam" to a "simply supported beam," nearly eliminating radial deflection.
1. Increase Pitch Diameter: Swap a 3-inch sheave for a 6-inch sheave (and adjust the driven sheave to maintain the ratio). This instantly cuts OHL in half.
2. Change Transmission Type: Switch from a Flat Belt (K=2.5) to a Roller Chain (K=1.0) to eliminate pre-tension radial loads.
3. Mount Closer to the Bearing: Slide the sprocket as far down the shaft as possible. Decreasing the lever arm distance drastically reduces the bending moment.
4. Add an Outboard Bearing: Support the free end of the motor shaft with a pillow block bearing. This changes the physics from a "cantilevered beam" to a "simply supported beam," nearly eliminating radial deflection.
⚙️ Master Heavy Power Transmission
Designing industrial drive systems requires strict management of torque, inertia, and electrical limits. Explore our full engineering series:
- Shaft Loading: Overhung Load (OHL) Motor Shaft Calculations
- Gearbox Selection: Worm Gear vs Planetary Gearbox Efficiency
- Torque Limits: Ball Detent Torque Limiters & Overload Clutches
- Tension Dynamics: Conveyor Belt Tension Calculation (T1/T2)
You calculated the bending moment. Can you bend the project schedule?
The Sheet Mechanic is the field manual for the chaotic space between the CAD model and the factory floor. Learn how to manage vendors, defend your designs, and prevent downstream project failures.
About the Author:
This article is written by a mechanical design engineer with over 25 years of experience in industrial automation, material handling, and power transmission specification.
This article is written by a mechanical design engineer with over 25 years of experience in industrial automation, material handling, and power transmission specification.
As an Amazon Associate, I earn from qualifying purchases.
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