Enter the torque, pitch diameter of the sprocket (or other mounted element), and the transmission element factor into the calculator to determine the overhung load.
- Gear Reduction Calculator
- PPR To RPM Calculator
- Pulley Torque Calculator
- Load Force Calculator
- All Miscellaneous Calculators
Overhung Load Formula
Overhung load is the radial force applied to a shaft by a mounted element such as a pulley, sprocket, or gear when that element is positioned outside the nearest supporting bearing. This calculator estimates that load from shaft torque, pitch diameter, and a transmission element factor that reflects the type of drive component being used.
OHL = \frac{2T}{PD}\times TEFThe equation scales the transmitted torque into a force at the pitch circle, then adjusts that force based on the transmission element. For the same torque, a smaller pitch diameter produces a larger overhung load, while a larger pitch diameter reduces it.
Variable Definitions
| Symbol | Description | Typical Units |
|---|---|---|
| OHL | Overhung load acting on the shaft | N, kN, lbf |
| T | Transmitted torque | N·m, lbf·ft, lbf·in |
| PD | Pitch diameter of the sprocket, pulley, or gear | m, cm, mm, in, ft |
| TEF | Transmission element factor | Unitless |
Rearranged Forms
If you are solving for a different variable, the same relationship can be rewritten as follows:
T = \frac{OHL \times PD}{2 \times TEF}PD = \frac{2T \times TEF}{OHL}TEF = \frac{OHL \times PD}{2T}Typical Transmission Element Factors
Use the factor that most closely matches the mounted component. These are practical screening values and should be treated as estimating factors rather than universal design constants.
| Transmission Element | Typical TEF | General Interpretation |
|---|---|---|
| Spur gear | 1.15 | Usually near the basic tangential force with a modest adjustment |
| Chain sprocket, 12 teeth or fewer | 1.40 | Higher load factor due to smaller sprocket geometry |
| Chain sprocket, 13 to 19 teeth | 1.25 | Moderate chain loading condition |
| Chain sprocket, 20 teeth or more | 1.10 | Lower factor as sprocket size increases |
| V-belt pulley | 1.75 | Typically higher radial load because belt tensions add shaft loading |
| Flat belt pulley | 2.50 | Often produces the largest estimated overhung load of these common cases |
How to Use the Calculator
- Enter the shaft torque.
- Enter the pitch diameter of the mounted element.
- Select or enter the transmission element factor.
- Leave the unknown field blank if solving for a missing value.
- Confirm that torque and diameter units are compatible so the resulting load is meaningful.
Conceptually, the length unit embedded in torque should match the length unit used for pitch diameter. For example, if torque is expressed in pound-inches, pitch diameter should also be interpreted in inches. Consistent units prevent force values from being overstated or understated.
What the Result Means
- Higher torque increases overhung load in direct proportion.
- Smaller pitch diameter increases overhung load because the same torque must be carried through a shorter radius.
- Higher transmission element factor increases estimated shaft load, which is why belts often create more radial load than larger gears or sprockets for the same torque.
- Higher overhung load generally means more bearing reaction, more shaft bending, and potentially more deflection and wear.
Overhung load is primarily a radial loading issue. It should not be confused with axial thrust, which acts along the shaft centerline.
Related Shaft Bending Check
After finding the overhung load, designers often estimate the bending moment at the nearest bearing or shoulder by using the overhang distance from the bearing centerline to the load centerline.
M = OHL \times L
In this relationship, M is bending moment and L is the overhang distance. This step is useful when evaluating shaft stress, shaft deflection, bearing life, and alignment sensitivity.
Example
If a shaft transmits 120 N·m through a 0.20 m chain sprocket and the selected transmission element factor is 1.25, the estimated overhung load is:
OHL = \frac{2(120)}{0.20}\times 1.25 = 1500The resulting overhung load is 1500 N. If that same torque were transmitted through a smaller pitch diameter, the load would increase further.
Practical Notes
- Use pitch diameter rather than outside diameter whenever the transmission element is defined by pitch geometry.
- For preliminary sizing, the calculator is a fast way to compare design options before a full shaft and bearing analysis.
- If the equipment manufacturer provides allowable overhung load limits, compare your calculated result against those limits directly.
- Where shock loading, misalignment, or unusual belt tensioning exists, a conservative factor or manufacturer-specific method may be more appropriate.
