Power Transmission Shaft
Design a power shaft by torsional rigidity (twist ≤0.25°/m) and shear strength; take the larger diameter.
Inputs
Formula
T=9550P/n; d_rig=⁴√(32T/(πGθ)); d_str=∛(16T/(π[τ]))
Fundamentals
Shaft power is the mechanical power transmitted by a shaft — the basis for sizing motors and turbines.
Power $P=T\omega=T\cdot2\pi n/60$, $\omega$ angular speed (rad/s), $n$ speed (r/min). Given power and speed, required torque follows.
History
Power equals torque times angular speed, set by Watt (1782); the unit moved from horsepower (hp) to kilowatt (kW, 1889).
Engineering applications
Used to size motors, turbines, pumps and fans and to find their economical operating point.
Glossary
| Power $P$ | Work per unit time, $P=T\omega$ (W). |
| Angular speed $\omega$ | $\omega=2\pi n/60$, proportional to speed. |
| Torque $T$ | Back-solved from power and speed. |
How to use
- Fill in Power P, Speed n, Shear mod. G, Allow. shear [τ], Allow. twist in the Inputs section (watch the unit on each field).
- Click Calculate; the tool evaluates the formula shown above.
- Read Torque T, By rigidity, By strength, Recommended in the results area.
Formula notesShaft power P = T·ω = T·2πn/60 (kW); torque T = 9550·P/n (P:kW, n:r/min).
Formula · Worked Example · Knowledge
Formula
Torque $T=9550P/n$; diameter by rigidity $d_{rig}=\sqrt[4]{32T/(\pi G\theta)}$ and strength $d_{str}=\sqrt[3]{16T/(\pi[\tau])}$; take the larger.
Worked Example
P=15 kW, n=1500, G=80 GPa, [τ]=35 MPa, θ=0.25°/m → recommended ≈24.3 mm.
Key Points
- Rigidity limits twist to avoid shaft-system vibration.
- Strength usually governs at high power.
- Keyways weaken the shaft; thicken locally if needed.
Parameters
Inputs
| Parameter | Symbol | Unit | Default |
|---|---|---|---|
| Power P (kW) | P | kW | 15 |
| Speed n (rpm) | n | rpm | 1500 |
| Shear mod. G (GPa) | G | GPa | 80 |
| Allow. shear [τ] (MPa) | tau | MPa | 35 |
| Allow. twist (°/m) | theta | °/m | 0.25 |
Outputs
| Result | Symbol | Unit |
|---|---|---|
| Torque T | T | N·m |
| By rigidity | d_rig | mm |
| By strength | d_str | mm |
| Recommended | d_rec | mm |
Applications
- Common engineering use cases
FAQ
What formula does this tool use?
This tool computes per ISO / AGMA / ASME standard formulas: T=9550P/n; d_rig=⁴√(32T/(πGθ)); d_str=∛(16T/(π[τ]))
How accurate are the results?
Results match input precision, based on SI units and common engineering approximations; for critical duty re-check with a safety factor.
Where is it used?
Common engineering use cases