Calculation
τmax=αt·16Mt/(πd₁³); αt=(144−240ε+415ε²)/[(12−37ε)(11.3+48ε²+13ε³+59ε⁴)]
Preliminary calculation with a fixed result quantity: τmax=αt·16Mt/(πd₁³); αt=(144−240ε+415ε²)/[(12−37ε)(11.3+48ε²+13ε³+59ε⁴)]
Sauer 2023, Gl. 9.15–9.17
P3G polygon shaft: maximum torsional stress
Preliminary calculation with a fixed result quantity: τmax=αt·16Mt/(πd₁³); αt=(144−240ε+415ε²)/[(12−37ε)(11.3+48ε²+13ε³+59ε⁴)]
MINTSI
02
Result
Select a target and calculate.
Understand the inputs
- Maximum shear stress τmax — Maximum elastic torsional stress in the P3G shaft.
- Torque Mt — Torsional moment.
- Reference diameter d₁ — Nominal diameter of the P3G profile.
- Eccentricity e — Profile offset; for standard profiles ε=2e/d₁ must be between 0.0622 and 0.09.
Example
Mt=500 N·m, d₁=40 mm and e=1.6 mm give ε=0.08, αt≈1.214 and τmax≈48.29 MPa.
Assumptions and limits
Elastic torsion of a P3G profile within Sauer's stated ε range; not a fatigue or notch-effect verification.
Understand P3G polygon shaft: maximum torsional stress
This Sauer machine-element calculator provides a clearly scoped preliminary calculation based on the local Sauer reference. The result quantity is fixed and every input is explained physically; a complete component verification remains separate.
What does this quantity describe?
The model translates the defined geometry and load into a characteristic machine-element quantity. It is intentionally narrower than a complete strength verification.
Formula and variables
τmax=αt·16Mt/(πd₁³); αt=(144−240ε+415ε²)/[(12−37ε)(11.3+48ε²+13ε³+59ε⁴)]
Relationship from the cited Sauer section; approximations are identified on the individual calculator page
| Symbol / input | Meaning |
|---|---|
| Maximum shear stress τmax | Maximum elastic torsional stress in the P3G shaft. |
| Torque Mt | Torsional moment. |
| Reference diameter d₁ | Nominal diameter of the P3G profile. |
| Eccentricity e | Profile offset; for standard profiles ε=2e/d₁ must be between 0.0622 and 0.09. |
Choose the inputs correctly
Each input is identified as nominal, effective or mean. Lengths, forces, torques, stresses, angles and dimensionless factors are converted internally to coherent SI units. Absolute pressure must be distinguished from gauge pressure.
How to use the calculator
Use the fixed result quantity, copy the inputs from the drawing, load case or material data sheet, and check every unit. Then compare the result, worked example and model limits.
Worked example
The page example deliberately uses rounded, technically plausible values. It is an independent plausibility check, not a universal table value.
Understand the result and units
The result is a preliminary design quantity. A small or large value is meaningful only together with allowable stress, wear, temperature, manufacturing and safety factors.
Display units can be selected per field; the shared unit core calculates internally in SI. Enter percentages as decimal factors unless the field explicitly carries a percent unit.
Typical applications
Typical uses are option comparison, early sizing, teaching and plausibility checking of a detailed calculation.
Assumptions, limits and common mistakes
Automatic norm-table selection, fatigue, local stress peaks, tolerance chains, temperature and wear models, and design release are not included.
Common mistake: Common mistakes are using the wrong reference diameter, confusing full and half angles, entering gauge instead of absolute pressure, using percent instead of a decimal factor, and treating a preliminary result as a standard verification.
Frequently asked questions
Is this a complete strength verification?
No. It is a closed-form preliminary calculation; material, safety, fatigue and detail checks remain separate.
Why are mean and effective quantities identified?
Pressure, diameter, load share and deflection act at different geometric locations depending on the model.
Can the result automatically select a standard size?
No. Standard and manufacturer series must be matched to the actual output and tolerance situation.
How do I check the order of magnitude?
Use the worked example, test an analytical limiting case, and then verify units and signs.
When is FEM or a supplier calculation needed?
For sharp geometry steps, local contact, large deflection, dynamic excitation, heat, wear or safety-critical release.