Calculation
ct=Gπd⁴/(32l); nK=30/π·√[ct(JA+JB)/(JA·JB)]
Preliminary calculation with a fixed result quantity: ct=Gπd⁴/(32l); nK=30/π·√[ct(JA+JB)/(JA·JB)]
Sauer 2023, Gl. 7.61 und 7.67–7.69
Two-mass torsional critical speed
Preliminary calculation with a fixed result quantity: ct=Gπd⁴/(32l); nK=30/π·√[ct(JA+JB)/(JA·JB)]
MINTSI
02
Result
Select a target and calculate.
Understand the inputs
- Critical speed nK — Torsional natural frequency expressed as speed.
- Inertia JA — First concentrated rotational inertia.
- Inertia JB — Second concentrated rotational inertia.
- Shear modulus G — Shear modulus of the shaft material.
- Shaft diameter d — Diameter of the solid circular shaft section.
- Shaft length l — Torsionally active length between the inertias.
Example
JA=0.08 kg·m², JB=0.12 kg·m², G=80 GPa, d=25 mm and l=400 mm give nK≈3,817 rpm.
Assumptions and limits
Two concentrated inertias and a massless solid shaft; damping, shaft mass and higher modes are excluded.
Understand Two-mass torsional critical speed
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
ct=Gπd⁴/(32l); nK=30/π·√[ct(JA+JB)/(JA·JB)]
Relationship from the cited Sauer section; approximations are identified on the individual calculator page
| Symbol / input | Meaning |
|---|---|
| Critical speed nK | Torsional natural frequency expressed as speed. |
| Inertia JA | First concentrated rotational inertia. |
| Inertia JB | Second concentrated rotational inertia. |
| Shear modulus G | Shear modulus of the shaft material. |
| Shaft diameter d | Diameter of the solid circular shaft section. |
| Shaft length l | Torsionally active length between the inertias. |
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.