KEVOS® MAKEOS · Mechanics
Drive Shaft Torsional Check (Natural Frequency, Resonance Margins, Stress, Twist)
Does the torsional natural frequency of my motor, shaft and load fall clear of the running-speed excitations, and are the shaft stress and twist acceptable?
Check of a two-inertia drive (motor and load joined by a shaft): torsional stiffness of the shaft, effective inertia and natural frequency (as the torsional vibration tool), the excitation bands for the first few orders of running speed over the speed range, the separation of the natural frequency from each band against your margin, the critical speeds, and the shaft shear stress and angle of twist at the drive torque.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Shear modulus | GPa | Shear modulus of the shaft material (steel about 79 GPa). |
| Shaft outside diameter | mm | Outside diameter of the shaft. |
| Shaft bore (0 = solid) | mm | Bore of a hollow shaft; 0 for solid. |
| Shaft length | mm | Length of shaft between the motor and the load. |
| Motor inertia | kg·m² | Moment of inertia of the motor rotor and coupling half. |
| Load inertia | kg·m² | Moment of inertia of the driven load. |
| Operation | ||
| Lowest running speed | rpm | Lowest speed the drive runs at continuously. |
| Highest running speed | rpm | Highest speed the drive runs at. |
| Excitation orders to check (1 to …) | Number of running-speed orders that excite the system (1× from unbalance, 2× from universal joints and so on). | |
| Separation margin | % | How far the natural frequency must stay from each excitation band. |
| Drive torque | N·m | Torque the shaft transmits. |
| Allowable shear stress | MPa | Allowable torsional shear stress of the shaft. |
Method and formulas
- K = G π (d⁴ − d_i⁴) ÷ 32L; J_eff = J₁ J₂ ÷ (J₁ + J₂); f_n = √(K ÷ J_eff) ÷ 2π (as the torsional vibration tool).
- Order k excites from k n_min ÷ 60 to k n_max ÷ 60 Hz; f_n must lie below (1 − margin) × the band start or above (1 + margin) × the band end; critical speed = 60 f_n ÷ k.
- τ = 16 T d ÷ π (d⁴ − d_i⁴); twist = T ÷ K.
- Example: f_n = 66.277 Hz; the critical speed nearest the running range is 1,988.3 rpm; the shaft carries 28.294 MPa and twists 1.0903°.
Limitations
- Two-inertia model with a massless shaft; couplings and gear meshes add flexibility.
- Damping is ignored, so margins should be generous.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check a long drive shaft or line shaft
- Check a variable-speed drive for resonance
- Size a shaft for stiffness as well as strength
Who it is for
- Design engineers
- Machine designers
- Vibration analysts
What you get
- Stiffness, effective inertia and natural frequency
- Excitation bands, critical speeds and margins
- Shaft stress and twist
Interpreting the result
- Stiffening the shaft raises f_n with √K; a larger load inertia barely lowers it once J₂ ≫ J₁.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 3412–3413, 296–302. Topic reference; no source tables or recommended settings are reproduced.
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