Shaft Critical Speed Calculator - Free Online Rotor Dynamics Tool
Shaft Critical Speed Calculator
Calculate the critical speeds of rotating shafts to ensure safe operation and avoid resonance in turbomachinery and rotating equipment.
Shaft Configuration
Material Properties
Additional Masses
Critical Speed Guidelines
Operating Ranges
- • Rigid rotor: < 0.7 × N_c1
- • Flexible rotor: > 1.4 × N_c1
- • Avoid: 0.7-1.4 × N_c1
Safety Margins
- • API 610: ±20% separation
- • ISO 14839: ±15% margin
- • Critical equipment: ±25%
How to use this calculator
🔄 How to Use This Calculator
- Select shaft support type (simply supported, fixed, etc.)
- Choose shaft configuration (uniform, stepped, or hollow)
- Enter shaft dimensions and length
- Select material or enter custom properties
- Input operating speed in RPM
- Add concentrated masses if applicable
- Calculate to find critical speeds and safety margins
📐 Critical Speed Theory
Fundamental Equation
ω_n = (λ/L)² × √(EI/m)
N_c = 60ω_n/(2π) RPM
Where:
λ = mode shape constant
L = shaft length
EI = bending stiffness
m = mass per unit length
Operating Ranges
- • Rigid rotor: N < 0.7 × N_c1
- • Critical range: 0.8-1.2 × N_c1 (avoid!)
- • Flexible rotor: N > 1.4 × N_c1
🌟 Practical Examples
100mm diameter, 2m length, 3600 RPM
Critical speed: 4850 RPM (rigid rotor operation)
Stepped shaft, 3m length, 12000 RPM
Must operate above 1st critical (flexible rotor)
Hollow shaft, fixed supports, 1800 RPM
Ensure 20% margin from critical speeds
💡 Design Guidelines
- • Maintain minimum 20% separation margin (API 610)
- • Consider higher modes for long shafts
- • Include bearing stiffness in detailed analysis
- • Account for gyroscopic effects in overhung rotors
- • Use damping to reduce resonance amplitude
- • Balance rotors per ISO 1940-1 standards
- • Monitor vibration during commissioning
⚠️ Important Limitations
- • Simplified beam theory - neglects shear deformation
- • Does not include bearing/support flexibility
- • Ignores fluid film bearing dynamics
- • No gyroscopic effects considered
- • Single mode only - higher modes not calculated
- • Requires detailed FEA for final design
- • Temperature effects not included
About this calculator
Calculate critical speeds for rotating shafts to avoid resonance. Essential for turbomachinery and rotating equipment design.
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