What Is the Jeffcott Rotor Critical Speed & Whirling Resonance Calculator?
Introduced by H. H. Jeffcott in 1919, the Jeffcott rotor model represents a single concentrated mass disk mounted at the midpoint of a flexible massless elastic shaft supported by rigid bearings.
It is the foundational model for understanding shaft whirling, resonance passage, and self-centering above critical speed.
How Does the Jeffcott Rotor Critical Speed & Whirling Resonance Calculator Work?
Residual unbalance exerts a rotating centrifugal force proportional to speed squared (ω²).
When speed matches the bending natural frequency √(k/m), dynamic magnification peaks.
Above the critical speed (supercritical operation), the rotor undergoes a 180° phase shift and rotates around its center of mass rather than its geometric center (automatic self-centering).
Jeffcott Rotor Critical Speed & Whirling Resonance Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
Jeffcott analytical rotordynamic formulation for synchronous lateral shaft vibration response.
How to Use the Jeffcott Rotor Critical Speed & Whirling Resonance Calculator
- Input rotor disk mass and shaft lateral bending stiffness.
- Specify damping ratio and residual unbalance eccentricity.
- Verify that operating speed has at least a 15% to 20% separation margin from critical speed.
Step-by-Step Example Calculation
10 kg Flexible Rotor Disk at 2500 RPM
Input Values:
Understanding Your Result
Critical speed in RPM indicates the resonant threshold.
Whirl amplitude in microns shows dynamic deflection under unbalance forces.
Factors That Affect the Result
- Bearing flexibility: Real hydrodynamic bearings add compliance and damping, lowering critical speeds compared to rigid supports.
- Damping: Higher damping suppresses peak vibration when passing through critical speed.
When Should You Use This Calculator?
- API 610 / 617 turbomachinery rotordynamic lateral vibration audits.
- Dynamic balancing specifications and speed margin verification.
Assumptions & Limitations
- Assumes symmetric isotropic rotor without gyroscopic moment coupling.
Frequently Asked Questions
Calculation Accuracy & Reference Note
Classical analytical rotordynamics solution.