The Mechanics
Chatter isn't magic. It's resonance. When your spindle's rotational frequency hits the natural frequency of the tool-workpiece system, the cut becomes unstable. The result? A ruined surface finish and a broken carbide tip.
fₙ = (1 / 2π) × √(k / m)
Critical RPM = (fₙ × 60) × Harmonic
Critical RPM = (fₙ × 60) × Harmonic
Variables:
k = System Stiffness (N/m)
m = Effective Mass (kg)
π ≈ 3.14159
Based on classical structural dynamics (Timoshenko, 1961).
Fig 1: Industrial milling setup. Note the rigid tool holder—stiffness is king.