SHAFT DESIGN (TORSION, CRITICAL SPEED, KEYS)

Power-transmission shafts carry torque T, often combined with bending from gears or pulleys. Torsional stress τ = T·r/J reaches maximum at the outer fiber. Angle of twist θ = T·L/(J·G) limits acceptable misalignment. Rotating shafts have a critical (whirling) speed where natural frequency coincides with rotation rate, producing resonance; the Rayleigh method estimates it from static deflection. Keys transfer torque to mounted hubs; standard sizing follows AGMA/ANSI B17.1.

• τ = 16T / (π·d³) (solid shaft)
• θ = T·L / (J·G)
• d = [(16/πSy)·sqrt((K·M)² + (K·T)²)]^(1/3) (ASME)
• ω_cr = sqrt(g/δ_static) (Rayleigh)

References & StandardsASME B106.1M, ANSI B17.1, AGMA 2001

Size the shaft diameter to satisfy torsional stress, bending stress, deflection, and critical-speed constraints simultaneously. Use the ASME shaft design equation for combined loading. Operate at less than 75% of first critical speed to avoid resonance, or pass through it quickly if startup transients are unavoidable. Verify key shear stress and hub bearing stress separately.