crankshaft-design

name	crankshaft-design
description	Crankshaft design — bending and torsional stress, pin/journal sizing, Goodman fatigue, counterweight, torsional vibration (critical speeds, Holzer method), material, forging vs. cast, SAE/ISO standards.
metadata	{"priority":7,"promptSignals":{"phrases":["crankshaft design","crankshaft fatigue","crankshaft torsional","crank pin stress","crankshaft vibration","crankshaft sizing"],"minScore":3}}

Crankshaft Design — Complete Skill

Crankshaft Loads

Forces on crankpin from combustion/reciprocating masses: F_gas = (π/4) × D_bore² × P_cylinder [N; gas pressure force] F_inertia = -m_recip × r × ω² × (cos θ + λ cos 2θ) [reciprocating inertia; λ = r/L_conrod; r = crank radius] F_total = F_gas + F_inertia [net force on piston pin → transmitted to crankpin via connecting rod]

Connecting rod angle: sin φ = (r/L) sin θ → tan φ = sin θ / (√(1/λ²- sin²θ)) F_crank_radial = F_total × cos(θ + φ) / cos φ [force along crank radius] F_crank_tangential = F_total × sin(θ + φ) / cos φ [torque-producing force]

Bearing loads: R_main = vector sum of pin forces distributed to adjacent main bearings R₁ = F_pin × (a₂/L_span); R₂ = F_pin × (a₁/L_span) [simple beam; a₁, a₂ = distances from bearings]

Stress Analysis

Bending Stress in Crankpin

Maximum bending moment: M_pin = R_bearing × (L_bearing_half + L_cheek_half) [conservative] Or from detailed analysis: M = R × e [e = distance from main bearing to crankpin CL]

Bending stress: σ_b = M × (D_pin/2) / I_pin = 32M / (π × D_pin³) [Pa; D_pin = crankpin diameter]

Torsional Stress in Main Journal

Torsional moment: T = F_tangential × r [N·m; accumulated for multicylinder engines with phase angle] τ = 16T / (π × D_journal³) [Pa]

Combined Stress

Von Mises equivalent: σ_eq = √(σ_b² + 3τ²)

Alternating and mean components: σ_a = (σ_max - σ_min)/2 [alternating bending] σ_m = (σ_max + σ_min)/2 [mean bending] τ_a = (τ_max - τ_min)/2 [alternating torsion]

Fatigue Assessment (Goodman)

Modified Goodman for combined loading: σ_a/σ_e + σ_m/σ_u ≤ 1/SF [SF = 1.5–2.5] σ_e = endurance limit (corrected) = σ_e_base × k_a × k_b × k_c × k_d × k_e σ_e_base = 0.5 × σ_u (for steel, S_e ≈ 700 MPa max for σ_u > 1400 MPa)

Stress concentration factors: k_t_fillet ≈ 1.5–3.5 (oil hole: k_t_oil = 3.0–4.0; sharp fillet: k_t = 3.5) k_f = 1 + q(k_t - 1) [q = notch sensitivity, 0.7–0.95 for high-strength steel]

Fillet radius (critical for fatigue): r_fillet ≥ 0.06 × D_pin (minimum); 0.08–0.12 × D preferred → k_t ≈ 1.7–2.0

Surface finish correction (k_a): Ground journal: Ra ≤ 0.4 μm → k_a ≈ 0.9 Rolled fillet (cold rolling): k_a can be > 1.0 (beneficial compressive residual stress)

Crankpin and Journal Diameter Sizing

Initial sizing (empirical — bending governed): D_pin ≈ (32M / (π × σ_allow))^(1/3) For automotive steel: σ_allow = σ_e / (SF × k_f) ≈ 150–200 MPa → D/bore ≈ 0.5–0.6

L/D ratios (bearing): Main bearing L/D ≈ 0.5–0.8 Crankpin L/D ≈ 0.5–0.7 Longer L → lower bearing pressure; shorter L → less crank weight

Bearing specific load: p = P / (D × L) ≤ p_allow [p_allow for engine bearings: 20–40 MPa for steel-backed; 50 MPa for trimetal]

Counterweight Design

Purpose: balance rotating masses + partial balance of first-order reciprocating forces Rotating unbalance: m_counterweight × r_cw = m_crankpin × r_pin + m_conrod_lower × r_pin First-order balance: counter-rotating balancer shafts for in-line engines (full reciprocating balance) V-engine: opposed throws provide partial balance inherently

Counterweight moment: M_cw = m_cw × r_cw (for single weight) Typical: counterweight offsets 100% rotating + 50% reciprocating (compromise)

Torsional Vibration Analysis

Holzer Method (Forced Torsional Vibration)

Discretize crankshaft into N lumped inertia/stiffness elements: θ₁, θ₂,..., θ_N = angular amplitudes T_i = J_i × ω² × θ_i (inertia torque for each disk) Σ T_i = 0 (for free vibration mode)

Critical speed (1-node): ω_crit = √(K_t / (J_1 × J_2 / (J_1 + J_2))) [two-mass system]

Multicylinder critical speeds: Critical orders m = 1/2, 1, 3/2,..., k (k = number of cylinders) For 4-stroke 6-cylinder: major critical orders = 3, 6, 9 Avoid coincidence of major orders with rated speed ± 20%

Torsional stiffness (crankshaft throw): K_throw = G × J_polar / L_eff L_eff = effective length (empirical: pin + 2/3 × cheek thickness) J_polar = π × d⁴ / 32 (for circular cross-section)

Campbell Diagram

Plot resonance frequencies (horizontal lines) vs. speed (x-axis) with excitation orders (diagonal lines) Mark critical intersections within operating range; calculate amplitudes using modal analysis

Dampers (Torsional)

Viscous damper (Houdaille): inertia disk in viscous fluid; broadband damping Optimal inertia ratio J_ring/J_crankshaft ≈ 0.2–0.5 Attenuation: 40–60% reduction in torsional amplitude at critical speed

Rubber coupling: tuned to specific critical speed; narrow-band

Materials

Material	σ_u [MPa]	σ_e [MPa]	Application
Cast iron (nodular GGG60)	600	180	Low-output diesel
Carbon steel 1045 (forged)	700	350	Light automotive
Alloy steel 4340 (forged)	1000–1200	500–600	High-performance engine
Microalloyed steel 38MnVS6	900	450	Production automotive (forged)
EN19 (UK, 709M40)	1000	500	Standard high-duty diesel

Heat treatment: induction hardening of journals (55–62 HRC surface); shot peening of fillets

Standards

Standard	Scope
SAE J1986	Engine crankshaft design
ISO 8217	Fuel quality for marine (affects crankshaft fouling)
ASTM A148	Steel castings for structural applications
AMS 2759	Heat treatment of steel
DIN 17212	Case hardening steels

Output

Provide: crankpin diameter D_pin [mm], main journal diameter D_journal [mm], fillet radius r [mm], crankpin L/D ratio, maximum bending moment M [N·m], bending stress σ_b [MPa], torsional stress τ [MPa], Von Mises σ_eq [MPa], fatigue safety factor SF (Goodman), endurance limit σ_e [MPa], stress concentration k_f, counterweight mass and offset [kg, mm], torsional vibration critical speeds [RPM] by Holzer method, major critical orders for cylinder count, damper recommendation (type, J ratio), material (σ_u, σ_e), and applicable standard (SAE J1986, AMS 2759).