rigid-coupling

name	rigid-coupling
description	Rigid coupling design — flanged couplings (AGMA 9009, torque capacity, bolt pattern), sleeve/muff couplings, clamp couplings (split), key-and-keyway (ANSI B17.1, shear and bearing stress), interference fit (fretting fatigue), axial force from thermal expansion, alignment requirements (angular and parallel misalignment limits), torsional stiffness, rigid coupling selection guide, and ISO 14691 flanged shaft coupling standards.
metadata	{"priority":7,"promptSignals":{"phrases":["rigid coupling","flanged coupling","shaft coupling rigid","sleeve coupling","coupling bolt pattern","muff coupling"],"minScore":3}}

Rigid Coupling Design — Complete Skill

Types of Rigid Couplings

Flanged Coupling

Configuration: Two flanges bolted or clamped face-to-face; transmits torque via friction (bolted) or shear (fitted bolts/keys) Shaft connections: interference fit hub, keyway, or shrink fit

Torque capacity: Friction-bolted: T = μ × N_bolts × F_bolt × r_bolt_PCD / 2 [N·m; μ = friction = 0.15–0.20; F_bolt = bolt preload; r = bolt circle radius] Fitted bolts (in shear): T = N_bolts × τ_bolt_allow × A_bolt × r_PCD [shear bolts in matching reamed holes]

AGMA 9009 flanged coupling design: Check: T_rated ≤ T_coupling / K_service [K_service = application service factor; 1.0–3.0 per AGMA] Bolt shear stress: τ = 2T / (N × A_bolt × D_pcd) ≤ τ_allow = S_y / (√3 × S_F)

Sleeve (Muff) Coupling

Cylindrical sleeve slides over two shaft ends; transmits via key or splines: Simple, inexpensive, compact; requires axial slide for assembly (impractical for large shafts) Torque via key: limited by key shear and bearing stress (same as shaft keyway design) Applications: low-power, simple drives; pump-motor drives; not suitable for large misalignment

Split (Clamp) Coupling

Split into two halves; bolted together over shafts: Friction + interference between halves; key may also be used Torque: T = μ × N_bolts × F_bolt_per_half × r_shaft × 2 [both halves acting on shaft; factor of 2] Assembly: remove bolts → slide halves off shaft; easier maintenance than sleeve

Split coupling torque (friction only): T = μ × F_clamping × r_shaft [F_clamping = total normal force from all bolts on shaft]

Torque Transmission Analysis

Keyed Connection

Key shear stress: τ = 2T / (d_shaft × w_key × L_hub) [w_key = key width; L_hub = hub (and key) length] Allowable shear: τ_allow = S_sy / n = 0.577 × S_y / 1.5 = 0.385 × S_y [von Mises; n = 1.5]

Key bearing stress: σ_bearing = 4T / (d_shaft × h_key × L_hub) [h_key = key height] Allowable bearing: σ_allow = 0.9 × S_y (yield limit; hub material governs)

Key length from ANSI B17.1: L_key_min = max(L_from_shear, L_from_bearing) Rule: L_key ≈ 1.0–1.5 × d_shaft as starting point

Interference Fit (Press Fit) Hub

Contact pressure from interference δ: p_c = δ / [r × ((r²+a²)/(E_hub×(r²-a²)) + ν_hub/E_hub + (1-ν_s)/E_s)] [r = interface radius; a = hub bore radius = r] Torque capacity: T_fit = μ × p_c × π × d_shaft × L_hub [μ = 0.12–0.20 for steel-on-steel] Safety factor: T_cap / T_applied ≥ 2.0 (interference fit alone)

Hub bore stress: σ_θ_max = p_c × 2r²/(r²-a²) [hoop stress at bore; maximum stress in hub; check vs. S_y]

Alignment Requirements for Rigid Couplings

Critical Alignment Tolerances

Rigid couplings transmit misalignment as forces/moments to shafts and bearings: Rigid coupling cannot accommodate misalignment → must be near-perfectly aligned at installation

Angular misalignment: θ_angular_max ≤ 0.01 mm/mm (0.05°) → most rigid couplings; dial indicator test across coupling face Angular misalignment induces: bending moment M = E_shaft × I × Δθ / L → beam bending at coupling; fatigue risk

Parallel (offset) misalignment: e_parallel_max ≤ 0.025 mm → rigid flanged couplings; dial indicator on coupling OD Parallel misalignment induces: shear force F = 3EI × e / L³ (cantilever) → radial bearing load

Thermal growth: Account for thermal expansion between cold (alignment) and hot (operating): Δ_thermal = α × ΔT × L_machine [mm; α = CTE; ΔT = temperature rise; L = distance between shaft centerlines] Pre-alignment: offset coupling by Δ_thermal in direction that thermal growth will correct at operating temperature

Measurement: Laser alignment (SKF TKSA, Rotalign Ultra): ±0.001 mm accuracy; preferred for precision machinery Dial indicator: ±0.01 mm; standard method per API 686 Check coupling face for axial gap uniformity (angular): 3-point or 4-point measurement

Torsional Stiffness

Rigid coupling torsional stiffness: k_torsion = G × I_p / L_coupling [Nm/rad; G = shear modulus; I_p = polar moment; L = coupling length] For flanged coupling with large diameter: k_torsion → very high → treat as rigid in torsional vibration model

System torsional natural frequency: If rigid coupling connects two masses I₁ and I₂ through shaft stiffness k_s: ω_n = √(k_s × (I₁ + I₂) / (I₁ × I₂)) [rad/s; rigid coupling → coupling stiffness not limiting; shaft governs]

Axial Force Consideration

Thermal Expansion Between Machines

Axial thrust at coupling: F_axial = E_shaft × A_shaft × Δ_thermal,axial [N; Δ_thermal = thermal elongation of connected shaft] Rigid couplings transmit full axial force to shaft bearings → check bearing axial capacity

Typical situation: Pump-motor rigid coupled: motor shaft grows axially with heat → pushes pump shaft Solution: floating coupling (axial float) or define which machine has fixed bearing

Flanged coupling axial load capacity: F_axial,max = N_bolts × σ_bolt_allow × A_bolt (in tension) [bolt pattern holds halves together; not for sustained axial thrust without special design]

Standard Flanged Coupling Dimensions

ISO 14691 / DIN 740

Nominal torque ratings (ISO 14691 flange couplings for general industry):

Size	Nominal Torque (N·m)	Flange OD (mm)	Bore range (mm)
F10	10,000	250	40–90
F25	25,000	350	60–130
F63	63,000	450	80–180
F160	160,000	560	100–240
F400	400,000	710	160–320

AGMA 9000 coupling service factors: Uniform load (compressors, fans): K_s = 1.0; Moderate shock (centrifugal pumps): K_s = 1.25–1.5 Heavy shock (crushers, reciprocating compressors): K_s = 1.75–2.0

Rigid vs. Flexible Coupling Selection

When to use rigid coupling:

• Shafts perfectly aligned (pump-motor close-coupled)
• Need zero backlash (precision servo drives, CNC)
• No vibration isolation needed; torsional stiffness required

When NOT to use rigid coupling:

• Shafts cannot be perfectly aligned (thermal growth, mounting tolerance)
• Vibration isolation needed between driver and driven
• Long shaft spans → use flexible or multi-bearing with flexible

Standards and References

Standard	Scope
AGMA 9000-C90	Flexible couplings (reference for service factors applicable to rigid too)
ISO 14691	Petroleum, chemical and gas industry flanged shaft coupling
ANSI B17.1	Keys and keyseats
API 686	Recommended practice for machinery installation and installation design
ISO 10441	Petroleum and chemical flanged coupling
DIN 740	Flexible couplings; torque rating tables

Output

Provide: coupling type (flanged/sleeve/split; material; standard: ISO 14691 or custom), power and torque (P [kW]; n [rpm]; T = 9,549 P/n [N·m]; service factor K_s; T_design = K_s × T [N·m]), coupling rated torque T_coupling [N·m] vs. T_design (safety factor ≥ 1.5), hub connection (keyway: τ [MPa] ≤ 0.385S_y; σ_bearing [MPa] ≤ 0.9S_y; or interference fit: δ [μm]; p_c [MPa]; T_fit [N·m] ≥ 2×T; hub bore stress [MPa]), bolt pattern (N_bolts; bolt size; D_pcd [mm]; τ_bolt [MPa] or F_friction [N] vs. required; material grade), alignment tolerances (angular [mm/mm]; parallel [mm]; thermal offset allowance Δ [mm]; measurement method), torsional stiffness k [N·m/rad] (rigid: treat as infinite in model; verify shaft stiffness not limiting), axial load (F_axial from thermal expansion [N]; bearing capacity check), coupling size (ISO 14691 or DIN 740 designation), and applicable standard (ISO 14691, AGMA 9000, ANSI B17.1, API 686).