hydraulic-actuator

name	hydraulic-actuator
description	Hydraulic actuator design — linear cylinders, motor torque, flow/pressure relationships, force calculation, buckling of piston rod, seal selection, velocity control, servo valve integration, position control loop, MIL-H-5440, ISO 4413.
metadata	{"priority":7,"promptSignals":{"phrases":["hydraulic actuator","hydraulic cylinder design","hydraulic motor","servo hydraulic","hydraulic linear actuator","cylinder force calculation"],"minScore":3}}

Hydraulic Actuator Design — Complete Skill

Hydraulic Cylinder (Linear Actuator)

Force Calculation

Extend force (cap end pressurized): F_extend = P_supply × A_bore - P_return × A_rod_annulus [N] A_bore = π/4 × D_bore²; A_rod_annulus = π/4 × (D_bore² - D_rod²)

Retract force (rod end pressurized): F_retract = P_supply × A_rod_annulus - P_return × A_bore

Cylinder force balance: F_actuator = F_load + F_friction + F_seal (friction) + F_inertia (dynamic) F_friction (Coulomb): F_friction = μ_seal × F_normal ≈ 0.03–0.10 × P × A_bore (typically 3–10% of hydraulic force)

Differential cylinder (rod side connected to cap side): F_differential = P_supply × (A_bore - A_rod_annulus) = P_supply × π/4 × D_rod² [smaller force but faster regenerative speed] v_differential = Q / (A_bore - A_rod_annulus) = Q / (π/4 × D_rod²)

Flow Requirements

Cylinder velocity: v = Q / A_active [m/s; Q = flow rate [m³/s]; A_active = effective piston area]

Flow rate for desired velocity: Q = v × A_bore (extend) or Q = v × A_annulus (retract) [L/min; convert from m³/s]

Pump sizing: Q_pump ≥ max(Q_extend, Q_retract) × 1.1 (10% margin) + Q_leakage_system P_pump ≥ P_supply + ΔP_system_losses

Pressure losses in circuit: ΔP_piping = f × (L/D) × (ρv²/2) [pipe friction] ΔP_control_valve: 10–30 bar typical (servo valve or proportional valve) ΔP_filter: 2–5 bar differential across filter Total: P_pump = P_actuator + ΔP_piping + ΔP_valve + ΔP_filter + ΔP_cooler

Buckling of Piston Rod (Euler/Johnson)

For long stroke cylinders with end compressive load: P_critical (Euler) = π² × E × I / (L_eff)² [N; I = π/64 × D_rod⁴; L_eff = effective length]

Effective length (L_eff) for cylinder: Pin-pin: L_eff = full stroke (most conservative) Pin-clevis + cap end pin: L_eff = 0.7 × stroke Fixed base + free end: L_eff = 2 × stroke (cantilever; worst case)

Johnson formula (for slender ratio L/r < 120): P_cr = A_rod × [σ_y - (σ_y/(2π E))² × (L_eff/r)²] [r = radius of gyration = D_rod/4] For slender ratio > 120: use Euler formula

Safety factor on buckling: SF_buckling = P_cr / F_load ≥ 2.0 (minimum) or ≥ 3.5 for shock/uncertain load

Rod diameter from buckling: If SF insufficient: increase D_rod; or shorten stroke (reduce L_eff); or reduce unsupported length with guide

Cylinder Seal Selection

Piston seals: prevent fluid bypass from high to low pressure side of piston NBR O-ring (piston): -20 to +100°C; mineral oil and water glycol; most common Polyurethane U-cup: good wear resistance; dynamic sealing; -40 to +110°C PTFE-backed seals: low friction; excellent chemical resistance; -50 to +200°C; reduced stick-slip

Rod seals (gland seals): prevent fluid leakage to atmosphere; critical for cleanliness Standard: polyurethane lip seal + wiper seal combination High-speed: PTFE lip seal (< 1 mm/s stick-slip); spring-energized PTFE for low-friction servo

Seal friction model: F_seal = μ_seal × A_seal × P + F_preload [N; F_preload = spring force from interference fit] Effective μ: 0.02–0.05 for PTFE; 0.07–0.15 for NBR; 0.03–0.08 for PU

Seal pressure limits: NBR O-ring: 200 bar static; 100 bar dynamic; higher with backup rings PU U-cup: 250 bar static; 150 bar dynamic PTFE-energized: 700 bar static; 400 bar dynamic

Hydraulic Motor (Rotary Actuator)

Torque and Speed

Motor torque: T = ΔP × q / (2π × η_mech) [N·m; ΔP = pressure differential [Pa]; q = displacement [m³/rev]; η_mech = mechanical efficiency ≈ 0.90–0.96]

Motor speed: N = Q_motor / q [rev/s] = Q_motor / (q × 60) [RPM]

Motor types:

• Gear motor: simple; low torque; 100–2,000 RPM; η = 0.75–0.88
• Vane motor: smooth; medium torque; 500–4,000 RPM; η = 0.80–0.92
• Radial piston motor: high torque; low speed (Staffa); 0–500 RPM; η = 0.90–0.95
• Axial piston motor: highest performance; servo hydraulic; η = 0.92–0.97

Specific torque: T/q = ΔP / (2π) = 159 × ΔP [N·m/(bar·cm³/rev)] (for 100% efficiency) Example: q = 50 cm³/rev, ΔP = 200 bar: T = 50 × 200 / (2π × 100) = 159 N·m/bar × 200 bar × 0.05 L = 1592 N·m (ideal)

Electrohydraulic Servo System

Servo Valve

Purpose: precise proportional control of flow as function of electrical input signal Types:

• Flapper-nozzle (two-stage): fast response (100–300 Hz bandwidth); high precision; expensive; sensitive to contamination
• Spool valve (direct): simpler; up to 50–100 Hz; more contamination tolerant
• Proportional valve: lower precision; 10–30 Hz; less expensive than servo

Key parameters: Rated flow: Q_sv at 1,000 psi drop (nominal condition) [L/min] Null overlap: deadband around zero command; ideal: ≤ 0.5% of stroke Hysteresis: typically 0.5–2% of full rated flow; less for servo valves Contamination sensitivity: ISO 4406 Class 16/14/11 (servo requires Class 14/12/10 or better)

Position Control Loop

Transfer function (linear hydraulic motor/cylinder): G_actuator(s) = K_q / (A × s × (τ × s + 1)) [K_q = flow gain; A = piston area; τ = hydraulic time constant]

Hydraulic time constant: τ_h = V_total / (β_e × A_h² / m)^0.5 [V = total fluid volume; β_e = bulk modulus; m = load mass] Hydraulic natural frequency: ω_h = √(4β_e × A_h² / (V × m)) [rad/s]

Closed-loop position control: PID controller; inner velocity loop + outer position loop typical Bandwidth: f_-3dB ≤ 0.3 × ω_h (to maintain adequate stability margins)

Contamination control: ISO 4413: hydraulic cleanliness levels; servo valves require ≤ ISO Class 16/14/11 per ISO 4406 Filtration: 6 μm absolute filter on return line + 10 μm absolute on pressure line Flush procedure: initially flush system to target cleanliness before installing servo valve

Installation and Safety

ISO 4413 hydraulic safety: Maximum working pressure: design pressure ≥ 1.25 × relief valve setting; test pressure ≥ 1.5 × MAWP Relief valve: protect all actuators; set ≤ MAWP of lowest-rated component in circuit Cylinder design: burst pressure ≥ 4 × MAWP (ISO 4413 Cl. 7.2.3)

MIL-H-5440 (military hydraulic systems): Fluid: MIL-PRF-5606 (petroleum base, -65°C to +135°C); MIL-PRF-83282 (fire resistant; -40°C to +175°C) Cleanliness: NAS 1638 Class 6 (≈ ISO 4406 17/15/12) Proof pressure: 1.5 × MAWP; burst: 4 × MAWP

Standards

Standard	Scope
ISO 4413	Hydraulic fluid power — general rules for systems
ISO 4406	Fluid cleanliness levels (particulate)
MIL-H-5440	Military hydraulic systems
ISO 10100	Hydraulic cylinders — specification and testing
SAE J1273	Hydraulic hose and tubing recommendations
NFPA T3.4.7	Hydraulic motors — mounting dimensions

Output

Provide: actuator type (cylinder/motor), bore diameter D_bore [mm] and rod diameter D_rod [mm], operating pressure P_supply [bar] and return P_return [bar], extend force F_extend [kN] and retract F_retract [kN], flow rate Q [L/min] for target velocity v [m/s], rod buckling check (P_cr [kN] vs. load; SF), seal type (material and pressure rating), servo/proportional valve rated flow [L/min] and bandwidth [Hz], hydraulic natural frequency ω_h [rad/s] (if servo system), control loop bandwidth [Hz] (if servo), fluid cleanliness requirement (ISO 4406 class), and applicable standard (ISO 4413, MIL-H-5440, ISO 10100).