Fluid Power Systems
• Characteristics of fluid power systems • Basic FP modeling assumption – power transmission by fluid • Basic FP physical effects – resistance, compliance, inertia • Typical FP components • Some FP system examples
Mechatronic Systems Modeling - fluid power Slide 1 Characteristics of FP systems Some characteristics of fluid power, relative to mechanical and electrical power: • high speed of response for large force transmission • controllable at high power levels • good heat dissipation qualities • safe to use, but leakage, bursts a problem • moderately good for power transmission over moderate distances
Mechatronic Systems Modeling - fluid power Slide 2 Fluid power transmission • Power head in a flowing stream: p + ρv2/2 + ρgz • Fluid power assumption: p >> ρv2/2 • Fluid assumed “incompressible” • Two distinct areas –Hydraulics (hydrostatics): high p, low vol flow – Pneumatics (acoustics): low p, high vol flow
Mechatronic Systems Modeling - fluid power Slide 3 Fluid power transmission • Fluid power bond: Power = p*Q, where p denotes pressure and Q denotes volume flow.
p Q
Units: p, N/m2 ; Q, m3/s. (Scale factors.)
Mechatronic Systems Modeling - fluid power Slide 4 Some Basic Physical Effects
• Power losses (line friction, valving) • Compliance (stiffness) effects • Inertia effects • Drivers and loading effects • Transducer effects
Mechatronic Systems Modeling - fluid power Slide 5 Some loss effects - Porous plug: linear resistance
pa pb Q
Q
pa - pb Laminar flow (Hagen-Poiseuille law): µ − = π 4 pa pb (128 L / D )*Q
Mechatronic Systems Modeling - fluid power Slide 6 Some loss effects (cont.) - Turbulent flow: µ − = 0.25 ρ0.75 4.75 1.75 pa pb f *(L* * / D )*Q
Orifice flow (turbulent): Q = []− 1/ 2 Q Cd * Ad * Pa Pb
pa - pb
Mechatronic Systems Modeling - fluid power Slide 7 Some compliance effects
• fluid compressibility • compliance of hydraulic lines • accumulators • changes in elevation in gravity field • entrainment of gas
Mechatronic Systems Modeling - fluid power Slide 8 Gravity-induced compliance effects
p0 p
Q p
p = (1/C)*V + p0 V dV/dt = Q p C*dp/dt = Q C = ? Q C
Mechatronic Systems Modeling - fluid power Slide 9 Fluid compressibility effects
Mechatronic Systems Modeling - fluid power Slide 10 Line compliance effects
Mechatronic Systems Modeling - fluid power Slide 11 Fluid inertia effects
ab
Mechatronic Systems Modeling - fluid power Slide 12 Driver and loading effects • atmospheric pressure •valve: fully closed • hydraulic (pneumatic) pumps • hydraulic (pneumatic) motors
pressure source flow source p Se Sf Q
Mechatronic Systems Modeling - fluid power Slide 13 Some typical fluid power components • filters • cylinders •valves – flow control, check, logic, pressure relief cylinders •pumps •motors • lines
Mechatronic Systems Modeling - fluid power Slide 14 Hydraulic cylinder, single-sided
v
p F Q
Mechatronic Systems Modeling - fluid power Slide 15 Hydraulic cylinder: loss effects
Efficiency?
Mechatronic Systems Modeling - fluid power Slide 16 Hydraulic cylinder: dynamic (and loss) effects
Mechatronic Systems Modeling - fluid power Slide 17 Hydraulic Pump Modeling
High p
T w Shaft input Low p
Mechatronic Systems Modeling - fluid power Slide 18 Typical positive displacement (PD) pump
Examples: gear pump, vane pump, piston pump.
Basic operation of a PD pump:
Mechatronic Systems Modeling - fluid power Slide 19 Loss effects in a PD pump:
Power efficiency?
Mechatronic Systems Modeling - fluid power Slide 20 Dynamic (and loss) effects in a PD pump:
Mechatronic Systems Modeling - fluid power Slide 21 Mechatronic Systems Modeling - fluid power Slide 22 Multiport model.
Mechatronic Systems Modeling - fluid power Slide 23 Fluid power system modeling. • Label each distinct pressure point or region. – Write a 0-junction for each point. • Add components; identify their ports; assign power directions. • For each component, build a model. – e.g., add compliance, resistance, and inertia effects, using C’s, R’s, and I’s, respectively. • Select reference pressure (gauge or atmospheric). Eliminate the corresponding 0-junction(s). • Simplify the model.
Mechatronic Systems Modeling - fluid power Slide 24 Hydraulic line modeling
p1 p2
Q1 Q2 L
Properties (distributed over line length): • losses, due to wall friction • inertia • compliance, due to fluid and line
Mechatronic Systems Modeling - fluid power Slide 25 Hydraulic line: composite model 1
Mechatronic Systems Modeling - fluid power Slide 26 Hydraulic line: composite model 2
Mechatronic Systems Modeling - fluid power Slide 27 Hydraulic Line: model comparison
• Mode information – number of eigenvalues (what is their distribution?) – number of eigenvectors (what are the “mode shapes”?) • Steady-state for constant inputs
–Let pa = Pac and Qb = Qbc (what is the steady-state response?)
Mechatronic Systems Modeling - fluid power Slide 28 Hydraulic line: improving model accuracy
Mechatronic Systems Modeling - fluid power Slide 29 Matching boundary conditions
Se LINE Se
Inputs: Pa and Pb
Sf LINE Sf
Inputs: Qa and Qb
Mechatronic Systems Modeling - fluid power Slide 30 Matching boundary conditions
Se LINE Sf
Inputs: Pa and Qb
Sf LINE Se
Inputs: Qa and Pb
Mechatronic Systems Modeling - fluid power Slide 31 Matching boundary conditions: options
Mechatronic Systems Modeling - fluid power Slide 32 Valves
• Pressure relief valves • Spool valves for logic • Check valves • Servo valves
Mechatronic Systems Modeling - fluid power Slide 33