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 – (hydrostatics): high p, low vol flow – (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 , 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 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