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: − = µ0.25 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.