Mechatronic Systems Modeling - fluid power Slide 1

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 2

Characteristics of FP systemsSome 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 3

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 4

Fluid power transmission• Fluid power bond:

Power = p*Q,where p denotes pressure

and Q denotes volume flow.

pQ

Units: p, N/m2 ; Q, m3/s. (Scale factors.)

Mechatronic Systems Modeling - fluid power Slide 5

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 6

Some loss effects -

Q

pa - pb

Porous plug: linear resistancepa pb

Q

Laminar flow

(Hagen-Poiseuille law):

QDLpp ba *)/128( 4πµ=−

Mechatronic Systems Modeling - fluid power Slide 7

Some loss effects (cont.) -

Q

pa - pb

Turbulent flow:75.175.475.0

*25.0 *)/*(* QDLfpp ba ρµ=−

Orifice flow (turbulent):

[ ] 2/1** badd PPACQ −=

Mechatronic Systems Modeling - fluid power Slide 8

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 9

Gravity-induced compliance effects

V

p

p

p0

p = (1/C)*V + p0

dV/dt = Q

Q

C = ?C*dp/dt = Q CpQ

Mechatronic Systems Modeling - fluid power Slide 10

Fluid compressibility effects

Mechatronic Systems Modeling - fluid power Slide 11

Line compliance effects

Mechatronic Systems Modeling - fluid power Slide 12

Fluid inertia effects

a b

Mechatronic Systems Modeling - fluid power Slide 13

Driver and loading effects

Sep

SfQ

• atmospheric pressure

• valve: fully closed

• hydraulic (pneumatic) pumps

• hydraulic (pneumatic) motors

pressure source flow source

Mechatronic Systems Modeling - fluid power Slide 14

Some typical fluid power components• filters• cylinders• valves

– flow control, check, logic, pressure reliefcylinders

• pumps• motors• lines

Mechatronic Systems Modeling - fluid power Slide 15

Hydraulic cylinder, single-sided

Qp

F

v

Mechatronic Systems Modeling - fluid power Slide 16

Hydraulic cylinder: loss effects

Efficiency?

Mechatronic Systems Modeling - fluid power Slide 17

Hydraulic cylinder: dynamic (and loss) effects

Mechatronic Systems Modeling - fluid power Slide 18

Hydraulic Pump Modeling

Low p

High p

T

w

Shaftinput

Mechatronic Systems Modeling - fluid power Slide 19

Typical positive displacement (PD) pump

Examples: gear pump, vane pump, piston pump.

Basic operation of a PD pump:

Mechatronic Systems Modeling - fluid power Slide 20

Loss effects in a PD pump:

Power efficiency?

Mechatronic Systems Modeling - fluid power Slide 21

Dynamic (and loss) effects in a PD pump:

Mechatronic Systems Modeling - fluid power Slide 22

Mechatronic Systems Modeling - fluid power Slide 23

Multiport model.

Mechatronic Systems Modeling - fluid power Slide 24

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 inertiaeffects, 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 25

Hydraulic line modeling

Properties (distributed over line length):

• losses, due to wall friction

• inertia

• compliance, due to fluid and line

LQ1 Q2

p2p1

Mechatronic Systems Modeling - fluid power Slide 26

Hydraulic line: composite model 1

Mechatronic Systems Modeling - fluid power Slide 27

Hydraulic line: composite model 2

Mechatronic Systems Modeling - fluid power Slide 28

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 29

Hydraulic line: improving model accuracy

Mechatronic Systems Modeling - fluid power Slide 30

Matching boundary conditions

Se LINE Se

Inputs: Pa and Pb

Sf LINE Sf

Inputs: Qa and Qb

Mechatronic Systems Modeling - fluid power Slide 31

Matching boundary conditions

Se LINE Sf

Inputs: Pa and Qb

Sf LINE Se

Inputs: Qa and Pb

Mechatronic Systems Modeling - fluid power Slide 32

Matching boundary conditions: options

Mechatronic Systems Modeling - fluid power Slide 33

Valves

• Pressure relief valves

• Spool valves for logic

• Check valves

• Servo valves