# Design and Modeling of Fluid Power Systems ME 597/ABE Lecture 2

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1 Systems ME 597/ABE Lecture 2 Dr. Monika Ivantysynova MAHA Professor Flud Power Systems MAHA Fluid Power Research Center Purdue University

2 Contents 1. Introduction and overview of components, circuit and system design methods 2. Fluid properties, modeling of transmission lines, impedance model of lines 3. Displacement machines design principles 4. Steady state characteristics, measurement methods and modeling 5. Gap flow models 6. Flow and pressure pulsation 2

3 Fluid Power System Design Choose max operating pressure Size the hydraulic motor Calculate flow requirement Select type of control, in case of valve control select type and size of control valve Select pump size based on flow requirement and speed of prime mover Calculate required line diameter Add additional components like pressure relief valve, logic elements, filter, reservoir, accumulators 3

4 Fluid Power System Design Example φ φ during φ φmax max φmax Flight max Flight M l Fmax Flight max Flight /s /s 4

5 MAHA Distance Learning Fluid Properties Density Compressibility Viscosity Properties of Fluids Change of density with pressure Change of density with temperature Oxidative, hydrolytic and thermal stability Foaming (release air without forming emulsions) Lubricity (boundary lubricating property) 5 Viscosity - temperature behavior Viscosity - pressure behavior Air/Gas absorption Pour Point Flash point/ fire point

6 Fluid Properties Compressibility of a real fluid Density is defined: and Change of fluid volume with pressure and temperature: Isothermal coefficient of compressibility dv = -V β p dp Bulk modulus is defined as reciprocal of compressibility coefficient Therefore we can write: dp 6 17

7 Fluid Properties Bulk modulus Fluid can be compressed isothermally or isentropically (adiabatic process) Isothermal bulk modulus K Adiabatic bulk modulus K A (p 2 - p 1 ) dp V 1 1 V V 2 2 In practice secant bulk modulus K S is often used! p 1 p 2 p 7 18

8 Influence of entrapped air Due to entrapped air the compressibility of the fluid (fluid-air mixture) changes. For the bulk modulus of fluid air mixture K* can be derived: p 0 atmospheric pressure In a simplified way for the change of volume of the fluid air mixture dv M we can derive: For isothermal process follows: simplified: Change of air volume with pressure: and for the change of fluid volume: 8 19

9 Influence of entrapped air (1) and (2) Due to V Air << V F we can make the following simplification: V F =V then (3) Substituting Eq. (3) in Eq. (1) and (2) follows: Example: Calculate how the bulk modulus of the fluid air mixture with 0.5% undissolved air at p = 100 bar=10 7 Pa is changed. The bulk modulus of the fluid is K= Pa. 9 20

10 Viscosity of a real fluid The viscosity of a fluid is the measure of its resistance to flow or of its internal friction. According to Newton s law the shearing stress between adjacent layers of a viscous fluid is proportional to the rate of shear in the direction perpendicular to the fluid motion (flow direction). h µ dynamic viscosity [Pa s=n s/m 2 ] y p 1 =p 2 v 0 p 1 p 2 v x are empirical constants for a given fluid, whereas Typical values for mineral oil: 10 23

11 Viscosity of a real fluid Kinematic viscosity Kinematic viscosity: [m 2 s -1 ] or [cst] ISO Viscosity Grades for mineral oils (ISO 3448) ISO VG 10 mean value at 40 C 10 mm 2 s -1, (cst) ISO VG mm2 s-1 ISO VG mm2 s-1 ISO VG mm2 s-1 ISO VG mm2 s-1 11

12 Viscosity-Temperature Viscosity-temperature diagram Ordinate: lg lg (ν+0.8) Kinematic viscostiy [mm 2 /s] Abszissa: lg T Skydrol (Phosphate ester) Temperature [ C] ISO viscosity grade reference temperature 12

13 Types of Hydraulic Fluids Petroleum based fluids (mineral oils) usually with additives to -prevent oxidation and corrosion HL -reduce foaming -improve lubricity HLP -increase viscosity index HV Fire resistant fluids - oil water emulsions (20% H 2 O) - HFA - water in oil emulsion (about 40% H 2 O) - HFB - Polymer solutions with H2O - HFC - water free synthetic fluids ( Phosphate ester) - HFD Biodegradable fluids -Vegetable oil base HTG -Polyglycol base HPG -Synthetic ester HE Water 13

14 Water versus Mineral Oil Viscosity 30 lower 50% reduction of pressure loss Viscosity-temperature dependency 14 lower Specific heat 2.3 higher 5 times higher thermal conductivity Better coolingability 50% higher bulk modulus Air release ability 30times better Higher stiffness but Higher vapor pressure 14

15 Vapor Pressure of Water Vapor Pressure Water Pressure [bar] Water Vapor Temperature [ C] p V H2O = C p V mineral oil = 0.053Pa = C 15

16 Fluid Properties Thermal properties Specific heat c [ J/kg K] Thermal conductivity λ [W/m K] Solubility of gas Henry s law Cavitation 16

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