Lecture 5. Labs this week: Please review ME3281 Systems materials! Viscosity and pressure drop analysis Fluid Bulk modulus Fluid Inertance

Size: px

Start display at page:

Download "Lecture 5. Labs this week: Please review ME3281 Systems materials! Viscosity and pressure drop analysis Fluid Bulk modulus Fluid Inertance"

Cory Phillips
5 years ago
Views:

1 Labs this week: Lab 10: Sequencing circuit Lecture 5 Lab 11/12: Asynchronous/Synchronous and Parallel/Tandem Operations Please review ME3281 Systems materials! 132 Viscosity and pressure drop analysis Fluid Bulk modulus Fluid Inertance 1

2 Some fluid properties (Revised!!! 2/20/15) 134 Dynamic Viscosity N-s/(m^2) = Pa - s = sec * kg m/sec ^2/m = kg / (m sec) = 10 poise v / y 1 poise = 10-1 kg /m/s = 0.1 Pa-s 1 cp = centipoise = 1g/m/s = Pa-s Kinematic Viscosity Easy to measure. If density = 1000kg/m 3, Shear (N / m^2) Tangential speed gradient (1/sec) y Shear force v (y) No shear when there is no velocity gradient normal to flow m 2 /sec = stoke 1 stoke (St) = cm 2 /sec 1 centi-stoke (cst) =0.01 St 3.78 cp 3.78 cst Density (kg/m^3) 2

3 135 Viscosity decreases with temperature SAE cs at 100degC (212F) 150 cs at 40degC (104F) SAE 10W 4 cs at 100 deg C(212F) 20 cs at 40 degc (104F) Usually data is given at two temperatures use linear interpolation to find intermediate values 5 to 10 times variation with 60degC variation! Water has much lower viscosity than hydraulic oil Which one for winter or for summer? Water: ~1cS for wide range of temperature! 3

4 Example: 3MW Wind Turbine, 35MPa 136 4

5 Friction Factor Moody Diagram 137 5

6 138 Example L clearance = 0.1mm Cylindrical Spool P 90 deg elbow diameter = 0.5cm Sleeve Q = 30 LPM?1: Assuming small leakage, determine pressure P.?2: How long does L have to be for leakage to be less than 0.01% of the flow? 6

7 Fluid Compressibility: Bulk Modulus 139 Hydraulic fluid is slightly compressible: fluid volume decreases from V by dv on application of pressure dp dv V 1 dp is the bulk modulus - varies a lot with temperature and amount of aeration For = 200kPsi, 5000psi pressure compresses fluid by 2.5% Increases with pressure Decreased significantly by entrained air content 7

8 140 Bulk modulus: cont d For precise application, can be important, especially for long stroke, narrow, cylinders dl = pressure*l/ = force*l/(area*) D=0.5in bore, 6 in stroke 0.15in/1000 lb-f D=1 in bore, L=1.5in stroke (same volume) 0.01in/1000 lb-f 16 times smaller Note that compressibility equation looks like equation for a spring 8

9 Energy in Compressed Fluid (Li and Wang, 2011) 141 9

10 142 Accounting for Bulk Modulus Compressibility increases spring like action Possibility of having resonance M M V = Q/A Spring, K Q A Questions: How to pick K? Compressible cylinder Ideal cylinder (velocity generator) + Spring 10

11 Modeling compressibility in cylinders 143 Consider when the cylinder ports are blocked Suppose the load F is applied on the piston, how much does the piston move? Note: the chamber should include all the volumes between the piston and the valve (i.e. include hoses) Case 1: Double ended actuator Case 2: Single ended actuator F Does the spring constant change with position of the piston? 11

12 Equivalent Spring Constant 144 Data F Differentiating: K eq Finite if dead volumes (hoses) included Worst case x 12

13 Fluid Inertance (inertia) 145 F = m * a for the accelerating fluid (transients) Normally, the pressure needed to accelerate the fluid is neglected. When is this important? Momentum calculation for a hose: Length = L, Area = A P1 P2 AP d dt d dt LAv LQ P L A dq dt inertance Important for long, narrow pipes water hammer effect! 13

14 146 How to make a big mass out of little mass? v v Total weight of device = M Kinetic energy = (100 M) v 2 /2 What is in the pink box? 14

15 147 Power Computations A hydraulic device is generally an n-port system each port interacts with its environment - hydraulic, mechanical, (electric) Hydraulic power: energy flux through each port Power_in = F*vel_in = P*A*vel_in = P * Q hoses load P 1, Q 1 P 2, Q 2 E-power For a hose filled with incompressible fluid, Q_2 = -Q_1 Net hydraulic power in = (P 1 - P 2 )*Q How about a single ended or a double ended actuator, or a hydraulic motor? 15

16 148 Power Computation - cont d Hydraulic actuator / motor has 2 hydraulic port and 1 mechanical (load) port Net hydraulic power input = Net mechanical power input = Mechanical power variables: Force and velocity Torque and angular velocity For passive components, net power input not greater than 0. Calculate hydraulic power for hydraulic motor Relationship between hydraulic power and mechanical power? 16

Lecture 5. Labs this week:

Lecture 5. Labs this week: Labs this week: Lab 10: Bleed-off Circuit Lecture 5 Lab 11/12: Asynchronous/Synchronous and Parallel/Tandem Operations Systems Review Homework (due 10/11) Participation is research lab Hydraulic Hybrid