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 Vehicles Next week: Guest lecturer Mike Olson, Eaton Hydraulics 141 Review: Sequencing and Circuit analysis Fluid Bulk modulus Fluid Inertance Component modeling Pressure reducing valve Pressure compensated flow control valve 1
Lab Works: Prelabs TA explanation Matlab/Simulink Useful for learning Not works: Not enough connectors TA needs to smile Too many reports Clearer lab handouts Better labels Emphasize main points Requirements for lab reports What Work / What Don t 142 Lecture Works: Explanations of labs before hand In-class examples Slides / handouts available Theory useful Participation Not works: Answers to questions not available Behind with labs sometimes No-break Disconnect from lab More animations More examples 2
143 Sequencing Circuits Sequence valve cracking pressure settings to enable proper sequencing Too high never cracks Too low simultaneous motion instead of sequence P1 F Crack at P_R Hint: Sketch the time course of pressure P1. What determines the P1 when it cylinder 1 is moving and when it bottoms out 3
Example: 3MW Wind Turbine, 35MPa 144 4
Friction Factor Moody Diagram 145 5
146 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
Fluid Compressibility: Bulk Modulus 147 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
148 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
Energy in Compressed Fluid (Li and Wang, 2011) 149 9
Accounting for Bulk Modulus 150 Compressibility increases spring like action Possibility of having resonance M V = Q/A Spring, K M Q A Questions: How to pick K? Compressible cylinder Ideal cylinder (velocity generator) + Spring 10
Modeling compressibility in cylinders 151 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
Equivalent Spring Constant 152 Data F Differentiating: K eq Finite if dead volumes (hoses) included Worst case x 12
Fluid Inertance (inertia) 153 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 A P = d dt d dt LAv = LQ P = L A dq dt inertance Important for long, narrow pipes water hammer effect! 13
How to make a big mass out of little mass? 154 v v Total weight of device = M Kinetic energy = (100 M) v 2 /2 What is in the pink box? 14
155 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
156 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
157 Computer circuit analysis 0 Pump flow 0 Pressure Flow rate Flow Flow1 Pressure Pump 3 0.403 turns Constant Slider Gain Needle2 0 Pressure Pressure 0 Flow Flow 2 turns 0.019 3 Needle1 Slider Gain2 Constant1 17
Component Modeling - Pressure Reducing Valve 158 How do we write equations for this valve? Spool Force balance / Newton s law Spring Preload / Compression Orifice 18
Modeling 159 Function: Regulate pressure at B Operation: If P_B is too large (small), spool moves up (down) to reduce (increase) orifice size P B A B - ( F spring (x)- F seat ) - P D A D = M x A D F spr i n g A(x) B Preload x Possible Spring and area functions x 19