Lecture 6. This week: Lab 13: Hydraulic Power Steering [ Lab 14: Integrated Lab (Hydraulic test bench) ]
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1 133 Lecture 6 This week: Lab 13: Hydraulic Power Steering [ Lab 14: Integrated Lab (Hydraulic test bench) ] 4-way directional control valve; proportional valve; servo-valve Modeling / Analysis of a servo-valve Valve sizing Pumps and motors (part 1) 10/19/2012: Hydraulic Hybrids Guest lecture Mike Olson (Eaton Corporation)
2 134 Directional Control Valves (DCVs) Controls direction of flow Fluidic symbol signifies function Manually or electrically (solenoid or equivalent elements) Can also meter flow proportional valve servo valve
3 135
4 136 Way-Position-Port, centering etc. # Position = number of possible positions for the valve shifting mechanism 2way infinite-pos 2port 1 = no shifting, 2={left, right}, 3={left, right, center}, infinite # Way = number of flow paths (including reverse flow) check valve = 1 way 1-way, 2-way, 3-way, 4-way most common. # Port = number of plumbing connections. Center = connection while neutral closed, open, tandem... 3way, 3position 3port 4way, 3position 4port 4way, infinite-pos 4port
5 137 Influences rest of circuit Energy / pressure when this part of circuit not used 4 way valve center Open center unload pump, energy saving for fixed displacement pump Can you use 2 cylinders? Closed center high pressure / relief responsive Tandem center (lab) allows 2 circuits in series
6 138 Modeling of directional control valve Spool is driven by solenoid (in a single stage valve) or by pilot stage(s) valves xv > 0 (spool moves downward) Assume matched (i.e. supply and return orifices are the same) Critically lapped symmetric, +/- spool displacement give same orifice area Flow conserving load Qin = Qout e.g. double ended cylinder or hydraulic motor
7 D.C. Valve modeling 139 Flow paths: (neglect leakages) xv > 0: Orifices 1 and 3 xv < 0: Orifices 2 and 4 Area of each orifice A1(xv), A2(xv), A3(xv), A4(xv) For xv > 0, [Cd = discharged coeff approx 0.6 (see notes on orifice modeling) Q 2 Q ( 1 = Cd A1 xv ) ( Ps P1 ) ρ 2 ( xv ) ( P2 0) ρ 3 = Cd A3 P Q Q = 1 = 3 Q L
8 D.C. Valve Modeling 140 Now the pressure across the load is: P L = P 1 P 2 Area gradient, w, relates orifice area to spool displacement. For circular orifices: w = 2πR Area gradient = w w = da dx A1(xv) = A3(xv) = w * xv A2(xv) = A1(-xv) = -w*xv v ( x v Solve for Q L when A1(xv) = A3(xv) =w xv (matched) to get: ) Annular orifice land Top view Q L 1 ( xv, PL ) = Cd wxv ( Ps PL ) ρ circular Area versus xv Annular
9 DC Valve Modeling 141 Similar analysis for xv < 0: 1 Q L( xv, PL ) = Cd wxv ( Ps + PL ) ρ Normally P L < 0 when xv < 0. Putting formulae for +/- xv together: Load overrun Positive power Q L 1 ( xv, PL ) = Cd wxv ( Ps sgn( xv ) PL ) ρ Flow increases linearly with xv Flow decreases with pressure load Positive power Load overrun
10 142 Effect of lapping / centering For critically lapped (or sometimes called critically centered) valve Orifice is shut when xv = 0. At least one orifice will open when xv!=0 Critically lapped valves are desirable but expensive to make flow is linear with displacement (constant gain) Overlapped (closed centered) valves deadband => un-responsive Underlapped (open centered) valves valve always open => power loss nonlinear gain => more difficult to control
11 Valve Sizing 143 Valves are rated (i.e. their flow rate Q R given) at 1000 Psi pressure drop across the valve. i.e. Flow = Q R is flow when the valve is fully open and with 1000 PSI pressure drop There are two flow orifices (1 and 3) in flow path. It is assumed that pressure drop is 500psi across each orifice. Since one does not always use the valve when there is 1000 Psi pressure drop, one must translate the required flow to the equivalent flow at 1000 Psi. Basic equation: Q Q L L 2 ( xv, PL ) = Cd wxmax ( Ps P1 ) ρ 2 ( xv, PL ) = Cd wxmax ( P2 P0 ) ρ
12 Valve Sizing 144 At rated condition, Ps - P1= 500Psi, P2 - P0 = 500psi Q Q L L 2 ( xv, PL ) = Cd wxmax ( Ps P1 ) ρ 2 ( xv, PL ) = Cd wxmax ( P2 P0 ) ρ Suppose actual operating (Ps-P1) is 700 instead, with required flow Qd, then we would like: So the rated flow should be at least: Q R1 = Q d1 Q d = 500 P P C wx Similarly, calculate for the return orifice: pick the larger rated flow s 1 d max ρ Q R= Q d Q R = C d wx max ρ Pick this when picking valve
13 Valve sizing example 145 Given Ps = 3000 psi; P 0 = 0 psi Load is a 2:1 cylinder, capside A cap = m^2. Required extension speed = 1 m/s Load F = 500 lb-f. Step 1: Find Qd1 = speed * Acap.; Qd2 = Qd1/2 Step 2: find P1 and P2 during operating conditions 8F Ps P 1 = + 2Ps 2F P2 = 9A 9 cap 9A Step 3: find rated flow based on each orifice 9 cap P1 P2 A cap P P / 2) = ( 1 2 F ( P s P1 ) = 2 ( P2 P0 ) F Why? Q R1 = Q d1 500 P P s 1 Q R2 = Q d P P 2 0 Q Q R Q R1, R2
14 146 Actuator: Other component sizing stroke: how far does it have to travel? Area: load/pressure or pump-flow/area load can be friction, gravity, brake force, acceleration load etc. Motor: Disp= Q/speed; Disp = Torque/Pressure Pump flow: Supposed actuator area determined by load/pressure Qpump = actuator speed * area (beware of cap versus piston side) Multiple circuits: Add required flows from all circuits add safety factor! Beware of units!!!
15 147 Single stage proportional valves Solenoids Spool is stroked directly by solenoid actuator LVDT spool position feedback Spring (sometimes) for safety
16 Single Stage Proportional Valves 148 Advantages: Simple design Reliable Cost effective Disadvantages: Poor dynamic performance (bandwidth) At high flow rates and bandwidths, large stroking force is needed Large (and expensive) solenoids / torque motors needed. Low end market.. Research: Using unstable flow force to improve spool agility K. Krishnaswamy and P. Y. Li, On using unstable hydraulic valves for control ASME Journal of Dynamic Systems, Measurement and Control. Vol 124, No. 1, pp , March, Q.-H. Yuan and P. Y. Li, Using Steady Flow Force for Unstable Valve Design: Modeling & Experiments ASME Journal of Dynamic Systems, Measurement and Control. Vol 127, No. 3. pp , Q.-H. Yuan and P. Y. Li, Robust Optimal Design of Unstable Valves IEEE Transactions on Control Systems Technology. Vol. 15, No. 6, pp , November, 2007
17 Multi-stage valves 149 Use hydraulic force to drive the spool..
18 Electrohydraulic servo-valve Multi-stage valve Typically uses a flapper-nozzle pilot stage Built-in feedback via feedback wire Very high dynamic performance Bandwidth = Hz 150 Pilot stage Main stage For a fun place to learn how a servo-valve works: R. Dolid Electrohydraulic Valve Coloring Book pdf
19 Servo-Valve 151
20 Feedback spring: 1. Regulates the position of the mainstage by negative feedback on the flapper Servo-Valve 152 Nozzle-flapper pilot valve: 1. Electromagnetic torque motor moves flapper to left (or right) 2. Nozzle and restriction at source form two resistances in series 3. Flapper differentially opens and closes nozzle 4. Pressure increases on side with closed nozzle; decreases on side with open nozzle; creating pressure differential Main stage: 1. Four-way spool valve actuated by differential pressure generated by pilot stage
21 153 Two spool servo valve Main spool consists of two spools one for meter-in, one for meter-out Reduces tolerance requirement Pilot stage is a pressure servo valve Cost effective Bandwidth around 30 Hz See below for a model of such a valve R. T. Anderson and P. Y. Li, Mathematical Modeling of a Two-spool Flow Control Servovalve Using a Pressure Control Pilot ASME Journal of Dynamic Systems, Measurement and Control Vol 124 No. 3, Sept (Sauer-Danfoss)
22 154 Pumps Source of hydraulic power Converts mechanical energy to hydraulic energy prime movers - engines, electrical motors, manual power Two main types: positive displacement pumps non-positive displacement pumps
23 Pump - Introduction 155
24 156 Positive displacement pumps Displacement is the volume of fluid displaced cycle of pump motion unit = cc or in 3 Positive displacement pumps displace (nearly) a fixed amount of fluid per cycle of pump motion, (more of less) independent of pressure leak can decrease the actual volume displaced as pressure increases Therefore, flow rate Q gpm = D (gallons) * frequency (rpm) E.g. pump displacement = 0.1 litre Q = 10 lpm if pump speed is 100 rpm Q = 20 lpm if pump speed is 200 rpm
25 Non positive displacement pumps 157 Centrifugal Pump Impeller Pump
26 158 Non-positive displacement pump Flow does not depend on kinematics only - pressure important Also called hydro-dynamic pump (pressure dependent) Smooth flow Examples: centrifugal (impeller) pump, axial (propeller) pump Does not have positive internal seal against leakage If outlet blocks, Q = 0 while shaft can still turn Volumetric efficiency = actual flow / flow estimated from shaft speed = 0%
27 159 Positive vs. non-positive displacement pumps Positive displacement pumps most hydraulic pumps are positive displacement high pressure (10,000psi+) high volumetric efficiency (leakage is small) large ranges of pressure and speed available can be stalled! Non-positive displacement pumps many pneumatic pumps are non-positive displacement used for transporting fluid rather than transmitting power low pressure (<300psi), high volume flow blood pump (less mechanical damage to cells)
28 160 Types of positive displacement pumps Gear pump (fixed displacement) internal gear (gerotor) external gear Vane pump fixed or variable displacement pressure compensated Piston pump axial design radial design
29 161 External gear pump Driving gear and driven gear Inlet fluid flow is trapped between the rotating gear teeth and the housing The fluid is carried around the outside of the gears to the outlet side of the pump As the fluid can not seep back along the path it came nor between the engaged gear teeth (they create a seal,) it must exit the outlet port.
30 Gerotor pump 162 Inlet port Outlet port Inner gerotor is slightly offset from external gear Gerotor has 1 fewer teeth than outer gear Gerotor rotates slightly faster than outer gear Displacement = (roughly) volume of missing tooth Pockets increase and decrease in volume corresponding to filling and pumping Lower pressure application: < 2000psi Displacements (determined by length): 0.1 in 3 to 11.5 in 3
31 163 Vane Pump Vanes are in slots As rotor rotates, vanes are pushed out, touching cam ring Vane pushes fluid from one end to another Eccentricity of rotor from center of cam ring determines displacement Quiet Less than 4000psi
32 Fluid Power Controls Laboratory (Copyright Perry Li, ) 164 Pressure Compensated Vane Pump
33 PC Vane Pump (Cont d) 165 Eccentricity (hence displacement) is varied by shifting the cam ring Cam ring is spring loaded against pump outlet pressure As pressure increases, eccentricity decreases, reducing flow rate Spring constants determines how the P-Q curve drops: small stiffness (sharp decrease in Q as P increases) large stiffness (gentle decreases in Q as P increases) Preload on spring determines pressure at which flow starts cutting off
34 166 Each piston has a pumping cycle Axial Piston Pump Interlacing pumping cycles produce nearly uniform flow (with some ripples) Displacement is determined by the swash plate angle Generally can be altered manually or via (electro-) hydraulic actuator. Displacement can be varied by varying swashplate angle
35 167 Thrust-plate rotates with shaft Bent-Axis Piston Pump Piston-rods connected to swash plate Piston barrel rotates and is connected to thrust plate via a U-joint More efficient than axial piston pump (less friction)
36 168 Radial Piston Pump Similar to axial piston pump, pistons move in and out as pump rotates. Displacement is determined by cam profile (i.e. eccentricity) Displacement variation can be achieved by moving the cam (possible, but not common though) High pressure capable, and efficient Pancake profile
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