109 Lab this week: Lab 8 Sequencing circuit Lab 9 Flow divider Lecture 4 Review: Pilot-Open-Check Area ratio and pressure divider Cartridge valves Flow divider Properties of Hydraulic Fluids Viscosity friction and leakage Bulk modulus and Inertance (next week) Course feedback (2mins)
110 Pilot-to-Open Check Valve Area Ratios Acap Apiston Fload A2 A1 Under no load condition, when can the actuator retract? (Hint: force balance on actuator piston). What if Fload is not zero?
111 When will the POC open to reverse flow? Needle 1 Needle 2 P1 Pp Suppose PO check valve area ratio is 3:1 Needle valves: K2 given Find K1 so that PO check opens
112 Cartridge Valves Integrate circuits with many components using a manifold Manifold = aluminum block with internal passages Standard configurations
113 Cartridge valves Screw-in types (smaller flow rates, single unit) [as in lab] Single valve performs the intended function screws into cavities in manifold cavities are generally common Slip-in type (larger flow rates) essentially a check valve versatile functions accomplished by different covers that provide for additional circuits. Area ratio play a role in the operation of both types of cartridge valves.
114 Screw-in Cartridge Valve Single piece implements the function Plugs into standard manifold porting manifold itself being custom built
115 Slip-in example: check valve Possible leakage Preferred!
116 Slip-in Cartridge Valves Area Ratios Closing force: P A P A A P + F sp Opening force: P A A A + P B A B Open! Open or closed?
117 Slip-in Cartridge Pilot Operated Check x B A Slip-in part is just a poppet check valve
118 Slip-in Pilot Operated Relief Valve
Slip-in: Pilot Operated Directional Control Valve 119
120 Individually Controlled DCV configuration Potential for better energy savings.
121 Identify flow measurement sensors What happens when Q left > Q right? What happens when Q right > Q left? Equilibrium position? Flow Divider Valve How to design a flow divider with 2:1 ratio? Some valves are flow combiner/divider? Can this one combine flow?
122 Modeling and Analysis of Flow Divider Qa = Qb+Qc Qb = C1(x)*SQRT(Pa-Pb) Qc = C2(x)*SQRT(Pa-Pc) P1 = Pa-(Qb/c1(x))^2 P2 = Pa-(Qc/c2(x))^2 Adjust x based on P 1 and P 2
123 Fluid Properties Viscosity Bulk modulus Inertance
124 A (fake) Car Talk Puzzle You discovered that on your garage floor that your car is leaking oil. You took it in to the mechanic Joe. Joe was busy, so you had to leave the car at the shop s parking lot for the night. Next morning, Joe took your car into the shop and examined the car for leaks, and found nothing. You took your back home, but lo and behold, the car leaked again on your garage floor. Neither you nor Joe is delusional. What is going on?
125 Hydraulic Fluid in Fluid Power Systems Primary role is POWER TRANSMISSION Secondary roles Lubrication Enables moving parts prevents wear, metal/metal contact Load carrying ability parts spot welded together if lubrication film breaks down or too thin Sealing leaks Dimensional clearance may induce leak Certain property of fluid may prevent leak (viscosity) Heat transfer / cooling transfer of heat from work area to reservoir / heat exchanger some fluid properties may vary with temperature
126 From: M. Radhakrishnan, Hydraulic Fluids ASME Press
127 Some fluid properties Dynamic Viscosity v / N/(m^2s) = sec * kg m/sec ^2/m = kg / (m sec) = 1000 poise y Shear (N / m^2) Tangential speed gradient (1/sec) 1 poise = 10-3 kg /m/s 1 cp = centipoise = 0.01g/m/s y Shear force v (y) No shear when there is no velocity gradient normal to flow Kinematic Viscosity Easy to measure. If density = 1000kg/m 3, m 2 /sec = 10000 stoke 1 stoke (St) = cm 2 /sec 1 centi-stoke (cst) =0.01 St 3.78 cp 3.78 cst Density (kg/m^3)
128 SAE 40 Viscosity decreases with temperature 15 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!
129 High viscosity Viscosity is a compromise reduce leak (better sealing) lower chance of oil break down parts spot welded to each other requires larger pressure to sustain flow (sluggish) pump may cavitate (air getting into system) oil / air separation difficult Low viscosity lower drag better efficiency possibility of thin film break down worse leakage (water hydraulics)
130 Dynamic viscosity = 4500 cp Diameter of pipe D = 0.05m Length of pipe L = 1 m Velocity at y = 0.5cm is 5m/s Velocity at y = 0cm is 0m/s Example v y Find a) shear drag on and b) pressure drop across the pipe Assume linear velocity profile shear = 4500cP / (1000 N/m^2/sec) * (5m/s / 0.005m) = 4.5 (N/m^2)*sec * 1000/sec = 4500 N/m^2 Drag force = 4500 * pi * D * L = 706 N Pressure drop = Drag force / Area = 4500*4*L/D = 360 kpa
131 Darcy laws: P Resistance in Pipes and Hoses f (Re) L D v 2 2 f (Re) L D 8 Q 2 D 2 4 speed Re vd v Laminar f=64/re 128 L D P 4 Q Re < 2000 Kinematic viscosity Inertia versus viscous Turbulent Smooth pipe P 0.1364 / Re 1/ 4 L 8 Q 2 D D 2 4 10000 > Re > 4000
132 Friction Factor Moody Diagram
133 Example: 3MW Wind Turbine, 35MPa
134 Loss in Connectors K-factor P K v 2 2 v = (outlet) velocity [m/sec] g = gravity const [m/sec^2] K factors Tee s 1.8 45deg elbow 0.42 90deg elbow 0.75 Ball check valve 4.0 Return bend 2.2 Example: Elbow Q = 15gpm, Pressure drop = 0.6psi Q = 37.5gpm, Pressure drop = 4psi Note: K is unit-less and independent of units P Equivalent formula: g 2 v H L K 2g H L 2 v K 2g H L = head loss [m]
135 Leakage Leakage flow Q 3 a w 12 L P P2 Example: a spool in a sleeve w = pi * D (circumference) L = length of land a Q L a = clearance P1 w Note high viscosity decreases leaks
136 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?
137 Efficiency vs Viscosity vs Temperature For hydraulic components (e.g. pumps, motors, actuators) with moving parts, there is always a trade-off between Volumetric efficiency [leakage] Mechanical Efficiency [friction] Total efficiencies for pumps and motors given by: Optimal viscosity Optimal viscosity exists for a given component (and system) However, viscosity changes dramatically by temperature!
138 High V-I Fluids Viscosity Index (VI): measures temperature dependence of viscosity Modified using chemical additives High VI = low temperature dependence Low VI = large temperature dependence VI index is a measure of this slope! ( Defined relative to 2 standard fluids : VI=0, and VI=100 )
139 A (fake) Car Talk Puzzle You discovered that on your garage floor that your car is leaking oil. You took it in to the mechanic Joe. Joe was busy, so you had to leave the car at the shop s parking lot for the night. Next morning, Joe took your car into the shop and examined the car for leaks, and found nothing. You took your back home, but lo and behold, the car leaked again on your garage floor. Neither you nor Joe is delusional. What is going on?
140 Write on a piece of paper Do not write your name Labs: What works? What doesn t work / can be improved. Class / lecture: Course Feedback 2 mins What works? What doesn t work / can be improved.