98 Lecture 4 Labs coming week: Lab 8 Check valve and pilot-operated check valves Lab 9 Flow divider Update: Identifying lab objectives Review: Metering/Bleed-off (More) efficient circuits? Check and Pilot-to-Open-Check Flow divider Cartridge valves Properties of Hydraulic Fluids Viscosity friction and leakage Bulk modulus and Inertance (next week)
99 Control Circuit Efficiency Where are energy lost? More efficiency circuits? Displacement control Pulse-width-modulation Transformers Electrohydraulic- Actuator (EHA)
100 More efficient circuits Main goal: Avoid throttling losses in valves (active research) Displacement control (pump control) Hydraulic transformers Common pressure rail Electro-hydraulic actuator Pulse-width modulation
101 PWM - Throttle-less control Achieve throttle-less control through on/off control Create the hydraulic analog of a DC-DC Converter Controlled using Pulse-Width-Modulation (PWM) Many different architectures are possible (motor, pump, hydrostat, transformer) Low PQ losses in both on an off state, but PWM leads to a ripple on the output
Self-Spinning Rotary PWM Valve 102 H. Tu, M. B. Rannow, M. Wang, P. Y. Li, and T. R. Chase, Design, Modeling and Validation of a High-Speed Rotary PWM On/Off Valve for Use in Virtually Variable Displacement Pumps, ASME Journal of Dynamics Systems, Measurement and Control, Vol. 134-6, #061002, Nov, 2012. P I II L T
103 Allows flow only one direction one way directional control valve Check Valves ANSI symbol? Main uses are: by-pass components cylinder locking look mom. No hands!
Pilot Operated (open) Check Valves 104 Allows reverse flow when pilot pressure is turned on Enables cylinder locking and to retract cylinder when intended Consider force balance to calculate what pressures needed to open the check Check valve area ratio
105 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?
106 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 Pressure divider circuit
Cartridge Valves 107 Integrate circuits with many components using a manifold Manifold = aluminum block with internal passages Standard configurations
108 Flow Divider Valve Maintain same flow ratio (of 1 in the case) Q left =Q right despite different pressures Identify flow measurement sensors What happens when Q left > Q right? What happens when Q right > Q left? When does equilibrium occur? Some valves are flow combiner/divider? Can this one combine flow?
109 Modeling and Analysis of Flow Divider Q a = Q b +Q c Q b = C 1 (x)*sqrt(p a -P b ) Q c = C 2 (x)*sqrt(p a -P c ) P 1 = P a -(Q b /C 1 (x)) 2 P 2 = P a -(Q c /C 2 (x)) 2 Adjust x based on P 1 and P 2
110 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 Read on your own Slip-in type (larger flow rates) essentially a check valve versatile functions accomplished by different covers that provide for additional circuits. Area ratio plays key role in the operation
111 Screw-in Cartridge Valve Single piece implements the function Plugs into standard manifold porting manifold itself being custom built
112 Fluid Properties Viscosity Bulk modulus Inertance
A (fake) Car Talk Puzzle 113 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?
114 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
115 From: M. Radhakrishnan, Hydraulic Fluids ASME Press
Some fluid properties 116 Dynamic Viscosity N-s/(m 2 ) = Pa - s = sec * kg m/sec ^2/m = kg / (m sec) = 10 poise µ = τ v / y Kinematic Viscosity Easy to measure. If density = 1000kg/m 3, Shear (N / m 2 ) Tangential speed gradient (1/sec) 1 poise = 10-1 kg /m/s = 0.1 Pa-s 1 cp = centipoise = 1g/m/s = 0.001 Pa-s µ = 3.78 cp υ = 3.78 cst Updated: Spring 2015 υ = µ ρ y Shear force v (y) No shear when there is no velocity gradient normal to flow Density (kg/m 3 ) m 2 /sec = 10000 stoke 1 stoke (St) = cm 2 /sec 1 centi-stoke (cst) =0.01 St 1cSt = 10-6 m 2 /sec
117 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! (good!!)
High V-I Fluids 118 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 )
119 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)
120 Dynamic viscosity = 45 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 = 45cP * (0.001 Pa-sec/cP) * (5m/s / 0.005m) = 0.045 (N/m 2 )*sec * 1000/sec = 45 N/m 2 Drag force = 45 * pi * D * L = 7.06 N Pressure drop = Drag force / Area = 45*4*L/D = 3.6 kpa = 0.036 bar
Darcy laws: ΔP = Resistance in Pipes and Hoses f (Re) L ρv D 2 2 = f (Re) L D 8ρQ 2 π D 2 4 speed Re = vd v 121 Laminar: (Hagen-Poiseuille) f=64/re Δ 128µ L πd P = 4 Q Re < 2000 Kinematic viscosity Inertia versus viscous Turbulent Smooth pipe ΔP = 0.1364 / Re 1/ 4 L 8 ρq 2 D π D 2 4 10000 > Re > 4000
Friction Factor Moody Diagram 122
Example: 3MW Wind Turbine, 35MPa 123
Loss in Connectors 124 K-factor K factors ρv ΔP = K 2 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 2 v = (outlet) velocity [m/sec] g = gravity const [m/sec^2] Note: K is unit-less and independent of units ΔP Equivalent formula: ρg 2 v H L = K 2g = H L 2 v = K 2g H L = head loss [m]
125 Leakage Leakage flow Q = 3 a w 12µ L ΔP 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
126 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?
127 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!
A (fake) Car Talk Puzzle 128 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?