Lecture 6. Systems review exercise To be posted this afternoon Due in class (10/23/15)
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1 153 Systems review exercise To be posted this afternoon Due in class (10/23/15) Lecture 6 Coming week: Lab 13: Hydraulic Power Steering Lab 14: Integrated Lab (Hydraulic test bench) Topics today: 2 min course feedback Fluid Inertance Pumps and motors
2 154 Course Feedback 2 mins Write on a piece of paper, do not write your name Labs: What works? What doesn t work / can be improved. Class / lecture: What works? What doesn t work / can be improved. One or two things you have learned so far that you appreciate?
3 Fluid Inertance (inertia) 155 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 ΔP = d dt d dt [ ρ LAv] = [ ρlq] ΔP = ρl A dq dt inertance Important for long, narrow pipes water hammer effect!
4 156 How to make a big mass out of little mass? v v F = (100M) dv/dt Total weight of device = M Kinetic energy = (100 M) v 2 /2 What is in the box?
5 No Free Lunch (large is better) 157 Pressure drop through viscosity: Equivalent stiffness: Inertance: Δ 128µ L πd P = 4 ΔF = βa L Δx Q K eq = βa L " ΔP = ρl % # $ A & ' dq dt
6 158 Computer circuit analysis 0 Pump flow 0 Pressure Flow rate Flow Flow 1 Pressure Pump turns Constant Slider Gain Needle2 0 Pres s ure Pressure 0 Flow Flow 2 turns Needle1 Slider Gain2 Constant1
7 Component Modeling - Pressure Reducing Valve 159 How do we write equations for this valve? Spool Force balance / Newton s law Spring Preload / Compression Orifice
8 Modeling 160 Function: Regulate pressure at B Operation: If P_B is too large (small), spool moves up (down) to reduce (increase) orifice size ( ) P D A D = M x P B A B F spring (x) F seat F seat 0 F seat = ( 0 x>0 contact model x = 0 A D F s p r i n g Q = C d A(x)r 2 (PA P B ) A(x) B Preload x Possible Spring and area functions x
9 Modeling and Analysis of Flow Divider 161 Formulate models
10 162 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
11 Pump - Introduction ,000 psi
12 164 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
13 Non positive displacement pumps 165 Centrifugal Pump Impeller Pump
14 166 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%
15 167 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)
16 168 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
17 169 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.
18 Gerotor pump 170 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
19 171 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
20 Pressure Compensated Vane Pump 172
21 PC Vane Pump (Cont d) 173 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
22 174 Axial Piston Pump Each piston has a pumping cycle 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
23 175 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)
24 176 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
25 177 Piston Pump - flow ripples 1 piston Pumping Filling 2 piston Total flow Each cylinder has a pumping cycle Total flow = flow of each cylinder More cylinders, less ripple Frequency: Even # cylinders n*rpm Odd # cylinders (2n)*rpm Can be problematic for manual operator (ergonomic issue) Noise Displacement = # Cylinders x Stroke x Bore Area
26 # of Pistons Effect on Flow Ripples n=2 n=3 n=4 n= Flow Angle - rad
27 179 Pumping theory Create a partial vacuum (i.e. reduced pressure) Atmospheric / tank pressure forces fluid into pump usually tank check valve opens outlet check valve closes Power stroke expels fluid to outlet outlet check valve opens tank check valve closes Power demand for prime mover (ideal calculation) (piston pump) Power = Force*velocity = Pressure*area*piston speed = Pressure * Flow rate If power required > power available => Pumps stall or decrease speed
28 180 Aeration and Cavitation Disastrous events - cause rapid erosion Aeration air bubbles enter pump at low pressure side bubbles expand in partial vacuum when fluid+air travel to high pressure side, bubbles collapse micro-jets are formed which cause rapid erosion Cavitation fluid evaporates (boils) in partial vacuum to form bubbles bubbles expands then collapse as bubbles collapse, micro-jets formed, causing rapid erosion
29 181 Causes of cavitation and aeration For positive displacement pumps, the filling rate is determined by pump speed; (Q-demand) = D * freq) Filling pressure = tank pressure - inlet pressure Q-actual = f(filling pressure, viscosity, orifice size, dirt) If Q-actual < Q-demand, inlet pressure decreases significantly This causes air to enter (via leakage) or to evaporation (cavitates) To prevent cavitation/aeration increase tank pressure low viscosity, large orifice lower speed (hence lower Q-demand)
30 Aeration and Cavitation 182
31 183 Hydraulic Motor / Actuator Hydraulic motors / actuators are basically pumps run in reverse Input = hydraulic power Output = mechanical power For motor: Frequency (rpm) = Q (gallons per min) / D (gallons) * efficiency Torque (lb-in) = Pressure (psi) * D (inch^3) * efficiency efficiency about 90% Note: units
32 Models for Pumps and Motors 184
33 185 Non-ideal Pump/Motor Efficiencies Ideal torque = torque required/generated for the ideal pump/motor Ideal flow = flow generated/required for the ideal pump/motor Torque loss (friction) Flow loss (leakage) Signs different for pumping and motoring mode Q a c t u a l Pump volumetric eff: Friction Q i d e a l Pump mechanical eff: T in/out T ideal Q l o s s leakage (Reverse if motor case!! ) Total efficiency: vol Ideal pump Functions of speed, pressure and displacements
34 186 Hydro-static Transmission A combination of a pump and a motor Either pump or motor can have variable displacement Replaces mechanical transmission By varying displacements of pump/motor, transmission ratio is changed Various topologies: single pump / multi-motors multi (pump-motor) Open / closed circuit Open / closed loop control Integrated package / split implementation
35 Hydrostatic Transmission 187
36 188 Advantages: General Consideration - Hydrostats Wide range of operating speeds/torque Infinite gear ratios - continuous variable transmission (CVT) High power, low inertia (relative to mechanical transmission) Dynamic braking via relief valve Engine does not stall No interruption to power when shifting gear Disadvantage: Lower energy efficiency (85% versus 92%+ for mechanical transmission) Leaks!
37 189 Closed Circuit Hydrostat Circuit Notes: Charge pump circuit (pump + shuttle valve) Bi-directional relief Circuit above closed circuit because fluid re-circulates. Open circuit systems draw and return flow to a reservoir
38 190 Hydrostatic Transmission Let pump and motor displacements be D1 and D2, with one or both being variable. Let the torque (Nm) and speeds (rad/s) of the pump and motor be (T1, S1) and (T2,S2) Assuming ideal pumps and motors: Q = S 1D 1 2 = S 2D 2 2 P =2 T 1 D 1 =2 T 2 D 2 S 2 S 1 = D 1 D 2 T 2 T 1 = D 2 D 1 Transmission ratio Variable by varying D1 or D2 Infinite and negative ratios possible if pump can go over-center Note: Pow in = S 1 T 1 = S 2 T 2 = Pow out
39 191 Hydraulic Transformer Used to change pressure in a power conservative way Pressure boost or buck is accompanied by proportionate flow decrease and increase Note: Hydrostatic transmission can be thought of as a mechanical transformer (torque boost/buck) Q 1 Q 2 P 1 P 2 D 1 D 2 Research opportunity!
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