Positive Displacement Devices Displacement Formulae Characteristics Hydraulic Pumps Positive Displacement Devices Displacement Formulae Characteristics

Gear Pumps (External Gear) Pumping Mechanism

Gear Pumps (External Gear) Displacement parameters and determination Displacement = π/4(Do2 – Di2)L Do = Outer diameter of the two gears Di = Inner diameter of the two gears (Actually it is the diameter of the circle defined by the center of one gear and the outer diameter of the other.)

Gear Pumps (External Gear) Advantages: Cheap (easy to manufacture) Compact Cheap Did I say inexpensive?

Gear Pumps (External Gear) Disadvantages Limited pressure capability Unbalanced (note where pressure is) Results in large bearing loads Can be noisy (gear mesh noise) Volumetric efficiency? Fixed Displacement

Gear Pumps (Internal Gear) Pumping Mechanism

Gear Pumps (Internal Gear) Displacement is a function of the number of teeth on the internal and external gears and the size of the crescent divider. ( I don’t have a formula for the displacement. Perhaps you can derive one.)

Gear Pumps (Internal Gear) Advantages Similar to external gear pumps in many respects Quieter as gear slap is reduced Disadvantages Somewhat more difficult to manufacture Same issues of volumetric efficiency Same issues of unbalanced forces Fixed displacement

Gear Pumps (Internal Gear - Gerotor) Mechanism External (inside) gear is shaft driven Internal gear is driven by external Single tooth space is displaced Design keeps tolerance close throughout the cycle

Gear Pumps (Internal Gear - Gerotor) Advantages Cheap Simple

Gear Pumps (Internal Gear - Gerotor) Disadvantages Limited pressure capability Unbalanced design Fixed displacement Frequently used as a charge pump

Vane Pumps Pumping mechanism

Vane Pumps Displacement VD = π/2(Dc-DR)eL C = Cam R = Rotor E = eccentricity L= depth

Vane Pumps (Variations) Vane tip pressure control options Outlet pressure under the vanes Surface pressure under the vanes Intravanes: outlet pressure is applied always to a small area of the vane while surface pressure is applied to the rest of the area These are probably Vickers innovations and hence are highlighted in the text

Vane Pumps (Variations) Balanced designs

Vane Pumps Advantages Cartridges to quickly replace rotating group

Vane Pumps (Variations) Variable Displacement Design

Vane Pumps Advantages Disadvantages Quieter than gear pumps Higher pressure capability than gear pumps? Better volumetric efficiency than gear pumps? Can be balanced in design for longer life Variable displacement an option Disadvantages More complex and expensive than gear pumps

Piston Pump Designs Axial Piston

Piston Pump Designs Displacement of an axial piston pump VD = YAD tan(θ) Y = Number of Pistons in the rotating group A = the area of a single piston D = is the diameter of the centerline circle of the piston bores θ is the angle of the swashplate or the bend angle

Piston Pump Designs Radial piston design

Piston Pump Designs Bent axis design

Piston Pump Designs Bent axis – variable displacement design

Piston Pump Designs Axial piston – variable displacement design

Piston Pump Advantages Generally highest volumetric efficiency Generally highest pressure capability Variable displacement designs

Piston Pump Disadvantages Higher cost (complexity)

General Issues Pumps are not strictly continuous flow devices. Discrete chambers are involved. Flow is collected for discharge through valve plates Design of the valve plate and the pump mechanism affects pressure pulses and variation (ripple) of torque and pressure Design of pumps is not taught here

General Issues Our theoretical displacements can be used to determine theoretical pump flow Actual flow is a linear function of pump displacement, speed, a units constant, and an efficiency term Two kinds of inefficiencies Volumetric losses Friction losses

Actual Pump Output, Q Qp = (Vp np ηVp) /1000 where: Q: L/min Vp : cm3/rev ηVp: Volumetric efficiency (decimal) OR… Qp = (Vp np ηVp) /231 where: Q: GPM Vp: in3/rev ηVp: same as above (no units)

Torque to Drive a Pump Tp = (ΔP Vp)/(2π ηtp) where: Tp : Newton meters torque required ΔP : pressure rise across the pump in MPa Vp : Pump displacement in cm3/rev ηtp : Pump torque efficiency – a decimal OR…

Torque to Drive a Pump English Units Tp = (ΔP Vp)/(2π ηtp) where: Tp : inch lbs torque required ΔP : pressure rise across the pump in PSI Vp : Pump displacement in inches3/rev ηtp : Pump torque efficiency – a decimal

Power to Drive the Pump The hydraulic power is QpΔP/60 or QpΔP/1714 for SI and English units (note this is actual pump flow, not theoretical) Shaft power to drive the pump is given by Psp = Phydr / ηpp where: ηpp = ηvp ηtp which is total pump efficiency

What Determines ηvp & ηtp ? ηvp is a function of clearance spaces, system pressure, and pump speed Leakage flow at a given pressure is relatively fixed regardless of pump speed It is also affected by fluid viscosity as lower viscosity fluid will result in higher leakage flow and lower volumetric efficiency

What about Torque Efficiency? Torque efficiency is a function of speed and fluid viscosity Higher pump speeds will result in lower efficiency as viscous friction is speed dependent Lower viscosity fluid can reduce viscous losses but acts negatively on volumetric efficiency

Efficiencies (μ n)/(ΔP x 1000)

Sizing Pumps Component sizing begins with the LOAD Load and actuator will determine Flow requirement for this circuit Pressure range required by the circuit (We’ll do this with cylinders and motors… soon) Total the simultaneous flow requirements Select for the maximum load pressure Add pressure drops that will occur in valves, lines and fittings ( another topic to come…)

Pump Sizing With pump outlet pressure and flow known we will consider speed. Industrial apps will use synchonous speed of electric motors. Generally 1750 rpm, or possibly 1100. ($ decides) Small diesel apps such as skid loaders can operate directly from engine crankshaft and will have engine speed. (2000-3000 rpm). Larger diesel apps – pump splitter with gear reductions possible to optimize speed

Pump Sizing Determine appropriate speed for your app Use the equation for pump flow, solved for displacement Vp = 1000Q/p (np ηVp) What shall we use for ηVp?? This is a function of speed, pressure, and fluid viscosity Look for vendor data or curves and adjust…

Example Pump Problem Car Crusher Need 125,000 lbs of force 8 foot stroke 10 seconds to extend? Target system max pressure of 1500 psi What is the cylinder size needed? 125,000 lbs/ A (area) = 1500 psi Area = 83.33 in2 πr2 = 83.33 in2 r = 5.15 inches (let’s use 5”)

Car Crusher Pump cont’d What will the system pressure be? Cylinder area = 52 π = 78.53 in2 125,000 lbs / 78.53 in2 = 1592 psi We study our plumbing and valves and allow for 300 psi drops in our system Set PRV to 1900?

Car Crusher Pump cont’d What is flow is required of the pump? Q = cyl stroke x area /time Q = 96 in x 78.53 in2/ 10 sec = 754 in3/sec 754 in3/sec x 1 gal/231 in3 x 60 sec/min Q = 195.8 GPM Note that we have sized for one cylinder. We might have others (a cylinder to kick your crushed Hummer bale out of the machine). Size for those that will be used simultaneously.

Car Crusher Pump cont’d Pump speed: Electric power available? - 1750 rpm Remote from grid? Diesel at 2200 rpm Determine approximate size Vp = 1000Q/p (np ηVp) or 231Q/p (np ηVp) Vp = 231*196/(1750*.95) Vp = 27.2 inches3/revolution

Car Crusher Pump cont’d Large pump (27.2 in3/rev) Now we would look at vendors For this large, a piston design is likely Could also select two or more smaller pumps operating in tandem with outlets coupled Selection will be based upon costs of installation, costs of operation, and required life Continuous use favors efficiency Intermittent use may favor low initial cost

Pumps Selection Fixed or variable displacement? So far our circuit is simple and we would likely use a fixed displacement pump Later we will look at more efficient circuits and may wish to select a variable displacement pump with appropriate controls

Positive displacement pumps: External gear pump Reciprocating piston Double screw pump Sliding vane Three-lobe pump (left) Double circumferential piston (centre) Flexible tube squeegee (peristaltic)

Pumps in series and parallel Equivalent pump Parallel Equivalent pump

Pumps in Series Add the heads (H) at each flow rate (Q) For example, for two identical pumps the head will be double that of a single pump.

Pumps in Parallel Add the flow rates (Q) at each head (H) For example, for two identical pumps the flow rate will be double that of a single pump.

Pump-system operation System resistance (losses) curves (typically H  Q2) C = operating point

Positive Displacement Pumps Typical Characteristics Constant Flow at Various Pressures Pulse Flow is possible Most can pump solids suspended in liquids Self-priming

Types of PD Pumps Rotary Pumps Reciprocating Pumps Gear – Internal, External Lobe Vane Screw Reciprocating Pumps Piston Plunger Diaphragm

Rotary vs. Reciprocating Pumps Rotary pumps transfer liquid through the action of a rotating mechanism (gear, lobe or vane) operating inside a rigid container Pumping rates varied by changing speed of rotor

Rotary vs. Reciprocating Pumps Reciprocating pumps move liquids by changing the internal volume of the pump Require valves on the suction and discharge sides Pumping rates varied by changing the frequency or the stroke length Source: http://www.watson-marlow.com/wna-se/p-fmi.htm

Internal Gear Pumps Smaller gear rotating within a bigger gear Partial vacuum created by meshing and unmeshing of internal teeth with external teeth Crescent divides liquid flow between rotor and idler gears Source: http://www.pumpschool.com/principles/internal.htm

PD Pump Curve Constant speed, can’t control flow Source: http://www.driedger.ca/ce2_pdp/CE2_PDP.html