1. Positive Displacement Devices Displacement Formulae Characteristics
Hydraulic Pumps
Positive Displacement Devices
Displacement Formulae
Characteristics

2. Gear Pumps (External Gear)
Pumping Mechanism

3. 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.)

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

6. 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

7. Gear Pumps (Internal Gear)
Pumping Mechanism

8. 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.)

9. 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

10. 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

12. Gear Pumps (Internal Gear - Gerotor)
Advantages
Cheap
Simple

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

14. Vane Pumps
Pumping mechanism

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

16. 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

17. Vane Pumps (Variations)
Balanced designs

18. Vane Pumps Advantages
Cartridges to quickly replace rotating group

19. Vane Pumps (Variations)
Variable Displacement Design

20. 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

21. Piston Pump Designs
Axial Piston

22. 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

23. Piston Pump Designs
Radial piston design

24. Piston Pump Designs
Bent axis design

25. Piston Pump Designs
Bent axis – variable displacement design

26. Piston Pump Designs
Axial piston – variable displacement design

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

28. Piston Pump Disadvantages
Higher cost (complexity)

29. 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

30. 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

31. 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) / where:
Q: GPM
Vp: in3/rev
ηVp: same as above (no units)

32. 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…

33. 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

34. 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

35. 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

36. 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

37. Efficiencies
(μ n)/(ΔP x 1000)

38. 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…)

39. 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 ($ decides)
Small diesel apps such as skid loaders can operate directly from engine crankshaft and will have engine speed. ( rpm).
Larger diesel apps – pump splitter with gear reductions possible to optimize speed

40. 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…

41. 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 = in2
πr2 = in2 r = 5.15 inches (let’s use 5”)

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

43. Car Crusher Pump cont’d
What is flow is required of the pump?
Q = cyl stroke x area /time
Q = 96 in x in2/ 10 sec = 754 in3/sec
754 in3/sec x 1 gal/231 in3 x 60 sec/min
Q = 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.

44. Car Crusher Pump cont’d
Pump speed:
Electric power available? 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

45. 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

46. 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

47. 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)

48. Pumps in series and parallel
Equivalent pump
Parallel
Equivalent pump

49. 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.

50. 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.

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

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

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

54. 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

55. 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:

56. 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:

57. PD Pump Curve Constant speed, can’t control flow
Source: