Chapter:Hydraulic pumps

Dr. SALVADOR VARGAS DÍAZDepartamento de Ingeniería Mecánica

Universidad de San Buenaventura

Semestre 2015-I

RotodynamicsRotodynamic pumps derive their name from the fact that a rotating element (rotor) is an essential part of these machines. The mutual dynamic action between the rotor and the working fluid forms their basic principle of operation. The blades, fixed to the rotor, form a series of passages through which a continuous flow of fluid takes place as the rotor rotates. The transfer of energy from the rotor to the fluid occurs by means of rotodynamic action between the rotor and the fluid.

Positive displacementDisplacement pumps consist of one or several pumping chambers. These chambers are closed and have nearly perfect sealing. The volume of these chambers changes periodically with the rotation of the pump driving shaft. The fluid is displaced from the suction line to the delivery line by the successive expansion and contraction of the pumping chambers.

IntroductionHydraulic pumps are machines that act to increase the energy of the liquid flowing through them. The three main classes of pumps are displacement, rotodynamic, and special effect pumps. The displacement pumps act to displace the liquid by contracting their oil-filled chambers. In this way, the fluid pressure increases and the fluid is displaced out of the pumping chamber. The rotodynamic pumps increase mainly the kinetic energy of the liquid due to the momentum exchange between the liquid and the rotor. The special effect pumps, such as jet pumps and airlift pumps, operate using different principles.

Classifications of hydraulic pumps

Example of displacement pumps function (Piston)The function of the displacement pumps is explained by describing the construction and operation of the single-piston pump, shown in Figure. The piston (4), driven by a crank shaft (5), reciprocates between two dead points. During the suction stroke, the piston moves to the right and the oil is sucked from the tank (1) through a check valve (2) of very low cracking pressure. The cracking pressure is the minimum pressure difference needed to open the check valve. Then, during the delivery stroke, the piston moves to the left, displacing the oil to the exit line through the check valve (3). The pump acts on the oil by the pressure, P, needed to drive the load. Therefore, the pump drive should act on the piston by the force needed to produce this pressure, and the crank shaft should be acted on by a torque proportional to this force. The cylinder (6) retracts under the action of the loading force by opening the shut-off valve (7).

Ideal Pump AnalysisThe pump displacement is defined as the volume of liquid delivered by the pump per revolution, assuming no leakage and neglecting the effect of oil compressibility. It depends on the maximum and minimum values of the pumping chamber volume, the number of pumping chambers, and the number of pumping strokes per one revolution of the driving shaft. This volume depends on the pump geometry; therefore, it is also called the geometric volume, Vg. It is given by the following equation:

Wherei = Number of pumping strokes per revolutionVg = Pump displacement (geometric volume), m3/revVmax = Maximum chamber volume, m3

Vmin = Minimum chamber volume, m3

z = Number of pumping chambers

Assuming an ideal pump, with no internal leakage, no friction, and no pressure losses, the pump flow rate is given by the following expression:

WhereQt = Pump theoretical flow rate, m3/sn = Pump speed, rev/s

The input mechanical power is equal to the increase in the fluid power as shown by the following equation:

WhereTt = Pump theoretical driving torque, NmΔP = Pressure increase due to pump action, Pa

Example A gear pump of 12.5 cm3 geometric volume operated at 1800 rev/min delivers the oil at 16 MPa pressure. Assuming an ideal pump, calculate the pump flow rate, Qt, the increase in the oil power, ΔPot, the hydraulic power at the pump exit line, Potout, and the driving torque, Tt, if the inlet pressure is 200 kPa.

Real Pump AnalysisThe hydraulic power delivered to the fluid by the real pumps is less than the input mechanical power due to the volumetric, friction, and hydraulic losses. The actual pump flow rate, Q, is less than the theoretical flow, Qt, mainly due to:

• Internal leakage• Pump cavitation and aeration • Fluid compressibility• Partial filling of the pump due to fluid inertia

The first source of power losses is the internal leakage. Actually, when operating under the correct design conditions, the flow losses are mainly due to internal leakage, QL. The leakage flow through the narrow clearances is practically laminar and changes linearly with the pressure difference (see Figure). The resistance to internal leakage, RL, is proportional to oil viscosity, μ, and inversely proportional to the cube of the mean clearance, c.

Where

The effect of leakage is expressed by the volumetric efficiency, ηv, defined as follows:

The volumetric efficiency of displacement geometric) pumps ranges from 0.8 to 0.99. Piston pumps are of high volumetric efficiency, while vane and gear pumps are, in general, of lower volumetric efficiency.

The friction is the second source of power losses. The viscous friction and the mechanical friction between the pump elements dissipate energy. A part of the driving torque is consumed to overcome the friction forces. This part is the friction torque, TF. It depends on the pump speed, delivery pressure, and oil viscosity. Therefore, to build the required pressure, a higher torque should be applied. The friction losses in the pump are evaluated by the mechanical efficiency, ηm, defined as follows:

WhereT = Actual pump driving torque, NmTF = Friction torque, NmT – TF = Torque converted to pressure, Nmω = Pump speed, rad/s

The third source of power losses in the pump is the pressure losses in the pump’s inner passages. The pressure, built inside the pumping chamber, PC, is greater than the pump exit pressure, P. These losses are caused mainly by the local losses. The hydraulic losses are of negligible value for pumps running at speeds less than 50 rev/s, and mean oil speeds less than 5 m/s. For greater speeds of oil, the pressure losses are proportional to the square of the flow rate. These pressure losses are evaluated by the hydraulic efficiency, ηh.

WherePC = Pressure inside the pumping chamber, PaP = Pump exit pressure, Pa

An expression for the total pump efficiency, ηT, is deduced as follows:

The mechanical power ω(T -TF ) is converted into equal hydraulic power, Qt PC, then

In the steady-state operation, the real displacement pump is described by the following relations:

WhereNh = Hydraulic power, WNm = Mechanical power, WΔP = Difference between the pump output and input pressures, ΔP = P − Pi, Pa

If the pump input pressure, Pi, is too small compared with the delivery pressure, P, then it may be neglected, and the pressure difference, ΔP, equals the pump exit pressure, P. If so, then

Cavitation in Displacement PumpsThe cavitation characteristics of a pump describe the effect of input pressure on the pump flow rate. The reduction of the pump inlet pressure to values less than the vapor pressure leads to the evaporation or boiling of oil. The fluid flow to the pump inlet becomes a mixture of liquid, liberated gases, and vapors. At zero or very lowexit pressure, when the pump is bypassed for example, the vapors do not condensate and the vapor cavities do not collapse. But during normal operating conditions, the pump is loaded by great load pressures. The vapor cavities collapse due to the rapid condensation of vapors when transmitted to the high-pressure zone. Therefore, the net flow rate of the pump decreases. Generally, a 1% increase in the vapor volume in the oil-vapor flow reduces the pump volumetric efficiency by about 1%.

The impact pressure reaches very high values, up to 7000 bar. When subjected to cavitation, the pump noise level increases and a very loud sharp noise is heard. The surfaces of the inner pump elements are damaged due to the pitting resulting from the impact pressure forces. Therefore, the pump inlet pressure should be higher than the saturated vapor pressure of oil at the maximum operating temperature by a convenient value. This value is called cavitation reserve and ranges from 0.3 to 0.4 bar, see Figure.

WhereA = Piston area, m2D = Pitch circle diameter, md = Piston diameter, mh = Piston stroke, mz = Number of pistonsα = Inclination angle, rad

1. Drive shaft, 2. Disk, attaching pistons, 3. Cylinder block, 4. Piston, 5. Port plate

Whereα = Swash plate inclination angle, rad.

1. Drive shaft, 2. Swash plate, 3. Slipper pad, 4. Retaining plate, 5. Cylinder block, 6. Piston, 7. Port plate, 8. Fixed guide of the retaining plate, 9. Cylinder block loading spring

1. Housing, 2. Mounting flange, 3. Drive shaft, 4. Two bearing blocks, side plates, 5. Bearing bush, 6. Discs, 7 and 8. Inlet and exit ports, 9. Driving gear, 10. Driven gear

Whereb = Tooth length, mm = Module of tooth, mz = Number of teeth per gearγ = Pressure angle of tooth, rad

1. Shaft, 2. Rotor, 3. Stator ring (cam ring), 4. Vanes, 5. Fixed side plates, 6. Casing,7. Bearing mount, 8. Intra-vane

Pump SpecificationThe following list shows the basic specifications that should be available to specify the pump precisely:

• Size (displacement)• Speed (maximum and minimum speeds)• Maximum operating pressure (continuous/intermittent)• For open/closed circuit• Direction of rotation (viewed to shaft end; clockwise [R], counterclockwise [L])• Controller (for variable displacement pumps)• Seals (oil)• Drive shafts• Port connections• Mounting type• External dimensions• Installation position• Operating temperature range• Further details in clear text

The magnitude of flow pulsation is evaluated by the pulsation coefficient and is defined as

WhereσQ = Flow pulsation coefficientQmin = Minimum value of pump flow rate, m3/sQmax = Maximum value of pump flow rate, m3/sQm = Vg n = mean flow rate, m3/s

Considering the case of a throttled pump exit line and neglecting the fluid compressibility, the pressure at the pump exit is given by

WhereσP = Pressure pulsation coefficientPmin = Minimum value of pump exit pressure, PaPmax = Maximum value of pump exit pressure, PaPm = Mean exit pressure, PaIf the flow rate oscillates between 0.9Qm and 1.04Qm, then σQ = 14% and σP = 27.16%. Actually, considering the effect of oil compressibility, the pressure oscillation decreases especially for the increased volume of the exit line.

Rotodynamic pumps, such as centrifugal pumps, are machines that transfer energy to the liquid by increasing its momentum. This class of pumps is used widely wherever high flow rates are required under low or medium heads. They offer advantages such as simple construction, low price, easy maintenance and repair, and the ability to work with liquids of low lubricity.

Impeller types of rotodynamic pumps

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