power plants short

8/8/2019 Power Plants Short

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ABSTRACT

The aircraft powerplantincorporatesengines which provide athrust force and allsystemsnecessary to provide their effective and

reliable operation.Systems consist ofassemblies and communications which aresituated on the engine directly, and also ofelements which areintegrated into construction of the aircraft.

Power, reliability and economy of powerplant are one of majorfactors, defining development of the aircrafts both civil, and defensiveassignment.

1. GENERAL INFORMATION ABOUT AIRCRAFT POWERPLANTS

1.1. The basic systems of the aircraft powerplantThe aircraft powerplant consists of the next basic systems:- engine with the propulsor;- fuel system;- lubricating system;- starting system;- cooling system;- engine air supply system;- gas exhaust system;- engine mounting and nosing system;- engine automatic control and diagnostic system.

1.2. Classification of the aircraft powerplants

The listed above systems of an aircraft powerplant, depending onassignment of the aircraft and such as the used engine, can have thediversified construction.

As the type of an engine in many respects defines constructions of

engine powerplant, now it is accepted to classify them as a used engine.

1.3. Requirements to the aircraft powerplant

Generally basic requirements to an aircraft powerplant can beformulated as follows:

1. The powerplant is to provide the necessary power or thrust.2. The powerplant is to have the minimal sizes and mass,

favorable from the aerodynamic point of view arrangement. Thus the

special attention should be given to mass performances of the powerplant.1


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The decrease of mass of a powerplant allows to receive major massoutput of an airplane, to increase container of fuel tanks, and, hence, toextend the range, to use more perfect equipment.

3. The powerplant is to have a high efficiency.The efficiency of the powerplant can be determined by expression:

e

pppp

N

N= 1 ,

where eN- effective power of the engine;ppN - expenditures of engine power, bound with placement of a

powerplant on an aircraft.4. The powerplant should have high reliabilityand operational

safetyon all conditions of flight, in any atmospheric conditions andadmissible positions of an aircraft.High reliability is understood as reliable start and fault-fre

operation. High safety is in the basic a fire safety.5. The powerplant should have high survivorship (),

i.e. small damageability, saving of serviceability (or possibility of fastreduction of serviceability at a defeat).

6. The powerplant should be convenient in maintenance, i.e.have light access to structural elements for their inspection, checking,mounting and repairing, to differ by simplicity of repair work, to haveminimum necessity in special repair inventory, instrument and deficientmaterials.

1.5. Assemblies of the powerplants

The powerplant includes some systems providing operation of theengine. In turn, each system consists on several assemblies, boundamong themselves by hydraulic, pneumatic or electrical communications.

The assemblyterms structurally self-maintainedunitof the

powerplant executing particular, restricted enough function on engineservicing.

On assignmentthis unit can fall into to assemblies of a fuel system,lubrication system, starting system, automatic control and diagnosticsystem.

On function indications to assemblies it is possible to refer pumps,motors (drives), compressors, governors, servomechanisms, startingdevices etc.

On a kind of a consumed energythe assemblies can be equipped

with mechanical, electrical, hydraulic, pneumatic and other driving.2


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Now majority of assemblies are unified work pieces and can go intocomposition of powerplants created on the basis of different types ofengines. To such assemblies it is possible to refer booster and transferpumps, starter-generators, compressors, components of a starting

system, monitoring system etc.The powerconsumed by assemblies of modern aircrafts, averages35 % of engine power and can reach 100200 kW and more.

The requirements produced to assemblies, can be formulated asfollows: the assemblies should have minimally possible overall dimensionsand weight, to consume possibly smaller power, to have high usereliability, to be convenient in maintenance and to differ by simplicity of aconstruction and low cost of manufacture.

Placementof assemblies and driving to them yield, taking intoaccount the following reasons:

- the driving must provide a transmission of a necessary power, aset reduction ratio, a set direction of rotation and simplicity ofmaintenance;

- the assemblies and driving to them should not considerablyincrease a midsection of an engine;

- the construction of driving and attachment points of assembliesshould ensure minimum influence of temperature strains andvibration on assemblies operation.

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2. AIRCRAFT FUEL SYSTEM

The fuel system represents a rather composite complex of differentinventory, which trial functions are:

- placement of a given quantity of fuel;- reliable supplying of an engine by a fuel under all possible flight

and operation conditions;- securing of an airplane center-of-gravity position at fuel use;- providing of maximal fuel use in tanks.Besides the fuel system should have minimum overall dimensions

and weight, to be safe in a fire ratio, to have high survivorship ()(in case of damage), to ensure simplicity both speed of a filling, andpossibility of emergency spill of a fuel.

2.1. Fuel system compositionThe fuel system of the modern aircrafts contains the following basic

elements:- tanks: main, additional, charging, pendant (), negative

overloads, intermediate (), starting fuel;- pipelines: supply, by-pass, transfer, filling, branch, venting

(), drainage ();- intakes: fuel, venting;- valves: check, reducing, relief, float, cutoff (shutoff), distribution,

spill;- pumps: booster, transfer, starting, reserve, pumps-governors;- filters and cleaners: cellular (), centrifugal, magnetic,

electrostatic;- fuel level indicators: potentiometric, capacitive, induction,

ultrasonic;- flow-meters, synchronizers, proportionizers, automatic control units

() of a center-of-gravity position and filling.Besides the different command lines go into many of modern fuel

systems: electrical, hydraulic and pneumatic.The listed above devices of a fuel system to functional attributes can

be integrated in some groups or systems:- filling system;- supply system;- tanks drain and pressurization system;- monitoring system;- emergency spilling system.

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2.3. Fuel filling system

The tank fuelling is carrying out on ground with the help of an

automobile - refueller, in which tank the necessary fuel capacity isdisposed. This fuel is submitted in aircraft tanks by the transfer pumpsthrough pipelines on diameter 100150 mm. The tank fuelling on groundcan be manufactured from above and from below.

At tankfilling from above fuel flows through filling ports located in atop of a tank. The retard grid ( ) having 250400 holes on1 m2 placed on ports. The mean conditional velocity of a filling does notexceed 2 m\s. A deficiency of a filling from above is the evaporation,spraying and saturation of fuel by air.

For elimination of these undesirable phenomena it is necessary todecrease velocity of filling, which results in intolerable ()major time of a filling, which (is especial for heavy airplanes) can reach ofseveral hours. For this reason the tank filling from above is applied nowonly on small airplanes.

More progressive method of a filling is the single-point filling of anairplane from below(fig. 1) through filling ports under pressure 0.30.5P, which allows sharply () to reduce duration of a filling and toremove a capability of evaporation of fuel and its saturation by air.

The termination of a filling in this case execute automatically with the

help of float valves, and the final replenishing, in quantity severalhundreds of liters, yields from above, manually.

Through filler hole ( ) 1 (fig. 1) the fuel flowsin a filling pipeline. Through cutout switches opening of filling valves 2 isproduced. The valve position is indicated by the lamps. After a filling of thetank 3 fuel magnetic sensors of a level 6 (and at recompression( ) also the warning indicators 7) give commands onautomatic closing of the filling valves. In case of malfunction() magnetic sensors there are float warning indicators of

a level, which double commands on closing of filling valves.In failing of the valve there are relief float valves of a limit level 4, not

supposing overflowing of tanks and ejection of a fuel through the ventingpipelines. At pressure above limit the relief valve 10 works. For fueltransfer from the pipeline the drain valve 9 is stipulated. On the fillingcontrol panel 8 the indicators of the fuel content in tanks can place. Exceptfor automatic control of a filling, is present also manual.

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Fig.1. Diagram of the closed fuel filling line: 1 filler hole ; 2 valve;3 tank; 4 relief float valve; 5 outer pipe branch of the venting

pipeline; 6 magnetic level sensor; 7 pressure sensor; 8 control panel;9 drain valve for a fuel scavenge for the pipeline; 10 relief valve of thelimit pressure.

The enclosed filling is executed faster, but the filled volume is less,than at an unclosed filling. It is explained to that float devices, locatedinside a tank, (magnetic sensors, warning indicators of a level, the reliefvalves) work up before a full tanking. At an enclosed filling the unclosedmanual replenishing () is necessary.

On some airplanes now discovers broad enough application a fillingin air from the tanker airplanes, specially intended for this purpose. Thereplenishing of airplanes in air allows extending the range, to facilitatetake-off, to increase an effective load and to reduce a takeoff distance.

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2.4. Engine fuel supply system

The fuel supply may be pump house, expulsive and gravity-flow(fig.3). Fuel consumption from tanks by gravity flow (fig. 3, ) is low efficient.

Such mode of consumption ( ) is applied on aircraftswith low-powered reciprocating engines, where the required engine pumpinlet pressure is insignificant. On aircrafts designed on a short-time flight,the expulsive supply system can be applied which expulses the fuel from atank by a compressed air or neutral gas (fig. 3, b). The expulsive systemappears is more expedient () than a pump house in massrelation, if the fuel capacity in tanks does not exceed 300400 kg.Deficiencies of such system: a major mass of pressure tanks and their lowsurvivorship at damage.

Now on airplanes both civil and military the pump house system offuel supply to an engine (fig. 3, c) is applied, as a rule.

.

Fig. 3. Methods of a fuel consumption from tanks: gravity-flow; b expulsive; c pump housing;

1 inlet of the atmospheric air; 2 tanks;3 fuel supply pipelines; 4 check valves; 5 inlet of the air from

the engine compressor; 6 relief valve; 7 feed pump.

Let's consider the principal diagram of the engine fuel supply linewith the feed pump (fig. 4). Such fuel consumption terms unclosed. It isbasic on a civil aircrafts. A space above a fuel in a tank is communicatedwith ambient air through the inlet 1. A tank 3 is filled through a filling portor fill hole 2. On modern A\C for providing of reliable fuel supply to enginesthe multi-stage pumping is applied. Usually use one low-pressure pump ofthe first stage (LPP1) 5 and one low-pressure pump of a second stage

based on the engine (LPP2) 12.7


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V

enginefue

lsupplyline

withthefeedpump

Thus LPP1 creates necessary upstream pressure in LPP2, and lastensures necessary upstream pressure in the main (high pressure) pumpof an engine (HPP) 20.

The advantages of such two-stage pumping are a smaller of massLPP1 and LPP2 and smaller power on their driving as contrasted to onelow-pressure pump, at the same required upstream pressure in HPP. TheLPP1 operational mode can be regulated, providing necessary pressure.The particular order of turning the LPP1 power on and off ensures aprogram fuel use from tanks.

The check valve ( ) 7 ensures a necessarydirection of motion of a fuel. For example, at presence at one tank twoinstalled in parallel LPP1, in fail of one of them, the fuel submitted byanother LPP1, would return through the disabled pump in a tank. But the

check valve located after a disabled LPP1 will cut off the fuel supply in atank. The check valves similarly operate at a going into an operation of thefuel accumulator 8, opening of the cross feed valve 10 and in other cases.Air from the fuel chamber of the accumulator through the throttle 9 goes ina tank.

The fire-protection valve 11 cuts off the fuel supply. At cooling of oilby fuel a fuel/oil heat exchanger 14 is included in an engine fuel supplyline, which also warms up fuel. Thus a fuel spraying is improved and the

filter 17 is saved from icing. If an engine needs less fuel, than it is neededfor cooling of oil in fuel/oil exchanger, a part of fuel, outgoing the radiator,is returned to a tank by a by-pass line supplied with the thermostat 15.The heightened pressure (after a shutdown) is released() by a by-pass of fuel in a tank by an unloading linethrough the relief valve 16. The checking-metering equipment irepresented by the capacitive transducer of a fuel quantity (level) 4,warning indicator of pressure 6, pressure alarm () or warning indicator of pressure 13, warning indicator of failure

of the filter 18, flow-meter 19 and pressure gauge 21 indicating the fuel8


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pressure before a fuel manifold 22.

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3. LUBRICATING SYSTEMS

The lubricating system at all possible operational modes and alltolerant maintenance conditions ( )

should satisfy the following functions:- supply of pure oil in an engine under sufficient pressure having

particular temperature and viscosity;- oil rejection from an engine;- oil cooling;- clearing of oil of gases and air and their exit at the atmosphere;- clearing of oil of mechanical impurities;- a capability of oil thinning () by fuel for facilitation

() of start at low temperatures.

3.1. Performances () of the aircraft powerplantslubricating systems

3.1.1. Operational conditions and requirements to oils

In aircraft powerplants preferential application have the liquidlubricants - lubricating oils. Perspective at a high operation temperature ofabrasion units ( ) aresolid(micro-laminated) andgaslubricants.

All kinds of lubricants execute two principal functions: reduce frictionforce between mutually displacing ( ) detailsand protect their contact surfaces from wearing (). Besides, theliquid and gas lubricants execute a third function also relating to aprincipal: draw off the heat, to which the friction work turns.

Alongside with main functions the lubricants can execute those orother sub-functions: to safeguard details from corrosion, to carry outparticles of wearing from abrasion units, to fill gaps () betweendetails, to be utilized as a working fluid in different gears etc.

In turbojets the normal operation of abrasion units is provided withpumping of rather small quantity of oil intensively circulating in a system(50130 times per hour). Temperature of oil (in a volume) because of adifference of the operation conditions can oscillate from - 30- 60o up to+130+150o and above.

So requirements for oil areflat viscosity-temperatureperformance ( ), low temperature ofhardening.

The bearings of the compressor at operation are heated up to 120

200o

, bearings of the turbine up to 250300o

, and after a stop of an10


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engine and termination of oil circulation and ventilation of housings ofbearings - is much higher. The heat of bearings promot() vaporization of oil and making of conditions for anoxidation both formation of precipitations and lacquer films (

). Therefore oil should differ by high thermo-oxidizing andthermal stability.The oil in a turbine engine moves to bearings through three- or four-

spray injectors in a gap between a ring and separator, is intensivelyatomized, coats a surfaces of rolling bodies, rings and separators, washesan exterior surface ( ) of bearings and, stronglyfoamed, drains () in oil collectors.

The required engine oil inlet pressure is determined by an oilconsumption and hydraulic resistance of the oil line.

3.2. Oil circulation consumption

Quantity of heat, which is necessary for removing from the bearing,is determined by friction work of the bearing and heating of the bearingfrom other details (shaft of the turbine, compressor casing etc.). Owing topresence of large number of the factors the calculation of quantity ofassigned heat represents rather complex problem, therefore in practice fordefinition of the circulating consumption of oil usually use empiricaldependences.

3.3. Lubricating system composition

Generally the lubricating system consists of: oil tank; heaexchanger; external and internal pipelines; booster, feed and scavengepumps; oil filters; gas separator; oil breather; reduction, shut-off and reliefvalves, nozzles, monitoring gears.

The internal lubrication system incorporates: the feed and scavengepumps and also the filters mounted after feed and before scavenge

pumps.The external lubrication system incorporates: heat exchanger, oil

tank with all accessories, oil pipelines of the feed (tank-engine) andscavenge (engine-tank) lines, drain and breathing pipelines, spill tubesand valves, temperature and pressure measuring gears.

Except for the specified devices, to an external lubrication systemsometimes add the filter on a line engine-tank, shutoff valve or valve on aline tank-engine, any different relief valves, thermostats etc.

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3.4. Structural diagrams of the lubricating systems

3.4.1. Classification of the lubricating systems

The lubricating systems on circulation ratio of lubricant can bedivided on three types:- recirculatory, in which the oil is utilized multiply; it is

distributed around the engine and returned to the oil tank by pumps;- opened(expendable), in which the oil is spilled overboard

after the engine has been lubricated;- combined, where the part of the oil is multiply utilized, and

the part is rejected after single-pass application.The opened scheme is most simple on a construction, but is not

costly-effective (). The application of the opened systemappears expedient on engines of one-time operation. In this case the fuelcan be used as lubricant.

The application of a combined system sometimes appears expedientfor lubrication of bearings of high-temperature turbine engines. In this caseat lubrication of the turbine bearings the oil will be utilized one time withconsequent exhaust, and at lubrication of others friction components -multiply.

The most costly-effective is the circulation lubrication systemobtaining the greatest propagation in a turbine engines.

The circulatory systems are divided on three groups:- normal or straight-line scheme;- reversible scheme;- scheme with a short-closed path.

3.4.2. Straight-line system

In the straight-line scheme (fig. 7) the oil is supplied from anengine by a scavenge pump to the radiator, then to an oil tank, whence

() by gravity flow through the filter goes to a feed pump supplyingpurified and cooled oil in an engine.

The oil tankis a main element of an oil supply system. In it placed asoil, circulating in a system and a reserve volume added to circulating oil inprocess of its burn-out.

The filtration of oilis made both in internal, and in external pipelines.The main filters in an internal system are: the fine (high-pressure) filter,located after a feed pump, and the mesh strainer located on at outlet of anengine before a scavenge pump.

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gsystem:1,14oilspillcocks;2tank

;3fillerneck;4feed

pump;5tankoillevelindicator;6reducingvalve;7te

6heatexchanger

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The main filters in an external system are: a grid on a filler neck, gridat the inlet union, filter between a tank and feed pump. Sometimes thepadding filter between an scavenge pump and radiator is installed.

The oil is cooledin the heat exchanger. The cooling medium may be

fuel or air and, in some instances, both fuel-cooled and air-cooled coolersare used. Some engines which utilize both types of cooler may incorporatean electronic monitoring system which switches in the air-cooled cooleronly when it is necessary. This maintains the ideal oil temperature andimproves the overall thermal efficiency. The fuel-cooled coolers are moreeffective due to less power losses on overcoming the external drag andless losses of a heat which is exhausted with a fuel. The air-cooledcoolers are more expedient for applying in powerplants, where quantity offuel, flowing in an engine, appears poor for necessary heat pick up (TPEand air reciprocating engines).

The fuel-cooled oil cooler has a matrix which is divided into sectionsby baffle plates (extended surfaces). A large number of tubes convey thefuel through the matrix, the oil being directed by the baffle plates in aseries of passes across the tubes. Heat is transferred from the oil to thefuel, thus lowering the oil temperature.

The straight-line oil system is the most simple on construction but itis applied at subsonic flight velocities and mean altitudes (about 78 km).The main disadvantage of this scheme is difficult air and gas separationfrom oil because of the backpressure caused by a presence of the radiator

in a scavenge pipeline, and also because of decrease of thetemperature before it enters a tank.

3.4.3. Reversible system

The lubricating system of the reversible scheme differs from earliersurveyed by placement of the radiator on a line tank-engine (fig. 8), due towhat the separation of air is facilitated ().

The oil in a tank flows hot, its viscosity is almost twice less, thereforea velocity of up-floating of air bubbles is twice more. Simultaneouslybecause of the absence of the cooler in a scavenge pipeline quantity ofbubbles of small diameter originating at pressure drop of oil behind thecooler decreases sharply. A relative volume of air, dissolved in a an oil, attransferring from a straight line to the revertive scheme will decrease twice(with 7 8 % up to 3 4 % near the ground).

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As a circulation of oil through the heat exchanger can not besupplied at the expense of sucking ability of a feed pump, the revertivescheme requires the installation of the additional pump on a pipelinebetween a tank and heat exchanger.

Owing to decreasing of air bubbles, and also owing to the installationof the padding pump the altitude performance of an oil system of therevertive scheme appears above, than the altitude performance of astraight line scheme, and reaches 10 12 km and more.

3.4.4. Short-closed path system

The short-closed path system is equipped with the oil tank whichcontains only reserve volume of oil, as due to application of the centrifugaldeaerator there is a possibility to provide oil purification without using an

oil tank (fig. 9).Air separated in a centrifuge, and some of oil (5 10 %), necessary

for a warm-up oil in a tank, directs to the tank. The oil from a tankcompensatory leakage of oil from a centrifugal breather and burn-out,through the pump (jet or volumetric) goes into the circulating circuit.

The main advantages of this system are:1) it allows to raise pressure before a feed pump, i.e. to raise altitude

performance of the system up to any necessary value;2) all oil moves through the deaerator, thus ensuring a high scale of

separation of air from oil;3) an inertia of the system is reduced, so a fast heating of circulatingoil is ensured.

However the short-closed path oil supply system is more complex ona construction, than earlier surveyed, and requires more carefuoperational development.

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Fig.9.Short-closedpathlubrica

tingsystem

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oillevelindicator;2,16oilspillcocks;3tank;4fillerneck;5feedpump;6,11reducingvalves;7chec

kvalve;8

filter;13pre

ssuregauge;14engine;15scavengepump

s;17deaerator;18cooler,19fixedrestrictor

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4. PUMPS

4.1. A general characteristic of pumps

4.1.1. Types of the pumps used in aircraft powerplants

Pumps are the most widespread assemblies () of aircraftpowerplants. Their purpose - transformation of a mechanical energyapplied to the pump into energy of a transferredfluid stream,appeared inpressure and velocity.

Pumpsinaircraft powerplants can perform the various functions: tosupply fuel for engine operation, to supplyoil for lubricating of wearsurfaces and heat abstraction from the heated up details, to supply a

operating fluid for a drivingof various mechanisms serving the engine, anaircraft powerplant, an aircraft and etc.

The volumetric and vaned (dynamic) pumps are wide spread inaviation.

Volumetric pumps operation is based on a periodic change ofoperation volume of their pumping elements. At increase of operationvolume there is its filling withfluid from a suction line, at reduction ofoperation volume - a fluid displacement into afeed line.

Each pumping element of the volumetric pump for one cycle

displaces the strictly certain fluid volume, constant for the given pump anda mode of its operation.Pressure behind the pump is determined by hydraulic resistance of

lines and components located behind the pump. Therefore the volumetricpumpin theory can render with no limit high pressures. Pressure actuallygenerated by the volumetric pump is limited by durability and rigidity of thepump parts and by sealing ability of its pumping unit.

On character of a pumping element motion volumetric pumps can bedivided on plunger (piston, fig. 1, a) and rotational (fig. 1, b, c).

In the plunger pump a fluid supply is carried out due toreciprocating motion of a pumping element and in rotational - due to rotarymotion. The last circumstance allows making the rotational pump morecompactly than plunger one and at the same dimensions the rotationalpump provides the more capacity.

The rotational pump operates without the fluid distribution elementsat the inlet and at the exhaust whereas in the plunger pump their presenceis necessary.

On an embodiment the rotational pumps can be a gear-type (fig. 1,b), a sliding-vane-type (a wing type, fig. 1, c) and other types.

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The vaned pumps (fig. 1, d) transfer fluid owing to thetransition to itenergy in theimpeller channels. Head pressure Hgenerated by thevaned pump considerably changes with the change of rotation speedandis limited to thecircumferential velocity on the outer diameter of the

impeller (fig. 2).

)

b)

c)

d)

Fig. 1. Pump diagrams:) plunger; b) gear-type; c) lobular pump();

d) centrifugal.

If the volumetric pump, operating at the constant rotation speed andvariable cross-sectionat the exhaust, provides theoretically constantconsumptionQ at variable pressurep (fig. 3), then the vaned pump willoperate both with the variable pressure and the variable consumption (fig.2). Vaned pumps advantage is that these pumps can operate at high

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rotation speed and at higher circumferential velocity of impeller (tens inm/s) whereasthe pump elementscircumferential velocity of volumetricpumps does not exceeds usually 10 m/s.

Fig. 2. Fig. 3.

In all types of pumps a rotor circumferential velocity is limited to thecavitation absencerequirement, but also fromthis point of view vanedpumps can operate at the big circumferential velocity of a rotor movement,than volumetric.

Vaned pumps advantage is uniformity on time of generated by it afluid flow while volumetric pumps develop a pulsating flow.

It is necessary to consider among the lacks of vaned pump aninability to start operate without preliminary fluidfilling that explainspresence of the large gaps in their pumping unit.

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Volumetric pumps

1.1.1. The volumetric pump capacity

The critical pump parameters: the pumping elements size and

quantity, and also the pumping unit rotation speed are determined bycapacity and necessary uniformity of supply.In turnpump capacity isdetermined by the required fluid consumption cQ necessary for one oranother system operation of an aircraft powerplant.

For any type volumetric pump the ideal (theoretical)capacity can bewritten down as

60

FbznQid= , m

3/s,

where F- operation volume cross-sectional area of each pumpingelement, m2;

b- axial size of a pumping element, m;z- number of pumping elements;n - rotation speed, rpm.Ideal capacity is calculated on the pump geometrical parameters or

measured by slow pumpslipping (n= 2030 rpm) at zero pressuredifference.

1.1.2.Volumetric pump efficiency

In the any type of volumetric pump always there are volumetricintrinsic losses which result in the valid pump capacity reduction.

Reducing of valid capacity in comparison with ideal occurs becauseof internal leakage of a fluid leakQ through gaps between the exhaust andthe inlet cavities and because of volumetric lossesduring the suction inQ at the cavitational operating mode approach, i.e.

inleakidp QQQQ = .The volumetric losses in the pump are characterized in volumetricefficiency v representing the valid capacity relation to ideal:

inleakid

in

id

leak

id

pv QQ

QQ

QQ

QQ === 11 .

v value depends on the pump design and on its operationconditions: pumping unit sealing degree, inlet conditions in the pump,pressure drop, pumping unit rotation frequency, a fluid temperature.

v can be varied from 0 up to 1 depending on influence of theseparameters.

The influence analysis of the listed above factors on v allow tomake the following conclusions.

1. On v value the greater influence is rendered with gaps values in22


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Fig. 4. Fig. 5.Thus, v will have the maximal value at such viscosity, at which the

total intrinsic losses will be minimal.According to this the v value will depend on fluid temperature: in

some interval v is saved in acceptable limits, at tincrease it decreasesowing to leakages increase and cavitation occurrence during suctionbecause of p increase, and at tdecrease it decreases owing toincrease of a suction line resistance because of working cavitunderfilling (fig. 7).

Fig. 6. Fig. 7.

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1.1.3.Power consumed by the pump

It is possible to write downfor any type of the pumpthat the powerconsumed by it, is equal

p

pc

QpN

= , W.

where p - pressure drop;pQ - pump capacity, m3/s.

The total pump efficiency p is equal to product mv , where m -mechanical pump efficiency dependent on pressure drop, pump designfeatures (gaps values in pumping unit, conditions of wear surfacesgreasing etc.).

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1.2. Gear-type pumps

1.2.1.Structure and operation principle

Nowadays the gear-type pumpsare most widespread.

The gear-type pumps deficiency () is gradual() gaps increase during theoperational process owing towearing of pumping unit details and as a result of this pump capacityreduction.

The gearpumping unitconsists usually of two gear wheels which arein gearing, installed with possible smaller gaps in the special housingborings ( ), communicated with inlet (suction) andexhaust (charging) chambers.

Fluid supplyby the pump occurs owing to transfer of fluid in gearwheels cavities from the inlet chamber to the exhaust chamberandreplacement it into the exhaust chamber byteeth of one gear wheel fromcavity of another.Getting into an inlet chamber, teeth leave cavities, a fluidagain enters in the emptied volume of cavities, and this process isrepeated.

Depending on operating pressure value gear type pumps are dividedinto three groups:

1) low-pressure pumps - up to 2 P;

2) mean-pressure pumps - from 2 up to 10P;3) high-lift pumps - more than 10P.

1.2.2.Pressure head provision

The main pump functions are theprovision of necessary fluidpressure (pressure head) and capacity (consumption).

The first requirement determines a design and substantiallymanufacturing method of those pump elements, on which the leakage

value of each unit depends. The second requirement defines tdimensions and the pump rotational speed.

Pressure value, generated by the pump at other equal conditions isdetermines with sealingdegree of pumping unit, and also the pump detailsdurability and rigidity.

The fluid leakage from a high pressure chamber to a low pressurechamber occurs in the gear-type pump through tip and face gaps betweengear wheels and case (fig. 8). The leakage on a profile of locked teeth( ) at high accuracy of gear wheels manufacturing can

be completely eliminated due to dense contact in gearing ()26


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from the torsion torque ( ).It is possible to consider approximately that along a tip gap the fluid

pressure between cavities of an inlet and outlet vary under the linear law(fig. 9). Under influence of pressure drop a fluid flow from an outlet to an

inlet chamber occurs.

Fig. 8. Leakage directionin the gear-type pump

gaps

Fig. 9. Pressure variation in a radialclearance at gears concentric location in the

wells

The gear wheels which rotate in a direction opposite to a leakageflow, oppose fluid flowing through a tip gap. Additional reduction of aleakage head pressure takes place due to fluid flowing through narrowingsand expansions of a cross-section(i.e. past teeth and cavities).

Thus the tip gaps role is rather insignificant.Virtually the tip gapvaries in the range from 0.02 up to 0.2 mm, and the minimal gap valuesuse in pumps operating with pressure more than 10 MPa.

Leakages in a face gap directed basically on radius of gear wheelfrom a tooth slot bottom ( ) up to the bearingand further on theinlet side. They also go partially across teeth located near to a gearingpole. In both cases a fluid it is necessary to overcome only narrowshoulder (), and here the gear wheel rotation does not oppose fluidflow.

The face gapshave an influence on leakages more strongly than tipgaps, therefore their value is smaller and makes 0.010.1 mm dependingon pressure and a fluid viscosity.

The leakages through face gaps make 7595% of total internal

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leakages in the pump.For the pump operation opportunity without jamming

() with small gaps in pumping unit of the gear wheels areprocessed with a high accuracy degree.

For elimination of the case material pilling-up on gear faces, thecase face surfaces cover with an antifriction material (textolite).For non-perpendicularity compensation of the gear rotation axes the

gear case face surfaces contact to shafts by means of three balls thatallows gear wheels during operation to self-adjust (fig. 10).

Fig. 10. The gear connection withshaft through the balls

The reduction of leakages is also achieved by increasing of detailsrigidity. With this purpose the case is sometimes ribbed, and the covers

() are made of the higher thickness and spherical shape. Close fitof joints is provided with a plenty ofcoupling bolts. In order to the liquidpenetrated under pressure in a joint does not opened it, fluid is ventedover channeling to suction chamber.

At high discharge pressure, and also at average pressure but lowfluid viscosity the special face gaps sealing by means of bronze cartridgespressed to gear faces by operating pressure of a discharged liquid isused. To eliminate a cartridgewarp () use differential tighteningtogear in accordance with character of the valid pressure distribution in a

face gap and in working slots.1.2.3.Capacity provision

Capacity of gear-type pump is determined by a tooth slot operationvolume, quantity of slots, rotation speed and the pump volumetefficiency.

The gear-type pump for each revolution supplies a fluid volumeequal to volume of all cavities of two gear wheels apart from radial gapvolumes in gearing, i.e.

28


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zn,FbQid 2=

where F- cross section of cavity operation volume;z- driving gear teeth (slots) number;

b - gear width (a tooth length);n - driving gear rotation speed, rps.Generally it is difficult to formulate F, especially forcorrected gears.

Most simply to formulate Fby the approximate formula, considering thatslots volume is equal to teeth volume and taking into account that volumeof slots bedplate with height headfoot hh is dead space

mDh

DFz inin ==2

,

where m - module;h - height of a tooth working segment (cavity effective depth);

inD - pitch (initial) circle diameter of driving gear.Thus,

mbnDQ inid = 2 .In fact slots volume is more than teeth volume, therefore mentioned

above formula gives a little bit underestimated (on 2 3 %) idQ values.For pumps with gear teeth numberz= 8 16 exacter results are

given with the empirical formulambnD,Q inid 56= .

Generally the valid pump capacity is equal

vinp mbnDKQ = 2 ,where K- correction factor dependent on teeth number, gearing angleand a tooth formationprocess. It is possible to use 151.K= in theapproximate calculations for corrected tooth.

Let's consider separate parameters influence on the gear-type pumpcapacity. Let's transform the capacity formulataking into account that

mzDin = :

vvin

p bnzmKbnz

DKQ == 2

2

22 .

1. Influence ofzon pQ .If ,constDin = that increase zresults in reduction pQ .If ,constQp = that increase zresults in growth inD proportionally z.

Thus, in the view of the maximal capacity provision at the minimalpump dimensions it is expedient to make pumps with the minimal teethnumber.

Most widespread are gears with 712 teeth number and m= 24mm module.

To eliminate a tooth root undercutting the corrected gears are used.29


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However correction results to tooth tipsharpening that causes a toothdurability reduction and leakages increase in a radial clearance. Toeliminate these undesirable phenomena zis applied by such, that widthof a tooth cylindrical segment on an outer diameter was not less (0.10.2)

m . 2. Influence ofbon v . The gear width increase without variationgaps in the pump results in growth idQ , reduces the leakages relativevalue and increases v (fig. 11).

Actually, at a constant face gap the leakages through it do notdepend from b and the radial leakages grow proportionally to b . As theabsolute value of radial leakages is much less then face ones, the totalleakages grow more slowly than gear width and pQ grows proportionallyb and consequently v is increased.

Fig. 11. Pump volumetric efficiency depending on gear width

Virtually increase b is limited to technological features -manufacturing difficulty of a long tooth with contact on all length. Therefore

in the majority of the performed designs of high-lift pumpsratioinD

b= 0,4

0,6 is sustained. In calculations of the pump values more often use aproportionality condition of gear width to its module:

cmb = ,where c= 410 proportionality factor which limit is determined bytechnological reasons.

3. Influence ofn on pQ is characterized by v variation as idQ grows proportionally to n .

For gear-type pumps as well as for other volumetric pumps at the

beginning with increase n the growth v is observed due to leakages30


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leakQ relative value reduction (see fig. 6).With the further growth n the fall v because of intensive increase

of losses on suction is marked. With growth n the tooth slot passes fasteran inlet chamber, and at insufficient () pressure in this

chamber the viscous fluid has limited time to fill in a tooth slot. Secondly,with increasing n the centrifugal forces developing in a fluid at gearrotation and aspiring to displace a fluid from tooth slots are also increased.

The minimally allowable pressure minop considers pressure at which

does not occur yet cavitation and which exceeds on certain value vaporpressure of a fluid at giventemperature.

For aeroengine oilusually accepts p mino = 0.04 MPa.

Fig.13. To the value definitionof fluid centrifugal forces in a gear

fillet

Fig.14. Pressure variation fromfluid centrifugal forces on gear fillet

radius

Knowing minop and the inlet pressure inp is possible to find allowable

angular rotation speedof gears from a condition, that hin pp = :

22

02

sloth

mininmax

rr

pp

.

In the performed designs the select such that the circumferentialvelocity on gear outer radius hudoes not exceed 10 m/s; usually hu= 68 m/s. It is possible to set the same values in pump calculations forcircumferential velocity on the gear pitch circle inu, as huand inu is closeenough to each other. The recommended values concern to pumpsoperating without pressure head on an inlet.

At increase nover allowed value the part of a tooth slot will be filledwith fluid vapor that leads to reduction pQ , causes a fluid emulsificationand increases the pump detail attrition.

For pump operation provision in allowable ranges of variations n thedrives to pumps make with the largetransmission ratio. Usually maxn =20004000 rpm. The tooth slot filling reliability depends not only on n ,

31


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but also on other factors:- an inlet chamber extension;- the rational shape and size of channels feeding a fluid to slots;- presence ofdissolved air and gases in a fluid;

-dead space values of a tooth slots.For elimination of losses at inlet the pump should be designed sothat in an inlet chamber there is not less than 1/4 of gear circumferences;fluid feed to slots fulfill on all gear width and also from faces of teeth roots.

For reduction ofhydraulic shockat incomplete cavities filling on wellsfrom to the exhaust chamber side gash narrow grooves of width 0.50.6mm and length 1012 mm.

The most effective method of cavitation elimination in cavities is thehead creation on the pump inlet. Perspective is also the use of rotary-gear-type pumps in which a fluid feed is realized on the cavities side sothe centrifugal forces promote cavities filling. Such pumps can operate athigh rotation frequencies and they do not require special pressurizingpumps.

1.2.4.The basis for calculation of gear-type pump sizes

Basis for calculations of the gear-type pump geometry is an equationof ideal pump capacity as:

bnzmKmbnDKQ inid 222 == .

Expressing gear rotation frequency through defined velocitynDu inin = and desired value of a pitch diameter mzDin = and also using

the proportionality equation cmb = we receive fractional expression for thegearing module:

in

id

Kcu

Qm

2= , m.

Having rounded of the received fractional module value up to thenearest standard value and having set teeth gear number, find rotationspeed of the designed pump and gear width.

Check the ideal pump capacity on the above mentioned equationbysubstituting to it the obtained and chosen values K, m , z, b and n . Ifthere is a necessity you can correct the mentioned values for requiredvalue idQ obtaining.

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1.3. Plunger pumps

1.3.1. Structure and operation principle

Plunger pumps are applied in high-pressure systems, for example inengine fuel supply system and in airplane hydraulic system.The plunger pumps differ by a high quality of a pumping unit seal

and at the same time high hardness of its details. Due to about mentionedthese pumps are capable of developing high and hyper-pressures.

Besides in plunger pumps, applying rather simple design devices, itis possible to regulate consumption at stationary rotation speed of adriving shaft.

However plunger pumps as contrasted to by other volumetric pumpsare more complex on a construction, have large overall dimensions andmass, differ by the high cost of manufacture, require a large cavitationsource (up to 0,150,35 MP and more), and also require careful filtrationof operating fluid.

The pumping unit of a plunger pump consists of cylinders withplungers causing reciprocation, and operating valves ensuring thealternate connection of a working cavity of each cylinder with inlet andoutlet chambers. Displacing from extreme internal (bottom dead) to the topdead point, the plunger sucks a fluid into the cylinder from an inletchamber. Moving in the opposite direction, the plunger pumps a fluid from

the cylinder in a charging chamber.Depending on plungers displacement we can distinguish pumps of

row, radial and drum schemes.At a row scheme plungers are driven by a camshaft, at radial by

eccentric shaft, at drum by a plate which can be cam or plane. Theplane plate (tilt(ing) block, inclined plate?) is situated under angle to adrum axis.

Constant contact between plunger and control element at suctionperiod is provided as a rule with springs.

Row-type pumps have a vide propagation in reciprocating internalcombustion engines.

Drum-type pumps with a cam-plate are used in aircraft star-shapereciprocating engines with fuel direct injection.

Radial-type pumps are used in aircraft hydraulic systems.Drum-type pumps with inclined plate are used as turbine engine

pump-governors and also in aircraft hydraulic systems.Depending on degree of mechanization differ constant and varied

(controlled) capacity pumps.

Control of capacity is usually provided:33


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- by rotation of a plunger - pilot valve with skew ends in rowpumps and in drum-type pumps with a cam plate;

- by variation of a rotor eccentricity in radial-type pumps;- by variation of plate-to-axis declination angle in drum-type pumps

with variable inclined plate (plane plate).In first case a plunger working stroke is varied at constant its fullstroke, in two last cases a full stroke is varied.

Capacity controlin drum-type pumps is provided:- by application of variableinclined plate, thus drum axis

coinsides with driving shaft axis;- by application of variable

drum declined to driving shaft axis, thus plane of a plate is perpendicularto a driving shaft axis.

Depending on plunger situation in drum-type pumps differ pumpswith plungers parallel to drum axis (fig. 15, a) and declined to it (fig. 15, b).

At parallel arrangement of plungers they have smaller, but moreuniform on turn angle a course; the centrifugal forces of plungers do nothelp a contact between plungers and spacer, owing to what the springsshould be more strong; the overall dimensions and mass of the pump areincreased.

At slant arrangement of plungers the course of a plunger is more,but on turn angle it less uniform; the centrifugal forces of plungers promotea contact of plungers with a plate and the springs can be less strong; the

overall dimensions of the pump at a slide valve and mass of the pumpdecrease, though the technique of manufacture of the pump becomescomplicated a little.

The last type pump is widely used in aircraft powerplants with thegas-turbine engine.

Depending on the adopted scheme of a mechanical drivingdistinguish pumps with mobile and fixed cylinder blocks.

In the pump with the fixed block it is necessary to have a rotateddistributive slide valve, owing to what the consumption regulation gear,

together with pump it appear more complex (fig. 16).In the pump with the rotated cylinder unit the slide valve is immobile,

the change of angle of a slant spacer does not call difficulties, the pumpreceives easier, though the operation conditions both loading of a drumand plungers owing to an operation of inertial forces in this case appearheavier.

So pumps of first scheme are made as a rule of non-controlledcapacity, and pumps of second scheme with controlled one.

34


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)

)Fig. 15

Fig. 16. Scheme of drum-type plunger pump with variable inclined plateand mobile operating valve

35


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Depending on operating fluid distribution methoddistinguish pumpswith slide valve ( ) and with on-off valve( ) distribution. The pilot valve distribution can beface and journal and is applied usually at moderate charging pressures. At

high discharge pressure the shuttle valve distribution is applied, as itensures higher impermeability of a pumping unit.Lets consider the features of drum-type plunger pumps operation

with a plate and rotated cylinder block obtaining the greatest propagationin systems of powerplants with turbine engine in detail enough surveyed.

1.3.2. Pressure maintenance by the plunger pump

From all volumetric pumps the plunger pump can create the highestpressure that is reached at the expense of high degree of sealingof thepumping unit at high durability and rigidity of itsdetails.

In the drum-type pump with inclined plate leakage of a liquidfrom ahigh pressure cavity to a cavity of the low pressure occursthrougha radialgap between the plunger andthe cylinder, and also through a face gapbetweena rotor and a slide.

Therefore plunger pumps are designed so thatto provide theminimum gaps in the pumping unit and at the same time to excludepossibility of jamming of moving details andthe raiseddeteriorationofrubbing surfaces.

It account for rigid requirements to accuracy of the geometricalsizes,cleanlinessof working surfaces, and also a carefulchoice of materials forrubbing pairs.

One of the basic requirements - circularity and circular parallelism ofplunger pairs (out-of-roundness and obliquity them should not exceed0.0010.003 mm).

Fitting of plunger in the cylinder is carried out with a gapwithin0.0050.020 mm that is provided with selection of plunger and thecylinder and their jointgrinding in.

Therefore details of the picked up pair are notinterchangeable.The roughness of working surfaces of plunger and the cylinder

should correspond Ra 0.32Ra 0.04, i.e. the arithmetic-meanheight ofmicroasperity should not exceed 0.51 micron. To improve workingconditions of the plunger pair, sometimes on a workingsurface of thecylinder do ring flutes (fig. 17 due to which pressure of a liquid on plungerin a gap withthe cylinderextends on all circle. Itreduceseccentricdisplacement of the plunger under the influence of centrifugal forces, andalso lossby a friction and leakthrough a radial gap (at eccentric

displacement of a plunger leakagesincrease almost in 2.5 times).36


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Besides, in flutes settled firm particles that reducelossesby a friction anddeterioration of the plunger pair.

For leak reduction in operating valve -rotor pair a wedging of theirface surfaces, and also misalignment of rotation axesshould not be more

than 0.050.010 mm, nonflatness not more than 0.005 mm.

Fig. 17. To definition of unbalancedforce of pressure of a liquidinan eccentricgap of plunger pair

The leak value in this pair dependsalso on effort of pressingof arotor to an operating valve. The rotor clasps toan operating valvebyefforts of springs in cylinders, and also by efforts from pressureof a liquid

upon the ring areas formed by a differenceof the areasof cylinders andexhaust outlets in a rotor. The effortof pressure of a liquid in ahydrodynamic wedge between a rotor end face and pilot valve, and alsothe effort of a forced liquidoperating on a part of a facesurface of a rotor,limited to a hole of an operating valve andexhaust outletsin a rotor, tendsto wring out a rotor from an operating valve.

The effort increases in a hydrodynamic wedgedue to increasingofpressurization andincreaseof a rotor rotational speed.

In pumps with an inclined arrangement of plungers and, hence , weaksprings reliability of pressing of a rotor to an operating valveprovide bycreation of the high pressure in a cavity of an inclined plate where theliquid flows under the influence of centrifugalforces from an input cavity onthe inclined channels locatedbetweencylindersof a rotor.

1.3.3. Kinematics of the drum-type plunger pump with a parallelarrangement of plungers and flat inclinedplate

At definition of the law of movement of plunger we suppose, that thecontact point of plunger and plate lays on an axis of plunger at any angles

37


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of an inclination of a plate and any angle of rotation of a rotor (as thoughthe plunger came to an end with an edge, fig. 18).

The plungerstroke from an inner (inside) dead point

( ) = tgcosRs 1 ,

where - is an angle of rotation of a rotor.The maximum plunger stroke (at rotor rotation of 180)

= Rtgsmax 2 .The value ofmaxs defines productivityof the pump.

Fig. 18. To a derivation of the equations of kinematics for the pump with aparallel arrangement of plungers and a flat inclinedwasher

Plungers speedin relative movementcanbe foundby differentiationon time of the equation for a plunger stroke:

= sintgRvr ,

where -dt

d= is an angular rotational speed of a rotor.

Plungers speedreaches the maximum absolutevalueat angles ofrotationof a rotor = 90 and = 270:

38


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= tgRvmaxr .

Plungers acceleration in relative movementit is found, bydifferentiation of time the equationof plungers speed

= costgRjr2 .

Acceleration rj gets the maximum absolute values at angles ofrotation of a rotor = 0 and 180 .

Except acceleration in relative movement theplunger experienceacceleration and intranslational motion:

2=Rje .

This acceleration is always directed perpendicularly to a rotor axis.In case of an inclined arrangement of plunger also appears Coriolis

(complementary) acceleration

== sinvvj rrc 22 ,

where - is an inclination angle of plungers to a rotor axis.

1.3.4. Capacity of the pump

Capacity of the plunger pump is defined by the formula

FbznQ = ,

where -4

2dF

= is the plungers cross-section area;

maxsb = - is the maximum plunger stroke;z - is the number of plungers;n - is the rotational speed, rps.

Thus,

max znsd

Q

=4

2

,

or for the pump with a parallel arrangement of plungers (fig. 18 see)

=

= tgRzndtgRznd

Q 2

2

2

12

4,

where - Ris the circle radius on whichaxes of cylinders of the pump are39


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located; - is an angle of an inclination of an inclined plate.Characteristics of plunger pumps are similar to characteristicsof

other volumetric pumps. Howeverthe maximum value forv of plungerpumps considerablyabove and makes 0.970.98 and even 0.99; the

minimum rotational speed at which capacity of the pump startsto prevailover leaks, less and makes 510 rpm against 80100 rpm for gearpumps.

1.3.5. Uniformity of fluid supply by plunger pumpsandfeaturesof filling of the cylinder

Instant capacity of every plunger is proportionalto relative velocity ofplunger at given time

dt

dQ

q = , or rFvq = ,and as - rva variable, instant capacityalso a variable.

Instant capacity of the whole pump can be found bysummarizing of instant supplies of all pressurizing plungers:

iqq = .

With increase in quantity of plungers supply of a liquidbecomes more uniform, pulsations decrease, but their frequency

grows. Pulsations can be expressed as

minmax

q

qq = 100, (%).

It was found, that at odd number of plungers the pulsationsare less, than at even. It can be explained by the fact that ateven number of plungers each of them has the pair plunger,located opposite; the beginning of work of one plunger coincideswith the end of work of the opposite, this leads to a suddendecrease in supply of liquid.

In approximate calculations to determine the pulsations it ispossible to use the following approximate dependences:

when the number of plungers is odd

2

251

z

.= 100;

when the number of plungers is even

2

251

z

.= 100.

40


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When several pumps are installed into one system they arelocated to reduce pulsations.

As plunger moves in the cylinder with variable speed sospeeds of a liquid at filling and clearing of the cylinder will be

also variables. Diameter of a joint hole in a rotor is less thandiameter of plunger and the area of the inlet during the processof sucking gradually changes from zero up to the maximal value.If pressure in an inlet cavity is not enough, so in a connectinghole, and then in the cylinder can appear cavitation.

To avoid the cavitation, the plunger pumps need the heightenedpressure on an inlet.

1.3.6. Dynamics of plunger pumps

At inclined plunger, the following forces and the momentsare applied (fig. 32). Under their action it is in equilibrium:

1. Force of a spring

sk +=1 ,

where is the force of a preliminary tightening of a spring in

the extreme position of plunger in the end of a stroke of filling ( = 180);

k

- is rigidity of a spring;s- is a current stroke of plunger.2. Hydraulic force

( Fpp =2 ,where p is pressure in the cylinder;

p - is pressure in a cavity of an inclined plate;

F- is the cross-sectional area of plunger.Hydraulic force during the process of pressurization tries to

press, and during filling to tear off plunger from an inclinedplate.3. Centrifugal force of inertia in translational motion

2 3 mP = ,where m - is the mass of plunger; - is the distance from an axis of rotation of a rotor to thecenter of masses of plunger at the given angle and at = 0.

Force 3 is always in a plane of rotation of plunger and in

case of its inclined position has components along an axis of41


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plunger and normal to it

sin33

= and cosn33

= .

4. Force of inertia in relative motion

r jm=

4 .Force 4 acts always along an axis of plunger; the size and

a direction of this force depend on size and a direction of relativeacceleration.

5. Coriolis (compound centrifugal) force for the case of aninclined position of plunger

c5 jmP = ,

i.e. force 5P , being constantly normal to a plane of plunger, acts

at an angle

= 0 180 against a direction of rotation of a rotor,and at = 180 360 in a direction of rotation.

Fig. 32. The scheme of the forces operating on plunger at = 0

6. Force of reaction of an inclined plate 6P , which is applied

in a point of a contact of plunger with an inclined plate anddirected normally to a surface of a washer. Considered force of

reaction has two components: along an axis of plunger P6 and

normal to it T . Between these forces there are obvious

42


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correlations (at = 0)( ) 2266 TPP += , tgPT 6= and cosPP 66 = .

7. Force of reaction of the cylinder .8. The jet moment of the cylinder .

Forces of friction are usually neglected because they areinsignificant.

Unknown efforts 6 , and are found from a relation ofbalance of all forces and the moments applied to plunger.

So, the sum of projections of all forces on an axis of plunger

43216 +++= ;

the sum of projections of all forces on an axis, perpendicular toaxis of plunger

Tn

+= 3 .

If we take the sum of the moments of all forces relatively tothe center of masses of plunger then moments of forces are

equal to zero ( 1 , 2 and 3 , 4 , 5 and

P6 ), and the others

give the moment equal hPTh += 6 ,

where 6h - distance from a point of contact of plunger with awasher to the center of masses; h - distance from a point ofapplication of force P , i.e. from the middle of a supportingsurface of plunger in the cylinder to the center of its masses.

LIST OF LITERATURE

.. . . .,"", 1968.

.. . . .,"", 1976.

.. . .,

, 1953. .., ..

, ., , 1965. .. . .,

"", 1974. .. . . .2, .,

. , 1959.Treager I.E. Aircraft gas turbine engine technology. 3-rd ed.

Glencoe/McGraw-Hill. 2001. 677 p.

The Jet engine. Roll-Royce plc. 278 p.43


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power plants short

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