FUNDAMENTALS OF GAS DYNAMICS Second Edition ROBERT D. ZUCKER OSCAR BIBLARZ

FUNDAMENTALS
OF GAS DYNAMICS
Second Edition
ROBERT D. ZUCKER
OSCAR BIBLARZ

Fundamentals of Gas Dynamics provides the essential applications and problem-solving techniques used in gas dynamics. Written in an accessible but rigorous style, this book includes all the equations, tables, and charts necessary to approach the problems and exercises in each chapter. Temperature-entropy diagrams and the role of entropy are highlighted throughout to make this elusive property more understandable and useful.

New to this Second Edition is a chapter covering real gas behavior. The information in this chapter provides a valuable bridge between the conventional types of lower-temperature applications and propulsion applications, both covered elsewhere in this book. Included in this new chapter on real gas behavior is a simplified technique for solving problems where the ratio of the heat capacities varies appreciably, as well as discussions and examples comparing this technique to more exact methods.

Unique coverage also includes:
* Updated information on propulsion applications and new engine photographs
* Key parameter variations plotted as a function of Mach number
* Updated material and appendixes on conical shocks
* Appendixes containing information to treat air as a real gas
* Enhanced gas property tabular entries that are given in both English Engineering and SI units
* Alternatives to using tabular information in calculations

Fundamentals of Gas Dynamics, Second Edition is an indispensable book for students in mechanical, aerospace, and chemical engineering courses, as well as aerospace engineers.

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Guidance for ASME EA-4, Energy Assessment for Compressed Air Systems ASME EA-4G–2010

Guidance for ASME
EA-4, Energy
Assessment for
Compressed Air
Systems
ASME EA-4G–2010

This guidance document was developed to be used as an application guide on how to utilize
ASME EA-4, Energy Assessment for Compressed Air Systems. This guidance document provides background and supporting information to assist in carrying out the standard.

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Energy Assessment for Compressed Air Systems ASME EA-4–2010

Energy
Assessment
for Compressed
Air Systems
ASME EA-4–2010


This Standard covers compressed air systems, which are defend as a group of subsystems comprised of integrated sets of components, including air compressors, treatment equipment, controls, piping, pneumatic tools, pneumatically powered machinery, and process applications utilizing
compressed air. The objective is consistent, reliable, and effcient delivery of energy to manufacturing equipment and processes.
The compressed air system can be considered as three functional subsystems. supply: conversion of primary energy resource to compressed air energy. The supply subsystem includes generation,
treatment, primary storage, piping, controls, performance measurement equipment, and reporting
systems. transmission: movement of compressed air energy from where it is generated to where it is used. 
The transmission subsystem includes distribution piping mainline and branch headers, piping drops, secondary storage, treatment, transmission controls, performance measurement equipment, and reporting systems. demand: the total of all compressed air consumers, including
productive end use applications and various forms of compressed air waste. The demand subsystem includes all end uses, point-of-use piping, secondary storage, treatment, point-of-use controls, performance measurement equipment, and reporting systems.

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Optimized Gas Treating ProTreat 5.0

Optimized Gas Treating ProTreat 5.0

Optimized Gas Treating ProTreat was originally designed to simulate H2S, CO2, and mercaptan removal processes from high and low pressure gas types by adsorption in aqueous solutions containing one or more amines. The newly added functionality includes the physical solvent DMPEG (diethyl ether from polyethylene glycol) to eliminate acid gas, and dehydrogenation using triethylene glycol(TEG). The ProTreat package allows for the unique use of a column model and separation behavior as a mass transfer process and completely eliminates the need for experimental settings to simulate new applications. The mass and heat transfer model applied to the ProTreat simulator column is based on absorption and amplifier, which can produce a considerable different temperature for the output of the vapor and liquid of the closed portion. Also, the amplifier allows modeling with the same high degree of reliability as the absorbent

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Quasi-Gas Dynamic Equations

The monograph is devoted to modern mathematical models and numerical methods for solving gas- and fluid-dynamic problems based on them. Two interconnected mathematical models generalizing the Navier–Stokes system are presented; they differ from the Navier–Stokes system by additional dissipative terms with a small parameter as a coefficient. The new models are called the quasi-gas-dynamic and quasi-hydrodynamic equations. Based on these equations, effective finite-difference algorithms for calculating viscous non-stationary flows are constructed and examples of numerical computations are presented. The universality, the efficiency, and the exactness of the algorithms constructed are ensured by the fulfillment of integral conservation laws and the theorem on entropy balance for them.

The book is a course of lectures and is intended for scientists and engineers who deal with constructing numerical algorithms and performing practical calculations of gas and fluid flows and also for students and post-graduated students who specialize in numerical gas and liquid dynamics

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The Properties of Gases and Liquids, Fifth Edition Bruce E. Poling, John M. Prausnitz, John P. O’Connell

The Properties of Gases and Liquids, 
Fifth Edition 
Bruce E. Poling, John
M. Prausnitz, John P. O’Connell



Must-have reference for processes involving liquids, gases, and mixtures
Reap the time-saving, mistake-avoiding benefits enjoyed by thousands of chemical and process design engineers, research scientists, and educators. Properties of Gases and Liquids, Fifth Edition, is an all-inclusive, critical survey of the most reliable estimating methods in use today --now completely rewritten and reorganized by Bruce Poling, John Prausnitz, and John O’Connell to reflect every late-breaking development. You get on-the-spot information for estimating both physical and thermodynamic properties in the absence of experimental data with this property data bank of 600+ compound constants. Bridge the gap between theory and practice with this trusted, irreplaceable, and expert-authored expert guide -- the only book that includes a critical analysis of existing methods as well as hands-on practical recommendations. Areas covered include pure component constants; thermodynamic properties of ideal gases, pure components and mixtures; pressure-volume-temperature relationships; vapor pressures and enthalpies of vaporization of pure fluids; fluid phase equilibria in multicomponent systems; viscosity; thermal conductivity; diffusion coefficients; and surface tension.

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The Ideal Gas Law

Gases are everywhere, and this is good news and bad news for chemists. The good news: when they are behaving themselves, it's extremely easy to describe their behavior theoretically, experimentally and mathematically. The bad news is they almost never behave themselves. In this episode of Crash Course Chemistry, Hank tells how the work of some amazing thinkers combined to produce the Ideal Gas Law, how none of those people were Robert Boyle, and how the ideal gas equation allows you to find out pressure, volume, temperature or number of moles. You'll also get a quick introduction to a few jargon-y phrases to help you sound like you know what you're talking about.

Gas Laws

Gas Laws 

An Introduction to Gas Laws , Expansion and compression of gases

An Introduction to Gas Laws , Expansion and compression of gases


Introduction 

Air, steam and other working substances used in thermodynamic systems pass through a cycle of processes as heat energy is changed into work and vice versa. Expansion and compression processes
often form an essential part of the cycle and we will now consider the laws, principles and properties associated with them.

One of the basic properties of a working substance is its temperature. Temperature is a measure of the hotness of a substance, which is directly proportional to the kinetic energy of its individual
molecules. Thermodynamic temperature is measured on the kelvin scale and is also known as absolute temperature. It has for its zero, the absolute zero of temperature at which all molecular movement ceases and the molecules of a substance have zero kinetic energy.
The SI unit of temperature is the kelvin, whose symbol is K. It is defined as the temperature interval between absolute zero and the triple point of water divided by 273.16. The triple point of water
occurs at a very low pressure, where the boiling point has been depressed to meet the freezing point. In this condition, ice, water and steam are able to exist together in the same container, which is
how the name arises. The kelvin is exactly the same temperature interval as the degree celsius (⁰C). The difference between the two scales lies in the points chosen for their definition. The degree
celsius is defined as the temperature interval between the freezing and boiling points of water at standard atmospheric pressure of 101 325 Pa, divided by 100. The freezing point of water at this
standard pressure is slightly below the triple point, being exactly 273K

The SI unit of pressure is the pascal (Pa). A pressure of 1 Pa is exerted when a force 1 N is evenly applied at right angles to a surface area of 1m². Another unit, which is widely used, is the ‘bar’. This is almost equal to standard atmospheric pressure.

1 bar=100 000 Pa or 1 × 10⁵ Pa or 100 kPa
Pressure-measuring devices such as mechanical gauges and the manometers measure the difference between the pressure inside a container and the outside atmospheric pressure. This, as you will recall, is known as gauge pressure.
 In gas calculations, however, it is often the total or absolute pressure, which must be used. This is obtained by adding atmospheric pressure to the recorded gauge pressure (figure 1), that is :

FIG 1

absolute pressure=gauge pressure+atmospheric pressure
Reference has been made above to standard atmospheric pressure. A substance is said to be at standard temperature and pressure (STP) when its temperature is 0⁰C or 273 K, and its pressure is
101 325 Pa. This definition has international acceptance. 
Sometimes a substance is said to be at normal temperature and pressure. A substance is at normal temperature and pressure (NTP) when its temperature is 15⁰C or 288 K, and its pressure is
again 101 325 Pa. This definition is used in the United Kingdom and other countries with a temperate climate.
the density of a working substance is often required for thermodynamic calculations (figure 2) . density is the mass per unit volume of a substance whose unit is kgm⁻³. 

FIG 2

Sometimes however, and particularly in steam calculations, it is more convenient to use specific volume. This is the volume per unit mass of a substance whose unit is m³ kg⁻1. Specific volume, vs is thus the reciprocal of density, that is
specific volume=volume occupied by 1 kg of a substance
For a substance of mass m kg and volume V m³, its specific volume will be given by

The gas laws

The gas laws which we need to consider are Boyle’s law, Charles’ law , Avogadro’s law, which is also called Avogadro’s hypothesis. Combined and ideal gas laws , and  Gay-Lussac's law

FIG 3

Boyle’s law
This states that the volume of a fixed mass of gas is inversely proportional to its absolute pressure provided that its temperature is constant. When plotted on a graph of absolute pressure against
volume, the process appears as shown in Figure 4. Expansion and compression processes which take place at constant temperature, according to Boyle’s law, are known as isothermal processes.

FIG 4

 For any two points on the curve whose co-ordinates are p1V1 and p2V2, it is found that

p×V = constant

Charles’ law
This states that the volume of a fixed mass of gas is proportional to its absolute temperature provided that its pressure is constant. When plotted on a graph of absolute temperature against volume, the
process appears as shown in Figure 5.

FIG 5

Expansion and compression processes which take place according to Charles’ law are referred to as constant pressure or isobaric processes. For any two points on the curve whose co-ordinates are
T1V1 and T2V2, it is found that

You will note from Figure 5 that in theory, the volume of the gas should decrease uniformly until at absolute zero, which is the origin of the graph, its volume would also be zero. This is how
an ideal gas would behave.
Real gases obey the gas laws fairly closely at the temperatures and pressures normally encountered in
power and process plant but at very low temperatures they liquefy, and may also solidify, before reaching absolute zero.

The general gas equation
This equation may be applied to any fixed mass of gas which undergoes a thermodynamic process taking it from initial conditions p1, V1 and T1 to final conditions p2,V2 and T2. Suppose the
gas expands first according to Boyle’s law to some intermediate volume V. Let it then expand further according to Charles’ law to its final volume V2.

FIG 6

Figure 6  shows the processes plotted on a graph of absolute pressure against volume. For the initial expansion according to Boyle’s law,
p1 V1=p2 V
For the final stage according to Charles’ law,
V/ T1 = V2 / T2
⇒
V =  (V2 T1) / T2

⇒ p1 V1 = p2 (V2 T1) / T2

Substituting in equation

This is the general gas equation which can be used to relate any two sets of conditions for a fixed mass of gas, irrespective of the process or processes which have caused the change. The constant in equation is the product of two quantities. One of them is the mass m kg of the gas. The other is a constant for the particular gas known as its characteristic gas constant. 
The characteristic gas constant R has unit of joules per kilogram kelvin (J kg⁻¹K⁻¹) and is related to the molecular weight of the gas. Equation  can thus be written as

In this form it is known as the characteristic gas equation which is particularly useful for finding the mass of a gas whose volume, absolute pressure and absolute temperature are known.
The general gas equation can be used to relate any two sets of conditions for a fixed mass of gas, irrespective of the process or processes which have taken place.

Avogadro’s hypothesis

This states that equal volumes of different gases at the same temperature and pressure contain the same number of molecules. It is called a hypothesis because it cannot be directly proved. It is impossible to count the very large number of molecules, even in a small volume, but there is lots of evidence to indicate that the assumption is true. Suppose we have three vessels of equal volume
which contain three different gases at the same temperature and pressure, as shown in Figure 7.

FIG 7

Avogadro’s hypothesis states that each vessel contains the same number of molecules. Let this number be N. The mass of gas in each vessel will be different, and given by

mass of gas in vessel = number of molecules × molecular mass 

m=N × M

Applying the characteristic gas equation to the first vessel gives

Substituting for m from equation for all gases in three vessels

Equating gives

The actual mass of a molecule is very small and so in place of it, engineers and chemists use the kilogram-molecule or kmol. This is the mass of the substance, measured in kilograms, which is

numerically equal to its molecular weight. The molecular weight is the weight or mass of a molecule of the gas relative to the weight or mass of a single hydrogen atom. Typical values for some common

gases are shown

The product MR is found to have a value of 8314 J kmol⁻¹ and is called the universal gas constant. It can be used to calculate the value of the characteristic gas constant R for a particular gas of known molecular weight.

M R =  8314

e.g. the molecular weight of oxygen is 32 and so the value of its characteristic gas constant will be

R= 8314 / 32 =260 J kg⁻¹  K⁻¹ 

Avogadro's law states that the volume occupied by an ideal gas is directly proportional to the number of molecules of the gas present in the container. This gives rise to the molar volume of a gas, which at STP (273.15 K, 1 atm) is about 22.4 L. The relation is given by

FIG 8

A kilogram-molecule or kmol of a substance is the mass in kilograms which is numerically equal to its bmolecular weight.

Gay-Lussac's law

Gay-Lussac's law, Amontons' law or the pressure law  for a given mass and constant volume of an ideal gas, the pressure exerted on the sides of its container is directly proportional to its absolute temperature.

As a mathematical equation, Gay-Lussac's law is written as either:

Dalton's law

In chemistry and physics, Dalton's law (also called Dalton's law of partial pressures) states that in a mixture of non-reacting gases, the total pressure exerted is equal to the sum of the partial pressures of the individual gases ( figure 9). 

FIG 9

The Total Gas Pressure shown in Container T is determined by adding the Partial Pressure of Gases A, B, and C.

Mathematically, the pressure of a mixture of non-reactive gases can be defined as

Polytropic expansion

A fixed mass of gas can expand from an initial pressure p1 and volume V1 in an infinite number of ways. This is what  mean by the word polytropic. Figure 10 shows some of possible expansion processes.

FIG 10

The particular expansion curve followed by a gas depends on the amount and direction of the heat transfer that takes place during the expansion process. All curves have an equation of the general form

For most practical expansion and compression processes, the value of the index n ranges from low negative values to positive values of around 1.5  . The values of n indicated as :

Some specific values of n correspond to particular cases:
      ∎ n=0 is  for an  isobaric process,
      ∎ n=+∞ is for an  isochoric process.
 In addition, when the ideal gas law applies:
      ∎ n=1 is  for an isothermal process,
      ∎ n= 𝛾 is  for an isentropic process.

Where 𝛾 is the ratio of the heat capacity at constant pressure  Cp to heat capacity at constant volume Cv

The value of the index n in a polypropic process depends on the magnitude and direction of the heat transfer that takes place.

Automotive Transmissions Fundamentals, Selection, Design and Application with Peter Fietkau

Automotive Transmissions
Fundamentals, Selection, Design
and Application
with Peter Fietkau

Introduction.- Overview of the Traffic-Vehicle-Transmission System.- Mediating the Power Flow.- Power Conversion: Selecting the Ratios.- Matching Engine and Transmission.- Vehicle Transmission Systems: Basic Design Principles.- Design of Gearwheel Transmissions for Vehicles.- Specification and Design of Shafts.- Gear shifting Mechanisms.- Moving-Off Elements.- Design and Configuration of Further Design Elements.- Typical Designs of Vehicle Transmissions.- Electronic Transmission Control.- Computer-Aided Transmission Development.- The Automotive Transmission Development Process.- Transmission Manufacturing Technology.- Reliability and Testing of Automotive Transmissions.- References.- Index of Companies/Transmissions.- Index of Names.- Subject Index.

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ISO 11425:1996 Rubber hoses and hose assemblies for automobile power-steering systems -- Specification

ISO 11425:1996
Rubber hoses and hose assemblies 

for automobile power-steering systems 

-- Specification

Specifies requirements for five types of hose and hose assembly used in automobile power-steering systems, the five types differing in their pressure ratings and volumetric expansion. They are for use with fluids in the temperature range -40 °C to +135 °C.

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VEHICLE DYNAMICS Martin Meywerk

VEHICLE DYNAMICS
Martin Meywerk

 Comprehensively covers the fundamentals of vehicle dynamics with application to automotive mechatronics * Presents a number of different design, analysis and implementation considerations related to automobiles, including power requirements, converters, performance, fuel consumption and vehicle dynamic models * Covers the dynamics, modeling and control of not only the entire vehicle system, but also of key elements of the vehicle such as transmissions, and hybrid systems integration * Includes exercise problems and MATLAB(R) codes * Accompanied by a website hosting animations 

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Automobile Mechanical and Electrical Systems Second Edition Tom Denton

Automobile Mechanical and Electrical Systems

Second Edition

Tom Denton

The second edition of Automobile Mechanical and Electrical Systems concentrates on core technologies to provide the essential information required to understand how different vehicle systems work. It gives a complete overview of the components and workings of a vehicle from the engine through to the chassis and electronics. It also explains the necessary tools and equipment needed in effective car maintenance and repair, and relevant safety procedures are included throughout. 

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An Introduction To Power Steering Pump Types , Components , and Selection

An Introduction To  Power Steering Pump Types , Components ,  and Selection


Introduction

Power steering systems have contributed to reduced driver fatigue and made driving a  more pleasant experience. Nearly all power steering systems at the present time use fluid pressure to assist the driver in turning the front wheels. Since driver effort required to  turn the front wheels is reduced, driver fatigue is decreased. the advantages of power  steering have been made available on many vehicles, and safety has been maintained in these systems.

There are several different types of power steering systems, including integral, rack and  pinion, hydro boost, and linkage type. In any of these systems, the power steering pump is the  heart of the system because it supplies the necessary pressure to assist steering.

The power steering pump drive belt is a simple, but very important, component in the  power steering system. A power steering pump in perfect condition will not produce the  required pressure for steering assist if the drive belt is slipping.

The power steering pump, a part of your vehicle's power steering system, is the component that compresses the power steering fluid. It is basically a rotary vane pump that is powered by the engine via a belt and pulley. The construction of the pump includes a set of retractable vanes and an oval chamber.

How a Power Steering Pump works?

The power steering pump is used to put additional force onto the steering system when you turn the wheel. The pressure it provides comes from a rotary vane pump which is powered by the car’s engine. Inside this pump are retractable vanes that will spin inside an oval chamber and take power steering fluid from the lines at low pressure and distribute it at high pressure into the steering rack. As the pump is powered by the engine the speed in which the the pump flows is relative to the speed of the engine , meaning at high engine speeds the steering will operate quicker than an engine running at a lower speed. The pump has a pressure relief valve which will ensure the pressure isn’t too high , which is extremely effective on engines that are running at high speeds

FIG 1

Power Steering Pump Types

Different types of power steering pumps are used to power the system. The main difference between the different types of pumps is the design of the fins that move the steering fluid that is inside the pump and expelled through built-up pressure. They are all similar in that they contain a rotor inside the pump housing that spins. There are four different types of pumps used in power steering systems.

FIG 2

Vane Power Steering Pump

Vane pumps  (figure 3) are the most common type of power steering pump used. In this type of pump the rotor is housed in an oval- or elliptical-shaped housing where it turns. Vanes fitted to the outside diameter of the rotor sit against the housing walls as the rotor turns. When power steering fluid enters into the vane pump housing it is trapped between the vanes, the housing wall and the rotor. A subsequent pressure increase causes the fluid to be pumped out of the housing and then through the outlet chambers. 

FIG 3

Roller Power Steering Pump
In a roller power steering pump(figure 4), wide V-shaped grooves cut into the side of the rotor allow steel rollers to ride along the inside contour of the pump. The pump is contained in an oval-shaped housing within the pump body. Centrifugal force pushes the rollers to the oval's outer edge where they trap fluid, similar to the way the vanes catch the fluid in a vane pump. The pressurized fluid is forced out through two outlets in the pump, driving the power steering system.

FIG 4

Slipper Power Steering Pump
Like the vane and roller pump, the slipper power steering pump(figure 5) has a rotor housed in an elliptical-shaped chamber that rotates within the body of the pump. Fitted into wide slots on the rotor are springs that are topped with scrubber-type "slippers." The springs keep the slippers in constant contact with the wall of the pump. As fluid enters into the pump, pressure is built up and released to drive the power steering system.

FIG 5

Gear Power Steering Pump

In gear power steering pump (figure 6) the gears rotate they separate on the intake side of the pump, creating a void and suction which is filled by fluid. The fluid is carried by the gears to the discharge side of the pump, where the meshing of the gears displaces the fluid.

FIG 6

Useful Hints 

Despite the new advances, the majority of the vehicles on the road today still share a similar hydraulic powers steering system. Like any system in your vehicle, the first step to fixing its problems is understanding how it is supposed to work so you can see what is going wrong.

Your vehicle’s power steering system needs a few different components to work properly:
1- A good engine belt
2- A health power steering pump
3- Clear passageways
4- The proper level of clean power steering fluid
5- No leaks either in or out of the system
Failure Symptoms Of Power Steering Pump
The power steering pump directs fluid from the reservoir into the steering gear, which applies the correct amount of pressure to turn the wheels smoothly. There are several symptoms of a bad or failing power steering pump, so if you notice the following, have the pump inspected by a professional mechanic as soon as possible:

What are the Symptoms of Failure?
Steering system may leak
Lack of assist
Line restriction
Whining or squealing noise
Wheels are difficult to turn
Steering wheel vibrates while idling

1.Whining noise while turning the wheel
If you hear a whining noise while turning the wheel of your vehicle, something is wrong with your power steering system. It could be a leak in the power steering pump or the fluid level could be low. If the fluid level is left this way for too long it can damage the whole power steering system. Either way, the power steering pump needs to be looked at and potentially replaced by a professional.

2.Steering wheel slow to respond
While turning a corner, if your steering feels slow to respond to the steering wheel inputs you are making, chances are your power steering pump is failing. Along with this, you may also hear a whining noise. If you notice these two symptoms together, contact your technician to have your power steering pump replaced.

3.Stiff steering wheel
Not only can your steering wheel be slow to respond, it can also become stiff if the power steering is failing. If your steering wheel starts to feel stiff, your power steering pump may be going bad.

4.Squealing noises when the vehicle starts
While whining noises are usually heard when you turn the vehicle, squealing noises come when the vehicle first starts. They can happen when you make sharp turns as well, but they are more likely to happen for a minute as you start your car. The squealing noise will come from the hood of your vehicle, and is a sign your power steering pump may be going bad and causing the belt to slip.

5.Groaning noises
Groaning noises are the worst noises your power steering pump can make. They will get worse and worse as your power steering pump continues to fail. If the power steering system fails from lack of fluid it can damage the whole system including the steering rack and lines, and require complete replacement.

Power Steering Pump Design

Various types of power steering pumps have been used by car manufacturers. Many vane-type  power steering pumps have flat vanes that seal the pump rotor to the elliptical pump cam  ring (Figure 7). Other vane-type power steering pumps have rollers to seal the rotor to the  cam ring. In some pumps, inverted, U-shaped slippers are used for this purpose. the major 

FIG 7

differences in these pumps are in the rotor design and the method used to seal the pump rotor  in the elliptical pump ring. the operating principles of all three types of pumps are similar.

A balanced pulley is pressed on the steering pump drive shaft. this pulley and shaft are belt-driven by the engine. A spring-loaded lip seal at the front of the pump housing prevents 

fluid leaks between the pump shaft and the housing. the oblong pump reservoir is made from steel or plastic. A large O-ring seals the front of the reservoir to the pump housing (Figure 8 )

FIG 8

Smaller O-rings seal the bolt fittings on the back of the reservoir.the combination cap and dipstick keeps the fluid reserve in the pump and vents the reservoir to the atmosphere. Some power steering pumps have a variable assist steering actuator in the back of the pump housing. the PCM operates this actuator to provide increased steering assist at low vehicle speeds.

The rotating components inside the pump housing include the shaft and rotor with  the vanes mounted in the rotor slots. A seal between the output shaft and the housing prevents oil leaks around the shaft. As the pulley drives the pump shaft, the vanes rotate inside an elliptically shaped opening in the cam ring .the cam ring remains in a fixed position inside the pump housing. A pressure plate is installed in the housing behind the cam ring (Figure 9 )

FIG 9

A spring is positioned between the pressure plate and the end cover, and a retaining ring holds the end cover in the pump housing. the flow control valve is mounted in the pump housing, and a magnet is positioned on the pump housing to pick up metal filings rather than allowing them to circulate through the power steering system (Figure 10 ).

FIG 10

The flow control valve is a precision-fit valve controlled by spring pressure and fluid pressure. Any dirt or roughness on the valve results in erratic pump pressure. the flow control valve contains a pressure relief ball (Figure 11 ). 

High-pressure fluid is forced past the control valve to the outlet fitting. A high-pressure hose connects the outlet fitting to the inlet fitting on the steering gear. A low-pressure hose returns the fluid from the steering gear to the inlet fitting in the pump reservoir.

FIG 11

Typical Maintenance Kit

You have to know the parts that are included in a steering pump repair kit so you can compare kits from different suppliers and retailers. A typical repair kit has:
1- Seals

2- O-rings
3- Rollers, slippers, vanes (depending on the type)
4- Washers
5- Gaskets

POWER STEERING PUMP ASSEMBLY

1- Seal, Pump Body (figure 12)
2- Body, w/Seal, Pump
3- Seal, Pump Body
4- Seal, O-Ring
5- Shaft, w/Retaining Ring, Pump Drive
6- Plate, Thrust
7- Spring, Valve
8- Valve, Flow Control, Assy
9- Ring, Pump -Not Serviced Separately-
10- Ring, Shaft Retaining -Not Serviced Separately-
11- Rotor, Pump -Not Serviced Separately-
12- Plate, Pressure
13- Pin, Pump Dowel
14- Spring, Pressure Plate
15- Cap, Reservoir Filler Assy
16- Reservoir, Pump
17- Seal, O-Ring
18- Stud, Pump Mounting
19- Connector, Hose, Assy
20- Seal -Not Serviced Separately-
21- Seal -Not Serviced Separately-
22- Ring, End Cover Snap
23- Cover, End

FIG 12

Hydraulic modelling 

The hydraulic subsystem is based on the Wheatstone bridge representation seen in Figure 13.. 

FIG 13

It is assumed that opposite orifices in the bridge are equal in size. The model thus considers the flow equation for the four orifices and the continuity equation for each cylinder chamber and the volume between the pump and the valve. . The pump flow qs and load flow ql can be described by

where A1 = A[Tsw] and A2 = A[−Tsw].

 Tsw = Steering wheel torque [Nm]

 qs = System flow [m³/s]

 ql  = Load flow [m³/s]

 Cq = Flow coefficient

 PL = Load pressure [Pa]

 ps = System pressure [Pa]

 𝝆 = Density [kg/m³]

From these equations the load pressure pL and the pump pressure ps can be derived as 

where q = qL /qs

The load pressure is shown in Fig 14. for both a positive and a negative load flow, which describes the static characteristic of the valve. Finally, the opening areas can be derived as

FIG 14

To calculate the steering effort  requires inputs as listed :

1. Tyre Width (with reference to tyre designation). 

2. Front Axle Weight 

3. King Pin Off-set on Ground (scrub) 

4. Steering Arm Length 

5. Drop Arm Length 

6. Gear Box Ratio 

7. Steering Wheel Diameter 

Length of Steering Arm and Drop Arm are considered as 203 mm and 225 mm respectively with reference to N1 category vehicle. A steering box with 18:1 gear ratio is considered which can be power assisted and a 200 mm radius Steering Wheel is taken, which is generally ergonomic.

TSW = Total Kingpin Torque required to steer axle. 

W = Vehicle Weight supported by the steered axle. 

F = Coefficient of friction (dimensionless). 0.7 as a Maximum

B = Nominal width of the tire print (tread width). 

E = Kingpin Eccentric (use nominal tire width).

the pump has to deliver at least the flow amount that the hydraulic cylinder is demanding at required maximal speed

where :

qp = Flow delivered by the pump [m³/s]

x∙rmax = Rack speed  [m/s]

Ap = Cylinder area [m² ]