PRODUCTION AND ANALYSIS OF AGE HARDENED Al 6061 GRADE ALLOY
TITANIUM BORIDE COMPOSITE
OPTIMIZATION OF HYDRAULIC POWER STEERING SYSTEM PARAMETERS
BYYUVARAJ S610812408020PROJECT REPORT(PHASE II)
Submitted to the
FACULTY OF MECHANICAL ENGINEERING
In partial fulfillment of the requirement
for the award of the degree OfMASTER OF ENGINEERING
INENGINEERING DESIGN
Er. PERUMAL MANIMEKALAI COLLEGE OF ENGINEERING, HOSUR
ANNA UNIVERSITYCHENNAI 600 025
June, 2014CERTIFICATE
Certified that this report titled OPTIMIZATION OF HYDRAULIC
POWER STEERING SYSTEM PARAMETERS, for the phase I of the project is
the bonafide work of Mr. YUVARAJ S (610812408020) who carried out
the project under my supervision for the partial fulfillment of the
requirements for the award of the degree of Master of Engineering
in Engineering Design. Certified further that to the best of my
knowledge and belief, the work reported herein does not form part
of any other thesis or dissertation on the basis of which a degree
or an award was conferred on an earlier occasion. Signature of
Supervisor Signature of HOD
Mr. P. ARULMOZHI, M.E., (Ph. D.,) Dr. C. SOLAIMUTHU, M. Tech.,
Ph. D.,
Associate Professor, Professor cum Director (Research) and HOD /
P.G
Department of Mechanical Engineering Department of Mechanical
Engineering
Er. Perumal Manimekalai College of Engg.. Er. Perumal
Manimekalai College of Engineering
Hosur 635 117.
Hosur 635 117.Submitted for the viva-voce examination held
on
Internal Examiner
External Examiner
DECLARATION
I affirm that the project report work entitled OPTIMIZATION OF
HYDRAULIC POWER STEERING SYSTEM PARAMETERS being submitted in
partial fulfillment for the award of Master of Engineering
(Engineering Design) is the original work carried out by me. It has
not formed the part of any other project submitted.
Signature of the Candidate
YUVARAJ S 610812408020I certify that the declaration made above
by the candidate is true.
Signature of Supervisor
Mr. P. ARULMOZHI, M.E., (Ph. D.,)
Associate Professor,
Department of Mechanical Engineering,
Er.Perumal Manimekalai college of Engineering,
Hosur. ACKNOWLEDGEMENTI first of all submit my prayerful thanks
to the ALMIGHTY for blessing & enabling me to take up this
project and for strengthening me till today and also in future
towards all my activities and duties.
I am highly indebted to express my hearty thanks to our beloved
Chairman Er. PERUMAL, most respected Secretary Er. P. KUMAR, and
our respected Trustee Mrs. P. MALLAR of Er. Perumal Manimekalai
College of Engineering. I am also very thankful to Dr. S. CHITRA,
M.E., Ph.D., Principal, Er. Perumal Manimekalai college of
Engineering, Hosur for giving me this wonderful opportunity. I
proudly render my thanks to Dr. C. SOLAIMUTHU, M. Tech., Ph.D,
Professor cum Director (Research) and HOD/P.G Mechanical
Engineering and Prof. P. RAJASEKARAN, M.E., (Ph.D), HOD/U.G
Mechanical Engineering for giving me this wonderful opportunity and
utilize all the facilities to the fullest. I express my deep sense
to my guide Mr. P. ARULMOZHI, M.E., (Ph. D.,) Associate Professor
of Mechanical Engineering Department and Department faculty members
for constantly motivating, guiding and encouraging me throughout
the project tenure.TABLE OF CONTENTS
S. NO. / Chap. No.DESCRIPTIONPAGE NO
Abstractxiii
CHAPTER I - INTRODUCTION1
1.1OBJECTIVE OF THE PROJECT1
1.2.OVERVIEW OF STEERING SYSTEM1
CHAPTER 2 LITERATURE REVIEW
2.1FRONT AXLE STEERING3
2.1.1 Condition for true rolling3
2.1.2 The Ackermann Principles as applied to steering5
2.1.3 Ackermann linkage:5
2.1.4 Ackermann linkage geometry6
2.2 STEERING DYNAMICS6
2.2.1 Kinematic Steering6
2.2.2 Vehicles with More Than Two Axles:11
2.2.3 Vehicle with trailer12
2.2.4 Steering Mechanisms13
2.2.5 Four wheel steering:14
2.2.6 Steering Mechanism Optimization16
CHAPTER 3 - PROJECT DESCRIPTION
3.1PROBLEM IDENTIFICATIONS18
3.2ONE DIMENSIONAL ANALYSIS19
3.3ABOUT THE SOFTWARE TOOL19
3.3.1 Software Basics19
3.4.MODEL BUILD PROCEDURE22
3.4.1 Torsion Bar23
3.4.2 Rotary Valve23
3.4.2.1 Procedure for Model build and simulation of Rotary
Valve:24
3.4.3 Hydraulic Pump30
3.4.4 Hydraulic Cylinder31
3.4.5 Front Axle 31
3.5INTEGRATING THE AGGREGATES32
3.6SIMULATION AND RESULTS32
3.7MATHEMATICAL ESTIMATION OF KEY PARAMETERS35
CHAPTER 4 RESULTS AND DSCUSSIONS38
4.1CASE STUDY : ESTIMATED RESULTS VS ACTUAL MEASUREMENTS38
4.2TESTS AND DATA MEASUREMETN40
4.3CORELATION : ESTIMATED VS MEASURED PARAMETERS43
5CHAPTER 5 RESULTS AND DISCUSSION46
6CHAPTER 6
SCOPE FOR FUTURE STUDY47
REFERENCES48
LIST OF FIGURESFig. No.TITLEPAGE No.
2.1.True Rolling condition3
2.2.Steering dynamics7
2.3.Inner Vs Outer wheel cut angle10
2.4.Vehicle with more than two axles11
2.5.Vehicle with trailer12
2.6.Steering Mechanism13
2.7.Four wheel steering14
2.8.Steering Mechanism Optimization16
3.1.Steering System18
3.2.AMESim modes19
3.3.Hydraulic Library20
3.4.Mechanical Library20
3.5.Control Library21
3.6.Hydraulic components Library21
3.7.Torsion Bar model and its super components23
3.8.Rotary valve and its super component23
3.9.Valve orifice27
3.10.Time vs Pressure30
3.11.Hydraulic Pump30
3.12.Hydraulic cylinder31
3.13.Front axle31
3.14.Hydraulic steering system circuit32
3.15Pressure Vs Torque By Simulation34
3.16Torque Vs Angle By Simulation34
3.17Pressure Vs Angle By Simulation35
3.18Pressure Vs Flow By Simulation35
3.19Pressure Vs Torque Measured41
3.20Torque Vs Angle Measured41
3.21Pressure Vs Angle Measured42
3.22Pressure Vs Flow Measured42
3.23Pressure Vs Torque Simulation and Measured43
3.24Torque Vs Angle Simulation and Measured44
3.25Pressure Vs Angle Simulation & Measured44
3.26Pressure Vs Flow Simulation & Measured45
LIST OF SYMBOLS
S. No.SYMBOLDESCRIPTION
1wTrackwidth
2iInner wheel cut angle
3.oOuter wheel cut angle
4.RTurning Circle Radius
5R1Projected distance from instantaneous center to inner pivot
center
6OCenter of Rotation
7CDistance between the pivot center
8dLength of track rod
92Distance from C to rear axle
10a1Distance from C to front axle
11a2Distance from C to third axle
12RtRadius of trailer axis from instantaneous center
13b1Tail center to rear axle distance
14B2Tail center to trailer axle distance
15Trailer angle
16BTail center
17WfRear track width
18LWheel base of the vehicles
ABSTRACT
This project is carried out to analyses of an automobile
hydraulic power steering system to optimize its functional
characteristics, an one dimensional circuit of the hydraulic power
steering system with its aggregates has been prepared using AMESIM
software and functional inter relation of the steering system has
been derived, embedded, so that this customized circuit is capable
to simulate the overall function of the hydraulic power steering
system.
A hydraulic power steering system consist of several aggregates
like steering wheel, steering column, steering gear with precious
rotary control valve, power steering pump, and hoses. The
cumulative functions of the system has been appropriately
integrated in this customized circuit prepared in AMESim software,
hence for the given input, this customized circuit shall simulate
the function of the steering system and able to predict the output
performance, the same shall be compared against the target vehicle
performance and optimized accordingly.
Traditionally the steering system supplier used to estimate the
system aggregates through very limited calculations as against the
target vehicle performance requirements and take support from the
OEMs to understand the cumulative performance and do necessary
design changes for optimizing the aggregates specification and meet
the target vehicle requirements. This customized one dimensional
circuit in AMESim software enables the user to predict the
cumulative system performance for various range of aggregates
specification and facilitate for optimization.
A live project has been taken for detailed study and the
predicted output of the same has been compared with the actual
vehicle measurement and concluded through the comparison.
CHAPTER 1INTRODUCTION1.1 OBJECTIVE OF THE PROJECT
Objective of the project is to derive the mathematical
relationship of the Hydraulic power steering system aggregates and
integrate their functionalities into customized one dimensional
circuit using AMESim software so that the functionalities of the
entire hydraulic power steering system shall be simulated,
cumulative output characteristics of the same shall be predicted
and optimized.
By Simulation and prediction of the cumulative output function
of the steering system the aggregates specification of the steering
system shall be optimized and the target vehicle performance shall
be achieved by virtual iterations which can deliver first time
right aggregates specification and eliminates vehicle trials and
engineering design changes.
1.2 OVERVIEW OF STEERING SYSTEM
Primary function of the steering system is to provide
directional control for the vehicle by converting the rotatory
input in to angular movements of tire in the desired manner, also
the steering system has several secondary functions such as isolate
the hand wheel from road wheel shocks while maintaining the road
wheel feel and return ability of hand wheel.
Power assisted steering system will continue the functionalities
of the conventional steering system, in addition to that it will
provide power assistance to reduce the driver fatigue and provide
better driving maneuver.
In general Rack & pinion type steering system is treated as
a sub system of an automobile, which will have the following major
aggregates
Rotary valve
Torsion bar
Hydraulic pump
Hydraulic Cylinder
Front axle
Hose lines
Combined functionality of the above aggregates delivers the
performance of a steering system.
CHAPTER 2
LITERATURE REVIEW
2.1 FRONT AXLE STEERING
2.1.1 Condition for true rolling
True rolling occurs only when the direction of motion of the
vehicle is perpendicular to the wheel axis, the wheel is subjected
to forward force. When wheel is subjected to side force that acts
parallel to the wheel axis, a true scrub action is produced, when
the wheel is subjected to both forward and side forces the movement
is compounded of true rolling and lateral distortion, this
condition occurs when the wheels are being steered, in other words
the direction of motion is neither parallel not perpendicular to
the axis of rotation.
Fig 2.1 True rolling condition
On a circular path true rolling condition occurs when the
projected axes of several wheels all moving in different occurred
paths intersect as a single point called the instantaneous center,
when these projected axes do not intersect at a single point a
degree of the tire scrub results .
Whenever a vehicle takes a turn the front wheels must turn in
definite manner both in relation to each and to the axis of the
rear wheels so that the lateral slip may be avoided and true
rolling for all the wheels is obtained, for this as explained above
all the wheels must always rotate about the instantaneous center .
Since the rear wheels have a common and fixed axis, it is quite
obvious that the common center, would lie somewhere on its
extension.
Form the fig
= angle of inside lock
o= angle of outside lock
W= wheel track also known as tread of vehicle
=wheel base of the vehicle
c = distance between the pivot centers
d = length of track rod
R1= projected distances from instantaneous center to the inner
pivot center therefore,
this equation gives the fundamental condition to be satisfied by
all types of steering mechanism if true rolling for all the wheels
is to be obtained avoiding any lateral slip. The steering linkage
used in the vehicles must maintain the proper angles with the
wheels when taking a turn. But practically it is not possible to
maintain absolutely angles for the wheels for all turning
angles.
2.1.2 The Ackermann Principles as applied to steering
To achieve true rolling for ta four wheeled vehicle moving on a
curved track the lines drawn through each of the four wheel axes
must intersect at the instantaneous center fig. the actual position
the instantaneous center constantly changes due to the alternation
of the front wheel angular position to correct the steered vehicles
path. Since both wheels are fixed on the same axis but the front
wheel axles are independent of each other, the instantaneous
centers lies somewhere along an imaginary line drawn through the
axis of the rear axle.
The Ackermann principle is based on the two front steered wheel
being pivoted at the ends of an axle beam. The original Ackermann
linkage has parallel set track rod arms so that both steered wheels
swivel at equal angles. Consequently the intersecting projection
lines do not meet at one point. If both front wheels are free to
follow their own natural paths they would converge and eventually
cross each other. Since the vehicle moves along both a single mean
path, both wheel tracks conflict continuously with each other
causing tire slip and treated scrub. Subsequent modified linkage
uses inclined track rod arms so that the inner wheel swivels about
its king pin slightly more than the outer wheel, hence the lines
drawn through the stub axles converge at a single more than the
outer wheel, hence the lines drawn through the stub axles converge
at a point somewhere along the rear axle projection.
2.1.3 Ackermann linkage:
The self-propelled motor vehicle almost from the beginning used
the double pivot wheel steering system. This was inverted for horse
drawn vehicles in 1817 by George lankensperger a Munich carriage
builder. In England, Rudolph Ackermann acted as Lankenspergers
agent and a patent of the double pivot steering arrangement was
taken in his name.
With this layout of the linkage the track rod arms are set
parallel to each other and a track rod joints them together. In the
straight ahead position of the steering, the linkage and axle beam
forms a rectangle but as the stub axles are rotated about their
kingpins the steering arrangement forms a parallelogram. This
linkage configuration turns both wheels the same amount, the
parallel set linkage positioned to provide both a 20 degree and a
40 degrees turn for the inner and outer wheels.
2.1.4 Ackermann linkage geometry
In parallel set steering arms layout of the track rod
dimensions, remain equal for all angles of turn. With the inclined
arms the inner wheel track rod end dimensions is always smaller
than the outer wheel dimensions while negotiating a curve.
Therefore for a given angular movement of the stub axles the
inner wheel track rod arm and track rod are more effective than the
outer wheel linkage in turning the steered wheel. For a given
amount of transverse track rod movement with inclined track rod
arms the least effective angular displacement of stub axle pivot
occurs in the straight ahead region, and the most effective angular
displacement takes places as the stub axles move away from the mid
position, thus the angular movement of the inner wheel relative to
the outer wheel becomes much greater as both wheels approach
movement of the inner wheel relative to the outer wheel becomes
much greater as both wheel full lock. With modern radial tires, the
difference between front and back lock steering angles is sometimes
reduced.2.2 STEERING DYNAMICS
2.2.1 Kinematic Steering
Consider a front-wheel-steering 4W S vehicle that is turning to
the left, as shown in Figure, When the vehicle is moving very
slowly, there is a kinematic condition between the inner and outer
wheels that allows them to turn slip-free. The condition is called
the Ackerman condition and is expressed by
where, i is the steer angle of the inner wheel, and o is the
steer angle of the outer wheel. The inner and outer wheels are
defined based on the turning centre O.
Fig 2.2 Steering Dynamics
The distance between the steer axes of the steerable wheels is
called the track and is shown by w. The distance between the front
and rear axles is called the wheelbase and is shown by l. Track w
and wheelbase l are considered as kinematic width and length of the
vehicle.
The mass centre of a steered vehicle will turn on a circle with
radius R,
Where is the cot-average of the inner and outer steer
angles.
The angle is the equivalent steer angle of a bicycle having the
same Wheel base l and radius of rotation R.Proof. To have all
wheels turning freely on a curved road, the normal line to the
centre of each tire-plane must intersect at a common point. This is
the Ackerman condition.
Figure 2.2 illustrates a vehicle turning left. So, the turning
centre O is on the left, and the inner wheels are the left wheels
that are closer to the centre of rotation. The inner and outer
steer angles i and o may be calculated.
The Ackerman condition is needed when the speed of the vehicle
is too small, and slip angles are zero. There is no lateral force
and no centrifugal force to balance each other. The Ackerman
steering condition is also called the kinematic steering condition,
because it is a static condition at zero velocity.
provides the Ackerman condition, which is a direct relationship
between i and o.
To find the vehicles turning radius R, we define an equivalent
bicycle model, as shown in figure. The radius of rotation R is
perpendicular to the vehicles velocity vector v at the mass centre
C, using the geometry shown in the bicycle model, we have
The Ackerman condition is needed when the speed of the vehicle
is too small, and slip angles are zero. There is no lateral force
and no centrifugal force to balance each other. The Ackerman
steering condition is also called the kinematic steering condition,
because it is a static condition at zero velocity.
Fig 2.3 Inner Vs Outer Wheel cut angle
A device that provides steering according to the Ackerman
condition is called Ackerman steering, Ackerman mechanism, or
Ackerman geometry. There is no four-bar linkage steering mechanism
that can provide the Ackerman condition perfectly. However, we may
design a multi-bar linkages to work close to the condition and be
exact at a few angles. Figure illustrates the Ackerman condition
for different values of w/l. The inner and outer steer angles get
closer to each other by decreasing w/l.2.2.2 Vehicles with More
Than Two Axles:
Fig 2.4 Vehicles with more than two Axle
If a vehicle has more than two axles, all the axles, except one,
must be steerable to provide slip-free turning at zero velocity.
When an n-axle vehicle has only one non-steerable axle, there are n
1 geometric steering conditions. A three-axle vehicle with two
steerable axles is shown in Figure.
To indicate the geometry of a multi-axle vehicle, we start from
the front axle and measure the longitudinal distance ai between
axles i and the mass centre C. Hence, a1 is the distance between
the front axle and C, and a2 is the distance between the second
axle and C. Furthermore, we number the wheels in a clockwise
rotation starting from the drivers wheel as number 1.
For the three-axle vehicle shown in Figure, there are two
independent Ackerman conditions:
2.2.3 Vehicle with trailer
Fig 2.5 Vehicle with trailer
If a four-wheel vehicle has a trailer with one axle, it is
possible to derive a Kinematic condition for slip-free steering.
Figure illustrates a vehicle with a one-axle trailer. The mass
canter of the vehicle is turning on a circle with radius R, while
the trailer is turning on a circle with radius Rt.
2.2.4 Steering Mechanisms
Fig 2.6 Steering Mechanism
A steering system begins with the steering wheel or steering
handle. The drivers steering input is transmitted by a shaft
through a gear reduction system, usually rack-and-pinion or
recirculating ball bearings. The steering gear output goes to
steerable wheels to generate motion through a steering mechanism.
The lever, which transmits the steering force from the steering
gear to the steering linkage, is called Pitman arm.
The direction of each wheel is controlled by one steering arm.
The steering arm is attached to the steerable wheel hub by a
keyway, locking taper, and a hub. In some vehicles, it is an
integral part of a one-piece hub and steering knuckle. To achieve
good manoeuvrability, a minimum steering angle of approximately 35
deg. must be provided at the front wheels of passenger cars.
A sample parallelogram steering mechanism and its components are
shown in Figure, The parallelogram steering linkage is common on
independent front-wheel vehicles. There are many varieties of
steering mechanisms each with some advantages and
disadvantages.2.2.5 Four wheel steering:
Fig 2.7 Four Wheel Steering
At very low speeds, the kinematic steering condition that the
perpendicular lines to each tire meet at one point, must be
applied. The intersection point is the turning centre of the
vehicle.
Figure illustrates a positive four-wheel steering vehicle, and
Figure illustrates a negative 4W S vehicle. In a positive 4W S
situation the front and rear wheels steer in the same direction,
and in a negative 4W S situation the front and rear wheels steer
opposite to each other. The kinematic condition between the steer
angles of a 4W S vehicle is
where, wf and wr are the front and rear tracks, if and of are
the steer angles of the front inner and outer wheels, ir and or are
the steer angles of the rear inner and outer wheels, and l is the
wheelbase of the vehicle.
We may also use the following more general equation for the
kinematic Condition between the steer angles of a 4W S vehicle
where, f l and f r are the steer angles of the front left and
front right wheels, and rl and rr are the steer angles of the rear
left and rear right wheels. If we define the steer angles according
to the sign convention shown in Figure then, the equation expresses
the kinematic condition for both, positive and negative 4W S
systems. Employing the wheel coordinate frame (xw, yw, zw), we
define the steer angle as the angle between the vehicle x-axis and
the wheel xw-axis, measured about the z-axis. Therefore, a steer
angle is positive when the wheel is turned to the left, and it is
negative when the wheel is turned to the right. Proof. The
slip-free condition for wheels of a 4W S in a turn requires that
the normal lines to the canter of each tire-plane intersect at a
common point. This is the kinematic steering condition. Figure
illustrates a positive 4W S vehicle in a left turn. The turning
canter O is on the left, and the inner wheels are the left wheels
that are closer to the turning canter. The longitudinal distance
between point O and the axles of the car are indicated by c1, and
c2 measured in the body coordinate frame.
2.2.6 Steering Mechanism Optimization
Fig 2.8 Steering mechanism optimization
Optimization means steering mechanism is the design of a system
that works as closely as possible to a desired function. Assume the
Ackerman Comparing the function of the designed steering mechanism
to the Ackerman condition, we may define an error function e to
compare the two functions.
An example for the e function can be the difference between the
outer steer angles of the designed mechanism Do and the Ackerman Ao
for the same inner angle i. The error function may be the absolute
value of the maximum difference,
or the root mean square (RMS) of the difference between the two
functions
in a specific range of the inner steer angle i.
The error e, would be a function of a set of parameters.
Minimization of the error function for a parameter, over the
working range of the steer angle i, generates the optimized value
of the parameter.
The RMS function is defined for continuous variables Do and Ao .
However, depending on the designed mechanism, it is not always
possible to find a closed-form equation for e. In this case, the
error function cannot be defined explicitly, and hence, the error
function should be evaluated for n different values of the inner
steer angle i numerically. The error function for a set of discrete
values of e is define by
The error function must be evaluated for different values of a
parameter. Then a plot for e = e (parameter) can show the trend of
variation of e as a function of the parameter. If there is a
minimum for e, then the optimal value for the parameter can be
found. Otherwise, the trend of the e function can show the
direction for minimum searching.
CHAPTER 3
PROJECT DESCRIPTION
3.1 PROBLEM IDENTIFICATIONS
A hydraulic power steering system is a combination of many
mechanical and hydraulically functional part and those are
interlinked through ways and means like belt drive, hydraulic
connections etc. also the functional behaviors of the system is
various with respect to many influencing external parameters like
road wheel friction, hand wheel signal ( torque and angle), engine
speed, vehicle speed and front axle load, considering the multiple
influencing factors and the performance characteristics of
aggregates of the system like hydraulic pump, hydraulic valve,
hydraulic cylinder and torsion bar, optimizing the performance
characteristics of a steering system is really a tough task, also
estimating the combination effect of multiple parameters with wide
range of input characteristics requires tremendous and tedious
mathematical calculations however inferring the parameters in
combination of input variants is almost impossible, hence its
necessary to take a help of an software packages to and model the
steering system aggregates in a one dimensional structure and
integrate them and perform various calculations for the full range
of input.
Fig 3.1 Steering System
3.2 ONE DIMENSIONAL ANALYSIS
The method adopted perform the performance prediction of
hydraulic power steering system is a One dimensional lumped
parameter time domain analysis.
3.3 ABOUT THE SOFTWARE TOOL
AMESim = Advanced Modelling Environment for performing
Simulations of engineering systems.
AMESim is a 1D lumped parameter time domain simulation platform.
AMESim uses symbols to represent individual components within the
system which are either, based on the standard symbols used in the
engineering field such as ISO symbols for hydraulic components or
block diagram symbols for control systems or when no such standard
symbols exist
3.3.1 Software Basics
Fig 3.2 AMISIM Modes
Different types of Library:
Each library tree will have different types of features.
a) Hydraulic library
Fig 3.3 Hydraulic Library
b) Mechanical library
Fig 3.4 Mechanical Library
c) Signal and controls library
Fig 3.5 Control library
d) Hydraulic components and design library
Fig 3.6 Hydraulic components library
3.4 MODEL BUILD PROCEDURE
The power steering system shown consists of a steering wheel, a
rotary valve with torsion bar, a rack, a hydraulic pump and the
lines. When the driver inputs a steering angle command, the
steering valve opens. This allows oil to flow into the hydraulic
cylinder, with a pressure proportional to the amount of valve
opening. The oil pressure acts on the cylinder piston to create an
actuating force proportional to the pressure. This actuating force
then assists the driver in moving the cylinder piston and the
mechanism connected to it (rack, wheels...). The notion of the
cylinder piston is then fed back to the valve by the rack and
pinion. The pinion rotation tends to close the valve, completing
the control loop.
The major functional components of the power steering system are
detailed as follows
Rotary valve
Torsion bar
Hydraulic Pump
Hydraulic CylinderFront Axle with tire
Hose lines
A hydraulic pump is connected to the rotary valve with lines and
hoses. A pinion-rack converts the rotation of the torsion bar in a
linear displacement of the front axle.
The simulation model considers that the pump gives out a flow
rate proportional to the engine speed and that the flow control
valve reduces this flow to a constant one. The hydraulic line from
this valve to the rotary valve and from the rotary valve to the
reservoir is a union of pipes, hoses and orifices. Hoses are
modeled with a lumped parameter sub model with compressibility of
oil and expansion of line walls. Pipes are modeled with additional
assumptions and take into account pipe friction and fluid inertia.
All AMESim line sub models are able to predict air release and
cavitation effect. In this case, it is vitally important that
density and bulk modulus are totally consistent to achieve rigorous
mass conservation.
3.4.1 Torsion Bar
Fig 3.7 - Torsion bar model and its super component
The torsion bar is the simplest model of the power steering
system. It consists in a rotary spring attached at one side to the
pinion and at the other to the steering column.
3.4.2 Rotary Valve
Fig 3.8 - Rotary valve and its super component
The rotary valve can be represented as a Wheatstone bridge,
where each branch is a way of the valve. The flow area of each path
depends on the relative deformation of the torsion bar. The flow
area on the valve is controlled by the relative deformation of the
torsion bar.
3.4.2.1 Procedure for Model build and simulation of Rotary
Valve: Since it is the hydraulic system the oil properties to be
defined properly.
Then the motor driven pump should be defined with the flow
condition. The relief pressure should be defined (example: 75
bar).Constant speed prime mover (motor) and Constant displacement
pump (ideal fixed displacement pump) with relief pressure
setting
The valve opening is changing based on the input shaft rotation.
So the valve opening will be defined as hydraulic variable orifice.
The other holes / openings where the diameter is not getting
affected because of the input shaft rotation can be represented by
the fixed displacement orifice. The hydraulic junctions can be used
to make the parallel / series connection based on the requirements.
3 port hydraulic junction 4 port hydraulic junction
A constant pressure reservoir / tank should be place to give the
hydraulic source to pump and the same will be connected with the
return line to close the circuit.
For the steering input the signal library can be used.
The above sub model can be used for giving steering input in one
direction. But in case of the steering wheel rotation in both sides
a gain can be used with signal splitters.
If we want to use the same signals for different location the
signal duplication sub model can be used.
By using all these sub models and the connectors the circuit can
be built as follows. The connector may be either direct connection
or with pipes. For signals, there will be direct connection (red
color dotted line).
Since this circuit is for 4 slot valve, it has been used 8
hydraulic variable orifices. This is because for each slot will
have two openings. When giving steering input one orifice will open
another one will close. And the signal also given to all variable
orifices. 6 orifices will be connected with the direct signal and 6
orifices will be connected with the signals after including the
gain.
There are about 8 constant displacement orifices being used in
this circuit. Among that the top 2 orifices are the pressure port
holes in the valve sleeve. The bottom most 2 orifices are for the
return hole in the input shaft. If there is only one hole in the
return line one orifice can be used.
In the middle of the circuit there are six orifices. These are
feed port holes which have been placed in the valve sleeve. 3
orifices for LH side and 3 orifices for RH side of the double
acting cylinder. This mass is to generate pressure inside the
system. We can use the zero force model to avoid the external
forces acting in the model.
The circuit will be built in the sketch mode only. Once the
circuit completed the mode can be changed to sub model mode. If the
circuit is incomplete it cannot be changed to sub model mode.
Once changed to sub model mode each model will ask which sub
model can be used. If we choose the standard option all standard
sub models will be chosen. If we want to use the specific sub model
by right click the model choose the required sub model.
Once the sub model definition completed the parameter to be
defined for all the sub models. These parameters can be changed
whenever we required.
For hydraulic oil properties can be defined by choosing the
hydraulic oil icon.
For prime mover, pump and the relief pressure setting can be
defined by choosing the respective models.
The fixed displacement orifice parameters can be defined as
follows;
The variable hydraulic orifice parameters can be defines as
follows;
In the variable orifice sub model properties the orifice area
and the hydraulic diameter should be given as separate test file
(.txt format). The area and the hydraulic diameter should be
calculated for each angle of rotation (example for each 0.1 of
rotation).
Here the section of the orifice in the input shaft is assumed as
rectangle and the height of the rectangle is constant and the width
of the rectangle is varies based on the angle of rotation. The
height of the input shaft pocket has been assumed as constant
(height = 10 mm) and the width of the pocket varies continuously
based on the angle of rotation. By multiplying height and width we
can get the orifice area. We have to calculate for both opening and
closing orifice area. If one orifice opens means the corresponding
another orifice in the same pocket will close.
The hydraulic diameter can be calculated as follows;
Hydraulic diameter = 4*orifice area/ hydraulic perimeter.
Hydraulic perimeter can be calculated by doing as follows;
Hydraulic perimeter = (2 * height of the pocket) + (2 * width of
the pocket).
The width of the pocket can be measured by using Auto CAD
software.
The input shat and valve sleeve cut section is as follows;
The width of the pocket (orifice) can be measured as
follows;
Fig 3.9 Valve Orifice
The perpendicular distance (from the valve sleeve pocket edge to
the input shaft) has to be measured always.
Like this the width of the pocket can be measured for all the
angle of rotation in both opening and closing orifices. The width
has to be measured up to 6 of angle of rotation.
The calculated orifice area and the hydraulic diameter should be
saved as separate text files (.txt format) and then give link to
the variable hydraulic orifice sub model.
Then the signal to the valve will be given in the linear signal
source. The no of stages may be varies depend on the usage. Here
the no of cycle has been selected as 8 stages. The stages
characteristics are as follows;
1. Increment from zero
2. Stable signal at positive peak
3. Decrement from positive peak to zero
4. Stable at zero
5. Increment in negative direction up to negative peak
6. Stable at negative peak
7. Decrement from negative peak to zero
8. Stable at zero
This signal should be select as cyclic to work continuously.
The gain values should be given as -1 to provide the negative
signal.
The hydraulic chamber (double acting cylinder with mass)
properties should be given.
At some stages in the hydraulic lines, it is difficult to give
direct connection. On that condition a hydraulic pie sub model will
be selected. In the hydraulic pipe sub model following parameters
need to be defined. Possibly specify very short length pipe with
bigger diameter.
Once finish the definition to all the required parameters, the
simulation mode should be selected. Once the simulation mode gets
selected the compilation of the program will happen to build the
model completely.
Select the run parameters to define the type of rum, program
running period and the interval.
Once the run parameters defined properly the simulation should
run by selecting the start simulation option.
Once the simulation started the simulation will run and complete
successfully. If there is any error or warning it will indicate
inside the simulation run window.
The plotting of the data can be do as follows;
1. Select the model in which the data to be plotted. If two or
more data to be plotted and compared simultaneously just drag the
data and put in the plot.
2. Normally the plot will be in the form of time domain.
3. If we want to plot XY of two different parameters the plot
can be done as follows;
a. Select convert 2D curves to XY 2D curved in the plot main
menu bar.
b. Then click inside the plot area.
If a parameter want to varies randomly / continuous with
different values the batch parameter option can be used. The batch
parameter run can be done as follows;
1. Keep the operation mode in the parameter mode condition. And
choose setting in the task bar and select batch parameters.
2. A variable / parameter which need to varied model should be
selected and the corresponding parameter should be select, drag and
drop in the batch parameter window as follows, one or more
parameters also can be selected for the batch run.
3. After that change to simulation mode. The compilation process
will start automatically and build the model completely.
4. Then choose the simulation run option and click batch
parameter and select batch options and choose the parameter which
we want to run the batch run.
5. Then run the simulation. The batch run will be as follows and
it will run as different sets based on the batch option we
selected.
If the data wanted to be exported to some other format (example:
excel file). Choose the following step in the plot window.
Choose file and then choose export.
Fig 3.10 Time Vs Pressure
The exported data will be in the form of text file. We can open
that file excel by choosing open with option.
3.4.3 Hydraulic Pump
Fig 3.11 Hydraulic Pump
3.4.4 Hydraulic Cylinder
Fig 3.12 Hydraulic Cylinder
There are, in the AMESimHydrauliclibrary, many cylinder sub
models. If require can use specific assumptions (for example
elastic end stops), it is possible to construct a new hydraulic
cylinder model using theHydraulic Component DesignLibrary.
3.4.5 Front Axle
Fig 3.13 Front Axle
The front axle is, in this study, modeled as a spring mass
system. The mass equivalent to the rotary inertia (tire and other
mechanical parts) is seen as a translation on the rack axis. The
spring is one of the stiff nesses of the tire in rotation around
the vertical axis. The stiction, Coulomb friction, and viscous
friction are taken into account to model the contact between the
tread and the ground. The detailed model and its associatedsuper
componentare shown in Figure.
It is also possible to model the front axle using the interface
with the multi-body software ADAMS. The full hydraulic system is
converted and imported into ADAMS for use within ADAMS. This
process involves using solely the integration methods provided by
ADAMS. However, as the run progresses, the hydraulic subsystem
results can be examined and plotted within AMESim, meanwhile ADAMS
animation can be used to view multi-body results. Without the
ability of plotting hydraulic subdomain results within the natural
environment, understanding of what is happening within the
simulation is almost impossible.
3.5 INTEGRATING THE AGGREGATES
Fig 3.14 Hydraulic Steering System Circuit
Linearization within AMESim can be performed in simulation
activity at different times. Control, observer and fixed variables
can be set. Even if the system of equations is differential
algebraic (D.A.E), it is possible with AMESim to produce the A, B,
C and D matrices. Then, AMESim can evaluate and list the complex
eigenvalues and this corresponding frequency and damping values.
Alternatively, we can use the Linear Analysis tools included in
AMESim to perform analyses like Bode and Nichols plot model
reduction, modal analysis and there on to performance
prediction.
3.6 SIMULATION AND RESULTS
On completion of aggregates are integration, aggregates are
constrained, parameterized with appropriate parameters like
Torsion bar
: Torsion rate
Flow control valve: Orifice range, orifice area
Pump
: Relief pressure, speed
Rack & Pinion
: Number of turns, Cylinder area
Fluid lines (pipe): Diameter,
Tire
: Load, friction Parameterized model has been subjected to model
check and simulation run, the following results are plotted from
the simulation results. Differential Pressure Vs Torque
Angle Vs Torque
Angle Vs Pressure
Pressure Vs FlowGraphical output of the simulation results are
as follows.
Differential Pressure Vs Torque
Fig 3.15 Diff Pressure Vs Torque By Simulation
Angle Vs Torque
Fig 3.16 Torque Vs Angle By Simulation
Angle Vs Pressure
Fig 3.17 Pressure Vs Angle - By Simulation
Flow Vs Pressure
Fig 3.18 Pressure Vs Flow By Simulation
3.7 MATHEMATICAL ESTIMATION OF KEY PARAMETERS
King Pin torqueWhere
Tk = Torque required at knuckle arm to turn the wheels
W= Front Axle Weight (FAW)
= Co-efficient of friction between tire and road surface
Wt= Tire patch widthRack force requiredRf = Tk / r
Where
Rf = Rack force required to pull / push the knuckle arm
Tk = Torque required at knuckle arm to turn the wheels
r= Knuckle arm radius
Rack force required = Torque required at Knuckle / Knuckle arm
radiusMax. Operating PressurePmax = Fr / A
Pmax = Maximum operating pressure
Rf= Rack force
Ap= Piston AreaMax. Flow required
Q = Ap * V
Where
Q = Flow required
Ap= Area of piston
V= Maximum velocity of Piston
Input torque Vs PressureQ = CA P = + CAc = Ao = Where
P = Differential pressure between cylinders
Ac = Area close
Ao = Area open
C = Flow Co-efficient
Dc = Distance at close
L = Length of the control edge
Tc = Secondary area open
OL = Overlapping distance
To = Secondary area close
Q = Flow through orifice
K = Flow constant of the fluid
n = Number of slots (orifice)
CHAPTER 44.1 CASE STUDY: ESTIMATED RESULTS VS ACTUAL
MEASUREMENTS
To ensure the correctness of the one dimensional simulation
analysis developed through AMESim Software, a case study has been
made and the estimated results and actual vehicle measurement
results are compared and reasonably appreciated level of
correlation has been evident.
A market available utility vehicle with Hydraulic Power Rack
& Pinion steering gear configuration has been choose for the
case study and the vehicle has been equipped with necessary
instrumentation in the steering system.
Following instruments are used.
Sl. No.Instrument NameMeasuring RangeMeasuring parameter
01Angle Sensor 600 degSteering Input angle
02Torque sensor0-25 N-mSteering Input torque
03Pressure sensor0- 200 barHydraulic System Pressure
04Flow Sensor1 to 10 lpmOil flow rate from pump
05Data loggerUp to 200k / Sec.To capture and Save the data
Angle and Torque SensorPressure & Flow Sensor
4.2 TESTS AND DATA MEASUREMENTSl.No.Test NameTest
ConditionsMeasuring Parameters
01Static Steering meanuaoverVehicle Condition : Static, Power
On
Surface : Dry tar surface
Steering maneuver : SAP to RH lock, LH lock and SAP
Measurement : Time DomainParameters
Steering angle Vs Steering torque, Hydraulic Pressure,
Hydraulic Flow
VEHICLE MEASUREMENT RESULTS
Differential Pressure Vs Torque
Angle Vs Torque
Angle Vs Pressure
Angle Vs Flow
Pressure Vs Flow
Pressure Vs Torque
Fig 3.19 Diff Pressure Vs Torque Measured
Torque Vs Angle
Fig 3.20 Torque Vs Angle Measured
Pressure Vs Angle
Fig 3.21 Pressure Vs Angle MeasuredPressure Vs Angle
Fig 3.22 Pressure Vs Angle Measured
4.3 CORELATION STUDY: ESTIMATED VS MEASURED PARAMTERS
Estimated results and measured results are exported to a neutral
file format (Microsoft Excel) and the resultant parameters are
compared as follows.
Simulation Vs Estimation of
Pressure Vs Torque
Torque Vs Angle
Pressure Vs Angle
Pressure Vs Flow
Pressure Vs Torque
Fig 3.23 Pressure Vs Angle Simulation & Measurement
Result
Torque Vs Angle
Fig 3.24 Torque Vs Angle Simulation & Measurement Result
Pressure Vs Angle
Fig 3.25 Pressure Vs Angle Simulation & Measurement
ResultPressure Vs Flow
Fig 3.26 Pressure Vs Flow Simulation & Measurement
Result
CHAPTER 5RESULTS AND DSCUSSIONS
5.1 Results of the projectIn the process of predicting the
performance characteristics of hydraulic power steering system all
the system related parameter as are predicted through the
simulation done in AMESim software with the help of newly evolved
1Dimensional steering circuit.
The Predicted results are also compared with practical
measurement data and more than 90% of correlation has been achieved
between the predicted result and simulated result, these variations
are duet to contribution of vehicle level parameters, which are not
been able to predict because those are be the permissible
variations of parts and its cumulative result.Simulation and
measurement result has been made and compared for
Differential Pressure Vs Torque
Torque Vs Angle
Pressure Vs Angle
Pressure Vs Flow
Now using this circuit and result we can able to optimise the
characteristics of Rack and Pinion steering system for any road
vehicle applications.
CHAPTER 6SCOPE FOR FUTURE STUDY
In this project the major performance parameters of the steering
system like Differential Pressure, Angle, Torque, Flow and
Pressure. Inter relation between these parameters are also been
estimated.
In this simulation process we have predicted the performance at
vehicle Static condition only, in the further action this circuit
can be integrated with multi body dynamic softwares so that we can
predict the resultant parameters at dynamic vehicle condition,
which includes different suspension condition, steering input
condition and different road condition.REFERENCES
1. T. Kenneth Garrett, Kenneth Newton and William Steeds, The
Motor Vehicle 13th Edition, Butterworth-Heinemann Limited, London,
2005.
2. Heinz Heisler, Vehicle and Engine Technology, Second Edition,
SAE, USA, 1999.
3. Kripal Singh, Automobile Engineering (Volume - 1), 12th
Edition, Standard Publishers and Distributors, 2011.
4. Heldt P.M., Automotive Chassis Chilton Co., New York,
1952
5. R.K. Rajput, A Text Book of Automobile Engineering, Laxmi
Publications Private Limited, 2007
6. N.K. Giri, Automotive Mechanics Khanna Publishers, New Delhi,
2005.
7. Antony Espossito, Fluid Power with Applications, Prentice
Hall, 1980
8. K.Shanmuga Sundaram, Hydraulic Systems, Butterworth
Heinemann, 19779. Help files from AMESim software.10. Help files
from Dewesoft.
EMBED Equation.3
Angle in N-m
i
_1463334073.unknown
