Analysis of Double Wishbone Suspension System Components
Transcript of Analysis of Double Wishbone Suspension System Components
Coventry University School of Engineering
MSc Dissertation in Automotive Engineering
ANALYSIS OF DOUBLE WISHBONE SUSPENSION SYSTEM COMPONENTS
Submitted By: MOHD ZAKARIA MOHAMMAD NASlR
Project Supervisor:
COVENTRY UNI : Dr. GURMAIL SlNGH
KUTKM: 1. Professor Dr. MD. RAZALI AYOB
2. Dr. KHISBULLAH HUDA
3oth August 2006
ABSTRACT
The durability of automotive components is a critical aspect in the product
development. Failure in component will lead to a serious damage not only the design of
the component itself, but the entire system of vehicle. In this thesis, a stress study of a
critical component was performed based on load prediction from multi-body simulation
system for double wishbone suspension system under braking and cornering load cases.
First, major coordinate points of front wheel drive Aston Martin Vanquish
suspension were measured via computer measuring machine. It was then followed by
modelling the suspension system linkages into multi-body system analysis via
MSC.ADAMS. Quasi-Static analysis was performed using load profile database to
determine the load acting on each component for typical load cases. Later, these
calculated loads were applied to the FEA stress analysis (MSC.PATRAN/NASTRAN)
for a critical component selected in order to predict the maximum stress, stress
concentration and displacement.
From the results of component load and stress study, 1G braking load cases
produces higher forces compare to cornering load case. Although the high-tension force
occurred at the lower control arm, this structure generated a low maximum stress with
factor of safety 7. Meanwhile, the tie-rod working in compression load produced the
highest stress during braking condition which then buckling analysis is performed.
However, both components did not exceed the yield stress of the material.
CHAPTER 1
INTRODUCTION
1.1 Introduction
The hnction of suspension system is to absorb vibration due to irregularities of
road conditions. Furthermore, it also designed to maximize the friction between tyre
contact patch and the road surfaces to provide vehicle stability under any circumstance
associated with accelerating, bralung, loaded or unloaded, uneven road, straight line or
cornering.. The suspension system significantly affects ride and handling of the vehicle
that is 'vibrational' behaviour including ride comfort, directional stability, steering
characteristics and road holding. Generally, suspension system can be broadly classified
as dependent and independent types. The factor which primarily affect the choice of
suspension type at the front or rear of the vehicle are the engine location and whether the
front wheels are driven Iundriven and /or steeredlunsteered .
DOUBLE W W B O N E SUSPENSION SYSTEM
Independent suspension (i.e. double wishbone, McPherson and multilink) leads to
better ride and handling capabilities [1,3,5]. It is important to analyze the suspension
systems that have been designed to predict the behaviour of the system than followed
with improvements. The suspension must be properly designed because it is a crucial
subsystem in vehicle in order to:
Cany the weight of vehicle and also its weight (unsprung weight).
Keep the wheels perpendicular to the road for maximum grip resultant good ride
and handling performance.
Take the forces for accelerating or braking the vehicle.
Ensure that steering control is maintained during manoeuvring.
Take the forces involved when cornering the vehicle.
Nowadays, the computational power has been developed to make the vehicle
dynamics analysis easier with better accuracy and less computing time. MSC.ADAMS
(Automatic Dynamic Analysis ofMechanica1 Systems) software is one of tools that widely
use as multi-body systems analysis (MBS). It is not only used in automotive industry but
other industries like aerospace, construction, electro-mechanical and general mechanical
industries. MSC-ADAMS software enables many 'what i f scenarios to be tested quickly
without a lot of development testing [2].
1.2 Problem Statement
The factor affecting design for instance to meet the certain performance targets
are varying across the range of vehicles. There are also other limitations such as cost,
weight, packaging space, requirement for robustness and reliability, manufacturing,
assembly and maintenance constraints. For example, sport car such required good ride
and handling. Therefore, it has large brake discs, lower arm, tie-rod and wheel knuckle to
provide good suspension characteristics. As a consequence, it increase fuel consumption
DOUBLE WISHBONE SUSPENSION SYSTEM
and reduce performances of the vehicle. Moreover, with higher value of unsprung mass
could lead the damage to roads surface and increase the vibration.
Although many researches have been done to enhance vehicle suspension
performance, there are some areas need to be improve using new technique. This research
applied new approach where multi-body analysis software (MSC ADAMS) was used to
predict the suspension behaviour. For instance cornering and braking load cases which
than help the design engineer to do an optimization of the suspension system component.
The data input program will develop for double wishbone suspension for 'virtual
development process' where reduces the development times, increase model diversity
and achieve optimization of the component that has been design. In this work, the author
only concentrates on quasi-static analysis of 3D model where a series of static
equilibrium solutions depend on time steps requirement. Two different load cases
(braking and cornering) have been identified to predict the dynamic load acting on
suspension component.
Finite element analysis for critical component is then carrying out through MSC
PATRAN 1 NASTRAN. The model imported from design tools Solidworks, meshing
with 3D-solid tetrahedron elements where the loads in local co-ordinate system
determined by multi-body system. The suspension is then modelled and later analyses
were done o n braking and cornering load cases input forces respectively. Linear stress
analysis will be performed to investigate the maximum stress concentration of each
component. In addition, buckling analysis will also performed for the tie rod component
to predict whether that component tends to buckle or not.
DOUBLE WISHBONE SUSPENSION SYSTEM
1.3 Objective and Scope
The objective of this thesis is to analyse in terms of component load and stress
study, a quarter vehicle of front wheel drive for typical double wishbone suspension
system using multi-body simulation system (MBS) together with computer aided design
and analysis environment (CAD & CAE).
The scopes of research are as follows:
Determine the co-ordinate system (marker point) of typical double wishbone
suspension system using computer measuring machine (Faro Arm)
Modelling of the suspension system using data input program into multi-body
system analysis (MSC-ADAMS)
Carry out quasi-static analysis for typical load cases (braking and cornering) to
predict the load acting on each components
Modelling of critical component selected using design tool (Solidworks) prior
import into FEA.
Further analysis of critical component of suspension system using CAE tool
(MSC.PATRAN / NASTRAN) to predict the maximum stress and deformation of
the structure.
Figure 1.0 Austin Martin Vanquish double wishbone suspension system
1.4 Research Methodology
The suspension systems in a vehicle play a crucial role to provide ride and
handling characteristic. The reason of this research is to study and analyse an independent
suspension typically double wishbone suspension system of mid-sized vehicle by using
selected loads using virtual 3D model via multi-body system software (MSC. ADAMS).
The work began with effort to measure the major co-ordinate points for the real
suspension system prior model into multi-body simulation software. The equipment used
in this research is the Co-ordinate Measuring Machine (Faro Arm) which is available in
the Coventry University. This equipment is used to determine the co-ordinate system (as
primary data) for Austin Martin Vanquish double wishbone suspension system.
DOUBLE WISHBONE SUSPENSION SYSTEM
In the second stage, the data input program for using major develops suspension
coordinates points and ADAMS command language program. Quasi-static analysis is
to determine load acting on suspension components under braking and
cornering conditions using multi-body simulation method (MSC.ADAMS).
The use of quasi-static analysis is to simulate the diffusion of loads from tyre
contact patch through the suspension system and into the body mounts. This type of
analysis is used to represent typical service loads carry out by Proving Ground test. The
outputs from these analyses represent the peak loads produced at typical location setting
by user such as lower wishbone to body mounts, tie rod connection to wheel knuckle and
tyre to ground. A critical component was selected for each load cases based on results
from ADAMS simulation in the next stages.
Next, the critical component selection was selected based on ADAMS results
prior modelled into finite element software via MSC.PATRAN 1 NASTRAN Educational
version. Finally the results from multi-body system analysis were used as inputs in finite
element analysis in order to predict the structural stress and displacement of the
suspension component.
Stage 1 { - Measure co-ordinate of typical suspension using CMM (Faro Arm)
1 <=> Stage 2
Running Quasi-Static - To determine the maximum load
with typical Load cases acting on components.
Critical component selection-based on results in ADAMS
Stage 3 component in FEA
Stage 4 1 f
Run Simulation
Stress El Buckling El
Figure 1.1 Flow chart of Thesis
DOUBLE WISHBONE SUSPENSION SYSTEM
1.5 Thesis outline
This thesis consists of eight chapters. The introduction of this work is presented in
Chapter 1. This chapter described the problem statements, objectives and scope of the
study, research methodology as well as the overall outline of the thesis.
Chapter 2 consists of literature reviews on related subjects concerning this thesis.
In this chapter, history of suspension system, the classifications of vehicle suspension
systems are reviewed. Review on recently published articles related to multi-body system
simulation using MSC.ADAMS and stress analysis via finite element method is also
presented. The history of Finite Element Method, how does it works in NASTRAN are
presented. Lastly, the displacement method that applied in MSC.NASTRAN is presented.
The equipment used to collect all the required data were presented in Chapter 3.
Coordinate measuring machine technique is an appropriate method used to convert data
fiom a real model of suspension into a multi-body simulation system. In this chapter, the
analysis of a double wishbone suspension system model is presented. Finally, step by
step measuring procedures was explained.
Chapter 4 describes the basic definition of vector and explained the notations that
were being used throughout this work. The vector theory for double wishbone
suspension is developed to predict the force acting on each component at particular
points. This will be further developed using similar model via MSC.ADAMS so that
results could be compared.
Chapter 5 describes the component loading, degree of freedom and data input
program set up prior to running the simulation. Quasi-static analysis is performed to
determine the load acting on the components with cornering and braking load cases.
Finally, the critical components are selected based on results fiom the multi-body system
analysis.
DOUBLE WISHBONE SUSPENSION SYSTEM
Chapter 6 describes analysis regarding the Finite Element Method, particularly for
the critical component selected (tie rod and lower wishbone). The step-by-step
procedures include importing files of both structures, load and boundary conditions,
material used and meshing is presented. Linear Static analysis is performed for the
critical component selected based on a multi-body simulation (MSC.ADAMS) results.
Chapter 7 discusses the results of all testing involving a quarter vehicle of double
wishbone suspension systems in a multi body system analysis and a finite element
analysis. This chapter also highlights the suspension behaviour of vehicle during
cornering and braking. Lastly, the graphical results predictions were provided for the tie
rod and lower wishbone structures under two 'worst case' scenario a in multi body
simulation. Buckling analysis via classical and simulation method for the tie rod
structure in finite element is also presented.
Chapter 8 is the final chapter where conclusion and recommendations were made.
It summarizes the work done in the entire study and provides recommendations for future
work.
DOUBLE WISHBONE SUSPENSION SYSTEM
CHAPTER 2
LITERATURE STUDY
2.1 Introduction
The Multi Body System analysis using data input programs is often used to
determine the load acting on suspension components. The established loads were then
used as data input to finite element models of components or vehicle structure [2,4].
These simulations results can be used to match a series of tests that were performed by
many vehicle manufacturers via proving ground test to predict the durability of the
vehicle structures. A literature review was conducted to investigate the past research done
in many areas related to this work. In addition, histories and theory as well as the main
function of multi-body and finite element method were presented.
DOUBLE WISHBONE SUSPENSION SYSTEM
2.2 Brief history of suspension systems
In the 16 '~ century, researchers tried to solve the problem of 'feeling every bump
in the road' of coaches e.g. wagons and carries, by slinging the carriage body from
leather straps attached at four posts of a chassis that looked like an unturned table.
Because the carriage body was suspended from the chassis, the system came to be known
as a 'suspension', and this term still used today to describe the entire class of solution [5 ] .
Gottlieb Daimler in Germany and some European vehicle manufacturers have
tried to applied coil springs. However, most manufacturers stood fast with leaf spring
which was less costly, easy to produce and assemble to the vehicle. Obadiah Elliot of
London invented the venerable leaf spring, which some manufacturers still use in rear
suspensions today, in 1804 [24]. He simply piled one steel plate on top of another,
pinned them together and shackled each end to a carriage.
A Frenchman named J.M.M Truffault fit the first shock absorbers to a racing
bicycle in 1898. By 1934, General Motors introduced the coil spring suspension with
each tyre sprung independently (independent suspension). After that, most vehicles
started using hydraulic shock absorbers and balloon (low-pressure) tyres.
2.3 Function of suspension systems
Suspension is the term given to the system consists of spring, shock absorbers and
linkages that connect a vehicle chassis to its wheels. Suspension systems are designed to
contribute handling and braking of vehicle. Moreover, the suspension also kept vehicles
occupant comfortable and reasonably well isolated from noise, bumps and vibrations.
I Traditionally, automotive suspension designs have been a compromise between
the two conflicting criteria of road holding and passenger comfort. The suspension
system must support the weight of the vehicle to provide directional control during
or manoeuvres, and also provide effective isolation of passengers as well as
payload from road disturbances [8]. Most automobile engineers consider the dynamics of
moving vehicles from two perspectives:
Ride - the ability of vehicle to smooth out a bumpy road
Handling - the ability of vehicle to perform safely during acceleration, braking
and cornering
The design of a suspension needs to satisfy a number of requirements whose aims
partly conflict due to the different operating conditions such as loaded or unloaded,
acceleration or braking, straight running or cornering and uneven road surface [1,6]. The
forces and moments that operate in the wheel area must be directed into the body.
There are two main categories of suspension system;
i) Dependent suspension (i.e. Rigid axle, semi rigid axle, trailing arm)
ii) Independent suspension (i.e. Mcpherson, Double wishbone, Multilink)
For dependent suspension system, the motion of a wheel on one side of the
vehicle is dependent on the motion of wheel on the other side. When one wheel of the
vehicle strikes a pothole, the effect is transmitted directly to its partner (wheel) on the
other side. This has a detrimental effect on ride and handling of the vehicle [5]. With
independent suspension system, the motion of wheel is independent of the other wheel,
so that a disturbance at one wheel is not directly transferred to a wheel on the other side.
This leads to better ride and handling capabilities.
DOUBLE WISHBONE SUSPENSION SYSTEM
In this thesis, the author intended to study double wishbone suspension from
independent suspension category. A double wishbone in United Kingdom also popular in
United Stated, where it is often referred to as Short Long Arm (SLA) [7].
Figure 2.0 shows different types of double wishbone configurations.
Figure 2.0 Example of independent suspension system [23]
2.4 MSC.ADAMS as multi-body simulation software
In automotive industry, predicting of durability performance at the early stage of
design through simulation is very important [ l 11. The reason is that it strongly affects on
increasing reliability and reduction of weight, costs and product development time.
The development of multi-body systems analysis has given new opportunities to
design engineers in terms of simulation and analysis. Besides that, these techniques can
be applied to the simulation of vehicle kinematics and dynamics, offering the ability to
model road loading and vehicle manoeuvres with ever increasing accuracy [13]. These
techniques are being developed giving benefits to engineers and ultimately customers
through lower cost optimization of components .
DOUBLE WISHBONE SUSPENSION SYSTEM
Cheon-Soo Jang 1111 presents an interesting method for optimization a
lightweight suspension component. He performed a dynamic load analysis using
ADAMS to determine the loads prior applied to the FEM stress analysis of the cross
member. The method to achieve strain field with respect to each load case via quasi-static
analysis which ignoring the inertia effect of mass. Comparisons of the stress and
durability results were used for optimization.
Study by Murali M.R Krishna [lo] explored the effects of shape optimization
techniques for suspension, component. Direct linearization method of MSC.NASTRAN
software was performed for optimization of a lower control arm suspension. Static
analysis of the model was performed with 3D solid tetrahedron elements to predict the
stress distribution on component. Optimization was used to ensure there was a minimal
increase of weight in order to reduced stresses. Murali et.al. [9], performed optimisation
analysis for Upper Control arm in MSC.NASTRAN using five different load cases
provided fiom ADAMS simulation.
2.4.1 MSC. ADAMS history
The study carry out by Crolla in 1995 [2,4] identified the main types of computer
tools based that can be used for the vehicle dynamic simulation. He categorised the tools
as follows:
i) Purpose designed simulation codes
ii) Multibody simulation packages based on numerical and algebraic
methods
iii) Toolkits such as MATLAB
The ADAMS program is a typical example of the multibody analysis programs
and categorised as numeric where the user is concerned with assembling a physical
description of the problem rather than writing equation of motion. Blundell [12]
DOUBLE WISHBONE SUSPENSION SYSTEM
published papers that summarised the process involved by using ADAMS to simulate full
vehicle handling. He described an overview of the usage of multi-body system analysis
in vehicle dynamics and followed by suspension modelling and analysis methodologies.
He demonstrated in his papers the accuracy of simple efficient models based on design
parameters amenable to the sensitivity study.
Research initiated by Chase at University of Michigan traced back the origin of
ADAMS in 1967. Chase and Korybalski had completed the original version on DAMN
(Dynamic Analysis of Mechanical Networks) in 1969. Orlandea completed the first
ADAMS program in 1973 and also published two ASME papers (Orlandea et. al., 1976A,
1976B). This was an earlier development of two-dimensional code to a three
dimensional code without computer capability support called DRAM. In 1980,
Mechanical Dynamics Incorporated (MDI) was formed and took responsibility to develop
the ADAMS program at University of Michigan. Since 2002, MDI has been part of MSC
Software Corporation.
The study by Blundell [12] described the behaviour of systems consisting of
flexible or rigid parts connected by joints and used large displacement code of motion
and in particular the application of ADAMS in vehicle dynamics. Blundell et.al. [13]
identified the criteria which would be involved in the decision process in multibody
system analysis for instance modelling capability, Pre and Post-processing and analysis
modes that would be able to perform. In early 90's, ADAMSNiew was released which
allowed users to built, simulate and examine results in a single environment.
2.4.2 Types of simulations in MSC.ADAMS
Static System have DOF > 0 All system velocities and accelerations are set to zero Can fail if the static solution is a too long fiom initial
Kinematics System have DOF = 0 Measure the reaction forces in constraints. Driven by constraints (motions)
Dynamic System have DOF > 0 Driven by a set of external forces and excitations Algebraic equations and nonlinear differential can be cnlweA
Figure 2.1 Summary of simulation in MSC.ADAMS [22]
Figure 2.1 shows that multi-body system analysis such MSC.ADAMS has
capability to simulate a real model of suspension system or even full vehicle in three
basic conditions such as static, dynamic and kinematics analysis. These 'virtual product
development' tools can be used to investigate the suspension behaviour and continue
further with design and system optimisation.
DOUBLE WISHBONE SUSPENSION SYSTEM
2.4.3 Standard Joints
There are a few types of mechanical joints can be used to constraint the motion of
bodies. Most common joints used in multibody system analysis are shown in Figure 2.2
Revolute Spherical Cylindrical Translational
Planar Fixed Universal Rack & Pinion
Figure 2.2 Examples of constraints joint used in MSC.ADAMS [2]
Modelling the connections between the suspension links will depend on the type
of vehicle and suspension position in the vehicle. For instance, lower control arm and
wheel knuckle connection can be modelled using spherical joints to represent the ball-
joints. An example of the syntax used to define a joint and markers in ADAMS is shown
below.
PART10 I, GROUND
PART102, MASS=I , CM=0200, IP=l ,I, 1
MARKERIO200,QP = 25 1,2OO,lOO,ZP= 400,20,100
JOINTIOI, SPH, I = 0101, J = 0201,
DOUBLE WISHBONE SUSPENSION SYSTEM
The first statement of this program defines as ground part. Using the system of
units used throughout this text, the second statement defines as a part with 1 kg of mass
where centre marker located at the position of marker 0200. The IP argument represents
three sequential mass moments of inertia in kg.rnrn2 about the x-axis, y-axis and z-axis.
In this example, marker 0200 is defined as part 02 and located relative to the local part
reference frame of part 01 by the co-ordinates specified through the QP argument.
The method used in ADAMS program to use ZP parameter for each marker to
represent the local z-axis of the markers. For the universal joint the axes of the spindles
need to be defined perpendicular to one another. For other joints such as the revolute,
cylindrical and translational, the user have to define the orientation of the axis associated
with the mechanical characteristics, rotation and/or translation, of the joint through the
coordinates I and J marker.
2.4.4 Degrees of Freedom
The determination degrees of freedom (DOF) in mechanical system started from
any free floating rigid body in three-dimensional spaces that have six degrees of freedom.
. VERTICAL
Figure 2.3 Degrees of freedom associated with unconstrained rigid body
DOUBLE WISHBONE SUSPENSION SYSTEM
Figure 2.3 shows the vehicle produces degree of freedom associated with
translational motion in the longitudinal direction X, the lateral direction Y and the
vertical direction Z. The rotational motions will involve roll about the x-axis, pitch about
the y-axis and yaw about the z-axis. A tyre model will through the forces and moments
generate the only contact.
For any multibody systems model where represent the real model, it is important
that the user could determine and understand the total degrees of freedom in the system.
This can be achieved by using the Gruebler equation as follows:
Total DOF = 6 x (Number of parts -1) - (Number of constraints) (2.1)
The degrees of fi-eedom removed by typical constraint elements are surnrnarised
in Table 2.0 and also can be used to complete the calculation.
Table 2.0 DOF removed by constraint elements [2]
Constraint Element Translational Rotational Coupled Total Constraints Constraints Constraints Constraints
Cylindrical Joint 2 2 0 4 Fixed Joint 3 3 0 6 Planar Joint 1 2 0 3 Rack-and-pinion Joint 0 0 1 1 Revolute Joint 3 2 0 5 Spherical Joint 3 0 0 3 Translational Joint 2 3 0 5 Universal Joint 3 1 0 4
Atpoint Joint Primitive 3 0 0 3 Inline Joint Primitive 2 0 0 2 Inplane Joint Primitive 1 0 0 1 Orientation Joint Primitive 0 3 0 3 Parallel Joint Primitive 0 2 0 2 Perpendicular Joint Primitive 0 1 0 1
Motion (Translational) 1 0 0 1 Motion (Rotational) 0 1 0 1 Coupler 0 0 1 1
uild a model of your design using:
Joints . Motion generators
; + Contacts
i
~ e s t your design using:
4 Measures . Animations I
i 4 Simulations 4 Plots j 1 validate your model by:
:. j . Importing test data i' ;j + Superimposing test data
.J Review your model by adding : :I ! ;
I + Friction Forcing functions
1 . Flexible parts . Control systems !
I Iterate your design through variations using:: ; 1 . Parametrics ? /
i '$,j . Design variables
/
,{ Improve your design using: . . . .
4 DOES . Optimization I
!;&&.+*%I : ..--., .2; , Automate your design process using : (. : ...->? ;: ,. :,I> :.-. , :y
. . ..-:'s. ~ i L . .;..?.,. -.. SGL. 1 Custom menus
. . . Macros
"k, + Custom dialog boxes -- .
Figure 2.4 Virtual prototype process applied in MSC.ADAMS [22]
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2.4.5 Modelling method
There are two methods used to model the suspension system in MSC.AD
Graphic User Interface (GUI) and text programming.
I.nouse button to d i sp lq options.
solid shapes and consnucnon garnotzy
solid features.
M a ~ n Toolbox Model name
r Menus
contalner I \/iejva
tnad L Status bar
Figure 2.5 Graphic User Interface (GUI) method in ADAMSI View [22]
DOUBLE WISHBONE SUSPENSION SYSTEM
The intermediate user usually uses the programming method since the program
command language, the coordinates position and behaviour of the model need to be
understood fully.
Table 2.1 An example of data input program set up in Notepad for ADAMSI View
2.5 Finite Element Method
The finite element (FE) method was developed by engineers using physical
insight as opposed to abstract method used by mathematicians [15]. The FE method does
not produce a formula as a solution, nor does solve a class of problems. Moreover, the
solution is a presentation of the approximation values except for a very simple problem
that is congruent with formula that already available.
DOUBLE WISHBONE SUSPENSION SYSTEMBUSHING
! LOADCASE ; POTHOLE BRAKING
PART10 1 ,GROUND MARKENO 101 ,QP=2802,3 97,l 65,ZP=2500,470, 1 17 ! ground MARKENO102,QP=2500,470,117,ZP=2802,397,165 MARKER/O104,QP=2803,3 14,-24,ZP=2418,357,-24 MARKENO1 05,QP=2418,357,-24,ZP=2803,3 14,-24 MARKER/0108,QP=2924,307,79 MARKER101 09,QP=2798,800,-222 MARKENO112,QP=2700,500,250 MARKEN1 ,ZP=l ,O,O MARKER/2,ZP=O, 1 ,O MARKEN3,ZP=O,O, 1
Wiliam.J.Kroppe et.al. [14] presented the flexibility of the independent
suspension components such as lower control arm and wheel knuckle via finite element
analysis. He found that the overall forces and stresses have a minor effect in a rigid body
DOUBLE WISHBONE SUSPENSION SYSTEM
analysis of the suspension components. He also realised that the flexibility analysis was
very time consuming to run and CPU intensive.
2.5.1 Short history of Finite Element
In 1943, a mathematician, R. Courant, developed a Finite Element Analysis
(FEA). He utilised the Ritz method of numerical analysis and minimization of variational
calculus to obtain approximate solutions to vibration systems [23,28]. Courant [17]
described a piecewise of polynomial solution for the torsional problem. Shortly thereafter,
a paper published in 1956 by R.W Clough, H.C. Martin, M.J Turner and L.J Topp that
explored the 'stiffness and deflection of complex structures' which established a broader
definition of numerical analysis.
The 'finite element' terminology was first used in 1960 [18,19]. Only a few
general purpose FE software began to appear in the 1970s due to initial cost and limited
computer capabilities. In the mid 1980s, since the cost of computers rapidly declined and
also increasing their power capability, FEA has been developed to an incredible precision,
complete with colour graphic as well as Pre and Post processors. About 40,000 papers
and books regarding the FE method and its applications had been published by mid 1990s
[151.
2.5.2 What is Finite Element Method?
The FE method is a numerical approximation method [15,22] to investigate the
structures behaviour. Basically, the FE method started by cutting (discretization) a
structure into several pieces of elements which depends on problem that describes the
behaviour in each element in a simple way. After that, the elements are connected to
each other at 'nodes'. The assembly of elements and nodes is called a finite element
DOUBLE WISHBONE SUSPENSION SYSTEM
model [22]. This process produces a set of simultaneous algebraic equations. For the
stress analysis, these equations are equilibrium equations of the nodes where may require
computer implementation due to thousand of equations generated. 2D and 3D modelling
are two types of analysis generally used in industry [28].
2.5.3 How does FEM works in MSC.NASTRAN
FEA uses a complex system of points called nodes which make a grid called mesh.
This mesh is programmed to contain the material and structural properties which define
how the structure will react to certain loading. A structure model is discretised by
dividing the original domain into simply shaped elements which connected to one another
by nodes. Each node is capable of moving in six degrees of fi-eedom (DOF) as shown in
Figure 2.6
Three translations ( ux , u,, u, )
Three rotations ( Ox, e,, 8, )
{u) = displacement vector
= { ux uy uz e x ey 8 z 1 .
Figure 2.6 Capabilities of nodes moving in six DOF
The relationship between one element and its surrounding nodes can be described
by the following equation: