Heavy vehicle ride and endurance

Anders Forsén

Department of Vehicle Engineering Royal Institute of Technology

TRITA-FKT 99:33 ISSN 1103-470X ISRN KTH/FKT/D--99/33--SE

Submitted to the School of Mechanical and Materials Engineering, Royal Institute of Technology, in partial fulfilment of the requirements for the degree of Doctor of Philosophy.

Stockholm 1999

© Anders Forsén

Printed by KTH Högskoletryckeriet, Stockholm 1999

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Result differences between physical vehicle tests and computer simulations are some- times large enough to suggest contrary decisions, e.g. accepting or rejecting the tested design. Until the ability of simulations to produce reliable predictions is thoroughly demonstrated, costly and time-consuming experimental tests cannot be replaced by quicker and cheaper computer simulations. When developing models and methods for prediction, a necessary (but not sufficient) condition is the ability to reproduce already performed experiments. The present thesis addresses but a few of the associated problems: how to compare physical and numerical experiments, how to model heavy trucks and how to find optimal parameter values.

Experimental data from heavy truck measurements are used to establish parameter val- ues in simulation models. Two vehicle configurations and several test cases are investi- gated, with five experiments for each combination demonstrating repeatability. The ensuing comprehensive database enables detailed studies of experimental repeatability and provides an excellent basis for modelling and parameter identification studies.

Measured and simulated signals are compared in the time domain, a ‘time domain discrepancy index’, TDDI, is defined. Identity in the time domain (TDDI=0) makes evaluated (filtered, averaged, PSD) signals identical, but the inverse is not necessarily true. Additional performance indices are defined to describe comfort and endurance discrepancies.

Numerical procedures find parameter values minimising simulation-experiment discrep- ancy, model performance is evaluated by comparison with experimental variation. The mean experimental variation is suggested as a simulation performance target.

Model performance target and achieved results, time domain discrepancy index.

1D model (1/4 vehicle)

(3 signals)

2D model (half vehicle)

(10 signals)

3D model (29 signals)

Average experimental scatter 0.05 0.28 0.31

Suggested model performance target 0.05 0.30 0.30

Achieved model performance 0.28 0.57 0.58

Simulation model improvements and/or better parameter values are needed to reach the suggested target. Three areas can be highlighted for model upgrading; tyre models, leaf spring models and frame flexibility. Improved identification processes and upgraded software may produce better parameter values, and find them quicker.

.H\ZRUGV Heavy vehicles, ride comfort, endurance, simulation, modelling, parameter identification

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The present thesis is the result of the author’s ignorance and lack of knowledge.

In my former professional capacity, I could not provide answers to some important questions, namely: How should trucks be analysed to get accurate enough fatigue life predictions? What must be included in a simulation model and, more important, what can be excluded without compromising accuracy? How can such a model be validated?

It was quickly realised that the answers require more research and method development than any single individual can undertake, but it was also necessary to get started. A research project entitled “The truck as a dynamic system” was formulated, The Swedish National Council for Technical Research and Vehicle Engineering agreed to finance the project together with Scania, the company performing the experimental work.

Scania very generously granted me long-term leave to undertake the analytic and computing part of the project in academic surroundings. The amount of additional support given by Scania has often astonished me; Scania as a company has supported the project far beyond the original commitment. Many individuals within the company have provided helpful hints and generous encouragement, mentioning them all by name would (almost) mean reproducing Scania’s phone directory. I have also been given moral support and been incited to continue when my own belief in the project faltered.

Engineers employed by industry work with current problems, but in my first engineering post, Mr Kenneth Fagerström encouraged me to simultaneously keep an eye on the future and maintain contact with the academic world. While working for him I was allowed to complete most of the formal course-work required for a doctors degree, thus I was started on the route towards this thesis.

During my renaissance as a full-time student, my academic guide and guardian Professor Erik Wennerström mostly allowed me to make my own mistakes, while steering me in the right direction at critical points. I’m grateful on both counts, being allowed to learn by finding out and being guided past the bottomless pits.

Scania’s Mr Gunnar Strandell has been an enthusiastic supporter of this project from the first discussions to the very end. To him goes most of the credit for enabling the project in financial and practical terms. He has quickly removed any administrative difficulty, allowing me to concentrate on the technical and scientific aspects of the project. I’m immensely grateful.

During the project a bit has been learned about trucks, and a lot more about the vastness of the unknown. The incredible patience of my wife Britt made it possible for me to finish this work. To her and our daughters Kerstin, Ingrid and Eva (all born during the project!) I dedicate the thesis.

Stockholm, September 1999 Anders Forsén

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1.1 COMPARISON OF EXPERIMENTS... 1

1.2 MODELLING OF HEAVY VEHICLES... 2

1.3 PARAMETER VALUES... 4

1.4 PARAMETER SENSITIVITY... 5

1.5 SUMMARY OF APPENDED PAPERS... 5

 9(+,&/(  2.1 TEST VEHICLE... 7

2.2 SENSORS... 7

 (;3(5,0(176  3.1 OBSTACLES AND ROAD INPUT... 11

3.2 TEST PROGRAM... 11

3.3 EXPERIMENTAL DATA... 12

 6,08/$7,2102'(/6  4.1 ONE-DIMENSIONAL (QUARTER VEHICLE) MODEL... 13

4.2 TWO-DIMENSIONAL (HALF VEHICLE) MODEL... 14

4.3 THREE-DIMENSIONAL MODEL... 15

4.4 FRAME FLEXIBILITY MODELS... 16

4.5 TYRE MODELS... 17

4.6 EXCLUDED ELEMENTS AND PHENOMENA... 18

 (9$/8$7,210(7+2'6±3(5)250$1&(,1',&(6  5.1 VEHICLE PERFORMANCE EVALUATION... 19

5.2 SIMULATION MODEL PERFORMANCE EVALUATION... 21

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6.1 LINEAR (QUARTER VEHICLE) MODEL... 25

6.2 NON-LINEAR MODELS (TWO- AND THREE-DIMENSIONAL) ... 27

 5(68/76  7.1 EXPERIMENTAL REPEATABILITY... 31

7.2 IDENTIFICATION TARGETS... 33

7.3 IDENTIFICATION RESULT... 34

7.4 PARAMETER SENSITIVITY... 41

7.5 LONGITUDINAL WHEEL FORCES... 45

7.6 FRAME FLEXIBILITY... 47

 ',6&866,21  8.1 SIMULATION MODEL IMPROVEMENTS... 49

8.2 IDENTIFICATION PROCESS IMPROVEMENTS... 51

8.3 SOFTWARE IMPROVEMENTS... 52

8.4 ROAD PROFILE INPUT... 52

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This dissertation comprises an introduction and the following four papers:

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Forsén, A.; Thorvald, B., 0%6FRPELQHGZLWK)(0LQKHDY\YHKLFOHVLPXODWLRQ, Proceedings AVEC’96, International Symposium on Advanced Vehicle Control, Aachen University of Technology, 1996. Vol. 2, pp 887 - 902.

Thorvald performed the simulations, Forsén evaluated simulation results.

Forsén and Thorvald wrote the paper together.

Thorvald presented the paper at AVEC’96, International Symposium on Advanced Vehicle Control, Aachen University of Technology, 1996.

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Forsén, A., 5RDGLQGXFHG/RQJLWXGLQDO:KHHO)RUFHVLQ+HDY\9HKLFOHV, SAE paper 973260

Forsén planned and evaluated experiments. Experiments were conducted by Scania.

The remainder of the work was done by Forsén.

Forsén presented the paper at the 1997 SAE International Truck & Bus Meeting in Cleveland, Ohio, USA

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Forsén, A., 3DUDPHWHU6HQVLWLYLW\LQ+HDY\9HKLFOHV

Report 99:10, Vehicle Engineering, Royal Institute of Technology, Stockholm, 1999

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Forsén, A., 3DUDPHWHU,GHQWLILFDWLRQLQ6LPXODWLRQRI+HDY\9HKLFOHV, Accepted for publication in “Vehicle System Dynamics”

Forsén planned and evaluated experiments. Experiments were conducted by Scania.

The remainder of the work was done by Forsén.

Forsén presented the paper at the 16^th IAVSD Symposium, Dynamics of Vehicles on Road and Tracks, Pretoria, South Africa, 1999

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Nomenclature in appended papers is defined explicitly in the text of each paper.

Nomenclature in the main chapters is summarised below. Additional definitions are included in the text.

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Systems are x, y, z, right-hand orthogonal with z-axis in local ‘upwards’ direction.

Body-fixed co-ordinate axis changes their direction to follow body motion.

Simulations utilise ‘vehicle dynamics’ co-ordinates, x-axis in local forwards direction.

Sensor positions and measured signals are in ‘vehicle design’ co-ordinates, x-axis in rearwards direction. Results are compared in ‘vehicle design’ co-ordinates, positive directions are explicitly reported in appendix 1.

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Notation Description

[ scalar variable, italics [ vector, lowercase bold

; matrix, uppercase bold

[& derivative with respect to time, dot

[&& second derivative with respect to time, double-dot

∂(/∂P partial derivative of ( with respect to P

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Symbol Description

i sample number

j signal channel index, summation index

k summation index

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Symbol Description

* measured value from vehicle test

 inverse of a matrix

7 transpose of a matrix or vector

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Symbol Unit Description

α 1/s tyre stiffness to damping ratio, kt/ct

∆ s sampling interval

τ s integration variable, time

$ matrix with measured accelerations and distances, right front wheel DLM L:th sample in signal M, measurement D

DM mean of signal M, measurement D E vector with 1D-model parameters ELM L:th sample in signal M, measurement E

EM mean of signal M, measurement E F Ns/m shock absorber damping, 1D model FW Ns/m tyre damping, 1D model

G m distance from unsprung to sprung mass, 1D-model ', - ride discomfort index, payload discomfort index

( - sum of errors squared

H - vector with sample-by-sample discrepancies, 1D-model ) - object function, sum of scaled and squared discrepancies )' - fatigue damage, all load cycles

)'', - fatigue damage discrepancy index )'N - fatigue damage caused by load cycle N

Symbols (continued):

Symbol Unit Description

ILM L:th sample in signal M, simulation I J m/s² gravity, J = 9.81 m/s²

*M - time domain discrepancy index for signal M M - signal channel no.

N N/m suspension stiffness, 1D model NW N/m tyre stiffness, 1D model

0 kg sprung mass, 1D model P kg unsprung mass, 1D model

Q - fatigue exponent

1 - number of samples in signal

S N vector with vertical wheel forces, right front wheel p N wheel force (1D-model)

3'', - payload discomfort discrepancy index T - number of compared signal channels 5'', - ride discomfort discrepancy index

6 N, Nm fatigue strength

VN N, Nm amplitude, load cycle N (rain-flow count)

W s time

7'', - time domain discrepancy index

Y - vector with scaled sample-by-sample discrepancies Z m road profile height

[ - input vector, gradient calculations

[ m position along the road profile, 1D-model ] m unsprung mass vertical position, 1D-model

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Label Description A, B, C, D, E test run identity

a, b, c, d, e measured signals

F simulation run identity, 3D model f simulated signals

H simulation run identity, 2D model K simulation run identity, 1D model

DU30 test case identities, cf. table 1 (Two uppercase letters and two digits) MyH signal designations (44), cf. figure 2 and appendix 1

RLX 2D model parameters (43), cf. figure 5 and appendix 5 TIR_M 3D model parameters (241), cf. appendix 5

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Abbreviation Description

1D One-Dimensional

2D Two-Dimensional

3D Three-Dimensional

ABS Anti-lock Brake System

CPU time Central Processing Unit time (used to perform a specific task)

DOF Degrees of Freedom

FEM Finite Element Method

MBS Multi-Body Simulation (-method, -program)

RMS Root Mean Square

PSD Power Spectral Density

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Result differences between physical vehicle tests and computer simulations are sometimes large enough to suggest contrary decisions, e.g. accepting or rejecting the tested design. Until the ability of simulations to produce reliable predictions is thoroughly demonstrated, costly and time-consuming experimental tests cannot be replaced by quicker and cheaper computer simulations. When developing models and methods for prediction, a necessary (but not sufficient) condition is the ability to reproduce already performed experiments. The present thesis addresses but a few of the associated problems: how to compare physical and numerical experiments, how to model heavy trucks and how to find optimal parameter values. The benefits of computer simulations are demonstrated by a parametric study that would be prohibitively expensive to perform experimentally.

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Two experiments never produce exactly the same result. Frequently both the acceptable and the expected discrepancy magnitudes are unstated. Identical results are expected from two runs of the same experiment, using the same vehicle, the same test set-up, conducted in one day by one team of test engineers, but some scatter is accepted. When two nominally identical vehicles (built to the same specification) are submitted to identical tests, conducted by two different teams of engineers, each using its own test track and instrumentation, similar but different results are expected.

When simulations are compared to vehicle tests, the simulation should be seen as a numerical experiment and the second situation outlined above considered. The physical and numerical experiments are conducted with different ‘vehicles’, on different ‘test tracks’ and usually performed by separate teams of engineers.

The numerical experiment vehicle model is probably built with nominal dimensions and properties, but simplified to suit the available computer and simulation programs. The physical vehicle is from the production line, with production tolerances on all components. How much their differences affect the test results is usually unknown.

Road input on the test track and in the computer differ in a similar manner, but a very simple obstacle can be measured and have its geometry well reproduced in the computer model. However, the difficulties caused by road/tyre friction modelling and by road deformation under dynamic load remains.

In simulations, each test run can start at exactly the intended velocity, but on a test track there is always a bit of variation.

Instrumentation and signal processing may cause spurious differences when results are compared. Sensor location and direction are always slightly uncertain in a physical vehicle, there is a tolerance on sensor installation. Signal processing from physical tests usually includes anti-aliasing (low-pass) filtering of analogue signals before digitising, while simulation program output is generated directly in digital form.

The truth remains an enigma; practical tests are plagued by tolerances and their influence, simulations by modelling and simulation program shortcomings.

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The simulation model is a simplification of the physical vehicle. The simplifications limits the model’s ability to reproduce vehicle motion, but the only perfect model, i.e. a model that in every respect behaves exactly as the actual vehicle, is the vehicle itself.

The smallest (lowest number of parameters) model able to adequately reproduce the studied phenomena is often seen as optimal. A simple model makes it easier to identify the most important vehicle properties. In such a model, each parameter represents the sum of many components and their various features.

The present models are ‘physical’ in the sense that every model entity (mass, inertia, spring, damper etc.) is meant to represent one or several physical objects. This makes it possible to perform parametric studies and enables prediction of changes in vehicle behaviour caused by component changes.

With the exception of aerodynamic forces, all forces influencing vehicle motion are caused by or reacted through vehicle-road interaction. Tyre modelling and the simulation model’s ability to reproduce measured wheel forces are essential. When vehicle deformation is studied, heavy trucks differ from passenger cars. Frame flexibility has to be considered, while the corresponding body deformation of passenger cars often can be ignored, at least when low-frequency phenomena are studied.

1.2.1 Tyre models

Tires are important components, difficult to describe properly in a simulation model, where both accurate results and quick computations are required. Structurally, the tyre is a shell stiffened by internal overpressure. Forces are transmitted from the road contact

via tyre belt and sidewalls to the wheel rim. Most of the tyre mass and almost all axis- of-rotation inertia is located in the belt, which suggest splitting the tyre model into two, one describing sidewall elasticity and deformation, the other describing belt mass and inertia. In multibody simulation programs it is convenient to model sidewall elasticity with a bushing element, and the belt as a (possibly rigid) body [1]¹. Such a model may accurately describe tyre eigenfrequencies and vibration modes, leaving road contact the remaining problem. Available (published and implemented) tyre models are utilised in the present work, no tyre modelling research or development beyond adaptation of parameter values is included.

1.2.2 Wheel forces

The forces at the interface between vehicle and road determine vehicle movements, while also influencing the amount of road damage caused by passing vehicles.

Accordingly, road-vehicle interface forces are studied by road authorities [2] and vehicle manufacturers. Wheel force measurements from instrumented roads are reported [3], but instrumented vehicle results are more frequent [4].

Studies of heavy-duty truck ride comfort, vehicle endurance and chassis fatigue are traditionally focused on vertical forces. In passenger car chassis design, suspension compliance in all directions is optimised to achieve the very high standard of handling and comfort experienced in recent models [5]. Road-induced longitudinal and lateral forces in heavy-duty trucks are less well researched.

Forces at the road-vehicle interface are caused by the interaction of road and vehicle.

The road surface profile and its load-deformation properties are part of the operating environment, outside the control of the vehicle manufacturer, while the vehicle itself, i.e. everything ‘above’ the road-tyre interface, is designed or influenced by the vehicle manufacturer.

Calculating road-vehicle interface forces requires comprehensive knowledge of both road and vehicle mechanical properties. However, road properties are usually unknown to the vehicle designer, who circumvents the problem by assuming that the road is completely rigid, or at least much stiffer than the tires, which means that it can be treated as completely rigid in a simulation model. Heavy trucks on slender bridges are

1 Numbers in brackets refer to chapter 11

an obvious exception, where elastic bridge properties should be considered when calculating forces at the vehicle-bridge interface [6].

With a known road profile and the assumption of a rigid road surface, vehicle properties provide all the input needed for a simulation/calculation of the forces at the road-vehicle interface. Measured wheel forces are used to validate simulation models, showing that enhanced knowledge of vehicle and tyre mechanical properties is essential.

1.2.3 Frame flexibility

Heavy vehicle motion is influenced by frame flexibility. Early attempts to include frame flexibility in simulation models consisted of modelling the frame with a few rigid parts connected to each other with torsion springs [7], or simplifying the frame by a structure that easily described analytically e. g. a beam. In finite element programs, ride analysis of vehicle models with detailed frame modelling is performed with frequency domain simulations [8]. With multibody simulation programs, time domain simulations with detailed frame modelling are possible through coupling to finite element models.

Four different models of a semi-trailer tractor frame illustrate the influence of flexibility representation. A detailed finite element model with shell elements, a condensed version of this, a beam element model and a completely rigid model. The first is used as a benchmark, results and computational effort being compared.

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Vehicle simulation requires a relevant model and pertinent parameter values. Parameter values can be estimated from (summation of) known component properties, or by identification based on vehicle test data. Some properties are difficult to measure or calculate; a combination of the two methods is employed in the present work.

Repeatable experiments are a prerequisite of model validation and parameter identification. Without them, parameter identification degenerates into curve fitting, adaptation to a specific test run.

Parameter identification maximises model performance in reproducing experimental results by finding the ‘best’ parameter values. Identification procedures require a scalar- valued performance index. Several index definitions are possible, one describing time- domain signal discrepancies is utilised for parameter identification. Experimental repeatability is quantified with the same index. When the difference between the

identified model’s output and a specific experimental run’s result is less than the scatter between nominally identical experiments, then further improvements of the simulation model’s predictive power cannot be verified experimentally; simulation results in the experimental scatter-band are satisfactory.

The volume of calculations necessitates automated procedures. Ready-made software to handle all aspects is not found; instead customised procedures are developed.

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Vehicle design may be described as an art of compromise. Compromises between many contradictory demands, e. g. sturdy structure - low weight, high quality - low cost etc., which also includes a trade-off between different properties of the final vehicle, is it more important to increase ride comfort than structural fatigue life or vice versa?

Systematic studies require numerical performance measures, not only to find whether performance is increased or decreased, but also by how much.

Tentative design changes can be tried out on physical vehicles or in computer simulations. Time and cost considerations strongly favour computer ‘tests’, being quicker and easier to repeat, but a carefully validated simulation model is required for reliable results. Once the baseline model is tuned to reproduce the corresponding experiment well enough, it can easily be modified in order to study design variations.

Predicted performance changes indicate which design change to include in WKH verifying experiment.

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Paper A [9]: MBS combined with FEM in heavy vehicle simulation

Heavy vehicle ride is influenced by frame flexibility. The influence of flexibility representation is illustrated by comparing four different simulation models of a semi- trailer tractor frame: Two shell models, a beam model and a rigid model. A model condensation method resulting in high simulation speed is suggested. The special care needed in mass matrix condensation is highlighted and a new interface for importing FEM flexibility data to a MBS program is reported. The vehicle’s movements when travelling over two different road profiles are calculated with a multi-body simulation program. Simulation time, frame deformation, fatigue damage and cab accelerations are compared. With the most detailed shell model used as a benchmark, the condensed shell model ranks as the best of the four models investigated in this study.

Paper B [10]: Road-Induced Longitudinal Wheel Forces in Heavy Vehicles Road unevenness induces longitudinal as well as vertical forces in the suspension. The variation of vertical and longitudinal wheel forces can be of the same magnitude. Much work on vertical loads has been accomplished in heavy vehicle development, but less on longitudinal forces. Wheel forces have been measured on a semi-trailer tractor driven over a test track obstacle. The consistency of test results inspires confidence in the measured loads. Measured forces are compared with results from a simple simulation model. The influence of road-induced longitudinal forces on ride and chassis loads is demonstrated through simulations. The importance of longitudinal suspension compliance is discussed.

Paper C [11]: Parameter Sensitivity in Heavy Vehicles

Tentative design changes can be tried out on physical vehicles or in computer simulations. Time and cost considerations strongly favour computer studies, with predicted performance changes indicating which design to include in one verifying experiment. Three kinds of vehicle performance are considered: structural endurance, ride comfort and payload comfort. Passage over a very rough road is simulated with a multi-body model. Parameter sensitivity is observed with respect to the selected performance indices, with parameters governed by truck use having a larger influence than parameters governed by design. Unexpected results are investigated in detail and possible explanations suggested. The need for concise presentation of results, attainable precision, parametric study of actual design problems and the application of advantageous results are briefly discussed.

Paper D [12]: Parameter Identification in Simulation of Heavy Vehicles

Experimental data from heavy truck measurements establish parameter values in a multi-body model. Two vehicle configurations and several test cases are investigated, five reruns demonstrate repeatability. Measured and simulated signals are compared in the time domain. These comparisons are sensitive to phase shifts, the influence of corresponding test velocity variations is minimised using single obstacle experiments as parameter identification input. Numerical procedures find parameter values minimising simulation-experiment discrepancy, model performance is evaluated by comparison with experimental variation.

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Heavy trucks are built in numerous varieties, but the most frequent configuration is the four-wheeled semi-trailer tractor, designed with five large assemblies: Frame, Front axle, Rear axle, Cab, and Driveline (engine/gearbox assembly). These almost rigid units are connected by flexible elements.

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Figure 1 Test vehicle, Scania R144L

The test vehicle is equipped with parabolic leaf springs at the front axle and trailing arm air suspension at the rear, rated loads are 7500 kg and 13000 kg. Ballast attached to a load frame facilitates experiments with different axle loads.

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Load sensing wheels [13] on the front axle register force and torque between rim and hub in wheel-fixed co-ordinates. Three forces and one torque are recorded, though the wheels can measure six components. Rotation angle measured by transducers in the wheel centres enable transformation of forces and torque to vehicle-fixed directions.

Four displacement transducers measure vertical axle displacements, an additional

transducer records longitudinal displacement of the engine and gearbox assembly. The right front wheel ABS sensor and 16 accelerometers complement the equipment.

Figure 2 Sensor location

Sensors are fixed to the vehicle; signals are recorded in vehicle-fixed directions. Frame and cab directions differ due to cab suspension movement and similarly front axle and frame directions differ. The vertical rod seen in figure 1 gives front wheel rotation datum. One of its ends is connected to the wheel centre and the other to a frame-fixed

bracket, located to minimise suspension movement influence, but wheel forces are recorded in yet another set of directions. It should be noted that all components are (more or less) flexible, so varying deformations may affect sensor orientation.

Positive directions are defined to coincide with the vehicle design co-ordinate system.

As measured, all signals are stored as voltages, and then calibration factors are applied to transform signals to engineering units.

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Three different inputs are used; a rectangular bar (200x50 mm) bolted to a flat and smooth part of the test track and two very rough road sections. The rectangular obstacle excites one side or both sides of the vehicle, i.e. located in the right-hand wheelpath or across the whole road width.

200 mm

50 mm

Figure 3 Obstacle

Left and right tracks of rough road sections are different. They have profiles corresponding to ISO road class D [14] for wavelengths in the interval 0.1 - 10 m. The disturbance level falls below ISO class D at longer wavelengths. 0.1 - 10 m wavelength corresponds to a disturbance frequency of 1.1 - 111 Hz when travelling at 40 km/h.

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Five measurements are made with each combination of vehicle load, road input and test velocity, the test matrix is shown in table 1. Test case identities are introduced to keep track of the program. First letter identifies an obstacle or road section, second letter the vehicle state, “U” for unladen and “M” for laden vehicle. The two following figures indicate the nominal test velocity.

Table 1 Nominal test velocities (km/h).

Road input Test case ID Vehicle

Unladen front 5441 kg rear 2306 kg

Laden front 7770 kg rear 13041 kg

Obstacle, both sides DUxx, DMxx 30 60 30 60

Obstacle, right ONLY EUxx, EMxx 30 60 30 60

Rough road I RU15, RM15 15 15

Rough road II SUxx, SMxx 20 30 40 20 30 40

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Experimental data stored as ASCII files on CD-ROM ensures long-time readability and software independence. The total amount of data is approximately 620 MB, with one file for each individual channel and test, i.e. 44*16*5 = 3520 files. (The 32 measured signals result in 44 stored channels, because wheel forces are stored both in wheel-fixed and vehicle-fixed directions.) To facilitate bookkeeping, files are designated by test case, followed by a letter (A – E) indicating measurement, and the channel number.

Thus “DM30A60” has right front wheel longitudinal force data (channel 60) from the first measurement (A) run at 30 km/h with laden vehicle (M) travelling over the simple obstacle placed across both left and right wheel-path (D).

Of 32 measured signals, 29 are used to compare different experiments, wheel rotation angle signals and ABS sensor output being excluded.

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Several simulation models are utilised. Three are intended for parameter identification and comparison with experimental data, four other for comparing methods to include frame flexibility in truck simulations.

The parameter identification models are: A one-dimensional quarter-car model with two rigid bodies and 2 DOF (degrees of freedom), a two-dimensional ‘half vehicle’ model with five rigid bodies and 15 DOF, and a three-dimensional model with 23 rigid bodies and 74 DOF.

The frame flexibility models consist of eight rigid bodies and a rigid or flexible frame, with 54 rigid body DOF and additional DOF describing frame flexibility.

The quarter car model is described by a few equations, simulations are performed with MATLAB [15]. The other models are described as multi-body systems (MBS) [16, 17], using the MBS program DADS [18], which represents the vehicle as a system of rigid and flexible bodies connected by joints and linear and non-linear force elements. The input consists of simulation task definition and vehicle, road profile and initial condition description; output is any desired force, acceleration, velocity or displacement signal as a function of time. Simulation models are equipped with ‘sensors’ equivalent to the experimental set-up, e.g. recording acceleration at the same point and in the same (vehicle-fixed) direction as the corresponding sensor.

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FW NW

N F

S

S

0

P

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]

Z

F [Ns/m] suspension damping (‘shock absorber’) FW [Ns/m] tire damping

G [m] displacement of sprung mass relative to unsprung mass

N [N/m] ‘suspension’ stiffness NW [N/m] ‘tire’ stiffness

P [kg] unsprung mass

0 [kg] sprung mass

S [N] vertical wheel force

Z [m] road input

] [m] unsprung mass displacement Figure 4 One-dimensional (quarter vehicle) model

The quarter vehicle model is one-dimensional, only vertical movement is modelled.

This model is maybe the simplest possible, the main advantage being the simplicity and the possibility of an analytical description.

S, G and ] are unknown functions of time, Z a known function of time. 0, P, F, FW, N and NW parameters and J a known constant. The model is also described by:

0 ) ( ) ( )) ( ) (

(] W +G W +FG W +NG W =

0 && && & (1)

0 ) (

) ( ) ( ) ( )

(W −FG W −NG W − S W + P+0 J= ]

P&& & (2)

) ( ) ( ) ( ) ( )

( )

(W P 0 J FW] W NW] W FWZW NWZ W

S − + + & + = & + (3)

The third equation and S are introduced to facilitate comparison to measured wheel- forces.

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The vehicle is almost symmetrical, the double-sided obstacle is perfectly symmetrical and the vehicle is driven straight at it, contacting with both front wheels simultaneously.

When simulating tests with the double-sided obstacle, a two-dimensional model may well be sufficient. Compared to a full three-dimensional model it offers considerably shorter simulation run-time and is simpler and quicker to design and update.

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The present 2D model includes five rigid bodies, joints, connections, springs and dampers, fully parameterised. The five bodies are sprung mass, front axle, rear axle,

front tyre and rear tyre. Shock absorbers are modelled with measured non-linear characteristics, rear axle air suspension by an analytical expression describing adiabatic air compression, while the ‘vertical’ front spring is modelled with a linear spring. The

‘horizontal’ links joining axles and sprung mass are modelled as linear springs and dampers. The 43 parameters used to describe the 2D model and its initial conditions are listed in appendix 5.

Apart from the tyre model and the limitations imposed by a two-dimensional model of a three-dimensional reality, one major limitation is obvious: The sprung mass is modelled as one rigid body. In the actual vehicle, the sprung mass consists of a flexible frame and three almost rigid bodies (cab, engine/gearbox and ballast), connected to the frame with compliant elements.

 7KUHHGLPHQVLRQDOPRGHO

The three-dimensional model contains 23 bodies, connected by joints, springs and dampers. Each body adds 6 DOF (degrees of freedom), but constraints and joints reduce the final model to 74 DOF. 6 DOF per wheel reduces to one (wheel rotation), the rest follows the motion of the axle, and similar reductions apply to other bodies.

Figure 6 3D Simulation model

The geometry of the model is the nominal design of the vehicle, while mass, inertia, stiffness and damping properties are described by parameters. Additional parameters describe tires, initial conditions and the ‘driver’, a simple control system to run the vehicle straight ahead (‘driver model’ [19]) and maintain approximately constant velocity (‘cruise control’). Three-dimensional dynamics includes three-dimensional

geometric non-linearities and secondary force excitation. Severe bumps and potholes in road input test the abilities of vehicle and driver models, considerable tuning of parameters is required.

Shock absorbers are modelled with measured non-linear characteristics, rear axle and cab suspension air springs by an analytical expression describing adiabatic air compression. Front suspension is modelled with a three-link spring model [20], rubber elements as non-linear springs, while the remaining flexibilities are modelled with linear springs and dampers. The 241 parameters used to describe the three-dimensional model and its initial conditions are listed in appendix 5.

It is believed that the most significant aspects of the vehicle are adequately included in the present three-dimensional model. However, the frame and all other bodies are modelled as perfectly rigid, thus limiting simulation model performance, especially at high frequencies.

 )UDPHIOH[LELOLW\PRGHOV

Figure 7 Beam element model, 104 nodes, 88 beam elements.

A simplified three-dimensional model of a four-wheeled semi-trailer tractor is used to illustrate the influence of different frame flexibility representations. This model is not a complete representation of a physical vehicle, batteries, cooling pack, fuel tank and many other components are missing. The frame flexibility model is equipped with air suspension at front and rear axles, avoiding the difficulties associated with leaf spring modelling.

The departure from the three-dimensional identification model facilitates quicker simulation runs, but results cannot be compared to measurements. Two finite element models of the frame are analysed with a commercially available program, ANSYS [21].

Figure 8 Shell element model, 958 nodes, 822 shell elements.

Four frame flexibility models are compared: two representations of the shell model, the beam model (figure 7) and a completely rigid frame.

 7\UHPRGHOV

A real tyre is a very complex structure, with distributed stiffness and diffused road contact. However, the internal workings of the tyre itself are not a part of the present study, tires are treated as ‘black box’ components, required to reproduce physical tyre input-output characteristics adequately, while being as simple and fast as possible.

In the one-dimensional quarter vehicle model, the tyre is represented by a linear spring and damper, as shown in figure 4.

The two-dimensional model utilises a rigid ring model [22, 23], shown in figure 9. The tyre belt is modelled as a rigid body with single-point road contact, the slip model being DADS [18] ‘point-point contact’ friction.

The three-dimensional parameter identification model utilises a three-dimensional rigid ring model [1]. Sidewall elasticity is modelled with a bushing element, and the tyre belt as a rigid body. Sidewall stiffness and belt mass parameters are based on measured data [24]. Road contact is modelled with DADS tyre model, contact parameter values established by the validation procedure.

Figure 9 Rigid ring tyre model [23]

Frame flexibility models use a DADS tyre model. Tyre belt inertia, important in dynamic longitudinal force description, is excluded to increase simulation speed.

 ([FOXGHGHOHPHQWVDQGSKHQRPHQD

The simplest possible models adequately describing the studied phenomena are sought.

Many features in actual vehicles are excluded or lumped together. Steering system linkages, frame flexibility and aerodynamic forces are not included in present parameter identification models. Steering system linkages are excluded to keep down model size and complexity, but some compensation is offered in the three-dimensional model by different left and right-hand suspension properties. Frame flexibility is excluded to improve simulation speed. At highway velocities, aerodynamic drag forces acting on the cab cause redistribution of cab suspension forces, and by compensating action of the cab-levelling device, a change in cab suspension air pressure and stiffness. These effects are beginning to show up at higher test velocities, but are excluded to reduce modelling effort and complexity.

 (YDOXDWLRQPHWKRGV±3HUIRUPDQFHLQGLFHV

Vehicle performance and simulation model performance are evaluated. Concise presentation requires a number (performance index) to summarise the result. Some interesting information is lost when a complex phenomenon (ride comfort, payload comfort, fatigue etc) is described by just one number. However, very detailed information, presented as a multitude of numbers and diagrams, is probably not well understood by anyone. The results are then unlikely to be applied.

 9HKLFOHSHUIRUPDQFHHYDOXDWLRQ

Three kinds of vehicle performance are considered, structural endurance, ride comfort and payload comfort. Endurance improves when the vehicle’s structure is better insulated from road-induced disturbances, in essence different kinds of comfort, the vehicle’s, the driver’s and the payload’s are studied.

5.1.1 Endurance

Cyclic loading eventually causes the structure to crack and break down if the load amplitude is large enough. In a truck, cyclic loads are present at almost every location, but the load amplitude, relative to local fatigue strength, varies enormously. The front wheel is selected to show how endurance can be influenced by parameter variations.

This component is chosen for several reasons:

a) It is fatigue critical.

b) The forces are measured at this location in the experimental study.

c) It is fairly close to the road surface. (Road properties are not influenced by vehicle design.)

d) Wheel forces affect the whole vehicle, smaller wheel forces means smaller forces in the vehicle, resulting in less fatigue damage and improved endurance.

The time history of wheel forces is evaluated with the rain-flow count method [25].

Fatigue damage caused by the resulting load cycles is calculated with the linear damage hypothesis [26, 27].

Fatigue damage is calculated by:

Q

N 6N

)' V 



 



= (5)

where: VN amplitude of load cycle N 6 fatigue strength

Q fatigue exponent

)'N fatigue damage caused by load cycle N Failure occurs when:

=1

=

∑

N )'N

)' (6)

To calculate actual fatigue damage, the component strength and fatigue exponent must be known, but relative changes can be calculated with an assumed exponent, a typical value for vehicle components, Q = 6, is used. Eight signals are evaluated, four for each front wheel, longitudinal, lateral and vertical force and axis of rotation torque. The fatigue damage caused by each signal is evaluated independently of the other load signals. Rain-flow count and fatigue damage calculations are performed with a MATLAB toolbox [28].

5.1.2 Ride comfort

Ride comfort is evaluated with cab acceleration signals, filtered and weighted according to ISO2631(1997) [29]. This revision of ISO2631 is a significant improvement when compared to the previous issue (1985)[30]. The 1997 issue has been applied everywhere except in the frame flexibility study, which was originally published in 1996 [9].

In a truck, at least four spring-damper systems are connected in series to insulate the driver from road-induced vibrations. They are the tires, the axle suspension, the cab suspension and the seat suspension, often split into two subsystems, a vertical spring and damper between seat and cab structure, and the cushions of the seat itself. An objective measure of driver discomfort is given by the accelerations at the interface between driver and seat. A procedure to reduce the time-histories of seat accelerations in different directions to a single ‘discomfort number’ is suggested in ISO2631.

Although it is possible to measure and to calculate the accelerations at the driver-seat interface, it is difficult. Accelerations obviously depend on the mechanical properties of the driver and the seat cushions. Experimentally there is a lack of repeatability – the

driver may tense muscles or change position, or even be replaced by another driver.

Simulation of accelerations at the seat-driver interface requires a sophisticated approach, the cushions have non-linear characteristics to seat different-sized drivers comfortably and the human body is rather non-linear, calling for complex modelling.

To circumvent these difficulties cab accelerations are used to characterise comfort. It is assumed that driver comfort is improved as cab accelerations get smaller. Seat suspension enhances actual driving comfort, making it better than that indicated by cab accelerations.

5.1.3 Payload comfort

When a specific transportation task or a specific payload is considered, the allowable payload accelerations, absolute level and frequency content can be specified. To be useful such a specification should include a procedure to reduce time-histories of accelerations in different directions to a single number, which can be compared to the allowable or acceptable acceleration level.

Allowable accelerations are sometimes specified for specific cargoes, but no general- purpose standards have been found. In order to demonstrate how a payload comfort number may be influenced by vehicle parameter changes, payload comfort is evaluated by applying the ISO2631 filtering and weighing procedures to acceleration signals recorded at the gearbox cross-member, located between the axles. Five signals are used, longitudinal and vertical acceleration on left and right side and transverse acceleration on the right side of the frame. Due to the stiff cross-member, the difference between left and right side transverse acceleration is assumed negligible. Three linear accelerations on each side are filtered and weighted according to ISO2631 to produce two acceleration numbers, the average is used as a measure of payload comfort.

 6LPXODWLRQPRGHOSHUIRUPDQFHHYDOXDWLRQ

Simulation performance, i.e. how well vehicle behaviour is reproduced, is evaluated by signal comparison in the time domain. Identity in the time domain makes evaluated (filtered, averaged) signals identical, but the inverse is not necessarily true. Additional comparisons are made with integrated measures; ride comfort, payload comfort and structural endurance indices.

Simulation performance evaluation methods are also used to evaluate experimental repeatability by comparing different experimental runs.

5.2.1 Synchronisation

The initial contact between vehicle and road obstacle occurs at different times in different experiments/simulations. The right front wheel longitudinal force is used to synchronise signals in time. It is measured close to the vehicle-independent excitation (the road) and has a distinct peak (at 0.04 s in figure 10) as the wheel hits the obstacle or the initial bump.

0 0.2 0.4 0.6 0.8 1

−10 0 10

t [s]

Fx [kN]

5 signals

Figure 10 Synchronised signals, five different single obstacle test runs.

The excellent repeatability of single-obstacle experiments is due to the very short obstacle, making the load induced almost a pulse load, followed by damped oscillation of the vehicle. The phase difference after the rear axle pulse (at 0.45 s in figure 10) is due to the small velocity variation between different tests. Phase-shift due to velocity differences increases towards the end of the run, making it difficult to obtain meaningful time domain repeatability in longer, multi-obstacle experiments (figure 11).

0 0.4 0.8

−20

−10 0 10 20

t [s]

Fx [kN]

62.6 63 63.4

t [s]

2 signals

Figure 11 Phase-shift at start and end of two ‘Rough Road’ runs.

5.2.2 Time domain discrepancy index

After synchronisation the discrepancy index for signal channel j, *M, is calculated:

( )

( ) _∑ ( ) ^{∑ ∑}

∑

∑



 



 − + −

−

=

L L M L L M M

M

L L M M

L L M M

L L M L M

1 E E 1 D

D E

E D

D

E D M

* , ,

2 , 2

,

2 ,

, 1

1 ;

; 2

) 1

( (7)

Summation is over all samples, it is assumed that both signals, ‘a’ and ‘b’, have the same sampling interval and length, 1. The above formula is applicable when both signals have equal status, e.g. two experimental runs. When an experimental signal, ‘a’, is compared with a simulated signal, ‘f’, the expression is modified:

( )

( ) ^∑

∑

∑

−

−

=

L L M

M

L L M M

L L M L M

1 D D D

D I D M

* 2 ,

,

2 ,

, 1

; )

( (8)

In both cases the denominator is a scaling factor, making it possible to compare discrepancies from different signal channels, where signal magnitude may differ.

0 0.2 0.4 0.6 0.8 1

−10 0 10

t [s]

Fx [kN]

signal ’a’: longitudinal force, right front wheel signal ’b’: signal ’a’ delayed 0.01 seconds signal ’c’: mean of signal ’a’

Discrepancy Index: ’a’−’b’: 0.61

’a’−’c’: 1.00, ’b’−’c’: 1.00

Figure 12 Discrepancy Index illustration, three signals.

When the compared signals are identical the discrepancy index is zero. Two 180-deg.

out-of-phase sine signals give the value 2. Phase-shift sensitivity is illustrated in figure 12, where 0.01 s delay gives discrepancy index 0.61.

The average of all compared signal channels’ discrepancy index gives RQH number comparing two experimental runs:

∑

=

M

M T *

7'', 1 ( )

(9)

5.2.3 Ride comfort discrepancy index

Ride comfort is evaluated with cab acceleration signals. Time-histories of accelerations in different directions are reduced to a single ‘discomfort index’, DI, by the ISO2631:1997 method.

Ride comfort discrepancy is numerically evaluated by comparison of discomfort indices (DI). In analogy with the time domain comparisons:

( )

(

)

2 1

) ( ) (

E ', D ',

E ', D ', 5'', DEV

+

= − or

) (

) ( ) (

D ',

I ', D

5'',= ', − (10)

5.2.4 Payload comfort discrepancy index

Payload comfort is evaluated by applying the ISO2631 filtering and weighing procedures to acceleration signals recorded at the gearbox cross-member. One acceleration number is calculated for each side of the frame, the average is used as payload discomfort index (DI). Discrepancies are evaluated by:

( )

(

)

2 1

) ( ) (

E ', D ',

E ', D ', 3'', DEV

+

= − or

) (

) ( ) (

D ',

I ', D

3'',= ', − (11)

5.2.5 Fatigue damage discrepancy index

Eight wheel force signals are evaluated, four for each front wheel, longitudinal, lateral and vertical force and axis of rotation torque. The fatigue damage caused by each signal (FD) is evaluated independently of the other load signals. Discrepancies are numerically evaluated by:

( )

(

)

2 1

) ( ) ) (

(

E )' D )'

E )' D )' M DEV

)''

+

= − or

) (

) ( ) ) (

( )' D

I )' D M )'

)'' = − (12)

The average fatigue damage discrepancy is used as a fatigue damage discrepancy index:

∑

=

M

M T )''

)'', 1 ( )

(13)

 3DUDPHWHULGHQWLILFDWLRQPHWKRGV

Identification seeks the model parameter values that minimise discrepancies between measured and simulated vehicle behaviour. Optimal parameter values for the quarter vehicle model are calculated algebraically, without any simulation being necessary, but the non-linear two- and three-dimensional models require a more laborious procedure.

The time domain discrepancy index is used as a scalar object function; numerical optimisation finds the object function’s minima by varying parameter values in a systematic manner. The corresponding parameter values provide the best possible agreement between measurement and the present simulation model.

 /LQHDUTXDUWHUYHKLFOHPRGHO

The model is described by three equations (cf. chapter 4.1):

0 ) ( ) ( )) ( ) (

(] W +G W +FG W +NG W =

0 && && & (1)

0 ) (

) ( ) ( ) ( )

(W −FG W −NG W − S W + P+0 J= ]

P&& & (2)

) ( )

( ) ( ) ( )

( )

(W P 0 J FW] W NW] W FWZ W NWZW

S − + + & + = & + (3)

Unknown vehicle parameters 0, P, F, and N are determined from measured data and (2).

(3) is used to investigate how tyre enveloping modifies the quarter vehicle model’s impression of the road profile.

6.1.1 Parameter identification Time discretisation is introduced by:

no.

sample );

(W L G

G_L = _L (14)

interval sample

; ∆

∆

=L

W_L (15)

The governing equations are valid for all times, but introducing discrete time changes the notation slightly:

0 )

(]_L +G_L +FG_L +NG_L =

0 && && & (1a)

0 )

(]_L +J +0J−FG −NG_L − S_L =

P && & (2a)

Approximate derivatives are defined as:

∆

= ⁺ − ⁻ 2

1

1 L

L L

G

G& G (16)

2 1

1 2

∆ +

= ^L+ − ^{L L−}

L

G G

G&& G (17)

Measured data are designated by:







L L

L L

L L

W S

W ]

W G

at time FzH

signal

at time AFAHZ

signal

at time DBAH

signal

*

*

*

&&

Replacing exact derivatives by approximations introduces numerical errors, the replacement of unknown variables by measured data introduces discrepancies between model and ‘reality’. The sum of numerical errors and discrepancies is designated ‘err’:

L L L

L L

L

L GL G G FG G NG HUU

]

0 1

2

2 ^*₁ ^*_{1 *}

2

* 1

*

* 1

* + =

∆ + −





∆ +

+ ⁺ − ^{− + −}

&& (1b)

( )

L G G NG S HUU

F 0J J ]

P 2

2

*

*

* 1

* 1

* − − =

∆

− − +

+ ^{+ −}

&& (2b)

The approximate second derivative in (1b) may introduce substantial numerical errors, especially when multiplied with a large parameter (0, sprung mass). (2b) promises smoother behaviour with several terms and an approximate first derivative multiplied by a less influential parameter. (F, ‘shock absorber’ damping). (2b) represents 205 equations over the one-second time interval used for parameter identification (the sampling interval being ∆=1/204.8 s). It provides enough information for identification, and (1b) is not used for this purpose.

(2b) reformulated with matrix formalism:





















=





















−





















































∆ −

− − +

∆ −

− − +

∆ −

− − +

− +

− +

−

1 L

1 L

1 1 1 1

L L L L

HUU HUU HUU

S S S

N F 0 P

G G J G

J ]

G G J G

J ]

G G J G

J ]

2 2 2

2 2 2

0

*

*

* 0

*

* 1

* 1

*

*

* 1

*

* 1

* 0

* 1

* 1

* 1

M M

M M

&&

M M

M M

&&

M M

M M

&&

(2c)

or $E±S= H (2d)

$ and S are known (measured data and known constants), E contains the parameters and H the errors. The sum of errors squared is minimised by:

( )

E= ^{7 − 7} (2e)

(A short derivation of this well-known matrix algebra result is found in appendix 3.)

6.1.2 Road profile reconstruction

Measured vehicle response is combined with measured tyre parameters [24] and (3) to produce a fictitious road profile. The solution of (3) with respect to ZW is:

( )

(

)

W W W

W

W W W

N H J 0 G P

H F S

G W ] W ] H ]

H Z W Z

α τ

α

α α

τ τ

τ τ τ

−

−

−

−

−

+ −

− +

+

− +

+

− +

=

∫

∫

) 1 ) (

1 (

) )(

( ) 0 ( 1

) 0 ( )

0 ( ) (

) (

0

0

&&

&

(3b)

where _{α =NW FW}. Introduce discrete time, W_L =L∆, and the designation w* for the fictitious road profile. Replacement of unknowns by linearly interpolated measured data and evaluation of the integrals yields:

( )

( )

∑

∑

−

=

∆

−

− + −

∆

−

∆

−

∆

−

=

∆

−

∆

−

−

∆ −

−

−

− +

−

− +

+

−

∆

∆ +

−

∆ +

−

∆ +

− +

=

1

0

) 1 (

*

* 2 1

* 0

*

0

* 2

2

* 0

* 2

* 0 0 0

* 0

*

) 1

(

) 1

( ) 1 (

) 6 (

) 2 (

) 1

(

L M

M L M M W

W

L L L

W

L

M M

L L L L

H S S N H

F

H J 0 P H

S N S

] M L ]

L ] ] L ] H

] H

Z Z

α α

α α

α

α & && && &&

(3c)

The last row of (3c) is neglectable for realistic tires, where α = NW/FW >>1.

The vehicle’s position at time WL = L∆ can be estimated from measured wheel rotation and tyre roll radius. Comparison of Z^*_L([_L)with the actual road profile shows the tyre enveloping effects.

 1RQOLQHDUPRGHOV7ZRDQGWKUHHGLPHQVLRQDO

The two- and three-dimensional models are not only non-linear, they also hide their algebra inside large computer codes. Some non-linear models can be treated in a fashion similar to the linear quarter vehicle model when their governing equations are explicitly known and measured signals describes the movement of all bodies in the model. Neither the two-dimensional model (15 DOF, 10 measured signals), nor the three-dimensional model (74 DOF, 29 measured signals) meet these requirements. Thus, it is necessary to use numerical methods.

A scalar object function that describes discrepancies between measurement and simu- lation is defined. The object function’s value, i.e. the discrepancy between measured and simulated signals, is minimised by systematic variation of parameter values.