Damian Harty

Tyre characteristics and modelling

This chapter discusses the importance of mechanical force and moment-generating characteristics of the tires for efficient handling performance and directional response of a vehicle. In road-vehicle dynamics, the manner in which a vehicle accelerates, brakes, and corners is controlled by the forces generated over four relatively small tire-contact patches. This chapter describes the force and moment characteristics and introduces various mathematical tire models available and describes the methods used to implement these with multibody systems (MBS) vehicle models. Before a computer simulation can be performed, the tire force and moment characteristics must be estimated or obtained from experimental tests. A traditional approach is to test the tires using a tire test machine and to measure the resulting force and moment components for various camber angles, slip angles, and values of vertical force. The measured data is set up in tabular form, which is interpolated during the computer simulation to transfer the forces to the full vehicle model. Alternatively, mathematical functions are used to fit equations to the measured test data. These equations provide a mathematical tire model that can be incorporated into the full vehicle model. This method requires the generation of a number of parameters that must be derived from the measured data before the simulation can proceed. The quality of the model will be a compromise among the accuracy of the fit, relevance of the parameters, and availability of methods to generate the parameters.

Chapter 6 – Modelling and Assembly of the Full Vehicle

This chapter describes the modelling and assembly of the rest of the vehicle, including the anti-roll bars and steering systems. Near the beginning a range of simplified suspension modelling strategies for the full vehicle is described. This forms the basis for subsequent discussion involving the representation of the road springs and steering system in simple models that do not include a model of the suspension linkages. The chapter includes a consideration of modelling driver inputs to the steering system using several control methodologies and concludes with a case study comparing the performance of several full vehicle modelling strategies for a vehicle handling manoeuvre.

Simulation Output and Interpretation

Vehicle handling simulations are intended to recreate the manoeuvres and tests that vehicle engineers carry out using prototype vehicles on the test track or proving ground. Some are defined by the International Standards Organization, which outlines recommended tests in order to substantiate the handling performance of a new vehicle: ISO 3888-1:1999 Passenger cars — Test track for a severe lane-change manoeuvre — Part 1: Double lane-change ISO 3888-2:2002 Passenger cars — Test track for a severe lane-change manoeuvre — Part 2: Obstacle avoidance ISO 4138:1996 Passenger cars — Steady-state circular driving behaviour — Open-loop test procedure ISO 7401:2003 Road vehicles — Lateral transient response test methods — Open-loop test methods ISO 7975:1996 Passenger cars — Braking in a turn — Open-loop test procedure ISO/TR 8725:1988 Road vehicles — Transient open-loop response test method with one period of sinusoidal input ISO/TR 8726:1988 Road vehicles — Transient open-loop response test method with pseudo-random steering input ISO 9815:2003 Road vehicles — Passenger-car and trailer combinations — Lateral stability test ISO 9816:1993 Passenger cars — Power-off reactions of a vehicle in a turn — Open-loop test method ISO 12021 -1:1996 Road vehicles — Sensitivity to lateral wind — Part 1 : Open-loop test method using wind generator input ISO 13674-1:2003 Road vehicles — Test method for the quantification of on-centre handling — Part 1 : Weave test ISO 14512:1999 Passenger cars — Straight-ahead braking on surfaces with split coefficient of friction — Open-loop test procedure ISO 15037-1:1998 Road vehicles — Vehicle dynamics test methods — Part 1: General conditions for passenger cars ISO 15037-2:2002 Road vehicles — Vehicle dynamics test methods — Part 2: General conditions for heavy vehicles and buses ISO 17288-1:2002 Passenger cars — Free-steer behaviour — Part 1: Steering-release open-loop test method ISO/TS 20119:2002 Road vehicles — Test method for the quantification of on-centre handling — Determination of dispersion metrics for straight-line driving

Chapter 7 – Simulation Output and Interpretation

This chapter deals with the simulation output and interpretation of results. An overview of vehicle dynamics for travel on a curved path is included. The classical treatment of understeer/oversteer based on steady state cornering is presented followed by an alternative treatment that considers yaw rate and lateral acceleration gains. The subjective/objective problem is discussed with consideration of steering feel and roll angle as subjective modifiers. The chapter concludes with a consideration of the use of analytical models with a signal-to-noise approach.

Chapter 5 – Tyre Characteristics and Modelling

This chapter addresses the tyre force and moment generating characteristics and the subsequent modelling of these in a multibody systems (MBS) simulation. As a major area of importance it deserves to be the largest chapter in this book. Examples are provided of tyre test data and the derived parameters for established tyre models. The chapter concludes with a case study using an MBS virtual tyre test machine to interrogate and compare tyre models and data sets. Since the first edition new tyre models such as the FTire model from Gipser and the TAME Tire model from Michelin have become established and therefore receive a more extended coverage in this edition.

Chapter 8 – Active Systems

Chapter 8 concludes with a review of the use of active systems to modify the dynamics in modern passenger cars. The use of electronic control in systems, such as active suspension and variable damping, brake-based systems, active steering systems, active camber systems and active torque distribution is described. A final summary matches the application of these systems with driving styles described as normal, spirited or the execution of emergency manoeuvres.

Chapter 4 – Modelling and Analysis of Suspension Systems

Chapter 4 addresses the modelling and analysis of the suspension system. An attempt has been made to bridge the gap between the textbook treatment of suspension systems and the multibody systems (MBS) approach to building and simulating suspension models. As such a number of case studies have been included to demonstrate the application of the models and their use in the vehicle design process. The chapter concludes with an extensive case study comparing a full set of analytical calculations, using the vector-based methods introduced in Chapter 2, with the output produced from MSC ADAMS. It is intended that this exercise will demonstrate to readers the underlying computations in process when running an MBS simulation.

Chapter 2 – Kinematics and Dynamics of Rigid Bodies

Chapter 2 is included for completeness and covers the underlying formulations in kinematics and dynamics required for a good understanding of multibody systems formulations. A three-dimensional vector approach is used to develop the theory, this being the most suitable method for developing the rigid body equations of motion and constraint formulations described later.

Kinematics and Dynamics of Rigid Bodies

This chapter focuses on kinematics and dynamics of rigid bodies. The application of a modern multibody systems computer program requires a good understanding of the underlying theory involved in the formulation and solution of the equations of motion. It is necessary to examine the use of vectors for static analysis in multibody systems (MBS) to understand development of the equations of motion associated with large displacement rigid body dynamic motion. In multibody dynamics, bodies may undergo motion which involves rotation about all three axes of a given reference frame. An understanding that large rotations are not a vector is an important aspect of multibody systems analysis. In multibody systems analysis, it is often necessary to transform the components of a vector measured parallel to the axis of one reference frame to those measured parallel to a second reference frame. These operations should not be confused with vector rotation. If a rigid body comprises rigidly attached combinations of regular shapes, the overall inertial properties of the body can be found using the parallel axis theorem. It is possible to formulate six equations of motion corresponding with the six degrees of freedom resulting from unconstrained motion. In addition to the derivation of the equations of motion based on the direct application of Newtons laws, variational methods, including, Lagranges equations, provide an elegant alternative and are often employed in MBS formulations.

Modelling and analysis of suspension systems

This chapter discusses the role of the suspension system in a vehicle from a functional, analytical perspective. In its simplest form, a modern road vehicle suspension may be thought of as a linkage to allow the wheel to move relative to the body and some elastic element to support loads while allowing that motion. As suspensions become more complex, the need for well-controlled damping forces and multi-directional compliance emerges. Multibody systems (MBS) analysis can help quantify an existing design in terms of these parameters or help to synthesize a new design from a set of target parameters. For modern vehicles, the isolation of road inputs is a high priority; there is always a desire to introduce some elastomeric elements into the vehicle between the suspension elements and the vehicle body. MBS analysis tools allow the study of handling degradation due to the introduction of such elastomers and allow the fide/refinement compromise to be quantified before excessive experimentation is carded out on the vehicle. Modern multi-link rear suspensions are a good example of such well-separated systems and are a significant part of the simultaneous improvement in both ride and handling, traditionally areas of mutual exclusivity that have befallen modern road cars. Multibody systems analysis can help quantify an existing design in terms of these parameters or help to synthesize a new design from a set of target parameters.