Illustration 1: Dymola user view with chassis model diagram and Modelica text. NHTSA fishhook maneuver result plot and visualization. Chassis Design a

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1 Modeling and Simulation of Road Vehicle Dynamics The VehicleDynamics Library (VDL) is a tool for modeling, simulation and analysis of the dynamics of vehicle motion. Handling behavior is the primary target, but the library is also well-suited for studies of other vehicle properties. Compared to other tools, VDL is easy to get started with and yet features versatile multidomain modeling, fast simulation, and flexible analysis of both full vehicles and relevant subsystems. Consequently, the tool grows with the user and lets system and component design as well as integration be made within the same environment. The VDL is a model library for Dymola* and is based on the Modelica* modeling language, with the implementation and model details fully open for the users. This gives an intuitive tool that is easy to get started with and yet gives advanced users total flexibility to define their own models and experiments. The flexibility also stretches over multiple engineering domains so that, for example, full multi-body mechanics, hydraulics, pneumatics and electrics can be integrated in one single vehicle model. As a consequence, the VDL is also well suited for design of unconventional configurations such as hybrid electric or concept vehicles. Dymola with VDL offers user-friendly graphical dragand-drop component-based modeling, with the option for advanced users to work also with Modelica source code editing, see Illustration 1. Modeling and simulation tasks are performed from an integrated environment with versatile features for post-processing, plotting and visualization of simulation results. Chassis, suspension, and steering Driveline and brake systems Active systems System integration and tuning Algorithm development and HIL A stream-lined work flow is supported by structured partitioning of models into re-usable components, and the generous collection of model templates. Model variants of different fidelity are compatible and interchangeable, so that, for example, a brake system model can be tested with different chassis models and vice-versa. This makes it easy to set up different model variants and brings the effort of model maintenance to a minimum. The open environment allows users to customize models and templates to comply with in-house standards. This includes both components and complete systems. Simulation analysis of complete vehicles, subsystems, or components is intuitively carried out from experiment templates that mimic real-life tests on proving ground surfaces, roads, or in test rigs. Scripting enables automation of routine tasks so that, for example, batch simulations for tuning and sensitivity analysis can be set up. The possibility for users to encrypt models is very useful in industrial contexts since models can be shared without revealing modeling know-how or parameter tuning. This has proven to be an efficient mean to enhance communication among cooperating OEM's and suppliers. *See separate info boxes below

2 Illustration 1: Dymola user view with chassis model diagram and Modelica text. NHTSA fishhook maneuver result plot and visualization. Chassis Design and Road Interaction Design and analysis of the chassis subsystem is the main focus of VDL. For conventional passenger cars, chassis models are composed of front and rear suspension assemblies, the body with payloads and aerodynamic properties, and wheels with tires, as seen in the diagram window in Illustration 1. The VDL contains chassis models that range in fidelity from planar to fully 3D multi-body representations with the same model interfaces. This allows users to easily adapt the fidelity of composite models to any desired analysis. Full chassis analysis can be done with drivers or robots that control the vehicle on open surfaces or roads. Driver models look ahead along the road to control the positioning of the car, as, for example, when negotiating a curve, an evasive lane change or a slalom defined by cones.

3 Robots are used with chassis and vehicles on flat ground and control the motion in either open-loop or closedloop based on vehicle states. A typical open-loop test is to apply a steering wheel input to trigger yaw and roll instability, or tip-in/tip-out maneuvers. A closed-loop test can, for example, be to control the instant turning curvature to generate a handling characteristics diagram. Illustration 3: Avoidance of an unexpected obstacle behind a crest. Illustration 2: Vehicles and subsystems can be tested in rigs to isolate behavior. There is also an event-based driver that can take sequences of instructions such as accelerating to a certain speed, applying brakes, shifting gears, or maintaining a yaw velocity. Test rigs are used to isolate vehicle behavior that requires constraints on the chassis. A vehicle can, for example, be mounted in a rig to excite the vertical motion of the wheels, and thereby also the roll, pitch and bounce dynamics, to study ride and road holding, as shown in Illustration 2. Road/vehicle interaction studies are performed either on a flat ground or on a 3D road. The flat ground has optional constant inclination and is intended for openloop or closed-loop maneuvers where the road positioning is of no importance. Full 3D roads are used for tests where a given track is to be followed. Examples are following a curvy road, performing a lane change, negotiating a turn while braking, going through a slalom course or avoiding an obstacle, as in Illustration 3. Another benefit of the 3D roads is that performance of observers and vehicle state estimators can be evaluated under realistic driving conditions. Illustration 4: Running a wheel model in a test rig is a convenient way to compare the tire properties with measurements. The 3D roads use tabular inputs that allow an arbitrary surface geometry to be represented. This specification is open and allows users to input their own information and even measurement data. To simplify the generation of road data, a generic tool is supplied that allows the user to define curvature, banking, surface conditions and more. This gives great flexibility and examples show how to customize the tool for special purposes such as an ISO double lane-change. The VDL offers a set of commonly used tire models such as Pacejka02, Rill05, and Bakker87. The open implementation makes it possible for users to inspect and modify the supplied models or add their own if desired. To facilitate analyses of wheel components, there

4 are dedicated rigs that can be configured for a variety of standard experiments such as slip sweeps at various loads and camber angles, and also adapted to customized tests, as in Illustration 4. To capture the steering-wheel moment characteristics, accurate models of the kinematics, compliances and friction are included. The physical detail of the models makes it straightforward to add sensors and actuators to study new concepts in power assist, active front steering, steer-by-wire, and similar systems. Illustration 6 shows the steering torque-angle characteristics for varying combinations of friction levels at the rack and steering column, so-called secondary and primary friction. The blue curve shows the original lower friction level while the green and red curves indicate how characteristics change when primary and secondary friction increase, respectively. Illustration 5: Suspension mounted in a test rig for kinematic and compliance analysis. Suspension and Steering Systems The VDL features two main types of suspension models: tabular suspension where wheel motion constraints are described by table input, and geometric suspension where the actual mechanical topology is described by links, joints, and bushing elements. Tabular suspension models are convenient to use when empirical suspension data from K&C analysis is used for model tuning. The geometric suspension models are useful to study the effects of mechanical re-design, or to analyze or design actively controlled suspension with embedded actuators. A collection of variants of common suspension designs such as McPherson, trailing arm, double wishbone, multilink, twist beam, and rigid axle are pre-defined and readyto-use. For users that want to design their own suspensions, there are standard multi-body primitives such as joints and bodies and dedicated components such as bushings, leaf springs, links, struts, hubs. Suspension systems can be simulated and analyzed both as parts of full vehicles and separately in test rigs to facilitate design and verification, as shown in Illustration 5. This can also be done for individual suspension components. A typical example is strut force elements that can be tested in a 1D model of a quarter car before mounted in a suspension or used in full vehicle analysis. Illustration 6: Steering wheel torque characteristics for different combinations of primary and secondary friction. Powertrains and Drivelines Models of the powertrain are included to allow complete vehicle simulations. Special attention is given to the driveline since it has the most impact on vehicle dynamics. Drivelines and driveline components for variants of FWD, RWD, and AWD configurations are supplied, that efficiently represent the shaft motions also in three dimensions. Elasticities, backlashes, inertial effects, and kinematic imperfections of, for example, cardan and tripod joints can be included when desired. Models for engines with tabular characteristics and throttle dynamics, as well as different transmissions are supplied. These can easily be modified and extended with losses, compliances, additional gear sets and more.

5 It is also possible to use detailed models from other model libraries specialized on engines and transmissions, such as the PowerTrain library and the Transmission library. Active Systems and Signal Buses The open model architecture makes it easy to introduce sensors and actuators at virtually any location on a vehicle. Illustration 7 shows an example of an active roll control system that enhances yaw stability by applying a pretension on the anti-roll bars based on lateral acceleration feedback. The multi-domain support enables users to build actuator components including detailed models of, for example, electric drives, hydraulics, and pneumatics. Signal passing between components in active systems is realized with models that represent multiplexed buses. Imperfections of the bus such as time delays are also included. Illustration 7: Evasive lane change of a fully a loaded vehicle, with and without stability control. The hybridization of the powertrain is a field of increasing importance where the multi-domain capabilities are of significant importance. The openness and flexibility of VDL allow arbitrary configurations to be defined, from mild to series hybrids or even pure electric vehicles. Detailed models of electrical subsystems are available in the SmartElectricDrives library. Brake Systems Brake systems include typical components such as the pedal, booster, valves, cylinders, and wheel-brakes. Wheelbrake models are described with mechanical detail that allow all reaction torques to be described correctly. The friction models are designed to handle wheel lock in a numerically sound way and there are pre-defined components that allow temperature-dependent friction and interaction with other thermal components to manage heat accumulation and cooling. The models are well-suited for studies on brake system dimensioning, methods of brake force distribution, and active systems such as ABS and ESP. Interaction with other subsystems such as the steering allow for detailed analysis of, for example, effects of brake vibration on steering feel. Components from the Hydraulics Library can be integrated to obtain detailed brake system models with fluid dynamics effects. It is possible to use detailed vehicle models from VDL in Simulink, which is convenient for users that develop control algorithms in this tool. System Integration and Algorithm Development As the combination of several active systems such as ABS, ESP, AFS, ARC and DYC gain in importance, the development tools must manage the change from several systems acting independently towards more coordinated behavior. The VDL supports this and offers a platform for efficient system integration by the openness and flexibility, the ability to handle multiple engineering domains, and the variety of model fidelity levels. Illustration 8: Autonomous corner module applied on a compact car.

6 individually for each axle to improve both driving stability and mobility. Racing The VDL is currently being adapted also for racing applications. Compared to passenger cars, this involves other types of aerodynamic devices and special suspension geometries used for formula cars, as exemplified in Illustration 10. New experiment templates include, for example, G-G diagrams and lap time analysis. Illustration 9: Six-wheeled all terrain vehicle. Suppliers can use VDL to analyze their particular component or subsystem in a realistic vehicle environment. Correspondingly, OEMs can conveniently integrate models of components or subsystems from suppliers into a complete vehicle environment to analyze behavior at system level. The model encryption features makes this type of model sharing easy to realize in competitive industrial environments. Dymola's support for real-time simulation gives the possibility to perform hardware-in-the-loop simulations on the most commonly used hardware platforms such as dspace, RT-LAB, xpc Target, and Cramas. Heavy Vehicles Heavy vehicles benefit particularly from the open and flexible structure of VDL due to the large variety of configurations of axles, frames, loads, etc. An extension of VDL for heavy vehicles is under development. This covers combinations such as trucks with full trailers and tractors with semi-trailers, as in Illustration 11. The component set is complemented with models of, for example, pneumatic brakes, air suspensions, liquid loads, and twin tires. Concept Studies The VDL has also proven to be an efficient tool when dealing with concept vehicles and other unconventional configurations. Since the models are open, users can go beyond the predefined templates and define their own configurations. One example is Volvo's Autonomous Corner Module Concept (ACM) in Illustration 8 that allows each wheel to be steered, cambered, suspended, driven and braked individually. Rather than partitioning the vehicle into chassis, powertrain and brakes, each wheel with its actuators is considered as an autonomous unit. In this case, four corner modules together with the vehicle body, a vehicle motion controller, and an HMI form the complete vehicle. Another example is the six wheeled all terrain vehicle in Illustration 9, implemented with three suspension subsystems, electric wheel motors, adjustable ride height and by-wire steering of the front and rear axles. The ride height and thereby the load distribution can be set Illustration 10: Formula SAE chassis in a limit-handling analysis. Illustration 11: Avoidance maneuver with a tractorsemitrailer combination.

7 Modelica The object-oriented modeling language Modelica is designed to allow convenient, component-oriented modeling of complex physical systems, containing for example mechanical, electrical, electronic, hydraulic, thermal, control, electric power subcomponents. Recently, the interest in Modelica has grown rapidly and several suppliers has announced Modelica support in their products. Modelica is maintained and developed by the nonprofit, non-governmental Modelica Association. The organization also supplies the Modelica Standard Library (MSL) with open source standard models within different domains. Dymola Dymola is a tool dedicated to modeling and simulation of models implemented in Modelica. It has unique and outstanding performance for solving differential algebraic equations (DAE). The key to high performance and robustness is symbolic manipulation which also handles algebraic loop and reduced degrees-of-freedom caused by constraints. These techniques together with special numerical solvers gives fast simulation of complex high-fidelity models. Modelon AB Ideon Science Park SE Lund, Sweden visiting address: Alfa-building Ole Römers väg 16 phone: fax: info@modelon.se web: VehicleDynamics Library and Dymola are distributed through the Dynasim reseller network Sweden Dynasim AB Sales@Dynasim.se Japan Toyota Techno Service Corp dymola-info@post.tec-serv.co.jp Germany, AT and CH BAUSCH-GALL GmbH +49 (0) info@bausch-gall.de USA MathPros, Inc. +1 (508) sales@mathpros.com United Kingdom Claytex Services Ltd sales@claytex.com P.R. China Hwa Create Co. Ltd info@hwacreate.com.cn India Pricol technologies Pvt. Ltd corporate@pricoltech.com Korea Kimhua Technologies Inc sales@kimhua.co.kr Mexico MultiON Consulting, SA de CV +52 (5) Ext 140 trafico@multion.com.mx