# Driving dynamics

The driving dynamics is a specialized field of dynamics , which, starting from the laws of engineering mechanics and experiment consisting found dependencies, with the movement of land vehicles involved (wheel, chain and rail vehicles).

The driving dynamics include determinations of distance , time , speed , acceleration , energy expenditure , drive forces , power, resistance to movement, and in the case of rail-bound vehicles also the trailer loads to be transported and the efficiency of vehicles.

Driving dynamics uses technical, physical , mathematical and statistical principles and, in turn, provides the basis for subsequent mechanical, structural, operational and economic studies.

## Directions of movement

From the inertial system (X, Y, Z) to the body-fixed coordinate system (x ", y", z ") by yawing, pitching and rolling

Driving dynamics considers the three translational movements in the direction of the main axes as the spatial movement of bodies, namely

the three rotary movements around the three main axes (which result in the roll-pitch-yaw angle )

as well as two types of vibrations, each characterized by the periodic return to the starting position (and not tied to the main axes):

• Translation and
• Rotational vibration.

The sequence of the rotations is specified in DIN ISO 8855 (terms of driving dynamics) in order to get from a spatially fixed inertial system to a fixed coordinate system.

In a close examination (e.g. motor vehicles), the driving dynamics are limited to sub-areas such as

• Longitudinal dynamics (drive and braking, driving resistance , consumption, ...)
• Lateral dynamics (steering, cornering, tipping safety, ...)

The results of such considerations are then used in the design of the drive train (engine, transmission, ...) and the chassis , especially the axle construction, but also increasingly in electronic driver assistance systems such as anti-lock braking systems (ABS), traction control (ASR) and electronic stability programs (ESP) ).

With two-wheelers ( bicycles , motorcycles , ...) the weight and dimensions of the rider cannot be neglected. Therefore, driving dynamics considerations for the driver / two-wheeler system are carried out here. The results are incorporated into the design of the frame, the running wheels, any existing spring elements and, in the case of motorcycles, the installation position of the drive unit and the above-mentioned components, if any.

## Methods of driving dynamics

### Driving maneuvers

A large number of standardized maneuvers are carried out for the objective and subjective assessment of driving behavior. For example, various defined driving maneuvers such as

• Stationary circular travel
• (single / double) lane change (' VDA lane change test ' according to ISO 3888-2)
• Slalom maneuvers
• Braking attempts

carried out. This can be done

• in the "open loop" with a predetermined course of the steering wheel, accelerator pedal or brake, without taking their effects on the vehicle movement into account, or
• in the "closed loop" with a specified driving task. This is carried out in the simulation or in later development phases by (mostly) test drivers who take the vehicle reactions into account in their control inputs.

During these maneuvers, a large number of different variables are recorded in order to derive parameters for the objective description of the dynamic vehicle behavior. In addition to these objective parameters, the subjective assessment of driving behavior is still an important criterion when setting up the vehicles. Conversely, the subjective assessment has an effect on the definition of parameters which best depict the subjective impression.

On the other hand, load parameters are measured in longer test drives. They can be used, for example, to determine the collective load for the entire vehicle or individual components, or to determine the consumption that is relevant in practice, depending on the route profile, load condition, driver type, ...

### Driving dynamics simulation

The driving maneuvers were originally developed and carried out in test driving. However, digital product creation requires the simulation of these maneuvers in the vehicle dynamics simulation. For a realistic simulation, digital vehicle models of different complexity, from the flat single-track model of a solo vehicle to three-dimensional multi - body models (MKS) of, for example, multi-unit trucks with sprung and unsprung masses, complex axle kinematics and elastokinematics (K&C), complex tire models and other effects are used in simulation programs perform certain driving maneuvers virtually. To close the driver-vehicle-environment control loop, a corresponding driver model and lane model are also required. To simulate complex test scenarios, the driver model must be embedded in a maneuver control in order to be able to reliably process maneuver instructions. The decisive factor here is that dynamic switching between closed loop (driver-vehicle in the control loop) and open loop maneuvers (open control loop) is possible in the individual maneuver phases in longitudinal and lateral dynamics.

Control systems are an inseparable part of the vehicles. The influence of the control units relevant to driving dynamics is usually taken into account by a hardware in the loop or model in the loop simulation.

Here, too, there are simulation calculations of longer journeys in order to e.g. B. to determine fuel consumption or environmental pollution depending on the design of the vehicle and drive train (engine, gear ratios, shift points, masses, etc.). To simulate real routes such as B. the consumption lap of "auto motor und sport", the virtual driver must be able to adhere to the corresponding mandatory and prohibitive signs (e.g. speed limit).

The advantage of the simulation lies in the fact that detailed statements on the driving dynamics properties are possible in an early development phase. Given the increasing variety of products and the complexity of the vehicles, problem areas can be identified at an early stage.

Due to the extensive reproducibility (only approximate with hardware in the loop), different results can be clearly assigned to changed calculation specifications. For this it is often sufficient to simulate the vehicle in detail only with regard to the influencing variable considered. Another benefit is the knowledge of complex causes, effects and relationships, which is more difficult to achieve in the often limited perception / measurement of reality.

### Bench test

• Kinematics, elastokinematics
• suspension
• Structural moments of inertia, center of gravity
• Aerodynamic coefficients (wind tunnel)
• Component testing (component load, strength)

### Measuring equipment, measurands

The measured variables used in driving tests are typical

The most modern gyro platforms are implemented as GPS / INS systems. A special controller ( Kalman filter ) is used to merge the data from the two systems of the gyro platform and GPS in order to benefit from the advantages of satellite navigation and inertial navigation for the overall result. This increases u. a. the availability and the measurement accuracy, and leads to further observable quantities.

Depending on the task at hand, other measured variables are added, e.g. B. Brake pressures and wheel speeds. Since the vehicles themselves have sensors, these signals can be picked up via the CAN bus .

## Rail vehicles

### Driving time determination

The analytical-kinematic methods for analyzing the vehicle movement on the rails are based on the simplifying assumption that the vehicle shape is concentrated in a massless point. For motion models resulting therefrom in the form of differential equations , it is assumed that the underlying motion forms are continuous or continuous in sections. For the calculation it is also assumed that the jerk is constant in sections. The change in jerk , which is mathematically the 4th derivative of the path with respect to time, thus becomes zero.

Since the driving dynamics method for determining driving times has been used for a very long time, the following four types of methods have emerged:

1. General graphic differentiation and integration methods, which are relatively imprecise and are no longer used today,
2. Special graphical determination procedures of the driving dynamics. B. the travel time determination method according to Strahl , Müller and Unrein . This also includes Udo Knorr's "Fahrdiagraph" from the 1920s. All of these processes are only of historical significance.
3. Methods of analytical step-by-step differentiation and integration, also referred to as “step procedures” (time step, distance step, speed step and acceleration step method). These methods, which in the form of the "time step method" contain even the smallest methodological error, are very suitable for simulating the sequence of movements.
4. Methods of differentiating or integrating a closed function of the movement process. These can be used to calculate individual movement phases and can already be carried out on a pocket calculator, however, it is a prerequisite that at least one of the required variables can be represented as a closed, integrable or differentiable function.

### dynamics

The design of the wheel sets, suspension, suspension and damping of the bogies and other effects are the subject of the driving dynamics of rail vehicles. The generation of force in the wheel / rail contact zone plays a decisive role here. Knowledge of these relationships enables the analysis of dynamic processes, e.g. B. the sine wave .

## literature

• Transpress Lexicon Transport . Transpress VEB publishing house for transport, Berlin 1980.
• Dietrich Wende: Driving dynamics . Transpress VEB publishing house for transport, Berlin 1983.
• Manfred Mitschke, Henning Wallentowitz: Dynamics of motor vehicles . Springer, Berlin 2004, ISBN 3-540-42011-8 .
• Georg Rill: Simulation of motor vehicles . 2007 ( online [PDF; accessed September 4, 2011]).
• Bernd Heißing, Metin Ersoy, Stefan Gies: Chassis Manual : Basics, Driving Dynamics, Components, Systems, Mechatronics, Perspectives . Vieweg / Springer Vieweg 2007, 2008, 2011, 2013. Chapter 2: Driving dynamics ( online , 7 MB, 119 pages)
• Klaus Knothe, Sebastian Stichel: Rail Vehicle Dynamics . Springer, 2003, ISBN 978-3-642-62814-6 .