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Vortex® Studio includes the Tire Model feature in Vehicle Systems to accurately capture the interaction between the wheels of a vehicle and the ground surface material.

## Different Types of Tire Models

Tire models can be divided in two main categories: hard grounds and soft grounds. These models allow you to realistically capture the friction forces between the tire and the ground, taking into account both the material in contact and the driving maneuvers (i.e., whether the vehicle is accelerating, breaking or steering, the longitudinal and the lateral friction forces are changing). In case of soft ground models, the deflection of the ground is responsible for resistance to movement. This effect is important to capture, for example, in case of off-road mobility analysis fuel consumption or driver training ability.

### Hard ground

The hard ground category of models is used in cases where the ground is infinitely rigid. This category accurately captures the friction in the forward and the lateral direction of the tire movement which depends on the vehicle's maneuvers. Therefore, the traction available and the resistance to sideways movements are more realistic. Hard ground models also capture the alignment moment.

Vortex provides the following hard ground models:

• Magic Formula
• Pacejka Magic Formula 2002
• Composite Slip
• Fiala
• Coulomb
Note
The Coulomb model is not a tire model per se. However, it has been included for any users who still want to use it. It allows the user to treat all wheel interaction models in an unified way, particularly for the treatment of the tire pressure and rolling resistance.

### Soft Ground

As with the hard ground models, friction forces are accurately computed, including the fact that the friction depends on the size of the contacting tire patch. In addition, the compliance of the soil includes resistance to the wheel movement as a resistive force and a resistive torque.

Two fundamental mathematical relations have been developed for soft ground models: one that relates the pressure on the ground and the sinkage, and the other that defines the shear stress to the shear deformation (strain). Because of the wide variety of soil characteristics that can be found in nature, a single unique mathematical model that can describe all of the cases does not exist. For this reason, a few different models have been implemented.

Pressure sinkage models

• Bekker
• Wong
• Reece
• Muskek
• Snow

Shear stress- strain models

• Exponential
• Hump
• Wong

Lateral force Model

In the case of hard ground models, the lateral friction force is given directly from the models. In case of soft ground, the lateral force is obtained by a side force model that uses an exponential function of the lateral slip. More details can be found in the tire model's technical notes.

## Tire Pressure and Rolling Resistance

### Tire Pressure

Tire pressure is used to determine the tire stiffness which results in tire deflection. Some models of rolling resistance include the effect of tire pressure.

### Rolling Resistance

Hard ground tire models do not include any rolling resistance. Tire rolling resistance is then modeled by using some (external) rolling resistance models. Soft ground tire models capture the rolling resistance that comes from the ground deflection (compaction resistance force). Rolling resistance due to tire deflection caused by tire pressure is only considered for the Wong and Bekker models.

## Structure of the Tire Model Component

### Main Components

The Tire Model component is the main entry point to the Tire Model feature. Newly created vehicles come automatically equipped with a Tire Model component (which you can delete to revert to the material table). The Tire Model component can be added to vehicles loaded from a previous version.

The Tire Model component is structured as a tree of sub-components under the vehicle in the Explorer panel, the first level of which contains the following sections:

• Wheel Collection: contains a set of wheel adapters, one per wheel of the given vehicle.
• Tire Type Collection: contains a user-defined set of tire types and their tire model properties.
• Default Tire Model: contains the user-defined tire model property that is used during simulation when no tire model has been defined for a specific tire type/ground type interaction. By default, the Coulomb Tire model is selected, but it can be replaced by the user.

Expanding the Tire Model Component reveals:

1. The set of wheels contained in the current vehicle
2. The Tire Type Collection. In this example, the collection contains two user-defined tire types: Summer and Winter. Each collection contains a set of four user-defined Tire Models that will be used for specific tire type/ground type interactions during simulation.

First key point in setting up the Tire Model Component of a vehicle is to associate a Tire Type with every wheels of the vehicle. Having defined a set of tire models under a tire type, the second key point is to associate each of them to a ground material. In general, these materials are already assigned to the terrain database. When the wheel travels on some ground surface, the simulation system identifies the type of tire associated with this wheel and the material associated with the ground at the contact patch, and applies the appropriate ground reaction forces according to the given tire model. As such, for each pair of interacting tire type/ground material, the user can define a tire/ground interaction model which should be used to add the necessary reaction forces to the wheel.

The wheel adapter is used to assign specific tire type/ground type interactions to a given wheel in the vehicle. For this purpose, it lets the user select a tire type and gives control over the tire pressure of the wheel. Finally, it provides a selection of useful simulation outputs.

Selecting a wheel from the wheel collection opens up its Properties panel.

 Tire Type: Must be specified by picking one under the Tire Type Collection, otherwise you will see an error message. Tire Pressure: The tire pressure (in pascals). Ground Material Name: The name of the ground material in contact with the wheel. Tire Model Name: The name of the tire model interacting with the ground is formatted as: "Tire Type Name" / "Ground Material Name". "Void" is set when the wheel is not in contact. Normal Force: Average normal force at the wheel's contact patch (in newtons). Tire Compliance: The tire compliance at the wheel's contact patch (in m/N). Ground Compliance: The compliance of the soil at the contact patch (in m/N). Tire Deflection: The deflection of the tire (zero for infinite tire pressure), in meters. Ground Deflection: The ground deflection (due to compaction) at the contact patch (zero for hard ground tire models), in meters. Longitudinal Slip: Longitudinal slip at the previous step. Transversal Slip: Lateral slip at the previous step expressed in radians. Longitudinal Friction Bound: The maximum allowed lateral friction force according to the current tire model (in newtons). Longitudinal Friction Ratio: The ratio of the actual lateral friction force to the bound. Lateral Friction Bound: Maximum allowed lateral friction force according to the current tire model (in newtons). Lateral Friction Ratio: Ratio of the actual lateral friction force to "Lateral Friction Bound". Alignment Moment: Restoring moment according to the current tire model (in N·m). Tire Resistance Torque: Rolling resistance torque generated by the tire deformation (in N·m). Compaction Resistance Torque: Rolling resistance torque generated by the ground compaction. Value is zero in case of hard surface ground interaction (in N·m). Compaction Resistance Force: Rolling resistance force generated by the ground compaction. Value is zero in case of hard surface ground interaction (in newtons). Camber: Angle between the normal direction at the contact and the side wall of the wheel (in degrees). A value of zero means that the wheel is vertical.

### Tire Model Properties

Each tire type can have any number of tire models defined for it. Right-clicking the type (e.g., Summer) reveals a menu that give access to tire model properties. Selecting a model (e.g., Ice) open its Properties panel.

A tire model defines the way a wheel reacts to the ground taking into consideration ground penetration, traction, side force, and resistance to movement. All tire models introduced in here are further explained in the Tire Models section of the Technical Notes.

There are a few inputs common to all models. The following uses the Coulomb Tire Model as an example.

1. Ground Material: The name of the VxMaterial assigned to the ground.
2. Rolling Resistance Model: Sets the rolling resistance model.
3. Damping Ratio: The damping scale factor on the critical damping as computed automatically based on the stiffness at the contact. Stiffness at the contact is computed based on the tire pressure and the width of the tire.

Note
More information about the inputs shown above are found in the Tire Models section of the Technical Notes.

## Using the Tire Models

When creating a new vehicle system, the Tire Model component is also created. The set of wheels is already set up but the set of Tire Types is empty; the user has to create the tire types (e.g., front wheels, rear wheels).

For each tire type, you must define a set of tire model properties. Right-click on a tire type and choose one of the available tire models. Next, set the Ground Material field to one of the materials proposed by the drop-down menu (or add another entry, if desired). For a given tire type, all ground materials must be different, otherwise a warning message appears.

At the end of this process, each tire type should have a tire model property defined for each possible collision geometry's material that may eventually collide with the wheels in the scene.

Before running the simulation, check for warning messages.

Important:

• When using the Tire Models, the usual material table is not used to define the interaction between the wheels and other collision geometries of the scene. Instead, it's the "interaction table" defined in Tire Type Collection that is used. This table persists in the mechanism file.
• The VxMaterial assigned to a Vehicle System's wheel component is ignored.

The data set under the Tire Type Collection in the Explorer panel corresponds to the material table. In the usual material table, the first row and the first column represent the material and the entry of the table defines the classical contact interaction. In the Tire Type Collection, the tire type corresponds to the first column and each ground material corresponds to the top row. Each entry in the table becomes the tire model interaction.

Note
Combinations of tire type and ground material that are not defined use the Default Tire Model that is found under the Tire Model Component in the Explorer panel.