# Custom Tire Force and Torque

Compute interactions and spatial relationships between tire and ground surface

Since R2024a

Libraries:
Simscape / Multibody / Forces and Torques

## Description

The Custom Tire Force and Torque block computes the interactions and spatial relationships between a tire and the ground surface.

To model a custom tire, use the outputs from the block to compute the tire force and torque. Then, loop these signals back into the block as inputs. The tire force and torque must be calculated relative to the contact frame of the tire. The contact frame is located at the contact point and the z-axis of the frame is perpendicular to the contact plane. The tire force must be nonnegative; or the block clips the input force to zero. Additionally, you must maintain consistent units for force and torque throughout the simulation. The image shows the diagram of a custom tire model.

The block has two methods to calculate the data that characterizes the interactions and spatial relationships between the tire and the ground. The closest point method determines the contact point by finding the point on the ground surface that is closest to the center of the tire and lies in the plane of the tire. The contact normal vector is located at the contact point and perpendicular to the contact patch at the contact point.

For scenarios where tires experience multi-point contact, such as off-road terrain or obstacles like speed bumps, use the weighted-penetration method. To simplify the computation due to the irregularities of the contact surface, this method computes an equivalent contact plane at each simulation time step to approximate the actual contact area. The contact point is the nearest point on this equivalent plane to the center of the tire. The contact normal vector is located at the contact point and perpendicular to the equivalent plane. For example, the image shows how the weighted-penetration method computes the equivalent plane, contact point, and normal vector when a tire encounters a ramp.

The weighted-penetration normal vector, n, is orthogonal to the equivalent contact plane.

Note

When using the weighted-penetration method, the contact point may not lie on the actual ground geometry. For example, the contact point may be below or above the ground surface if the contact area is locally convex or concave.

## Ports

### Geometry

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Base geometry that represents the ground surface that the tire contacts. You must connect this port to an Infinite Plane or Grid Surface block.

### Frame

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Follower frame that represents the tire. The frame origin is located at the center of the tire.

### Input

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Physical signal input port that receives the computed custom tire force. Use the outputs from the Custom Tire Force and Torque block to compute the tire force. You must compute the tire force with respect to the contact frame of the tire.

The input contains three parts:

• Fx is the longitudinal force tangential to the contact plane and aligns with the x-axis of the contact frame.

• Fy is the lateral force, which is orthogonal to the plane defined by Fx and Fz.

• Fz is the normal force that is normal to the contact plane at the contact point.

The force must be nonnegative. If the block receives a negative force, the block clips the value to zero. In addition, you must ensure the units are consistent during the simulation.

Physical signal input port that receives the computed custom tire torque. Use the outputs from the Custom Tire Force and Torque block to compute the tire torque. You must compute the tire torque with respect to the contact frame of the tire.

The input contains three parts:

• Mx is the overturning moment.

• My is the rolling resistance moment.

• Mz is the aligning torque.

You must ensure the units are consistent during the simulation.

### Output

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Physical signal output port that indicates whether the tire and contact surface have a valid contact. When they are in contact and the contact is valid, the signal equals `1`, otherwise the signal equals `0`.

If the follower frame is below the contact surface, the tire and the surface have an invalid contact and the block does not apply force and torque to the tire.

#### Dependencies

To enable this port, under Sensing, select Contact Signal.

Linear Velocity

Physical signal output port that outputs the relative velocity between the tire frame and the contact point on the geometry along the x-direction of the contact frame. The value has a unit of length/time.

#### Dependencies

To enable this port, under Sensing > Linear Velocity, select Relative Longitudinal Velocity.

Physical signal output port that outputs the relative velocity between the tire frame and the contact point on the geometry along the y-direction of the contact frame. The value has a unit of length/time.

#### Dependencies

To enable this port, under Sensing > Linear Velocity, select Relative Lateral Velocity.

Yaw

Physical signal output port that outputs the first derivative of the yaw angle. The value has a unit of angle/time.

#### Dependencies

To enable this port, under Sensing > Yaw, select Velocity.

Camber

Physical signal output port that outputs the camber angle of the tire. The value has a unit of angle.

#### Dependencies

To enable this port, under Sensing > Camber, select Angle.

Physical signal output port that outputs the first derivative of the camber angle. The value has a unit of angle/time.

#### Dependencies

To enable this port, under Sensing > Camber, select Velocity.

Spin

Physical signal output port that provides the first derivative of the spin angle. The value has a unit of angle/time.

#### Dependencies

To enable this port, under Sensing > Spin, select Velocity.

Contact Frame

Physical signal port that outputs a 3-by-3 rotation matrix that maps the vectors in the contact frame to vectors in the reference frame of the base geometry. The output signal is resolved in the reference frame associated with the base geometry.

#### Dependencies

To enable this port, in the Sensing > Contact Frame section, select Base Rotation.

Physical signal port that outputs a 3-by-1 vector that contains the coordinates of the origin of the contact frame resolved in the reference frame of the base geometry.

#### Dependencies

To enable this port, in the Sensing > Contact Frame section, select Base Translation.

Physical signal port that outputs a 3-by-3 rotation matrix that maps vectors in the contact frame to vectors in the reference frame of the follower geometry. The output signal is resolved in the reference frame associated with the follower geometry.

#### Dependencies

To enable this port, in the Sensing > Contact Frame section, select Follower Rotation.

Physical signal port that outputs a 3-by-1 vector that contains the coordinates of the origin of the contact frame resolved in the reference frame of the follower geometry.

#### Dependencies

To enable this port, in the Sensing > Contact Frame section, select Follower Translation.

## Parameters

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Radius of the tire, specified as a positive scalar with a unit of length.

Method to use to compute the location and orientation of the contact frame, specified as:

• `Closest Point`: Use this method for on-road driving conditions where single-point contact is sufficient.

• `Weighted Penetration`: Use this method for rough-ground driving conditions that involve multi-point contacts, such as off-road scenarios.

You can use the computed data to develop custom tire models.

## Version History

Introduced in R2024a