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 into the block as inputs. The image shows the diagram of a custom tire model.

You must calculate the tire force and torque relative to the contact frame of the tire. The contact frame is at the contact point and the z-axis of the frame is perpendicular to the contact plane. The tire force must be nonnegative. If the tire force is negative, the block clips the input force to zero. Additionally, you must maintain consistent units for force and torque throughout the simulation.

The follower frame is at the center of the tire. The image shows the follower and contact frames of the tire at zero configuration.

The yaw, camber, and spin angles correspond to a y-x-z sequence rotation about the follower frame of a tire.

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 at the contact point and perpendicular to the contact patch at the contact point.

For scenarios where tires experience multiple-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 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.

You can use the con port to indicate whether the tire and the surface have a valid contact. If the tire and the surface are not in contact or the contact is not valid, all sensed outputs, such as the tire force, tire torque, and camber angle, become zero.

Ports

Geometry

B — Base geometry

geometry

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

Frame

F — Follower frame

frame

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

Input

ft — Tire force, N

physical signal

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:

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

• F_y is the lateral force, which is orthogonal to the plane defined by F_x and F_z.

• F_z 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.

tt — Tire torque, N*m

physical signal

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:

• M_x is the overturning moment.

• M_y is the rolling resistance moment.

• M_z is the aligning torque.

You must ensure the units are consistent during the simulation.

Output

con — Contact signal, unitless

physical signal

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

vx — Relative longitudinal velocity, m/s

physical signal

Physical signal output port that outputs the relative velocity between the follower 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.

vy — Relative lateral velocity, m/s

physical signal

Physical signal output port that outputs the relative velocity between the follower 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

psid — Yaw velocity, rad/s

physical signal

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

gamma — Camber angle, rad

physical signal

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.

gammad — Camber velocity, rad/s

physical signal

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

omega — Spin velocity, rad/s

physical signal

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.

Tire Radius

rl — Loaded radius, m

physical signal

Physical signal output port that provides the distance from the center of the tire to the contact point between the tire and the contact surface. The value has a unit of length.

Dependencies

To enable this port, under Sensing > Tire Radius, select Loaded Radius.

rho — Radial deflection, m

physical signal

Physical signal output port that provides the difference between the tire radius specified in the Tire Radius parameter and loaded radius output from the rl port. The value has a unit of length.

Dependencies

To enable this port, under Sensing > Tire Radius, select Radial Deflection.

Contact Frame

Rb — Base rotation, unitless

physical signal

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.

pb — Base translation, m

physical signal

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.

Rf — Follower rotation, unitless

physical signal

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.

pf — Follower translation, m

physical signal

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

Tire Radius — Radius of tire

1 m (default) | positive scalar

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

Contact Frame Computation Method — Method to use to compute location and orientation of the contact frame

Weighted Penetration (default) | Closest Point

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

R2024b: Compute radial deflection and loaded radius

You can use the rl and rho ports to compute the loaded radius and radial deflection for your custom tire model. The loaded radius is the distance from the center of the tire to the contact point between the tire and the contact surface, and the radial deflection is the difference between the loaded radius and tire radius specified in the Tire Radius parameter.