Road vehicle modeled with Magic Formula

Introduction

The behaviour of the creep forces between a air-filled rubber tire and ground is more complex than the creep forces between wheel and rail. The behaviour of a rubber tire is different than a steel tire. A road vehicle can steer freely, it doesn't need to follow a certain track. A wheel made of steel is very stiff in all directions. In an air-filled rubber tire, the flexibility in the rubber walls must be taken into account.
However, the properties of a rubber tire can measured in a test rig, and the data can be used as input data to the Magic Formula tire models

• List the contents of the tar-file with: tar -tvzk --file=three_piece_bogie.tgz
• Extract the contents of the tar-file with: tar -xvzk --file=three_piece_bogie.tgz

Input data model

The model describes a car standing in 4 wheels. The two leading wheels steers in a sinusoidal motion. The frequency of the steering wheels motions is varied from 0.05[Hz] up to 2.0[Hz].

Input data files

• runf/car4_magic_cos_.2_0.05.tsimf
Steering motion 0.05[Hz]
• runf/car4_magic_cos_.2_0.10.tsimf
Steering motion 0.10[Hz]
• runf/car4_magic_cos_.2_0.20.tsimf
Steering motion 0.20[Hz]
• runf/car4_magic_cos_.2_0.50.tsimf
Steering motion 0.50[Hz]
• runf/car4_magic_cos_.2_1.00.tsimf
Steering motion 1.[Hz]
• runf/car4_magic_cos_.2_2.00.tsimf
Steering motion 2.[Hz]

All cases can be run with script ./RunAll.bat.

Animate the simulations in program Glplot.

Results

The steering wheel moves in a sinusoidal motion of 0.10[Hz]:

As can be seen in the video above, the vehicle follows the steering motion of the front wheels.

The steering wheel moves in a sinusoidal motion of 2.00[Hz]:

In this video the steering motion is too fast. The vehicle is not able to follow the steering motion of the wheels.