Vertical vehicle behavior models

Simulation of the vertical behavior of vehicles. 3 models are presented, with two, four and seven degrees of freedom respectively.

https://www.youtube.com/channel/UCfCqAUwlfoBMwsYNvzL9LXw

Features simulation animations.
Read the complementary pdf for more information

3 models are proposed.

-Quarter car model:
Model with 2 degrees of freedom, relative to the vertical displacement $[Z_s]$ of the suspended mass $[m_s]$, as well as the vertical displacement $[Z_u]$ of the unsprung mass $[m_u]$.

The stiffness of the suspension is represented as $k_1$, and its damping as $c_1$.
The stiffness of the tire-wheel is represented as $k_{w_1}$, and damping is neglected.

--Half car model:
Model with 4 degrees of freedom, relative to the vertical displacement $[Z_s]$ of the suspended mass $[m_s]$, the vertical displacements $[Z_{1},Z_{2}]$ of the unsprung masses $[m_{u_{1}},m_{u_{2}}]$ and the rotation of the unsprung mass $\theta$, positive counterclockwise.

The parameters are defined following the same criteria as the previous case.Except that the suspended mass, which has a rotational movement, has a characteristic inertia $I_{\theta}$.

--Total car model:

Model with 7 degrees of freedom, relative to the vertical displacement $[Z_s]$ of the suspended mass $[m_s]$, the vertical displacements $[Z_{1},Z_{2},Z_{3},Z_{4}]$ of the unsprung masses $[m_{u_{1}},m_{u_{2}},m_{u_{4}},m_{u_{4}}]$ and the rotation of the unsprung mass $\phi$ and $\theta$, positive counterclockwise.

The model has two inertia parameters, relative to pitch $\phi$, and roll $\alpha$.

The others parameters are defined following the same criteria as the previous case.\\