Vertical dynamics characterisation of formula student suspension

Abstract

Surfaces of motorsport race tracks are not perfectly smooth and lead to driver discomfort and variation in the tyre vertical force that reduce the performance of the driver and the vehicle. The aims of the project are to quantify the effect of several parameters that influence the vertical behaviour of a formula student vehicle such as stiffness and damping using numerical simulations and experimental tests. A numerical model is implemented in MATLAB/Simulink allowing the behaviour of a quarter car vertical dynamics model to be simulated on any road profile defined by the user. The vertical tyre stiffness and shock absorber damping are modelled using empirical fits based on experimental data from a dedicated tyre testing rig and a suspension damper dyno. Three road profiles with different roughnesses are generated in accordance to ISO 8608 and tested using various vehicle speeds, tyre pressures, shock absorber damping settings, spring stiffnesses, sprung masses and unsprung masses. From a review of literature, it was found that the tyre damping is expected to be significantly higher for a non-rolling tyre compared to a rolling tyre. Additionally, tyre damping is observed to be highly nonlinear and difficult to quantify and model. Therefore, a common approach in literature is to assume negligible tyre damping. However, the validity of the assumption for the required results is analysed throughout the project. A multi-purpose experimental test rig is designed and constructed for the project. Tests to estimate the tyre damping of a non-rolling tyre are conducted using a free vibration logarithmic decrement method and a forced vibration method based on a gradient-based optimisation using the numerical model. The tyre damping is estimated and observed to be deformation, frequency and/or velocity dependent. The uncertainty related to Coloumb friction in the linear bearings of the experimental test rig is estimated and found to have a significant impact on the results at low velocities. Tests are conducted on the experimental test rig to validate the numerical quarter car model. The correlation of the numerical model to the experimental test rig is considered satisfactory although Coloumb friction in the shock absorber is found to have a significant impact at low damping settings and low damper speeds indicating that the empirical fit used should be adjusted to capture the stick-to-slip transition near zero velocity. The optimal shock absorber valve settings for driver comfort and tyre load variation are found and the effect of tyre damping on the results is considered negligible. The sensitivity of driver comfort and tyre road holding to tyre pressure, spring stiffness, sprung mass and unsprung mass is found. However, the non-rolling tyre damping value used significantly impacts the results indicating that a negligible tyre damping assumption is not adequate for sensitivity analysis. Further work is required to estimate the tyre damping for a rolling tyre to achieve representative sensitivities.