抄録
In this paper, a new tire dynamic model is proposed that using NSS(non singular slip) and magic formula. The NSS formula is a new developed function to avoid singularity of longitudinal and lateral slip. In the dynamic tire model, lateral and longitudinal slip functions are basic computed variables for tire force calculation. Many types of tire models are developed after vehicle dynamics study is begun but tire function basis of slip dependency is not changed. The original slip formula is consist of velocity state variables and is a denomination function so mathematical singularity is inherent at zero velocity. Simply, this mathematical singularity is possible to avoid by appending a microscopic number to denominator in mathematical solution. But this method is not effective to numerical integration in dynamic solution. Therefore the transient slip formula is developed to prevent from numerical singularity but this method also has abnormality in sudden brake condition, the slip state is oscillating at stop moment. Anyway, root problem of slip singularity is not solved. To find out the reason for slip divergence problem in numerical solution, solving process should be analyzed at the singularity condition. In this paper, Taylor series and difference equation of slip formula is used and a new concept of virtual stiffness that represents tire internal deformation force is adopted to tire slip mechanism. This virtual stiffness is usable as a monitoring variable for slip singularity. Finally, a new slip formulation is developed to avoid slip divergence. The new NSS(non-singular slip) function is adapted to MF(magic formula) tire model to test slip convergence in critical state of vehicle dynamic simulation. MF tire model is most useful tire model that show good accuracy and fast simulation to express nonlinearity so most of commercial automotive company using this tire model. A new tire model is tested on the TMPT model and compared with ADAMS MF tire solution. The new tire model shows good performance not only overall driving condition but critical state such as sudden braking and braking in turn simulation. Therefore, this tire model is useful for sequential driving simulation which include go and stop.
