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Based on the tire cornering properties in steady state condition, a theoretical model of non-steady state tire cornering properties (NSSTCP) with small lateral inputs is presented. The outputs of the model are lateral force and aligning moment, while the inputs are yaw angle and lateral displacement (or turn slip and slip angle). The deformation characteristics of contact patch are analyzed in non-steady state condition. The flexibility of tread and that of carcass are both taken into account. The deformation of carcass is assumed to compose of translating part, bending part and twisting part. The tests of NSSTCP including pure yaw motion and pure lateral motion are realized with step inputs of yaw angle and slip angle respectively and test data is then transformed into frequency domain. The model is validated through comparing the computational results with test frequency response.

Simulations of tire cornering properties with small-amplitude lateral inputs are carried out in non-steady state conditions. The simulation algorithm is derived and the discrete expressions are presented in detail. Based on the simulations, lateral force and aligning moment can be calculated numerically with time-varying yaw angle and lateral displacement as inputs in spatial domain. The flexibility of both tread and carcass along with tire width is taken into account effectively in the simulations, in which the flexibility of carcass includes translating, bending and twisting flexibility. The simulations in non-dimensional form are associated with four tire structure parameters only, which are non-dimensional parameters reflecting the characteristics of tire stiffness, tire width and contact length. Simulation results are validated by test data from step lateral inputs tests. Several typical simulation results are provided.

A tire enveloping model is described by a “four-ports network” system. A flexible roller contact (FRC) model is proposed, in which both tire geometric filtering effect and tire flexible filtering effect are taken into account. Furthermore, partial loss of contact and the variation of contact length are also considered effectively in this model. In the modelling of automobile vibration systems, because of the influences of tire enveloping properties, the road input could not be original road profile. So an effective road input is proposed which is filtered by the tire. Under different obstacles, tire loads and inflation pressures, the simulations of the effective road input are carried out based on the FRC model. The simulation results show that FRC model can describe tire enveloping properties more effectively than rigid roller contact (RRC) model.

Vehicle handling and stability performances are greatly determined by non-steady state (NSS) tire cornering properties. Analytical derivation of NSS tire cornering models are presented in this paper based on Pacejka's string-concept assumption, in which carcass is assumed to be a stretched string with lateral deformation and lateral relaxation. The lateral inputs of the models are either displacement-based (lateral displacement and yaw angle) or slip-based (slip angle and turn slip). The transient deformations in spatial domain in both longitudinal and lateral directions are obtained directly from geometric relationship of contact patch. The additional self-aligning moment due to longitudinal deformation of contact patch after effect of tire width is considered is also achieved according to geometric relationship of contact patch in longitudinal direction and two transient geometric conditions of contact point.

The STI (System Technology Inc.) tire model is one of the most important semi-empirical (steady-state) tire models currently applied in the vehicle dynamics simulation software package of the National Advanced Driving Simulator (NADS). The STI tire model is presented originally based on tire contact length directly and the contact length is required to provide. Based on the concepts of nominal slip in both longitudinal and lateral directions, the STI tire model is analyzed and rewritten. It shows that the STI tire model does not actually depend on the contact length. Meanwhile, the model parameters are partially assigned new physical definitions, for example, static/dynamic stiffness and shape factors. Some simplified expressions are given based on further assumption conditions. The simplified expressions are also obtained regarding longitudinal slip at arbitrary speeds (including low speed, zero speed and stand still), which is originally presented by Bernard.

All the frictional forces developed from tire-snow interfaces are closely associated with snow depth and snow sinkage. One of the important differences between tire-soil interaction and tire-snow interaction is that the latter is explicitly snow depth dependent. Based on our established depth-dependent upper bound indentation model, the effects of snow depth on tire-snow interaction are presented in this paper. Snow is considered as a pressure-sensitive Drucker-Prager material. The required snow material parameters of the model are Drucker-Prager material constants only. Snow sinkages, for longitudinal slip close to zero, under different snow depths are numerically solved through the sinkage solver. The comparison between sinkage obtained analytically and the sinkage computed from finite element simulation is very good.

Snow-covered ground severely affects vehicle mobility in cold regions due to low friction coefficients and snow sinkage. Simulation and evaluation of vehicle mobility in cold regions require real-time friendly tire-snow interaction models that are applicable for quasi-real driving conditions. Recently, we have developed tire-snow dynamics models that are snow depth dependent, sinkage dependent and normal load dependent. The number of model parameters is reduced through theoretical analysis of normal indentation, contact pressure and shear stress within the tire-snow interface. In-plane and out-of-plan motion resistances and traction forces (gross traction and net traction) are analytically calculated for combined slip conditions.

One of the most essential factors causing automobile and aircraft shimmy is energy import from road to tires due to tire hysteresis characteristic. The magnitudes and direction of the energy import are close to frequency responses of tire cornering properties (TCP), which can be calculated directly according to the presented non-steady state TCP theoretical model. Selfexcited shimmy is the main type of wheel shimmy and behaves as negative equivalent damping characteristic of the tire-road vibration subsystem. The values of energy import or equivalent damping determine the tendency of wheel shimmy. Tire structural parameters have certain effects on frequency response of TCP and thereby result in influences on wheel shimmy. Based on the tire model, some valid ways to decrease shimmy tendency are concluded through proper variations of carcass stiffness, tire-width, kingpin caster, tire pneumatic trail, tire cornering stiffness and so on.

Non-steady state (NSS) tire cornering properties show obvious differences from steady state (SS) tire cornering properties. A two-DOF automobile model with steer angle as an input is established based on the known NSS tire model considering complex carcass deformation. The tire model can certainly be applied to modelling of a multi-DOF automobile system. The frequency responses of lateral acceleration and yaw rate are then derived. An evaluation index, amplitude-frequency characteristic of relative error (AFCRE), is used to analyze the influences of NSS front wheels (FW) and/or rear wheels (RW) on automotive handling. The influences of NSS FW are much greater than those of NSS RW only on automotive handling. The established automobile model can also be applied to other similar studies of vehicle dynamics.