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This paper presents the development of a tire model for use in the simulation of vehicle dynamics. The model was developed to predict tire lateral and longitudinal force responses to dynamic inputs. In this new tire model, the contact patch of a tire is lumped into a number of elements to study the dynamic behavior of the displacement of the tire contact patch in the lateral and longitudinal directions. For each displacement, a differential equation governing the dynamic behavior of the displacement to the dynamic inputs is derived. Based on the differential equations for the lateral and longitudinal displacements, difference equations are derived for the purpose of simulating tire output responses. Since system parameters, such as mass, damping and stiffness, in the difference equations are unknown, estimation of system parameters is performed using the differential equations and experimental data measured for this research.

This paper presents the application of pulse input techniques to study tire dynamics in the frequency domain. Many tire researchers analyze tire dynamics by means of studying the frequency response of tire output responses to sinusoidal frequency inputs, for example, the frequency response of tire lateral force to sinusoidal slip angle input. To replace expensive and time-consuming sinusoidal frequency tests, pulse techniques are applied to obtain frequency responses. A series of slip angle pulse input tests in various conditions (several normal forces, speeds and magnitudes of slip angle inputs) are executed on a pneumatic tire. The tire output responses to the slip angle pulse inputs are transformed into the frequency domain using discrete Fourier transform. Several rules of Fourier transform related to the study of tire dynamics are detailed. The frequency responses obtained by pulse techniques are validated by comparison with the results from sinusoidal frequency tests.

This paper presents results from recent studies on using pulse inputs to generate simulated and experimental frequency responses. The purpose of the paper is to disseminate information on the application of pulse testing methods, and to compare the results with frequency response results obtained using other methods. Frequency responses were generated from a vehicle handling dynamics simulation, from full-scale vehicle handling tests, and from dynamic tire tests. The requirements on the input pulses used to drive the systems under study are discussed, including pulse size, shape, and duration, and the corresponding pulse frequency content and power spectral densities. Pulse testing is generally faster and cheaper than the alternative test methods, and for the case of full-scale vehicle testing, requires much less test area.