Analysis Methods for Time-Variant Harmonic Vehicle Dynamics Experiments

This paper proposes several new evaluation methods and their applications in time-variant vehicle dynamics. The basis is a dominant harmonic vehicle motion with time-variant characteristics (e.g. A(t)·cos(φ(t)); φ(t)= ∫ω(t)dt). There are two common methods to identify instantaneous parameters, namely the amplitude, phase, and frequency of a vehicle system: the Hilbert transform and the short-time Fourier transform (STFT). The advantages and disadvantages of these methods are evaluated and a new method, the moving-time-windowed-fast Fourier transform (MTWFFT), is introduced to optimize the accuracy of the STFT. The Hilbert transform and the MTWFFT are able to represent each dominant harmonic signal as instantaneous complex amplitudes. Therefore, signal operations in the frequency domain can be applied and instantaneous transfer functions can be calculated using the quotient of complex amplitudes. This new method improves vehicle dynamics analysis. It is now possible to determine the instantaneous axle slip angle, the axle cornering stiffness, and the instantaneous friction coefficient. The effective wheel load can be separated from other influences by considering the phase difference between axle load and axle lateral force: the fundamental contribution of the wheel load to the axle cornering stiffness becomes much clearer. The result is a coefficient, ζ, which describes cornering stiffness normalized by the effective wheel load. This new parameter opens the discussion of effects which are not related to the primary influence of wheel load. The methods have been validated for use in validating vehicle models, identifying their parameters, and analyzing stability properties of a car-trailer combination.