Inverse Reconstruction of the Spatial Distribution of Dynamic Tire-Road Contact Forces in Time Domain Using Impulse Response Matrix Deconvolution for Different Measurement Types

In tire development, the dynamic tire-road contact forces are an important indicator to assess structure-borne interior cabin noise. This type of noise is the dominant source in the frequency range from 50-450 Hz, especially when rolling with constant angular velocity on a rough road. The spatial force distribution is difficult or sometimes even impossible to simulate or measure in practice. So, the use of an inverse technique is proposed. This technique uses response measurements in combination with a digital twin simulation model to obtain the input forces in an inverse way. The responses and model properties are expressed in the time domain, since it is specifically aimed to trace back the impact locations from road surface texture indents on the tire. In order to do so, the transient responses of the travelling waves as a result of these impacts is used. The framework expresses responses as a convolution product of the unknown loads and impulse response measurements. Tikhonov regularization combined with L-curve optimization is used to limit the noise amplification on the reconstructed forces. A numerical experiment is performed to assess the estimation accuracy for different measurement types. Structural measurements, especially accelerations, measured close to the excitation area, result in the best reconstructed forces. The method is also illustrated in an experiment on a physical test tire.