Abstract
Base on the analysis of the Lyapunov dimension that can be used to characterize the system dynamic status and the irregularity degree, and according to the nonlinear dynamic characteristics on surface profile of shearing marks, the analysis method on characteristics of shearing marks based on Lyapunov dimension is proposed. The collected surface profile curve of shearing marks is treated as the time series. The time series are reconstructed by phase space reconstruction theory. In order to make the reconstructed phase space fully reflect the system dynamic characteristics, the determination problem of time delay and embedding dimension are discussed. On above basis, the Lyapunov dimension is calculated, and the ratio of embedding dimension and the time delay multiplied by the Lyapunov dimension are taken as the characteristic quantity of the mark surface. It can be seen that the Lyapunov dimension and the characteristic quantity of the mark surface are different according to the analysis and calculation of the Lyapunov dimension of the surface profile curve of the shearing marks. It is proved that the characteristic quantity is an effective parameter to characterize the surface profile of different shear marks. The characteristics of marks can be extracted and recognized effectively. Therefore the theoretical basis and technical method are provided for studying the surface characteristics of shearing marks.
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