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A two-stage straight bevel gear system is a gear system that can be used in various applications. The straight bevel gear is known for its complex tooth geometry. Due to the variation of the number of pairs of teeth in contact, the mesh stiffness function can be considered as a time-varying function. However, the mesh stiffness for the straight bevel gear is sensitive to measurement and modeling errors. Thus, at each time step, its value can not assigned to deterministic one. Generally, the uncertain parameters are assumed to be time-independent. In this paper, the interval process method has been used to represent the time-varying uncertain parameters, whose bounds are determined through the potential energy method. The lumped parameter model of two-stage straight bevel gear has been proposed. We have considered that the masses of the straight bevel gear system components and bearing stiffnesses along with time-varying mesh stiffnesses are uncertain parameters which can be represented by the interval process model. The Chebyshev polynomial expansion has been used to approximate the response of the two-stage straight bevel gear system with respect to the interval variables. The lower and higher bounds of the eigenvalues of the system have been determined. The bounds of dynamic displacements of the straight bevel gear system have been computed and compared with those computed by the Monte Carlo method.

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This paper deals with a numerical investigation for the estimation of dynamic system's excitation sources using the independent component analysis (ICA). In fact, the ICA concept is an important technique of the blind source separation (BSS) method. In this case, only the dynamic responses of a given mechanical system are supposed to be known. Thus, the main difficulty of such problem resides in the existence of any information about the excitation forces. For this purpose, the ICA concept, which consists on optimizing a fourth-order statistical criterion, can be highlighted. Hence, a numerical procedure based on the signal sources independency in the ICA concept is developed. In this work, the analytical or the finite element (FE) dynamic responses are calculated and exploited in order to identify the excitation forces applied on discrete (massspring) and continuous (beam) systems. Then, estimated results obtained by the ICA concept are presented and compared to those achieved analytically or by the FE and the modal recombination methods. Since a good agreement is obtained, this approach can be used when the vibratory responses of a dynamic system are obtained through sensor's measurements.