The stick-slip model of a Girling brake is composed of nonlinear and coupled differential equations that reproduce the friction occurring in this mechanical system. The brake is equivalent to a body sliding on a belt. The problem is very interesting since the possible solutions, which are very sensitive to the parameters of the system, show a chaotic behaviour. In this contribution, the model, which is designed following network method rules, is explained in detail and runs on standard electrical circuit simulation software to provide the displacement and the velocity of the sliding body and the phase planes. In comparison with other models, the considered system does not include dampers to get a more unstable behaviour. Furthermore, a suitable selection of parameters is implemented to reduce the computational time.

The study of everyday phenomena involving friction continues to maintain a high level of difficulty despite its long history. The causes of this problem lie in the different scale of the characteristics of the phenomenon, macroscopic and microscopic. Thus, very different models, valid in a narrow scope which prevents generalization, have been appearing. This survey presents the application of network simulation method to the numerical solution to the study of friction at very different scales. On the one hand, on a microscopic scale an atomic force microscope model has been studied, related to the analysis of soft surfaces at the atomic scale. Furthermore, on a macroscopic scale model related to the analysis of an industrial device, such as a brake mechanism has been studied. After presenting herein is a review of the different formulations of the friction force, the nature of the surfaces involved in the phenomenon, as well as the definition of the problems to be analyzed. The design of network models and the implementation of the initial conditions are explained. The results of the application of network models to selected problems are presented. In order to verify the reliability of the proposed models, their results are compared with the solutions obtained by other numerical methods or experimental results, one from a device developed during the preparation of this report.

One of the widely used processes to measure torsional vibration focuses on the analysis of a square signal from a device set in the machine shaft. The tools used for this purpose usually consist of a toothed wheel connected to an appropriate transducer, of an electromagnetic or optic type, which provides a square wave signal. If the rotation velocity is constant, the signal pulses are the same width, but when the velocity changes, the width of the pulses changes too, lengthening or shortening its width, resulting in a frequency modulated signal. When the shafts of the machines are misaligned angularly, the average speed changes due to variable torque action, so that spectral features of modulated signal show frequency components that are explained by the Bessel Functions. This work shows that these components are caused by a carrying (constant average speed) and a modulator signal (variable turning speed) between the harmonics surrounding the central frequency. Besides, it may also test their relationship with the presence of angular misalignment in the coupled-machine shafts. In addition, an iterative method is applied to construct the frequency spectral diagram of the induced square signal, once the appropriate modulation indices of the Bessel functions have been calculated. To compare and validate the method, different bench tests have been performed using pulse signal and laser interferometry.