Markov Chain Modelling of Reliability Analysis and Prediction under Mixed Mode Loading

The reliability assessment for an automobile crankshaft provides an important understanding in dealing with the design life of the component in order to eliminate or reduce the likelihood of failure and safety risks.The failures of the crankshafts are considered as a catastrophic failure that leads towards a severe failure of the engine block and its other connecting subcomponents.The reliability of an automotive crankshaft under mixed mode loading using the Markov Chain Model is studied.The Markov Chain is modelled by using a two-state condition to represent the bending and torsion loads that would occur on the crankshaft.The automotive crankshaft represents a good case study of a component under mixed mode loading due to the rotating bending and torsion stresses.An estimation of the Weibull shape parameter is used to obtain the probability density function,cumulative distribution function,hazard and reliability rate functions,the bathtub curve and the mean time to failure.The various properties of the shape parameter is used to model the failure characteristic through the bathtub curve is shown.Likewise,an understanding of the patterns posed by the hazard rate onto the component can be used to improve the design and increase the life cycle based on the reliability and dependability of the component.The proposed reliability assessment provides an accurate,efficient,fast and cost effective reliability analysis in contrast to costly and lengthy experimental techniques.

The effect of cubic potentials on discrete breathers in a mixed Klein-Gordon/Fermi-Pasta-Ulam chain

Nonlinearity has a crucial impact on the symmetry properties of dynamical systems. This paper studies a one-dimensional mixed Klein-Gordon/Fermi Pasta-Ulam diatomic chain using the expanded rotating plane-wave approximation and numerical calculations to determine the effect of cubic potentials on the symmetry properties of discrete breathers in this system. The results will be very useful to researchers in the field of numerical calculations on discrete breathers.

A Markov chain model of mixing kinetics for ternary mixture of dissimilar particulate solids

This paper presents a simple but informative mathematical model to describe the mixing of three dissimilar components of particulate solids that have the tendency to segregate within one another. A nonlinear Markov chain model is proposed to describe the process. At each time step, the exchange of particulate solids between the cells of the chain is divided into two virtual stages. The first is pure stochastic mixing accompanied by downward segregation. Upon the completion of this stage, some of the cells appear to be overfilled with the mixture, while others appear to have a void space. The second stage is related to upward segregation. Components from the overfilled cells fill the upper cells （those with the void space） according to the proposed algorithm. The degree of non-homogeneity in the mixture （the standard deviation） is calculated at each time step, which allows the mixing kinetics to be described. The optimum mixing time is found to provide the maximum homogeneity in the ternary mixture. However, this “common” time differs from the optimum mixing times for individual components. The model is verified using a lab-scale vibration vessel, and a reasonable correlation between the calculated and experimental data is obtained

Theoretical search for solutions to minimize negative influence of segregation in mixing of particulate solids

The objective of this study is to examine several optimization problems in the batch mixing of segregating particulate solids that can be set up and solved using Markov chain models. To improve the adequacy of such models and exclude some physical contradictions that arise in the linear form, a non-linear Markov chain model for the mixing of segregating components is proposed. Optimal solutions are obtained by controlling the particle flow outside the mixing operating volume while the components are being loaded, modifying particle circulation inside the mixing zone during the process, and by structuring the load in the mixing zone. Solutions are found that not only reduce the negative influence of segregation, but also exclude it altogether. The gain resulting from optimization grows with the rate of segregation. The optimal solutions presented here can be used to improve the design of mixers.