A lot of authors have proved various common fixed-point results for pairs of self-mappings under strict contractive conditions in metric spaces. In the case of cone metric spaces, fixed point results are usually proved under assumption that the cone is normal. In the present paper we prove common fixed point results under strict contractive conditions in cone metric spaces using only the assumption that the cone interior is nonempty. We modify the definition of property E.A , introduced recently in the work by Aamri and Moutawakil 2002 , and use it instead of usual assumptions about commutativity or compatibility of the given pair. Examples show that the obtained results are proper extensions of the existing ones.

This paper considers the problem of constrained multi-objective non-linear optimization of planetary gearbox based on hybrid metaheuristic algorithm. Optimal design of planetary gear trains requires simultaneous minimization of multiple conflicting objectives, such as gearbox volume, center distance, contact ratio, power loss, etc. In this regard, the theoretical formulation and numerical procedure for the calculation of the planetary gearbox power efficiency has been developed. To successfully solve the stated constrained multi-objective optimization problem, in this paper a hybrid algorithm between particle swarm optimization and differential evolution algorithms has been proposed and applied to considered problem. Here, the mutation operators from the differential evolution algorithm have been incorporated into the velocity update equation of the particle swarm optimization algorithm, with the adaptive population spacing parameter employed to select the appropriate mutation operator for the current optimization condition. It has been shown that the proposed algorithm successfully obtains the solutions of the non-convex Pareto set, and reveals key insights in reducing the weight, improving efficiency and preventing premature failure of gears. Compared to other well-known algorithms, the numerical simulation results indicate that the proposed algorithm shows improved optimization performance in terms of the quality of the obtained Pareto solutions.

Purpose This paper aims to present the methodology to determine Archard’s wear coefficient. By applying this coefficient into the numerical simulation of wear, it is possible to predict wear without long lasting and usually expensive experiments. Design/methodology/approach To determine necessary particles of Archard’s equation and calculate wear coefficient K, an experimental investigation is proposed. Afterwards, the wear simulation is executed in FEM software ANSYS 18.1. Analytical method is offered to determine worn volume for cylinder-in-cylinder contact, based on “inclination” of inner cylinder. Findings Comparing the value of Archard’s coefficient obtained by this experimental investigation with the values from the literature for the similar materials, high correlation is noted. Furthermore, numerically calculated contact pressure is confirmed with analytical method. Trend of pressure decrease due to wearing process, as well as due to increase of contact surface is observed. Practical implications Since the prediction of the wear is closely related to the life cycle assessment of bearings, and the machines in general, it has significant practical importance for designers. Originality/value Determination of Archard’s coefficient is usually performed by conventional pin-on-disk tribometers. This methodology offers a different approach for the determination of Archard’s wear coefficient for cylinder-in-cylinder contact, which is convenient for shaft-sliding bearing contact.

Purpose -This paper aims to develop a simulating model of a journal porous metal bearing under elastohydrodynamic conditions and combined (radial, friction and thermal) load distribution and to carry out structural optimization. Design/methodology/approach -The structure analysis is carried out for each kind of load separately and for the combined load distribution of the bearing, where a dynamically loaded porous metal bearing is simulated. This simulating model is developed by finite elements method using the structure analysis module of the CATIA V5 software. Further, a parameter optimization of a porous metal bearing is presented considering the elastic deformations of the bearing shell. Findings -It is revealed that the bearing, even at points with maximum displacements, could not reach the mounting clearance value during its operational life. Relatively small bearing dimensions produce very high values of eigenfrequency response (over 150 kHz) and common dynamic loads met in all sorts of sliding bearing are not dangerous for bearing damage compared with static loads. In the stage of structural optimization based on the correlation between stress and geometric bearing parameters like wall thickness and outer diameter, the influence of finite element dimension on calculated results can be also analyzed and a proper choice of the latter is achieved.Research limitations/implications -The present porous bearing optimization model with the aid of CATIA V5 module for optimum design uses only single objective optimization. For a complete optimum design a multi-objective optimization has to be carried out. Practical implications -The analysis under dynamic load conditions proved that relatively small dimensions of bearing commonly used in micro technique and precision mechanics result in extended safe and reliable operation. Originality/value -This paper provides a methodology for bearing stress and deformation analysis in the elastic range and on the basis of this analysis it is possible to develop an optimization model for porous bearings offering help to designers for the selection of optimal bearing dimensions considering the bearing load caused by dynamic radial force, friction and temperature variation.

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