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In the present paper, we describe a method of determination of the probability of reaching the critical crack length at the tooth root of the cylindrical geared wheels of the drive system of the Fiomax 2000 ring spinner. The Paris-Erdogan formula was utilised for calculations of the fatigue crack length depending on the number of load cycles. Experimental investigations were performed on cylindrical geared wheels. The wheel specimens were manufactured from 1.6523 steel (UE) according to a technical specification relevant to the drive system of the ring spinner. The experiments were performed using a professional pulsator (pulsating test machine). Based upon the experiments (series of 12 tests), material constants and were calculated. These parameters were utilised in the Paris law of crack propagation for further calculations. Moreover it was also ascertained that these unknowns are related via the deterministic relationship. Therefore a function allowing for approximation of constant in dependence on exponent m was derived. In the next step, for the values of parameter chosen – belonging to the variability interval, established from experimental data – we determined the times of reaching the critical length of the fatigue crack. It was stated that the best approximation distribution describing the simulated random values of times of reaching the critical length of the tooth crack for the drive system of the ring spinner is the asymptotic Gumbel’s distribution. Knowing the distribution and number of cycles until reaching the critical crack length at the tooth root, one can evaluate the fatigue life of the damaged wheel in the ring spinner (Fiomax) drive system for the assumed probability. The goal of the present paper is evaluation of the working time of the elements of the drive system of a ring spinner until the occurrence of damage. The highest fatigue life of geared wheels was achieved within the interval (4.3 – 4.5)x 105 cycles. However, it is recommended to change of the geared wheel in case of the spotting of early symptoms of defect. For the stretching apparatus, the authors of the present paper suggest the exchange of the idler geared wheels at least once per year.

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The article presents the methodology of optimal selection of material and the form of semi-product for the rotors of the spindle-less spinning machine. The multicriteria approach was utilized taking into account versatile criteria. The applied procedure consists of two stages: the optimum method in the Pareto sense and the method of distance function. Based on the analysis of the spinning head work, rotor and availability function, six different materials and three forms of semifinished products (extruded bar, forged element, and cast element) were considered. In consequence, the admissible set consisting of nine elements was obtained. For the evaluation of technological quality of the rotor, the following criteria were proposed: index of functionality of the material σf/ρ, maximum height of the surface peaks, Sp, and maximal hardness on surface of oxide layer μHV0,1. Finally, taking into account the economical criterion (unit cost), the Pareto-optimal set of solutions was determined based on four criteria. Due to the fact that this set contained five variants, the distance function was utilized for choosing the best final variant. The optimal material and the semi-product (because of the assumed criteria) chosen were as follows: alloy AlSi1MgMn and the forged element—because in this case the value of distance function was minimal.

This publication is a review of the work directed or inspired by the late Professor Andrzej Włochowicz in comparison to the current state of knowledge, and developed by his colleagues as an expression of memory and recognition of the contribution that he made to research on the strength of linear textile products. The article describes issues related to the fatigue strength of yarns. An analysis of literature related to the development of research on fatigue strength was carried out, and quantities describing load cycles and selected cases of periodically variable states of loads are presented. The article attempts to systematise certain problems related to the fatigue of textile materials. The body of the article presents the state of knowledge as well as the manner and the methods of assessment of the fatigue strength of textile materials.