The paper covers a wide range of issues in terms of longevity and reliability, which are presented in the modern theory and practice of designing for elements of knitting systems of sock machines. The relevance of the work is confirmed by the current trend in the production and modernization of relatively small batches of machines, which requires a reduction in time and cost of design, primarily due to the calculation recommendations. The analysis and generalizations concerning the choice of calculations on longevity in deterministic and reliability in probabilistic statements for details of difficult forms and limited in the sizes are offered, in particular knitting needles and malleable working surface of cams, which are characterized by random loads and variations of strength characteristics of materials. The mathematical apparatus for the analysis of influence on fatigue longevity of needles of increase of speed parameters of the automatic machine and of constructive measures for reduction of loadings in pair of a needle and cams is presented.. A complex approach is presented for knitting needles for the security of the given fatigue longevity using of the position of the dynamic analysis, calculation of the loading, mathematical statistics and the theory of probability, which allows to quickly evaluate the effectiveness of the proposals to constructive and technological solutions. The dependences for the calculations of cams of different construction for fatigue strength in the probabilistic setting, which in comparison with traditional (according to the normalized factor of safely) a sufficient level of reliability while minimizing of size. Specifics for cams with malleable working surface of equal reliability and with the provision of simultaneous beam and double cantilever deformations are presented. Shown the expediency of using trapezoidal consoles of equal resistance and the algorithm for calculating the sizes of their root and end sections according to the coefficient of shape and a given deflection, which minimizes the length of the cam consoles. The advantages of computer modeling by the finite element method are listed, primarily obtaining the final results with sufficient accuracy and convenience for analysis.
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