Статистичне оцінювання міцності пресових з’єднань приводних роликових ланцюгів закордонних фірм на основі теорії малих вибірок

Abstract

Базуючись на даних міцності пресових з’єднань валик-пластина приводних роликових ланцюгів закордонних фірм з використанням теорії малих вибірок, отримані статистичні характеристики розсівання моменту провертання валиків у отворах пластин, а саме: математичне сподівання та дисперсія розсіювання. Використавши критерії Стьюдента і Фішера, здійснено оцінювання суттєвості відмінностей отриманих характеристик досліджуваних ланцюгів.

Basing on the experimental data on the roll-plate pressed joints strength of the 19.05 mm pitch driving roll chains, produced by the foreign companies “Renold” (Great Britain), “Regine” (Italy), “Elite” (Sweden), “Chain-belt” (USA), using the small sampling theory and iteration method, distribution density f(t) of the random value T (T- turning moment of the roll in the plate hole), has been found and the mathematic expectation, dispersion and variation coefficient have been calculated. Тhe characteristic feature of the iteration is that of the distance [a,b] of the values change of the random value T which is considered to be known and to be equal to a=tk min, b=tk max (tk min, tk max - the smallest and the largest value respectively among tk(k=1,n) of the experimental meanings of the value T). At the initial stage of finding f(t) it is considered that no one experiment has been carried out and the value T is expected to be distributed according to the uniform law. During the next stage the result of the first experiment is taken into account to check the prior distribution density f0(t) of the random value T. With this purpose the prior distribution density f1(t) of the value T is presented as follows: f1(t)=c1·[f0(t)+φ1(t)], where c1 is found from the normalization conditions. Using similar approach to the n experiments, the distribution density of the random value T – fn(t), has been found. It was shown that minimal values of M(T)min and D(T)min are those of roll-plate pressed joints of the driving roll chains, produced by the company “Renold”, the maximal values of these characteristics being in the roll-plate pressed joints of the driving roll chains of the company “Elite”. According to the Student’s t-test and Fisher’s t-test, estimation of the sufficient differences of the obtained characteristics of the rolls turning moment scattering in the plates holes of the investigated chains, has been carried out. T value scattering field of the investigated chains was found to differ in 2,81 times and to be in the 4,16-11,7 N•m interval. The minimal T value scattering field is provided by the pressed joints of the “Renold” company and the maximal scattering field – in pressed joints of chains produced by the “Elite” company. Using variation coefficient k0 it was found that the highest stability of the turning moment is provided by the roll-plate pressed joints of the driving chains produced by companies “Renold” and “Regina”.