Probability of the Critical Length of a Fatigue Crack Occurring at the Tooth Foot of Cylindrical Geared Wheels of the Drive System of a Fiomax 2000 Ring Spinner

Abstract

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.

Fatigue Life Prediction of Knitted Fabrics Made of Cotton Yarns – A Statistical Approach

“…This phenomenon occurs usually in the case of loadings lower than the ultimate strength. The basic characteristics -which are used for further analyses -are versatile charts; but mainly the Wöhler chart is utilised, also called an S -N (σ -S) curve or Wöhler diagram (Figure 1) [3,[11][12]. It allows determination of the maximal loading level (σ), for which a specimen made of a particular material can work within the range of an unlimited number of cycles (N).…”

Influence of Teeth Manufacturing Tolerances of Cylindrical Geared Wheels on GearOperating Characteristics Based on Spinner Stretching Apparatus

“…Summarizing, the stretching apparatus should be considered as an essential part of the spinner drive system, therefore frequent changes in the rotational velocity have a direct influence on the dynamic character of load variability. The role of the stretching apparatus is the setting of tensions [11] via a system of co-operating geared wheels.…”