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1、Reliability assessment of hydraulic cylinders considering service loads and flaw distributionAlessandra Altamura a,*, Stefano Beretta ba Tenaris Dalmine, Research (ii) the fatigue properties of the plaintubes are not cl

2、ear as discussed in [6]; (iii) the flaw acceptance criteria are not explicitly connected to the fatigue properties. The application of the “design by analysis” can then become unsatis- factory when the component is subje

3、cted to severe fatigue loads or when thick parts have to be adopted: in both cases designers should apply an assessment with the so-called structural integrity triangle (flaw size, service loads, material properties). In

4、 this regard, analytical flaw assessment methods have been developed in the last decades for static loads using fracture mechanics concepts, applied in the form of failure assessment diagrams (FAD) or crack driving force

5、 failure (CDFF) procedures [7,8]. These methods can also be applied to probabilistic analyses [9,10]. The most critical input, considering that the distribution of fracture toughness can be accurately obtained with simpl

6、e tests [11], is a description of the flaw distribution: there are some indi- cations in the literature for some manufacturing defects (e.g. welding defects [12]), while in the case of detected defects their size is cons

7、idered as a random variable, by adopting a typical distribution of size for a given NDT method [9,13,14]. Under fatigue loads, the probabilistic analyses become more difficult because crack propagation has to be accurate

8、ly calculated and statistically modelled [15e17]. A widely used simplification, either in a semi-probabilistic or fully probabilistic formulation, for* Corresponding author.E-mail addresses: ale.altamura@tum.de (A. Altam

9、ura), stefano.beretta@polimi.it(S. Beretta).Contents lists available at SciVerse ScienceDirectInternational Journal of Pressure Vessels and Pipingjournal homepage: www.elsevier.com/locate/ijpvp0308-0161/$ e see front mat

10、ter ? 2012 Published by Elsevier Ltd.http://dx.doi.org/10.1016/j.ijpvp.2012.07.006International Journal of Pressure Vessels and Piping 98 (2012) 76e88variable approach, by using the Monte Carlo method. The third part sho

11、ws the results of a case study based on load spectra measure- ments of hydraulic cylinders of earth moving machines. The anal- ysis of the results yields to an evaluation of the most important factors influencing the pre

12、diction of fatigue life for these components.2. Experimental assessment of the distribution of initial surface flawsMany discontinuities are present on the surface of tubes due to the manufacturing process. Their maximum

13、 depth is limited by the threshold of non-destructive tests. According to experimental observations, there are two different populations of surface discontinuities: one having a characteristic value of one order of magni

14、tude lower than the NDT threshold, as shown in Fig. 1, another having a characteristic value of the same order of magni- tude of the non-destructive tests threshold. In this work only flaws with a depth of the same order

15、 of magnitude of the NDT threshold are considered. These flaws can be detrimental for the behaviour of tubes subjected to fatigue, since they are able to propagate, although their depth is smaller than the NDT threshold.

16、 Fig. 2a shows a flaw on the surface of a tube, Fig. 2b shows a SEM image of a longitudinal section of a surface flaw of depth of approximately 150 mm. The distribution of the largest flaws has been determined during an

17、extensive experimental activity on cold drawn and stress relieved tubes [24] produced according to [2,3]. Tubes previously subjected to eddy current NDT with a threshold set at 5% of the wall thickness have been inspecte

18、d using magnetic powder. The length of detected flaws has been measured using a pocket rule, as shown in Fig. 2a, while their depth has been measured with a micrometer gauge after grinding the surface of the tube and mea

19、suring the depth of the ground surface. Several tubes from seven production batches, with different diameter and wall thickness, have been inspected, being the total examined surface 363 m2. Table 1 summarizes the geomet

20、ry of the tubes from each examined batch as well as the total examined surface. Some tubes did not contain any flaw detectable with magnetic particles, while some others contained more than one. All exam- ined surface di

21、scontinuities have a ratio a/c lower than 0.1, which means they are long and shallow longitudinal flaws. As suggested by [13], flaws are usually described with a Weibull or a lognormal distribution. Fig. 3 shows the logn

22、ormal, the Weibull and the LEVD probability paper of lots 1, 2 and 3 as well as theprobability paper of the pooled data expressed as percentage of the tubes wall thickness. A LEVD distribution, the cumulative density fun

23、ction of which is reported in equation (1), is chosen to describe the depth of surface flaws, since it is the most suitable to experi- mental data, according to the KolgomoroveSmirnov test [25].FðaÞ ¼ exp?

24、? exp??a ? l d??(1)The simultaneous confidence interval test with 95% confidence level and the likelihood ratio test are applied in order to evaluate the dependence of the best fitting parameters l and d on the tube wall

25、 thickness or diameter. The analysis is carried out for lots 1, 2 and 3. No inference about a dependence can be stated, therefore flaws from the different batches can be described with the same parameters l and d obtaine

26、d by the maximum likelihood estima- tion with pooled data. Fig. 4 shows the plots referred to the simultaneous confidence interval test, where l and d have been normalized with respect to l and d. When modelling the stat

27、istical distribution of initial surface flaws, the probability of detection of standard non-destructive tests must be taken into account. For this reason the input flaw distri- bution for reliability evaluation is obtain

28、ed by formulating a hypothesis on the probability of detection of the flaws, which is modelled as a lognormal cumulative density function distribution [26,27], as reported in equations (2)e(4).Fig. 1. SEM image of the lo

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