| With the progress of science and technology,the understanding of the axle materials has been more comprehensive,and the manufacturing and processing technology related to axle has been improved.But there is no further decline in the number of accidents caused by axle failure.So there is still a need for further research on those issues such as reliability assessment of axles.There are two levels of security on the axle safety:first,the design in axles should en-sure enough fatigue strength;and during the operation,regular damage detection should be reasonably arranged.From these two aspects,many relative issues are studied,the theory combines the practice,and some open results are put forward.Those used meth-ods and concluded results can provide a certain foundation or guidance for engineering application or further research.The main work of this paper is as follows:1.In practice,It is often used to assess the reliability of the total damage by sum-ming all quantiles of damage under different stress levels.By function transformation,the random variables(RVs)in the damage space can be transformed into the probability space.The relation between the algebraic sum of RVs’ quantile and the quantile of total damage is studied,which will play a important role when examining the conservatism of the assessed reliability.Using the method provided in this paper,conservative assessment of damage or life could be calculated with guarantee.By using the uniform condition of conservative assessment,it is also possible to reduce or even avoid parameter estimation tests,which facilitate engineering applications.2.This paper established the ’statistical consistency condition of stress—life’,add proved that it follows the fact of‘life decrease with stress increase’.Using this condition with functional equations,A more accurate P-S-N curve models are inferred.Compared with traditional models,those models are more precision and efficiency.Those models also have a wide range of applicability,with high data-fitting ability.3.The ’statistical consistency conditions of damage—Life’ are provided,which is follows the basic fact that‘damage increases with the loading process’.Further research show that this condition can profoundly reveal relation among the damage distribution,life distribution and damage accumulation process.Two general frameworks of the dam-age accumulation model are provided based on the damage curves or probabilistic damage curves.The essences and limitations of these two models are analyzed theoretically.The necessary conditions for calculating the nonlinear damage accumulation and some math-ematical consistency of damage accumulation models are also given.4.The load spectra of hollow axle of intercity EMU is compiled according to the online testing data.Applying extreme value theory,the extreme loads are inferred statis-tically.According to measured data,compared with the method of general distribution fitting,it is shown that this method is more appropriate.The method to calculate axle reliability based on measured load data is presented.5.the reliability calculation method of axle damage detection interval based on prob-ability of missed detecting is presented,and the relevant results can be used in the schedule or optimization of damage detection interval.The method is suitable for stochastic crack propagation and can synthetically reflect the relationship among residual life,damage de-tection interval and reliability of axle.By abstracting the depth of crack on axle surface as a one-dimensional stochastic process,a model of axle crack propagation based on gamma process is established.Due to the strength redundancy of the axle,the criterion of crack propagation in fracture mechanics models is usually not satisfied.This method can over-come this kind of problem.From the application point of view,this method can not only calculate the reliability of arbitrary damage detection interval,but also schedule the dam-age detection interval under the given reliability.Which is more flexible when compared with the traditional method. |