We treat the bolt non-failure as a fuzzy random event, which is characterized by the domain), (+∞∞=U on the fuzzy set A. The fuzzy subset A means: in the universe U, for any U∈μ, A number <>1,0) is specified (∈μA, we call it) (μμA is the membership of μ to A. In the domain U, if A is a random variable, then A is called a fuzzy event. Fuzzy event The probability P is defined as dxxfxAPAu) (μ∫=(1) The force analysis of the bolt when the spreader lifts the lifting weight is the fuzzy reliability, denoted as R.
The fuzzy reliability design criterion for pre-tightening bolt connection can be expressed as: the material strength limit of the bolt is greater than the fuzzy probability of the bolt working stress, and must be greater than or equal to the fuzzy reliability R0 required by the design, ie 00Rs≥>σσ(2) bolt work The mean value of the stress caused by the load is 24dQPpπσ=(3) where: d is the thread diameter, in mm. The known working load coefficient of variation is PQQV3=<2>, then the dispersion PQpVσδσ=(4) each bolt is preloaded The prestressing stress caused by force is iσ. According to the literature <2>, the pre-tightening stress coefficient of variation σV is generally taken as 0.149, then its standard deviation iσδσ149.0=(5) according to the literature <1>, tight by axial load The total tensile force Q of the bolt connection is iPQCQ++=21 where: pQ is the bolt working load; iQ is the pre-tightening force; 1C, 2C are the stiffness of the coupling member and the connected member respectively, and the ratio is 12/CCC=, then the iPQCQ+=1 bolt The mean total working stress is iPCσ+×+=1(6), then the standard deviation is 2ipccσ. In the formula: cδ is the standard deviation of the mean value of the stiffness ratio coefficient C, which can be given by the following formula <2>: CVCc10.0 =δ(8) as the fuzzy variable, the ultimate strength is the same as the shear strength, and is also available. The membership function of the reduced half normal distribution is 01) (abxbxAμ(9) where ba is the distribution coefficient and can be determined by the amplification coefficient method.
The fuzzy reliability design of the bolt subjected to shearing is not negligible for the working condition b. The pre-tightening force is ignored. In the conventional design, the shear stress of the bolt is τ=4KQ/dπ2≤(12) where: τ is the bolt shear Shear stress, N/mm2; Q is the theoretical shear load of a single bolt, N; K is the uneven load bearing coefficient of a single bolt; d is the diameter of the shear-resistant part of the bolt, m.
When performing fuzzy reliability design, Q, K, and d are independent random variables, which can be considered to obey the normal distribution, which can be obtained by the probability theorem central limit theorem. When none of the above three random variables play a leading role, the shear The stress should also obey the normal distribution very well. The mean and standard deviation are obtained according to the first-order matrix theory of reliability design. τ=24dKQπ(13)τσ=21(14) Shear stress probability distribution density obeying the normal distribution. The function is f(τ)=τστσπ22)(exp<21>(15) as the shear strength of the fuzzy variable. There should be an intermediate transition process from fully permitted to incompletely permitted. It is generally described by membership function. There are many kinds of functions, such as a half-normal shape, a half-trapped trapezoid, a half-ridged shape, a half-reduced rectangle, etc. For the shear strength, a half-trapezoidal distribution is used, which is practical and simple, and the membership function of the half-trapezoid is ax. ≤><2)(1)(22)(2)(xbaxeababAPRδμδμπδμδμΦ=bxa≤ In the membership function, a1 selects the allowable value in the conventional design, a2 is selected by the amplification coefficient method: a2=(1.05~1.3), a1=(1.05~1.3). For the stress is a random variable, the probability density is (τf, the intensity is a fuzzy variable, and its membership function is) (τμ, the fuzzy reliability is defined by the probability of the fuzzy event ∫∞=≥=τμτdfPR)>(<2)> According to the formula (11) and the formula ( The formula 17) can calculate the fuzzy reliability of shearing and tensioning respectively, and take the fuzzy reliability R which is less reliable as the bolt does not fail. Under this condition, determine the relevant size of the bolt: diameter d, safety degree n. Conclusion (1) For the important equipment such as spreader, the introduction of fuzzy reliability design can make the designer know how safe the lifting is, and the reliability is more intuitive and clear than the average safety factor. (2) Although there are many people applying fuzzy fuzzy design research, some problems need to be further improved, such as a1, a2, a, b, K, etc. in the formula, so the experimental research in this aspect should be strengthened. Make fuzzy reliability design more practical.
Thermal Mass Flowmeter,Thermal Flow Meter,Thermal Gas Flow Meter,Thermal Dispersion Flow Meter
Wuxi Winsun Automation Instrument Co., Ltd , https://www.winsunwx.com