CN111310370B - Mechanical part fuzzy reliability calculation method based on random finite element - Google Patents
Mechanical part fuzzy reliability calculation method based on random finite element Download PDFInfo
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Abstract
The invention discloses a mechanical part fuzzy reliability calculation method based on a random finite element of an ultra-relaxation iterative method, which considers the influence of fuzzy factors and designs the fuzzy reliability of mechanical parts. The invention provides a new calculation method for fuzzy reliability of mechanical parts based on random finite elements of an ultra-relaxation iteration method. The method can be used for calculating the fuzzy reliability of the complex mechanical parts. And (3) solving the mean value and the variance of the stress borne by the mechanical part by using a random finite element of an ultra-relaxation iterative method. The mean and standard deviation of the intensity were determined. Membership functions are determined. The probability of failure of the fuzzy event is calculated. The fuzzy reliability of the mechanical part strength is R-1-Pf。
Description
Technical Field
The invention relates to a mechanical part fuzzy reliability calculation method based on a random finite element of a super-relaxation iterative method, belonging to the field of mechanical design, mechanical reliability design and mechanical modern design methods.
Background
The safety factor method in mechanical design cannot scientifically consider the possibility of failure and objectively reflect the real situation of product design and operation. The mechanical reliability design can answer the failure probability of the product in use, and the designed product is small and exquisite and is highly valued by designers. The mechanical performance index also varies due to factors such as the machining process, load mode, stress state, temperature and environment of the mechanical part itself. Therefore, the actual strength values of the materials used cannot be exactly equal to those in the design manual, but can only be considered "approximately equal", with ambiguity in the strength values of the materials. The design load and the actual load cannot be exactly equal, but can only be considered "approximately equal", and the stresses are ambiguous. Considering the influence of fuzzy factors, the mechanical parts should be subjected to fuzzy reliability design. The fuzzy reliability design of mechanical parts still uses material mechanics in the current stress calculation. Material mechanics can only calculate simple parts such as shafts, rods and the like. Finite element analysis of complex structures is feasible. The random finite element considers the influence of random factors and can calculate the deformation and stress of the complex mechanical part. The invention provides a new calculation method for fuzzy reliability of mechanical parts based on random finite elements of a super-relaxation iteration method. The method can be used for calculating the fuzzy reliability of the complex mechanical parts.
At present, no random finite element of a super-relaxation iterative method exists, and no mechanical part fuzzy reliability calculation method based on the random finite element of the super-relaxation iterative method exists.
Disclosure of Invention
The invention provides a mechanical part fuzzy reliability calculation method based on a random finite element of a super-relaxation iterative method, which comprises the following steps of:
(1) mean and variance of stress and intensity
And (3) solving the mean value and the variance of the stress borne by the mechanical part by using a random finite element of a super-relaxation iterative method.
The geometric parameters, the material parameters and the load of the mechanical part are regarded as n normal random variables a1,a2,…,ai,…,an. Generating N1Geometrical parameters, material parameters, load values of the group of mechanical parts.
[K]U＝{F}
The iterative method of hyperrelaxation solves the above formula as follows
(i＝1,2,…,n；k＝0,1)
Mean value of stress of
Variance of stress of
If the material strength is given in the design manual in the numerical range (. sigma.), (xmin，σxmax) Then the mean and standard deviation thereof are
(2) Fuzzy reliability calculation
The failure probability of the fuzzy event is defined as
Thus, the fuzzy reliability of the mechanical part strength is
R＝1-Pf
The invention can calculate the fuzzy reliability of the complex mechanical parts.
Drawings
FIG. 1 is a schematic diagram of a mechanical part fuzzy reliability calculation method based on a random finite element of an override relaxation iteration method.
Detailed Description
(1) Mean and variance of stress and intensity
The geometric parameters, material parameters and loads of the mechanical parts are regarded as n normal random variables a1,a2,…,ai,…,an. Generating N1Geometrical parameters, material parameters, load values of the group of mechanical parts.
The finite element governing equation under dead load can be written as
[K]U＝{F}
Where U is the displacement vector, F is the load, and K is the global stiffness matrix
The iterative method of hyperrelaxation solves the above formula as follows
(i＝1,2,…,n；k＝0,1)
Stress of the unit d is
{σ}＝[D][B]U
[D] Is an elastic matrix, [ B ] is a strain matrix, and U is a node displacement array.
Mean value of stress of
Variance of stress of
If the material strength is given in the design manual, the numerical range (sigma)xmin，σxmax) Then the mean and standard deviation thereof are
(2) Fuzzy reliability calculation of mechanical part strength
Defining X as a continuous random variable, P (X) as a fuzzy set of probability density, omega
Representing a fuzzy event, the probability of the fuzzy event is defined as
Here, the
Is that
Membership functions of (a).
When both the intensity and the working stress distribution conform to a normal distribution, i.e.
And
in the formula murAnd mutMathematical expectation of r and t, respectively, σrAnd σtStandard deviations of r and t, respectively. Given that y is r-t, and r and t are independent of each other, y also follows a normal distribution with mathematical expectations and standard deviations of, respectively
μy＝μr-μt
The membership function of the general engineering problem follows fuzzy normal distribution, and the membership function of the fuzzy interference set adopts the following form:
the membership function represents the complete information of the fuzzy set, and the failure probability of the fuzzy event is defined as
Thereby, the mechanical part has a fuzzy reliability of strength of
R＝1-Pf。
The above description is only exemplary of the present invention and should not be taken as limiting the invention, as any modification, equivalent replacement, or improvement made within the spirit and scope of the present invention should be included in the present invention.
Claims (1)
1. The mechanical part fuzzy reliability calculation method based on the random finite element of the super-relaxation iterative method comprises the following steps:
(1) mean and variance of stress and intensity
Solving the mean value and the variance of the stress borne by the mechanical part by using a random finite element of a super-relaxation iterative method;
the geometric parameters, material parameters and loads of the mechanical parts are regarded as n normal random variables a1,a2,…,ai,…,anTo generate N1Geometrical parameters, material parameters and load values of the group mechanical parts;
[K]U＝{F}
where U is the displacement vector, F is the load, and K is the global stiffness matrix
Solving the above formula by the super-relaxation iterative method as follows:
mean value of stress of
Variance of stress of
If the material strength is given in the design manual, the numerical range (sigma)xmin，σxmax) Then the mean and standard deviation thereof are
(2) Fuzzy reliability calculation
When both the intensity and the working stress distribution conform to a normal distribution, i.e.
And
in the formula ofrAnd mutMathematical expectation of r and t, respectively, σrAnd σtStandard deviations of r and t, respectively. Given that y is r-t, and r and t are independent of each other, y also follows a normal distribution with mathematical expectations and standard deviations of, respectively
μy＝μr-μt
The membership function of the general engineering problem follows fuzzy normal distribution, and the membership function of the fuzzy interference set adopts the following form:
the failure probability of the fuzzy event is defined as
Thus, the fuzzy reliability of the mechanical part strength is
R＝1-Pf。
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