CN111159824A - Joint bearing reliability analysis method considering fuzzy uncertainty - Google Patents
Joint bearing reliability analysis method considering fuzzy uncertainty Download PDFInfo
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Abstract
The invention relates to the technical field of reliability analysis, and provides a joint bearing reliability analysis method considering fuzzy uncertainty. The method comprises the following steps: establishing a function of the joint bearing with uncertainty represented by random variables and fuzzy variables; solving a membership interval of the fuzzy variable under a preset membership level; and calculating a reliability membership function and a maximum stress point stress mean value membership function of the joint bearing according to the random variable, the preset membership level, the membership interval and the functional function. The reliability analysis method provided by the invention considers the random variable and the fuzzy variable while establishing the function, and simultaneously considers the fuzzy variable and the random variable to carry out the reliability analysis, compared with the prior art, the reliability analysis is carried out from multiple aspects, the reliability of the joint bearing can be more comprehensively analyzed, and the guidance can be provided for the subsequent optimization design of the joint bearing.
Description
Technical Field
The invention relates to the technical field of reliability analysis, in particular to a joint bearing reliability analysis method considering fuzzy uncertainty.
Background
As a general mechanical part, the joint bearing has the characteristics of flexible rotation, compact structure, easy assembly and disassembly and the like, and can meet the requirements of heavy load and long service life. The accuracy of the analysis of the reliability of the oscillating bearing is very important to ensure its proper operation.
However, in the prior art, the reliability of the joint bearing is generally analyzed only from one side, and the accuracy of the obtained result is low.
Therefore, it is necessary to provide a joint bearing reliability analysis method that takes ambiguity into account.
The above information disclosed in this background section is only for enhancement of understanding of the background of the invention and therefore it may contain information that does not constitute prior art that is already known to a person of ordinary skill in the art.
Disclosure of Invention
The invention aims to overcome the defect that the reliability analysis method in the prior art is low in accuracy of analysis results, and provides the joint bearing reliability analysis method considering the fuzzy uncertainty, which is high in accuracy of the analysis results of the reliability analysis method.
Additional aspects and advantages of the invention will be set forth in part in the description which follows and, in part, will be obvious from the description, or may be learned by practice of the invention.
According to one aspect of the invention, a joint bearing reliability analysis method considering fuzzy uncertainty comprises the following steps:
establishing a function of the joint bearing with uncertainty represented by random variables and fuzzy variables;
solving a membership interval of the fuzzy variable under a preset membership level;
and calculating a reliability membership function and a maximum stress point stress mean value membership function of the joint bearing according to the random variable, the preset membership level, the membership interval and the function.
In an exemplary embodiment of the present disclosure, calculating a reliability membership function and a maximum stress point stress mean value membership function of the joint bearing according to the random variable, the preset membership level, the membership interval, and the function includes:
and calculating the reliability membership function of the joint bearing according to the random variable, the preset membership level, the membership interval and the functional function by adopting a digital simulation method.
In an exemplary embodiment of the present disclosure, calculating a reliability membership function of the joint bearing according to the random variable, the preset membership level, the membership interval, and the function by using a digital simulation method includes:
determining a value interval of the preset membership level;
calculating the maximum value and the minimum value of the reliability according to the preset membership level by adopting a Monte Carlo digital simulation method;
and traversing the value range to obtain the reliability membership function.
In an exemplary embodiment of the present disclosure, calculating the reliability and the maximum and minimum values of the reliability according to the preset membership level includes:
determining a joint probability density function of the random variables;
and calculating the maximum value and the minimum value of the failure probability according to the probability density function, the membership interval and the functional function by adopting a Monte Carlo digital simulation method.
And calculating the maximum value and the minimum value of the reliability according to the maximum value and the minimum value of the failure probability.
In an exemplary embodiment of the present disclosure, calculating a reliability membership function and a maximum stress point stress mean value membership function of the joint bearing according to the random variable, the preset membership level, the membership interval, and the function includes:
and calculating a reliability membership function and a maximum stress point stress mean value membership function of the joint bearing according to the random variable, the preset membership level, the membership interval and the functional function based on a linear weighted response surface method.
In an exemplary embodiment of the present disclosure, calculating the reliability and the membership function of the joint bearing according to the preset membership level, the membership interval, and the function based on a linear weighted response surface method includes:
determining a value interval of the preset membership level;
calculating the maximum value and the minimum value of the stress mean value of the maximum stress point of the joint bearing and the maximum value and the minimum value of the reliability according to the preset membership level and the functional function based on a linear weighted response surface method;
and traversing the value range to obtain the reliability membership function and the maximum stress point stress mean value membership function.
In an exemplary embodiment of the present disclosure, calculating a maximum value and a minimum value of a maximum stress point stress mean value and a maximum value and a minimum value of a reliability of the joint bearing according to the preset membership level and the functional function includes:
obtaining a first target function according to the value interval, the fuzzy variable and the function by adopting a linear weighted response surface method;
and solving the maximum value and the minimum value of the stress mean value of the maximum stress point and the maximum value and the minimum value of the reliability by adopting a Monte Carlo digital simulation method.
In an exemplary embodiment of the present disclosure, calculating a reliability membership function and a maximum stress point stress mean value membership function of the joint bearing according to the random variable, the preset membership level, the membership interval, and the function includes:
and calculating a reliability membership function and a maximum stress point stress mean value membership function of the joint bearing according to the random variable, the preset membership level, the membership interval and the functional function based on a weighted nonlinear response surface method.
In an exemplary embodiment of the present disclosure, calculating the reliability and the membership function of the joint bearing according to the random variable, the preset membership level, the membership interval, and the function based on a weighted nonlinear response surface method includes:
determining a value interval of the preset membership level;
calculating the maximum value and the minimum value of the stress mean value of the maximum stress point of the joint bearing and the maximum value and the minimum value of the reliability according to the preset membership level and the functional function based on a nonlinear weighted response surface method;
and traversing the value range to obtain the reliability membership function and the maximum stress point stress mean value membership function.
In an exemplary embodiment of the present disclosure, calculating a maximum value and a minimum value of a maximum stress point stress mean value and a maximum value and a minimum value of a reliability of the joint bearing according to the preset membership level and the functional function includes:
obtaining a second target function according to the value interval, the fuzzy variable and the function by adopting a nonlinear weighted response surface method;
and solving the maximum value and the minimum value of the stress mean value of the maximum stress point and the maximum value and the minimum value of the reliability by adopting a first secondary moment method.
According to the technical scheme, the invention has at least one of the following advantages and positive effects:
the invention relates to a joint bearing reliability analysis method considering fuzzy uncertainty, which comprises the steps of firstly establishing a function of a joint bearing with uncertainty represented by a random variable and a fuzzy variable; solving a membership interval of the fuzzy variable under a preset membership level; and calculating a reliability membership function and a maximum stress point stress mean value membership function of the joint bearing according to the random variable, the preset membership level, the membership interval and the functional function. The method considers the random variable and the fuzzy variable while establishing the function, and simultaneously considers the fuzzy variable and the random variable to perform reliability analysis, compared with the prior art, the reliability analysis is performed from multiple aspects, the reliability of the joint bearing can be analyzed more comprehensively, and guidance can be provided for the subsequent optimization design of the joint bearing.
Drawings
The above and other features and advantages of the present invention will become more apparent by describing in detail exemplary embodiments thereof with reference to the attached drawings.
FIG. 1 is a schematic view of a joint bearing structure according to an embodiment of the present invention;
FIG. 2 is a flow chart of a method for joint bearing reliability analysis that accounts for ambiguity in an embodiment of the present invention;
FIG. 3 is a diagram illustrating the result of analyzing the reliability membership function of the joint bearing structure according to a second embodiment of the present invention;
FIG. 4 is a diagram illustrating the analysis result of the mean membership function of the maximum stress of the joint bearing structure according to the second embodiment of the present invention;
FIG. 5 is a graph showing the result of the reliability membership function analysis of the joint bearing structure according to the third embodiment of the present invention;
fig. 6 is a schematic diagram of a second embodiment and a third embodiment of the present invention.
The reference numerals are explained below:
1. an inner spherical surface; 2. and an outer ring.
Detailed Description
Example embodiments will now be described more fully with reference to the accompanying drawings. Example embodiments may, however, be embodied in many different forms and should not be construed as limited to the embodiments set forth herein; rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the concept of example embodiments to those skilled in the art. The same reference numerals in the drawings denote the same or similar structures, and thus their detailed description will be omitted.
Referring to fig. 1, as a general mechanical part, the joint bearing has the characteristics of flexible rotation, compact structure, easy assembly and disassembly and the like, and can meet the requirements of heavy load and long service life. The bearing mainly comprises an inner ring with an outer spherical surface and an outer ring with an inner spherical surface 1, can bear larger load, and can bear radial load, axial load or combined load existing in both radial and axial directions according to different types and structures of the bearing. The joint bearing is generally used for swinging motion (namely angular motion) with low speed, and can also perform tilting motion (namely aligning motion) within a certain angle range because the sliding surface is spherical, and can still normally work when the concentricity of the supporting shaft and the shaft shell hole is large. The joint bearing can be divided into a radial joint bearing, an angular contact joint bearing and a thrust joint bearing according to the main stress form. Because the oscillating bearing has large oscillating angle and aligning performance, can realize rotation, oscillation and aligning, has simple structure and is beneficial to improving the flexibility of structural parts, the oscillating bearing is widely applied to various mechanical equipment such as mines, metallurgy, electric power, traffic, aerospace, textile and the like.
The structural reliability is very important for guaranteeing the safety of structural products, the structural reliability is developed on the basis of the reliability of electronic components, and the development of the structural reliability is lagged behind compared with the reliability of the electronic components. The method mainly comprises two aspects, one is that data required by the structure reliability analysis is relatively lacked, which has a great relationship with the high non-standardization degree of the structure; secondly, the reliability analysis and design theory method of the structure is relatively backward developed, especially the reliability analysis and design problem of the complex structure system, the reliability analysis and design of the complex structure depends on the mechanics, kinematics and dynamics analysis, and the imperfection of the mechanics, kinematics and dynamics analysis method restricts the development of the reliability analysis and design method of the complex structure to a certain extent. With the development of modern finite element technology and motion simulation technology, the foundation of structural reliability analysis is greatly improved.
The reliability problem arises from the existence of a large number of uncertain factors in engineering, and the uncertainty existing in the objective world can be generally divided into two types: ambiguity uncertainty and random uncertainty. In the reliability design process, the uncertainty needs to be quantified and passed on to get the reliability of the system. Random uncertainty, also referred to as objective uncertainty, is generally modeled as a random variable that obeys a certain probability distribution with a sufficient amount of statistical information and can be conveyed on the basis thereof using well-developed random reliability theory. The fuzzy uncertainty is also called subjective uncertainty, and is variable generated due to lack of understanding of the system, and at this time, fuzzy theory can be applied to represent the variables by fuzzy membership functions, and there is no reliability analysis method based on the fuzzy theory, or even no reliability analysis method taking both random uncertainty and fuzzy uncertainty into account. Therefore, the accuracy of the analysis result obtained by analyzing the reliability of the joint bearing is low.
Based on the above disadvantages, the present invention provides a joint bearing reliability analysis method considering ambiguity uncertainty, which, as shown in fig. 2, may include the following steps:
step S210, establishing a function of the joint bearing with uncertainty represented by a random variable and a fuzzy variable;
step S220, solving a membership interval of the fuzzy variable under a preset membership level;
and step S230, calculating a reliability membership function and a maximum stress point stress mean value membership function of the joint bearing according to the random variable, the preset membership level, the membership interval and the function.
The method considers the random variable and the fuzzy variable while establishing the function, and simultaneously considers the fuzzy variable and the random variable to perform reliability analysis, compared with the prior art, the reliability analysis is performed from multiple aspects, the reliability of the joint bearing can be analyzed more comprehensively, and guidance can be provided for the subsequent optimization design of the joint bearing.
The following embodiments are provided to illustrate the embodiments of the present invention
In step S210, a function of the joint bearing is established that represents uncertainty with a random variable and a fuzzy variable;
for the joint bearing structure shown in fig. 1, in order to simplify the analysis, assuming that the strength limits of the inner and outer races of the bearing are all 1960Mpa, the problem is simplified to a single failure mode, and the function can be established as follows:
M＝σb-σ(Eout,Ein,Fr,Fa)
wherein the random variable Fr,FaThe radial load and the axial load of the bearing are respectively subjected, the radial load and the axial load are subjected to normal distribution and are independent of each other, and the distribution parameters are shown in table 1. Modulus of elasticity E of outer ring of joint bearingoutAnd inner ring elastic modulus EinAre fuzzy variables, and their membership functions are symmetric triangular distributions represented by:
and (5) solving a membership function of the structural reliability of the joint bearing and the stress mean value of the maximum stress point by trial.
TABLE 1 distribution parameters of basic random variables
Random variable radial load FrMay be 40kN, standard deviation 4, coefficient of variation 0.1, and obey a normal distribution.
The mean of the random variable F α may be 10kN, standard deviation 1, coefficient of variation 0.1, and follow a normal distribution.
In step S220, a membership interval of the fuzzy variable at a preset membership level is solved.
The fuzzy variable is expressed by a fuzzy membership function, and the variable quantity of the fuzzy variable is an interval for a certain membership level lambda
Wherein xF(λ) represents the value of the fuzzy variable given a membership level λ.
Let the reliability be PrWhich is a fuzzy variable xFA function of, i.e. Pr＝G(xF). Then P isrMay be represented by xFThe calculation formula of the membership function is as follows:
according to the energy theory, the occurrence energy of a certain event is equal to the maximum value of the occurrence energy of all sub-events of the event. The same applies to the transformation of membership functions. If xFAnd PrThere is a many-to-one relationship between them, then PrThe occurrence energy of is all corresponding xFA maximum of energy levels occurs. For example, based on equations
In transformation of (A), Pr0Corresponding in general to two argument values xF01And xF02Then Pr0The energy value of (a) is equal to the maximum energy value corresponding to the two arguments,
in the present exemplary embodiment, the fuzzy variable E corresponding to the membership level λ can be found from the inverse function of the fuzzy variable membership functionoutAnd EinIs subject to the interval, i.e.
In step S230, a reliability membership function and a maximum stress point stress mean membership function of the joint bearing are calculated according to the random variable, the preset membership level, the membership interval and the function.
In a first exemplary embodiment, a digital simulation method is adopted to calculate the reliability membership function and the maximum stress point stress mean value membership function of the joint bearing according to the random variable, the preset membership level, the membership interval and the function.
Firstly, determining a value range of a preset membership degree lambda, wherein the value range of the lambda can be [0,1 ]. A joint probability density function for the random variables is then determined.
For a given level of membership x,
probability of failure P of the structure at this timef(λ) can be obtained by the following formula:
wherein
Is a random variable xROf the joint probability density function, xRWhen the two parts are mutually independent,
as can be seen from the above section, the first,
when is, Pf(lambda) has a maximum value
And minimum value
By the Monte Carlo method according to
Extracting N random variable samples xRi(i ═ 1,2,. N), the following equation can be used to determine
And
wherein IF(. is) the failure field F ═ x: g (x)R,xF(λ)) ≦ 0+, and I when x ∈ FF(x) 1, otherwise IF(x)＝0。
After the upper and lower bounds of the failure probability under the given membership degree lambda are obtained, the upper bound of the reliability can be simply obtained by the following formula
And lower bound
The following were used:
the upper and lower bounds of reliability corresponding to different lambadas can be obtained by adopting the process
And
traversing the value interval [0,1] of lambda]The membership function of the fuzzy reliability can be obtained.
Although the majority theorem can ensure that the convergence solution of the Monte Carlo digital simulation method tends to the true value when the number of samples N is large, when random variables and fuzzy variables coexist, in order to obtain the membership functions of the reliability, the upper and lower bounds corresponding to the reliability on each membership level must be calculated, which causes the calculation amount to increase exponentially on the sampling times of the original random variables, so that the calculation efficiency of the Monte Carlo method is relatively low when the problem of the fuzzy random variables is solved.
In a second exemplary embodiment, the reliability membership function and the maximum stress point stress mean value membership function of the joint bearing are calculated based on a linear weighted response surface method according to the random variable, the preset membership level, the membership interval and the function.
Firstly, determining a value interval of preset membership degree lambda, wherein the value interval of lambda can be [0,1], and then calculating the maximum value and the minimum value of the stress mean value of the maximum stress point of the joint bearing and the maximum value and the minimum value of the reliability according to the preset membership level and the functional function based on a linear weighted response surface method; and finally, traversing the value range to obtain a reliability membership function and a maximum stress point stress mean value membership function.
Simulating a function of the joint bearing structure by using a linear weighted response surface method, wherein lambda is 0, Eout＝1.94×105,Ein＝2.12×105For example, the maximum stress point stress mean value of the joint bearing is the minimum value when the membership level is zero, and the structural reliability is the maximum value. Executing the response surface method program, iterating for three times to obtain a corresponding function as
The lower limit of the mean value of the maximum stress is 1819.4MPa by using the direct Monte Carlo simulation of the explicit function; the probability of failure is 0.1441, the upper limit of reliability is 0.8559. The design point is MPP ═ 42.2110.91 at this time, and corresponds to the magnitude of the radial load and the axial load, respectively, in kN.
And (3) obtaining an explicit function of the joint bearing in a reduced random variable space at a specific fuzzy variable value point by a response surface method at each membership level, and further obtaining the upper and lower limits of the reliability of the joint bearing at each membership level as shown in table 2:
TABLE 2 Upper and lower limits of reliability of joint bearing
| Membership level λ | Lower limit of reliability | Upper limit of |
| 0 | 0.7930 | 0.8559 |
| 0.1 | 0.7981 | 0.8533 |
| 0.2 | 0.8006 | 0.8497 |
| 0.3 | 0.8033 | 0.8476 |
| 0.4 | 0.8079 | 0.8448 |
| 0.5 | 0.8107 | 0.8423 |
| 0.6 | 0.8133 | 0.8380 |
| 0.7 | 0.8166 | 0.8364 |
| 0.8 | 0.8211 | 0.8334 |
| 0.9 | 0.8241 | 0.8288 |
| 1.0 | 0.8264 | 0.8264 |
The upper and lower limits of the mean value of the maximum stress of the joint bearing structure at each membership level are shown in table 3:
TABLE 3 Upper and lower limits of the mean value of the maximum stress of the oscillating bearing
As shown with reference to fig. 3 and 4, since the obtained explicit approximation of the first objective function is linear, the results obtained by the respective reliability analysis methods are consistent and are not listed here.
In a third exemplary embodiment, a quadratic weighted response without cross terms is usedSimulating the function of the joint bearing structure by the surface method, wherein lambda is 0, Eout＝1.94×105,Ein＝2.12×105For example, the maximum stress point stress mean value of the joint bearing is the minimum value when the membership level is zero, and the structural reliability is the maximum value. Executing a response surface method program, iterating for five times, and obtaining a corresponding function as follows:
the probability of failure obtained by the explicit function using the AFOSM method is 0.14695, and the reliability is 0.8530. The design point is MPP ═ 41.61010.969 at this time, and corresponds to the magnitude of the radial load and the axial load, respectively, in kN.
The explicit function of the joint bearing in the reduced random variable space is obtained at the specific fuzzy variable value point by the response surface method at each membership level, and the upper and lower limits of the reliability of the joint bearing at each membership level (the result obtained by the primary second moment method) are shown in table 4:
TABLE 4 Upper and lower limits of reliability of joint bearing
And traversing the interval of the lambda, namely taking a plurality of lambda values to complete the calculation of the upper and lower limits of the reliability.
Referring to fig. 3, 4 and 5, compared with the results obtained by the linear weighted response surface method, the reliability membership function curves obtained by the two methods are substantially consistent. However, for the membership function of the maximum stress mean value, the weighted nonlinear response surface method cannot obtain a correct result, and the analysis reason may be that the nonlinear degree of the joint bearing structure is too high, and the quadratic weighted response surface method without cross terms still cannot obtain an approximation of a response surface function with sufficient precision, so that the method is not discussed here, and a response surface method with higher precision can be used for solving, and a satisfactory result may be obtained.
Referring to fig. 6, in the second exemplary embodiment and the third exemplary embodiment, when the reliability membership function and the maximum stress point stress mean membership function of the joint bearing are calculated to have the same point, the method may include a step a10 of determining a preset membership level dereferencing device [0,1]Dividing the obtained product into m +1 parts, and setting i to be 1; step A20, run λ(i)(i-1)/m step a30, calculation
Step A40 assigns k a value of 1; step A51, taking
Step A52, taking
A61, obtaining a first target function or a second target function according to the value range, the fuzzy variable and the function by adopting a response surface method; a62, obtaining a first target function or a second target function according to the value range, the fuzzy variable and the function by adopting a response surface method; step A71, solving the lower limit and the upper limit of the reliability of the stress mean value of the maximum stress point according to the first objective function or the second objective function; and A72, solving the upper limit and the lower limit of the reliability of the stress mean value of the maximum stress point according to the first objective function or the second objective function. Step A80, judging whether i is equal to m +1, if yes, ending; if not, performing the step A90, and operating i to i + 1; and returns to step a 20.
The described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments, and the features discussed in connection with the embodiments are interchangeable, if possible. In the above description, numerous specific details are provided to give a thorough understanding of embodiments of the invention. One skilled in the relevant art will recognize, however, that the invention may be practiced without one or more of the specific details, or with other methods, components, materials, and so forth. In other instances, well-known structures, materials, or operations are not shown or described in detail to avoid obscuring aspects of the invention.
Although relative terms, such as "upper" and "lower," may be used in this specification to describe one element of an icon relative to another, these terms are used in this specification for convenience only, e.g., in accordance with the orientation of the examples described in the figures. It will be appreciated that if the device of the icon were turned upside down, the element described as "upper" would become the element "lower". Other relative terms, such as "high", "low", "top", "bottom", "front", "back", "left", "right", etc., are also intended to have similar meanings. When a structure is "on" another structure, it may mean that the structure is integrally formed with the other structure, or that the structure is "directly" disposed on the other structure, or that the structure is "indirectly" disposed on the other structure via another structure.
In this specification, the terms "a", "an", "the", "said" and "at least one" are used to indicate the presence of one or more elements/components/etc.; the terms "comprising," "including," and "having" are intended to be inclusive and mean that there may be additional elements/components/etc. other than the listed elements/components/etc.; the terms "first," "second," and the like are used merely as labels, and are not limiting on the number of their objects.
It is to be understood that the invention is not limited in its application to the details of construction and the arrangement of components set forth in the description. The invention is capable of other embodiments and of being practiced and carried out in various ways. The foregoing variations and modifications fall within the scope of the present invention. It will be understood that the invention disclosed and defined in this specification extends to all alternative combinations of two or more of the individual features mentioned or evident from the text and/or drawings. All of these different combinations constitute alternative aspects of the present invention. The embodiments described in this specification illustrate the best mode known for carrying out the invention and will enable those skilled in the art to utilize the invention.
Claims (10)
1. A joint bearing reliability analysis method considering fuzzy uncertainty is characterized by comprising the following steps:
establishing a function of the joint bearing with uncertainty represented by random variables and fuzzy variables;
solving a membership interval of the fuzzy variable under a preset membership level;
and calculating a reliability membership function and a maximum stress point stress mean value membership function of the joint bearing according to the random variable, the preset membership level, the membership interval and the function.
2. The method of claim 1, wherein calculating the reliability membership function and the stress mean membership function of the joint bearing according to the random variable, the preset membership level, the membership interval and the function comprises:
and calculating the reliability membership function of the joint bearing according to the random variable, the preset membership level, the membership interval and the functional function by adopting a digital simulation method.
3. The method for analyzing the reliability of the spherical plain bearing considering the fuzzy uncertainty as claimed in claim 2, wherein the step of calculating the reliability membership function of the spherical plain bearing according to the random variable, the preset membership level, the membership interval and the function by using a digital simulation method comprises the steps of:
determining a value interval of the preset membership level;
calculating the maximum value and the minimum value of the reliability according to the preset membership level by adopting a Monte Carlo digital simulation method;
and traversing the value range to obtain the reliability membership function.
4. The method of claim 3, wherein calculating the reliability and the maximum and minimum of reliability according to the pre-set membership level comprises:
determining a joint probability density function of the random variables;
calculating the maximum value and the minimum value of the failure probability according to the probability density function, the membership interval and the functional function by adopting a Monte Carlo digital simulation method;
and calculating the maximum value and the minimum value of the reliability according to the maximum value and the minimum value of the failure probability.
5. The method of claim 1, wherein calculating the reliability membership function and the stress mean membership function of the joint bearing according to the random variable, the preset membership level, the membership interval and the function comprises:
and calculating a reliability membership function and a maximum stress point stress mean value membership function of the joint bearing according to the random variable, the preset membership level, the membership interval and the functional function based on a linear weighted response surface method.
6. The method for analyzing the reliability of the spherical plain bearing considering the fuzzy uncertainty as claimed in claim 5, wherein the step of calculating the reliability and the membership function of the spherical plain bearing according to the preset membership level, the membership interval and the function based on a linear weighted response surface method comprises the steps of:
determining a value interval of the preset membership level;
calculating the maximum value and the minimum value of the stress mean value of the maximum stress point of the joint bearing and the maximum value and the minimum value of the reliability according to the preset membership level and the functional function based on a linear weighted response surface method;
and traversing the value range to obtain the reliability membership function and the maximum stress point stress mean value membership function.
7. The oscillating bearing reliability analysis method considering fuzzy uncertainty according to claim 6, characterized in that calculating the maximum and minimum values of the stress mean of the maximum stress point and the maximum and minimum values of the reliability of the oscillating bearing according to the preset membership level and the functional function comprises:
obtaining a first target function according to the value interval, the fuzzy variable and the function by adopting a linear weighted response surface method;
and solving the maximum value and the minimum value of the stress mean value of the maximum stress point and the maximum value and the minimum value of the reliability by adopting a Monte Carlo digital simulation method.
8. The method of claim 1, wherein calculating the reliability membership function and the stress mean membership function of the joint bearing according to the random variable, the preset membership level, the membership interval and the function comprises:
and calculating a reliability membership function and a maximum stress point stress mean value membership function of the joint bearing according to the random variable, the preset membership level, the membership interval and the functional function based on a weighted nonlinear response surface method.
9. The method of claim 8, wherein calculating the joint bearing reliability and membership function based on the weighted nonlinear response surface method according to the random variable, the preset membership level, the membership interval, and the function comprises:
determining a value interval of the preset membership level;
calculating the maximum value and the minimum value of the stress mean value of the maximum stress point of the joint bearing and the maximum value and the minimum value of the reliability according to the preset membership level and the functional function based on a nonlinear weighted response surface method;
and traversing the value range to obtain the reliability membership function and the maximum stress point stress mean value membership function.
10. The oscillating bearing reliability analysis method considering fuzzy uncertainty according to claim 9, characterized in that calculating the maximum and minimum values of the stress mean of the maximum stress point and the maximum and minimum values of the reliability of the oscillating bearing according to the preset membership level and the functional function comprises:
obtaining a second target function according to the value interval, the fuzzy variable and the function by adopting a nonlinear weighted response surface method;
and solving the maximum value and the minimum value of the stress mean value of the maximum stress point and the maximum value and the minimum value of the reliability by adopting a first secondary moment method.
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