CN115688311B - Uncertainty analysis method and system for planetary roller screw pair - Google Patents

Uncertainty analysis method and system for planetary roller screw pair Download PDF

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CN115688311B
CN115688311B CN202211339968.8A CN202211339968A CN115688311B CN 115688311 B CN115688311 B CN 115688311B CN 202211339968 A CN202211339968 A CN 202211339968A CN 115688311 B CN115688311 B CN 115688311B
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planetary roller
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CN115688311A (en
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姚琴
张猛创
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Suzhou University of Science and Technology
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Abstract

The invention discloses an uncertainty analysis method and system of a planetary roller screw pair, which are characterized in that a limit state function under a contact fatigue failure mode of a thread of the planetary roller screw pair is constructed, the limit state function is simplified, an expected risk learning function is introduced to construct an active learning agent model of the planetary roller screw pair, a Monte Carlo method is adopted to generate sampling sample points, the established active learning agent model is called to calculate a simplified limit state function corresponding to each group of sample points, and uncertainty analysis is carried out on the planetary roller screw pair to obtain failure probability and reliability sensitivity of the planetary roller screw pair under any working condition. The method can effectively reduce the times of calling the function in the limit state, reduce the calculation cost, improve the uncertainty analysis efficiency of the planetary roller screw pair, help a designer find out main factors influencing the structural reliability, and further lay a theoretical foundation for the design optimization of products.

Description

Uncertainty analysis method and system for planetary roller screw pair
Technical Field
The invention relates to the technical field of planetary roller screw precise thread transmission, in particular to an uncertainty analysis method and an uncertainty analysis system for a planetary roller screw pair.
Background
The planetary roller screw pair is one kind of precise screw driver and is used mainly as the executing mechanism of electromechanical actuator. Typically, a lead screw is coupled to a servo motor, a nut is coupled to a load, and a plurality of rollers are in planetary motion between the lead screw and the nut. The screw threads on the two sides of the roller are meshed with the screw rod and the nut at the same time, so that the rotary motion of the screw rod can be converted into linear thrust of the nut. The planetary roller screw pair has a large number of contact points and has no rolling body circulating device, so that the planetary roller screw pair has the advantages of high bearing capacity, good robustness, high speed, high acceleration and the like.
The uncertainty widely existing in the manufacturing, assembling, measuring and operating processes of the planetary roller screw pair can aggravate the degree of uneven load distribution, so that excessive contact stress can occur to threads even in the rated load range, and the same batch of products have different service lives under the same working condition. Therefore, the load distribution and contact characteristics of the multi-threaded pair considering uncertainty greatly affect the durability and reliability of the planetary roller screw pair.
Uncertainty analysis is often used as an evaluation criterion for measuring product quality and is considered as an essential part of the design process. However, a reasonable and effective uncertainty analysis model is still lacking at present to primarily evaluate the reliability of the planetary roller screw pair. The uncertainty analysis of the planetary roller screw pair is beneficial to a designer to find out main factors influencing the failure of the planetary roller screw pair before the material of the product is selected, so that measures for preventing or delaying the failure are provided, theoretical basis is provided for the design optimization of the planetary roller screw pair, and important theoretical significance and engineering application value are provided for realizing the development of the domestic high-performance planetary roller screw pair and improving the comprehensive performance of an electromechanical servo actuation system.
Disclosure of Invention
The invention aims to provide a reasonable and effective uncertainty analysis method for a planetary roller screw pair.
In order to solve the above problems, the present invention provides an uncertainty analysis method of a planetary roller screw pair, the uncertainty analysis method of the planetary roller screw pair comprising the steps of:
s1, solving the load distribution and the contact characteristic of the screw thread of the planetary roller screw pair through structural parameters, material properties and boundary conditions, and constructing a limit state function of the screw thread of the planetary roller screw pair in a contact fatigue failure mode based on an S-N curve and a stress-intensity interference theory by considering the structural parameters, the material properties and the uncertainty existing in the boundary conditions;
s2, introducing a deterministic low-deviation point set Halton sequence, analyzing sensitivity and contribution degree of uncertainty factors to the influence of the thread bearing capacity and the contact performance of the planetary roller screw pair by adopting a test design method, and taking parameters with the importance degree ranked forward as random variables to reduce the dimension of a limit state function so as to obtain a simplified limit state function;
s3, introducing a desired risk learning function to construct an active learning agent model of the planetary roller screw pair, generating sampling sample points by adopting a quasi-Monte Carlo method, calling the established active learning agent model to calculate a simplified limit state function corresponding to each group of sample points, and carrying out uncertainty analysis on the planetary roller screw pair to obtain failure probability and reliability sensitivity of the planetary roller screw pair under any working condition.
As a further improvement of the present invention, in step S1, the planetary roller screw pair thread load distribution and contact characteristics are solved by structural parameters, material properties and boundary conditions, including:
an iteration algorithm is adopted to solve a planetary roller screw pair thread load distribution model, and the method comprises the following steps:
Figure SMS_1
wherein P is S ,P R And P N Respectively the screw pitches of a screw rod, a roller and a nut, wherein tau is the number of threads of the roller which participate in contact, z is the number of the roller, the threads are numbered sequentially from the fixed end to the free end of the screw rod, i=1, 2, …, tau and F are axial external loads, and F is a load SRi For axial load applied to the ith pair of threads on the contact side of the roller with the screw, F NRi An axial load borne by the ith pair of threads on the contact side of the roller and the nut;
Figure SMS_2
for screw shaft section rigidity->
Figure SMS_3
For the rigidity of the roller axle segment->
Figure SMS_4
For the rigidity of the nut shaft section,/->
Figure SMS_5
For screw thread tooth rigidity +.>
Figure SMS_6
For the rigidity of the thread tooth of the roller>
Figure SMS_7
The rigidity of the thread teeth of the nut is the rigidity;
solving the contact stiffness of the screw rod and the roller as follows:
Figure SMS_8
wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure SMS_9
the contact rigidity of the screw rod and the roller is as follows; />
Figure SMS_10
Elastic contact deformation of the screw rod and the ith pair of thread teeth of the roller is realized;
solving the contact stiffness of the nut and the roller thread pair as follows:
Figure SMS_11
wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure SMS_12
for the contact stiffness of the nut and the roller thread pair, +. >
Figure SMS_13
Is the elastic contact deformation of the nut and the ith pair of thread teeth of the roller.
As a further improvement of the invention, the elastic contact deformation of the screw and the ith pair of threads of the roller
Figure SMS_14
The calculation formula of (2) is as follows:
Figure SMS_15
Figure SMS_16
wherein K (e) and L (e) are the complete elliptic integrals of the first and second types, a is the long half-axis of the contact ellipse, b is the short half-axis of the contact ellipse,
Figure SMS_17
to contact the eccentricity, k of ellipse e ＝b/a，
Figure SMS_18
For equivalent elastic modulus, E S And v S For the elastic modulus and poisson ratio of the screw, E R And v R For the modulus of elasticity and poisson's ratio of the roller, +.>
Figure SMS_19
And lambda is the contact angle and the helix angle of the roller.
As a further improvement of the invention, a limit state function under the contact fatigue failure mode of the screw thread of the planetary roller screw pair is constructed based on an S-N curve and a stress-intensity interference theory, and is as follows:
Figure SMS_20
Figure SMS_21
Figure SMS_22
wherein x= (x) 1 ,x 2 ,…x i …,x n ) To influence the random variables of the limit state function, x i For the ith random variable, n is the number of random variables, sigma Hlim Sigma for contact fatigue limit SRi For the contact stress on the ith pair of threads of the screw rod and the roller,
Figure SMS_23
for maximum contact stress, sigma, between the roller and all the threads on the contact side of the screw NRi For the contact stress on the nut and roller ith pair of threads, +.>
Figure SMS_24
For maximum contact between the roller and all the threads on the contact side of the nut Stress; f (F) SRi For axial load applied to the ith pair of threads on the contact side of the roller with the screw, F NRi An axial load borne by the ith pair of threads on the contact side of the roller and the nut; a is the major half axis of the contact ellipse, b is the minor half axis of the contact ellipse, +.>
Figure SMS_25
And lambda is the contact angle and the helix angle of the roller.
As a further improvement of the present invention, step S2 includes:
s21, for each random variable x of the planetary roller screw pair i At [0,1]Is generated in the interval of (a) and the input parameter matrix is obtained from the Halton sequence as X= (X) 1 ,x 2 ,…,x i ,…,x n ) Wherein x is i ＝(x i1 ,x i2 ,…,x ij ,…,x iN ) T Is x i Is a sample vector of (a);
s22, the response quantity comprises: maximum load distribution coefficient of both contact sides of the roller:
Figure SMS_26
maximum contact stress
Figure SMS_27
And localized contact stress sigma on the thread pair SRi ,σ NRi The response matrix is obtained through calculation as follows: y= (Y) 1 ,y 2 ,…,y k ,…,y m ) Wherein y is k ＝(y k1 ,y k2 ,…,y kj ,…,y kN ) T For the kth response y k Is a sample vector of (a);
s23, the data in the matrix X and the matrix Y are within [ -1,1]Normalization was performed in range, and the data were fitted using the polynomial response surface method:
Figure SMS_28
s24, adding polynomial coefficients
Figure SMS_29
In percentFormally, the influence degree of each input parameter on the kth response quantity can be reflected;
s25, selecting a parameter with the front importance degree sequence to reduce the dimension of the random variable, and obtaining a simplified limit state function of the planetary roller screw pair. Optionally, the top five parameters are selected.
As a further improvement of the present invention, step S3 includes:
s31, randomly generating N in the uncertainty domain 0 The method comprises the steps of (1) calculating a simplified limit state function value by 20 samples, introducing a desired risk learning function to construct an active learning agent model of a planetary roller screw pair, and firstly constructing an initial agent model as follows:
Figure SMS_30
Figure SMS_31
u＝F T R -1 r-f(x)
wherein y= [ g (x) 1 ),g(x 2 ),…,g(x n )] T For a true response function with n sample points, f (x) = [ f 1 (x),f 2 (x),…f i (x),…,f p (x)] T As a regression polynomial basis function vector, beta= [ beta ] 1 ,β 2 ,…β i ,…,β p ] T For regression coefficient vector, p is the number of regression polynomials, r is the correlation vector function between the point to be measured and the sample point, and F= [ F (x 1 ) T ,f(x 2 ) T ,…,f(x n ) T ] T For an n x p order expansion matrix, R is an n x n order symmetric positive correlation matrix,
Figure SMS_32
estimated value of approximate limit state function g (x), for>
Figure SMS_33
Is->
Figure SMS_34
The variance of g (x) is calculated as follows:
Figure SMS_35
wherein z (x) is a variable which is subject to N (0, sigma) 2 ) A normal distributed random process, the covariance between any two sample points w and x is:
cov[z(w),z(x)]＝σ 2 R(θ,w,x)
wherein θ= [ θ ] 1 ,θ 2 ,…,θ n ] T For the correlation parameter, R (θ, w, x) is a function representing the correlation of the variables θ, w, x and can be described as a continuously differentiable gaussian correlation function:
Figure SMS_36
wherein the regression coefficient beta and variance sigma 2 The generalized least squares regression method can be expressed as:
β＝(F T R -1 F) -1 F T R -1 Y
Figure SMS_37
S32, generating N in uncertainty domain c ＝10 5 Candidate samples;
s33, calculating N according to the initial proxy model c Estimated value of each sample point
Figure SMS_38
And an estimate of expected risk
Figure SMS_39
Taking the point with the maximum ERF value as a training point x #,/>
Figure SMS_40
Calculation methodThe following are provided:
Figure SMS_41
wherein sign (x) is a sign function, when x > 0, sign (x) = 1, when x < 0, sign (x) = -1, Φ () is a probability density function of a standard normal distribution, and ψ () is a cumulative distribution function of the standard normal distribution;
s34, setting a threshold or convergence condition as epsilon=10 -5 The method comprises the steps of carrying out a first treatment on the surface of the If max (ERF)>Epsilon, adding x as a new training point, and updating an active learning agent model of the planetary roller screw pair;
s35, repeating the steps S33-S35 until max (ERF) is less than or equal to epsilon;
s36, utilizing the updated star roller screw pair active learning agent model, generating sampling sample points by adopting a pseudo Monte Carlo method, calling the established active learning agent model to calculate a simplified limit state function corresponding to each group of sample points, and carrying out uncertainty analysis on the star roller screw pair to obtain failure probability and reliability sensitivity of the star roller screw pair under any working condition.
As a further improvement of the invention, the adoption of the pseudo Monte Carlo method to generate sampling sample points, the call of the established active learning agent model to calculate the simplified limit state function corresponding to each group of sample points, and the uncertainty analysis of the planetary roller screw pair to obtain the failure probability and the reliability sensitivity of the planetary roller screw pair under any working condition comprises the following steps:
S361, for each random variable xi of the planetary roller screw pair, is 0,1]Generates a halon sequence in the interval of (a), the variables are independent of each other and are all normally distributed, and the cumulative probability distribution function F (x) ij ) Can be expressed as:
Figure SMS_42
wherein x is ij The jth sample value, f (x i ) As a random variable x i N is the number of samples,
Figure SMS_43
is the x th ij Corresponding Halton numbers, wherein the specific generation process of the Halton sequence is as follows:
if q is any prime number, then any natural number j has a unique q-ary expression:
j＝j 0 +j 1 q+j 2 q 2 +···+j K q K
Figure SMS_44
j i ∈{0,1,···,q-1}；i＝0,1,···,K
where K represents the integer portion of lnj/lnq, and the base inverse function, with q as the base, is defined as:
Figure SMS_45
for any natural number j > 0, it satisfies
Figure SMS_46
If the first n prime numbers are q 1 ,q 2 ,…,q n The n-dimensional halon sequence can be expressed as:
Figure SMS_47
s362, obtaining random variable x ij Is a sample value of (2)
Figure SMS_48
S363, sample point for obtaining allowable contact stress
Figure SMS_49
S364, calculating the sample x of each group of random vectors j ＝(x 1j ,x 2j ,…,x nj ) T The load distribution and the local contact characteristics under action, the maximum contact stress on the contact side of the roller with the screw or nut is obtained, and then the limit state function g (x j ) If g (x j ) Less than or equal to 0, a status indication function I F (x j ) =1, otherwise I F (x j )＝0；
S365, failure probability
Figure SMS_50
Is a function of the estimation of (1) and its coefficient of variation- >
Figure SMS_51
The calculation is as follows:
Figure SMS_52
Figure SMS_53
wherein N is f Is the number of failed samples;
s366, the estimated value of reliability sensitivity is as follows:
Figure SMS_54
wherein f x (x) As a joint probability density function of random variables,
Figure SMS_55
as a substantially random variable x i The kth distribution parameter, m i As the ith random variable x i Is a normal distribution random variable with mean +.>
Figure SMS_56
And standard deviation
Figure SMS_57
The reliability sensitivity can be calculated as two distribution parameters:
Figure SMS_58
the present invention also provides a computer-readable storage medium including a stored program, wherein the program executes the uncertainty analysis method of the planetary roller screw pair described in any one of the above.
The invention also provides an electronic device, comprising: one or more processors, a memory, and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, the one or more programs comprising an uncertainty analysis method for performing the planetary roller screw pair of any of the above.
The invention also provides an uncertainty analysis system of the planetary roller screw pair, which comprises the following modules:
The limit state function construction module is used for solving the load distribution and the contact characteristic of the screw thread of the planetary roller screw pair through the structural parameters, the material performance and the boundary conditions, considering the uncertainty existing in the structural parameters, the material performance and the boundary conditions, and constructing a limit state function of the screw thread of the planetary roller screw pair in a contact fatigue failure mode based on the S-N curve and the stress-intensity interference theory;
the limit state function simplifying module is used for introducing a deterministic low-deviation point set Halton sequence, analyzing sensitivity and contribution degree of uncertainty factors to the influence of the thread bearing capacity and the contact performance of the planetary roller screw pair by adopting a test design method, and reducing the dimension of the limit state function by taking the parameter with the forward importance degree sequence as a random variable to obtain a simplified limit state function;
the uncertainty analysis module is used for introducing a desired risk learning function to construct an active learning agent model of the planetary roller screw pair, adopting a quasi-Monte Carlo method to generate sampling sample points, calling the established active learning agent model to calculate a simplified limit state function corresponding to each group of sample points, and carrying out uncertainty analysis on the planetary roller screw pair to obtain the failure probability and reliability sensitivity of the planetary roller screw pair under any working condition.
The invention has the beneficial effects that:
according to the invention, the limit state function is simplified by constructing the limit state function under the contact fatigue failure mode of the thread teeth of the planetary roller screw pair, the expected risk learning function is introduced to construct the planetary roller screw pair active learning agent model, the sample points are generated by adopting the quasi-Monte Carlo method, the simplified limit state function corresponding to each group of sample points is calculated by calling the established active learning agent model, and the uncertainty analysis is carried out on the planetary roller screw pair, so that the failure probability and the reliability sensitivity of the planetary roller screw pair under any working condition are obtained. The method can effectively reduce the times of calling the function in the limit state, reduce the calculation cost, improve the uncertainty analysis efficiency of the planetary roller screw pair, help a designer find out main factors influencing the structural reliability, and further lay a theoretical foundation for the design optimization of products.
The foregoing description is only an overview of the present invention, and is intended to be implemented in accordance with the teachings of the present invention, as well as the preferred embodiments thereof, together with the following detailed description of the invention, given by way of illustration only, together with the accompanying drawings.
Drawings
FIG. 1 is an overall flow chart of a method of uncertainty analysis of a planetary roller screw pair in an embodiment of the present invention;
FIG. 2 is a schematic diagram of a planetary roller screw pair in an embodiment of the present invention;
FIG. 3 is a computational flow chart of a method of uncertainty analysis of a planetary roller screw pair in an embodiment of the present invention;
FIG. 4 is a chart showing the importance of uncertainty factors to the load bearing characteristics and contact performance of a planetary roller screw pair in an embodiment of the present invention;
FIG. 5 is a graph comparing convergence speed and calculation time of estimating failure probability of a planetary roller screw pair by using a Monte Carlo method and a quasi Monte Carlo method in an embodiment of the invention;
FIG. 6 is a three-dimensional mesh surface graph of a limit state function of a planetary roller screw pair in an embodiment of the invention;
FIG. 7 is a three-dimensional mesh surface diagram of a limit state function of a planetary roller screw pair under different working conditions in an embodiment of the invention.
Marking: 1. a screw rod; 2. a roller; 3. a nut; 4. an inner gear ring; 5. a planet carrier; 6. and (5) a circlip.
Detailed Description
The present invention will be further described with reference to the accompanying drawings and specific examples, which are not intended to be limiting, so that those skilled in the art will better understand the invention and practice it.
As shown in fig. 1, the method for analyzing the uncertainty of the planetary roller screw pair in the preferred embodiment of the present invention comprises the following steps:
step S1, solving the load distribution and the contact characteristic of the screw thread of the planetary roller screw pair through structural parameters, material properties and boundary conditions, and constructing a limit state function of the screw thread of the planetary roller screw pair in a contact fatigue failure mode based on an S-N curve and a stress-intensity interference theory by considering the structural parameters, the material properties and the uncertainty existing in the boundary conditions;
as shown in fig. 2, a common planetary roller screw pair structure includes: a screw 1, a nut 3, a plurality of rollers 2, a pair of planet carriers 5, a pair of ring gears 4, a pair of circlips 6, etc.;
the inner gear ring 4 is arranged at two ends of the nut 3, the planet carrier 5 is arranged in the inner gear ring 4, the plurality of rollers 2 are uniformly distributed between the screw rod 1 and the nut 3 through the planet carrier 5, the two ends of each roller 2 are provided with straight teeth which are respectively meshed with the inner gear ring 4, the screw rod 1 is a multi-head trapezoid external thread, the nut 3 is a multi-head trapezoid internal thread, the screw rod 1 and the nut 3 have the same thread head number, each roller 2 is a single-head external thread, the tooth profile of each roller is arc-shaped, the circle center of each roller is positioned on the axis of each roller, the screw rod 1 and the nut 3 are respectively contacted with thread teeth at two sides of each roller 2 to jointly participate in bearing, the axes of each roller 2, each screw rod 1 and the nut 3 are parallel, each roller 2 rotates around the axis of each screw rod 1, each roller 2 and the nut 3 keep the same speed to axially displace, and the nut 3 does not have circular motion.
In one embodiment, the step S1 specifically includes:
an iteration algorithm is adopted to solve a planetary roller screw pair thread load distribution model, and the method comprises the following steps:
Figure SMS_59
wherein P is S ,P R And P N Respectively the screw pitches of a screw rod, a roller and a nut, wherein tau is the number of threads of the roller which participate in contact, z is the number of the roller, the threads are numbered sequentially from the fixed end to the free end of the screw rod, i=1, 2, …, tau and F are axial external loads, and F is a load SRi For axial load applied to the ith pair of threads on the contact side of the roller with the screw, F NRi An axial load borne by the ith pair of threads on the contact side of the roller and the nut;
Figure SMS_60
for screw shaft section rigidity->
Figure SMS_61
For the rigidity of the roller axle segment->
Figure SMS_62
For the rigidity of the nut shaft section,/->
Figure SMS_63
For screw thread tooth rigidity +.>
Figure SMS_64
For the rigidity of the thread tooth of the roller>
Figure SMS_65
The rigidity of the thread teeth of the nut is the rigidity;
Figure SMS_66
for screw shaft section rigidity->
Figure SMS_67
For the stiffness of the roller shaft segment,
Figure SMS_68
for the rigidity of the nut shaft section E S ,E R And E is N Elastic modulus of materials of screw rod, roller and nut respectively, A S , A R And A N The smallest cross-sectional areas of the screw, roller and nut, respectively.
Figure SMS_69
For screw thread tooth rigidity +.>
Figure SMS_70
For the deformation of the ith thread of the screw, including bending deformation +>
Figure SMS_71
Shear deformation->
Figure SMS_72
Root of tooth oblique deformation->
Figure SMS_73
Root shear deformation->
Figure SMS_74
And radial contraction deformation- >
Figure SMS_75
The specific calculation is as follows:
Figure SMS_76
wherein v is S ,h S ,β S ,d S ,
Figure SMS_77
And c S Respectively representing the poisson ratio, the thread tooth thickness, the tooth flank angle, the thread pitch diameter, the thread root width and the thread top width of the screw rod.
Figure SMS_78
For the rigidity of the thread of the roller, on the side contacting the threaded spindle, < > on>
Figure SMS_79
For the deformation of the ith thread of the roller, including bending deformation +>
Figure SMS_80
Shear deformation->
Figure SMS_81
Root of tooth oblique deformation->
Figure SMS_82
Root shear deformation->
Figure SMS_83
And radial contraction deformation->
Figure SMS_84
The specific calculation is as follows:
Figure SMS_85
wherein v is R ,h R ,β R ,d R ,
Figure SMS_86
And c R Respectively representing the Poisson's ratio, thread tooth thickness, tooth flank angle, thread pitch diameter, thread root width and thread crest width of the roller. On the contact side of the roller and the nut, the method for calculating the rigidity of the thread teeth of the roller is the same, and only the F is needed SRi Change to F NRi 。
Figure SMS_87
For the rigidity of the thread teeth of the nut,/>
Figure SMS_88
for the deformation of the ith thread of the nut, including bending deformation +>
Figure SMS_89
Shear deformation->
Figure SMS_90
Root of tooth oblique deformation->
Figure SMS_91
Root shear deformation->
Figure SMS_92
And radial expansion deformation->
Figure SMS_93
The specific calculation is as follows:
Figure SMS_94
wherein v is N ,h N ,β N ,d N ,
Figure SMS_95
And c N Respectively representing the Poisson's ratio, the thread tooth thickness, the tooth flank angle, the thread pitch diameter, the thread root width and the thread top width of the nut.
The following calculations were performed:
Figure SMS_96
for the contact stiffness of the screw with the roller, +.>
Figure SMS_97
The elastic contact deformation of the screw rod and the ith pair of thread teeth of the roller is specifically calculated as follows:
Figure SMS_98
Figure SMS_99
wherein K (e) and L (e) are the complete elliptic integrals of the first and second types, a is the long half-axis of the contact ellipse, b is the short half-axis of the contact ellipse,
Figure SMS_100
To contact the eccentricity, k of ellipse e ＝b/a，
Figure SMS_101
For equivalent elastic modulus, E S And v S For the elastic modulus and poisson ratio of the screw, E R And v R For the modulus of elasticity and poisson's ratio of the roller, +.>
Figure SMS_102
And lambda is the contact angle and the helix angle of the roller.
Figure SMS_103
For the contact stiffness of the nut and the roller thread pair, +.>
Figure SMS_104
Elastic contact deformation of the nut and the ith pair of thread teeth of the roller, and +.>
Figure SMS_105
The calculation method is the same and will not be described in detail here.
Based on an S-N curve and a stress-intensity interference theory, constructing a limit state function under a contact fatigue failure mode of a planetary roller screw pair thread, wherein the limit state function is as follows:
Figure SMS_106
/>
Figure SMS_107
Figure SMS_108
wherein x= (x) 1 ,x 2 ,…x i …,x n ) To influence the random variables of the limit state function, x i For the ith random variable, n is the number of random variables, sigma Hlim Sigma for contact fatigue limit SRi For the contact stress on the ith pair of threads of the screw rod and the roller,
Figure SMS_109
for maximum contact stress, sigma, between the roller and all the threads on the contact side of the screw NRi For the contact stress on the nut and roller ith pair of threads, +.>
Figure SMS_110
Is the maximum contact stress between the roller and all the threads on the contact side of the nut.
S2, introducing a deterministic low-deviation point set Halton sequence, analyzing sensitivity and contribution degree of uncertainty factors to the influence of the thread bearing capacity and the contact performance of the planetary roller screw pair by adopting a test design method, and reducing the dimension of a limit state function by taking a parameter with the front importance degree as a random variable to obtain a simplified limit state function;
In one embodiment, the step S2 specifically includes:
step S21, for each random variable x of the planetary roller screw pair i At [0,1]Is generated in the interval of (a) and the input parameter matrix is obtained from the Halton sequence as X= (X) 1 ,x 2 ,…,x i ,…,x n ) Wherein x is i ＝(x i1 ,x i2 ,…,x ij ,…,x iN ) T Is x i Is a sample vector of (a);
step S22, the response quantity comprises the following steps: maximum load distribution coefficient of both contact sides of the roller:
Figure SMS_111
maximum contact stress
Figure SMS_112
And localized contact stress sigma on the thread pair SRi ,σ NRi The response matrix is obtained through calculation as follows: y= (Y) 1 ,y 2 ,…,y k ,…,y m ) Wherein y is k ＝(y k1 ,y k2 ,…,y kj ,…,y kN ) T For the kth response y k Is a sample vector of (a);
step S23, data in the matrix X and Y are in [ -1,1]Normalization was performed in range, and the data were fitted using the polynomial response surface method:
Figure SMS_113
step S24, polynomial coefficients are obtained
Figure SMS_114
Expressed in terms of a percentage, the extent to which each input parameter affects the kth response may be reflected;
and S25, selecting a parameter with the front importance degree sequence to reduce the dimension of the random variable, and obtaining a simplified limit state function of the planetary roller screw pair.
S3, introducing a desired risk learning function to construct a planetary roller screw pair active learning Kriging (active learning Kriging, ALK) proxy model, generating sampling sample points by adopting a Quasi-Monte Carlo method (QMC), calling the established active learning proxy model to calculate a simplified limit state function corresponding to each group of sample points, and carrying out uncertainty analysis on the planetary roller screw pair to obtain failure probability and reliability sensitivity of the planetary roller screw pair under any working condition.
Referring to fig. 3, in one embodiment, step S3 specifically includes:
s31, randomly generating N in the uncertainty domain 0 The method comprises the steps of (1) calculating a simplified limit state function value by 20 samples, introducing a desired risk learning function to construct an active learning agent model of a planetary roller screw pair, and firstly constructing an initial agent model as follows:
Figure SMS_115
/>
Figure SMS_116
u＝F T R -1 r-f(x)
wherein y= [ g (x) 1 ),g(x 2 ),…,g(x n )] T For a true response function with n sample points, f (x) = [ f 1 (x),f 2 (x),…f i (x),…,f p (x)] T As a regression polynomial basis function vector, beta= [ beta ] 1 ,β 2 ,…β i ,…,β p ] T For regression coefficient vector, p is the number of regression polynomials, r is the correlation vector function between the point to be measured and the sample point, and F= [ F (x 1 ) T ,f(x 2 ) T ,…,f(x n ) T ] T For an n x p order expansion matrix, R is an n x n order symmetric positive correlation matrix,
Figure SMS_117
estimated value of approximate limit state function g (x), for>
Figure SMS_118
Is->
Figure SMS_119
The variance of g (x) is calculated as follows:
Figure SMS_120
wherein z (x) is a variable which is subject to N (0, sigma) 2 ) A normal distributed random process, the covariance between any two sample points w and x is:
cov[z(w),z(x)]＝σ 2 R(θ,w,x)
wherein θ= [ θ ] 1 ,θ 2 ,…,θ n ] T R (θ, w, x) is a correlation parameter representing the correlation of the variables θ, w, xThe function and can be described as a continuously differentiable gaussian correlation function:
Figure SMS_121
wherein the regression coefficient beta and variance sigma 2 The generalized least squares regression method can be expressed as:
β＝(F T R -1 F) -1 F T R -1 Y
Figure SMS_122
S32, generating N in uncertainty domain c ＝10 5 Candidate samples;
s33, calculating N according to the initial star roller screw pair active learning agent model c Estimated value of each sample point
Figure SMS_123
And estimate of the desired risk ∈ ->
Figure SMS_124
Taking the point with the maximum ERF value as a training point x #,/>
Figure SMS_125
The calculation method comprises the following steps:
Figure SMS_126
wherein sign (x) is a sign function, when x > 0, sign (x) = 1, when x < 0, sign (x) = -1, Φ () is a probability density function of a standard normal distribution, and ψ () is a cumulative distribution function of the standard normal distribution;
s34, setting a threshold or convergence condition as epsilon=10 -5 The method comprises the steps of carrying out a first treatment on the surface of the If max (ERF)>Epsilon, adding x as a new training point, and updating an active learning agent model of the planetary roller screw pair;
s35, repeating the steps S33-S35 until max (ERF) is less than or equal to epsilon;
s36, utilizing the updated star roller screw pair active learning agent model, generating sampling sample points by adopting a pseudo Monte Carlo method, calling the established active learning agent model to calculate a simplified limit state function corresponding to each group of sample points, and carrying out uncertainty analysis on the star roller screw pair to obtain failure probability and reliability sensitivity of the star roller screw pair under any working condition.
The method for generating sampling sample points by adopting the quasi-Monte Carlo method, calling the established active learning agent model to calculate the simplified limit state function corresponding to each group of sample points, and carrying out uncertainty analysis on the planetary roller screw pair to obtain the failure probability and reliability sensitivity of the planetary roller screw pair under any working condition, comprises the following steps:
Step S361, for each random variable xi of the planetary roller screw pair, is set to [0,1 ]]Generates a Halton sequence in the interval of (a) and the variables are independent of each other and are all normally distributed, and the cumulative probability distribution function F (x ij ) Can be expressed as:
Figure SMS_127
wherein x is ij The jth sample value, f (x i ) As a random variable x i N is the number of samples,
Figure SMS_128
is the x th ij Corresponding Halton numbers, wherein the specific generation process of the Halton sequence is as follows:
if q is any prime number, then any natural number j has a unique q-ary expression:
j＝j 0 +j 1 q+j 2 q 2 +···+j K q K
Figure SMS_129
j i ∈{0,1,···,q-1}；i＝0,1,···,K
where K represents the integer portion of lnj/lnq, and the base inverse function, with q as the base, is defined as:
Figure SMS_130
for any natural number j > 0, it satisfies
Figure SMS_131
If the first n prime numbers are q 1 ,q 2 ,…,q n The n-dimensional halon sequence can be expressed as:
Figure SMS_132
step S362, obtaining random variable x ij Is a sample value of (2)
Figure SMS_133
Step S363, obtaining sample points of allowable contact stress
Figure SMS_134
Step S364, calculating samples x of each set of random vectors j ＝(x 1j ,x 2j ,…,x nj ) T The load distribution and the local contact characteristics under action, the maximum contact stress on the contact side of the roller with the screw or nut is obtained, and then the limit state function g (x j ) If g (x j ) Less than or equal to 0, a status indication function I F (x j ) =1, otherwise I F (x j )＝0；
Step S365, failure probability
Figure SMS_135
Is a function of the estimation of (1) and its coefficient of variation->
Figure SMS_136
The calculation is as follows:
Figure SMS_137
Figure SMS_138
wherein N is f Is the number of failed samples;
step S366, the estimated value of reliability sensitivity is as follows:
Figure SMS_139
wherein f x (x) As a joint probability density function of random variables,
Figure SMS_140
as a substantially random variable x i The kth distribution parameter, m i As the ith random variable x i Is a normal distribution random variable with mean +.>
Figure SMS_141
And standard deviation->
Figure SMS_142
The reliability sensitivity can be calculated as two distribution parameters:
Figure SMS_143
according to the random structural parameters of the planetary roller screw pair given in table 1, 2000 groups of sample points obtained in the flow shown in fig. 3 are analyzed by adopting a test design method, and the importance degree ordering of the obtained uncertainty factors on the bearing characteristics and the contact performance of the planetary roller screw pair is shown in fig. 4. Wherein the pitch has the greatest effect on the maximum contact stress and the maximum load distribution coefficient in all thread pairs, and the half angle and pitch diameter of the thread teeth of the roller have the greatest effect on the contact stress of a single pair of thread pairs. Taking the first five important parameters P S ,P R ,P N ,β R And d R Used for constructing the active learning Kriging proxy model in step S3.
Table 1 random structural parameters of planetary roller screw pair
Figure SMS_144
/>
Figure SMS_145
The calculation flow shown in fig. 3 is adopted, and the obtained estimated value of the failure probability of the planetary roller screw pair is compared with the convergence speed and the calculation time consumption of the Monte Carlo method, such as shown in fig. 5. The result shows that the calculated result by adopting the pseudo-Monte Carlo method has good robustness, high convergence rate and high calculation efficiency. Comparison uses 5X 10 6 Subsampled Monte Carlo method, 10 5 The results of the subsampled quasi-Monte Carlo method and the planetary roller screw pair uncertainty analysis performed by the method of the present invention are shown in Table 3. Wherein Table 3 lists only P R And P S Since the reliability sensitivity of the remaining parameters is small.
Table 3 comparison of uncertainty analysis calculations
Figure SMS_146
Figure SMS_147
/>
Obviously, the relative error of the failure probability and the reliability sensitivity obtained by the quasi-Monte Carlo method and the Monte Carlo method is less than 1 percent. Therefore, under the condition of fewer simulation times, the precision of the quasi-Monte Carlo method can be ensured, and the calculation time is effectively reduced. The ALK-QMC method can obviously reduce the times of limit state function call, and further save the calculation cost. In addition, the ALK-QMC method has a relative error of 3.53% compared to the failure probability obtained by the monte carlo method with an increase of 6 training calls. Because the ALK-QMC method has five random variables after simplifying the limit state function, the obtained reliability and sensitivity are relatively large in error, but the result can still be used for effectively exploring the main factors influencing the reliability.
Fig. 6 is a three-dimensional mesh surface plot of a planetary roller screw pair limit state function from 1600 halon sample points showing the relationship between the pitch and reliability of the most dominant influencing parameter.
Referring to fig. 6, in the (a) diagram, a gray curved surface represents a limit state function g (x) =0, which is an interface between a security domain and a failure domain. The intersection line of the gray plane and the grid curved surface is represented by red, and the black point and the red point are respectively a safety sample point and a failure sample point. In (b), the roller-to-nut contact side has no failure point. In addition, at P R >P S And P R >P N The presence of the ridge structure areas that maximize g (x) on the mesh surface, suggests that higher reliability can be achieved by optimization, while increasing the probability of failure away from the ridge areas.
A three-dimensional grid curved surface diagram of the pitch and limit state function under different working conditions is shown in FIG. 7. Contact fatigue limit sigma when external load F is unchanged Hlim The larger the failure sample point, the fewer; when sigma is Hlim When the working condition is unchanged, the failure probability can be reduced by reducing F, for example, no failure point exists under the working condition of 20 kN. Therefore, the material with higher contact fatigue limit is selected, or the structural design of the planetary roller screw pair is optimized, so that the value of g (x) is maximized when the working condition is unchanged, and the reliability of the planetary roller screw pair can be improved.
The preferred embodiment of the present invention also discloses a computer-readable storage medium comprising a stored program, wherein the program executes the method for analyzing the uncertainty of the planetary roller screw pair according to the above embodiment.
The preferred embodiment of the invention also discloses an electronic device, which comprises: the device comprises one or more processors, a memory and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, and the one or more programs comprise an uncertainty analysis method for executing the planetary roller screw pair described in the embodiment.
The preferred embodiment of the invention also discloses an uncertainty analysis system of the planetary roller screw pair, which comprises the following modules:
the limit state function construction module is used for solving the load distribution and the contact characteristic of the screw thread of the planetary roller screw pair through the structural parameters, the material performance and the boundary conditions, considering the uncertainty existing in the structural parameters, the material performance and the boundary conditions, and constructing a limit state function of the screw thread of the planetary roller screw pair in a contact fatigue failure mode based on the S-N curve and the stress-intensity interference theory;
the limit state function simplifying module is used for introducing a deterministic low-deviation point set Halton sequence, analyzing sensitivity and contribution degree of uncertainty factors to the influence of the thread bearing capacity and the contact performance of the planetary roller screw pair by adopting a test design method, and reducing the dimension of the limit state function by taking the parameter with the forward importance degree sequence as a random variable to obtain a simplified limit state function;
The uncertainty analysis module is used for introducing a desired risk learning function to construct an active learning agent model of the planetary roller screw pair, adopting a quasi-Monte Carlo method to generate sampling sample points, calling the established active learning agent model to calculate a simplified limit state function corresponding to each group of sample points, and carrying out uncertainty analysis on the planetary roller screw pair to obtain the failure probability and reliability sensitivity of the planetary roller screw pair under any working condition.
The uncertainty analysis system of the planetary roller screw pair in the embodiment of the invention is used for realizing the uncertainty analysis method of the planetary roller screw pair, so that the specific implementation of the system can be seen from the embodiment part of the uncertainty analysis method of the planetary roller screw pair in the foregoing, and therefore, the specific implementation of the system can be referred to the description of the corresponding various part embodiments, and is not further described herein.
In addition, since the uncertainty analysis system of the planetary roller screw pair of the present embodiment is used to implement the uncertainty analysis method of the planetary roller screw pair, the function thereof corresponds to the function of the above method, and the description thereof will not be repeated here.
The above embodiments are merely preferred embodiments for fully explaining the present invention, and the scope of the present invention is not limited thereto. Equivalent substitutions and modifications will occur to those skilled in the art based on the present invention, and are intended to be within the scope of the present invention. The protection scope of the invention is subject to the claims.

Claims (9)

1. The uncertainty analysis method of the planetary roller screw pair is characterized by comprising the following steps of:
s1, solving the load distribution and the contact characteristic of the screw thread of the planetary roller screw pair through structural parameters, material properties and boundary conditions, and constructing a limit state function of the screw thread of the planetary roller screw pair in a contact fatigue failure mode based on an S-N curve and a stress-intensity interference theory by considering the structural parameters, the material properties and the uncertainty existing in the boundary conditions;
in step S1, the load distribution and contact characteristics of the screw thread of the planetary roller screw pair are solved by the structural parameters, the material properties and the boundary conditions, including:
an iteration algorithm is adopted to solve a planetary roller screw pair thread load distribution model, and the method comprises the following steps:
Figure FDA0004229832850000011
wherein P is S ,P R And P N Respectively the screw pitches of a screw rod, a roller and a nut, wherein tau is the number of threads of the roller which participate in contact, z is the number of the roller, the threads are numbered sequentially from the fixed end to the free end of the screw rod, i=1, 2, …, tau and F are axial external loads, and F is a load SRi For axial load applied to the ith pair of threads on the contact side of the roller with the screw, F NRi An axial load borne by the ith pair of threads on the contact side of the roller and the nut;
Figure FDA0004229832850000012
for screw shaft section rigidity- >
Figure FDA0004229832850000013
For the rigidity of the roller axle segment->
Figure FDA0004229832850000014
For the rigidity of the nut shaft section,/->
Figure FDA0004229832850000015
For screw thread tooth rigidity +.>
Figure FDA0004229832850000016
For the rigidity of the thread tooth of the roller>
Figure FDA0004229832850000017
The rigidity of the thread teeth of the nut is the rigidity;
solving the contact stiffness of the screw rod and the roller as follows:
Figure FDA0004229832850000018
wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure FDA0004229832850000019
the contact rigidity of the screw rod and the roller is as follows; />
Figure FDA00042298328500000110
Elastic contact deformation of the screw rod and the ith pair of thread teeth of the roller is realized;
solving the contact stiffness of the nut and the roller thread pair as follows:
Figure FDA0004229832850000021
wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure FDA0004229832850000022
for the contact stiffness of the nut and the roller thread pair, +.>
Figure FDA0004229832850000023
Elastic contact deformation of the nut and the ith pair of thread teeth of the roller is realized;
s2, introducing a deterministic low-deviation point set Halton sequence, analyzing sensitivity and contribution degree of uncertainty factors to the influence of the thread bearing capacity and the contact performance of the planetary roller screw pair by adopting a test design method, and taking parameters with the importance degree ranked forward as random variables to reduce the dimension of a limit state function so as to obtain a simplified limit state function;
s3, introducing a desired risk learning function to construct an active learning agent model of the planetary roller screw pair, generating sampling sample points by adopting a quasi-Monte Carlo method, calling the established active learning agent model to calculate a simplified limit state function corresponding to each group of sample points, and carrying out uncertainty analysis on the planetary roller screw pair to obtain failure probability and reliability sensitivity of the planetary roller screw pair under any working condition.
2. The method for analyzing uncertainty of planetary roller screw assembly according to claim 1, wherein elastic contact deformation of screw and i-th pair of screw threads of roller
Figure FDA0004229832850000024
The calculation formula of (2) is as follows:
Figure FDA0004229832850000025
Figure FDA0004229832850000026
wherein K (e) and L (e) are a first type of sumThe second type of complete elliptic integral, a is the long half-axis of the contact ellipse, b is the short half-axis of the contact ellipse,
Figure FDA0004229832850000027
to contact the eccentricity, k of ellipse e ＝b/a，
Figure FDA0004229832850000028
For equivalent elastic modulus, E S And v S For the elastic modulus and poisson ratio of the screw, E R And v R For the modulus of elasticity and poisson's ratio of the roller, θ and λ are the contact angle and the helix angle of the roller.
3. The method for analyzing uncertainty of a planetary roller screw pair according to claim 1, wherein the limit state function in the fatigue failure mode of the planetary roller screw pair thread contact is constructed based on an S-N curve and a stress-intensity interference theory as follows:
Figure FDA0004229832850000031
Figure FDA0004229832850000032
Figure FDA0004229832850000033
wherein x= (x) 1 ,x 2 ,…x i …,x n ) To influence the random variables of the limit state function, x i For the ith random variable, n is the number of random variables, sigma Hlim Sigma for contact fatigue limit SRi For the contact stress on the ith pair of threads of the screw rod and the roller,
Figure FDA0004229832850000034
for maximum contact stress, sigma, between the roller and all the threads on the contact side of the screw NRi For the contact stress on the nut and roller ith pair of threads, +. >
Figure FDA0004229832850000035
Is the maximum contact stress between the roller and all the threads on the contact side of the nut; f (F) SRi For axial load applied to the ith pair of threads on the contact side of the roller with the screw, F NRi An axial load borne by the ith pair of threads on the contact side of the roller and the nut; a is the major half axis of the contact ellipse, b is the minor half axis of the contact ellipse, and θ and λ are the contact angle and the helix angle of the roller.
4. The method of uncertainty analysis of a planetary roller screw set according to claim 3, wherein step S2 includes:
s21, for each random variable x of the planetary roller screw pair i At [0,1]Is generated in the interval of (a) and the input parameter matrix is obtained from the Halton sequence as X= (X) 1 ,x 2 ,…,x i ,…,x n ) Wherein x is i ＝(x i1 ,x i2 ,…,x ij ,…,x iN ) T Is x i Is a sample vector of (a);
s22, the response quantity comprises: maximum load distribution coefficient of both contact sides of the roller:
Figure FDA0004229832850000036
maximum contact stress->
Figure FDA0004229832850000037
And localized contact stress sigma on the thread pair SRi ,σ NRi The response matrix is obtained through calculation as follows: y= (Y) 1 ,y 2 ,…,y k ,…,y m ) Wherein y is k ＝(y k1 ,y k2 ,…,y kj ,…,y kN ) T For the kth response y k Is a sample vector of (a);
s23, matrix XAnd Y is at [ -1,1]Normalization was performed in range, and the data were fitted using the polynomial response surface method:
Figure FDA0004229832850000038
s24, adding polynomial coefficients
Figure FDA0004229832850000039
Expressed in terms of a percentage, the extent to which each input parameter affects the kth response may be reflected;
S25, selecting a parameter with the front importance degree sequence to reduce the dimension of the random variable, and obtaining a simplified limit state function of the planetary roller screw pair.
5. The method of uncertainty analysis of a planetary roller screw assembly according to claim 4, wherein step S3 comprises:
s31, randomly generating N in the uncertainty domain 0 The method comprises the steps of (1) calculating a simplified limit state function value by 20 samples, introducing a desired risk learning function to construct an active learning agent model of a planetary roller screw pair, and firstly constructing an initial agent model as follows:
Figure FDA0004229832850000041
Figure FDA0004229832850000042
u＝F T R -1 r-f(x)
wherein y= [ g (x) 1 ),g(x 2 ),…,g(x n )] T For a true response function with n sample points, f (x) = [ f 1 (x),f 2 (x),…f i (x),…,f p (x)] T As a regression polynomial basis function vector, beta= [ beta ] 1 ,β 2 ,…β i ,…,β p ] T For regression coefficient vector, p is the number of regression polynomials, r is the correlation vector function between the point to be measured and the sample point, and F= [ F (x 1 ) T ,f(x 2 ) T ,…,f(x n ) T ] T For an n x p order expansion matrix, R is an n x n order symmetric positive correlation matrix,
Figure FDA0004229832850000043
estimated value of approximate limit state function g (x), for>
Figure FDA0004229832850000044
Is->
Figure FDA0004229832850000045
The variance of g (x) is calculated as follows:
Figure FDA0004229832850000046
wherein z (x) is a variable which is subject to N (0, sigma) 2 ) A normal distributed random process, the covariance between any two sample points w and x is:
cov[z(w),z(x)]＝σ 2 R(θ,w,x)
wherein θ= [ θ ] 1 ,θ 2 ,…,θ n ] T For the correlation parameter, R (θ, w, x) is a function representing the correlation of the variables θ, w, x and can be described as a continuously differentiable gaussian correlation function:
Figure FDA0004229832850000047
Wherein the regression coefficient beta and variance sigma 2 The generalized least squares regression method can be expressed as:
β＝(F T R -1 F) -1 F T R -1 Y
Figure FDA0004229832850000051
s32, generating N in uncertainty domain c ＝10 5 Candidate samples;
s33, calculating N according to the initial proxy model c Estimated value of each sample point
Figure FDA0004229832850000052
And an estimate of expected risk
Figure FDA0004229832850000053
Taking the point with the maximum ERF value as a training point x #,/>
Figure FDA0004229832850000054
The calculation method comprises the following steps:
Figure FDA0004229832850000055
wherein sign (x) is a sign function, when x > 0, sign (x) = 1, when x < 0, sign (x) = -1, Φ () is a probability density function of a standard normal distribution, and ψ () is a cumulative distribution function of the standard normal distribution;
s34, setting a threshold or convergence condition as epsilon=10 -5 The method comprises the steps of carrying out a first treatment on the surface of the If max (ERF)>Epsilon, adding x as a new training point, and updating an active learning agent model of the planetary roller screw pair;
s35, repeating the steps S33-S35 until max (ERF) is less than or equal to epsilon;
s36, utilizing the updated star roller screw pair active learning agent model, generating sampling sample points by adopting a pseudo Monte Carlo method, calling the established active learning agent model to calculate a simplified limit state function corresponding to each group of sample points, and carrying out uncertainty analysis on the star roller screw pair to obtain failure probability and reliability sensitivity of the star roller screw pair under any working condition.
6. The method for uncertainty analysis of a planetary roller screw pair according to claim 5, wherein the step of generating sampling sample points by using a pseudo-monte carlo method, and calling the established active learning proxy model to calculate a simplified limit state function corresponding to each group of sample points, and performing uncertainty analysis on the planetary roller screw pair to obtain failure probability and reliability sensitivity of the planetary roller screw pair under any working condition comprises the following steps:
s361, for each random variable xi of the planetary roller screw pair, is 0,1]Generates a Halton sequence in the interval of (a) and the variables are independent of each other and are all normally distributed, and the cumulative probability distribution function F (x ij ) Can be expressed as:
Figure FDA0004229832850000056
wherein x is ij The jth sample value, f (x i ) As a random variable x i N is the number of samples,
Figure FDA0004229832850000061
is the x th ij Corresponding Halton numbers, wherein the specific generation process of the Halton sequence is as follows:
if q is any prime number, then any natural number j has a unique q-ary expression:
j＝j 0 +j 1 q+j 2 q 2 +···+j K q K
Figure FDA0004229832850000062
q K ≤j＜q K+1 ；
j i ∈{0,1,···,q-1}；i＝0,1,···,K
where K represents the integer portion of lnj/lnq, and the base inverse function, with q as the base, is defined as:
Figure FDA0004229832850000063
for any natural number j > 0, it satisfies
Figure FDA0004229832850000064
If the first n prime numbers are q 1 ,q 2 ,…,q n The n-dimensional halon sequence can be expressed as:
Figure FDA0004229832850000065
S362, obtaining random variable x ij Is a sample value of (2)
Figure FDA0004229832850000066
S363, sample point for obtaining allowable contact stress
Figure FDA0004229832850000067
S364, calculating the sample x of each group of random vectors j ＝(x 1j ,x 2j ,…,x nj ) T The load distribution and the local contact characteristics under action, the maximum contact stress on the contact side of the roller with the screw or nut is obtained, and then the limit state function g (x j ) If g (x j ) Less than or equal to 0, a status indication function I F (x j ) =1, otherwise I F (x j )＝0；
S365, failure probability
Figure FDA0004229832850000068
Is a function of the estimation of (1) and its coefficient of variation->
Figure FDA0004229832850000069
The calculation is as follows:
Figure FDA00042298328500000610
Figure FDA00042298328500000611
wherein N is f Is the number of failed samples;
s366, the estimated value of reliability sensitivity is as follows:
Figure FDA0004229832850000071
wherein f x (x) As a joint probability density function of random variables,
Figure FDA0004229832850000072
as a substantially random variable x i The kth distribution parameter, m i As the ith random variable x i Is a normal distribution random variable with mean +.>
Figure FDA0004229832850000073
And standard deviation->
Figure FDA0004229832850000074
The reliability sensitivity can be calculated as two distribution parameters:
Figure FDA0004229832850000075
7. a computer-readable storage medium, characterized in that the storage medium includes a stored program, wherein the program performs the uncertainty analysis method of the planetary roller screw pair according to any one of claims 1 to 6.
8. An electronic device, comprising: one or more processors, a memory, and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, the one or more programs comprising an uncertainty analysis method for performing the planetary roller screw assembly of any of claims 1-6.
9. An uncertainty analysis system of a planetary roller screw pair is characterized by comprising the following modules:
the limit state function construction module is used for solving the load distribution and the contact characteristic of the screw thread of the planetary roller screw pair through the structural parameters, the material performance and the boundary conditions, considering the uncertainty existing in the structural parameters, the material performance and the boundary conditions, and constructing a limit state function of the screw thread of the planetary roller screw pair in a contact fatigue failure mode based on the S-N curve and the stress-intensity interference theory;
solving the load distribution and the contact characteristic of the screw thread of the planetary roller screw pair through the structural parameters, the material performance and the boundary conditions, and comprises the following steps:
an iteration algorithm is adopted to solve a planetary roller screw pair thread load distribution model, and the method comprises the following steps:
Figure FDA0004229832850000081
wherein P is S ,P R And P N Respectively the screw pitches of a screw rod, a roller and a nut, wherein tau is the number of threads of the roller which participate in contact, z is the number of the roller, the threads are numbered sequentially from the fixed end to the free end of the screw rod, i=1, 2, …, tau and F are axial external loads, and F is a load SRi For axial load applied to the ith pair of threads on the contact side of the roller with the screw, F NRi An axial load borne by the ith pair of threads on the contact side of the roller and the nut;
Figure FDA0004229832850000082
is a screw shaft Segment stiffness (I)>
Figure FDA0004229832850000083
For the rigidity of the roller axle segment->
Figure FDA0004229832850000084
For the rigidity of the nut shaft section,/->
Figure FDA0004229832850000085
For screw thread tooth rigidity +.>
Figure FDA0004229832850000086
For the rigidity of the thread tooth of the roller>
Figure FDA0004229832850000087
The rigidity of the thread teeth of the nut is the rigidity;
solving the contact stiffness of the screw rod and the roller as follows:
Figure FDA0004229832850000088
wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure FDA0004229832850000089
the contact rigidity of the screw rod and the roller is as follows; />
Figure FDA00042298328500000810
Elastic contact deformation of the screw rod and the ith pair of thread teeth of the roller is realized;
solving the contact stiffness of the nut and the roller thread pair as follows:
Figure FDA00042298328500000811
wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure FDA00042298328500000812
for the contact stiffness of the nut and the roller thread pair, +.>
Figure FDA00042298328500000813
Elastic contact deformation of the nut and the ith pair of thread teeth of the roller is realized;
the limit state function simplifying module is used for introducing a deterministic low-deviation point set Halton sequence, analyzing sensitivity and contribution degree of uncertainty factors to the influence of the thread bearing capacity and the contact performance of the planetary roller screw pair by adopting a test design method, and reducing the dimension of the limit state function by taking the parameter with the forward importance degree sequence as a random variable to obtain a simplified limit state function;
the uncertainty analysis module is used for introducing a desired risk learning function to construct an active learning agent model of the planetary roller screw pair, adopting a quasi-Monte Carlo method to generate sampling sample points, calling the established active learning agent model to calculate a simplified limit state function corresponding to each group of sample points, and carrying out uncertainty analysis on the planetary roller screw pair to obtain the failure probability and reliability sensitivity of the planetary roller screw pair under any working condition.
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