CN110390173B - Time-varying reliability evaluation method for kilometer deep well elevator considering residual strength degradation - Google Patents
Time-varying reliability evaluation method for kilometer deep well elevator considering residual strength degradation Download PDFInfo
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Abstract
A time-varying reliability assessment method for a kilometer deep well elevator considering residual strength degradation belongs to the technical research field of mechanical structure reliability of mechanical products. A time-varying reliability assessment method for a kilometer deep well elevator. Firstly, defining random variables, generating a sampling matrix by using a Latin hypercube sampling method, substituting each group of sample variables into Ansys to solve to obtain corresponding maximum equivalent stress, and establishing probability random response of the elevator by using a Kriging agent model. And then, simulating the tension process of the steel wire rope by using Simulink software, and establishing a residual strength degradation model of the main shaft of the elevator according to a fatigue theory. And finally, establishing a performance function of the main shaft of the elevator according to the stress-intensity interference model, solving the first four moments by using a binary dimension reduction method and a sparse grid method, and solving the time-varying reliability of the elevator by using a saddle point approximation method. The method considers the time-varying reliability of the residual strong degradation, can reflect the variation relation between the reliability and the lifting times, and is favorable for ensuring the reliable operation of the lifter.
Description
Technical Field
The invention relates to a time-varying reliability assessment method for a kilometer deep well elevator considering residual strength degradation, and belongs to the technical field of mechanical structure reliability research of mechanical products.
Background
Coal resources buried in shallow ground surfaces are continuously reduced along with excessive mining, and the coal resources are deeply developed into a coal mining strategy in China. The elevator is an important transportation tool and takes the task of conveying coal from the bottom of a kilometer well to the ground. With the increase of service life, the fatigue strength degradation becomes an important factor influencing the reliable operation of the hoister. Due to loose materials and coarse grains caused by incorrect heat treatment, the main shaft of the kilometer deep well hoisting machine made of 45MnMo has sudden brittle fracture, and the phenomenon of the sudden brittle fracture occurs when the stress is lower than the yield stress of the material. The external reason for the occurrence of the fracture accident is that the stress of the main shaft has great randomness due to uncertain factors such as vibration in the lifting process. The internal reason of the method is that the main shaft has tiny cracks, and the cracks are continuously expanded under the action of alternating load, so that brittle failure is finally caused.
Disclosure of Invention
The invention aims to provide a time-varying reliability evaluation method for a kilometer deep well elevator considering residual strength degradation, and solve the technical problem of predicting the probability of sudden brittle failure of a main shaft of the kilometer deep well elevator due to high-cycle fatigue.
The purpose of the invention is realized as follows: a time-varying reliability evaluation method of a kilometer deep well elevator considering the degradation of residual strength,
firstly, defining random variables, generating a sampling matrix by using a Latin hypercube sampling method, substituting each group of sample variables into Ansys finite element simulation software for solving to obtain corresponding maximum equivalent stress, and fitting the sampling matrix and the corresponding maximum equivalent stress by using a Kriging agent model to obtain the probability random response of the elevator;
then, defining the operation parameters of the steel wire rope, simulating the tension process of the steel wire rope by using Simulink kinetic system modeling and simulation software, correcting a stress-life curve, namely an S-N curve, of the main shaft, and establishing a residual strength model of the main shaft of the elevator according to a Palmgren-Miner linear accumulated damage theory;
and finally, establishing a performance function of the main shaft of the elevator according to the stress-intensity interference model, reducing the dimension of the performance function by using a binary dimension reduction method, solving the first four moments of the performance function by using a sparse grid method, solving the time-varying reliability of the elevator by using a saddle point approximation method, and drawing a time-varying reliability curve.
The method comprises the following specific implementation steps:
step 4, substituting each group of sample variables into Ansys finite element simulation software to solve according to the sampling matrix determined in the step 3, and obtaining corresponding maximum equivalent stress;
step 6, defining steel wire rope operation parameters, establishing a differential equation of tension, and simulating the tension process of the steel wire rope by using Simulink kinetic system modeling and simulation software;
step 7, correcting the S-N of the spindle by using an average stress correction method;
and 11, solving the time-varying reliability of the elevator by using a saddle point approximation method, and drawing a time-varying reliability curve.
The step 7 specifically comprises the following steps:
and correcting a stress-life curve of the main shaft, namely an S-N curve by using a Goodman average stress correction method or a Morrow average stress correction method.
The step 9 specifically includes:
establishing a performance function of the main shaft of the hoister according to the stress-intensity interference model;
and (3) reducing the dimension of the performance function by using a binary dimension reduction method, wherein the approximate performance function after dimension reduction is as follows:
in the formula: n-the dimension of the random vector X;
x is a random vector;
the random vector of U-X after Rosenblatt transform, the formula of Rosenblatt is as follows:
U＝Φ -1 [F(X)]
in the formula: f represents a joint cumulative distribution function of the random vector X; phi -1 [·]Representing the inverse of a standard normal distribution function.
The method has the advantages that by adopting the scheme, the time-varying reliability of the kilometer deep well elevator can be evaluated, the variation relation between the reliability of the elevator and the lifting times can be predicted, the reliable operation of the elevator can be guaranteed, measures can be taken in time before a brittle failure accident occurs, meanwhile, the calculation efficiency is greatly improved for a complex performance function, particularly for the use of a project problem, a binary dimension reduction method and a sparse grid method, and meanwhile, the project precision is also guaranteed.
1) For the use of a complex performance function, a binary dimension reduction method and a sparse grid method, the calculation efficiency is greatly improved, and meanwhile, the engineering precision is also ensured.
2) The time-varying reliability evaluation method considering the residual strong degradation can predict the change relation between the reliability of the elevator and the lifting times, and is beneficial to ensuring the reliable operation of the elevator.
The technical problem of predicting the probability of sudden brittle failure of the main shaft of the kilometer deep well elevator due to high cycle fatigue is solved, and the purpose of the invention is achieved.
The advantages are that: the method considers the time-varying reliability of the residual strong degradation, can reflect the change relation between the reliability of the elevator and the lifting times, is favorable for ensuring the reliable operation of the elevator, and simultaneously greatly improves the calculation efficiency for a complex performance function, particularly for the engineering problem, and the use of a binary dimension reduction method and a sparse grid method, and also ensures the engineering precision.
Drawings
Fig. 1 is a technical route diagram of the time-varying reliability evaluation method for the kilometer deep well elevator considering the residual strength degradation.
Fig. 2 is a two-dimensional structural view of a main shaft of a hoist according to the present invention.
Fig. 3 is a sample plot of the maximum equivalent stress response of the hoist main shaft of the present invention.
Fig. 4 is a tension history chart of the steel wire rope simulated by Simulink software according to the invention.
Fig. 5 is a graph of the time varying reliability of the hoisting machine of the invention.
In the figure, 1, a shaft segment I; 2. a second shaft section; 3. a shaft section III; 4. a shaft section IV; 5. a fifth shaft section; 6. a shaft section six; 7. a shaft section seven; 8. a shaft section eight; 9. a shaft section nine; 10. a shaft section ten; 11. and eleven shaft sections.
Detailed Description
A time-varying reliability evaluation method of a kilometer deep well elevator considering the degradation of residual strength,
firstly, defining random variables, generating a sampling matrix by using a Latin hypercube sampling method, substituting each group of sample variables into Ansys finite element simulation software for solving to obtain corresponding maximum equivalent stress, and fitting the sampling matrix and the corresponding maximum equivalent stress by using a Kriging agent model to obtain the probability random response of the elevator;
then, defining the operation parameters of the steel wire rope, simulating the tension process of the steel wire rope by using Simulink kinetic system modeling and simulation software, correcting a stress-life curve, namely an S-N curve, of the main shaft, and establishing a residual strength degradation model of the main shaft of the elevator according to a Palmgren-Miner linear accumulated damage theory;
and finally, establishing a performance function of the main shaft of the elevator according to the stress-intensity interference model, reducing the dimension of the performance function by using a binary dimension reduction method, solving the first four moments of the performance function by using a sparse grid method, solving the time-varying reliability of the elevator by using a saddle point approximation method, and drawing a time-varying reliability curve.
The method comprises the following specific implementation steps:
step 4, substituting each group of sample variables into Ansys finite element simulation software to solve according to the sampling matrix determined in the step 3, and obtaining corresponding maximum equivalent stress;
step 6, defining steel wire rope operation parameters, establishing a differential equation of tension, and simulating the tension process of the steel wire rope by using Simulink kinetic system modeling and simulation software;
step 7, correcting the S-N of the spindle by using an average stress correction method;
and 11, solving the time-varying reliability of the elevator by using a saddle point approximation method, and drawing a time-varying reliability curve.
The step 7 specifically comprises the following steps:
and correcting a stress-life curve of the main shaft, namely an S-N curve by using a Goodman average stress correction method or a Morrow average stress correction method.
The step 9 specifically comprises the following steps:
establishing a performance function of the main shaft of the elevator according to the stress-intensity interference model;
and (3) reducing the dimension of the performance function by using a binary dimension reduction method, wherein the approximate performance function after dimension reduction is as follows:
in the formula: n-the dimension of the random vector X;
x is a random vector;
the random vector of U-X after Rosenblatt transform, the formula of Rosenblatt is as follows:
U＝Φ -1 [F(X)]
in the formula: f represents a joint cumulative distribution function of the random vector X; phi -1 [·]Representing the inverse of a standard normal distribution function.
The invention is further described below with reference to the accompanying drawings and examples.
Example 1: as shown in fig. 1, the method for evaluating time-varying reliability of a deep kilometer hoist considering degradation of residual strength provided by the present invention comprises the following steps:
And 2, performing equation modeling on the elevator, and performing statics analysis on the established three-dimensional model by using Ansys finite element simulation software.
And 3, sampling the variables by using a Latin hypercube sampling method according to the variable mean value and the variance determined in the step 1, and generating a sampling matrix.
And 4, substituting each group of sample variables into Ansys finite element simulation software to solve according to the sampling matrix determined in the step 3, and obtaining the corresponding maximum equivalent stress.
And 5, fitting the sampling matrix and the corresponding maximum equivalent stress by using a Kriging proxy model to obtain the probabilistic random response of the elevator.
And 6, defining the operation parameters of the steel wire rope, establishing a differential equation of the tension, and simulating the tension process of the steel wire rope by using Simulink kinetic system modeling and simulation software.
Step 7, correcting a stress-life curve of the spindle, namely an S-N curve, by using an average stress correction method; the average stress correction method is a Goodman average stress correction method or a Morrow average stress correction method.
And 8, establishing a residual strength degradation model of the main shaft of the elevator according to a Palmgren-Miner linear accumulated damage theory.
And 9, establishing a performance function of the main shaft of the elevator according to the stress-intensity interference model, and reducing the dimension of the performance function by using a binary dimension reduction method.
Establishing a performance function of the main shaft of the elevator according to the stress-intensity interference model;
and (3) reducing the dimension of the performance function by using a binary dimension reduction method, wherein the approximate performance function after dimension reduction is as follows:
in the formula: n-the dimension of the random vector X;
x is a random vector;
the random vector of U-X after Rosenblatt transform, the formula of Rosenblatt is as follows:
U＝Φ -1 [F(X)]
in the formula: f represents a joint cumulative distribution function of the random vector X; phi (phi) of -1 [·]Representing the inverse of a standard normal distribution function.
And step 10, solving the first four moments of the performance function by using a sparse grid method.
And 11, solving the time-varying reliability of the hoister by using a saddle point approximation method, and drawing a time-varying reliability curve.
In order to more fully understand the characteristics and the engineering applicability of the invention, the time-varying reliability evaluation considering the residual strength degradation is carried out on the main shaft structure of the kilometer deep well hoisting machine shown in figure 2.
Defining the size of the main shaft as a variable, determining the mean value and the variance of each size, and defining the size variable to obey normal distribution; defining the load of the elevator as a variable, determining the mean value and the variance of the load according to the lifting working condition, and defining that the load variable obeys log-normal distribution.
And performing equation modeling on the main shaft of the elevator, and importing the established three-dimensional model into Ansys finite element simulation software for statics analysis.
And sampling the variables by using a Latin hypercube sampling method according to the determined mean value and variance of the variables, and generating a sampling matrix. And substituting each group of sample variables into Ansys finite element simulation software for solving, and acquiring the corresponding maximum equivalent stress, as shown in figure 3.
And fitting the sampling matrix and the corresponding maximum equivalent stress by using a Kriging proxy model to obtain the random response of the probability of the main shaft of the elevator.
Defining the operation parameters of the steel wire rope, and establishing a differential equation of tension:
and (3) accelerating and lifting:
a uniform lifting stage:
and (3) a deceleration lifting stage:
in the formula: m-terminal mass, 9000kg.
L (t) -the length of the rope when lifted, in m.
a 1 -lift acceleration, 0.75m/s 2.
a 2 -lift deceleration, 0.75m/s 2.
E-elastic modulus of the steel wire rope, 1.0e5N/mm ^ 2.
F is the cross section area of the steel wire rope, 698mm ^2.
Rho is the weight of the steel wire rope per meter, and is 6.5kg/m.
v m Maximum hoisting speed, 8m/s.
P is the rope end tension.
And simulating the tension course of the steel wire rope by using Simulink kinetic system modeling and simulation software, as shown in FIG. 4.
And correcting a stress-life curve, namely an S-N curve, of the main shaft by using a Goodman average stress correction method, and establishing a residual strength degradation model of the main shaft of the elevator according to a Palmgren-Miner linear accumulated damage theory.
Establishing a performance function of the main shaft of the elevator according to the stress-intensity interference model; and (4) reducing the dimension of the performance function by using a binary dimension reduction method.
Solving the first four moments of the performance function by using a sparse grid method; solving the time-varying reliability of the hoister by using a saddle point approximation method; a time-varying reliability curve is plotted as shown in fig. 5.
In conclusion, the method provides a time-varying reliability assessment method for the kilometer deep well elevator, which considers the degradation of residual strength. Firstly, defining random variables, generating a sampling matrix by using a Latin hypercube sampling method, substituting each group of sample variables into Ansys finite element simulation software for solving to obtain corresponding maximum equivalent stress, and fitting the sampling matrix and the corresponding maximum equivalent stress by using a Kriging proxy model to obtain the probabilistic random response of the elevator.
Then, defining the operating parameters of the steel wire rope, simulating the tension process of the steel wire rope by using Simulink kinetic system modeling and simulation software, correcting a stress-life curve, namely an S-N curve, of the main shaft, and establishing a residual strength degradation curve of the main shaft of the elevator according to a Palmgren-Miner linear accumulated damage theory.
And finally, establishing a performance function of the main shaft of the elevator according to the stress-intensity interference model, reducing the dimension of the performance function by using a binary dimension reduction method, solving the first four moments of the performance function by using a sparse grid method, solving the time-varying reliability of the elevator by using a saddle point approximation method, and drawing a time-varying reliability curve.
Parts of the invention not described in detail are well known to the skilled person.
Claims (4)
1. A kilometer deep well elevator time-varying reliability assessment method considering residual strength degradation is characterized by comprising the following steps: a time-varying reliability evaluation method of a kilometer deep well elevator considering the degradation of residual strength,
firstly, defining random variables, generating a sampling matrix by using a Latin hypercube sampling method, substituting each group of sample variables into Ansys finite element simulation software for solving to obtain corresponding maximum equivalent stress, and fitting the sampling matrix and the corresponding maximum equivalent stress by using a Kriging agent model to obtain the probability random response of the elevator;
then, defining the operation parameters of the steel wire rope, simulating the tension process of the steel wire rope by using Simulink kinetic system modeling and simulation software, correcting a stress-life curve, namely an S-N curve, of the main shaft, and establishing a residual strength degradation model of the main shaft of the elevator according to a Palmgren-Miner linear accumulated damage theory;
and finally, establishing a performance function of the main shaft of the elevator according to the stress-intensity interference model, reducing the dimension of the performance function by using a binary dimension reduction method, solving the first four moments of the performance function by using a sparse grid method, solving the time-varying reliability of the elevator by using a saddle point approximation method, and drawing a time-varying reliability curve.
2. The method for evaluating the time-varying reliability of the kilometer deep well elevator in consideration of the deterioration of the residual strength as recited in claim 1, wherein: the method comprises the following specific implementation steps:
step 1, defining the size and the load of a main shaft as variables, determining the mean value and the variance of each variable, and determining the distribution type of each variable;
step 2, performing equation modeling on the elevator, and performing statics analysis on the established three-dimensional model by using Ansys finite element simulation software;
step 3, sampling variables by using a Latin hypercube sampling method according to the variable mean value and the variance determined in the step 1 to generate a sampling matrix;
step 4, substituting each group of sample variables into Ansys finite element simulation software to solve according to the sampling matrix determined in the step 3, and obtaining corresponding maximum equivalent stress;
step 5, fitting the sampling matrix and the corresponding maximum equivalent stress by using a Kriging agent model to obtain the probability random response of the elevator;
step 6, defining steel wire rope operation parameters, establishing a differential equation of tension, and simulating the tension process of the steel wire rope by using Simulink kinetic system modeling and simulation software;
step 7, correcting the S-N of the spindle by using an average stress correction method;
step 8, establishing a residual strength degradation model of the main shaft of the elevator according to a Palmgren-Miner linear accumulated damage theory;
step 9, establishing a performance function of the main shaft of the elevator according to the stress-intensity interference model, and reducing the dimension of the performance function by using a binary dimension reduction method;
step 10, solving the first four moments of the performance function by using a sparse grid method;
and 11, solving the time-varying reliability of the elevator by using a saddle point approximation method, and drawing a time-varying reliability curve.
3. The method for evaluating the time-varying reliability of the kilometer deep well elevator in consideration of the deterioration of the residual strength as recited in claim 2, wherein: the step 7 specifically comprises the following steps:
and correcting a stress-life curve of the main shaft, namely an S-N curve by using a Goodman average stress correction method or a Morrow average stress correction method.
4. The method for evaluating the time-varying reliability of the kilometer deep well elevator considering the degradation of the residual strength as recited in claim 2, wherein: the step 9 specifically comprises the following steps:
establishing a performance function of the main shaft of the elevator according to the stress-intensity interference model;
and (3) reducing the dimension of the performance function by using a binary dimension reduction method, wherein the approximate performance function after dimension reduction is as follows:
in the formula: n-the dimension of the random vector X;
x is a random vector;
the standard normal random vector of U-X after Rosenblatt transformation is as follows:
U＝Φ -1 [F(X)]
in the formula: f represents a joint cumulative distribution function of the random vector X; phi -1 [·]Representing the inverse of a standard normal distribution function.
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