CN110096796A - The analysis method for reliability of industrial robot RV retarder under a kind of multi-invalidation mode - Google Patents
The analysis method for reliability of industrial robot RV retarder under a kind of multi-invalidation mode Download PDFInfo
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Abstract
The invention discloses a kind of analysis method for reliability of industrial robot RV retarder under multi-invalidation mode, this method is started with from dominant failure mode, establish the power function under corresponding limiting condition, determine the uncertain factor under different failure modes, corresponding to the parametric variable in power function, its distribution character is determined；After obtaining the power function of dominant failure mode, it is translated into Kriging model, determines the learning function type in model, is sampled in conjunction with Monte Carlo simulation method, established power function is fitted；It is further required to determine study stop condition according to the required accuracy, forms complete learning process；Failure probability and the coefficient of variation are calculated according to the AK-MCS reliability analysis model established, verifies whether to meet required precision；Obtained fail-safe analysis result can feed back the integrity problem and optimization method of industrial robot RV retarder under multi-invalidation mode, provide strong foundation for its reliability design.
Description
Technical Field
The invention belongs to the technical field of reliability analysis of industrial robot RV reducers, and particularly relates to a reliability analysis method of an industrial robot RV reducer under a multi-failure mode based on an AK-MCS model.
Background
The RV reducer of an industrial robot is a transmission device for causing the robot to perform a work operation, is frequently used in a joint portion of the industrial robot, and is a core component for determining the working performance of the industrial robot. Compared with the traditional gear transmission device, the RV reducer has the advantages of high transmission rigidity, large transmission ratio, small inertia, large output torque, stable transmission, small size, strong impact resistance and the like, and can meet the requirements of the industrial robot on structural rigidity and service life. Therefore, it is widely used in the field of industrial robots.
Along with the continuous improvement of the requirements of the industrial robot on the performances such as the movement speed, the positioning accuracy, the bearing capacity and the like, the performance parameter requirements of the RV reducer are also continuously improved, the working environment and the working load of the RV are more complicated than before, the failure problem is more and more prominent, once the RV reducer fails, the failure of the whole industrial robot system is inevitably caused, the unpredictable economic loss is caused, and even the personal safety is threatened. In actual operating environment, RV reduction gear operational environment is abominable, lubricated and the cooling is not enough, the vibration and the big scheduling problem of impact load that bear will aggravate RV reduction gear's damage degree, promote its fault rate. Because the RV reducer requires high matching precision, the constitution is relatively complex, the clearance between the gears is very small, and when the RV reducer works for a long time, the complete machine of the RV reducer is likely to fail due to the failure of certain gear teeth. The RV reducers are difficult and costly to maintain, which requires that the RV reducers must have a high reliability.
At present, for reliability analysis and research of the RV reducer, only a single failure mode is usually concerned, the result of combined action of various failure modes of the RV reducer cannot be truly and effectively reflected, and the result of too low or too high result is usually obtained for reliability evaluation of the whole RV reducer. Therefore, the method which can establish the reliability model of the RV reducer under the multiple failure modes and simultaneously analyze the reliability of the multiple failure modes of the RV reducer has important practical significance.
Disclosure of Invention
The invention aims to: in order to solve the problems in the reliability analysis of the existing industrial robot RV reducer, the invention provides a reliability analysis method of the industrial robot RV reducer under a multi-failure mode based on an AK-MCS model.
The technical scheme of the invention is as follows: a reliability analysis method for an industrial robot RV reducer in a multi-failure mode comprises the following steps:
s1, analyzing the failure modes of the RV reducer of the industrial robot, and selecting the main failure mode as a reliability analysis object;
s2, analyzing parts and failure reasons corresponding to the main failure mode in the step S1, determining a failure physical model and uncertain factors, and establishing a function of the main failure mode;
s3, determining a learning function and a learning stopping condition in the Kriging model, and establishing the Kriging model;
s4, establishing an AK-MCS reliability analysis model of the industrial robot RV reducer under the multi-failure mode based on the Kriging model and a MonteCarlo simulation method according to the function of the main failure mode in the step S2 and the Kriging model in the step S3, and obtaining failure probability and reliability under the multi-failure mode.
Further, the step S1 is specifically:
summarizing and analyzing the failure mode of the RV reducer of the industrial robot according to the fault and maintenance statistical data of the RV reducer of the industrial robot; analyzing the risk evaluation of various failure modes according to an FMEA report table of the RV reducer, determining a judgment standard, and obtaining a main failure mode of the RV reducer, wherein the method specifically comprises the following steps: the tooth surface of the planetary gear is worn, the gear teeth of the planetary gear are broken, the tooth surface of the cycloidal gear is worn, and the rolling bearing is worn.
Further, the step S2 specifically includes the following sub-steps:
s21, determining failure parts corresponding to the main failure mode according to the main failure mode determined in the step S1, and analyzing failure reasons;
s22, determining a corresponding failure physical model according to the parts and the failure reasons corresponding to the main failure modes determined in the step S21;
s23, analyzing uncertain factors in failure reasons according to the failure physical model determined in the step S22 and by combining the actual situation of the RV reducer;
s24, according to the uncertain factors obtained in the step S23, quantifying the variables in the failure physical model determined in the step S22, determining the distribution types and the distribution parameters of the variables, and establishing a function of the main failure mode.
Further, the function of the planetary gear tooth surface wear failure mode in step S24 is specifically expressed as:
wherein σHlimDenotes the contact fatigue limit, Z, of the test gearNDenotes the life factor, ZRExpressing the coefficient of roughness of the tooth surface, ZVDenotes the velocity coefficient, ZWDenotes the work hardening coefficient, ZLDenotes the coefficient of lubricant, ZXDenotes the size factor, ZHRepresenting the node area coefficient, ZEDenotes the coefficient of elasticity, ZεDenotes the coefficient of degree of overlap, ZβRepresenting the helix angle coefficient, KpRepresenting the imbalance coefficient of load distribution among planet wheels, P representing input power, d representing the reference circle diameter of the gear, b representing the tooth width, npIndicating the number of planet gears, nμRepresenting input speed, u representing gear ratio, KA1Expressing the coefficient of use in the tooth flank wear failure mode, KV1Expressing the coefficient of dynamic load, K, in the tooth flank wear failure modeHβExpressing the tooth load distribution coefficient, K, in the tooth flank wear failure modeHαRepresenting the tooth flank load distribution coefficient in the tooth flank wear failure mode.
Further, the function of the planetary gear tooth breakage failure mode in step S24 is specifically expressed as:
wherein σFlimShows the bending fatigue strength, Y, of the test gearSTDenotes a stress correction coefficient, Y, of the test gearNTDenotes the life factor, YδrelTIndicating the relative root fillet sensitivity, YRrelTRepresenting the coefficient of relative root surface condition, YXSize factor, m, representing the calculation of bending StrengthnDenotes the normal modulus, YFaRepresenting the tooth form coefficient, Y, of the load acting on the tooth tipSaIndicating the stress correction coefficient, Y, of the load acting on the tooth tipεDenotes the coefficient of degree of overlap, YβRepresenting the helix angle coefficient, KA2Expressing coefficient of use in failure mode of tooth breakage, KV2Representing the dynamic load coefficient, K, in the failure mode of tooth breakageFβExpressing the tooth load distribution coefficient, K, in the failure mode of tooth breakageFαRepresenting the tooth-to-tooth load distribution coefficient in the tooth fracture failure mode.
Further, the function of the cycloid gear tooth surface wear failure mode in the step S24 is specifically expressed as:
wherein σHlimRepresenting the contact fatigue limit, σ, of the test gearH0Denotes the initial value of the calculated contact stress, K denotes the calculation coefficient, KHRepresenting the interdental load distribution coefficient.
Further, the function of the wear failure mode of the rolling bearing in the step S24 is specifically expressed as:
wherein, CrIndicating the dynamic load rating, P, of the bearingrDenotes the equivalent dynamic load of the bearing, nμRepresenting input shaft speed, nvRepresents the output shaft speed, and epsilon represents the life factor.
Further, the step S3 specifically includes the following sub-steps:
s31, determining a learning function in the Kriging model according to a Monte Carlo simulation method and a function, wherein the learning function is expressed as:
wherein, muG(x) Is the mean value of the sample points, σG(x) Is the sample point variance;
s32, according to the characteristics of the learning process and the requirement of reliability precision, combining the characteristics of the sample data, determining the condition of learning stop, which is expressed as:
min(U(x))≥Ulimit
wherein, UlimitA threshold is indexed for the learning function.
Further, the step S4 specifically includes the following sub-steps:
s41, generating a candidate sample total by adopting a Monte Carlo simulation method;
s42, generating test design sample points by adopting a Latin hypercube method, and calculating the response value of an actual function;
s43, establishing a Kriging prediction model according to the test design sample points and the actual function response values obtained in the step S42;
s44, judging whether learning stop conditions are met according to the Kriging prediction model obtained in the step S43; if yes, stopping learning and carrying out the next step; if not, sequentially stepping forward, adding the sample point with the minimum learning function value in the candidate sample population into the test design sample point, and turning to the step S43;
s45, calculating the failure probability and the variation coefficient by using the Kriging prediction model obtained in the step S43;
s46, judging whether the variation coefficient obtained in the step S45 meets the precision requirement; if so, ending the operation and outputting a result; if not, the number of samples of the candidate sample population is increased, and the process proceeds to step S43.
Further, the calculation formula for calculating the failure probability in step S45 is specifically expressed as:
wherein,as an estimate of the probability of failure, If(G(xi) Is an indicative function, xiThe ith sample point, N, obtained for MC simulationG≤0Number of sample points falling into the failure domain, NMCTotal number of samples simulated for MC.
The calculation formula for calculating the coefficient of variation is specifically expressed as:
the invention has the beneficial effects that: aiming at the problems of single failure mode analysis, various failure reasons, complex calculation process and the like in the reliability analysis of the current RV reducer of the industrial robot, starting from a main failure mode, establishing a function under a corresponding limit state, determining uncertain factors under different failure modes, corresponding to parameter variables in the function, and determining the distribution characteristics of the function functions; after the functional function of the main failure mode is obtained, the functional function is converted into a Kriging model, the type of a learning function in the model is determined, sampling is carried out by combining a Monte Carlo simulation method, and the established functional function is fitted; further determining a learning stopping condition according to the required precision requirement to form a complete learning process; calculating failure probability and variation coefficient according to the established AK-MCS reliability analysis model, and verifying whether the accuracy requirement is met; the obtained reliability analysis result can feed back the reliability problem and the optimization method of the RV reducer of the industrial robot in the multi-failure mode, and a favorable basis is provided for the reliability design of the RV reducer.
Drawings
FIG. 1 is a schematic flow chart of a reliability analysis method of an industrial robot RV reducer in a multi-failure mode;
FIG. 2 is a schematic diagram of a structure of an RV reducer of an industrial robot provided by the embodiment of the invention;
fig. 3 is a flowchart of an AK-MCS model analysis of an RV reducer of an industrial robot according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
FIG. 1 is a schematic flow chart of a reliability analysis method for an RV reducer of an industrial robot in multiple failure modes according to the invention; a reliability analysis method for an industrial robot RV reducer in a multi-failure mode comprises the following steps:
s1, analyzing the failure modes of the RV reducer of the industrial robot, and selecting the main failure mode as a reliability analysis object;
s2, analyzing parts and failure reasons corresponding to the main failure mode in the step S1, determining a failure physical model and uncertain factors, and establishing a function of the main failure mode;
s3, determining a learning function and a learning stopping condition in the Kriging model, and establishing the Kriging model;
s4, establishing an AK-MCS reliability analysis model of the industrial robot RV reducer under the multi-failure mode based on the Kriging model and a MonteCarlo simulation method according to the function of the main failure mode in the step S2 and the Kriging model in the step S3, and obtaining failure probability and reliability under the multi-failure mode.
In an optional embodiment of the present invention, the step S1 is specifically:
summarizing and analyzing the failure mode of the RV reducer of the industrial robot according to the fault and maintenance statistical data of the RV reducer of the industrial robot; and analyzing the risk evaluation of various failure modes according to an FMEA report table of the RV reducer, determining a judgment standard, and obtaining a main failure mode of the RV reducer.
The RV reducer generally comprises a rolling bearing, a cycloid gear, a needle bearing, a planetary gear, an input shaft, a needle gear, a crank shaft, and the like. The schematic structure diagram of the RV reducer is shown in fig. 2, and comprises a rear end cover 1, a rolling bearing 2, a positioning bearing 3, a cycloidal gear 4, a needle bearing 5, an output disc 6, a planetary gear 7, an input shaft 8, needle teeth 9, a shell 10 and a crankshaft 11; among them planetary gear, cycloid wheel, antifriction bearing are comparatively important: the planetary gear is a part of a first-stage speed reducing device of the RV speed reducer; the cycloidal gear is a part of a second-stage speed reducer of the RV reducer, and transmits the torque and the rotating speed transmitted by the first-stage speed reducer to the output mechanism after further speed reduction; the rolling bearing reduces friction between parts of the RV reducer in the operation process and can play a supporting role.
And selecting the failure mode with the risk priority number larger than 190 as a main failure mode according to the statistical data of the faults and maintenance of the RV reducer and an FMEA report table of the RV reducer. Therefore, the main failure modes chosen are: the tooth surface of the planet gear is worn, and the gear teeth of the planet gear are broken; wear of the tooth surface of the cycloid wheel; the rolling bearing wears.
In an alternative embodiment of the present invention, the step S2 is to determine the failed component and the failure cause according to the primary failure mode selected in the step S1; analyzing the extreme state of the failure mode and establishing a corresponding function; determining the parameter values and the distribution types of the variables in the function, which specifically comprises the following steps:
s21, determining failure parts corresponding to the main failure mode according to the main failure mode determined in the step S1, and analyzing failure reasons;
from the analysis in step S1, the primary failure mode and its cause:
(1) the planetary gear tooth surfaces wear. Because the industrial robot RV reducer has characteristics such as drive ratio is big, impact load changes greatly, and the tooth surface contact stress of planet gear changes greatly, and when tooth surface contact stress was greater than contact fatigue intensity, the planet wheel will take place tooth surface contact fatigue failure, leads to planet gear flank wear.
(2) The planetary gear teeth break. Because industrial robot RV reduction gear has characteristics such as the drive ratio is big, impact load changes greatly, and the tooth root bending stress of planetary gear changes greatly, and when tooth root bending stress was greater than bending fatigue intensity, the planet wheel will take place tooth root bending fatigue and lose efficacy, leads to the planetary gear teeth of a cogwheel to break.
(3) The tooth surface of the cycloid wheel is abraded. Due to the complexity and the particularity of the structure of the cycloid wheel, when the cycloid wheel is meshed with the needle teeth, the stress change is large, and when the tooth surface contact stress is larger than the contact fatigue strength, the tooth surface contact fatigue failure of the cycloid wheel can occur, so that the tooth surface of the cycloid wheel is abraded.
(4) The rolling bearing wears. Because the load born by the rolling bearing is large, and the borne rotating speed may be the sum of the input rotating speed and the output rotating speed, the working environment of the rolling bearing is high-speed and heavy-load, the service life of the rolling bearing cannot meet the required rated service life, the bearing is easy to fail due to fatigue, and the bearing is abraded.
S22, determining a corresponding failure physical model according to the parts and the failure reasons corresponding to the main failure modes determined in the step S21;
(1) the tooth surface of the planet gear is worn and corresponds to a contact stress-strength failure physical model of the gear;
(2) the gear teeth of the planetary gear are broken, and the physical model corresponds to the bending stress-strength failure of the gear;
(3) wear of the tooth surface of the cycloidal gear corresponds to a contact stress-strength failure physical model of the gear;
(4) bearing wear, corresponding to a physical model of fatigue life failure of the bearing.
S23, analyzing uncertain factors in failure reasons according to the failure physical model determined in the step S22 and by combining with the actual conditions of the machining process, the working environment and the like of the RV reducer;
errors exist in the size of an actual gear due to the machining process of the gear, and errors may exist in the diameters and the tooth widths of the planetary gear and the cycloidal gear, so that the errors become uncertain factors in reliability analysis; the RV reducer has a severe working environment, so that the working environment of a gear and a bearing is changed greatly, and the input rotating speed, the output rotating speed and the input power are uncertain and also become uncertain factors in reliability analysis.
S24, according to the uncertain factors obtained in the step S23, quantifying the variables in the failure physical model determined in the step S22, determining the distribution types and the distribution parameters of the variables, and establishing a function of the main failure mode.
(1) When the tooth surface contact stress of the planetary gear is greater than the tooth surface contact fatigue strength, the tooth surface of the gear is abraded, the limit state of the planetary gear in the planetary gear tooth surface abrasion failure mode can be obtained, and the function in the failure mode is further obtained as follows:
the physical meanings and distribution types of the coefficients and variables in the formula are shown in table 1.
TABLE 1
By substituting the individual coefficients into a function G1In (G)1Can be simplified as follows:
(2) when the bending stress of the tooth root of the planetary gear is larger than the bending fatigue strength of the tooth root of the planetary gear, the tooth of the gear is broken, the limit state of the planetary gear in the tooth breaking failure mode of the planetary gear can be obtained, and the function in the failure mode is further obtained as follows:
the physical meanings and distribution types of the coefficients and variables in the formula are shown in Table 2.
TABLE 2
By substituting the individual coefficients into a function G2In (G)2Can be simplified as follows:
(3) when the contact stress of the tooth surface of the cycloidal gear is greater than the contact fatigue strength of the tooth surface, the tooth surface of the gear is abraded, so that the limit state of the cycloidal gear under the cycloidal gear tooth surface abrasion fault mode can be obtained, and further the function under the fault mode is obtained:
the physical meanings and distribution types of the coefficients and variables in the formula are shown in Table 3.
TABLE 3
By substituting the individual coefficients into a function G3In (G)3Can be simplified as follows:
G3＝1.24σHlim-1.42σH0
(4) when the actual service life of the ball bearing is shorter than the rated service life, the ball bearing is worn, the limit state of the ball bearing in the ball bearing wear failure mode can be obtained, and the function in the failure mode is further obtained as follows:
the physical meanings and distribution types of the coefficients and variables in the formula are shown in Table 4.
TABLE 4
By substituting the individual coefficients into a function G4In (G)4Can be simplified as follows:
in an optional embodiment of the present invention, determining the learning function required in the model in step S3, determining a learning termination condition, and building a Kriging model specifically includes the following sub-steps:
s31, determining a learning function in the Kriging model according to a Monte Carlo simulation method and a function, and selecting a reasonable learning function;
as can be seen from the Monte Carlo simulation method, the predicted symbol of the sample point near the boundary surface of the extreme state where g (x) is 0 is most likely to be wrong, and if the sample point where the predicted symbol is most likely to be wrong is added to the experimental design to fit the prediction model, a very good effect is exerted on the prediction model. To find the location of the best point for fitting the prediction function, a learning function is defined as:
wherein, muG(x) Is the mean value of the sample points, σG(x) Is the sample point variance;
as a result of the analysis, the smaller the U value, the greater the probability of a predicted symbol error at the point x, indicating that the position of the point x may be closer to the limit state plane g (x) than 0 (i.e., | μ |)G(x) The smaller the value of | is), or point x may have a higher uncertainty (i.e., | σ)G(x) The value of | is large), it is also possible that both cases exist. In a large number of sample points obtained by the Monte Carlo simulation method, the point x corresponding to the Umin has the characteristics, namely the point x corresponding to the Umin is closer to the extreme state and has higher prediction uncertainty. Therefore, it is reasonable to use the sample point corresponding to the minimum U as the rule for actively selecting points in the algorithm.
And S32, determining the learning stopping condition according to the characteristics of the learning process and the requirement of reliability precision by combining the characteristics of the sample data.
Using the minimum value of the learning function values of all sample points larger than a certain value as the condition for stopping iteration, and expressing as follows:
min(U(x))≥Ulimit
wherein, UlimitThe threshold value is an index of a learning function, and the probability of predicting all sample point symbols to be correct by using a Kriging model is at least phi (U)limit) When U is formedlimitWhen 2, the probability that all sample point symbols are correct is at least Φ (U)limit)＝0.977。UlimitThe magnitude of the value is selected and controlled according to the actual problem requirements, i.e. the higher the reliability accuracy requirement, the more samples are needed to fit the function.
In an optional embodiment of the present invention, in the step S4, the Kriging model in the step S2 and the Kriging model in the step S3 are combined with the Monte Carlo simulation method to establish the AK-MCS reliability analysis model of the RV reducer of the industrial robot based on the Kriging model and the Monte Carlo simulation method in the multiple failure modes, so as to obtain the corresponding failure probability and reliability.
An AK-MCS (active learning model based on a learning model and Monte Carlo simulation) model is an active learning reliability algorithm based on a Kriging model and a Monte Carlo simulation method, the method fully exerts the advantages of the stochastic characteristic and the nonlinear fitting of the Kriging model prediction, and realizes the reliability calculation problem of efficiently and accurately solving the implicit function.
As shown in fig. 3, step S4 specifically includes the following sub-steps:
s41, generating a candidate sample total by adopting a Monte Carlo simulation method;
generating N from a joint probability density function of basic random variablesMCA random sample, andto indicate. In S, these sample points do not need to calculate the function value G (x)i) The actual function g (x) is calculated only when needed during the active learning process, and therefore these random samples S are referred to as the candidate sample population.
S42, generating test design sample points by adopting a Latin hypercube method, and calculating the response value of an actual function;
adopting Latin hypercube method, and obtaining the product in random variable space (-5 sigma)i,+5σi) Generating initial Design of Experiment (DOE) sample points, using SDOE＝[s(1)s(2)…s(N)]TTo represent and calculate SDOEActual function response value Y ofDOEG (x), a smaller number of initial DOEs are typically selected, and the design for experiment sample points DOEs are updated in the course of subsequent learning point selection.
S43, establishing a Kriging prediction model according to the test design sample points and the actual function response values obtained in the step S42;
from SDOEAnd YDOEEstablishing a Kriging prediction model and calculating candidate samplesAll sample points x in the population SiPredicted value of (2)Sum varianceAnd calculates these sample points xiCorresponding learning function value U (x)i)。
S44, judging whether learning stop conditions are met according to the Kriging prediction model obtained in the step S43; if yes, stopping learning and carrying out the next step; if not, sequentially stepping forward, adding the sample point with the minimum learning function value in the candidate sample population into the test design sample point, and turning to the step S43;
x is to beiAccording to UiThe values are arranged from large to small, and the rearranged candidate sample population S is usedIs represented by x'iIs the ith sample point, U'iIs sample point x'iCorresponding learning function values, andget a plurality ofRespectively judge whether the requirements are metCorresponding learning stop conditions:
wherein,lower bound of learning function value for ith sample point, phi (U)limit) Indexing a threshold U for a learning functionlimitThe corresponding probability value is set to be,for learning the lower bound of the functionThe corresponding probability value. If the learning stop condition is met, stopping learning; otherwise, sequentially increasing N to N +1(N is the number of cycles), and selecting the best sample point in S (i.e. corresponding to the learning function value U (x)i) Minimum sample point) is added to the design for test sample point DOE and the process goes to step S43.
S45, calculating the failure probability and the variation coefficient by using the Kriging prediction model obtained in the step S43;
the calculation formula for calculating the failure probability is specifically expressed as:
wherein,as an estimate of the probability of failure, If(G(xi) Is an indicative function, xiThe ith sample point obtained for MC simulation, when G (x)i) When the temperature is less than or equal to 0, If(G(xi) 1 when G (x)i) When > 0, If(G(xi))＝0；NG≤0Number of sample points falling into the failure domain, NMCTotal number of samples simulated for MC.
The calculation formula for calculating the coefficient of variation is specifically expressed as:
according to the two calculation formulas, the current Kriging prediction is adopted to calculateProbability of failureAnd coefficient of variation
S46, judging whether the variation coefficient obtained in the step S45 meets the precision requirement; if so, ending the operation and outputting a result; if not, the number of samples of the candidate sample population is increased, and the process proceeds to step S43.
If the coefficient of variationStopping the active learning reliability algorithm and outputting a result; otherwise, the number of samples in the candidate sample population S is increased to reduce the coefficient of variation of the failure probability estimation value, and the process goes to step S43.
According to the established function and the corresponding AK-MCS model, the reliability of the RV reducer of the industrial robot under the combined action of the four failure modes is as follows: r is 1-Pf1-0.0128-0.9872. Selection of [ delta ]]When the coefficient of variation is 0.03, the coefficient of variation is calculated to beSatisfy the requirement ofTherefore, the reliability result obtained in the embodiment meets the precision requirement.
The method can adaptively select points to estimate the function, can exert many advantages of a Monte Carlo simulation method, fully exert limited sample information, and obtain a better Kriging model by using fewer experimental design points.
The reliability modeling and analysis under various main failure modes of the RV reducer of the industrial robot are considered, a Kriging model and a Monte Carlo simulation method are combined, a new AK-MCS reliability analysis model is established, failure probability and reliability under the multiple failure modes are obtained, results are more in line with engineering practice, the calculation process is greatly simplified, and time is saved. The result of the method has important significance for the reliability analysis of the RV reducer of the industrial robot; at the same time, the result also has a positive effect on the reliability design.
It will be appreciated by those of ordinary skill in the art that the embodiments described herein are intended to assist the reader in understanding the principles of the invention and are to be construed as being without limitation to such specifically recited embodiments and examples. Those skilled in the art can make various other specific changes and combinations based on the teachings of the present invention without departing from the spirit of the invention, and these changes and combinations are within the scope of the invention.
Claims (10)
1. The reliability analysis method for the RV reducer of the industrial robot in the multi-failure mode is characterized by comprising the following steps of:
s1, analyzing the failure modes of the RV reducer of the industrial robot, and selecting the main failure mode as a reliability analysis object;
s2, analyzing parts and failure reasons corresponding to the main failure mode in the step S1, determining a failure physical model and uncertain factors, and establishing a function of the main failure mode;
s3, determining a learning function and a learning stopping condition in the Kriging model, and establishing the Kriging model;
s4, establishing an AK-MCS reliability analysis model of the industrial robot RV reducer under the multi-failure mode based on the Kriging model and the MonteCarlo simulation method according to the function of the main failure mode in the step S2 and the Kriging model in the step S3, and obtaining failure probability and reliability under the multi-failure mode.
2. The reliability analysis method for the RV reducer of the industrial robot in the multi-failure mode as claimed in claim 1, characterized in that the step S1 is specifically as follows:
summarizing and analyzing the failure mode of the RV reducer of the industrial robot according to the fault and maintenance statistical data of the RV reducer of the industrial robot; analyzing the risk evaluation of various failure modes according to an FMEA report table of the RV reducer, determining a judgment standard, and obtaining a main failure mode of the RV reducer, wherein the method specifically comprises the following steps: the tooth surface of the planetary gear is worn, the gear teeth of the planetary gear are broken, the tooth surface of the cycloidal gear is worn, and the rolling bearing is worn.
3. The reliability analysis method for the RV reducer of the industrial robot in the multi-failure mode as claimed in claim 2, characterized in that the step S2 specifically comprises the following substeps:
s21, determining failure parts corresponding to the main failure mode according to the main failure mode determined in the step S1, and analyzing failure reasons;
s22, determining a corresponding failure physical model according to the parts and the failure reasons corresponding to the main failure modes determined in the step S21;
s23, analyzing uncertain factors in failure reasons according to the failure physical model determined in the step S22 and by combining the actual situation of the RV reducer;
s24, according to the uncertain factors obtained in the step S23, quantifying the variables in the failure physical model determined in the step S22, determining the distribution types and the distribution parameters of the variables, and establishing a function of the main failure mode.
4. The reliability analysis method for the RV reducer of the industrial robot under the multiple failure modes as claimed in claim 3, characterized in that the function of the planetary gear tooth surface abrasion failure mode in the step S24 is specifically expressed as:
wherein σHlimDenotes the contact fatigue limit, Z, of the test gearNDenotes the life factor, ZRExpressing the coefficient of roughness of the tooth surface, ZVDenotes the velocity coefficient, ZWDenotes the work hardening coefficient, ZLDenotes the coefficient of lubricant, ZXDenotes the size factor, ZHRepresenting the node area coefficient, ZEDenotes the coefficient of elasticity, ZεDenotes the coefficient of degree of overlap, ZβRepresenting the helix angle coefficient, KpRepresenting the imbalance coefficient of load distribution among planet wheels, P representing input power, d representing the reference circle diameter of the gear, b representing the tooth width, npIndicating the number of planet gears, nμRepresenting input speed, u representing gear ratio, KA1Expressing the coefficient of use in the tooth flank wear failure mode, KV1Expressing the coefficient of dynamic load, K, in the tooth flank wear failure modeHβExpressing the tooth load distribution coefficient, K, in the tooth flank wear failure modeHαRepresenting the tooth flank load distribution coefficient in the tooth flank wear failure mode.
5. The reliability analysis method for the RV reducer of the industrial robot under the multiple failure modes as claimed in claim 4, characterized in that the function of the planetary gear tooth fracture failure mode in the step S24 is specifically expressed as:
wherein σFlimShows the bending fatigue strength, Y, of the test gearSTDenotes a stress correction coefficient, Y, of the test gearNTDenotes the life factor, YδrelTIndicating the relative root fillet sensitivity, YRrelTRepresenting the coefficient of relative root surface condition, YXSize factor, m, representing the calculation of bending StrengthnDenotes the normal modulus, YFaRepresenting the tooth form coefficient, Y, of the load acting on the tooth tipSaIndicating the stress correction coefficient, Y, of the load acting on the tooth tipεDenotes the coefficient of degree of overlap, YβRepresenting the helix angle coefficient, KA2Expressing coefficient of use in failure mode of tooth breakage, KV2Representing the dynamic load coefficient, K, in the failure mode of tooth breakageFβExpressing the tooth load distribution coefficient, K, in the failure mode of tooth breakageFαRepresenting the tooth-to-tooth load distribution coefficient in the tooth fracture failure mode.
6. The reliability analysis method for the RV reducer of the industrial robot under the multiple failure modes as claimed in claim 5, characterized in that the function of the cycloidal gear tooth surface abrasion failure mode in the step S24 is specifically expressed as:
wherein σHlimRepresenting the contact fatigue limit, σ, of the test gearH0Denotes the initial value of the calculated contact stress, K denotes the calculation coefficient, KHRepresents the interdental load distribution coefficient, KA3Expressing the coefficient of use in the tooth flank wear failure mode, KV3Representing the dynamic load coefficient in the tooth flank wear failure mode.
7. The reliability analysis method for the RV reducer of the industrial robot in the multiple failure modes as claimed in claim 6, characterized in that the function of the wear failure mode of the rolling bearing in the step S24 is specifically expressed as:
wherein, CrIndicating the dynamic load rating, P, of the bearingrDenotes the equivalent dynamic load of the bearing, nμRepresenting input shaft speed, nvRepresents the output shaft speed, and epsilon represents the life factor.
8. The reliability analysis method for the RV reducer of the industrial robot in the multi-failure mode as claimed in claim 7, characterized in that the step S3 specifically comprises the following substeps:
s31, determining a learning function in the Kriging model according to a Monte Carlo simulation method and a function, wherein the learning function is expressed as:
wherein, muG(x) Is the mean value of the sample points, σG(x) Is the sample point variance;
s32, according to the characteristics of the learning process and the requirement of reliability precision, combining the characteristics of the sample data, determining the condition of learning stop, which is expressed as:
min(U(x))≥Ulimit
wherein, UlimitA threshold is indexed for the learning function.
9. The reliability analysis method for the RV reducer of the industrial robot in the multi-failure mode as claimed in claim 8, characterized in that the step S4 includes the following sub-steps:
s41, generating a candidate sample total by adopting a Monte Carlo simulation method;
s42, generating test design sample points by adopting a Latin hypercube method, and calculating the response value of an actual function;
s43, establishing a Kriging prediction model according to the test design sample points and the actual function response values obtained in the step S42;
s44, judging whether learning stop conditions are met according to the Kriging prediction model obtained in the step S43; if yes, stopping learning and carrying out the next step; if not, sequentially stepping forward, adding the sample point with the minimum learning function value in the candidate sample population into the test design sample point, and turning to the step S43;
s45, calculating the failure probability and the variation coefficient by using the Kriging prediction model obtained in the step S43;
s46, judging whether the variation coefficient obtained in the step S45 meets the precision requirement; if so, ending the operation and outputting a result; if not, the number of samples of the candidate sample population is increased, and the process proceeds to step S43.
10. The reliability analysis method for the RV reducer of the industrial robot under the multiple failure modes according to claim 9, characterized in that the calculation formula for calculating the failure probability in the step S45 is specifically expressed as:
wherein,as an estimate of the probability of failure, If(G(xi) Is an indicative function, xiThe ith sample point, N, obtained for MC simulationG≤0Number of sample points falling into the failure domain, NMCTotal number of samples simulated for MC;
the calculation formula for calculating the coefficient of variation is specifically expressed as:
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