CN110096796B - Reliability analysis method for RV reducer of industrial robot in multiple failure modes - Google Patents

Abstract

The invention discloses a reliability analysis method for an RV reducer of an industrial robot under multiple failure modes. The method starts from the main failure mode, establishes the function function under the corresponding limit state, determines the uncertain factors under different failure modes, and corresponds to The parameter variables in the function function are used to determine their distribution characteristics; after the function function of the main failure mode is obtained, it is converted into a Kriging model, the type of learning function in the model is determined, and the Monte Carlo simulation method is used for sampling and fitting the established Function function; further determine the learning stop condition according to the required accuracy requirements to form a complete learning process; calculate the failure probability and variation coefficient according to the established AK‑MCS reliability analysis model to verify whether the accuracy requirements are met; the obtained reliability analysis results The reliability problems and optimization methods of the industrial robot RV reducer under multiple failure modes can be fed back, and a strong basis for its reliability design can be provided.

Description

A reliability analysis method for industrial robot RV reducer under multiple failure modes

technical field

The invention belongs to the technical field of reliability analysis of an industrial robot RV reducer, in particular to a reliability analysis method of an industrial robot RV reducer under multiple failure modes based on an AK-MCS model.

Background technique

The industrial robot RV reducer is a transmission device used to make the robot perform work actions. It is mostly used in the joints of industrial robots and is the core component that determines the performance of industrial robots. Compared with the traditional gear transmission, the RV reducer has many advantages such as high transmission rigidity, large transmission ratio, small inertia, large output torque, stable transmission, small size, strong impact resistance, etc. rigidity and service life requirements. Therefore, it is widely used in the field of industrial robots.

With the continuous improvement of the performance requirements of industrial robots such as movement speed, positioning accuracy, and bearing capacity, the performance parameters of RV reducers are also continuously improved. The working environment and workload of RV are more complicated than before, and the failure problem is becoming more and more prominent. , once the RV reducer fails, it will inevitably lead to the failure of the entire industrial robot system, causing inestimable economic losses and even threatening personal safety. In the actual working environment, problems such as harsh working environment, insufficient lubrication and cooling, and large vibration and impact load of RV reducer will aggravate the damage of RV reducer and increase its failure rate. Because the RV reducer requires high matching precision, and the structure is relatively complex, the gap between the gears is very small, when the RV reducer works for a long time, it is likely that the whole RV reducer will fail due to the failure of some gear teeth. The maintenance of the RV reducer is difficult and the cost is high, which requires the RV reducer to have high reliability.

At present, the reliability analysis and research of RV reducer often only focuses on a single failure mode, which cannot truly and effectively reflect the combined effect of various failure modes of the RV reducer. The reliability assessment of the entire RV reducer, Often results are too low or too high. Therefore, it is of great practical significance to propose a method that can establish the reliability model of RV reducer under multiple failure modes and analyze the reliability of multiple failure modes of RV reducer at the same time.

SUMMARY OF THE INVENTION

The purpose of the invention is: in order to solve the above problems existing in the reliability analysis of the existing industrial robot RV reducer, the present invention proposes a reliability of the industrial robot RV reducer under multiple failure modes based on the AK-MCS model Analytical method.

The technical scheme of the present invention is: a reliability analysis method of an industrial robot RV reducer under multiple failure modes, comprising the following steps:

S1. Analyze the failure mode of the industrial robot RV reducer, and select the main failure mode as the reliability analysis object;

S2, analyze the parts and failure causes corresponding to the main failure modes in step S1, determine the failure physical model and uncertain factors, and establish the function functions of the main failure modes;

S3. Determine the learning function and the learning stop condition in the Kriging model, and establish the Kriging model;

S4. According to the function function of the main failure mode in step S2 and the Kriging model in step S3, establish an AK-MCS reliability analysis model based on the Kriging model and MonteCarlo simulation method of the industrial robot RV reducer under multiple failure modes, and obtain multiple failure modes. failure probability and reliability.

Further, the step S1 is specifically:

According to the failure and maintenance statistics of the industrial robot RV reducer, the failure mode of the industrial robot RV reducer is summarized and analyzed; and according to the FMEA report form of the RV reducer, the risk assessment of various failure modes is analyzed and determined Judging criteria, the main failure modes of the RV reducer were obtained, including: planetary gear tooth surface wear, planetary gear tooth fracture, cycloidal gear tooth surface wear, and rolling bearing wear.

Further, the step S2 specifically includes the following sub-steps:

S21, according to the main failure mode determined in step S1, determine the failure components corresponding to the main failure mode, and analyze the failure cause;

S22, according to the components and failure causes corresponding to the main failure modes determined in step S21, determine the corresponding failure physical model;

S23, according to the failure physical model determined in step S22, combined with the actual situation of the RV reducer, analyze the uncertain factors in the failure cause;

S24. According to the uncertain factors obtained in step S23, quantify the variables in the failure physical model determined in step S22, determine the distribution type and distribution parameters of the variables, and establish the function function of the main failure mode.

Further, the function function of the wear failure mode of the planetary gear tooth surface in the step S24 is specifically expressed as:

Among them, σ _Hlim represents the contact fatigue limit of the test gear, Z _N represents the life factor, Z _R represents the tooth surface roughness factor, Z _V represents the speed factor, Z _W represents the work hardening factor, Z _L represents the lubricant factor, and Z _X represents the Size coefficient, Z _H is the node area coefficient, Z _E is the elastic coefficient, Z _ε is the coincidence coefficient, Z _β is the helix angle coefficient, K _p is the unbalanced load distribution coefficient between the planetary gears, P is the input power, and d is the gear. The diameter of the index circle, b represents the tooth width, n _p represents the number of planetary gears, n _μ represents the input speed, u represents the transmission ratio, K _A1 represents the service coefficient under the tooth surface wear failure mode, and K _V1 represents the tooth surface wear failure mode K _Hβ represents the tooth-tooth load distribution coefficient under the tooth surface wear failure mode, and K _Hα represents the tooth-tooth load distribution coefficient under the tooth surface wear failure mode.

Further, the function function of the planetary gear tooth fracture failure mode in the step S24 is specifically expressed as:

Among them, σ _Flim is the bending fatigue strength of the test gear, Y _ST is the stress correction coefficient of the test gear, Y _NT is the life coefficient, Y _δrelT is the relative root fillet sensitivity coefficient, Y _RrelT is the relative root surface condition coefficient, Y _X represents the dimension coefficient for bending strength calculation, m _n represents the normal modulus, Y _Fa represents the tooth shape coefficient when the load acts on the tooth top, Y _Sa represents the stress correction coefficient when the load acts on the tooth top, and Y _ε represents the coincidence degree Coefficient, Y _β is the helix angle coefficient, K _A2 is the service factor in the tooth fracture failure mode, K _V2 is the dynamic load coefficient in the tooth fracture failure mode, K _Fβ is the tooth load distribution in the tooth fracture failure mode coefficient, K _Fα represents the inter-tooth load distribution coefficient in the tooth fracture failure mode.

Further, the functional function of the wear failure mode of the cycloidal gear tooth surface in the step S24 is specifically expressed as:

Among them, σ _Hlim represents the contact fatigue limit of the test gear, σ _H0 represents the initial value of the calculated contact stress, K represents the calculation coefficient, and K _H represents the inter-tooth load distribution coefficient.

Further, the functional function of the rolling bearing wear failure mode in the step S24 is specifically expressed as:

Among them, C _r represents the rated dynamic load of the bearing, P _r represents the equivalent dynamic load of the bearing, n _μ represents the rotational speed of the input shaft, n _v represents the rotational speed of the output shaft, and ε represents the life factor.

Further, the step S3 specifically includes the following sub-steps:

S31. Determine the learning function in the Kriging model according to the Monte Carlo simulation method and the function function, which is expressed as:

Among them, μ _G (x) is the sample point mean, σ _G (x) is the sample point variance;

S32. According to the characteristics of the learning process and the requirements of reliability and accuracy, combined with the characteristics of the sample data, determine the condition for stopping the learning, which is expressed as:

min(U(x))≥U _limit

Among them, U _limit is the learning function index threshold.

Further, the step S4 specifically includes the following sub-steps:

S41, using the Monte Carlo simulation method to generate a candidate sample population;

S42, using the Latin hyper-dimension method to generate experimental design sample points, and calculate the actual functional function response value;

S43, establishing a Kriging prediction model according to the experimental design sample points and actual function function response values obtained in step S42;

S44. Determine whether the learning stop condition is satisfied according to the Kriging prediction model obtained in step S43; if yes, stop the learning and go to the next step; Experiment design sample point, go to step S43;

S45, using the Kriging prediction model obtained in step S43 to calculate the failure probability and the coefficient of variation;

S46, determine whether the coefficient of variation obtained in step S45 meets the accuracy requirements; if so, the operation ends, and the result is output; if not, the sample size of the candidate sample population is increased, and the process goes to step S43.

Further, the calculation formula for calculating the failure probability in the step S45 is specifically expressed as:

为失效概率的估计值，I_f(G(x_i))为示性函数，x_i为MC模拟得到的第i个样本点，N_G≤0为落入失效域样本点的个数，N_MC为MC模拟的总样本数量。in,

is the estimated value of failure probability, If (G(x _i )) is an indicative function, x _i is the _ith sample point obtained by MC simulation, N _G≤0 is the number of sample points falling into the failure domain, N _MC is the total sample size of MC simulation.

The formula for calculating the coefficient of variation is specifically expressed as:

The beneficial effects of the present invention are: the present invention aims at the problems existing in the reliability analysis of the current industrial robot RV reducer, such as single failure mode analysis, diverse failure causes, and complex calculation process, starting from the main failure mode, and establishing functions under corresponding limit states. function, determine the uncertain factors under different failure modes, correspond to the parameter variables in the function function, and determine its distribution characteristics; after the function function of the main failure mode is obtained, it is converted into a Kriging model, and the learning function in the model is determined According to the Monte Carlo simulation method, sampling is carried out to fit the established function function; the learning stop condition is further determined according to the required accuracy requirements to form a complete learning process; the failure probability and The coefficient of variation is used to verify whether it meets the accuracy requirements; the obtained reliability analysis results can feed back the reliability problems and optimization methods of the industrial robot RV reducer under multiple failure modes, and provide a favorable basis for its reliability design.

Description of drawings

Fig. 1 is the reliability analysis method flow chart of the industrial robot RV reducer under the multi-failure mode of the present invention;

2 is a schematic structural diagram of an industrial robot RV reducer provided by an embodiment of the present invention;

FIG. 3 is a flow chart of model analysis of an AK-MCS model of an industrial robot RV reducer provided by an embodiment of the present invention.

Detailed ways

In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention, but not to limit the present invention.

As shown in Figure 1, it is a schematic flow chart of the reliability analysis method of the industrial robot RV reducer under the multiple failure modes of the present invention; a reliability analysis method of the industrial robot RV reducer under the multiple failure modes, comprising the following steps:

S1. Analyze the failure mode of the industrial robot RV reducer, and select the main failure mode as the reliability analysis object;

S2, analyze the parts and failure causes corresponding to the main failure modes in step S1, determine the failure physical model and uncertain factors, and establish the function functions of the main failure modes;

S3. Determine the learning function and the learning stop condition in the Kriging model, and establish the Kriging model;

S4. According to the function function of the main failure mode in step S2 and the Kriging model in step S3, establish an AK-MCS reliability analysis model based on the Kriging model and MonteCarlo simulation method of the industrial robot RV reducer under multiple failure modes, and obtain multiple failure modes. failure probability and reliability.

In an optional embodiment of the present invention, the above step S1 is specifically:

According to the failure and maintenance statistics of the industrial robot RV reducer, the failure mode of the industrial robot RV reducer is summarized and analyzed; and according to the FMEA report form of the RV reducer, the risk assessment of various failure modes is analyzed and determined Judging criteria, get the main failure mode of RV reducer.

The RV reducer is generally composed of rolling bearings, cycloidal wheels, needle bearings, planetary gears, input shafts, pin teeth, crankshafts, etc. The principle structure diagram of RV reducer is shown in Figure 2, including rear end cover 1, rolling bearing 2, positioning bearing 3, cycloidal wheel 4, needle bearing 5, output disc 6, planetary gear 7, input shaft 8, pin teeth 9. Shell 10, crankshaft 11; among them, planetary gears, cycloidal wheels, and rolling bearings are more important: planetary gears are the components of the first-stage reduction gear of the RV reducer; It further decelerates the torque and speed transmitted by the first-stage reduction gear and transmits it to the output mechanism; the rolling bearing reduces the friction between the parts of the RV reducer during operation and can play a supporting role.

According to the statistical data of RV reducer failure and repair, and the FMEA report form of the RV reducer, the failure mode with a risk priority number greater than 190 is selected as the main failure mode. Therefore, the main failure modes selected are: planetary gear tooth surface wear, planetary gear tooth fracture; cycloidal gear tooth surface wear; rolling bearing wear.

In an optional embodiment of the present invention, the above step S2 selects the main failure mode in step S1 to determine the failure component and the failure cause; analyzes the limit state of the failure mode, and establishes the corresponding function function; determines the parameters in the function function The type of distribution of values and variables, including the following sub-steps:

S21, according to the main failure mode determined in step S1, determine the failure components corresponding to the main failure mode, and analyze the failure cause;

According to the analysis in step S1, the main failure modes and their causes:

(1) The tooth surface of the planetary gear is worn. Because the industrial robot RV reducer has the characteristics of large transmission ratio and large impact load change, the tooth surface contact stress of the planetary gear changes greatly. When the tooth surface contact stress is greater than the contact fatigue strength, the tooth surface contact fatigue failure of the planetary gear will occur. , resulting in wear of the planetary gear tooth surface.

(2) The planetary gear teeth are broken. Because the industrial robot RV reducer has the characteristics of large transmission ratio and large impact load change, the bending stress of the tooth root of the planetary gear changes greatly. When the bending stress of the tooth root is greater than the bending fatigue strength, the tooth root bending fatigue failure of the planetary gear will occur. , causing the planetary gear teeth to break.

(3) The tooth surface of the cycloidal gear is worn. Due to the complexity and particularity of the cycloidal wheel structure, when meshing with the needle teeth, the stress changes greatly. When the tooth surface contact stress is greater than the contact fatigue strength, the cycloidal wheel will experience tooth surface contact fatigue failure, resulting in the pendulum The tooth surface of the wire wheel is worn.

(4) The rolling bearing is worn. Because the load borne by the rolling bearing is relatively large, and the rotating speed may be the sum of the input speed and the output speed, the working environment of the rolling bearing is high-speed and heavy load, which is easy to cause its life to fail to meet the required rated life, resulting in bearing fatigue failure, resulting in bearing failure. wear.

S22, according to the components and failure causes corresponding to the main failure modes determined in step S21, determine the corresponding failure physical model;

(1) The wear of the planetary gear tooth surface corresponds to the contact stress-strength failure physical model of the gear;

(2) The gear teeth of the planetary gear are broken, corresponding to the bending stress-strength failure physical model of the gear;

(3) The wear of the cycloidal gear tooth surface corresponds to the contact stress-strength failure physical model of the gear;

(4) Bearing wear, corresponding to the fatigue life failure physical model of the bearing.

S23, according to the failure physical model determined in step S22, combined with the actual conditions such as the processing technology and working environment of the RV reducer, analyze the uncertain factors in the failure cause;

The machining process of the gears will cause errors in the size of the actual gears, and there may be errors in the diameter and tooth width of the planetary gears and cycloidal gears, which become uncertain factors in the reliability analysis; the working environment of the RV reducer is relatively bad, resulting in gears Due to the large changes in the working environment of the bearing and the bearing, there will be uncertainties in the input speed, output speed and input power, which will also become uncertain factors in reliability analysis.

S24. According to the uncertain factors obtained in step S23, quantify the variables in the failure physical model determined in step S22, determine the distribution type and distribution parameters of the variables, and establish the function function of the main failure mode.

(1) When the contact stress of the tooth surface of the planetary gear is greater than the contact fatigue strength of the tooth surface, the tooth surface of the gear will be worn, and the limit state of the planetary gear in the failure mode of the tooth surface of the planetary gear can be obtained, and further obtained under the failure mode. The function function is:

The physical meanings and distribution types of the coefficients and variables in the formula are shown in Table 1.

Table 1

Bringing the individual coefficients into the functional function G ₁ , G ₁ can be simplified to:

(2) When the bending stress of the tooth root of the planetary gear is greater than the bending fatigue strength of the tooth root, the teeth of the gear will be broken, and the limit state of the planetary gear in the failure mode of the tooth fracture of the planetary gear can be obtained. The function function is:

The physical meanings and distribution types of the coefficients and variables in the formula are shown in Table 2.

Table 2

Bringing the individual coefficients into the functional function G ₂ , G ₂ can be simplified to:

(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 will be worn, so the limit state of the cycloidal gear in the fault mode of the tooth surface of the cycloidal gear can be obtained, and the Functional functions in failure mode:

The physical meanings and distribution types of the coefficients and variables in the formula are shown in Table 3.

table 3

Bringing the individual coefficients into the functional function _G3 , _G3 can be simplified to:

G ₃ =1.24σ _Hlim -1.42σ _H0

(4) When the actual life of the row ball bearing is less than the rated life, it will cause the wear of the ball bearing. The limit state of the ball bearing under the wear failure mode of the ball bearing can be obtained, and the function function under the failure mode can be obtained as follows:

The physical meanings and distribution types of the coefficients and variables in the formula are shown in Table 4.

Table 4

Bringing the individual coefficients into the functional function _G4 , _G4 can be simplified to:

In an optional embodiment of the present invention, determining the learning function required in the model in the above-mentioned step S3, determining the learning termination condition, and establishing a Kriging model, specifically includes the following sub-steps:

S31. Determine the learning function in the Kriging model according to the Monte Carlo simulation method and the functional function, and select a reasonable learning function;

It can be seen from the Monte Carlo simulation method that the prediction symbols of the sample points near the limit state interface of G(x)=0 are the most likely to be wrong. If the sample points with the most error-prone prediction symbols are added to the experimental design to fit the prediction model, It will have a very good effect on the prediction model. To find the location of the best point for fitting the prediction function function, define the learning function as:

Among them, μ _G (x) is the sample point mean, σ _G (x) is the sample point variance;

The analysis shows that the smaller the U value, the greater the probability of wrong prediction symbol at the point x, which means that the position of the point x may be closer to the limit state surface _G (x)=0 (that is, the higher the value of |μG(x)| small), or the point x may have high uncertainty (that is, the |σ _G (x)| value is large), or both conditions may exist at the same time. Among the large number of sample points obtained by the Monte Carlo simulation method, the point x corresponding to the minimum U has the above characteristics, that is, the point x corresponding to the minimum U is closer to the limit state and has a higher prediction uncertainty. Therefore, it is very reasonable to use the sample point corresponding to the minimum U as the rule for active point selection in this algorithm.

S32 , according to the characteristics of the learning process and the requirements of reliability and accuracy, combined with the characteristics of the sample data, determine the conditions for stopping the learning.

The minimum value of the learning function value of all sample points is greater than a certain value as the condition for iterative stop, which is expressed as:

min(U(x))≥U _limit

Among them, U _limit is the learning function index threshold, which means that the Kriging model is used to predict that the probability of correct symbols of all sample points is at least Φ(U _limit ), and when U _limit = 2, the probability of correct symbols of all sample points is at least Φ (U _limit ) )=0.977. The size of the U _limit value is selected and controlled according to the actual problem requirements, that is, the higher the reliability accuracy requirement, the more samples are needed to fit the functional function.

In an optional embodiment of the present invention, the above step S4 establishes a Kriging-based model of the industrial robot RV reducer under multiple failure modes according to the function function established in step S2 and the Kriging model in step S3, combined with Monte Carlo simulation method And the AK-MCS reliability analysis model of MonteCarlo simulation method to get the corresponding failure probability and reliability.

AK-MCS (An active learning model based on Kiging model and Monte Carlosimulation) model is an active learning reliability algorithm based on Kriging model and Monte Carlo simulation method. This method makes full use of the random characteristics and nonlinear fitting predicted by Kriging model. It realizes the reliability calculation problem of solving implicit function functions efficiently and accurately.

As shown in Figure 3, step S4 specifically includes the following sub-steps:

S41, using the Monte Carlo simulation method to generate a candidate sample population;

来表示。在S中，这些样本点并不需要计算功能函数值G(x_i)，仅在主动学习过程中需要时，才计算实际功能函数G(x)，因此，称这些随机样本S为候选样本总体。Generate N _MC random samples from the joint probability density function of basic random variables, and use

To represent. In S, these sample points do not need to calculate the function function value G(x _i ), and only calculate the actual function function G(x) when it is required in the active learning process. Therefore, these random samples S are called candidate sample populations .

S42, using the Latin hyper-dimension method to generate experimental design sample points, and calculate the actual functional function response value;

Using the Latin hypercube method, the initial experimental design sample points (Design of Experiment, DOE) are generated in the random variable space (-5σ _i , +5σ _i ), with S _DOE = [s ⁽¹⁾ s ⁽²⁾ ... s ^(N) ] ^T to represent, and calculate the actual functional function response value of S _DOE Y _DOE = G(x), the initial DOE is generally selected in a small number, and the experimental design sample point DOE is updated in the process of subsequent learning point selection.

S43, establishing a Kriging prediction model according to the experimental design sample points and actual function function response values obtained in step S42;

和方差

并计算这些样本点x_i对应的学习函数值U(x_i)。The Kriging prediction model is established by S _DOE and Y _DOE , and the predicted value of all sample points x _i in the candidate sample population S is calculated.

and variance

And calculate the learning function value U( _xi ) corresponding to these sample points _xi .

S44. Determine whether the learning stop condition is satisfied according to the Kriging prediction model obtained in step S43; if yes, stop the learning and go to the next step; Experiment design sample point, go to step S43;

表示，x′_i为第i个样本点，U′_i为样本点x′_i对应的学习函数值，且有

取多个

分别判断是否满足

对应的学习停止条件：Arrange x _i according to the value of U _i from large to small, and the rearranged candidate sample population S is

means that x' _i is the ith sample point, U' _i is the learning function value corresponding to the sample point x' _i , and there are

take multiple

Determine whether it is satisfied

The corresponding learning stop condition:

为第i个样本点的学习函数值的下界，Φ(U_limit)为学习函数指标阈值U_limit所对应的概率值，

为学习函数下界

所对应的概率值。若满足学习停止条件，则学习停止；否则，依次递进N＝N+1(N为循环次数)，将S中最好的样本点(即对应学习函数值U(x_i)最小的样本点)加入到试验设计样本点DOE中，转到步骤S43。in,

is the lower bound of the learning function value of the ith sample point, Φ(U _limit ) is the probability value corresponding to the learning function index threshold U _limit ,

is the lower bound of the learning function

the corresponding probability value. If the learning stop condition is met, the learning stops; otherwise, progressively N=N+1 (N is the number of cycles), and the best sample point in S (that is, the sample point with the smallest corresponding learning function value U(x _i ) is selected ) is added to the DOE of the experimental design sample point, and goes to step S43.

S45, using the Kriging prediction model obtained in step S43 to calculate the failure probability and the coefficient of variation;

The calculation formula for calculating the probability of failure is specifically expressed as:

为失效概率的估计值，I_f(G(x_i))为示性函数，x_i为MC模拟得到的第i个样本点，当G(x_i)≤0时，I_f(G(x_i))＝1，当G(x_i)＞0时，I_f(G(x_i))＝0；N_G≤0为落入失效域样本点的个数，N_MC为MC模拟的总样本数量。in,

is the estimated value of failure probability, If (G(x _i )) is an indicative function, and x _i is the _ith sample point obtained by MC simulation. When G(x _i )≤0, If (G(x _i ) _i ))=1, when G(x _i )>0, If (G(x _{i )} )=0; N _G≤0 is the number of sample points that fall into the failure domain, N _MC is the total number of MC simulations Number of samples.

The formula for calculating the coefficient of variation is specifically expressed as:

和变异系数

According to the above two calculation formulas, the current Kriging prediction is used to calculate the failure probability

and coefficient of variation

S46, determine whether the coefficient of variation obtained in step S45 meets the accuracy requirements; if so, the operation ends, and the result is output; if not, the sample size of the candidate sample population is increased, and the process goes to step S43.

则主动学习可靠度算法停止，并输出结果；否则，增加候选样本总体S的样本数量以减小失效概率估计值的变异系数，转到步骤S43。If the coefficient of variation

Then the active learning reliability algorithm stops, and outputs the result; otherwise, the number of samples of the candidate sample population S is increased to reduce the coefficient of variation of the estimated value of failure probability, and the process goes to step S43.

满足

所以本实施例中得到的可靠度结果满足精度要求。According to the established function function and the corresponding AK-MCS model, the reliability of the industrial robot RV reducer under the combined action of the four failure modes is: R=1-P _f =1-0.0128=0.9872. Select [δ] = 0.03, the calculated coefficient of variation is

Satisfy

Therefore, the reliability results obtained in this embodiment meet the accuracy requirements.

The invention can adaptively select points to estimate the function function, can take advantage of many advantages of the Monte Carlo simulation method, fully utilize the limited sample information, and obtain a better Kriging model by using fewer experimental design points.

The invention considers the reliability modeling and analysis under various main failure modes of the industrial robot RV reducer, combines the Kriging model and the Monte Carlo simulation method, and establishes a new AK-MCS reliability analysis model. The failure probability and reliability are better, which makes the results more in line with the actual engineering, and greatly simplifies the calculation process and saves time. The results of the invention are of great significance to the reliability analysis of the industrial robot RV reducer; at the same time, the results also have a positive effect on its reliability design.

Those of ordinary skill in the art will appreciate that the embodiments described herein are intended to assist readers in understanding the principles of the present invention, and it should be understood that the scope of protection of the present invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations without departing from the essence of the present invention according to the technical teaching disclosed in the present invention, and these modifications and combinations still fall within the protection scope of the present invention.

Claims (4)

1. a reliability analysis method of industrial robot RV reducer under multiple failure modes, is characterized in that, comprises the following steps: S1. Analyze the failure mode of the industrial robot RV reducer, and select the main failure mode as the reliability analysis object; the details are: According to the failure and maintenance statistics of the industrial robot RV reducer, the failure mode of the industrial robot RV reducer is summarized and analyzed; and according to the FMEA report form of the RV reducer, the risk assessment of various failure modes is analyzed and determined According to the judgment criteria, the main failure modes of the RV reducer are obtained, including: planetary gear tooth surface wear, planetary gear tooth fracture, cycloidal gear tooth surface wear, and rolling bearing wear; S2, analyze the parts and failure causes corresponding to the main failure modes in step S1, determine the failure physical model and uncertain factors, and establish the function functions of the main failure modes; the specific steps include the following: S21, according to the main failure mode determined in step S1, determine the failure components corresponding to the main failure mode, and analyze the failure cause; S22, according to the components and failure causes corresponding to the main failure modes determined in step S21, determine the corresponding failure physical model; S23, according to the failure physical model determined in step S22, combined with the actual situation of the RV reducer, analyze the uncertain factors in the failure cause; S24, according to the uncertain factors obtained in step S23, quantify the variables in the failure physical model determined in step S22, and determine the distribution type and distribution parameters of the variables, and establish the function function of the main failure mode; The functional function of the wear failure mode of the planetary gear tooth surface in the step S24 is specifically expressed as:

Among them, σ _Hlim represents the contact fatigue limit of the test gear, Z _N represents the life factor, Z _R represents the tooth surface roughness factor, Z _V represents the speed factor, Z _W represents the work hardening factor, Z _L represents the lubricant factor, and Z _X represents the Size coefficient, Z _H is the node area coefficient, Z _E is the elastic coefficient, Z _ε is the coincidence coefficient, Z _β is the helix angle coefficient, k _p is the unbalanced load distribution coefficient between the planetary gears, P is the input power, and d is the gear. The diameter of the index circle, b represents the tooth width, n _p represents the number of planetary gears, n _μ represents the input speed, u represents the transmission ratio, K _A1 represents the service coefficient under the tooth surface wear failure mode, and K _V1 represents the tooth surface wear failure mode K _Hβ represents the tooth-tooth load distribution coefficient under the tooth surface wear failure mode, K _Hα represents the tooth-tooth load distribution coefficient under the tooth surface wear failure mode; The function function of the planetary gear tooth fracture failure mode in the step S24 is specifically expressed as:

Among them, σ _Flim is the bending fatigue strength of the test gear, Y _ST is the stress correction coefficient of the test gear, Y _NT is the life coefficient, Y _δrelT is the relative root fillet sensitivity coefficient, Y _RrelT is the relative root surface condition coefficient, Y _X represents the dimension coefficient for bending strength calculation, m _n represents the normal modulus, Y _Fa represents the tooth shape coefficient when the load acts on the tooth top, Y _Sa represents the stress correction coefficient when the load acts on the tooth top, and Y _ε represents the coincidence degree Coefficient, Y _β is the helix angle coefficient, K _A2 is the service factor in the tooth fracture failure mode, K _V2 is the dynamic load coefficient in the tooth fracture failure mode, K _Fβ is the tooth load distribution in the tooth fracture failure mode coefficient, K _Fα represents the inter-tooth load distribution coefficient under the gear tooth fracture failure mode; The functional function of the wear failure mode of the cycloidal gear tooth surface in the step S24 is specifically expressed as:

Among them, σ _Hlim represents the contact fatigue limit of the test gear, σ _H0 represents the initial value of the calculated contact stress, K represents the calculation coefficient, K _H represents the inter-tooth load distribution coefficient, K _A3 represents the service factor under the tooth surface wear failure mode, and K _V3 Indicates the dynamic load coefficient under the tooth surface wear failure mode; The functional function of the rolling bearing wear failure mode in the step S24 is specifically expressed as:

Among them, C _r represents the rated dynamic load of the bearing, P _r represents the equivalent dynamic load of the bearing, n _μ represents the rotational speed of the input shaft, n _v represents the rotational speed of the output shaft, and ε represents the life coefficient; S3. Determine the learning function and the learning stop condition in the Kriging model, and establish the Kriging model; S4. According to the function function of the main failure mode in step S2 and the Kriging model in step S3, establish the AK-MCS reliability analysis model of the industrial robot RV reducer based on the Kriging model and the MonteCarlo simulation method under the multi-failure mode, and obtain the multi-failure mode Failure probability and reliability in the mode. 2. the reliability analysis method of the industrial robot RV reducer under multiple failure modes as claimed in claim 1, is characterized in that, described step S3 specifically comprises the following sub-steps: S31. Determine the learning function in the Kriging model according to the Monte Carlo simulation method and the function function, which is expressed as:

Among them, μ _G (x) is the sample point mean, σ _G (x) is the sample point variance; S32. According to the characteristics of the learning process and the requirements of reliability and accuracy, combined with the characteristics of the sample data, determine the condition for stopping the learning, which is expressed as: min(U(x))≥U _limit Among them, U _limit is the learning function index threshold. 3. the reliability analysis method of the industrial robot RV reducer under multiple failure modes as claimed in claim 2, is characterized in that, described step S4 specifically comprises the following sub-steps: S41, using the Monte Carlo simulation method to generate a candidate sample population; S42, using the Latin hyper-dimension method to generate experimental design sample points, and calculate the actual functional function response value; S43, establishing a Kriging prediction model according to the experimental design sample points and actual function function response values obtained in step S42; S44. Determine whether the learning stop condition is satisfied according to the Kriging prediction model obtained in step S43; if yes, stop the learning and go to the next step; Experiment design sample point, go to step S43; S45, using the Kriging prediction model obtained in step S43 to calculate the failure probability and the coefficient of variation; S46, determine whether the coefficient of variation obtained in step S45 meets the accuracy requirements; if so, the operation ends, and the result is output; if not, the sample size of the candidate sample population is increased, and the process goes to step S43. 4. the reliability analysis method of industrial robot RV reducer under multiple failure modes as claimed in claim 3, is characterized in that, the calculation formula that calculates failure probability in described step S45 is specifically expressed as:

in,

is the estimated value of failure probability, If (G(x _i )) is an indicative function, x _i is the _ith sample point obtained by MC simulation, N _G≤0 is the number of sample points falling into the failure domain, N _MC is the total number of samples simulated by MC; The formula for calculating the coefficient of variation is specifically expressed as:

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