CN107977481B - Reliability analysis method for transmission system of robot harmonic speed reducer test bed - Google Patents

Reliability analysis method for transmission system of robot harmonic speed reducer test bed Download PDF

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CN107977481B
CN107977481B CN201710992650.2A CN201710992650A CN107977481B CN 107977481 B CN107977481 B CN 107977481B CN 201710992650 A CN201710992650 A CN 201710992650A CN 107977481 B CN107977481 B CN 107977481B
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key connection
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侯卫国
瞿金平
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South China University of Technology SCUT
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Abstract

The invention discloses a method for analyzing the reliability of a transmission system of a robot harmonic speed reducer test bed. The transmission system of the test bed of the harmonic speed reducer of the robot to be analyzed is a series system consisting of a plurality of components and mainly consists of components such as a driving motor, a coupler, an input end torque sensor, a brake and the like. Therefore, the analysis idea of the method is to firstly use the traditional reliability analysis method to primarily analyze and obtain which components in the whole system have the key influence on the reliability of the system and which components have the weak and negligible influence, and then use the reliability analysis method provided by the invention to analyze and calculate the reliability of each key component. On the basis, the overall reliability of the test bed transmission system is finally calculated according to the reliability calculation formula of the series system.

Description

Reliability analysis method for transmission system of robot harmonic speed reducer test bed
Technical Field
The invention relates to the technical field of reliability research of machinery equipment, in particular to a reliability analysis method for a transmission system of a robot harmonic speed reducer test bed.
Background
The harmonic reducer has the characteristics of high reliability and long service life, so that higher requirements are provided for the overall reliability of the transmission test bench of the harmonic reducer. In the process of testing the reliability of the harmonic reducer, the high-precision test is kept, meanwhile, the load needs to be accelerated, and the requirement of halt disassembly detection exists. The reliability of the transmission system is more critical than the control system. Therefore, an analysis method for quantifying reliability is needed in the field, and weak parts of a traditional system of the whole test bed are found through analysis, so that theoretical support is provided for further improving the reliability of a transmission system of the test bed of the harmonic speed reducer of the robot, and data support is provided for making a maintenance strategy.
Disclosure of Invention
The invention aims to solve the defects in the prior art, provides a method for building a reliability analysis model of each key part of a harmonic speed reducer test bed transmission system based on a truncation distribution theory aiming at the defects in the reliability analysis method of the harmonic speed reducer test bed transmission system of a robot, analyzes and calculates the reliability of each key part by combining an expert database and a base line database, and finally calculates the reliability of the whole harmonic speed reducer test bed transmission system.
The purpose of the invention can be achieved by adopting the following technical scheme:
a reliability analysis method for a transmission system of a robot harmonic speed reducer test bed comprises the following steps:
s1, determining the component composition of the transmission system of the robot harmonic speed reducer test bed, and preliminarily analyzing by adopting a fault mode and influence analysis method to obtain key components needing reliability resolution in the transmission system of the robot harmonic speed reducer test bed, neglecting the components with small influence on the reliability of the transmission system when analyzing the reliability of the transmission system, and simplifying the reliability model of the transmission system while ensuring the analysis precision;
s2, building a reliability analysis model of each key part in the transmission system of the robot harmonic speed reducer test bed by adopting a tail-cutting distribution theory;
s3, analyzing and calculating to obtain corresponding reliability according to the established reliability analysis model of each key part by applying a truncation distribution theory;
and S4, determining the overall reliability, and obtaining the reliability of the whole transmission system by using a related calculation formula of a reliability series theoretical model after obtaining the reliability of the key parts and other parts.
Further, by simplifying the reliability model of the transmission system in the step S1, the reliability of the entire transmission system is calculated from 25 system elements to 15 system elements,
wherein the 25 system elements include: the device comprises a driving motor, a motor mounting bracket, a key connection 1, a coupler 1, a key connection 2, a torque sensor 1, a torque sensor mounting bracket 1, a key connection 3, a coupler 2, a key connection 4, an input shaft, a key connection 5, a tested speed reducer mounting bracket, an output flange plate, a key connection 6, a coupler 3, a key connection 7, a torque sensor 2, a key connection 8, a coupler 4, a key connection 9, a magnetic powder brake, a cast iron mounting base and a mounting base leveling pad;
the 15 system elements include key components for transmitting power weak links: key connection 1, shaft coupling 1, key connection 2, key connection 3, shaft coupling 2, key connection 4, key connection 5, the speed reducer of being surveyed, output ring flange, key connection 6, shaft coupling 3, key connection 7, key connection 8, shaft coupling 4, key connection 9.
Further, in the step S3, a truncated distribution theory is applied, and the corresponding reliability is obtained by analyzing and calculating the coupling, the ordinary flat key, and the output flange in the transmission system.
Further, the step S3 applies a truncated distribution theory, and the concrete steps of obtaining the coupler reliability solving function are as follows:
s311, obtaining pressure and bending stress, in the elastic sleeve pin coupling, the pressure sigma acting on the unit area of the elastic sleeve1And bending stress σ of the pin2Are respectively as
Figure GDA0002490271660000031
Figure GDA0002490271660000032
Wherein z is the number of pins, D0Is the diameter of the circle of the center of the pin, d is the diameter of the pin, l' is the total length of the elastic ring, l is the length of the cantilever end of the pin, TcCalculated torque transmitted for the coupling:
Tc＝KT
k is the coefficient of working condition, and manufacturing and assembling errors and load T are inevitable in the coupler in practicecInfluence of random fluctuation factor of σ1And σ2The values of (A) are all random, so that the values are taken as random variables;
s312, solving the mean value and standard deviation of the pressure and bending stress, and aiming at the load TcThe maximum value T can be obtained by actual measurement or empirical datac maxAnd a minimum value Tc minThe statistical quantity, i.e. mean, is determined approximately according to the 3 sigma rule
Figure GDA0002490271660000033
And standard deviation of
Figure GDA0002490271660000039
And a dimension parameter D0L' and l are generally normally distributed and their statistics are determined by the 3. sigma. rule based on data provided by the test or literature
Figure GDA0002490271660000034
And
Figure GDA0002490271660000035
the parameters z, d are approximately processed as constants, so σ1、σ2Can be assumed to be normal distribution, and the mean value and standard deviation thereof are respectively obtained according to the moment method
Figure GDA0002490271660000036
Figure GDA0002490271660000037
Figure GDA0002490271660000038
Figure GDA0002490271660000041
S313, obtaining a coupler reliability solving formula, and performing tail cutting treatment on a membership function of the coupler by using a tail cutting theory to obtain the following function form
Figure GDA0002490271660000042
In the formula (I), the compound is shown in the specification,
Figure GDA0002490271660000047
respectively represent [ P]And [ sigma ]b]Fuzzy variable [ P ]]For the strength of the elastic sleeve pin coupling, i.e. the allowable pressure of the elastic sleeve, [ sigma ]b]The pin is allowed to take bending stress,
Figure GDA0002490271660000043
determined by the amplification factor method,. sigma.)1And σ2Are all normally distributed with a probability density function of
Figure GDA0002490271660000044
According to the above obtained solving formula of the related parameters, the following formula is substituted
Figure GDA0002490271660000046
Fuzzy reliability R of elastic sleeve without crushing failure1. Fuzzy reliability R of pin without bending damage2The formula is as follows
Figure GDA0002490271660000045
Assuming that these two failures are independent of each other, the fuzzy reliability of the coupler against failure is
R＝R1R2；
And S314, obtaining the reliability of the coupler 1, the coupler 2, the coupler 3 and the coupler 4 respectively according to the known parameters of the selected coupler and the solving function.
Further, the step S3 is implemented by applying a truncated distribution theory, and the key connection reliability solving function is obtained by the following steps:
s321, obtaining the total extrusion force N of the key working side surface according to the following formula:
Figure GDA0002490271660000051
in the formula TnTorque transmitted by key connection, d is the diameter of the shaft;
s322, establishing an extrusion failure reliability model according to the form of extrusion and shearing of the key during working
R1＝P(σ1＜[σ1])
Figure GDA0002490271660000052
R1Reliability, σ, for key press failure1For flat key extrusion working stress, [ sigma ]1]The tensile strength of the material, h is the height of the flat key, and L is the working length of the flat key;
s323, the shear failure reliability calculation model is described by the following formula
R2＝P(τ＜[τ])
Figure GDA0002490271660000053
R2For the reliability corresponding to the failure of key shear, τ is the working stress of flat key shear, [ τ []Is the shear strength of the material, and b is the width of the flat bond;
and S324, respectively obtaining the reliability of the key connections 1 to 9 according to the known parameters of the selected key connections and the solving function.
Further, the step S3 is implemented by applying a truncated distribution theory, and the specific steps of obtaining the output flange reliability solving function are as follows:
s331, transverse load F solving formula
Figure GDA0002490271660000054
In the formula, TnThe torque is transmitted for key connection and the torque is transmitted by an output flange, D is the diameter of a bolt distribution circle, and n is the theoretical value of the rotating speed of an output shaft;
s332, according to the structural characteristics and failure modes of the bolt connection, the reliability model of the bolt connection is described by the following formula
R＝P(Sτb＜)
Figure GDA0002490271660000061
Wherein R is bolt reliability, bolt material strength, SτbThe shear working stress of a single bolt, and d is the diameter of a bolt column;
and S333, substituting the related known material data of the bolts used by the output flange plate into the formula to obtain the overall reliability of the output flange plate.
Compared with the prior art, the invention has the following advantages and effects:
1. the method of the invention adopts a fault mode and an influence analysis method (FMEA) to find out all possible failure modes of parts and a transmission system and adopts a tail-cutting distribution theory to build a reliability analysis model of the transmission system of the harmonic speed reducer test bed.
2. Considering that the transmission system of the robot harmonic speed reducer test bed is composed of a plurality of part subsystems, elements of each subsystem have completely different functions and have different functions on the reliability of the transmission system, the analysis method provided by the invention further distinguishes the elements of the system according to the size influencing the reliability of the system, and forms corresponding grades.
3. And establishing a reliability solving arithmetic model of the key parts by applying the adopted theoretical analysis method, and solving to obtain the corresponding reliability. And finally, solving a formula according to the reliability of the reliability series model to obtain the overall reliability, thereby ensuring the accuracy of the result.
Drawings
FIG. 1 is a block diagram showing the components of a harmonic reducer test stand transmission test system, which is an object to be studied in the reliability analysis of the present invention;
FIG. 2 is a simplified block diagram of the harmonic reducer test stand drive test system, which is the subject of the reliability analysis of the present invention;
FIG. 3 is a flow chart of a method for analyzing reliability of a transmission system of a robot harmonic reducer test bed, disclosed by the invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Examples
To solve the overall reliability of the transmission test system of the robot harmonic speed reducer test bed, the components of the transmission system are detailed firstly (see fig. 1); then preliminarily analyzing by combining an expert database and a reliability common method to obtain the failure mode of each component and the influence of failure on the system so as to be used as a basis for further dividing the importance of parts; and finally, after determining the key parts in the whole transmission system, building a reliability analysis model of each key part of the transmission system of the harmonic speed reducer test bed by adopting a truncation distribution theory, analyzing and calculating to obtain corresponding reliability, and finally obtaining the reliability of the whole system. The specific process is as follows:
and step S1, simplifying modeling. Considering that a transmission system of a harmonic speed reducer test bed of a robot is a complex system consisting of a coupler, an input end torque sensor, an input end of a tested speed reducer, an output end torque sensor, a brake and the like, all possible failure modes of the parts and the system are found out by adopting a failure mode and influence analysis method (FMEA), and the failure modes have various influences on the system and whether the influences are fatal or not, and a failure mechanism is preliminarily judged to find out weak links of the transmission system. The influence of each part on the reliability of the transmission system is qualitatively analyzed, key parts influencing the reliability of the transmission system are found out, parts with small influence on the reliability of the transmission system are ignored during reliability analysis of the transmission system, and the reliability model of the transmission system is simplified while the analysis precision is ensured.
The method comprises the following steps:
s11, when starting the analysis, all components of the system should be determined, and the components in the transmission system of the robot harmonic reducer test bed in this embodiment include 25 system elements, that is, components (see fig. 1 in particular).
And S12, on the premise that abnormal data of the harmonic speed reducer are collected based on an abnormal data detection algorithm in the specific test process of the expert database, the baseline database and the harmonic speed reducer test, further dividing parts in the transmission system according to the size influencing the reliability of the system. The reliability of the transmission system is calculated by considering the influence of the A-type elements only. Empirical values are used for the B-type elements and the C-type elements, and the B-type elements and the C-type elements have little transmission correlation and influence. The reliability calculation of the transmission system is mainly considered, so that the B-type elements and the C-type elements are not considered temporarily in the calculation.
The method comprises the steps of determining the component composition of a transmission system of a robot harmonic speed reducer test bed and preliminarily analyzing by adopting a fault mode and influence analysis method (FMEA) to obtain key components needing solution reliability in the transmission system of the robot harmonic speed reducer test bed (see figure 2). Through preliminary analysis and classification, the reliability of the whole transmission system is calculated and reduced to 15 from 25 system elements.
The 25 system elements include: driving motor, motor installing support, key-type connection 1, shaft coupling 1, key-type connection 2, torque sensor 1, torque sensor installing support 1, key-type connection 3, shaft coupling 2, key-type connection 4, the input shaft, key-type connection 5, the speed reducer of being surveyed, the speed reducer installing support of being surveyed, the output ring flange, key-type connection 6, shaft coupling 3, key-type connection 7, torque sensor 2, key-type connection 8, shaft coupling 4, key-type connection 9, magnetic powder brake, cast iron installation base, installation base leveling pad foot.
The 15 system elements for which reliability is critical include critical parts of the transmission power weak link: key connection 1, shaft coupling 1, key connection 2, key connection 3, shaft coupling 2, key connection 4, key connection 5, the speed reducer of being surveyed, output ring flange, key connection 6, shaft coupling 3, key connection 7, key connection 8, shaft coupling 4, key connection 9.
And then establishing a reliability solving function expression of each key component.
And step S2, determining a theoretical method adopted by reliability analysis modeling. After key parts in the whole system are determined through preliminary analysis, a theoretical method adopted for reliability analysis is determined, and a reliability analysis model of each key part of a harmonic speed reducer test bed transmission system is built through a tail-cutting distribution theory.
And step S3, calculating the reliability of the key parts by applying a truncation distribution theory. And analyzing and calculating to obtain corresponding reliability according to the established reliability analysis model of each key part (mainly for a coupler, a common flat key and an output flange in the whole system).
Step S31, applying a truncation distribution theory, and acquiring a coupler reliability solving function specifically comprises the following steps:
and S311, obtaining the pressure and the bending stress. Pressure σ acting on the elastic sleeve per unit area in an elastic sleeve pin coupling1And bending stress σ of the pin2Are respectively as
Figure GDA0002490271660000091
Figure GDA0002490271660000092
Wherein z is the number of pins (as 1/2); d0The diameter of the circle where the center of the pin is located; d is the diameter of the pin; l' is the total length of the elastic ring; l is the length of the cantilever end of the pin; t iscCalculated torque transmitted for the coupling:
Tc＝KT
k is a working condition coefficient and can be searched by a mechanical design manual. Calculated according to conventional design methods, σ1And σ2Are all deterministic values. In fact, the inevitable manufacturing and assembling errors of the coupling, in addition to the load TcRandom fluctuation of (a) and the like, σ1And σ2All the values of (A) are random, so the values are taken as random variables.
S312, compressive and bending stressAnd (4) solving a mean value and a standard deviation. For load TcThe maximum value T can be obtained by actual measurement or empirical datac maxAnd a minimum value Tc minThe statistical quantity, i.e. mean, is determined approximately according to the 3 sigma rule
Figure GDA0002490271660000093
And standard deviation of
Figure GDA0002490271660000094
And a dimension parameter D0L', and l are generally normally distributed, and their statistics may also be determined by 3 σ rule based on data provided by test or related literature
Figure GDA0002490271660000101
And
Figure GDA0002490271660000102
the parameters z, d (which have small dimensional deviations) can be treated approximately constant. Thus σ1、σ2Can be assumed to be normal distribution, and the mean value and standard deviation thereof can be respectively obtained according to the moment method
Figure GDA0002490271660000103
Figure GDA0002490271660000104
Figure GDA0002490271660000105
Figure GDA0002490271660000106
S313, obtaining a coupler reliability solving formula
The following function form can be obtained by applying truncation theory to perform truncation processing on the membership function of the coupler
Figure GDA0002490271660000107
In the formula (I), the compound is shown in the specification,
Figure GDA00024902716600001010
respectively represent [ P]And [ sigma ]b](fuzzy variable [ P ]]The strength of the elastic sleeve pin coupling, namely the allowable pressure of the elastic sleeve; [ sigma ]b]The allowable bending stress for the pin),
Figure GDA0002490271660000108
can be determined by the amplification factor method. As mentioned previously, σ1And σ2Are all normally distributed with a probability density function of
Figure GDA0002490271660000109
According to the above obtained solving formula of the related parameters, the following formula is substituted
Figure GDA00024902716600001011
Fuzzy reliability R of elastic sleeve without crushing failure1. Fuzzy reliability R of pin without bending damage2The formula is as follows
Figure GDA0002490271660000111
Assuming that these two failures are independent of each other, the fuzzy reliability of the coupler against failure is
R＝R1R2
S314, coupling selected by the system at this time, wherein the known parameters are as follows:
1) nominal torque: 250 Nm; 2) allowable rotating speed r: 15000 pm; 3) weight: 2.5 kg; 4) moment of inertia: 8010- 4kgm2；5)d：10-42mm；6)D：106mm；7)A：45mm；8)D1：50mm；9)L：60mm。
According to the known parameters and the solving function, the reliability that the coupler 1 does not fail can be finally obtained to be 0.992. According to the process for solving the reliability of the coupler, the reliability of the couplers 2, 3 and 4 can be respectively solved to be 0.991, 0.992 and 0.992.
S32, applying a truncation distribution theory and obtaining the key connection reliability calculation solving function form, wherein the key connection reliability calculation solving function form comprises the following specific steps:
and S321, acquiring the total extrusion force N of the key working side. The formula can be obtained according to the formula in a mechanical design manual.
Figure GDA0002490271660000112
In the formula TnThe key connects the torque transmitted and d is the diameter of the shaft.
S322, establishing an extrusion failure reliability model according to the form of extrusion and shearing of the key during working
R1＝P(σ1＜[σ1])
Figure GDA0002490271660000113
R1Reliability, σ, for key press failure1For flat key extrusion working stress, [ sigma ]1]For the tensile strength of the material, h is the flat key height, and L is the flat key working length.
S323, the shear failure reliability calculation model is described by the following formula
R2＝P(τ＜[τ])
Figure GDA0002490271660000121
R2For the reliability corresponding to the failure of key shear, τ is the working stress of flat key shear, [ τ []Is the shear strength of the material and b is the flat key width.
S324, keys selected by the transmission system have known parameters:
Figure GDA0002490271660000122
the reliability of each of the keys 1 to 9 obtained by substituting the known parameters into the above formula is 0.994, 0.995, 0.992, and 0.992, respectively.
S33, the concrete steps of obtaining the reliability calculation solving function form of the output flange plate are as follows:
s331, transverse load F solving formula
Figure GDA0002490271660000123
In the formula, TnTorque transmitted for key connection and torque transmitted by an output flange; d is the diameter of the bolt distribution circle, and n is the theoretical value of the rotating speed of the output shaft.
S332, according to the structural characteristics and failure modes of the bolt connection, the reliability model of the bolt connection is described by the following formula
R＝P(Sτb＜)
Figure GDA0002490271660000124
Wherein R is bolt reliability, bolt material strength, SτbIs the shear working stress of a single bolt and d is the bolt shank diameter.
S333, the reliability of the whole flange plate is 0.988 by substituting the relevant known material data of the bolts used by the flange plate into the formula.
S4, combining the coupler reliability analysis result, the key connection reliability analysis result and the output flange reliability analysis result, and bringing the corresponding results into a reliability series theoretical model reliability calculation formula to obtain the reliability of the whole transmission system:
RS＝0.899
through the reliability analysis of the transmission system, the following results can be obtained: (1) the reliability of the transmission system is 0.899, the reliability is relatively low, and a reliability improvement design is required. (2) The weak link of the transmission system is that more key connections are used in the transmission system, because the key connections have multiple failure modes such as key crushing, key groove crushing and shearing. In order to improve the reliability of a transmission system, in the optimization of subsequent schemes, the connection mode of key connection is improved, for example, a spline connection mode is adopted, the load of a single key is reduced by increasing the number of the keys distributed in the circumferential direction, and the reliability of the key connection is improved.
The above embodiments are preferred embodiments of the present invention, but the present invention is not limited to the above embodiments, and any other changes, modifications, substitutions, combinations, and simplifications which do not depart from the spirit and principle of the present invention should be construed as equivalents thereof, and all such changes, modifications, substitutions, combinations, and simplifications are intended to be included in the scope of the present invention.

Claims (3)

1. A reliability analysis method for a transmission system of a robot harmonic speed reducer test bed is characterized by comprising the following steps:
s1, determining the component composition of the transmission system of the robot harmonic speed reducer test bed, and primarily analyzing by adopting a fault mode and influence analysis method to obtain the key components needing to solve the reliability in the transmission system of the robot harmonic speed reducer test bed, neglecting the components having smaller influence on the reliability of the transmission system when analyzing the reliability of the transmission system, and simplifying the reliability model of the transmission system while ensuring the analysis precision, wherein in the step S1, through simplifying the reliability model of the transmission system, the reliability of the whole transmission system is calculated by reducing 25 system elements to 15 system elements, wherein the 25 system elements comprise: the device comprises a driving motor, a motor mounting bracket, a key connection 1, a coupler 1, a key connection 2, a torque sensor 1, a torque sensor mounting bracket 1, a key connection 3, a coupler 2, a key connection 4, an input shaft, a key connection 5, a tested speed reducer mounting bracket, an output flange plate, a key connection 6, a coupler 3, a key connection 7, a torque sensor 2, a key connection 8, a coupler 4, a key connection 9, a magnetic powder brake, a cast iron mounting base and a mounting base leveling pad;
the 15 system elements include key components for transmitting power weak links: the device comprises a key connection 1, a coupling 1, a key connection 2, a key connection 3, a coupling 2, a key connection 4, a key connection 5, a tested speed reducer, an output flange plate, a key connection 6, a coupling 3, a key connection 7, a key connection 8, a coupling 4 and a key connection 9;
s2, building a reliability analysis model of each key part in the transmission system of the robot harmonic speed reducer test bed by adopting a tail-cutting distribution theory;
s3, applying a truncation distribution theory, and respectively analyzing and calculating to obtain corresponding reliability aiming at a coupler, a common flat key and an output flange in a transmission system according to the established reliability analysis model of each key part; the method comprises the following specific steps of obtaining a coupler reliability solving function:
s311, obtaining pressure and bending stress, in the elastic sleeve pin coupling, the pressure sigma acting on the unit area of the elastic sleeve1And bending stress σ of the pin2Are respectively as
Figure FDA0002490271650000021
Figure FDA0002490271650000022
Wherein z is the number of pins, D0Is the diameter of the circle of the center of the pin, d is the diameter of the pin, l' is the total length of the elastic ring, l is the length of the cantilever end of the pin, TcCalculated torque transmitted for the coupling:
Tc＝KT
k is the coefficient of working condition, and manufacturing and assembling errors and load T are inevitable in the coupler in practicecInfluence of random fluctuation factor of σ1And σ2The values of (A) are all random, so that the values are taken as random variables;
s312, solving the mean value and standard deviation of the pressure and bending stress, and aiming at the load TcObtaining its maximum value T from measured or empirical datacmaxAnd a minimum value TcminApproximately by the 3 sigma methodDetermine its statistic, i.e. mean
Figure FDA0002490271650000023
And standard deviation of
Figure FDA0002490271650000024
And a dimension parameter D0L' and l are normally distributed, and the statistics are determined according to the 3 sigma rule based on the data provided by the test or literature
Figure FDA0002490271650000025
And
Figure FDA0002490271650000026
the parameters z, d are approximately processed as constants, so σ1、σ2All assume normal distribution, and the mean and standard deviation are respectively obtained according to the moment method
Figure FDA0002490271650000027
Figure FDA0002490271650000031
S313, obtaining a coupler reliability solving formula, and performing tail cutting treatment on a membership function of the coupler by using a tail cutting theory to obtain the following function form
Figure FDA0002490271650000032
In the formula (I), the compound is shown in the specification,
Figure FDA0002490271650000033
respectively represent [ P]And [ sigma ]b]Fuzzy variable [ P ]]For the strength of the elastic sleeve pin coupling, i.e. the allowable pressure of the elastic sleeve, [ sigma ]b]The pin is allowed to take bending stress,
Figure FDA0002490271650000034
determined by the amplification factor method,. sigma.)1And σ2Are all normally distributed with a probability density function of
Figure FDA0002490271650000035
According to the above obtained solving formula of the related parameters, the following formula is substituted
Figure FDA0002490271650000036
Fuzzy reliability R of elastic sleeve without crushing failure1Fuzzy reliability R of pin without bending damage2The formula is as follows
Figure FDA0002490271650000037
Assuming that these two failures are independent of each other, the fuzzy reliability of the coupler against failure is
R＝R1R2；
S314, obtaining the reliability of the coupler 1, the coupler 2, the coupler 3 and the coupler 4 according to the known parameters of the selected coupler and the solving function;
and S4, determining the overall reliability, and obtaining the reliability of the whole transmission system by using a related calculation formula of a reliability series theoretical model after obtaining the reliability of the key parts and other parts.
2. The method for analyzing the reliability of the transmission system of the robot harmonic reducer test bed according to claim 1, wherein the step S3 is implemented by applying a truncated distribution theory, and the key connection reliability solving function is obtained by the following steps:
s321, obtaining the total extrusion force N of the key working side surface according to the following formula:
Figure FDA0002490271650000041
in the formula TnTorque transmitted by key connection, d is the diameter of the shaft;
s322, establishing an extrusion failure reliability model according to the form of extrusion and shearing of the key during working
R1＝P(σ1＜[σ1])
Figure FDA0002490271650000042
R1Reliability, σ, for key press failure1For flat key extrusion working stress, [ sigma ]1]The tensile strength of the material, h is the height of the flat key, and L is the working length of the flat key;
s323, the shear failure reliability calculation model is described by the following formula
R2＝P(τ＜[τ])
Figure FDA0002490271650000043
R2For the reliability corresponding to the failure of key shear, τ is the working stress of flat key shear, [ τ []Is the shear strength of the material, and b is the width of the flat bond;
and S324, respectively obtaining the reliability of the key connections 1 to 9 according to the known parameters of the selected key connections and the solving function.
3. The method for analyzing the reliability of the transmission system of the robot harmonic reducer test bed according to claim 1, wherein the step S3 is implemented by applying a truncation distribution theory, and the specific steps of obtaining the reliability solving function of the output flange plate are as follows:
s331, transverse load F solving formula
Figure FDA0002490271650000051
In the formula, TnThe torque is transmitted for key connection and the torque is transmitted by an output flange, D is the diameter of a bolt distribution circle, and n is the theoretical value of the rotating speed of an output shaft;
s332, according to the structural characteristics and failure modes of the bolt connection, the reliability model of the bolt connection is described by the following formula
R＝P(Sτb＜)
Figure FDA0002490271650000052
Wherein R is bolt reliability, bolt material strength, SτbThe shear working stress of a single bolt, and d is the diameter of a bolt column;
and S333, substituting the related known material data of the bolts used by the output flange plate into the formula to obtain the overall reliability of the output flange plate.
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