CN111159895A - Mechanical element motion assembly precision reliability analysis method based on fuzzy theory - Google Patents
Mechanical element motion assembly precision reliability analysis method based on fuzzy theory Download PDFInfo
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Abstract
A mechanical element motion assembly precision reliability analysis method based on a fuzzy theory is characterized by comprising the following steps: establishing a mechanical element motion assembly unit, defining assembly precision reliability and element motion assembly unit assembly precision reliability, analyzing the assembly precision reliability, defining assembly precision fuzzy reliability and element motion assembly unit assembly precision fuzzy reliability, analyzing the assembly precision fuzzy reliability, determining an assembly precision reliability membership function, and establishing a mechanical assembly precision fuzzy reliability basic model. The invention has the advantages that: the invention provides a method for analyzing the assembly precision and reliability of mechanical element actions based on a fuzzy theory.
Description
Technical Field
The invention relates to the technical field of assembling precision research of electromechanical products, in particular to a mechanical element action assembling precision reliability analysis method based on a fuzzy theory.
Background
With the development of complex products towards the direction of precision, optical-mechanical-electrical integration and intellectualization, the guarantee of assembly precision becomes one of the difficult problems in the assembly of complex products. At present, in the field of mechanical assembly precision research, a functional relation between assembly precision and operating force is deduced, and then an assembly precision optimization method is provided.
The main methods of precision prediction include: establishing a three-dimensional error transfer model by using a state space method; performing assembly precision prediction research by taking the machining error and the clamp position error as error sources; the differential motion vector is adopted to describe the error state of the assembly process, a state space model of the precision machine tool in the assembly process is established, and precision machine tool assembly precision prediction is realized. The methods are mainly researched aiming at the design and prediction of the assembly precision, a theoretical basis is provided for the guarantee of the assembly precision, however, the mapping mechanism of the assembly precision caused by the machining error of each part in the specific assembly process directly influences the assembly reliability, and therefore the reliability of the assembly precision needs to be further analyzed.
In the aspect of assembling precision reliability research, the main research methods include: researching the mapping relation between the machine tool function and the machine tool structure and the assembling process, and establishing an evaluation index of the reliability of the machine tool assembling precision; the method comprises the steps of analyzing error composition and a calculation method thereof, establishing an assembly error model by adopting a pose transformation matrix method, analyzing the transmission process of errors in parts and between matching surfaces, calculating the total assembly error, determining the probability distribution of the assembly error according to the total assembly error, and the like. The method mainly analyzes the problem of assembling precision reliability by researching an error transfer mechanism in the assembling process, but the influence of part errors on the assembling precision in the actual assembling process has ambiguity, and further research is needed for how to establish a fuzzy mathematical relationship and a reliability model between the machining errors and the assembling precision from the perspective of probability theory.
Therefore, although the prior art has a certain research foundation in the aspects of precision prediction method and assembly precision reliability, the prior art does not carry out comprehensive systematic research on the aspects of fuzziness of influence of part errors on assembly precision, assembly reliability and assembly precision in the actual assembly process, so that the development of a fuzzy mathematical relationship and a reliability model between machining errors and assembly precision is urgently needed from the perspective of probability theory.
Disclosure of Invention
In order to solve the defects of the prior art, the invention provides a method for analyzing the assembling precision and reliability of mechanical element actions based on a fuzzy theory.
A mechanical element motion assembly precision reliability analysis method based on a fuzzy theory comprises the following steps:
(1) establishing a mechanical element action assembly unit: the element action assembling unit is an independent component which takes an executing element for realizing element action as an assembling core, and a group of parts can be independently assembled to meet the specified element action performance requirement and enable the element action to complete the specified function in the assembling process;
(2) defining the assembly precision reliability and the element motion assembly unit assembly precision reliability: the assembly precision reliability refers to the capability that the actual assembly precision meets the design requirement of the element motion assembly unit under the specified assembly condition; the assembly precision reliability of the element motion assembly unit refers to the probability that the actual assembly precision meets the design requirement under the specified assembly condition of the element motion assembly unit;
(3) analyzing the reliability of the assembly precision: suppose that a certain assembly item of the aforementioned meta-motion assembly unit is MiThen the aforementioned assembly item MiThe assembling precision reliability is as follows:
Ri＝P(xi)＝P(ximin＜xi＜ximax)
wherein the assembly item MiFor elements on a part in a unit assembled for element movement and assembly items, x, combined with elements on the assembled partiFor assembling item MiFitting clearance or interference of (x)iminMinimum clearance or maximum interference; x is the number ofimaxMaximum clearance or minimum interference;
assuming that the meta-motion assembling unit has n assembling items, the assembling precision reliability of the meta-motion assembling unit is as follows:
(4) defining the fuzzy reliability of the assembly precision and the fuzzy reliability of the assembly precision of the element motion assembly unit: in the assembling process, due to the influence of the processing precision of parts, the rigidity of the parts, the thermal deformation of the parts and the assembling method, the assembling precision presents a fuzzy characteristic, and the capability that the actual assembling precision meets the requirement of an ideal state under the specified assembling condition of the element action assembling unit is called the assembling precision fuzzy reliability of the element action assembling unit; the probability that the actual assembly precision of the meta-motion assembly unit meets the requirement of an ideal state is called the fuzzy reliability of the assembly precision of the meta-motion assembly unit;
(5) analyzing the fuzzy reliability of the assembly precision: assuming a certain assembly precision x of the aforementioned meta-motion assembly unitsiConsidering the fuzziness of the element action assembling process behavior, the requirement that the actual assembling precision meets the ideal assembling precision is a fuzzy event
The fuzzy reliability of the assembly precision of the assembly items is recorded
It is briefly described as
Then is frontThe fuzzy reliability of the assembly precision of the element motion assembly unit is recorded as
(6) Determining an assembly precision reliability membership function: each assembly item in the meta-action assembly unit is MiBy using
Representing the assembly precision fuzzy event of the assembly items
The membership function of the assembly precision reliability of the general assembly items of the meta-action units obtained by analyzing the actual fit clearance or interference magnitude characteristics of the assembly items of the meta-action units in the general meta-action assembly precision data can approximately adopt an intermediate ridge type distribution form, and the membership function meets the formula I, namely the membership function is the intermediate ridge type distribution form
Formula one
In the formula: a is1Representing a gap or interference magnitude, a, determined by analysis of the assembly accuracy data, which initially is higher to meet the desired performance requirements of the meta-action2The clearance or interference value which is determined after the assembly precision data analysis and cannot meet the ideal performance requirement of the element action at a high level is represented;
(7) establishing a basic model of mechanical assembly precision fuzzy reliability: according to the fuzzy event probability definition, a model for the assembly precision reliability of a certain assembly item of the element building action assembly unit is expressed as a formula II, namely
Formula two
If the assembly precision sample data of the assembly item obeys normal distribution, f (x)i) Expressed as formula three, namely
Formula three
In the formula III, the first step is carried out,
the mean value of the clearance or the interference of each assembly item in the element action assembly unit is expressed as a formula IV, namely the mean value is
Formula four
In the formula IV, m represents the sample size of a certain assembly item, i represents a certain assembly item, and j represents a certain sample of a certain assembly item;
Formula five
Substituting the formula I and the formula III into the formula II to obtain the formula VI, namely the assembling precision reliability of a certain assembling item of the element action assembling unit
Is composed of
Formula six
The assembly precision of the element motion assembly unit is ensured by the assembly precision of each assembly item, so the fuzzy reliability of the assembly precision of the element motion assembly unit is formed by connecting fuzzy reliabilities of the assembly items in series, namely the fuzzy reliability of the assembly precision of the element motion assembly unit
Expressed as formula seven, is
Formula (II)Seven-piece
Preferably, the element motion assembly unit comprises a support member, a power source, an actuating member, an intermediate transmission and a fastener.
Preferably, the element motion assembly unit may be a worm rotation element motion.
Preferably, the assembly precision fuzzy event of the assembly items
The membership functions of (a) may be obtained according to statistical methods.
The present invention is advantageous in that,
the invention provides a mechanical element action assembly precision reliability analysis method based on a fuzzy theory, which resolves a complex product assembly problem into an element action unit assembly problem.
The invention provides a fuzzy theory-based mechanical element action assembly precision reliability analysis method, which introduces the fuzzy theory into element action assembly precision reliability analysis, establishes a unified model of a mechanical element action assembly unit by analyzing element action composition structures, and provides concepts of assembly precision reliability and assembly precision fuzzy reliability by combining fuzzy characteristics of assembly information.
3, the method for analyzing the reliability of the mechanical element action assembly precision based on the fuzzy theory establishes a fuzzy reliability model of the mechanical element action assembly precision by determining the membership function of the element action assembly precision reliability, so that the reliability analysis of the mechanical element action assembly precision has higher flexibility and feasibility.
4, the invention provides a method for analyzing the reliability of the mechanical element action assembly precision based on the fuzzy theory, which processes the fuzzy phenomenon in the reliability analysis in the assembly process by means of the fuzzy theory and establishes a fuzzy mathematical relationship and a reliability model between the processing error and the assembly precision from the perspective of the probability theory.
5, the invention provides a method for analyzing the assembly precision reliability of mechanical element actions based on a fuzzy theory, which utilizes the fuzzy mathematical theory to establish an assembly precision reliability membership function. And according to an assembly error transfer mechanism, a fuzzy reliability model of mechanical element motion assembly precision is established.
Drawings
Fig. 1 is a schematic flow chart of a method for analyzing the assembly precision and reliability of mechanical element actions based on a fuzzy theory.
Detailed Description
Taking the worm rotation element as an example, the fuzzy reliability analysis of the mechanical element motion assembly precision is carried out, and the method specifically comprises the following steps:
(1) establishing a mechanical element action assembly unit: the element action assembling unit is an independent component which takes an executive component for realizing element action as an assembling core, a group of parts can be independently assembled to meet the specified element action performance requirement and enable the element action to complete the specified function in the assembling process; taking the worm rotation element as an example, the worm rotation element comprises 10 parts and 9 parts which are matched, and the assembling precision information list 1 of each part of the worm rotation unit is shown.
TABLE 1 information table of various assembling items in worm rotation assembling unit
(2) Defining the assembly precision reliability and the element motion assembly unit assembly precision reliability: the assembly precision reliability refers to the capability that the actual assembly precision meets the design requirement of the element action assembly unit under the specified assembly condition; the reliability of the assembly precision of the meta-motion assembly unit refers to the probability that the actual assembly precision meets the design requirement of the meta-motion assembly unit under the specified assembly condition.
(3) Analyzing the reliability of the assembly precision: suppose that a certain assembly item of the meta-action assembly unit is MiThen assemble item MiThe assembling precision reliability is as follows:
Ri＝P(xi)＝P(ximin＜xi＜ximax)
wherein the assembly item MiFor elements on a part in a unit assembled for element movement and assembly items, x, combined with elements on the assembled partiFor assembling item MiFitting clearance or interference of (x)iminMinimum clearance or maximum interference; x is the number ofimaxMaximum clearance or minimum interference;
assuming that the meta-motion assembling unit has n assembling items, the assembling precision reliability of the meta-motion assembling unit is as follows:
(4) defining the fuzzy reliability of the assembly precision and the fuzzy reliability of the assembly precision of the element motion assembly unit: in the assembling process, due to the influence of the processing precision of parts, the rigidity of the parts, the thermal deformation of the parts and the assembling method, the assembling precision presents a fuzzy characteristic, and the capability that the actual assembling precision meets the requirement of an ideal state under the specified assembling condition of the element action assembling unit is called the assembling precision fuzzy reliability of the element action assembling unit; the probability that the actual assembly precision of the meta-motion assembly unit meets the requirement of an ideal state is called the fuzzy reliability of the assembly precision of the meta-motion assembly unit.
(5) Analyzing the fuzzy reliability of the assembly precision: assuming a certain assembly precision x of meta-action assembly unitsiConsidering the fuzziness of the element action assembling process behavior, the requirement that the actual assembling precision meets the ideal assembling precision is a fuzzy event
The fuzzy reliability of the assembly precision of the assembly item is recorded
It is briefly described as
Yuan action deviceThe fuzzy reliability of the assembly precision of the units is recorded
(6) Determining an assembly precision reliability membership function: each assembly item in the meta-action assembly unit is MiBy using
Fuzzy event A & -E representing assembly item assembly precisioniThe membership function of the assembly precision reliability of the general assembly items of the meta-action units obtained by analyzing the actual fit clearance or interference magnitude characteristics of the assembly items of the meta-action units in the general meta-action assembly precision data can approximately adopt an intermediate ridge type distribution form, and the membership function meets the formula I, namely the membership function is the intermediate ridge type distribution form
Formula one
In the formula: a is1Representing a gap or interference magnitude, a, determined by analysis of the assembly accuracy data, which initially is higher to meet the desired performance requirements of the meta-action2The value of the gap or the interference which is determined by the analysis of the assembly precision data and can not meet the requirement of ideal performance of the element action is shown.
(7) Establishing a basic model of mechanical assembly precision fuzzy reliability: according to the fuzzy event probability definition, a model for the assembly precision reliability of a certain assembly item of the element building action assembly unit is expressed as a formula II, namely
Formula two
F (x) if the assembly precision sample data of the assembly item obeys normal distributioni) Expressed as formula three, namely
Formula three
In the formula III, the first step is carried out,
the mean value of the clearance or the interference of each assembly item in the element action assembly unit is expressed as a formula IV, namely the mean value is
Formula four
In the formula IV, m represents the sample size of a certain assembly item, i represents a certain assembly item, and j represents a certain sample of a certain assembly item;
according to the information of each assembly item of the worm rotation assembly unit in the table 1, combining with actual assembly precision (gap or interference) sample (sample size 50) data in each assembly item measured by actual research in nearly 5 years, solving the mean value of the actual gap or interference of corresponding elements of multiple samples in the ith assembly item of the worm rotation unit by using a formula (4)
As shown in table 2.
TABLE 2 mean fitting accuracy of various assembly items of worm rotary unit
Formula five
According to the average assembly precision of each assembly item of the worm rotating unit in the table 2, the standard deviation of the fit precision of each assembly item is solved by using a formula five in combination with the actual clearance or interference magnitude of the corresponding element as shown in the table 3.
TABLE 3 Standard deviation of assembling precision of each assembling item of worm rotating unit
Substituting the formula I and the formula III into the formula II to obtain the formula six, namely the reliability of the assembly precision of a certain assembly item of the element motion assembly unit
Is composed of
Formula six
The data in table 1, table 2 and table 3 are substituted into the formula six, and the fuzzy reliability of the assembly precision of each assembly item is shown in table 4.
TABLE 4 fuzzy reliability of assembling precision of each assembling item of worm rotating unit
The assembly precision of the element motion assembly unit is ensured by the assembly precision of each assembly item, so the fuzzy reliability of the assembly precision of the element motion assembly unit is formed by serially connecting the fuzzy reliabilities of the assembly items, namely the fuzzy reliability of the assembly precision of the element motion assembly unit
Expressed as formula seven, is
Formula seven
Substituting the data in the table 4 into a formula seven to obtain the fuzzy reliability of the assembly precision of the worm rotating unit:
it should be understood that the above-described specific embodiments are merely illustrative of the present invention and are not intended to limit the present invention. Obvious variations or modifications which are within the spirit of the invention are possible within the scope of the invention.
Claims (4)
1. A mechanical element motion assembly precision reliability analysis method based on a fuzzy theory is characterized by comprising the following steps:
(1) establishing a mechanical element action assembly unit: the element action assembling unit is an independent component which takes an executive component for realizing element action as an assembling core, a group of parts can be independently assembled to meet the specified element action performance requirement and enable the element action to complete the specified function in the assembling process;
(2) defining the assembly precision reliability and the element motion assembly unit assembly precision reliability: the assembling precision reliability refers to the capability that the actual assembling precision of the element motion assembling unit meets the design requirement under the specified assembling condition; the reliability of the assembly precision of the meta-motion assembly unit refers to the probability that the actual assembly precision meets the design requirement of the meta-motion assembly unit under the specified assembly condition;
(3) analyzing the reliability of the assembly precision: suppose that a certain assembly item of the meta-action assembly unit is MiThen the assembly item MiThe assembling precision reliability is as follows:
Ri＝P(xi)＝P(ximin＜xi＜ximax)
wherein the assembly item MiFor elements on a part in a unit assembled for element movement and assembly items, x, combined with elements on the assembled partiFor assembling item MiFitting clearance or interference of (x)iminMinimum clearance or maximum interference; x is the number ofimaxMaximum clearance or minimum interference;
if the meta-motion assembling unit has n assembling items, the assembling precision reliability of the meta-motion assembling unit is as follows:
(4) defining the fuzzy reliability of the assembly precision and the fuzzy reliability of the assembly precision of the element motion assembly unit: in the assembling process, due to the influence of the processing precision of parts, the rigidity of the parts, the thermal deformation of the parts and the assembling method, the assembling precision presents a fuzzy characteristic, and the capability that the actual assembling precision meets the requirement of an ideal state under the specified assembling condition of the element action assembling unit is called the assembling precision fuzzy reliability of the element action assembling unit; the probability that the actual assembly precision of the meta-motion assembly unit meets the requirement of an ideal state is called the fuzzy reliability of the assembly precision of the meta-motion assembly unit;
(5) analyzing the fuzzy reliability of the assembly precision: setting assembly precision x of certain assembly item of the meta-motion assembly unitiConsidering the fuzziness of the element action assembling process behavior, the requirement that the actual assembling precision meets the ideal assembling precision is a fuzzy event
Then the fuzzy reliability of the assembly precision of the assembly item is recorded as
It is briefly described as
Then the fuzzy reliability of the assembly precision of the meta-motion assembly unit is recorded as
(6) Determining an assembly precision reliability membership function: each assembly item in the meta-action assembly unit is MiBy using
Representing the assembly precision fuzzy event of the assembly item
The element is obtained by analyzing the characteristic of the actual fit clearance or interference magnitude of each assembly item of the element action unit in the general element action assembly precision dataThe general assembly item assembly precision reliability membership function of the action units can approximately adopt an intermediate ridge type distribution form, and the formula I is
Formula one
In the formula: a is1Representing a gap or interference magnitude, a, determined by analysis of the assembly accuracy data, which initially is higher to meet the desired performance requirements of the meta-action2The clearance or interference value which is determined after the assembly precision data analysis and cannot meet the ideal performance requirement of the element action at a high level is represented;
(7) establishing a basic model of mechanical assembly precision fuzzy reliability: according to the fuzzy event probability definition, a model for the assembly precision reliability of a certain assembly item of the element building action assembly unit is expressed as a formula II, namely
Formula two
If the assembly precision sample data of the assembly item obeys normal distribution, f (x)i) Expressed as formula three, namely
Formula three
In the formula III, the first step is carried out,
the mean value of the clearance or the interference of each assembly item in the element action assembly unit is expressed as a formula IV, namely the mean value is
Formula four
In the formula IV, m represents the sample size of a certain assembly item, i represents a certain assembly item, and j represents a certain sample of a certain assembly item;
Formula five
Substituting the formula I and the formula III into the formula II to obtain the formula VI, namely the assembling precision reliability of a certain assembling item of the meta-motion assembling unit
Is composed of
Formula six
The assembly precision of the element motion assembly unit is ensured by the assembly precision of each assembly item, so the fuzzy reliability of the assembly precision of the element motion assembly unit is formed by serially connecting the fuzzy reliabilities of the assembly items, namely the fuzzy reliability of the assembly precision of the element motion assembly unit
Expressed as formula seven, is
Formula seven
2. The method for analyzing the assembly accuracy and reliability of the mechanical element motion based on the fuzzy theory as claimed in claim 1, wherein the element motion assembly unit comprises five parts, namely a support part, a power source, an execution part, an intermediate transmission and a fastener.
3. The method for analyzing the assembly accuracy and reliability of mechanical element actions based on the fuzzy theory as claimed in claim 2, wherein the element action assembly unit can be a worm rotating element action.
4. The method according to claim 3, wherein the fuzzy event A &basedon assembly item assembly precision is characterized in thatiThe membership functions of (a) may be obtained according to statistical methods.
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| CN107038321A (en) * | 2017-05-24 | 2017-08-11 | 重庆大学 | Mission reliability expectancy analysis method based on metaaction unit |
| US20190080040A1 (en) * | 2017-09-13 | 2019-03-14 | Dalian University Of Technology | Integration method for accurate modeling and analysis and reliability-based design optimization of variable stiffness composite plate and shell structures |
| CN110083916A (en) * | 2019-04-22 | 2019-08-02 | 湖南工业大学 | Based on the mechanical structure Fuzzy fatigue reliability optimization method from structure membership function |
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