CN112749517A - Tolerance optimization distribution method - Google Patents

Tolerance optimization distribution method Download PDF

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CN112749517A
CN112749517A CN202110238564.9A CN202110238564A CN112749517A CN 112749517 A CN112749517 A CN 112749517A CN 202110238564 A CN202110238564 A CN 202110238564A CN 112749517 A CN112749517 A CN 112749517A
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曹衍龙
吴紫涧
杨凯莉
叶晓平
杨将新
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Zhejiang University ZJU
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Abstract

The invention discloses a tolerance optimization allocation method, which comprises the following steps: (1) constructing a fitness function which takes the total processing cost, the total mass loss and the total sensitivity cost as objective functions and the processing capacity and assembly tolerance constraints as constraint conditions, and determining weight factors among the objective functions by adopting an analytic hierarchy process; (2) importing the assembly information into a fitness function; (3) and solving the fitness function by adopting an improved bat algorithm and outputting a result, wherein the improved bat algorithm is obtained by introducing a crossover operator and a mutation operator of the genetic algorithm into the bat algorithm.

Description

Tolerance optimization distribution method
Technical Field
The invention relates to the field of machine manufacturing, in particular to a tolerance optimization distribution method.
Background
With the development of the mechanical manufacturing industry, the product innovation and the economy become the key for enterprises to improve the comprehensive strength. In the whole life cycle process of a product, design is the main stage for realizing innovation, and tolerance is a key factor for ensuring design rationality and economy. The optimization of tolerance distribution with the objective of obtaining the lowest cost is taken as a main technology influencing the economic performance of tolerance, at present, research focuses on minimizing the sum of processing cost and quality loss cost, and there are parallel design researches related to processing procedures, environmental robustness and the like, and few researches are comprehensively considered to ensure the capability of resisting tolerance variation influence of products. Tolerance optimization allocation belongs to a multi-objective optimization problem, but the application of an optimization algorithm for solving the problem is more traditional and still imperfect at present.
Disclosure of Invention
In view of the above-mentioned drawbacks of the prior art, the technical problem to be solved by the present invention is to provide a more feasible and effective solution to the problem of tolerance optimization.
To achieve the above object, the present invention provides a tolerance optimization assigning method, comprising the steps of:
(4) constructing a fitness function which takes the total processing cost, the total mass loss and the total sensitivity cost as objective functions and the processing capacity and assembly tolerance constraints as constraint conditions, and determining weight factors among the objective functions by adopting an analytic hierarchy process;
(5) importing the assembly information into a fitness function;
(6) and solving the fitness function by adopting an improved bat algorithm and outputting a result, wherein the improved bat algorithm is obtained by introducing a crossover operator and a mutation operator of the genetic algorithm into the bat algorithm.
Further, the objective function of the total processing cost is:
Figure BDA0002961241290000011
wherein n is the total component ring tolerance number in the product; wherein
Figure BDA0002961241290000012
In the formula, C (T)i) For processing cost, TiFor the tolerance value of the ith component ring, a0、a1、a2And a3Is a known parameter related to tolerance, where i ═ 1,2,3, …, n.
Further, the total mass loss objective function is:
Figure BDA0002961241290000021
where n is the total component ring tolerance number in the product, and
Figure BDA0002961241290000022
in the formula, TiThe tolerance value of the ith composite ring is A, which refers to the loss caused by unqualified products produced by a factory and has the unit of yuan.
Further, the total sensitivity cost objective function is:
Figure BDA0002961241290000023
wherein n is the total component ring tolerance number in the product, k1、k2Respectively representing the processing cost and the quality loss costThe influence coefficient of the total tolerance sensitivity cost function.
Further, the constraints of the processing capacity are:
Tmin≤Ti≤Tmax
in the formula, TiminForming a tolerance value with the minimum ring machining capacity for the ith group; t isimaxThe tolerance value with the largest ring processing capacity is formed for the ith group.
Further, the constraints of the assembly tolerance constraints are:
Figure BDA0002961241290000024
wherein Ti is the i-th compositional ring tolerance, SiAnd for the sensitivity coefficient of the ith dimensional tolerance, increasing the ring by 1, decreasing the ring by-1, and taking deltay as the required value of the assembly function.
Further, the fitness function is:
Figure BDA0002961241290000025
in the formula, alphai、βi、γiThe total processing cost, the total mass loss cost, and the total sensitivity cost respectively account for the influence coefficients of the ring tolerance values, i.e., the weight factors, and the sum thereof is 1.
Further, the analytic hierarchy process is for alphai、βi、γiFirst, the criterion C is determinediI.e. the tolerance value T of the constituent rings in the dimension chainiA total of (n-1); criterion CiThe dominant next-level element is ωi1、ωi2、ωi3Respectively representing the processing cost, mass loss, sensitivity, element omegai1、ωi2、ωi3For criterion CiThe relative weight of (a) is alphai、βi、γiBy the element omegai1、ωi2、ωi3Comparing two by two to obtain a pair criterion CiThe degree of importance of, the importance ofThe ratio is compared to obtain a judgment matrix
Figure BDA0002961241290000031
Wherein
Figure BDA0002961241290000032
Finger element omegaij、ωikWith respect to criterion CiIn the significance scale of (A), and finally, normalizing AiThe arithmetic mean is obtained after m row vectors, i.e.:
Figure BDA0002961241290000033
wherein i is 1,2,3, …, n-1; j is 1,2,3, …, m. From this, alpha is calculatedi、βi、γi。
Further, the improved bat algorithm comprises the steps of:
step 1: initializing a population, setting the number m of bat populations, the iteration times n, constants alpha and gamma, the initial values of pulse loudness A and emission rate r, and population genetic update probability PgaCross probability PcProbability of variation Pm；
Step 2: determining the dimension of a population according to the number of loop formed by assembling size chains, generating an initial population by applying a generation mode of a basic bat algorithm, calculating the fitness value of the population, and finding out and storing the current optimal solution;
and step 3: generating a random number rand if rand is less than or equal to PgaIf not, performing step 4, otherwise, performing step 7;
and 4, step 4: adopting a classical roulette method for primary selection, and selecting individuals capable of carrying out crossover and variation operations of a genetic algorithm;
and 5: if rand is less than or equal to PcPerforming cross operation and reserving descendants with small fitness function values;
step 6: if rand is less than or equal to PmCarrying out variation operation, and accepting the individual with small fitness function value, otherwise, not accepting the individual;
and 7: through the lower partVelocity v for updating bat population in formulaiAnd position xi；
fi＝fmin+(fmax-fmin)·β
Figure BDA0002961241290000034
Figure BDA0002961241290000035
In the formula (f)i、fmax、fminRespectively representing the pulse frequency, the maximum pulse frequency and the minimum pulse frequency of the ith bat sent out at the current iteration times; beta is [0,1 ]]Upper uniform random distribution number, X* iIs the current optimal solution.
And 8: generating a random number rand1 if rand1>riIf so, the current optimal solution is disturbed, and a new position x is generated according to the following formulanew；
xnew＝xold+εAt
And step 9: from xnewDetermining a fitness value f (x)i) If rand1<AiAnd f (x)i)<f(xi *) Accepting a new solution;
step 10: r is updated byiAnd AiIf i is<m, performing the step 7, otherwise, turning to the step 11;
Figure BDA0002961241290000041
Figure BDA0002961241290000042
wherein α and γ are constants of 0<α<1.0，γ>0,ri 0Is the initial pulse rate;
step 11: whether the condition of stopping iteration times is met or not is judged, if not, the step 3 is returned, otherwise, the step 12 is carried out;
step 12: and outputting the optimal individual solution set and the total function value of the fitness.
According to the invention, by summarizing a previous research method and a previous result in the aspect of tolerance optimization, aiming at the problem of tolerance optimization distribution of an assembly body size chain, a multi-objective optimization mathematical model which takes machining cost, mass loss and sensitivity as objective functions and takes machining capacity and assembly tolerance as constraint conditions is established, and an improved sensitivity function model which simultaneously constrains the machining cost and the mass loss cost variation sensitivity is provided based on a robustness thought. Applying the bat algorithm to tolerance optimization design, and introducing a crossover and mutation operator mechanism of the genetic algorithm aiming at the defect that the bat algorithm is easy to fall into local optimum; a coefficient factor is added at the position updating position of the bat, so that the overall searching efficiency and convergence of the operation of the algorithm are improved; an improved bat algorithm is designed by adopting an analytic hierarchy process to determine the weight coefficient, so that a more feasible and effective solution is provided for the tolerance optimization problem.
The conception, the specific structure and the technical effects of the present invention will be further described with reference to the accompanying drawings to fully understand the objects, the features and the effects of the present invention.
Drawings
FIG. 1 is a flow chart of the improved bat algorithm of the present invention;
FIG. 2 is a schematic view of a reduction gearbox assembly to which the present invention is applied;
FIG. 3 is a chain of assembled dimensions of the reduction gearbox assembly of FIG. 2;
FIG. 4 is a graph of tolerance values of the various component rings of the reduction gearbox assembly of FIG. 2 as a function of iteration;
FIG. 5 is a trend plot of fitness function values for the reduction gearbox assembly of FIG. 2 at three iterations; a
Detailed Description
The technical contents of the preferred embodiments of the present invention will be more clearly and easily understood by referring to the drawings attached to the specification. The present invention may be embodied in many different forms of embodiments and the scope of the invention is not limited to the embodiments set forth herein.
The invention provides a tolerance optimization method based on an improved bat algorithm. On the basis of a two-dimensional size chain, a multi-objective optimization mathematical model taking comprehensive consideration of processing cost, mass loss and improved sensitivity cost as an objective function and tolerance processing capacity and assembly tolerance constraint as constraint conditions is established, and the model is solved by using the algorithm provided by the invention, so that the obtained distribution result meets the requirements of larger tolerance and lowest total cost.
First, an objective function of a fitness function model of the tolerance optimization allocation method according to the invention is constructed.
In the production of mechanical products, the processing cost is the most dominant of the total cost, which mainly includes manufacturing processing, assembly testing, and other costs in the product's full life cycle. Generally, smaller tolerances result in greater processing costs, whereas larger tolerances result in lower processing costs. The establishment of the relation of the classical tolerance-cost function follows the principle of monotonous decrease, so the invention adopts the classical function to establish a new tolerance-processing cost model, and the graph of the function in the first quadrant is required to be monotonous and at least comprises a decreasing function. The invention selects an index and inverse index composite model as a new tolerance cost target function, and the expression is as follows:
Figure BDA0002961241290000051
in the formula, C (T)i) For processing cost, TiFor the tolerance value of the ith component ring, a0、a1、a2And a3Is a known parameter related to tolerance, where i ═ 1,2,3, …, n.
In order to ensure the validity of the relation between the part processing cost and the tolerance, the mathematical model in the invention aims at 45#The part of the steel material, and the condition that medium-sized part production is carried out by medium-sized mechanical production enterprises with the selection of processing parameters. In the prior art based onThe same processing characteristics have more applicable cost engineering models, wherein
The machining cost-tolerance model of the excircle characteristic dimension is as follows:
Figure BDA0002961241290000052
the machining cost-tolerance model of the characteristic dimension of the inner hole is as follows:
Figure BDA0002961241290000053
the machining cost-tolerance model for locating feature sizes is:
Figure BDA0002961241290000054
the machining cost-tolerance model for planar feature sizes is:
Figure BDA0002961241290000055
different sizes and form and position tolerances correspond to different cost functions, and researches show that the influence of the direction tolerance value on the processing cost is not obvious, so that the invention does not consider the orientation tolerance. According to the invention, the minimum sum of the processing costs corresponding to all the component rings is determined as an optimized objective function, and then the total processing cost is expressed as:
Figure BDA0002961241290000061
where n is the total component ring tolerance number in the product.
The mass loss-to-tolerance mathematical model of the present invention is next constructed.
The invention adopts the mass loss function in the prior art to quantitatively describe the quality of the product, which is respectively the mass loss function of the target characteristic, the small characteristic and the large characteristic. Generally, the mass loss function for dimensional tolerances of the component ring and the closed ring is the desired characteristic, and the tolerance function is expressed as:
L(y)＝k(y-m)2 (6)
in the formula, y is a mass characteristic value, m is a target value, and k is a mass loss coefficient independent of y.
Where (y-m) refers to the dimensional tolerance T produced by the manufacturing process, there are generally two distributions, bi-directional and uni-directional, with:
Figure BDA0002961241290000062
the tolerance is then TiThe mass loss cost due to the size of (a) is:
Figure BDA0002961241290000063
the form and position tolerance is expressed by a function of the desired small characteristic, and the functional expression is as follows:
Figure BDA0002961241290000064
where Δ t is the product tolerance allowed by the user, P is the loss caused when the product tolerance reaches the product tolerance allowed by the user, and assuming that the tolerance is bilaterally symmetric distribution, there are:
Figure BDA0002961241290000065
according to the invention, the minimum sum of the mass loss costs corresponding to all the component rings is set as an optimized objective function, and then the total mass loss cost is expressed as:
Figure BDA0002961241290000071
where n is the total component ring tolerance number in the product.
Next, a sensitivity-tolerance mathematical model of the present invention is constructed.
Sensitivity is an important standard for measuring the robustness of a product, and the robust design can effectively help a designer to find out the optimal parameters of a group of products or process design, so that the group of products can realize high-stability output on the premise of lowest cost. The mathematical function is considered, that is, the partial derivative of the function value at the point is a minimum value, so that the change of the point has little influence on the function value.
For the tolerance optimization allocation, the invention references the most common minimum sensitivity theory in engineering, and establishes the solution of tolerance sensitivity problem to enhance the tolerance variation resistance of the product while the former two cost values are smaller, thereby improving the manufacturability and the reliability. It can be found that the first order partial derivative formula of the taylor formula embodies the design concept of robustness, as shown in the following formula
Figure BDA0002961241290000072
At the minimum, any change in Δ T has minimal effect, at which point
Figure BDA0002961241290000073
Referred to as the sensitivity of machining costs to variations in tolerance values. In combination with the above analysis, the present invention requires modeling of the sensitivity of processing and mass loss costs to generate a sensitivity-tolerance function model.
If the mean value of the new tolerance cost objective function in the design variable T is based on Taylor formula
Figure BDA0002961241290000074
Where the spread is taken, Δ T represents the difference between the tolerance and the mean, as follows:
Figure BDA0002961241290000075
and removing the high-order term of the formula, taking the partial derivative at the first order as an approximate solution, and establishing a sensitivity expression of one of the processing costs. In order to ensure that most parts produced can meet the assembly requirement of the closed ring without selection or repair during assembly operation, the invention uses an incomplete interchange method (also called a probability method) to restrict a sensitivity function, so that the produced product can have a larger component ring tolerance distribution value when the tolerances of the closed rings are equal than that of the complete interchange method. The method improves economic benefits, has more scientific technology, meets the requirement of ensuring the interchange of most products, and obtains a processing cost sensitivity function as shown in the following formula
Figure BDA0002961241290000076
Similarly, the Taylor expansion of the mass loss cost at the mean Δ T is expressed as:
Figure BDA0002961241290000081
the mass loss sensitivity function is given by the formula:
Figure BDA0002961241290000082
in summary, a sensitivity function based on the combined processing cost and mass loss cost is established as follows:
Figure BDA0002961241290000083
wherein n is the total component ring tolerance number in the product, k1、k2The two coefficient values, which represent the influence coefficients of the processing cost and the mass loss cost, respectively, on the total tolerance sensitivity cost function, are determined according to a weighted average method, which can also be referred to as the weighting factor of the sensitivity cost function, and are 1 in order to achieve equality.
Constraints are then constructed for the fitness function model of the present invention.
Firstly, constraint conditions of machining capacity are explained, when the component rings of the assembly dimension chain are subjected to common difference matching, due to different manufacturing equipment, environments and the like, the tolerance of the component rings of each part has a certain machining limit range, and in order to ensure the economy of a machining method, the actual machining capacity is required to constrain the tolerance value of each component ring, namely:
Tmin≤Ti≤Tmax (17)
in the formula, TiminForming a tolerance value with the minimum ring machining capacity for the ith group; t isimaxThe tolerance value with the largest ring processing capacity is formed for the ith group.
Next, the assembly tolerance constraints will be explained. To ensure the accuracy and precision of the assembly, the tolerance determination method for the closed ring is usually to add assembly function constraints to the dimensional chain to ensure that the sum of the tolerances of the component rings is less than the tolerance value of the closed ring. The method is equivalent to an extreme value method and a root mean square method used in a tolerance analysis process, and the two methods are used as one of constraint conditions of tolerance distribution, so that the assembly performance can be met in advance, and the design efficiency is improved. Because the root mean square method of the assembly dimension chain tolerance can obtain a larger tolerance value while meeting the assembly tolerance constraint compared with the extreme method, the root mean square method is selected for the tolerance constraint. The constraint equations for both methods are as follows:
Figure BDA0002961241290000084
Figure BDA0002961241290000091
in the formula, TiFor the ith ring tolerance, T0Is a closed loop tolerance; k is a radical of0、kiThe relative distribution coefficients of the closed ring and the ith component ring are respectively, under the condition that the number of the component rings is not more than 6, the component rings of the size chain are normally distributed, the relative distribution coefficient is 1, if the number of the component rings exceeds 6, in order to ensure the assembly success rate of the product, the relative distribution coefficients are required to be 1Distinguishing relative distribution coefficients of component rings of each part, wherein the relative distribution coefficients comprise uniform distribution, normal distribution and triangular distribution, and the component rings are normally distributed; siFor the sensitivity (or transfer) coefficient of the ith dimensional tolerance, 1 is taken as the increasing ring, 1 is taken as the decreasing ring, and the deltay is the required value of the assembly function.
The following describes the establishment of the tolerance assignment multi-objective optimization model of the present invention.
To sum up, in order to ensure that the tolerance value obtained by the optimized distribution has more economical efficiency and practicability, the invention constructs a mathematical model which ensures that the processing cost and the quality loss cost are lower and the product has stronger capacity of resisting the influence of tolerance variation. The established tolerance distribution multi-objective optimization function is as follows:
Figure BDA0002961241290000092
wherein C (T) is a fitness function; alpha is alphai、βi、γiThe influence coefficients of the processing cost, the quality loss cost and the sensitivity on the component ring tolerance value are respectively, and the sum is 1; c1(T)、C2(T)、C3(T) objective functions of total processing cost, total mass loss, and total sensitivity cost for each component ring, respectively; t isiminFor the i-th component, the tolerance value, T, with the smallest ring processing abilityimaxFor the ith component ring with the largest tolerance value, TiForming a ring actual tolerance value for the ith; g (T) is the root mean square value of the dimensional chain tolerance, and Δ y is the assembly function requirement value.
The determination of the weighting factors for the multi-objective optimization function is explained next.
Considering the influence factor of tolerance design, the invention adopts an analytic hierarchy process under the concept of system engineering. An Analytic Hierarchy Process (AHP) is a method in which an element layer always related to a decision is first divided into a target, a criterion, a scheme and the like according to a structure, and then analyzed by a qualitative or quantitative decision theory. On the basis of deeply analyzing the essence, internal relation, decision-making elements and the like of a complex management problem, the method utilizes less quantitative information to mathematically process a logic method of a decision-making process, and is favorable for simplifying a complicated multi-target non-structural characteristic decision-making problem.
Weighting factor alpha for the present inventioni、βi、γiFirst, the criterion C is determinediI.e. the tolerance value T of the constituent rings in the dimension chainiA total of (n-1); criterion CiThe dominant next-level element is ωi1、ωi2、ωi3Respectively representing the processing cost, the quality loss and the sensitivity to the criterion CiThe relative weight of (a) is alphai、βi、γiBy the element omegai1、ωi2、ωi3Comparing two by two to obtain a pair criterion CiThe importance degree of (2) is calculated by referring to the importance degree values of the scale of 1-9 listed in the following table. Comparing the importance to obtain a judgment matrix
Figure BDA0002961241290000093
Wherein
Figure BDA0002961241290000101
Finger element omegaij、ωikRelative to CiThe importance scale of. Finally, the weight vector is referred to as normalized AiThe arithmetic mean obtained after m row vectors, i.e.:
Figure BDA0002961241290000102
wherein i is 1,2,3, …, n-1; j is 1,2,3, …, m. Calculating a weight factor alpha in the fitness function according to the weight factor alphai、βi、γi。
Figure BDA0002961241290000103
The improved bat algorithm for tolerance multi-objective optimized allocation of the present invention is next described.
The invention introduces crossover and mutation operators of a Genetic Algorithm (GA) into an initial Bat Algorithm (BA) to form the Genetic Bat Algorithm (GBA) so as to ensure that the diversity enhancement is achieved in the population iteration process and the global search range and the convergence of the algorithm are improved. The GBA algorithm flow diagram is shown in fig. 1.
The basic flow is as follows:
step 1: initializing a population, setting the number m of bat populations, the iteration times n, constants alpha and gamma, the initial values of pulse loudness A and emission rate r, and population genetic update probability PgaCross probability PcProbability of variation Pm；
Step 2: determining the dimension of a population according to the number of loop formed by assembling size chains, generating an initial population by applying a generation mode of a basic bat algorithm, calculating the fitness value of the population, and finding out and storing the current optimal solution;
and step 3: generating a random number rand if rand is less than or equal to PgaIf not, performing step 4, otherwise, performing step 7;
and 4, step 4: adopting a classical roulette method for primary selection, and selecting individuals capable of carrying out crossover and variation operations of a genetic algorithm;
and 5: if rand is less than or equal to PcPerforming cross operation and reserving descendants with small fitness function values;
step 6: if rand is less than or equal to PmCarrying out variation operation, and accepting the individual with small fitness function value, otherwise, not accepting the individual;
and 7: updating velocity v of bat population byiAnd position xi；
fi＝fmin+(fmax-fmin)·β (22)
Figure BDA0002961241290000111
Figure BDA0002961241290000112
In the formula (f)i、fmax、fminRespectively representing the pulse frequency, the maximum pulse frequency and the minimum pulse frequency of the ith bat sent out at the current iteration times; beta is [0,1 ]]Upper uniform random distribution number, X* iIs the current optimal solution.
And 8: generating a random number rand1 if rand1>riIf so, the current optimal solution is disturbed, and a new position x is generated according to the following formulanew；
xnew＝xold+εAt (25)
In the formula, xoldRepresents a solution randomly selected from the current optimal solution set, with ε being [ -1.0,1.0 [ -1.0 ]]D-dimensional random vector of, AtRepresents the average value of the current population loudness.
And step 9: from xnewDetermining a fitness value f (x)i) If rand1<AiAnd f (x)i)<f(xi *) Accepting a new solution;
step 10: r is updated byiAnd AiIf i is<m, performing the step 7, otherwise, turning to the step 11;
Figure BDA0002961241290000113
Figure BDA0002961241290000114
wherein α and γ are constants of 0<α<1.0，γ>0,ri 0Is the initial pulse rate;
step 11: whether the condition of stopping iteration times is met or not is judged, if not, the step 3 is returned, otherwise, the step 12 is carried out;
step 12: and outputting the optimal individual solution set and the total function value of the fitness, and ending the program.
The invention is applied to tolerance-optimized allocation of a gearbox assembly. As shown in fig. 2, the nominal dimensions of the surfaces of the parts in the known assembly, based on the assembly constraint relationship between the parts, these associated dimensions form an assembly dimension chain, which is shown in fig. 3, and the assembly dimension chain equation is:
Y＝X1+X2-X3-X4-X5 (28)
in which Y denotes the tolerance of the closed ring, X1，X2，X3，X4And X5Respectively refer to the tolerance value T of each component ring1，T2，T3，T4And T5。
The cost function under different processing environments is different, and the embodiment adopts a processing cost-tolerance model under the positioning characteristic of the two-dimensional size chain, namely, the formula (3) as described above:
Figure BDA0002961241290000121
and for the mass loss function, i.e. the previous equation (8):
Figure BDA0002961241290000122
wherein
Figure BDA0002961241290000123
The method is characterized in that the method refers to the influence coefficients of different tolerance sizes on the quality loss cost, the tolerances are distributed in a bidirectional symmetrical mode, A refers to the loss caused by unqualified products produced in a factory, the unit is element, the price of an enterprise is already obtained, and the method can be changed according to actual needs. In this embodiment, if a 21-tuple loss is caused when a product is rejected, the corresponding coefficient of influence value is 80. And then performing operations such as first-order partial derivation on the positioning size processing cost and the mass loss function to obtain a tolerance sensitivity mathematical model, and finally establishing a tolerance multi-objective optimization mathematical model based on the reduction gearbox assembly body as follows:
Figure BDA0002961241290000124
the GBA in this embodiment is implemented using MATLAB R2014a version of the software platform programming. Setting the bats population size to be 50; the number of iterations is set to 500,1000,2000 respectively; the values of the weight factors are approximately solved to be 0.35, 0.35 and 0.3 by using an analytic hierarchy process, and then the two weight factors of the sensitivity cost function are determined to be 0.15 by using a weighted average method; population genetic update probability PgaTake 0.8, the crossover probability PcTake 0.5, the mutation probability PmTake 0.1. The following table of the solving results shows that a graph of variation of tolerance values of all the component rings of the GBA optimization along with the iteration times is shown in fig. 4, and variation trends of fitness function values under three iteration times are shown in fig. 5.
Figure BDA0002961241290000131
As can be seen from the operation result of fig. 5, under three iteration times, the optimization result does not reach the optimal state when the iteration time is 500, the curve of the fitness value gradually tends to be stable when the iteration time is 1000 times, and when the iteration time reaches 2000 times, the operation result is basically unchanged, which proves the stability of the algorithm, and meanwhile, as can be seen from the yellow curve, the function value is basically unchanged after the iteration time is about 1100 times; along with the reduction of the fitness value, the processing cost, the quality loss cost and the sensitivity of the fitness value gradually tend to the optimal state, and the convergence and the feasibility of the algorithm are proved.
The foregoing detailed description of the preferred embodiments of the invention has been presented. It should be understood that numerous modifications and variations could be devised by those skilled in the art in light of the present teachings without departing from the inventive concepts. Therefore, the technical solutions available to those skilled in the art through logic analysis, reasoning and limited experiments based on the prior art according to the concept of the present invention should be within the scope of protection defined by the claims.

Claims (9)

1. A tolerance-optimized dispensing method, comprising the steps of:
(1) constructing a fitness function which takes the total processing cost, the total mass loss and the total sensitivity cost as objective functions and the processing capacity and assembly tolerance constraints as constraint conditions, and determining weight factors among the objective functions by adopting an analytic hierarchy process;
(2) importing the assembly information into the fitness function;
(3) and solving the fitness function by adopting an improved bat algorithm and outputting a result, wherein the improved bat algorithm is obtained by introducing a crossover operator and a mutation operator of a genetic algorithm into the bat algorithm.
2. The tolerance optimized allocation method of claim 1, wherein the objective function of the total machining cost is:
Figure FDA0002961241280000011
wherein n is the total component ring tolerance number in the product; wherein
Figure FDA0002961241280000012
In the formula, C (T)i) For processing cost, TiFor the tolerance value of the ith component ring, a0、a1、a2And a3Is a known parameter related to tolerance, where i ═ 1,2,3, …, n.
3. The tolerance optimized allocation method of claim 2, wherein the total mass loss objective function is:
Figure FDA0002961241280000013
where n is the total component ring tolerance number in the product, and
Figure FDA0002961241280000014
in the formula, TiThe tolerance value of the ith composite ring is A, which refers to the loss caused by unqualified products produced by a factory and has the unit of yuan.
4. The tolerance optimized allocation method of claim 3, wherein the total sensitivity cost objective function is:
Figure FDA0002961241280000015
wherein n is the total component ring tolerance number in the product, k1、k2The impact coefficients of the machining cost and the mass loss cost on the total tolerance sensitivity cost function are respectively expressed.
5. The method of claim 4, wherein the process capability constraints are:
Timin≤Ti≤Timax
in the formula, TiminForming a tolerance value with the minimum ring machining capacity for the ith group; t isimaxThe tolerance value with the largest ring processing capacity is formed for the ith group.
6. The tolerance optimized allocation method of claim 5, wherein the constraints of the assembly tolerance constraints are:
Figure FDA0002961241280000021
wherein Ti is the i-th compositional ring tolerance, SiAnd for the sensitivity coefficient of the ith dimensional tolerance, increasing the ring by 1, decreasing the ring by-1, and taking deltay as the required value of the assembly function.
7. The tolerance optimized allocation method of claim 6, wherein the fitness function is:
min：
Figure FDA0002961241280000022
s.t.αi+βi+γi＝1
Timin≤Ti≤Timax
g(T)≤Δy
in the formula, alphai、βi、γiThe total processing cost, the total mass loss cost and the total sensitivity cost respectively are the influence coefficients of the combined ring tolerance value, namely the weight factors, and the sum of the weight factors is 1.
8. The tolerance optimized allocation method of claim 7, wherein said analytic hierarchy process is for said αi、βi、γiFirst, the criterion C is determinediI.e. the tolerance value T of the constituent rings in the dimension chainiA total of (n-1); the criterion CiThe dominant next-level element is ωi1、ωi2、ωi3Respectively representing processing cost, mass loss, sensitivity, the element omegai1、ωi2、ωi3For criterion CiIs said alpha as the relative weight ofi、βi、γiBy applying to said element ωi1、ωi2、ωi3Comparing every two to obtain the criterion CiComparing the importance to obtain a judgment matrix
Figure FDA0002961241280000023
Wherein
Figure FDA0002961241280000024
Finger element omegaij、ωikWith respect to the criterion CiIn the significance scale of (A), and finally, normalizing AiThe arithmetic mean is obtained after m row vectors,namely:
Figure FDA0002961241280000025
wherein i is 1,2,3, …, n-1; j is 1,2,3, …, m. Calculating the alpha according to the abovei、βi、γi。
9. The tolerance optimized dispensing method of claim 8, wherein said improved bat algorithm comprises the steps of:
step 1: initializing a population, setting the number m of bat populations, the iteration times n, constants alpha and gamma, the initial values of pulse loudness A and emission rate r, and population genetic update probability PgaCross probability PcProbability of variation Pm；
Step 2: determining the dimension of a population according to the number of loop formed by assembling size chains, generating an initial population by applying a generation mode of a basic bat algorithm, calculating the fitness value of the population, and finding out and storing the current optimal solution;
and step 3: generating a random number rand if rand is less than or equal to PgaIf not, performing step 4, otherwise, performing step 7;
and 4, step 4: adopting a classical roulette method for primary selection, and selecting individuals capable of carrying out crossover and variation operations of a genetic algorithm;
and 5: if rand is less than or equal to PcPerforming cross operation and reserving descendants with small fitness function values;
step 6: if rand is less than or equal to PmCarrying out variation operation, and accepting the individual with small fitness function value, otherwise, not accepting the individual;
and 7: updating velocity v of bat population byiAnd position xi；
fi＝fmin+(fmax-fmin)·β
Figure FDA0002961241280000031
Figure FDA0002961241280000032
In the formula (f)i、fmax、fminRespectively representing the pulse frequency, the maximum pulse frequency and the minimum pulse frequency of the ith bat sent out at the current iteration times; beta is [0,1 ]]Upper uniform random distribution number, X* iThe current optimal solution is obtained;
and 8: generating a random number rand1 if rand1>riIf so, the current optimal solution is disturbed, and a new position x is generated according to the following formulanew；
xnew＝xold+εAt
And step 9: from xnewDetermining a fitness value f (x)i) If rand1<AiAnd f (x)i)<f(xi *) Accepting a new solution;
step 10: r is updated byiAnd AiIf i is<m, performing the step 7, otherwise, turning to the step 11;
Figure FDA0002961241280000033
Figure FDA0002961241280000034
wherein α and γ are constants of 0<α<1.0，γ>0,ri 0Is the initial pulse rate;
step 11: whether the condition of stopping iteration times is met or not is judged, if not, the step 3 is returned, otherwise, the step 12 is carried out;
step 12: and outputting the optimal individual solution set and the total function value of the fitness.
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