CN116679614B - Multi-feature cutter comprehensive adaptation method based on evolution game - Google Patents
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Abstract
The invention discloses a multi-feature tool comprehensive adaptation method based on evolution game, which relates to the technical field of machining and comprises the following steps: establishing a tool strategy set of machining characteristics; establishing a cutter scheme evaluation system; establishing a multi-feature cutter comprehensive matching model; solving a multi-feature cutter comprehensive fit model based on an evolution game theory to obtain an optimal cutter strategy combination; the invention can obtain the complete tool proposal of the full cutting process of the multi-feature part which meets the requirements of users.
Description
Technical Field
The invention relates to the technical field of machining, in particular to a multi-feature tool comprehensive adaptation method based on an evolution game.
Background
The tool adaptation for single features is a locally optimized model with respect to the full cutting process of multi-feature parts, without taking into account the cost and efficiency of the full cutting process complete tool solution, as well as the commonality of tools between similar features. Therefore, the multi-feature tool comprehensive fit service in the industrial internet environment can be provided, the tool changing times can be reduced, the manufacturing efficiency can be improved, the tool cost can be controlled, the tool fit range can be expanded, the tool fit cost can be reduced, and the cutting tool preparation work of the end user can be reduced.
The research on the multi-feature tool comprehensive matching technology of the parts can maximize the utilization of the existing processing resources. Although there have been some studies on the fit of a tool heddle, it is basically focused on how to perform tool combinations for a certain profiled machining feature. The comprehensive tool adaptation research for the multi-feature parts is relatively few, and at home and abroad tool service platforms almost have no capability of multi-feature comprehensive tool adaptation, and end users generally perform unidirectional feature tool adaptation at first and finally combine the obtained tools to generate a complete tool scheme of the part full cutting process. As described above, the process related to the mode is wide in knowledge, and needs to be completed by the cooperation of the process personnel of different kinds, so that the problems of long tool adaptation period, low efficiency, increased tool changing times and the like can be caused. In addition, many known tool manufacturers can provide professional solutions to the processing problems of specific industries by researching requirements and based on the strong tool development capability of the manufacturers. Obviously, the proposal provided by the specific cutter manufacturer for the special problem has low universality and sharing performance and long development period although the expertise degree is high.
Disclosure of Invention
In order to solve the problems in the prior art, the invention aims to provide a multi-feature cutter comprehensive adaptation method based on evolution game, and the method can obtain a complete cutter scheme which accords with the multi-feature part full cutting process expected by a user.
In order to achieve the above purpose, the invention adopts the following technical scheme: a multi-feature tool comprehensive adaptation method based on evolution game comprises the following steps:
step 1, establishing a cutter strategy set of machining characteristics;
step 2, establishing a cutter scheme evaluation system;
step 3, establishing a multi-feature cutter comprehensive matching model;
and 4, solving the multi-feature cutter comprehensive fit model based on the evolution game theory to obtain the cutter optimal strategy combination.
As a further improvement of the present invention, the step 1 is specifically as follows:
for single feature f of single-tool machining i Selectable tool strategy S i For the set T of available tools i Any one of the elements; for the complex features, a plurality of cutters are adopted for combined cutting, and the method specifically comprises the following steps: first for complex feature f c Is set of available tools T c ＝(T c 1 ,T c 2 …T c kc ) According to the diameter D (T c kc ) Sequencing; then obtaining the key cutter quantity kc according to the minimum inner contour arc radius of the machining characteristics * The method comprises the steps of carrying out a first treatment on the surface of the And finally, taking the given total number x of the cutters as a boundary to obtain all cutter combination strategies.
As a further improvement of the present invention, the step 2 is specifically as follows:
the characteristic value of the tool is dimensionless processed by the following steps:
V j MIN and V j MAX The maximum and minimum values of the j-th characteristics of the tools in the set of available tools, respectively; x is x ij A value of a j-th characteristic of an i-th tool in the set of available tools; the positive-oriented characteristic refers to a characteristic positively correlated with the evaluation index; negative-going characteristic negative-going refers to a characteristic that is negatively related to the index;
modeling cutter matching M: firstly, carrying out dimensionless treatment on the characteristics of the cutters, and then carrying out matching degree calculation on each cutter by the following formula:
wherein n is the number of processing features; n is the characteristic quantity related to M; w (w) j Is a characteristic rule vector corresponding to the cutting processing of the workpiece material; m is then i The matching between the ith tool plan and the machining requirement can be represented; the characteristics of the tool include material characteristics including strength S, hardness H, thermal conductivity T of the tool material, and geometric characteristics c And heat resistance H r The method comprises the steps of carrying out a first treatment on the surface of the The geometrical characteristics include the rake angle R o Rear angle alpha, knife tip arc N r The number Z of teeth, the diameter D of teeth and the clamping mode;
efficiency E f Modeling: the specific formula is as follows:
f is the number of cutter characteristics affecting the efficiency of the static cutter scheme; g i A tool characteristic value related to the efficiency of the static tool scheme, which is standardized after dimensionless processing;
(3) Modeling additional indexes: the following analytic hierarchy process is used to construct a computing system for index I and its m influencing factors (k 1 ,k 2 …k m ) The value of I is calculated by the following formula:
wherein c i The weight coefficient of the i-th factor; w (w) i Is k j Relative contribution to I; the j-th influencing factor k j Having n j (k 1 j ，k 2 j …k nj j ) The value of the jth influencing factor can be obtained by a hierarchical analysis method, and the specific flow is as follows:
first, a relative contribution matrix A shown in the following formula is constructed:
a pq when k is expressed as j Respectively take k p j And k q j The ratio of the contribution degree to I at the time of the reaction, therefore, a pq ＝1/a qp The method comprises the steps of carrying out a first treatment on the surface of the To ensure different k j The logic of the evaluation of the contribution degree of the value to the I is accurate, and consistency check is carried out on the A according to the following formula:
wherein lambda is max Is the maximum eigenvalue of matrix a; n is the size of the matrix;
if CR is<0.1, passing the consistency check; otherwise, the value of A is adjusted until the condition is met; when the consistency check of A passes, k j The I-th value of (2) is the relative contribution degree w of the I to the I i Can be calculated by the following formula:
wherein w is * j Is corresponding to lambda max The j-th element of the feature vector of (a); w (w) i j Is k j Taking k i j Contribution degree to I;
according to the complexity of accessories and clamping procedures required by different clamping modes, a contribution degree matrix A of clamping mode factors of the indexable tool to manufacturability is constructed based on a 9-point scoring method 1 ；
The contribution of the tool interchangeability factor to manufacturability P is as follows:
wherein w is the contribution degree of tool interchangeability factors to tool scheme manufacturability P, f * i The method is characterized in that the method is an ith same type of feature which can be processed by the cutter, and m is the sum of all features which can be processed by the cutter; by calculating w of each tool strategy, a contribution degree matrix A of tool interchangeability factors to tool scheme manufacturability is constructed 2 。
As a further improvement of the present invention, in step 3, the multi-feature tool ensemble fitting model is as follows:
Max(M,E f ,P,E,)&&Min(C)
C ij the price of the jth tool strategy for the ith machining feature; the utility value of the complete tool plan for the q-th part full cut process is calculated by:
wherein k is 1 Is the number of positive expected indicators; k (k) 2 Is the number of negative expected indicators; q is the conversion coefficient of the negative expectation index.
As a further improvement of the present invention, the step 4 is specifically as follows:
mapping each of the processed features to a game player; mapping the cutter strategy set of the processing characteristics into a strategy set of a player; the price of the tool strategy and the budget of the complete tool scheme of the user in the whole cutting process of the part are mapped into constraints; the objective function F is mapped into a utility function U of the algorithm; and solving the multi-feature cutter comprehensive fit model by using an evolution game method through a mapping process, wherein after the evolution game method reaches the set convergence accuracy, the outputted optimal strategy combination is mapped into a corresponding cutter scheme, so that the complete cutter scheme optimization of the whole cutting process of the part under the budget cost constraint of the terminal user can be realized.
The beneficial effects of the invention are as follows:
in order to improve cutter adaptation efficiency, control the cost of a complete cutter scheme in the whole cutting process of a part, realize the integral optimization of the whole cutting cutter scheme of the part, develop the research of a method for comprehensive matching of multi-feature cutters under the condition of industrial Internet, provide evaluation indexes and methods of the complete cutter scheme in the whole cutting process of the part in a network environment, map each processing feature of the part to a game player, and map an available cutter set of the corresponding feature to a player policy set. Under the condition of considering cutter commonality, a multi-feature cutter comprehensive matching model of the part with cost as constraint and comprehensive utility value as target is constructed. Based on an evolution game theory, a solving method of a multi-feature tool comprehensive fit model is researched, efficient and high-response speed solving in a network environment is realized, and the effectiveness and the practicability of the method are verified by taking a motorcycle engine single-throw crankshaft and a stainless steel square test piece as examples.
Drawings
FIG. 1 is a schematic diagram of a combined tool machining cavity case in an embodiment of the invention;
FIG. 2 is a schematic view of a machining cavity of a combined tool according to an embodiment of the invention;
FIG. 3 is a flow chart of a tool assembly strategy generation in an embodiment of the invention;
FIG. 4 is a graph of a model of available tool matching in an embodiment of the invention;
FIG. 5 is a flowchart of an evolutionary game algorithm in accordance with an embodiment of the invention;
FIG. 6 is a diagram illustrating a mapping process of a problem space to an algorithm space according to an embodiment of the present invention.
Detailed Description
Embodiments of the present invention will be described in detail below with reference to the accompanying drawings.
Examples
In order to improve the cutter adaptation efficiency, control the cutter scheme cost of the part full cutting process and realize the integral optimization of the cutter scheme of the part full cutting process, a method for researching the comprehensive proper matching of multi-feature cutters in the industrial Internet environment is urgently needed. The implementation provides a multi-feature cutter comprehensive adaptation method based on evolution game, wherein processing features of parts are mapped to game players, and available cutter sets of corresponding features are mapped to player strategies. Under the condition of considering cutter commonality, constructing a multi-feature cutter comprehensive matching model of the parts with cost as constraint and comprehensive utility value as target, and solving the model by improving an evolutionary game algorithm to obtain a complete cutter scheme which accords with the multi-feature part full cutting process expected by a user; the method specifically comprises the following steps:
multi-feature cutter comprehensive matching model:
for a given part with multiple machining features, and a set of available tools for each machining feature, it is investigated how to intelligently give an economical, efficient, and user-desired tool solution from a multitude of tool combinations. The specific expression of the problem is as follows: the workpiece P has n machining features (f 1 ，f 2 …f i …f n ) The available tool set corresponding to the ith machining feature is T i ＝(T i 1 ,T i 2 …T i ki ) Ki is the number of available tools. For basic characteristics, directly adopting a single cutter to process; for complex features, research shows that the combined machining efficiency of a plurality of cutters is often better than that of a single cutter, so that the cutter combination problem facing to a single complex feature needs to be considered when the multi-feature cutters are comprehensively matched.
Let P contain m complex features, (n-m) basic features. Then for each basic feature f j Its optional tool strategy is T j Among themThus processing f j Is available tool strategy S of (1) j The formula is as follows:
wherein A is an arrangement formula. For complex features f c ，T c The included tools can be processed by a single tool, and can be processed by a combined tool. Setting the maximum number of cutters in the combination scheme to be x (x<kc) and the combination of each set of tools must contain critical tools (tools that can machine the entire feature without interference), f c Is a set S of selectable tool strategies c The formula is as follows:
wherein kc * Taking the cavity shown in fig. 1 as an example, the number of key cutters is taken, and the smallest inner contour circular arc diameter in the cavity is 4mm, so that the cutters with the diameter phi less than or equal to 4mm meet the condition that a single cutter processes the whole cavity, namely the key cutter. Therefore, the number of cutters with phi less than or equal to 4mm is kc * 。
To this end, the problem studied in the present embodiment can be described as the following optimization problem. For n machined features (f) contained by part P 1 ，f 2 …f i …f n ) And a set of selectable tool strategies for each machining feature (S 1 ，S 2 …S i …S n ) And S is i ＝(s 1 i ，s 2 i …s j i …s ni i ) Ni is S i Is a number of elements of (a). How to construct S i Policy utility evaluation system of (2), and from S i (i=1, 2 … n) selecting a global best strategy s * i Complete tool solution S for a complete cutting process of a part P * ＝(s * 1 ，s * 2 …s * i …s * n ) And has the highest utility value while satisfying the user's expectations.
Tool strategy set of features:
for single feature f of single-tool machining i Alternative tool strategies S, e.g. drilling and tapping i For the set T of available tools i Any one of the elements; but for the complex characteristics, the mode of cutting by adopting a plurality of cutters has better processing efficiency. Taking the machining area shown in fig. 2 as an example, a large-diameter cutter can be used for efficiently removing a large amount of machining allowance, and then a key cutter is used for machining the whole cavity without interference, so that the cutting task is completed. Thus, in order to provide an efficient tool solution, the machining of complex features must take into account the strategy of multi-tool combined machining.
The following focuses on a method for generating a complex characteristic multi-cutter combination processing strategy set, wherein the generation rule of the multi-cutter combination is shown in fig. 3:
(1) In order to ensure that the entire complex feature is machined without interference, at least one key tool must be provided in each tool set.
(2) In order to ensure the machining efficiency, a feasible cutter with a larger diameter should be arranged in the combined cutter.
(3) The tool items of the machining strategy should be arranged in diameter, and since the workable area of the same diameter tool is the same, tools with the same diameter must not be present in each tool combination.
(4) According to the principle of less tool changing, the total number of tools in a certain local working area is as small as possible.
Thus, first for complex feature f c Is set of available tools T c ＝(T c 1 ,T c 2 …T c kc ) According to the diameter D (T c kc ) Sequencing; then obtaining the key cutter quantity kc according to the minimum inner contour arc radius of the feature * The method comprises the steps of carrying out a first treatment on the surface of the Finally, with a givenThe total number of tools x is used as a boundary, and all tool combination strategies are obtained through the flow shown in fig. 3 (S in the figure i Representing the state of the set of tool strategies at x=i).
Cutter scheme evaluation system:
the current tool proposal research aiming at processing characteristics is almost directed to workshop tool libraries, and the efficient and low-cost processing is realized by combining the cutting parameter optimization technology. Although this process can provide a complete set of cutting solutions including tools and optimization parameters, its selection range is limited to shop tools, and the main consideration is the integrated optimization of the geometric parameters and cutting parameters of the tools, without comprehensive and comprehensive evaluation of the tool solution itself.
On the other hand, the integrated optimization of the cutter combination and the cutting parameters tends to cause the problems of large calculation amount, slow response speed, poor user experience and the like, and an optimal static cutter scheme is difficult to obtain. Therefore, referring to the current research and processing experience, the present embodiment proposes a static tool solution evaluation method that takes into account the tool matching, manufacturability, efficiency, environmental friendliness, and economy of the tool solution.
In particular, in order to eliminate the influence of units, comparison analysis is conveniently performed, and firstly, the characteristic value of the cutter is subjected to dimensionless treatment by the following formula:
V j MIN and V j MAX The maximum and minimum values of the j-th characteristics of the tools in the set of available tools, respectively; x is x ij A value of a j-th characteristic of an i-th tool in the set of available tools; the positive-oriented characteristic refers to a characteristic positively correlated with an evaluation index, for example, a larger radius of the arc of the tool nose should be selected during rough machining; negative-going (negative-oriented) property refers to and refers toFor the characteristics of negative correlation, such as rough machining, a smaller rake angle should be selected to ensure the strength of the tip.
(1) Modeling cutter matching M: to further determine the match between the available tools and the part being machined, the present embodiment models the match M of the available tools. The model of M is shown in fig. 4.
The material characteristics comprise the strength S, the hardness H and the thermal conductivity T of the cutter material c And heat resistance H r The method comprises the steps of carrying out a first treatment on the surface of the The geometrical characteristics include the rake angle R o Rear angle alpha, knife tip arc N r Tooth number Z and diameter D (rotary tool), and clamping mode (indexable tool). The values of these characteristics are provided by the tool manufacturer, and for each characteristic, the dimensionless processing is performed first, and then the matching degree calculation is performed on each tool by the following formula:
n is the number of processing features; n is the characteristic quantity related to M; w (w) j Is a characteristic rule vector corresponding to the cutting processing of the workpiece material; m is then i A match between the ith tool plan and the machining requirement may be indicated.
(2) Efficiency E f Modeling: the efficiency of the static cutter scheme is mainly characterized by the geometric dimension of the cutter, for example, the larger the diameter of the cutter is, the higher the material removing potential is, so the higher the machining efficiency is; the larger the radius of the arc of the tip, the larger the diameter of the inscribed circle of the blade, the larger the thickness of the blade, the larger the cutting load which the cutter can bear, and the larger the allowable cutting load, and the higher the efficiency is evaluated. E (E) f The model of (2) is specifically represented by the following formula:
f is the number of cutter characteristics affecting the efficiency of the static cutter scheme; g i Is a tool characteristic value related to the efficiency of the static tool scheme standardized after dimensionless processing.
(3) Modeling additional indexes: except M and E f Besides, the evaluation of the cutter scheme also comprises an environment friendliness index E, a cost C, manufacturability P and other additional indexes. Where C is the cutter price, priced by the cutter manufacturer. Indirection indexes such as manufacturability, environmental friendliness, economy and the like are difficult for cutter manufacturers to directly provide accurate evaluation values for the cutter manufacturers.
In order to solve the problem of evaluating the indirection index, the present embodiment adopts the following analytic hierarchy process (Analytic Hierarchy Process, AHP) to construct a computing system. For index I, and its m influencing factors (k 1 ,k 2 …k m ) The value of I can be obtained by the following formula:
wherein c i The weight coefficient of the i-th factor; w (w) i Is k j Relative contribution to I. The j-th influencing factor k j Having n j (k 1 j ，k 2 j …k nj j ) The value of the jth influencing factor can be obtained by analytic hierarchy process [160] The specific flow is as follows:
first, a relative contribution matrix A shown in the following formula is constructed:
a pq when k is expressed as j Respectively take k p j And k q j The ratio of the contribution degree to I at the time of the reaction, therefore, a pq ＝1/a qp . To ensure different k j The logic of the evaluation of the contribution degree of the value to the I is accurate, and consistency check is needed for the A according to the following formula:
wherein lambda is max Is the maximum eigenvalue of matrix a; n is the size of the matrix. The RI values for factors 3 to 13 are shown in table 1:
RI values of the factors of tables 13 to 13
If CR is<0.1, passing the consistency check; otherwise, the value of a is adjusted until the condition is met. When the consistency check of A passes, k j The I-th value of (2) is the relative contribution degree w of the I to the I i Can be calculated by the following formula:
wherein w is * j Is corresponding to lambda max The j-th element of the feature vector of (a); w (w) i j Is k j Taking k i j Contribution to I at that time.
Taking the manufacturability P of the tool solution as an example, P is affected by two factors, namely the assemblability of the indexable tool and the interchangeability of the tool between features. According to different requirements, different clamping modes are needed for the indexable cutting tool, however, the clamping modes are different in the number of accessories, time consumption of clamping and difficulty in assembly; for proper matching of multi-feature cutter healds, cutter sharing among the same type of features is realized, the number of cutters and the number of cutter changing times are necessarily reduced, and then the cutting efficiency is improved.
The indexable tool comprises clamping modes of C, D, M, P, S, W and the like, and a contribution degree matrix A of clamping mode factors of the indexable tool to manufacturability is constructed based on a 9-point scoring method according to parts and complicated clamping procedures required by different clamping modes 1 . The assemblability evaluation values of the different clamping modes are shown in table 2:
table 2 evaluation values of assemblability for different clamping modes
Tool interchangeability is a process in which the same type of machining feature is machined using the same tool while meeting size constraints, thereby reducing the number of passes and the number of tools. Specifically, the contribution of the tool interchangeability factor to manufacturability P may be expressed as follows:
wherein w is the contribution degree of tool interchangeability factors to tool scheme manufacturability P, f * i For the i-th type of feature that the tool can process, m is the sum of all features that the tool can process. By calculating w of each tool strategy, a contribution degree matrix A of tool interchangeability factors to tool scheme manufacturability is constructed 2 。
Multi-feature cutter comprehensive matching model:
considering that the end-user of the tool has a clear cost budget and personalized preference when faced with the need for a complete tool solution for a full cut process of a part, the cost becomes a feature of the solution for viable solutions within the budget, subject to the constraint of the solution budget. Therefore, by constructing a judgment and evaluation model of a feasible scheme, a priority sequence conforming to the preference of a user can be obtained in a plurality of schemes.
For a wafer having n machined features (f 1 ，f 2 …f i …f n ) Is a set of available tool strategies for each machining feature (S 1 ，S 2 …S i …S n ) S obtained i Evaluation index i= (I) of each policy in (I) i 1 ，I i 2 …I i k ) And preferences W given by the user through page interactions c ＝(w 1 c ，w 2 c …w k c ) And workpiece material cutting processing characteristic rule W m ＝(w 1 m ，w 2 m …w k m ). Considering that there are both indexes of positive expectancy (the larger the user hopes to be, the better, such as matching between the tool and the machining condition, efficiency, environmental friendliness and the like) and indexes of negative expectancy (the smaller the user hopes to be, the better, such as cost), under the constraint of budget cost, a model of the multi-feature tool ensemble fit of the part can be represented by the following formula:
Max(M,E f ,P,E,)&&Min(C)
C ij the price of the jth tool strategy for the ith machining feature. The utility value of the complete tool plan for the q-th part full cut process can be calculated by:
wherein k is 1 Is the number of positive expected indicators; k (k) 2 Is the number of negative expected indicators; q is the conversion coefficient of the negative expectation index.
Solving method based on evolution game:
the evolution game algorithm (Evolutionary Game Algorithm, EGA) is an intelligent method based on economic playing and dynamic evolution calculation. EGA searches the entire solution space generated by the game player policy combination with maximum utility value as an optimization objective under simultaneous consideration of local and global performance. Compared with the random selection process of the evolutionary algorithm, EGA converges to global optimum with a probability equal to 1, and has a very high convergence rate. In addition, in the dynamic evolution process, EGA only involves addition and subtraction operation, and has the characteristics of low consumption and high efficiency. Therefore, the GA is adopted to process massive cutter data in a network environment so as to realize the comprehensive adaptation of the multi-feature cutter in a highly efficient manner.
One basic gaming ring includes a gaming player i, a set of player policies S, and a utility value u. Two basic theories for EGA are as follows:
(1) If a policy combination S, for any policy S of any game player i i ∈S i Satisfying the constraint shown in the following formula, then S is called Nash equalization, S i Representing the policy set for player i.
Wherein S is -i Is a policy combination that removes the remaining players of i; s is S * -i Is a Nash equalization strategy combination that removes i; s is(s) * i Is the best strategy for i under nash equalization. On this basis, the combination of strategies satisfying the constraints described by the following formula is called a strict nash equalization.
(2) Suppose S -i ＝∏S k (k=1, 2..n, k+.i). If the constraint shown in the following formula is satisfied, then B is called i The optimal response for i corresponds (Best-Response Correspondence). B (B) i The underlying meaning is that i the policy selected under the current situation hasMaximum utility value. The Dynamic process of all game players sequentially completing the Optimal Response is called an Optimal Response Dynamic (Optimal-Response Dynamic).
Expression form of evolutionary game algorithm:
the EGA can be expressed as a five-tuple, i.e., EGA= { G, S 0 The specific meaning of each constituent element is as follows:
(1) Game structure g= [ I, S, U ]: a game structure G includes specific information I of a game player, a current game situation S and a utility value U of the current situation. Under a given situation, all game players select one strategy from the corresponding strategy set, and the objective function value of the current strategy combination is calculated to be the utility value under the situation. The specific form of the utility function is as follows:
wherein U is i Is the utility value under situation S; f (f) max Is the maximum utility value that occurs during dynamic evolution. Obviously, f is compared with the penalty function form used by other evolutionary algorithms max Can be obtained by calculation in advance, and for the situation that the constraint condition is not satisfied, the method is realized by combining f max The subtraction of (2) greatly reduces the utility value and eliminates it.
(2) Initial situation S 0 : evolution of EGA from initial situation S 0 Starting, S 0 Generated by a random method.
(3) The optimization value alpha: gaming theory is premised on the assumption that all players pursue economy, and that each player best strives to choose the strategy that is most effective for himself during gaming. Thus, the optimal reaction correspondence of a player is referred to as the player's optimization operator for the maximum utility value.
(4) Equalizing perturbation operator β: in order to realize global optimization of EGA, an equalization disturbance operator beta is introduced to break the Nash equilibrium state under the current situation, and the evolution situation is guided to develop to the Nash equilibrium state with a better next utility value after multiple iterations. A new nash equilibrium can then be obtained by performing optimal reflection dynamics and continually breaking the equilibrium state. The specific form of beta is as follows:
wherein p is i To assign an equilibrium disturbance probability, p, based on the contribution of each game player to the utility value i The function of (2) is to drive the initial situation to evolve in a specific direction. Thus, more important players need to be given a higher probability of disturbance, while players with a lesser degree of global impact are given a lesser probability of disturbance; x is X i Is a random number from 0 to 1; z is Z i Is a player perturbation operator, which means that player i can randomly select a strategy from the strategy set to replace the current value; s is(s) i It means that i maintains the current policy unchanged.
(5) Termination condition τ: in a given situation, the execution of an optimal response dynamic is called a round, a Nash equilibrium state can be achieved through two rounds, and the Nash equilibrium state formed through two game rounds is called a generation of an evolution process. Classical EGA generally sets the termination condition of the evolution process to be τ.gtoreq.T, where T is the expected evolution algebra set in advance. However, in a network environment, the underlying algorithm is not known to the end user, and it is difficult to rely on the end user to set a specific value of T. In addition, since different parts have different types and numbers of machining features, the complexity of the problem is very different, and it is difficult to satisfy the diversity of the problem by presetting the termination condition formed by the T value. Therefore, the embodiment improves the termination condition of the EGA, increases the dynamic applicability of the EGA, and can better process the diversified demands in the network environment. The specific form is shown in the following formula:
τ i ＝U i -U (i-1)
N(τ)＞T 0
U i the utility value corresponding to the ith Nash equilibrium state; u (U) (i-1) A utility value corresponding to the (i-1) th Nash equilibrium state; n (τ) represents that the value of τ remains unchanged in N evolutions; t (T) 0 The convergence accuracy is set. For any problem, convergence accuracy T 0 The method can be used for measuring the evolution state, ensuring that the loop is exited under the convergence precision, and improving the solving efficiency.
EGA solving flow:
EGA starts from an initial situation, nash equilibrium is achieved through game play of a player, disturbance is conducted on the Nash equilibrium, and finally global optimization is achieved. A specific flow is shown in fig. 5.
Step 1: setting initial parameters including importance vector (disturbance probability p) of each machining feature input by end user, preference vector W of user for cutter scheme c And convergence accuracy T of system settings 0 。
Step 2: initializing game situation S 0 Updating the state of the game structure from G to G by a random method 0 Generating an initial game situation S 0 And sets the evolution algebra τ=0. The system is from S 0 And τ=0.
Step 3: calculate the utility value of the initial situation based on f (S 0 ) Function calculation initial situation S 0 Utility value U of (2) 0 。
Step 4: executing the optimization operators alpha, alpha being used to estimate utility values of each player after updating the policies, if better utility values are obtained after updating the policies, combining the policies of all players from S j Evolution to S j+1 The method comprises the steps of carrying out a first treatment on the surface of the Otherwise, maintain situation S j Is unchanged.
Step 5: judging the situation stability (Nash equilibrium state), if at a certain evolution time tau=tau (i), meeting U i ＝U i-1 Then the current situation S i The policy combination under the method corresponds to a Nash equilibrium state, and the current situation is judged to be a stable situation.
Step 6: and calculating the utility value under the stable situation, and calculating the utility value under the stable situation again.
Step 7: comparing the magnitude of the utility value, judging whether the strategy combination under the current situation is a better solution, and if the strategy combination is the better solution, storing the current situation.
Step 8: judging termination conditions, judging whether the current evolution algebra meets the set convergence precision, if so, outputting a result, and otherwise, executing a disturbance operator.
Step 9: executing disturbance operator beta can obtain new stable situation, i.e. situation S j Update to S j+1 And calculates utility value U of new situation j+1 . Finally, to U j And U j+1 Comparing and selecting S j And S is j+1 The higher utility value is the new equilibrium state.
Mapping of problem space to algorithm space:
mapping each of the processed features to a game player; mapping the cutter strategy set of the processing characteristics into a strategy set of a player; the price of the tool strategy and the budget of the complete tool scheme of the user in the whole cutting process of the part are mapped into constraints; the objective function F is mapped to the utility function U of the algorithm. The mapping from problem space to algorithm space can be expressed as fig. 6.
In FIG. 6, f i Is the ith machined feature of the part; s is(s) j i Is f i A corresponding j-th tool plan; n is n i Is the number of possible tool scenarios for the ith machining feature; i i Is the ith game player. Through the mapping process, the proposed multi-feature tool adaptation model can be solved by using an evolution game method, and after the EGA reaches the set convergence accuracy, the output optimal strategy combination is mapped into the corresponding tool scheme, so that the complete tool scheme optimization of the part in the complete cutting process under the budget cost constraint of the end user can be realized.
The embodiment researches the generation rule of the multi-tool combination strategy with complex features (taking a cavity as an example), provides the generation method of the multi-tool combination tool strategy with complex features, and provides a tool strategy set crossing suppliers for the subsequent evolutionary game process. The multi-feature tool comprehensive matching model of the part is constructed, the model takes the tool cost budget of an end user as a constraint condition, the matching property between the tool and a workpiece, the manufacturability, the efficiency, the environmental friendliness and the economy of the whole tool scheme are comprehensively considered, an evaluation system of the static tool scheme is provided, and an objective function of comprehensive evaluation of the whole tool scheme in the whole cutting process is constructed by combining the user preference.
Based on an evolution game algorithm, a solving method for the proposed model is researched. Specifically, in order to solve the problem that the user group is complex and the types of parts to be processed are various in the network environment, a convergence precision factor is introduced to dynamically form an evolution termination condition. Compared with a given evolution algebra form, the method can occupy computing resources as required according to the size of the solving problem and has better universality. Compared with classical optimization algorithms, such as genetic algorithm, local search evolution algorithm, fuzzy self-adaptive algorithm and the like, the evolutionary game method has higher efficiency, and the feasibility of processing a large amount of product data from a plurality of cutter brands in a network environment is proved.
In order to verify the feasibility of the method, in the embodiment, a motorcycle single-throw crankshaft with turning processing as a main manufacturing means and a square test piece with milling processing as a main manufacturing means are used as research cases, processing characteristics are game players, the method is used for adapting from a cutter product database of a platform to obtain an available cutter set corresponding to the characteristics, finally, cutter comprehensive adaptation of multi-characteristic parts is performed through evolution game, and a complete cutter scheme of the whole cutting process of the parts is obtained. The result shows that the method can efficiently carry out comprehensive adaptation of the multi-feature tool for the tool terminal user in the network environment. Compared with the cutter scheme provided by a single cutter supplier, the cutter scheme adapted by the embodiment greatly expands the cutter adaptation range, improves the cutter adaptation efficiency and saves the labor cost while considering indexes such as the commonality, the efficiency and the environment of the cutter.
The foregoing examples merely illustrate specific embodiments of the invention, which are described in greater detail and are not to be construed as limiting the scope of the invention. It should be noted that it will be apparent to those skilled in the art that several variations and modifications can be made without departing from the spirit of the invention, which are all within the scope of the invention.
Claims (1)
1. The multi-feature cutter comprehensive adaptation method based on the evolution game is characterized by comprising the following steps of:
step 1, establishing a cutter strategy set of machining characteristics;
step 2, establishing a cutter scheme evaluation system;
step 3, establishing a multi-feature cutter comprehensive matching model;
step 4, solving a multi-feature cutter comprehensive fit model based on an evolution game theory to obtain an optimal cutter strategy combination;
the step 1 specifically comprises the following steps:
for single feature f of single-tool machining i Selectable tool strategy S i For the set T of available tools i Any one of the elements; for the complex features, a plurality of cutters are adopted for combined cutting, and the method specifically comprises the following steps: first for complex feature f c Is set of available tools T c ＝(T c 1 ,T c 2 …T c kc ) According to the diameter D (T c kc ) Sequencing; then obtaining the key cutter quantity kc according to the minimum inner contour arc radius of the machining characteristics * The method comprises the steps of carrying out a first treatment on the surface of the Finally, taking the given total number x of the cutters as a boundary to obtain all cutter combination strategies;
the step 2 specifically comprises the following steps:
the characteristic value of the tool is dimensionless processed by the following steps:
V j MIN and V j MAX The maximum and minimum values of the j-th characteristics of the tools in the set of available tools, respectively; x is x ij A value of a j-th characteristic of an i-th tool in the set of available tools; the positive-oriented characteristic refers to a characteristic positively correlated with the evaluation index; negative-going characteristic negative-going refers to a characteristic that is negatively related to the index;
modeling cutter matching M: firstly, carrying out dimensionless treatment on the characteristics of the cutters, and then carrying out matching degree calculation on each cutter by the following formula:
wherein n is the number of processing features; n is the characteristic quantity related to M; w (w) j Is a characteristic rule vector corresponding to the cutting processing of the workpiece material; m is then i The matching between the ith tool plan and the machining requirement can be represented; the characteristics of the tool include material characteristics including strength S, hardness H, thermal conductivity T of the tool material, and geometric characteristics c And heat resistance H r The method comprises the steps of carrying out a first treatment on the surface of the The geometrical characteristics include the rake angle R o Rear angle alpha, knife tip arc N r The number Z of teeth, the diameter D of teeth and the clamping mode;
efficiency E f Modeling: the specific formula is as follows:
f is to influence the efficiency of the static tool schemeThe number of cutter characteristics; g i A tool characteristic value related to the efficiency of the static tool scheme, which is standardized after dimensionless processing;
modeling additional indexes: the following analytic hierarchy process is used to construct a computing system for index I and its m influencing factors (k 1 ,k 2 …k m ) The value of I is calculated by the following formula:
wherein c i The weight coefficient of the i-th factor; w (w) i Is k j Relative contribution to I; the j-th influencing factor k j Having n j (k 1 j ，k 2 j …k nj j ) The value of the jth influencing factor can be obtained by a hierarchical analysis method, and the specific flow is as follows:
first, a relative contribution matrix A shown in the following formula is constructed:
a pq when k is expressed as j Respectively take k p j And k q j The ratio of the contribution degree to I at the time of the reaction, therefore, a pq ＝1/a qp The method comprises the steps of carrying out a first treatment on the surface of the To ensure different k j The logic of the evaluation of the contribution degree of the value to the I is accurate, and consistency check is carried out on the A according to the following formula:
wherein lambda is max Is the maximum eigenvalue of matrix a; n is the size of the matrix;
if CR is<0.1, passing the consistency check; otherwise, the value of A is adjusted until the condition is met; when the consistency check of A passes, k j The I-th value of (2) is the relative contribution degree w of the I to the I i Can be calculated by the following formula:
wherein w is * j Is corresponding to lambda max The j-th element of the feature vector of (a); w (w) i j Is k j Taking k i j Contribution degree to I;
according to the complexity of accessories and clamping procedures required by different clamping modes, a contribution degree matrix A of clamping mode factors of the indexable tool to manufacturability is constructed based on a 9-point scoring method 1 ；
The contribution of the tool interchangeability factor to manufacturability P is as follows:
wherein w is the contribution degree of tool interchangeability factors to tool scheme manufacturability P, f * i The method is characterized in that the method is an ith same type of feature which can be processed by the cutter, and m is the sum of all features which can be processed by the cutter; by calculating w of each tool strategy, a contribution degree matrix A of tool interchangeability factors to tool scheme manufacturability is constructed 2 ；
In step 3, the multi-feature tool heald fitting model is as follows:
Max(M,E f ,P,E,)&&Min(C)
C ij the price of the jth tool strategy for the ith machining feature; the utility value of the complete tool plan for the q-th part full cut process is calculated by:
wherein k is 1 Is the number of positive expected indicators; k (k) 2 Is the number of negative expected indicators; q is the conversion coefficient of the negative expectation index;
the step 4 specifically comprises the following steps:
mapping each of the processed features to a game player; mapping the cutter strategy set of the processing characteristics into a strategy set of a player; the price of the tool strategy and the budget of the complete tool scheme of the user in the whole cutting process of the part are mapped into constraints; the objective function F is mapped into a utility function U of the algorithm; and solving the multi-feature cutter comprehensive fit model by using an evolution game method through a mapping process, wherein after the evolution game method reaches the set convergence accuracy, the outputted optimal strategy combination is mapped into a corresponding cutter scheme, so that the complete cutter scheme optimization of the whole cutting process of the part under the budget cost constraint of the terminal user can be realized.
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