CN113721462A - Multi-target cutting parameter optimization method and system under cutter determination condition - Google Patents
Multi-target cutting parameter optimization method and system under cutter determination condition Download PDFInfo
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Abstract
The invention discloses a multi-target cutting parameter optimization method and a multi-target cutting parameter optimization system under cutter determination conditions, and a solving process of a cutting parameter optimization problem considering carbon emission is established; then establishing a function of processing time, carbon emission and processing cost in the cutting process by taking the cutting parameters as variables; and finally, establishing a multi-target cutting parameter optimization model taking minimum carbon emission and minimum processing cost as optimization targets, and performing optimization solution on the multi-target cutting parameter optimization model by using an improved grid-based multi-target particle swarm algorithm. The method comprehensively considers the targets of carbon emission and processing cost, meets the actual application requirements of enterprises, is simple, effective and easy to realize in the optimization solving process of the cutting parameters of the cutter, can effectively avoid the algorithm from falling into the local optimal solution due to the non-uniform variation operation in the multi-target particle swarm algorithm, ensures the searching capability of the algorithm, and reduces the instability of the algorithm.
Description
Technical Field
The invention belongs to the technical field of advanced manufacturing and automation, and particularly relates to a multi-target cutting parameter optimization method and system under cutter determination conditions.
Background
In recent years, the manufacturing industry has been rapidly developed and the problems of high energy consumption and high emission are increasingly highlighted. International Energy Agency (IEA) reports indicate that: around the world 33% of energy consumption and 38% of CO2 emissions originate from the manufacturing industry. It is seen that manufacturing has become one of the major sources of energy consumption and carbon emissions today. As an important component in the machining process, the selection of cutting parameters during the characterization process has a significant impact on carbon emissions: first, different cutting parameters can cause differences in the length of characteristic processing times, thereby affecting material carbon, waste carbon, and energy carbon; secondly, different cutting parameters can significantly influence the power of the machine tool in the machining process, particularly the spindle rotation power and the cutting power; third, different cutting parameters can affect the life of the tool, thereby affecting the carbon of the material and the carbon of the waste material from which the tool is machined. Likewise, variations in machining time, machine tool machining power, and tool life due to changes in cutting parameters can also cause corresponding fluctuations in production costs.
Aiming at the multi-objective optimization problem, because different objectives are in conflict and cannot achieve the optimal condition at the same time, how to balance the conflict among the multiple objectives and find the most suitable solution is the most difficult part in the multi-objective optimization. There are two common treatment methods: the first is a multi-objective optimization method based on a single objective, i.e. the multi-objective is given weight (such as experience, analytic hierarchy process, etc.) by various ways to make it transform into a single objective problem before solving. However, the method has high requirement on the reasonability of the weight, a decision maker needs to have global prior knowledge of each target, and the defect of strong subjectivity in weight distribution exists. The second method is that a multi-objective optimization algorithm (such as a non-dominated sorting genetic algorithm (NSGA-II) with an elite strategy, a multi-objective particle swarm algorithm (MOPSO) and the like) is used for resolving the multi-objective problem to obtain a group of non-dominated solution sets, namely a pareto optimal solution set, and then the solution is converted into a single objective or a new objective is set to find an objective solution. However, this method also needs to solve the problem of subjectively determining the target weight.
Disclosure of Invention
The technical problem to be solved by the invention is to provide a multi-target cutting parameter optimization method and system under the cutter determination condition aiming at the defects in the prior art, and provide method support for reducing carbon emission in the machining process and lowering enterprise cost.
The invention adopts the following technical scheme:
a multi-objective cutting parameter optimization method under the condition of cutter determination comprises the following steps:
s1, under the condition that the specification parameters of the cutter are determined, selecting three basic cutting factors as optimization variables, and additionally adding cutting width as the optimization variables when the machining mode is milling; selecting the minimum carbon emission of characteristic processing and the minimum cost of the characteristic processing process as optimization targets, adding constraint conditions to establish a multi-target cutting parameter optimization model taking the minimum carbon emission and the minimum processing cost as optimization targets;
s2, determining the optimal solution of the multi-target problem, designing a grid-based multi-target particle swarm algorithm to solve the multi-target cutting parameter optimization model, and obtaining the cutting parameters with the minimum carbon emission and the minimum processing cost as the optimization targets.
Specifically, in step S1, the optimization variable X is specifically:
X＝(v,f,ap,ae)T＝(x1,x2,x3,x4)T
wherein v is the cutting speed/mm.min-1(ii) a f is the feed speed/mm min-1；apIs the cutting depth/mm; a iseCutting width/mm; x is the number of1,x2,x3,x4Is v, f, ap,aeAliases in the computation process; t denotes transposition.
Specifically, in step S1, the optimization target minf (x) is:
wherein f is1(X) is the total carbon emission, f2(X) is the process cost, CE (X) is a carbon emissions calculation function, and C (X) is a process cost function.
Further, the carbon emission ce (x) is:
wherein, tcThe processing time of the cutter under specific processing conditions; t istIs the tool life of the tool under specific machining conditions; m istThe mass of the tool; CEFtoolproCarbon emission factor for the production of cutters; m0The initial mass of the cutting fluid; maThe quality of the cutting fluid supplemented for the replacement cycle; CEFcoolantCarbon emission factor for production of cutting fluids; t is0The workshop cutting fluid replacement period is set; CEFelecIs an electric energy discharge factor; ptotalConsuming the total power for the machine tool; CEFtoolwasTreating carbon emission factors for the waste cutters; CEFcoolwasCarbon emission factors are treated for the waste cutting fluid.
Further, the processing cost function c (x) is:
C(X)＝(C1+C2+Ct+Ccl)×tc
wherein, C1Is the sum of the management cost per unit time and the equipment depreciation cost; c2The labor cost per unit time; ctThe cost of the tool in the machining time; cclCost of cutting fluid for machining time, tcIs the machining time of the tool under specific machining conditions.
Specifically, in step S1, the constraint conditions are:
wherein: n isminAllowing the lowest rotation speed for the main shaft; n ismaxAllowing the highest rotation speed for the main shaft; f. ofminMinimum feed speed for machine tool/; f. ofmaxThe maximum feeding speed of the machine tool; a isp minIs the minimum cut depth; a isp maxThe maximum cutting depth is obtained; pmaxThe maximum power of the machine tool; eta is the power efficiency of the machine tool; fcIs the main cutting force;Fc maxallowing maximum cutting force for the machine tool; gamma rayεThe radius of the tool nose of the tool; rmaxThe maximum surface roughness value allowed for finishing.
Specifically, in step S2, the determining the optimal solution of the multi-objective problem specifically includes:
firstly, solving the optimal solution of each optimization target under the condition of a single target; then, the proportions of a plurality of targets are multiplied together in this way, and the overall proportion of each target of the non-inferior solution close to the optimal solution of the target can be obtained.
Specifically, in step S2, the grid-based multi-target particle swarm algorithm specifically includes:
s2021, initializing particles, taking a first position as an initial pbest, updating speed and position, carrying out target calculation on the updated position to obtain a target vector, and carrying out domination judgment on the target vector and the previous pbest target vector; if the dominant relationship exists, the position vector corresponding to the dominant solution is used as a new pbest; if no domination relation exists, determining which vector is used as a new particle individual optimal solution by roulette;
s2022, dividing grids of the whole search domain according to a certain number in each dimension, respectively storing non-dominated solutions into corresponding grids according to positions, counting the number of the non-dominated solutions in each grid, and then determining which grid is selected according to roulette; after determining which grid is selected by roulette, determining a non-dominant solution serving as a global optimal solution pbest by random selection, and determining a global optimal solution;
s2023, after the particles are initialized, storing the first batch of non-dominated solutions in an external file; then, after the position of the particle is changed, taking the non-dominated solution again, merging the non-dominated solution set obtained this time with a non-dominated solution set stored by an external file per se, carrying out domination judgment, removing the dominated solution from the external file, and directly carrying out next iteration if the number of the non-dominated solution in the external file is less than the maximum number of the external file; otherwise, deleting the non-dominated solutions with the number exceeding the maximum number to finish the maintenance of the external files;
s2024, generating a new particle position in each iteration process, changing the positions of the particles according to the set variation probability, and gradually reducing the variation probability and the variation range along with the change of the iteration times to realize variation operation;
and S2025, calculating a target vector of the particle according to the value obtained after the optimization variable is subjected to the variation operation in the step S2024, and adjusting pbest of the particle for the next iteration.
Further, in step S2024, the mutation probability pmutComprises the following steps:
wherein: it is the current iteration number; MaxIt is the maximum iteration number; u is a variation probability attenuation coefficient;
range of variation rmutComprises the following steps:
ri min＝max(xi-rmut,xi min)
ri max＝min(xi+rmut,xi max)
wherein: r ismutIs the variation range; x is the number ofi maxThe upper limit of the allowable value of the ith dimension is optimized; x is the number ofi minThe lower limit of the allowable value of the ith dimension is optimized; v is the attenuation coefficient of the variation range; r isi minThe lower limit of allowable coordinates of the ith dimension is optimized; r isi maxAnd (4) using an upper limit of allowable coordinates for the ith dimension to optimize the variables.
Another technical solution of the present invention is a multi-objective cutting parameter optimization system under a cutter-determined condition, comprising:
the parameter module selects three basic cutting factors as optimization variables under the condition that the specification parameters of the cutter are determined, and additionally adds cutting width as the optimization variables when the machining mode is milling; selecting the minimum carbon emission of characteristic processing and the minimum cost of the characteristic processing process as optimization targets, adding constraint conditions to establish a multi-target cutting parameter optimization model taking the minimum carbon emission and the minimum processing cost as optimization targets;
and the optimization module is used for determining the optimal solution of the multi-target problem, designing a grid-based multi-target particle swarm algorithm to solve the multi-target cutting parameter optimization model, and obtaining the cutting parameters with the minimum carbon emission and the minimum processing cost as the optimization targets.
Compared with the prior art, the invention has at least the following beneficial effects:
a multi-objective cutting parameter optimization method under the cutter determining condition is characterized in that firstly, constraint conditions implemented by a definite method are determined for cutter specification parameters; secondly, selecting cutting parameters which are controllable in machining process and have important influence on machining results as optimization targets, and conforming to actual machining conditions; the carbon emission and the processing cost are taken as optimization targets to respond to national development policies, and actual requirements of enterprises are met; and a multi-target particle swarm algorithm is selected, so that the calculation efficiency is higher, and the method is suitable for function characteristics and solution forms of different forms.
Furthermore, experimental analysis verifies that under the condition that the specification of the cutter is determined, different cutting parameters have obvious influence on carbon emission and cost in the machining process, so that the optimization effect can be effectively improved by selecting the cutting parameters as optimization variables.
Furthermore, the carbon emission and the processing cost are taken as optimization targets, so that the development policy of national energy conservation and emission reduction is responded, and the actual requirements of enterprise production are met.
Furthermore, the material carbon, the energy carbon and the waste carbon in the machining process are calculated, the comprehensive and detailed consideration is given, and the method accords with the real factory production condition.
Furthermore, the processing cost is set as an optimization target, the actual requirements of enterprises are considered, and the implementation of the method is facilitated.
Furthermore, the cutter specification parameters are set to be determined as constraint conditions, so that a plurality of uncertain factors caused by different cutter specifications are eliminated, and the complexity of optimization of the method is reduced.
Further, the two targets of magnitude and dimension of the characteristic processing carbon emission and the processing cost are different, and in order to avoid that a small change of one target causes a large fluctuation of the other target, a comparison between the two targets should not be made. Therefore, according to the characteristic that the pareto optimal solution set is a non-inferior solution, the optimal solution of each optimization target under the condition of a single target is firstly obtained, at the moment, the ratio of the value of a certain solution in the pareto optimal solution set on the single target to the optimal solution of the target on the single target optimization problem is the condition that the non-inferior solution is close to the optimal condition on the target, and the proportion of a plurality of targets is multiplied together in this way, so that the overall proportion of each target of the non-inferior solution close to the target optimal solution can be obtained.
Furthermore, a non-dominant solution can be searched, a plurality of non-dominant solutions can be generated through one iteration, and the algorithm is high in calculation efficiency; the particle swarm algorithm has a memory function (the optimal solution of the particles is memorized), so that the particles can track the global optimal solution and the individual optimal solution for searching, and the searching speed and the calculating efficiency are increased; the particle swarm algorithm can be applied to the problems with different function characteristics and solution forms, and has wide application and strong applicability.
Furthermore, the mutation operation with the probability decreasing along with the iteration times is added, so that the solution of the multi-target particle swarm algorithm is prevented from being too dense, the possibility of convergence on the local optimum is reduced, and the optimization effect is more stable.
In conclusion, the method comprehensively considers the carbon emission and the processing cost target, meets the actual application requirements of enterprises, is simple, effective and easy to realize in the multi-target optimization solution of the cutting parameters, and can effectively avoid the algorithm from being premature and entering the local optimal solution by adding the variation operation in the grid-based multi-target particle swarm algorithm.
The technical solution of the present invention is further described in detail by the accompanying drawings and embodiments.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a flow chart of a multi-objective particle swarm algorithm;
FIG. 3 is a drawing of rough turning of an outer circle using an FTC20 numerically controlled lathe;
fig. 4 is a schematic diagram of the pareto frontier and the single-target optimal solution obtained in Matlab.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, not all, embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
It will be understood that the terms "comprises" and/or "comprising," when used in this specification and the appended claims, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof.
It is also to be understood that the terminology used in the description of the invention herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. As used in the specification of the present invention and the appended claims, the singular forms "a," "an," and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise.
It should be further understood that the term "and/or" as used in this specification and the appended claims refers to and includes any and all possible combinations of one or more of the associated listed items.
Various structural schematics according to the disclosed embodiments of the invention are shown in the drawings. The figures are not drawn to scale, wherein certain details are exaggerated and possibly omitted for clarity of presentation. The shapes of various regions, layers and their relative sizes and positional relationships shown in the drawings are merely exemplary, and deviations may occur in practice due to manufacturing tolerances or technical limitations, and a person skilled in the art may additionally design regions/layers having different shapes, sizes, relative positions, according to actual needs.
The selection of cutting parameters during actual feature machining has a significant impact on carbon emissions: first, different cutting parameters can cause differences in the length of characteristic processing times, thereby affecting material carbon, waste carbon, and energy carbon; secondly, different cutting parameters can significantly influence the power of the machine tool in the machining process, particularly the spindle rotation power and the cutting power; third, different cutting parameters can affect the life of the tool, thereby affecting the carbon of the material and the carbon of the waste material from which the tool is machined. Likewise, variations in machining time, machine tool machining power, and tool life due to changes in cutting parameters can also cause corresponding fluctuations in production costs. Therefore, the carbon emission in the processing process can be reduced and the processing cost of enterprises can be reduced by optimizing multiple cutting parameters.
The invention provides a multi-target cutting parameter optimization method under the condition of cutter specification determination, which is characterized in that under the condition of cutter specification determination (namely under the condition that all specification parameters of a cutter are determined and same), a multi-target cutting parameter optimization model taking minimum carbon emission and minimum processing cost as optimization targets is established, and a grid-based multi-target particle swarm algorithm is utilized for solving.
Referring to fig. 1, the method for optimizing multi-objective cutting parameters under the condition of cutter determination according to the present invention includes the following steps:
s1, selecting three basic cutting factors as optimization variables, and additionally adding a cutting width as the optimization variables when the machining mode is milling;
s101, selecting three basic cutting factors as optimization variables, and when the machining mode is milling, additionally adding a cutting width as the optimization variable and performing multi-target parameter optimization to reasonably determine parameters in machining, so that the optimization variables select the three basic cutting factors, namely cutting linear speed, feeding amount and cutting depth. However, considering that when the machining mode is milling, a variable is still needed to express the cutting width, the optimization variable is determined as follows:
X＝(v,f,ap,ae)T＝(x1,x2,x3,x4)T
when the machining mode is not milling, the variable x4Is set to 0.
S102, selecting the minimum feature processing carbon emission and the minimum feature processing process cost as optimization targets, wherein the optimization targets comprise the minimum feature processing carbon emission and the minimum feature processing process cost, and the objective function is as follows:
where CE (X) is a function of carbon emissions and C (X) is a function of process cost.
S1021, processing time function
In the formula: l is the feed length/mm; ceil () is a rounding function; delta is the machining allowance/mm; v is the material removal volume/mm3。
S1022, carbon emission function
In the whole characteristic processing process, the generated carbon emission is divided into three types by considering the multi-source generated by the carbon emission: material carbon, energy carbon and waste carbon. When the material, the size and the specification of the characteristic material are fixed aiming at the same characteristic, the material size and the generated cutting chip quantity are fixed no matter what processing mode and cutting parameters are adopted, namely the characteristic material preparation carbon emission and the cutting chip treatment carbon emission are constant. Therefore, the two-part carbon emission calculation is not meaningful and is not calculated by the invention.
The carbon emission CE (X) is calculated by the following method:
wherein, tcThe processing time/s of the cutter under specific processing conditions; t istFor tools in special applicationsTool life/s under working conditions; m istIs the mass of the cutter/g; CEFtoolproCarbon emission factor/kgCO for tool production2·kg-1；M0The initial mass/kg of the cutting fluid; maThe mass/kg of the cutting fluid supplemented in the replacement period; CEFcoolantCarbon emission factor/kgCO for production of cutting fluids2·kg-1；T0The workshop cutting fluid replacement cycle/s; CEFelecAs an electric energy emission factor/kgCO2·kWh-1；PtotalConsuming the total power/W for the machine tool; CEFtoolwasCarbon emission factor/kgCO for waste cutter treatment2·kg-1；CEFcoolwasCarbon emission factor/kgCO for waste cutting fluid treatment2·kg-1。
S1023 processing cost function
The machining cost is mainly composed of five parts, namely management cost, equipment depreciation cost, labor cost, cutter cost and cutting fluid cost, as follows:
C(X)＝(C1+C2+Ct+Ccl)×tc
wherein, C1Is the sum of the management cost per unit time and the depreciation cost of the equipment/yuan/min-1；C2Is the unit time manpower cost/yuan.min-1；CtFor the cost/yuan/min of the tool in the machining time-1；CclFor the cost/yuan/min of the cutting fluid in the processing time-1Calculated from the following equation:
wherein: c3Cost, sharpening and post-treatment expense/dollar for a single cutter; r is the grindable times of the cutter; t istFor tool life/min, calculated from the following formula:
wherein: s, p, q and r are undetermined coefficients;
wherein M isoInitializing the cutting fluid mass/kg; maThe mass of the cutting fluid added each time is/kg; c4Cost per unit cutting fluid/unit kg-1；ToThe cutting fluid replacement period/min is adopted.
S103, adding constraint conditions
The constraint conditions mainly consider various performance limitations of the machine tool, such as the total power limitation of the machine tool, the rotating speed range of a main shaft, the feeding power range and the like; in addition, tool performance limitations are included, such as the cutting forces must not exceed the upper limit of insert tolerance.
In particular, when the characteristic machining is finish machining, the roughness of the machined surface needs to meet the actual machining requirements.
The constraints are as follows:
wherein n isminAllowing the lowest rotation speed/r.min for the main shaft-1；nmaxAllowing maximum rotation speed r.min for main shaft-1；fminFor the minimum feed speed/m.min of the machine tool-1；fmaxFor the maximum feeding speed/m.min of the machine tool-1；ap minMinimum cutting depth/mm; a ispmaxMaximum cutting depth/mm; pmaxThe maximum power/W of the machine tool; eta is the power efficiency/W of the machine tool; fcMain cutting force/N; fc maxAllowing maximum cutting force/N for the machine tool; gamma rayεThe radius of the tool nose of the tool/mm; rmaxThe maximum surface roughness value/μm allowed for finishing.
S104, problem description and related assumptions
The multi-objective cutting parameter optimization method under the cutter determining condition can be described as a multi-objective cutting parameter optimization problem considering carbon emission and enterprise processing cost under the condition that the cutter specification is determined (namely all specification parameters of the cutter are determined and are the same).
The assumed conditions of the invention are as follows: the specification of the tool is determined (i.e. all specification parameters of the tool are determined) and the same, and only the optimization studies on carbon emission and machining cost related to cutting parameters (including linear cutting speed, feed, cutting depth, cutting width) are carried out.
And S2, solving the model by using a multi-target particle swarm algorithm based on grids.
S201, determining the optimal solution of the multi-target problem
The two targets of the characteristic processing carbon emission and the processing cost related to the optimization algorithm are different in magnitude and dimension, in order to avoid the fact that the small change of one target causes the huge fluctuation of the other target, the two targets should not be compared, therefore, according to the characteristic that the pareto optimal solution set is a non-inferior solution, the optimal solution of each optimization target under the condition of a single target is firstly obtained, at the moment, the ratio of the value of a certain solution in the pareto optimal solution set on the single target to the optimal solution of the target on the optimization problem of the single target is the condition that the non-inferior solution is close to the optimal solution on the target, the proportions of the multiple targets are multiplied together in the mode, and the overall proportion (shown in the following formula) of each target of the non-inferior solution close to the optimal solution of the target can be obtained.
Since the objectives of the present invention are all as small as possible, the smaller the ratio, the closer all the individual objectives of the solution are to the single-objective minimum, and therefore the solution with the minimum ratio is considered as the optimal solution in the pareto optimal solution set.
Wherein, F (x)bestIs the minimum scale factor; f. of1(x) Optimizing the value of the vector at target 1 for x; f. of1(x)minThe optimal solution of the target 1 in a single target state is obtained; f. of2(x) Optimizing the value of the vector at target 2 for x; f. of2(x)minThe optimal solution of the target 2 in the single-target state is obtained.
S202, designing a grid-based multi-target particle swarm algorithm, and specifically comprising the following substeps:
s2021, determining the optimal solution of the particle individual: after the particle is initialized, its first location is the initial pbest. Subsequently, when the speed and position are updated, the updated position is subjected to target calculation to obtain a target vector, and dominance determination is performed with the previous pbest target vector. If there is a dominance relationship, then the position vector corresponding to the dominance solution will be the new pbest; on the contrary, if no dominance relation exists, the roulette determines which vector is used as the new particle individual optimal solution.
S2022, determining a global optimal solution: the whole search domain is divided into grids according to a certain number in each dimension (taking the example of dividing 10 grids in each dimension as an example), non-dominant solutions are respectively stored into corresponding grids according to positions, the number of the non-dominant solutions in each grid is counted, and then the grid to be selected is determined according to roulette.
To avoid premature algorithm, the probability that a grid with a high number of non-dominant solutions is selected is reduced, so the probability that each grid is selected is as follows:
wherein, p [ h ]i]Is hiProbability of being selected; n [ it [ ]]The total number of grids with non-dominated solutions under the ith iteration algebra;
is hiThe number of non-dominant solutions contained by the grid.
After determining which grid to select by roulette, a non-dominant solution is determined as the global optimal solution pbest by random selection.
S2023, maintenance of external files: after particle initialization, storing a first batch of non-dominated solutions in an external archive; and then, after the positions of the particles are changed, taking the non-dominated solution again, merging the non-dominated solution set obtained this time with a non-dominated solution set stored in an external file per se, and then carrying out domination judgment to remove the domination solution from the external file. At this time, if the number of non-dominated solutions in the external archive is less than the maximum number of the external archive, directly performing the next iteration; otherwise, the non-dominated solutions that exceed the maximum number are deleted.
In order to avoid the premature of the algorithm, when deleting the non-dominated solution of the external archive, the non-dominated solution is randomly selected from the grids containing the most non-dominated solution to delete, and if a plurality of grids containing the most non-dominated solution exist, the grid selection is randomly performed until the number of the non-dominated solutions in the external archive does not exceed the maximum number of the external archive.
S2024, mutation operation;
in order to avoid the algorithm from falling into the local optimal solution early, the invention introduces a variation operation, namely after a new particle position is generated in each iteration process, the positions of partial particles are changed according to a certain variation probability, and the variation probability and the variation range need to be gradually reduced along with the change of the iteration times, which is specifically as follows:
wherein p ismutIs the variation probability; it is the current iteration number; MaxIt is the maximum iteration number; u is the variation probability attenuation coefficient.
ri min＝max(xi-rmut,xi min)
ri max＝min(xi+rmut,xi max)
Wherein r ismutIs the variation range; x is the number ofi maxThe upper limit of the allowable value of the ith dimension is optimized; x is the number ofi minThe lower limit of the allowable value of the ith dimension is optimized; v is the attenuation coefficient of the variation range; r isi minThe lower limit of allowable coordinates of the ith dimension is optimized; r isi maxAnd (4) using an upper limit of allowable coordinates for the ith dimension to optimize the variables.
The variation mode adopts non-uniform variation, firstly, the variation probability is calculated, a value is randomly generated, if the value is smaller than the calculated variation probability, the optimized variable is subjected to variation operation, otherwise, the variation operation is not performed; then calculating a variation range, namely randomly taking out a certain dimension of the optimized variables, and then calculating the upper and lower allowable coordinate limits of the variation range of the optimized variables in the ith dimension; and finally, randomly taking a value in the range of the upper limit and the lower limit of the coordinate, namely the value after the ith dimension variation of the optimized variable.
The non-uniform variation operation designed by the invention can effectively avoid the algorithm from falling into local optimum in the early stage of the multi-target particle swarm algorithm, ensure the searching capability of the algorithm and reduce the instability of the algorithm.
And S2025, obtaining a value after the optimization variable is mutated according to the mutation operation in the step S2024, calculating a target vector of the particle, and adjusting pbest of the particle for the next iteration.
The multi-target particle swarm algorithm designed by the invention has a flow shown in fig. 2, and is different from the grid-based multi-target particle swarm algorithm mainly in variation operation.
In another embodiment of the present invention, a multi-objective cutting parameter optimization system under a tool determination condition is provided, which can be used to implement the multi-objective cutting parameter optimization method under the tool determination condition.
The parameter module selects three basic cutting factors as optimization variables under the condition that the specification parameters of the cutter are determined, and additionally adds cutting width as the optimization variables when the machining mode is milling; selecting the minimum carbon emission of characteristic processing and the minimum cost of the characteristic processing process as optimization targets, adding constraint conditions to establish a multi-target cutting parameter optimization model taking the minimum carbon emission and the minimum processing cost as optimization targets;
and the optimization module is used for determining the optimal solution of the multi-target problem, designing a grid-based multi-target particle swarm algorithm to solve the multi-target cutting parameter optimization model, and obtaining the cutting parameters with the minimum carbon emission and the minimum processing cost as the optimization targets.
In yet another embodiment of the present invention, a terminal device is provided that includes a processor and a memory for storing a computer program comprising program instructions, the processor being configured to execute the program instructions stored by the computer storage medium. The Processor may be a Central Processing Unit (CPU), or may be other general purpose Processor, a Digital Signal Processor (DSP), an Application Specific Integrated Circuit (ASIC), an off-the-shelf Programmable gate array (FPGA) or other Programmable logic device, a discrete gate or transistor logic device, a discrete hardware component, etc., which is a computing core and a control core of the terminal, and is adapted to implement one or more instructions, and is specifically adapted to load and execute one or more instructions to implement a corresponding method flow or a corresponding function; the processor provided by the embodiment of the invention can be used for the operation of the multi-objective cutting parameter optimization method under the cutter determination condition, and comprises the following steps:
selecting three basic cutting factors as optimization variables under the condition of determining specification parameters of the cutter, and additionally adding cutting width as the optimization variables when the machining mode is milling; selecting the minimum carbon emission of characteristic processing and the minimum cost of the characteristic processing process as optimization targets, adding constraint conditions to establish a multi-target cutting parameter optimization model taking the minimum carbon emission and the minimum processing cost as optimization targets; and determining an optimal solution of the multi-target problem, designing a grid-based multi-target particle swarm algorithm to solve the multi-target cutting parameter optimization model, and obtaining cutting parameters with minimum carbon emission and minimum processing cost as optimization targets.
In still another embodiment of the present invention, the present invention further provides a storage medium, specifically a computer-readable storage medium (Memory), which is a Memory device in a terminal device and is used for storing programs and data. It is understood that the computer readable storage medium herein may include a built-in storage medium in the terminal device, and may also include an extended storage medium supported by the terminal device. The computer-readable storage medium provides a storage space storing an operating system of the terminal. Also, one or more instructions, which may be one or more computer programs (including program code), are stored in the memory space and are adapted to be loaded and executed by the processor. It should be noted that the computer-readable storage medium may be a high-speed RAM memory, or may be a non-volatile memory (non-volatile memory), such as at least one disk memory.
The processor can load and execute one or more instructions stored in the computer readable storage medium to realize the corresponding steps of the multi-objective cutting parameter optimization method under the relevant cutter determination conditions in the embodiment; one or more instructions in the computer-readable storage medium are loaded by the processor and perform the steps of:
selecting three basic cutting factors as optimization variables under the condition of determining specification parameters of the cutter, and additionally adding cutting width as the optimization variables when the machining mode is milling; selecting the minimum carbon emission of characteristic processing and the minimum cost of the characteristic processing process as optimization targets, adding constraint conditions to establish a multi-target cutting parameter optimization model taking the minimum carbon emission and the minimum processing cost as optimization targets; and determining an optimal solution of the multi-target problem, designing a grid-based multi-target particle swarm algorithm to solve the multi-target cutting parameter optimization model, and obtaining cutting parameters with minimum carbon emission and minimum processing cost as optimization targets.
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. The components of the embodiments of the present invention generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations. Thus, the following detailed description of the embodiments of the present invention, presented in the figures, is not intended to limit the scope of the invention, as claimed, but is merely representative of selected embodiments of the invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Referring to fig. 3, an FTC20 numerically controlled lathe is used for rough turning of the outer circle, the workpiece material is alloy steel 38CrMoAl, two WNMG080408-HM turning tools produced by xiamen herou are selected as the blades, the wear loss of the flank face is 0.1 and 0.215 respectively, and a rod-shaped blank with the length of 200mm and the diameter of 75mm is machined. The unilateral cutting thickness is 4.5 mm; the FTC20 machine tool has the measured stand-by power of 1616W, the illumination power of 63W, no automatic chip removal device and no cooling liquid used in the processing.
The feed power calculation model, the rotating speed power calculation model and the cutting power calculation model of the FTC20 are as follows:
Pfeed＝-7.680(nf)2+22.614nf+1.491
the power carbon emission factor is 0.7045kgCO according to related literature and database query2kWh, carbon emission factor for tool production 33.75kgCO2The carbon emission factors of the waste cutter treatment and the cutting fluid treatment are respectively 0.0135kgCO2Perkg and 0.361kgCO2In terms of/kg. WNMG080408-HM unit price of the tool is about 28 yuan, tool mass is about 10g, and tool life formula is as followsThe following:
the sum of the unit management time cost, the equipment depreciation cost and the labor cost is set to be 15.3 yuan/min, and the industrial electricity consumption cost is 0.8651 yuan/kWh.
A multi-objective particle swarm algorithm was written using Matlab R2012b (version 8.0.0.783), with the following parameters set: the population scale is 150, the maximum number of external files is 100, the number of single-target optimization iterations is 50, the number of multi-target optimization iterations is 100, the individual learning coefficient and the overall learning coefficient are both 1.49, the inertia coefficient is 0.73, the initial variation probability is 0.5, and the number of grid divisions in each dimension is 10. The procedure was run 3 times and the optimization results for inserts with flank wear of 0.1 and 0.215 are shown in table 1 below:
TABLE 1 Multi-objective particle swarm optimization results
Analysis of the above case shows that:
1) the algorithm basically ensures convergence, but small-range fluctuation exists to compare the experimental results of the uniform abrasion loss of the serial numbers 1-3, so that the three results are approximately the same, but small-range fluctuation still exists, wherein when the abrasion loss of the rear cutter face is 0.1mm, the difference between the data of the serial numbers 2 and 3 is 3.5 r.min-1(ii) a When the flank wear amount was 0.215mm, the difference between the data of No. 1 and No. 2 was about 5 r.min-1. The method mainly depends on the condition of an initial population by a multi-target particle swarm algorithm, so that small fluctuation occurs.
2) Under the same conditions, the insert results with a small flank wear amount are more preferable to the experimental results of No. 1, and the cases of pareto fronts obtained in Matlab and a single-target optimal solution are given as shown in fig. 4. It can be seen that in the blade optimization results with flank wear of 0.215mm under otherwise identical conditions with only different degrees of wear, the pareto front is significantly dominated by the pareto front with flank wear optimized at 0.1 mm. This means that, when the machining conditions, the machine tool conditions, and the tool specifications are all the same, the characteristic machining carbon emission value and the machining cost of the insert having a large tool wear amount are necessarily higher, that is, under the same conditions, the smaller the tool flank wear amount is, the better each target result of optimization is.
3) Optimizing the cutting parameters without considering the cutter wear to obtain the most reasonable optimization result by taking the data of the serial number 1 as an example, using the optimal cutting parameters obtained by the blade with the flank wear amount of 0.1mm on the blade with the flank wear amount of 0.215mm, and comparing the results; on the contrary, the optimum cutting parameter obtained for the insert having the flank wear amount of 0.215mm was used for the insert having the flank wear amount of 0.1mm, and the results were compared. The two sets of comparison results obtained are shown in table 2:
TABLE 2 calculation of optimal cutting parameters for different wear rate tools
It can be seen that for experimental group 1, although the carbon emission was reduced by 1.08%, the cost increased by 8.31%; in experimental group 2, carbon emissions and costs increased by 1.08% and 4.71%, respectively, and were significantly worse than the current optimal solution as a whole. Therefore, the selection of different cutters with the same specification has certain influence on the final cutting parameter optimization result, and the most reasonable optimization result cannot be obtained without considering the cutting number optimization of the cutters.
In summary, the multi-objective cutting parameter optimization method and system under the cutter determination condition of the invention establish the solving process of the cutting parameter optimization problem considering carbon emission; then establishing a function of processing time, carbon emission and processing cost in the cutting process by taking the cutting parameters as variables; and finally, establishing a multi-target cutting parameter optimization model taking minimum carbon emission and minimum processing cost as optimization targets, and performing optimization solution on the multi-target cutting parameter optimization model by using an improved grid-based multi-target particle swarm algorithm. The carbon emission and processing cost targets are comprehensively considered, the method meets the actual application requirements of enterprises, the optimization and solving process of the cutting parameters of the cutter is simple, effective and easy to realize, the nonuniform variation operation in the multi-target particle swarm algorithm can effectively avoid the algorithm from falling into the local optimal solution, the searching capability of the algorithm is ensured, and the instability of the algorithm is reduced.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
The above-mentioned contents are only for illustrating the technical idea of the present invention, and the protection scope of the present invention is not limited thereby, and any modification made on the basis of the technical idea of the present invention falls within the protection scope of the claims of the present invention.
Claims (10)
1. A multi-objective cutting parameter optimization method under the condition of cutter determination is characterized by comprising the following steps:
s1, under the condition that the specification parameters of the cutter are determined, selecting three basic cutting factors as optimization variables, and additionally adding cutting width as the optimization variables when the machining mode is milling; selecting the minimum carbon emission of characteristic processing and the minimum cost of the characteristic processing process as optimization targets, adding constraint conditions to establish a multi-target cutting parameter optimization model taking the minimum carbon emission and the minimum processing cost as optimization targets;
s2, determining the optimal solution of the multi-target problem, designing a grid-based multi-target particle swarm algorithm to solve the multi-target cutting parameter optimization model, and obtaining the cutting parameters with the minimum carbon emission and the minimum processing cost as the optimization targets.
2. The method according to claim 1, wherein in step S1, the optimization variable X is specifically:
X＝(v,f,ap,ae)T＝(x1,x2,x3,x4)T
wherein v is the cutting speed/mm.min-1(ii) a f is the feed speed/mm min-1；apIs the cutting depth/mm; a iseCutting width/mm; x is the number of1,x2,x3,x4Is v, f, ap,aeAliases in the computation process; t denotes transposition.
3. The method according to claim 1, wherein in step S1, the optimization target minf (x) is:
wherein f is1(X) is the total carbon emission, f2(X) is the process cost, CE (X) is a carbon emissions calculation function, and C (X) is a process cost function.
4. The method of claim 3, wherein the carbon emission CE (X) is:
wherein, tcThe processing time of the cutter under specific processing conditions; t istIs the tool life of the tool under specific machining conditions; m istThe mass of the tool; CEFtoolproCarbon emission factor for the production of cutters; m0The initial mass of the cutting fluid; maThe quality of the cutting fluid supplemented for the replacement cycle; CEFcoolantCarbon emission factor for production of cutting fluids; t is0The workshop cutting fluid replacement period is set; CEFelecIs an electric energy discharge factor; ptotalConsuming the total power for the machine tool; CEFtoolwasTreating carbon emission factors for the waste cutters; CEFcoolwasCarbon emission factors are treated for the waste cutting fluid.
5. The method of claim 3, wherein the process cost function C (X) is:
C(X)＝(C1+C2+Ct+Ccl)×tc
wherein,C1is the sum of the management cost per unit time and the equipment depreciation cost; c2The labor cost per unit time; ctThe cost of the tool in the machining time; cclCost of cutting fluid for machining time, tcIs the machining time of the tool under specific machining conditions.
6. The method according to claim 1, wherein in step S1, the constraint conditions are:
wherein: n isminAllowing the lowest rotation speed for the main shaft; n ismaxAllowing the highest rotation speed for the main shaft; f. ofminMinimum feed speed for machine tool/; f. ofmaxThe maximum feeding speed of the machine tool; a ispminIs the minimum cut depth; a ispmaxThe maximum cutting depth is obtained; pmaxThe maximum power of the machine tool; eta is the power efficiency of the machine tool; fcIs the main cutting force; fcmaxAllowing maximum cutting force for the machine tool; gamma rayεThe radius of the tool nose of the tool; rmaxThe maximum surface roughness value allowed for finishing.
7. The method according to claim 1, wherein in step S2, the determining the optimal solution of the multi-objective problem is specifically:
firstly, solving the optimal solution of each optimization target under the condition of a single target; then, the proportions of a plurality of targets are multiplied together in this way, and the overall proportion of each target of the non-inferior solution close to the optimal solution of the target can be obtained.
8. The method according to claim 1, wherein in step S2, the grid-based multi-objective particle swarm algorithm is specifically:
s2021, initializing particles, taking a first position as an initial pbest, updating speed and position, carrying out target calculation on the updated position to obtain a target vector, and carrying out domination judgment on the target vector and the previous pbest target vector; if the dominant relationship exists, the position vector corresponding to the dominant solution is used as a new pbest; if no domination relation exists, determining which vector is used as a new particle individual optimal solution by roulette;
s2022, dividing grids of the whole search domain according to a certain number in each dimension, respectively storing non-dominated solutions into corresponding grids according to positions, counting the number of the non-dominated solutions in each grid, and then determining which grid is selected according to roulette; after determining which grid is selected by roulette, determining a non-dominant solution serving as a global optimal solution pbest by random selection, and determining a global optimal solution;
s2023, after the particles are initialized, storing the first batch of non-dominated solutions in an external file; then, after the position of the particle is changed, taking the non-dominated solution again, merging the non-dominated solution set obtained this time with a non-dominated solution set stored by an external file per se, carrying out domination judgment, removing the dominated solution from the external file, and directly carrying out next iteration if the number of the non-dominated solution in the external file is less than the maximum number of the external file; otherwise, deleting the non-dominated solutions with the number exceeding the maximum number to finish the maintenance of the external files;
s2024, generating a new particle position in each iteration process, changing the positions of the particles according to the set variation probability, and gradually reducing the variation probability and the variation range along with the change of the iteration times to realize variation operation;
and S2025, calculating a target vector of the particle according to the value obtained after the optimization variable is subjected to the variation operation in the step S2024, and adjusting pbest of the particle for the next iteration.
9. The method according to claim 8, wherein in step S2024, the mutation probability pmutComprises the following steps:
wherein: it is the current iteration number; MaxIt is the maximum iteration number; u is a variation probability attenuation coefficient;
range of variation rmutComprises the following steps:
rimin＝max(xi-rmut,ximin)
rimax＝min(xi+rmut,ximax)
wherein: r ismutIs the variation range; x is the number ofimaxThe upper limit of the allowable value of the ith dimension is optimized; x is the number ofiminThe lower limit of the allowable value of the ith dimension is optimized; v is the attenuation coefficient of the variation range; r isiminThe lower limit of allowable coordinates of the ith dimension is optimized; r isimaxAnd (4) using an upper limit of allowable coordinates for the ith dimension to optimize the variables.
10. A system for multi-objective cutting parameter optimization under tool-specific conditions, comprising:
the parameter module selects three basic cutting factors as optimization variables under the condition that the specification parameters of the cutter are determined, and additionally adds cutting width as the optimization variables when the machining mode is milling; selecting the minimum carbon emission of characteristic processing and the minimum cost of the characteristic processing process as optimization targets, adding constraint conditions to establish a multi-target cutting parameter optimization model taking the minimum carbon emission and the minimum processing cost as optimization targets;
and the optimization module is used for determining the optimal solution of the multi-target problem, designing a grid-based multi-target particle swarm algorithm to solve the multi-target cutting parameter optimization model, and obtaining the cutting parameters with the minimum carbon emission and the minimum processing cost as the optimization targets.
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