CN102609591A - Optimization method of cutting parameters of heavy machine tool - Google Patents

Optimization method of cutting parameters of heavy machine tool Download PDF

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CN102609591A
CN102609591A CN2012100352139A CN201210035213A CN102609591A CN 102609591 A CN102609591 A CN 102609591A CN 2012100352139 A CN2012100352139 A CN 2012100352139A CN 201210035213 A CN201210035213 A CN 201210035213A CN 102609591 A CN102609591 A CN 102609591A
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machine tool
particle
cutting
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evaluation function
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马超
邓超
吴军
邵新宇
熊尧
王远航
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Huazhong University of Science and Technology
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Abstract

The invention discloses an optimization method of cutting parameters of a heavy machine tool. The optimization method comprises the following steps: (1) establishing a cutting optimization model for the machine tool cutting to obtain technical parameters of the machine tool and determining constraints in the optimization model according to the obtained parameters; and (2) obtaining the best cutting parameter set and an optimal evaluation function value by utilizing the cutting optimization model and the constraints, firstly transforming a target function and the constraints in the cutting optimization model of the heavy machine tool into a single target function, namely a target evaluation function, and secondly solving the cutting optimization model by utilizing a hybrid particle swarm to obtain the best cutting parameter set and a corresponding evaluation function value of the heavy machine tool. In the optimization method, processing time, processing cost, processing quality and processing stability are used as optimization goals, and the optimization model is established according to processing performance parameters of the used machine tool at the same time. The optimization method is suitable for the optimization of the cutting parameters of the heavy machine tool.

Description

A kind of optimization method of heavy machine tool cutting parameter
Technical field
The present invention relates to the machined parameters optimization method of lathe, the optimization method of optimum cutting parameter belongs to the mechanical processing technique field in particularly a kind of heavy machine tool cut.
Background technology
The heavy type numerical control lathe is mainly used in large-scale, super-huge parts processing, is to be major industry mainstay industry and the services of key state project project such as defence and military, space flight and aviation, boats and ships, the energy (generating), metallurgy.The cost of heavy machine tool and desirable age all are different from machine tool more greatly; Therefore; In order to utilize the processing characteristics of heavy machine tool fully, the choose reasonable cutting data is that the economy of a very important link, particularly current high speed development in the metal cutting process has had the higher requirement of renewal to processing manufacturing industry; Along with continuing to bring out of new material, new technology, new technology, process parameter optimizing research is developing towards high-performance, high function, high intelligent direction.And current, along with popularizing and use of numerically-controlled machine, what the setting of machined parameters more showed in the working angles is flexible and accurate.Particularly modern age is along with the reach of sciences such as new technology and materials; The processing characteristics of lathe had have more the requirement that is different from traditional sense; Like this, suitable machined parameters for guarantee crudy, cutting down finished cost and enhancing productivity all has great importance.But lathe in use for some time; The wearing and tearing of parts, aging, corrosion etc. can occur and cause phenomenons such as machine finish decline, crudy difference; Working process parameter originally is current inherent characteristic and the duty of incompatibility lathe, need come optimized choice working process parameter again according to present lathe duty.Reach the purpose that improves the machine tooling performance through the combination of process parameters of optimizing the heavy machine tool process.Through suitable simplified model, utilize appropriate analytical approach to obtain the best of breed of parameter, for the choose reasonable of machined parameters provides scientific methods, avoided looking into the limitation that handbook or experience are selected parameter simultaneously.
Current implementation method for cutting parameter optimization has: based on test, based on optimized Algorithm and expert system, based on finite element analysis, based on mechanical kinetics etc.; But based on said method often some limitation of finding the solution to process parameter optimizing; Such as: test method(s) relies on produces reality; The needs that gear to actual circumstances, but efficient is low, labor capacity is big, cost is high; Optimized Algorithm and expert system efficient are high, and test is few, but high to the degree of dependence of model and algorithm itself; Finite element analysis can reach the virtual emulation effect, and it is many to obtain technical indicator, but more dependency theory and experience; Mechanical kinetics can reach the precision height based on theoretical and experiment, but data processing complex.Can know according to preamble; Cutting parameter optimization is a multiple goal multiple constraint process; Processing mode to the normal employing of this type problem in the engineering is to utilize Means of Penalty Function Methods to become unconstrained problem to constrained issues; Adopt the weight method of superposition to be converted into the single goal problem to multi-objective problem, can obtain an objective appraisal function, and the optimized Algorithm of a high-efficient high performance of design is directly connected to result's precision in finding the solution this process through such conversion.
Genetic algorithm (be called for short GA), main thought are evolved opinion and science of heredity of mimic biology, teach proposition in 1975 by the J.Holland of Michigan university; This algorithm is a kind of global optimization approach; Have very strong ability of searching optimum, simple, general-purpose, strong robustness, be suitable for advantages such as parallel processing, theoretical maturation; But efficiency of algorithm has much room for improvement, and particularly the later stage is prone to be absorbed in locally optimal solution.Eberhart and Kennedy are as far back as the common particle cluster algorithm that proposes of nineteen ninety-five, and its basic thought is to receive them in early days the group behavior of many birds to be carried out the inspiration of modeling and simulation result of study.The variable that each particle representative needs to optimize is gathered, and comprises the speed of mainshaft, speed of feed, cutting depth etc. as the variables set unification that the heavy machine tool cutting is optimized.The particle cluster algorithm principle is simple, search speed is fast, but early stage easy " precocity ".Have difference according to " No Free Lunch " theoretical two kinds of algorithms performance in the finding the solution of certain type of problem, but should be identical the average behavior of two kinds of algorithms of all problems collection.Therefore two kinds of algorithms are merged, learn from other's strong points to offset one's weaknesses, to realize the purpose of global optimization.
Summary of the invention
The present invention is directed to the problem that exists in the prior art, propose a kind of optimization method of heavy machine tool cutting parameter, utilize mangcorn subgroup mode to select optimum cutting parameter, solve the present problem that optimization method efficient is low, precision is not high.
Realize that the concrete technical scheme that the object of the invention adopted is:
A kind of optimization method of heavy machine tool cutting parameter specifically comprises the steps:
(1) sets up the objective appraisal function according to the heavy machine tool working angles, simultaneously, as constraint,, determine the cutting parameter Optimization Model according to this objective appraisal function and constraint with rated power, maximum centripetal force, peak torque and cutting parameter scope.
The objective appraisal function is multiobject evaluation function, and wherein target comprises machining period, processing cost, crudy and processing stability.
(2) utilize described cutting Optimization Model and constraint, obtain optimum cutting parameter set and optimum evaluation function value, be specially:
The objective function and the constraint of (2.1) heavy machine tool being cut in the Optimization Model convert a single goal function, i.e. objective appraisal function to.
(2.2) utilize the mangcorn subgroup that the cutting Optimization Model is found the solution according to said target evaluation function and lathe parameter, obtain the optimum cutting parameter set and corresponding evaluation function value of heavy machine tool, accomplish the optimization of cutting parameter.The detailed process that heavy machine cut Optimization Model is found the solution is:
(2.2.1) set the particle population number, the random initializtion particle, and, obtain the evaluation function value of each particle according to said objective appraisal function, and confirm individual extreme value and the global extremum of primary population thus;
(2.2.2) confirm the particle evolutionary generation, and evolve, promptly carry out particle's velocity and position renewal according to evolutionary generation;
(2.2.3) according to the objective appraisal function, judge optimum extreme value and all extreme values in the current population; And the differentiation iterations, when iterations reaches maximum iteration time, continue step (2.2.4), otherwise forward step (2.2.2) to;
(2.2.4) the global optimum position and the optimum solution of output optimal particle.
In the step according to the invention (2.2.2); Select the different Evolution strategy to evolve according to the evolutionary generation value; Be specially: the evolutionary generation value be even number for the time; With genetic operator particle is carried out position and Velocity Updating, when the evolutionary generation value is odd generation, carry out particle's velocity and position renewal with particle flight operator.
After step according to the invention (2.2.2) was evolved, if the aggregation extent of the particle after evolving in search optimum solution process during less than predefined threshold values, the part of the selection at random particle in the particle population carries out Gaussian mutation to be handled.
The present invention is according to the actual conditions of machine tooling process; Proposition is the model of optimization aim with machining period, processing cost, crudy and processing stability; Adopt blending heredity and particle group optimizing method that model is found the solution, to adapt to the characteristics of non-linear, the multipole value of cutting Optimization Model, multiple goal, multiple constraint.The present invention has reached certain height on efficient that solves optimization problem and precision, can be used for the cutting parameter optimization of heavy machine tool.
Description of drawings
Fig. 1 is the flow process frame diagram that cutting parameter is optimized.
Fig. 2 is mangcorn subgroup optimization principle figure.
Fig. 3 is the process flow diagram that the mangcorn subgroup is optimized.
The sample calculation figure of Fig. 4 surfaceness.
Fig. 5 machine cut limit of stability figure.
Fig. 6 machine dynamic characteristics parameter fitting curve map.
Fig. 7 cutting Model parameter fitting curve map.
The practical implementation method
Below in conjunction with accompanying drawing the present invention is further described.
Cutting parameter optimization method of the present invention specifically comprises the steps:
1. set up the cutting parameter Optimization Model of heavy machine tool according to the heavy machine tool working angles
At first; Set up the multiple goal evaluation function that comprises machining period, processing cost, crudy and processing stability according to the heavy machine tool working angles; Simultaneously, with rated power, maximum centripetal force, peak torque, the cutting parameter scope is as constraint; According to this multiple goal evaluation function and constraint, determine the cutting parameter Optimization Model.
Wherein, each target to set up process following:
(1.1) machining period t w: t w=t m+ t h+ t Ot
Figure BDA0000136241410000031
It is the operation feed cutting time; T = ( C v d 0 q v Vf z y v a p x v a e u v Z p v k v ) 1 m Be cutter life, t h = t Ct × t m T = t Ct × ( π d 0 L 1000 Vf z Z ) × ( C v d 0 q v Vf z y v a p x v a e u v Z p v k v ) 1 m , Be because the tool change time that tool wear produces, wherein t CtAfter being the cutter blunt, the time that one time tool changing consumed (comprise and unload cutter, dress cutter, tool setting equal time); t OtOther non-cutting time in the production.The implication of each parameter: d wherein 0Tool diameter (mm), v cutting speed (m/min), f zFeed engagement (mm/z), the Z cutter number of teeth; M, C v, q v, k v, y v, x v, u v, p vThe cutter life parameter is referring to relevant handbook.
(1.2) unit cost C p:, wherein, C tBe the cost of charp tool; H cBe list
C p = t w × H c + t m × c t T
Bit time is by labor cost and remaining recurrent cost.
(1.3) crudy R a: be reduced to single free vibration process to the cutting process of heavy machine tool, following mathematical model arranged: x · · ( t ) + 2 ξ ω n x · ( t ) + ω n 2 x ( t ) = - ω n 2 k Δ F ( t ) - - - ( 1 )
ΔF ( t ) = F 1 ( t ) - F 2 ( t ) - F 3 ( t ) F 1 ( t ) = Da p s μ ( t ) F 2 ( t ) = Da p s 0 μ F 3 ( t ) = Da p c μs 0 μ - 1 60 x · ( t ) zn - - - ( 2 )
Wherein, x (t) is the relative movement orbit on milling surface normal direction between milling blade and the workpiece, and ξ is a damping ratio, ω nBe natural frequency, k is a stiffness coefficient; Δ F (t) is the dynamic change part of Milling Force, F 1(t) represent total Instantaneous Milling Force that Instantaneous Milling thickness causes, F 2(t) represent the average Milling Force that nominal milling thickness causes, F 3(t) the expression workpiece material is to the drag of blade incision.D and μ are coefficient, are confirmed by the Milling Force experiment; a pBe milling depth, s (t) is an Instantaneous Milling thickness, s 0(t) be nominal milling thickness, c is the penetration rate coefficient, and n is the speed of mainshaft, and z is a cutter tooth number.
Roughness is one of important evaluation index of machine finish, and profile arithmetic average error R aAs the important measurement index of machined surface roughness, its computing method are arithmetic mean of profile offset distance absolute value in sample length, that is:
Figure BDA0000136241410000051
Wherein, l is a sample length, x iFor each point on the tested profile to the distance of profile center line, also be the numerical solution (referring to Fig. 4) of formula (1), N is the numerical solution number in the sample length.
(1.4) machine cut processing stability S t: the purpose of the analyses and prediction of cutting stability is to improve material removing rate and obtain high crudy.The assurance of high crudy is stable cutting, and under the prerequisite of stable cutting, material removing rate is high more good more, i.e. speed of mainshaft n and corresponding stable cutting axial depth ultimate value a PlimProduct n * a PlimBe the bigger the better.Corresponding to the maximum principal axis rotating speed near zone in the different process be not in the stable region and the stabilized zone maximum is S t=n * a PlimSize estimate the stability of machine cut process.(referring to Fig. 5)
In addition; Select machining tool based on the cutting process characteristics, and consult corresponding machine tool technology parameter, such as: rated power, maximum centripetal force, peak torque; Cutting parameter scopes etc. are confirmed the parameter in the cutting object function through searching technical manual with corresponding part experiment;
Simultaneously,, consult Tool in Cutting parameter area and workpiece processing accuracy requirement according to cutting tool and processing work index, and the value of intrafascicular each variable of objective function peace treaty in definite Optimization Model.
And needs are confirmed the target evaluation function of cutting parameter.Target evaluation function in the present embodiment is to adopt weight method of superposition and Means of Penalty Function Methods to cut heavy machine tool objective function (man-hour, cost, quality and stability) in the Optimization Model and retrain a single goal function that converts to.
2. the solution procedure of heavy machine tool cutting parameter Optimization Model
(2.1) confirm parameter in the mangcorn subgroup, comprising: population number, iterations, weight variation range, study factor variations scope, crossover probability, variation probability, particle gather parameter value sizes such as threshold values;
(2.2) need to confirm the cutting parameter variable of optimization to gather based on the cutting Optimization Model, promptly the variable dimension is the optimization variable set with the speed of mainshaft, the amount of feeding, cutting depth etc. generally.According to variable dimension and cutting parameter variable range, in the mangcorn subgroup, adopt and encode based on the coded system of real number, be convenient to understanding like this to Optimization Model, meet actual demands of engineering;
(2.3) according to the particle population number that sets, random initializtion particle.Each particle is used vector representation, and a particle is represented one group of cutting parameter set (speed of mainshaft, the amount of feeding, cutting depth etc.).
(2.4), obtain the evaluation function value of each particle, and come to confirm individual extreme value and the global extremum of primary population thus according to the target evaluation function of cutting parameter Optimization Model;
(2.5) evolutionary generation of judgement particle is selected the different Evolution strategy according to evolutionary generation;
(2.5.1) even number for the time carry out position and Velocity Updating to particle with genetic operator (binding sequence select operator and crossover operator).See formula 4 and 5
p i = q · ( 1 - q ) i - 1 1 - ( 1 - q ) U - - - ( 4 )
child(x i)=p·parent 1(x i)+(1-p)·parent 2(x i)
child ( V i ) = parent 1 ( V i ) + parent 2 ( V i ) | parent 1 ( V i ) + parent 2 ( V i ) | · | parent 1 ( V i ) | - - - ( 5 )
In the formula, q representes individual selection probability, and U is the population size, p iBe the selection probability of i particle after the ordering, p representes interindividual crossover probability, parent 1(x i) and parent 2(x i) the expression parent and the current location in female generation, parent 1(V i) and parent 2(V i) the expression parent and the particle flying speed in female generation.Carry out parent according to formula (4) 1(x i) and parent 2(x i) selection, carry out the renewal of particle according to formula (5).
(2.5.2) carry out particle's velocity and position renewal with particle flight operator during odd generation, see formula (6):
v id j + 1 = w · v id j + c 1 r 1 ( p id - z id j ) + c 2 r 2 ( p gd - z id j ) (6)
z id j + 1 = z id j + v id j + 1
In the formula, wherein, w is an inertia weight, is used for balance global search and Local Search, and j is an iterations, r 1, r 2Be the random number between (0,1), c 1, c 2Be the study factor.If z i=(z I1, z I2..., z Id), z iBe the d dimension position vector of i particle, d is the variable dimension, and the variable dimension that cutting is optimized is 3.According to z iCalculate current fitness evaluation functional value, weigh the quality of particle position thus; v iIt is the flying speed of i particle; p iBe optimal particle when former generation; p gBe the preceding j optimal particle seat in generation.
(2.6) also be whether aggregation extent in the renewal process of position is lower than certain threshold values according to particle in evolutionary process; Test is found according to data; Threshold values is better to particle convergence effect about 5, to a part of particle in the particle population according to formula (7) processing that makes a variation.
z i=P b(i)·(1+0.5μ) (7)
Wherein, P b(i) be i particle desired positions so far, μ is the random vector of obeying (0,1) normal distribution.
(2.7), judge optimum extreme value and all extreme value, the i.e. optimum cutting parameter of optimum cutting parameter of current population and historical population in the current particle population according to the target evaluation function of cutting Optimization Model;
(2.8) differentiate iterations, when reaching maximum iteration time (testing generally about 500 times), continue (2.9), otherwise just turn to (2.5) according to data;
(2.9) the global optimum position and the optimum solution of output optimal particle, i.e. optimum cutting parameter and optimum evaluation function value.The global optimum position and the optimum solution of output optimal particle, i.e. optimum cutting parameter and optimum evaluation function value.
In the inventive method is implemented; Can also carry out parameter adjustment to the stuff and other stuff group optimizing method that is designed according to optimizing trial function; Such as confirming the study factor, inertia weight, iterations, the isoparametric value of aberration rate size; Make mangcorn subgroup method all have superior performance aspect solving precision and the efficient; Can obtain according to optimizing trial function, carry out the precision comparing result, verify the superiority of the mangcorn subgroup solving-optimizing model that is designed with this with existing other optimization method.IGPSO is used for the optimized Algorithm that the solving-optimizing model is designed in the table 1 among the present invention, and there have been other optimized Algorithm in QPSO, AMPSO, AMQPSO, and f1 to f8 is the standard testing function of using always.The standard testing function is repeatedly found the solution, and adopt the foundation of the mean value of objective function as the good quality of evaluation algorithms, effect is seen table 1.
The contrast of table 1 mangcorn subgroup IGPSO and other optimized Algorithm
The contrast algorithm IGPSO QPSO AMPSO AMQPSO
Sequence number Mean value Mean value Mean value Mean value
f1 1.06E-197 7.69E+00 2.86E-52 3.29E-98
f2 2.02E-108 4.20E+00 2.42E-24 1.85E-47
f3 9.12E-133 3.07E-01 2.20E-23 4.43E-56
f4 3.97e-085 3.94E-69 3.26E-25 2.02E-125
f5 1.29E-05 1.97E+02 8.96E+00 8.82E+00
f6 0.00E+00 5.72E+01 1.78E-15 0.00E+00
f7 8.88E-16 2.85E+00 8.88E-16 8.48E-16
f8 0.00E+00 1.86E+00 0.00E+00 0.00E+00
Among the present invention; Characteristics according to cutting parameter optimization in the heavy machine tool cut field; With the rated power of lathe, maximum centripetal force, peak torque and cutting parameter scope is constraint, obtains the heavy machine tool cutting parameter model of lathe, and through correlation method model is found the solution; Obtain the optimized parameter in the machine cut processing, thereby can effectively accomplish cutting.
In order to verify operational feasibility of the present invention; To the two plane milling and boring machines of the heavy type numerical control of certain heavy machine tool plant; According to technical method that summary of the invention adopted according to test, pertinent literature handbook and lathe relevant design parameter; Obtain the partial parameters and the working process parameter scope of lathe, accomplish optimization aim and constraint function.
1. part handbook parameter:
(1) cutter life parameter:
m=0.15,p v=0.1,u v=0.5,y v=0.4,x v=0.1,q v=0.2,C v=25?K v=1.0
(2) lathe constrained parameters:
C F=30、x F=1.0、y F=0.65、u F=0.83、w F=0、q F=0.83、k Fc=0.4
2. test condition:
(1) workpiece material: casting pig HT250;
(2) process technology requires: the cutting stroke L=workpiece length+ultra amount of cutting=230+43.5=273.5 (mm), short t in man-hour w, lower cost C p, crudy R preferably aAnd higher processing stability S t
(3) working condition: single operation one-pass;
(4) process tool: diameter d 0=315mm facing cutter, blade model YBC301, cutting number of teeth Z=10, cost of charp tool C t=3000 yuan, non-cutting time t Ot=2min, tool change time t Ct=2min, time cost: Co=5 unit/min (according to the production status estimation).
The dynamic characteristic parameter of lathe: natural frequency w n=447, stiffness coefficient k=1.1133e+009, damping ratio ξ=0.0274 (obtain by the dynamic characteristic parameter test experiments, see Fig. 6).Milling Process cutting Force Model parameter: D=276.7339, μ=0.4408 (, seeing Fig. 7) by obtaining in the cutting force experiment.
3. Optimization Model initial parameter
(1) cutting parameter hunting zone: cutting speed 160m/min≤v≤300m/min; Feed engagement 0.1mm/z≤f z≤0.28mm/z; Cutting depth 0<a p≤4mm
(2) parameter in the Hybrid Particle Swarm Optimization (IGPSO): population number U=20, iterations j=150, weight variation range 0.9>=w>=0.4, study factor 2 .0>=c 1>=0.5; 0.5≤c 2≤2.25, crossover probability p=0.5, variation probability q=0.6, particle gather threshold values Q=5 etc.
4. cutting parameter Optimization result
According to the needs in the Optimization Model, the spacing in this instance between employing individual particles and the optimal particle is seen formula (8) as the objective appraisal function
F=w1·(t w-t w0)^2+w2·(C p-C p0)^2+w3·(R a-R a0)^2+w4·(S t-S t0)^2
(8)
In the formula, t W0, C P0, R A0, S T0Represent the target function value when machining period, processing cost, surface quality, processing stability are optimum separately respectively.W1, w2, w3, w4 represent the weighted value of each objective function.Numerical optimization the results are shown in Table 2, and single goal optimization is the Optimization result when only considering the single target function in the table, and multiple-objection optimization is the result who considers each optimization aim function simultaneously, only lists a kind of result of optimization aim combination in the table.
Table 2 adopts the mangcorn subgroup to ask the result of cutting parameter Optimization Model
Figure BDA0000136241410000091

Claims (5)

1. the optimization method of a heavy machine tool cutting parameter specifically comprises the steps:
(1.1) set up the multiple target evaluation function based on the heavy machine tool working angles; Simultaneously; As constraint,, determine the cutting parameter Optimization Model of heavy machine tool with rated power, maximum centripetal force, peak torque and cutting parameter scope based on this multiple target evaluation function and constraint;
(1.2) utilize described cutting parameter Optimization Model and constraint, obtain optimum cutting parameter set and optimum evaluation function value, be specially:
The multiple goal evaluation function and the constraint of (1.2.1) heavy machine tool being cut in the Optimization Model convert a single goal evaluation function to;
(1.2.2) utilize the mangcorn subgroup that said cutting Optimization Model is found the solution, obtain the optimum cutting parameter set and corresponding evaluation function value of heavy machine tool, accomplish the optimization of cutting parameter according to said single goal evaluation function and lathe parameter.
2. the optimization method of heavy machine tool cutting parameter according to claim 1 is characterized in that, in the described step (1.2.2), the detailed process that heavy machine cut Optimization Model is found the solution is:
(2.1) set the particle population number, the random initializtion particle, and, obtain the evaluation function value of each particle according to said single goal evaluation function, and confirm individual extreme value and the global extremum of primary population thus;
(2.2) confirm the particle evolutionary generation, and evolve, promptly carry out particle's velocity and position renewal according to evolutionary generation;
(2.3) judge optimum extreme value and all extreme values in the current population according to said single goal evaluation function, and differentiate iterations, when iterations reaches the iterations of setting, continue step (2.4), carry out otherwise forward step (2.2) circulation to;
(2.4) the global optimum position and the optimum solution of output optimal particle, promptly obtain lathe optimum cutting parameter set and corresponding evaluation function value.
3. the optimization method of heavy machine tool cutting parameter according to claim 2; It is characterized in that; In the said step (2.2); Select the different Evolution strategy to evolve according to the evolutionary generation value, be specially: if the evolutionary generation value be even number for the time, with genetic operator particle is carried out position and Velocity Updating; When if the evolutionary generation value is odd generation, carry out particle's velocity and position renewal with particle flight operator.
4. according to the optimization method of the described heavy machine tool cutting parameter of one of claim 1-3; It is characterized in that; After said step (2.2) is evolved; If the aggregation extent of the particle after evolving in search optimum solution process then selected a part of particle to carry out Gaussian mutation in the particle population at random and handled less than predefined threshold values.
5. according to the optimization method of the described heavy machine tool cutting parameter of one of claim 1-4, it is characterized in that the target in the described multiple goal evaluation function comprises machining period, processing cost, crudy and processing stability.
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