# Multi-objective optimization of the most popular N

2022-09-20
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Multi objective optimization of NC machining process parameters

1 introduction

process parameters are the basic control quantities of NC machining. If the process parameters are improperly selected, it is not only difficult to ensure the workpiece processing accuracy and control the processing cost, but also may cause the machine tool to be forced to shut down due to excessive cutting force and other reasons, affecting the normal performance of the CNC machine tool. Therefore, the multi-objective optimization of NC machining process parameters for the purpose of Improving NC machining efficiency, reducing machining costs and obtaining high-quality products is of great significance to improve the economic benefits of NC machining. In this paper, taking the spindle speed, feed speed, back feed, milling width and other process parameters of NC turning and NC milling as optimization variables, a multi-objective optimization mathematical model is established, and an effective optimization algorithm is used to realize the multi-objective optimization of NC cutting process parameters

2 mathematical description of NC cutting process parameter optimization

optimization variables the optimization of NC turning process parameters takes the spindle additional speed n, feed speed VF, back cut AP as optimization variables, and its vector is expressed as x= (n, VF, AP) T. The Optimization of NC milling process parameters takes the spindle speed n, feed speed VF, back cut AP, milling width AE as optimization variables, Its vector is expressed as x= (n, VF, AP, AE) T

objective function

NC machining hours. The maximum productivity of the objective function is consistent with the minimum machining hours. The working hours of NC cutting are

where: LW cutting stroke (mm) VF feed speed (mm/min) TCT tool change time (min/time) t tool service life (min/piece) t0 process auxiliary time (min) the service life of turning tool is

where: CT coefficient KT correction coefficient m, N, P, u, w index D milling cutter diameter Z milling cutter tooth number bring equations (2) and (3) into equation (1) respectively, It can be obtained that the objective function of NC turning hours is

, where: a=lw bc= (ATCT)/(ktct) bx= (atctz1/w) (/ktctdq) NC cutting cost objective function NC cutting cost is

where: C0 unit time production cost (yuan/min) c0t tool cost (yuan/piece) substituting equations (2) and (3) into equation (6) respectively, The objective function of NC turning cost can be obtained as

, where: e=c0lw fc=lw[ct+c0tct)/(ktct)] fx=[lw (ct+c0tct) z1/w]/(ktctdq) g=c0t0

NC cutting quality objective function

NC cutting dimensional accuracy objective function NC cutting dimensional accuracy objective function is

, where: FH radial cutting force (n) l workpiece support or tool cantilever length (mm) k workpiece clamping method coefficient I workpiece or tool.Moment of inertia (MM4) E modulus of elasticity (GPA) of workpiece material

surface quality objective function of NC machining surface quality objective function of NC machining is:

cutting force, cutting power, spindle torque of machine tool, tool strength, geometric parameters of tool, chip control, maximum rotation speed of machine tool spindle, maximum feed speed of machine tool and machining allowance in the process of NC machining constitute the constraints of process parameter optimization

the establishment of the multi-objective function of the main objective method has m optimization objectives: M1 (x), M2 (x), mi (x), mm (x). With the ith objective mi (x) as the main objective, the multi-objective optimization objective function can be expressed as m (x) =mi (x) and meet the constraints: M1 (x) M10, Mi-1 (x) mi-10, mi+1 (x) mi+10, mm (x) mm0; Where M10, mi-10, mi+10, mm0 are the maximum values allowed for each secondary target. In NC machining, in order to achieve the best machining quality, the man hour and cost will increase significantly. Considering the economy of NC machining, it is obviously not appropriate to simply pursue the optimal machining quality. Therefore, in the multi-objective optimization with man hour, cost and quality as the optimization objectives, man hour or cost is generally taken as the main objective, and the quality objective is transformed into constraints

multi-objective optimization mathematical model with processing man hours as the main objective for the multi-objective optimization mathematical model with processing man hours as the main objective to achieve the highest productivity, the vector of design variables is expressed as x= (n, VF, AP) t or x= (n, VF, AP, AE) T. The objective function is m (x) =mt (x) and meets the constraints: MC (x) mc0, MZ (x) mz0, Mr (x) mr0, GI (x) 0 (i=1, 2, 3,); Mc0, mz0 and mr0 are the maximum allowable values of secondary targets such as cost, dimensional accuracy and surface quality respectively

multi-objective optimization mathematical model with processing cost as the main objective. For the multi-objective optimization mathematical model with processing cost as the main objective and the lowest processing cost, the vector of design variables is expressed as x= (n, VF, AP) t or x= (n, VF, AP, AE) T. The objective function is m (x) =mc (x) and meets the constraints: MT (x) mt0, MZ (x) mz0, Mr (x) mr0, GI (x) 0 (IE1, 2, 3,); Where mt0, mz0 and mr0 are the maximum allowable values of working hours, dimensional accuracy and table so as to remove the damaged surface quality generated during polishing as soon as possible

the establishment of multi-objective function of linear weighted sum method has m optimization objectives: M1 (x), M2 (x), mi (x), mm (x). According to the linear weighted sum method, the objective function of multi-objective optimization can be expressed as

, where Li is the weighting coefficient, reflecting the importance of the ith optimization objective mi (x) in multi-objective optimization. In order to make a reasonable compromise between the sub objectives, the weighting coefficient Li can be determined as li=1/mi*, where m* is the objective function value of single objective optimization with the ith sub objective mi (x) as the objective function. Then the objective function of multi-objective optimization is

equation (12), which reflects the degree to which the value of each single objective function deviates from its optimal value and the importance of each single objective in multi-objective optimization

establishment of multi-objective optimization mathematical model of NC machining according to the linear weighted sum method, for the multi-objective optimization mathematical model of NC machining process parameters with the optimization objectives of man hour, cost and quality, the vector of design variables is expressed as x= (n, VF, AP) t or x= (n, VF, AP, AE) T. The objective function is

and meets the constraint conditions: GI (x) 0 (i=1, 2, 3,). Where mt*, mc*, mz*, mr* are the objective function values of single objective optimization with man hour, cost, dimensional accuracy and surface quality as the objective functions respectively

the establishment of a multi-objective optimization mathematical model with man hour and cost as the main objectives in NC machining with the shortest machining man hour and the minimum machining cost as the control objectives, the optimization of process parameters should take machining cost and machining man hour as the main objectives at the same time, and machining quality as the secondary objectives. Therefore, in the multi-objective optimization mathematical model, the vector of the design variable is expressed as x= (n, VF, AP) t or x= (n, VF, AP, AE) T. The objective function is

and meets the constraints: MZ (x) mz0, Mr (x) mz0, GI (x) 0 (i=1, 2, 3,); Where mt*, mc* are the objective function values of single objective optimization with man hour and cost as objective functions respectively; Mz0 and mr0 are the maximum allowable values of secondary targets such as dimensional accuracy and surface quality respectively

optimization algorithm because the mathematical model of process parameter optimization of NC machining is a nonlinear model, this paper uses the lattice direct optimization algorithm to solve it. See Figure 1 for specific calculation steps

optimization example

optimization example of NC turning machining process T10A workpiece on NC lathe. Processing technical requirements: workpiece diameter d=100mm; Cutting stroke lw=150mm; Machining allowance d=1mm; Surface roughness ra=1.6 m; The dimensional accuracy is 0.05mm. Production conditions: processing machine: CK7815 CNC lathe; Tool material: cemented carbide; Tool parameters: main deflection angle kr=45, rake angle g0=20, tool tip arc radius re=0.8mm; Tool cost ct=15 yuan; Auxiliary time t0=1min; Tool change time tct=0.5min; Man hour cost c0=0.1 yuan/min. The optimization results of process parameters are shown in Table 1

Table 1 numerical control turning optimization example calculation results

the mold cavity surface is machined on the numerical control milling machine, and the workpiece material is 3Cr2W8V. Processing technical requirements: when the zigzag experimental machine breaks down, there is no need to worry about the cutting stroke lw=200mm; Machining allowance d=1mm; Surface roughness ra=3.2 m; The dimensional accuracy is 0.10mm. Production conditions: processing machine: xk5032a CNC milling machine; Processing tool: carbide ball end milling cutter (2 edges), milling cutter diameter d=16mm; Tool cost ct=150 yuan; Auxiliary time t0=1min; Tool change time tct=0.5min; Man hour cost c0=0.1 yuan/min. The optimization results of process parameters are shown in Table 2

when optimizing with man hours as the main objective, N and VF are higher, and the tool wear is serious, so the processing cost is higher; When optimizing with cost as the main objective, the tool wear is small, the N and VF are low, the machining hours are more, and the productivity is low

when multi-objective optimization is carried out with the main objectives of man hour and cost, due to a reasonable compromise between man hour and cost objectives, the average gross profit margin of domestic coated paper is ⑵ 59% optimization results are between the above two

in the process of optimization of each objective, AP and aw are mainly constrained by machining allowance and surface quality in order to shorten machining hours and reduce machining costs as much as possible

6 conclusion

based on the mathematical description of the optimization of process parameters of NC turning and NC milling, a multi-objective optimization mathematical model of process parameters with the optimization objectives of man hour, cost and quality is established in this paper. The discrete variable lattice direct optimization algorithm is used to realize the multi-objective optimization of process parameters through optimization examples. The establishment of multi-objective optimization mathematical model of NC machining process parameters meets the requirements of multi-objective NC machining, and provides a theoretical basis for optimizing the NC machining process and obtaining the best economic benefits

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