Multi-objective Optimization of Numerical Control Machining Process Parameters

1 Introduction The process parameters are the basic control of CNC machining. If the process parameters are not properly selected, it is difficult to ensure the workpiece processing accuracy and control the processing cost, and the machine may be forced to shut down due to excessive cutting force and affect the normal performance of CNC machine tools. Therefore, the multi-objective optimization study of numerical control cutting process parameters for the purpose of improving the efficiency of CNC machining, reducing the processing cost, and obtaining high-quality products is of great significance to improving the economic benefits of CNC machining. In this paper, CNC turning, CNC milling spindle speed, feed rate, back-to-eat knife, milling width and other process parameters as optimization variables, established a multi-objective optimization mathematical model, and at the same time using effective optimization algorithm to achieve CNC machining process parameters Multi-objective optimization. 2 Mathematical description of CNC cutting process parameter optimization variables Optimization of CNC turning process parameters optimization Spindle speed n, feed speed vf, back eater ap as an optimization variable, the vector is expressed as X = (n, vf, ap ) T CNC milling process parameters are optimized with the spindle speed n, feed speed vf, back feed amount ap, milling width ae as an optimization variable, the vector is expressed as X = (n, vf, ap, ae) T objective function The highest productivity and the shortest machining man-hours are the same for the numerically-controlled cutting process target function. CNC cutting work time is t = lw (1+ tct) + t0 vf T (1) Where: lw - cutting stroke (mm) vf - feed speed (mm/min) tct - tool change time (min /times) T——tool life (min/piece) t0——process auxiliary time (min) The service life of the turning tool is T= KTCT n1/mvf1/nap1/p (2) The service life of the milling tool is T = KTCTDqn1/mvf1/nap1/pae1/uZ1/w (3) where: CT - coefficient KT - correction factor m, n, p, u, w - index D - cutter diameter Z - The number of teeth of the milling cutter brings equations (2) and (3) into equation (1), respectively. The objective function of CNC turning operations is Mt(X)=Avf-1+Bcvf(1/n-1)n1/map1/. p+t0 (4) The objective function of numerically controlled milling machining is Mt(X)=Avf-1+Bxvf(1/n-1)n1/map1/pae1/u+t0 (5) Where: A=lwBc=( Atct)/(KTCT) Bx=(AtctZ1/w)(/KTCTDq) CNC cutting cost objective function CNC cutting cost is c = lw (c0 + c0tct + ct) + t0c0 vf T (6) where: c0 - Unit time production cost (yuan/min)c0t——tool cost (yuan/pc) Substituting equations (2) and (3) into formula (6), the target cost function of CNC turning can be Mc(X)=Evf- 1+Fcvf(1/n-1)n 1/map1/p+G (7) CNC milling cost objective function is Mc(X)=Evf-1+Fcvf(1/n-1)n1/map1/pae1/u+G (8) where: E= c0lwFc=lw[ct+c0tct)/(KTCT)] Fx=[lw(ct+c0tct)Z1/w]/(KTCTDq) G=c0t0 CNC Machining Quality Objective Function CNC Machining Dimensional Accuracy Objective Function CNC Machining Size The accuracy objective function is Mz(X)=d (9) where: d—deformation of the tool or workpiece under cutting force When CNC Turning: d= 5l3FH 103KEI During CNC Milling: d= l3FH 103·3KEI Medium: 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 - elasticity of the workpiece material Modulus (GPa) Numerically controlled cutting surface quality objective function Numerically controlled cutting surface quality The objective function is: MR(X)=Ra (10) Constrained design variables The general form of constraint conditions is gi(X)≤0 (i=1 ,2,3,...) (11) Cutting force, cutting power, machine tool spindle torque, tool strength, tool geometry, chip control, maximum spindle speed, machine tool Factors such as the large feed rate and the machining allowance constitute constraints for optimizing the process parameters. 3 MULTIOBJECTIVE OPTIMIZATION MATHEMATICAL MODEL BASED ON MAJOR OBJECTIVE METHODS MAIN GOAL METHOD The establishment of multiobjective functions has m optimization objectives: M1(X), M2(X), ..., Mi(X), ..., Mm(X), Taking the ith goal Mi(X) as the main goal, the multi-objective optimization objective function can be expressed as M(X)=Mi(X) and satisfy the constraint condition: 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 allowable for each secondary target. value. In CNC machining, the time and cost are significantly increased in order to achieve optimum machining quality. From the economical point of view of numerical control processing, it is obviously not appropriate to simply pursue optimal processing quality. Therefore, in the multi-objective optimization with the optimization objectives of working hours, cost, and quality, the man-hour or cost is generally the main goal, and the quality goal is transformed. For the constraints. Multi-objective optimization mathematical model with processing time as the main objective For the multi-objective optimization mathematical model with the main objective of achieving maximum productivity and processing time, 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 satisfies the constraint condition: Mc(X)≤Mc0, MZ(X)≤MZ0, MR(X)≤MR0, Gi(X) ≤ 0 (i=1, 2, 3,...); Among them, Mc0, MZ0, and MR0 are the allowable maximum values ​​of secondary targets such as cost, dimensional accuracy, and surface quality, respectively. The multi-objective optimization mathematical model with the main objective of processing cost is the multi-objective optimization mathematical model that requires the lowest processing cost and the processing cost as the main objective. The vector of design variables is X=(n,vf,ap)T or X. =(n,vf,ap,ae)T The objective function is M(X)=Mc(X) and satisfies the constraint condition: Mt(X)≤Mt0, MZ(X)≤MZ0, MR(X)≤MR0,gi (X) ≤ 0 (iE1,2,3,...); Among them, Mt0, MZ0, and MR0 are the maximum allowable secondary goals such as working hours, dimensional accuracy, and surface quality, respectively. 4 Multi-objective optimization mathematical model based on linear weighted summation method Linear weighted sum method The establishment of multi-objective function has m optimization objectives: M1(X), M2(X),..., Mi(X),..., Mm(X) According to the linear weighted sum method, the objective function for multi-objective optimization can be expressed as M(X) = m liMi(X) S i = 1 where li is the weighting factor, reflecting the i th optimization goal Mi(X) at The importance of multi-objective optimization. To make a reasonable trade-off between the sub-targets, the weighting factor li can be determined as li = 1/Mi* where M* is the objective function value of the single-objective optimization with the i-th sub-object Mi(X) as an objective function. Then the objective function of multi-objective optimization is M(X) = M1(X) + M2(X) +... + Mi(X) M1* M2* Mi* (12) Equation (12) reflects the deviation of the values ​​of each single objective function. The degree of its optimal value and the importance of each single target in multi-objective optimization. Multi-Objective Optimization Mathematical Model for NC Machining Based on the linear weighted sum method, the multi-objective optimization mathematical model for numerical control cutting process parameters with optimization goals of man-hours, cost and quality is represented by the vector of design variables X=(n,vf ,ap)T or X=(n,vf,ap,ae)T The objective function is M(X) = Mt(X) + Mc(X) + MZ(X) + MR(X) Mt* Mc* MZ* MR* satisfies the constraint: gi(X) ≤ 0 (i=1, 2, 3,...). In the formula, Mt*, Mc*, MZ*, and MR* are objective function values ​​of a single objective optimization with time, cost, dimensional accuracy, and surface quality as objective functions, respectively. The establishment of a multi-objective optimization mathematical model with the main objective of man-hours and cost is the main goal in the numerical control cutting process with the shortest processing time and the minimum processing cost as the control targets. The optimization of process parameters should be based on the processing cost and the processing time. With processing quality as a secondary goal. Therefore, in this multi-objective optimization mathematical model, 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 ) + Mc(X) Mt* Mc* and satisfy the constraint condition: MZ(X) ≤ MZ0, MR(X) ≤ MZ0, gi(X) ≤ 0(i=1, 2, 3, ...); *,Mc* are objective function values ​​optimized by single objective when working time and cost are objective functions respectively; MZ0, MR0 are the maximum allowable secondary goals such as dimensional accuracy and surface quality, respectively. 5 Optimization Algorithms and Calculation Examples Optimization Algorithms Because the mathematical model of the optimization of process parameters for CNC machining is a non-linear model, this paper uses a grid-directed optimization algorithm to solve the problem. The specific calculation steps are shown in Figure 1. Optimization study

1
Figure 1 Grid algorithm flow chart

An example of numerical control turning machining is to machine T10A workpieces on CNC lathes. Processing technology requirements: workpiece diameter D = 100mm; cutting stroke lw = 150mm; machining allowance d = 1mm; surface roughness Ra = 1.6μm; Production conditions: Machine tools: CK7815 CNC lathe; Tool material: Cemented carbide; Tool parameters: Main declination angle kr=45°, rake angle g0=20°, tip radius of arc re=0.8mm; tool cost Ct=15 Auxiliary time t0 = 1min; tool change time tct = 0.5min; man-hour cost C0 = 0.1 yuan / min. The optimization results of the process parameters are shown in Table 1. Table 1 Optimization results of CNC turning calculation results Optimization results Taking man-hour as the main objective Cost as the main objective Working hours, cost multi-target t(min) 1.92 2.47 2.24 c (yuan) 0.72 0.61 0.65 n (r/min) 824 542 573 vf (mm/min) 165 103 114.6 ap(mm) 1 1 1 Numerically Controlled Milling Optimization Study Table 2 Numerically Controlled Milling Optimization Example Calculation Results Optimization Results Taking time as the main objective Cost as the main objective Working hours, cost multiple objectives t(min ) 1.71 2.69 2.36 c (yuan) 3.67 2.87 3.04 N(r/min) 1790 788 1182 vf(mm/min) 286.4 118.2 189.2 ap(mm) 1 1 1 aw(mm) 0.32 0.32 0.32 Molding on a CNC milling machine Curved surface processing, workpiece material 3Cr2W8V. Processing technology requirements: cutting stroke lw = 200mm; machining allowance d = 1mm; surface roughness Ra = 3.2μm; dimensional accuracy 0.10mm. Production conditions: processing machine: XK5032A CNC milling machine; processing tool: carbide ball-end milling cutter (2 edge), 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 the process parameters are shown in Table 2. When the optimization result analysis is optimized with man hours as the main objective, n and vf are high, tool wear is severe, so the machining cost is high; when the cost is the main objective, the tool wear is smaller, and the n and vf are lower. More, lower productivity. When multi-objective optimization is performed with the main goal of working hours and costs, due to reasonable trade-offs between man-hours and cost targets, the optimization results are between the above two. In each objective optimization process, in order to shorten the processing time and reduce the processing cost as much as possible, ap and aw are mainly constrained by the machining allowance and the surface quality. 6 Conclusion In this paper, based on mathematical descriptions of numerical control turning and CNC milling process parameter optimization, a multi-objective optimization mathematical model of process parameters based on man-hour, cost and quality is established. A discrete variable grid direct optimization algorithm was adopted. Through optimization examples, multi-objective optimization of process parameters was achieved. The establishment of multi-objective optimization mathematical model for numerical control cutting processing parameters meets the requirements of multi-target numerical control cutting processing, and provides a theoretical basis for optimizing CNC cutting processing process and obtaining the best economic benefits.

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