Yun-feng ZHOU, De-chao WANG, Shan-hai JIN,Cheng-dao PIAO

(Engineering College, Yanbian University, Yanji 133002, China)

Abstract: This paper investigates the influence of the vibration generated by the CNC milling machine during the cutting process on the surface quality of the workpiece. The optimization objectives are to optimize the cutting parameters with low vibration and high surface quality. This paper uses the VDF-850A milling to carry out milling orthogonal test on 45 steel and establishes a vibration acquisition system. Vibration signals were collected to obtain the vibration characteristic value and measure the surface roughness value of the workpiece. In this paper, two mathematical models of vibration and roughness are established by fitting the least-squares method to the data. The weights of the two objective functions are determined by the analytic hierarchy process. Then the two objective functions are weighted and fitted into the comprehensive objective function by the square sum weighting method, and the particle swarm optimization (PSO) algorithm is used to optimize the cutting parameters. The result shows that the machining parameters optimized by particle swarm optimization algorithm can effectively reduce vibration and improve surface quality.

Key words: Cutting vibration, Surface roughness, Particle swarm optimization algorithm, Multi-objective milling parameters optimization

1 Introduction

“Made in China 2025”, for the first time, regards advanced manufacturing technology as one of the development directions of China’s manufacturing industry in the next decade [1]. As the mother machine of the manufacturing industry, the numerical control processing equipment reduces the cutting vibration and the processing quality in the processing process, which is very important for the development of the manufacturing industry. In recent years, with the continuous improvement of the manufacturing level, CNC milling machines are widely used in the manufacturing industry due to their flexible processing, high versatility, high processing precision, and high production efficiency. Cutting parameters are the main factors affecting the processing of milling machines, therefore, optimizing milling parameters is imperative [2]. There are many process indicators for milling parameters optimization studies such as material removal rate, surface roughness, energy consumption, and milling cutter flutter. At present, there have been many researchers devote to this area. Zhou [3] established a single-objective cutting parameters optimization model with roughness as the objective. Yan [4] established cutting parameters optimization model with surface roughness, material removal rate and cutting force as the optimization objectives. Huang et al. [5] established a cutting parameters optimization model with reduced energy consumption as the objective. The above process indicators were based on traditional optimization objective and rarely based on cutting vibration was the optimization objective, but cutting vibration is closely related to the surface quality of the workpiece. Therefore, in order to scientifically improve the surface quality of the workpiece, multi-objective milling parameters are optimized with milling vibration and surface roughness as optimization objectives.

Proper selection of cutting parameters is essential to reduce vibration during machining and to ensure surface quality of workpiece during milling. Milling cutter flutter is a self-excited vibration in the milling process, which seriously affects the surface quality of the product, severely limits the efficiency of milling, and reduces the service life of the tool and the accuracy of the spindle. Roughness is an important indicator for evaluating the surface quality of a product. At present, most of the metal cutting processing is based on the experience or reference cutting manual to select the cutting parameters [6], which often did not reach the best cutting parameters. Therefore, optimizing the milling parameters is of great significance for reducing the vibration during the machining process and improving the surface quality of workpiece.

2 Vibration acquisition system

2.1 Vibration data acquisition system

We selected the type VDF-850A produced by Dalian Machine Tool Plant as the test platform. The machine uses the Japanese FANUC0i MF (5) CNC system with a maximum speed of 8 000 r/min. The 4-channel dynamic signal analyzer is type DP700 produced by American Difei Company, and the sensitivity of the acceleration sensor 352C33 type ICP produced by American PCB Company is 10.38 mv/(m/s2). The original vibration acceleration is recorded and monitored by connecting to the PC. The vibration acquisition system of the established CNC machine tool is shown in Fig.1.

2.2 Test design

This paper performed grooved milling experiments. The Taiwan Richen cemented carbide end mill was used as a test tool. The parameters of the tool are: the diameter of 10mm, the total length of 75mm, the number of teeth of 4, and the workpieces of 90mm*90mm*30mm square 45 steel. The real-time vibration is transmitted to the dynamic signal analyzer and the PC through the acceleration sensor mounted on the spindle [7] to collect the original vibration signal during the cutting process. Based on the engineering experience, the cutting parameters of manual and the VDF-850A CNC milling machine manual produced by Dalian Machine Tool, select the appropriate cutting parameters to design the three-factor four-levelL32(43) groups orthogonal test. The three factors are spindle speed (n), cutting depth (ap) and feed rate (f). The orthogonal test factor level is shown in Table 1.

Table 1 Cutting factor level table

2.3 Test results and analysis

The original vibration time-domain signal was obtained by the vibration acquisition system, of which time is the independent variable and acceleration value is the dependent variable. Since the original signal contains interference signals that are independent of the experimental factors, it cannot accurately reflect the actual vibration during the cutting process. Therefore, it is necessary to process the original signal and extract the signal characteristic value closely related to the experimental factors. Many indicators can be used to represent vibration eigenvalues such as peak, mean, root mean square, variance, autocorrelation function, and cross-correlation function. The root mean square is an effective parameter to characterize the signal strength, which can reflect the strength of the vibration signal energy [8-9]. Therefore, in this paper, the root mean square is selected as the vibration characteristic value for analysis.

The calculation formula is as follows:

(1)

Where,RMSis root mean square;xiis the original value of the vibration signal;nis number of samples.

The vibration original signal is calculated according to formula (1) and produced according to the orthogonal table design principle results as shown in Table 2. And the results of variance analysis of the vibration RMS using SPSS software are shown in Table 3.

As shown in Table 3, the spindle speed (n), depth of cut (ap), feed rate (f) and the interaction between the various factors are significant factors.

Table 2 RMS of vibration orthogonal test

Table 3 Variance analysis F value and significant results

3 Mathematical modeling of vibration and roughness

3.1 Vibration model establishment

The generation of vibration during the whole process of CNC machine tool processing is inevitable. It is only possible to reduce the vibration as much as possible, thus reducing the damage caused by vibration and improve surface quality. Therefore, there are the results of the variance analysis of Table 3, and the linear function [10] mathematical model with minimum vibration as the objective is as follows:

Min(RMS)=y(1)=a0+a1n+a2ap+a3f+

a4nap+a5nf+a6fap

(2)

The multivariate linear regression analysis was carried out by applying the least-squares method to the formula (2) using the test data in Table 2, and results are shown in Table 4. The correlation coefficient of the linear function model is 0.89, which indicates that the model can accurately predict the root mean square value of cutting vibration.

Table 4 Vibration mathematical model fitting coefficient table

Sorting in as follows:

Min(RMS)=y(1)=-31.637+0.01n+

32.989ap+0.028f-0.006nap-

1.056×10-5nf-0.016fap

3.2 Roughness model establishment

Surface roughness is one of the main characteristics to measure the surface quality of parts. It is closely related to the mating property, wear resistance and fatigue strength of mechanical parts, which affects the service life and reliability of parts. The above 32 groups of orthogonal test workpieces were subjected to multiple multi-segment measurements using the Mitutoyo SV-3100 surface roughness measuring instrument produced by Mitutoyo Corporation of Japan and averaged as shown in Table 5.

Table 5 Roughness Orthogonal Test Measurements

The results of the variance analysis of roughness data are made using SPSS software as shown in Table 6.

As shown in Table 6, the interactionFbetween n and ap is 0.188, It is shown that the interaction between the two has almost no effect on the roughness. Therefore, the linear function [10] mathematical model with minimum roughness as the objective is as follows:

Min(Ra)=y(2)=b0+b1n+b2ap+

b3f+b4nf+b5fap

(3)

Table 6 Variance analysis F value and significant results

The multivariate linear regression analysis was carried out by applying the least-squares method to the formula (3) using the test data in Table 5, and the results are shown in Table 7. The correlation coefficient of the linear function model is 0.94, which indicates that the model can predict the cutting roughness well.

Table 7 Roughness coefficient mathematical model fitting coefficient table

Sorting in as follows:

Min(Ra)=y(2)=2.776-0.001 2n+0.627ap-

0.008f+4.911×10-6nf-0.003fap

3.3 Comprehensive objective function model

For multi-objective optimization, objectives are often contradictory and cannot be optimal at the same time. At present, methods commonly used to solve multi-objective optimization problems include maximal entropy method, interaction method, delaminating sequence method, and comprehensive objective function method. The comprehensive objective function method is the most direct and effective one. It determines the constraint condition and finds the non-inferior solution by transforming the multi-objective function into a comprehensive objective function. Therefore, in this paper, the analytic hierarchy process [12] is used to determine the weight of the two objective functions, and the squared weighting method [11] is used to construct the comprehensive objective function.

The comprehensive objective function model based on the square weight method is established as follows:

(4)

Where,R(n,ap,f) is comprehensive objective function;kiis weighting coefficient;ωiis weight coefficient;yiis optimize the objective function.

The principle of determining the weighting coefficientki[11] is to make the two objective functions in the same order of magnitude during the conversion process, and determinek1=0.1,k2=2 according to Table 2 and Table 5.

The comparison judgment matrix is constructed by the analytic hierarchy process to determine the weights of the two objective functions. The comparison judgment matrix compares the importance of the two objective functions and constructs the judgment matrix according to relative importance.

The value of the judgment matrix is as follows:

aji=1/aij

(5)

Where,αjiandαijare relative importance values.

The specific judgment matrix value method is shown in Table 8[12].

Table 8 Judgment matrix value table

According to the formula (5) and the judgment matrix construction value table 8, the weight judgment matrix E [12] of the vibration objective function and the roughness objective function is determined as follows:

There are many methods for determining the weight in the analytic hierarchy process. The root-weight method is the most common one. Therefore, the root-weight method was used to determine the weight.

Determine the geometric mean formula of each row of elements in matrixEis as follows:

(6)

Where,αijis thei-th row and thej-th column element;miis the geometric mean of thei-th row;nis the number of elements per row.

Normalization the weight formula is as follows:

(7)

Where,ωiis the normalized weight of the two objective functions.

According to formulas (6) and (7), the weights of the normalized vibration and roughness objective functions in constructing the comprehensive objective function is as follows:

ω=(0.33，0.67)

When the judgment matrix is 2nd order, the judgment matrix can always pass the consistency test. Therefore, there is no need to test [12].

According to the instructions of the VDF-850A CNC milling machine, the constraints are determined as shown in Table 9.

Table 9 Constraints

In summary, the milling parameters optimization model is as follows:

(8)

4 Optimization analysis

4.1 Optimization

Particle swarm optimization (PSO) is an optimization algorithm for group intelligence in the field of computational intelligence. The PSO algorithm is derived from the study of predation behavior of birds. When birds prey, the easiest and most effective way to find food is to search for the area around the bird that is closest to the food. The PSO algorithm is inspired by this biological population behavioral feature and used to solve the optimization problem. Each particle in the algorithm represents a potential solution to the problem. Each particle corresponds to a fitness value determined by a fitness function that filters the global optimal value by tracking the current search optimal value. As an emerging evolutionary computing technology, more and more researchers [13] focus on the PSO algorithm to achieve the advantages of easy, high precision, fast convergence and superiority in solving practical problems. According to the definition and principle of the PSO algorithm, the flow chart of the algorithm is shown in Fig.2.

Fig.2 PSO optimization algorithm flow chart

4.2 Optimize model results

Firstly, the PSO algorithm initializes a group of random particles in the feasible region, and each particle is the optimal solution to the optimization problem. Then it determine the pros and cons of each particle according to the value of the fitness function [14-16]. Then, MATLAB is used to optimize the parameters of the objective function using the PSO algorithm using the cutting parameters constraints in Table 9. The result is shown in Fig.3.

As shown in Fig.3, the comprehensive objectiveRreached the minimum when the iterative optimization number was about 200 generations. The milling parameters optimization achieved a global optimal solution of around 200 generations with a combined objective value of 0.631. The resulting global optimal solution is shown in Table 10. It should be noted that since the initial population is randomly generated, the results of each optimization are not identical.

Fig.3 PSO algorithm optimization iteration graph

Table 10 PSO algorithm optimization results

4.3 Optimization analysis

The selection of cutting parameters during actual on-site production is often processed according to the manufacturer’s experience and the cutting conditions manual. According to the empirical cutting parameters in Tables 2 and 5, the cutting parameters optimized by the PSO algorithm are compared and analyzed. The result is shown in Table 11.

Table 11 Comparison of cutting parameters and results before and after optimization

By comparing the empirical cutting values in Table 11 with the optimized cutting values, it is noticeable that the RMS and roughness values of the cutting vibration are reduced with the optimized cutting parameters and compare to the empirical cutting amount RMS was reduced 36%, and the roughness was reduced 27%. The result shows that the cutting parameters optimized by the PSO optimization algorithm effectively reduce vibration and roughness.

5 Conclusions

The goal of this paper is to reduce the vibration of the CNC machine tool during the cutting process and improve the surface quality of the machined workpiece. In this paper, the vibration acquisition system was established. The vibration and roughness are proposed as the objective functions. MATLAB was used to fit the orthogonal experimental vibration and roughness data by the least-squares method, and the linear function mathematical models of the two objective functions were obtained.

Since multi-objective functions are often unable to achieve optimality at the same time, in this paper, the weighted coefficients and weights of the two objective functions were determined by the square weighting method and the analytic hierarchy process respectively. The objective function of the comprehensive objective was established.

The particle swarm optimization algorithm was used to optimize the cutting parameters of the comprehensive objective function. The optimized parameters, which include the spindle speed of 3 500 r/min, the cutting depth of 1.56 mm and the feed rate of 250 mm/min, reduced the RMS by 36%, the Ra by 27% and effectively reduced the vibration and surface roughness during the cutting process. This method provides a reference for the optimization and selection of milling machine milling parameters in practical engineering.