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Optimization of process parameters for CN turning of Al7075-T6 using RSM and GA to minimize the vibration amplitude.


In the last three decades or so, there have been magnificent improvements and technical revolutions in manufacturing industries, namely computer integrated manufacturing process, robot controlled machining processes, and others. Today customer demands high quality products for lowest possible price. To achieve such goals the manufacturers are focusing on the technical problems namely, how to achieve uninterrupted automated machining process for longer duration with least human supervision.

Turning operations are one of the most significant manufacturing processes in metal-cutting operations. In industry, manufacturing processes are planned and improved in order to obtain either maximum quality or minimum cost. The phenomenon of vibration is an inextricable part of any machining processes and modern machine shops are well aware of its detrimental effects. Uncontrolled vibration can destabilize a machining process and in extreme situations lead to chatter with severe implications for quality, tool life and process capability. During a metal turning process, complex dynamic interaction takes place at the interface between the workpiece and the cutter. As a result, chatter may occur. Analytical solutions for turning chatter are mostly based on the regenerative chatter mechanism: as the cutter encounters a wavy surface of a workpiece left from the previous cut, the undulations generated in the previous revolution affect the cutter-workpiece vibration and may cause dynamic instability. The need for high technology in machining has greatly accelerated the development of optical control and adaptive control systems. There may be several different purposes for such a control scheme, but one of the main objectives is to decrease the relative vibratory motion between the workpiece and the cutting tool. The results are an increase in machine tool stability and an improvement in workpiece geometry. The self-excited vibration, called chatter, is one of the main limitation in metal removal processes. Chatter may spoil the surface of the part and can also cause large reduction in the life of the different components of the machine tool including the cutting tool itself. The last several techniques have been proposed to suppress chatter. The appearance of chatter on machine tools is disastrous since they prevent from obtaining the required surface finishes and decrease the life of tools and mechanical components. These vibration occurs in a wide range of machining operations and is still one of the major limitation for productivity. The recent advances in industry, especially aerospace, mould and automotive sectors, have encouraged a considerable evolution in machine tools, which became more powerful, precise, rigid and automatic.

In turning process, three types of mechanical vibrations are present. They are free, forced and self-excited vibrations [17]. They occur due to lack of dynamic stiffness/rigidity of the machine tool system comprising tool, tool holder, workpiece and machine tool. Machining vibrations, also called as chatter, correspond to the relative movement between the workpiece and the cutting tool. These vibrations affect typical machining processes, such as turning, milling and drilling. Relative vibration amplitude between the workpiece and cutting tool influences the tool life.

In the present study, an investigation on vibration amplitude is undertaken in order to study its effect on stability in CNC turning process together with its predictive model from process parameters by way of response surface methodology. Several research analyses have been carried out on the vibration amplitude in turning using diverse tools, work materials and experimental methodologies. The literature survey pertaining to the work done by other researchers is given below.

The study would provide better understanding the concentrates on metal turning with the results from experiments using plane tool inserts analysed and presented the results of tests conducted using tool inserts with controlled chip contact chip-breaker were presented [8].A mathematical model based on the RSM was proposed for modeling and analyzing the vibration and surface roughness in the precision machining process with the diamond cutting tool [4, 7]. To determine whether only vibration signals can be used in in-process prediction of surface roughness during turning of Ti-6Al-4V alloy [19]. The author proposed, if only vibration signals are not able to provide good prediction then to select a set of significant cutting parameters and vibration signals to predict surface roughness with sufficient accuracy using multiple regression and artificial neural network technique. The feasibility of using an adaptive control algorithm to develop an active vibration control system based on piezo-actuators [7]. Determined how a cutting tool vibrates when chatter occurs and how this motion is related to the acoustic emission signal from [13]. The cutting instability using a 3 DOF model that incorporates; regenerative effect, cutting force and structural nonlinearities, simultaneous workpiece- tool vibration, and whirling induced by workpiece material inhomogeneity [1]. The Acoustic emission (AE) based tool wear condition monitoring in turning, which includes AE signal generation and correction in cutting processes, AE signal processing, and tool wear estimation reviewed from [20].The procedure for estimating the forcing function during chatter is developed, and the mechanism responsible for the transition from stable cutting to chatter is presented [3]. Elaboration of a surface roughness model in the case of hard turning by exploiting the response surface methodology. The author was highlighted optimal cutting condition and tool vibrations leading to the minimum surface roughness[16].

Studies have reported the deduction of Acceleration amplitude of various grades of aluminum alloy for a number of machining process but for the Acceleration amplitude in Al7075-T6 for CNC turning process in which very less research work has been accounted so far. The main objective of the work is to develop a mathematical model to predict the Acceleration amplitude in terms of process parameters such as nose radius of cutting tool, cutting speed, cutting feed, and depth of cut. The mathematical model helps us to study the direct and interactive effect of each of these process parameters.

The major evolution achieved in the current study is given below. A plan to devise the Acceleration amplitude in an Al7075-T6 aluminum alloy which has so far not attracted much get through in research. By formulating a mathematical model, it becomes realistic to appraise the effects of process parameters, selection of process parameters based on main and interaction effects of the process parameters with nominal Acceleration amplitude. The model for predicting Acceleration amplitude has been evolved by most researchers based on cutting parameters. But a holistic real model can be developed only by considering both tool geometrical and machining parameters. The present study focuses on the influence of the nose radius, cutting speed, cutting feed rate and depth of cut during machining on Acceleration amplitude. The optimization of CNC turning process parameters to acquire minimum Acceleration amplitude was done by genetic algorithms (GA). A MATLAB genetic algorithm solver was used to do the optimization.

2. Experimental Design:

In this study, geometrical parameter such as nose radius of cutting tool insert and machining parameters such as cutting speed, cutting feed rate and depth of cut have been considered as the process parameters for turning cutting condition monitoring, and the Acceleration amplitude is taken as a response variable. The response Acceleration amplitude can be expressed as a function of process parameter radial nose radius (R), cutting speed (V), cutting feed (f) and depth of cut ([a.sub.p]).

Acceleration amplitude [T.sub.a] = [phi] ([R.sub.iu], [V.sub.ciu, [f.sub.ziu], [a.sub.piu]) + [e.sub.u] (1)

where [phi] =response surface, [e.sub.u] =residual, u=no of observations in the factorial experiment, and iu represents level of the [] factor in the [] observation. To find out [phi] this function can be approximated satisfactorily within the experimental region by process parameter variables. The proposed central composite rotatable design for fitting a second-order response surface based on the criterion of rotatability [6]. The chosen design scheme [14] selection consists of 31 experiments. It is four factors--five level central composite rotatable design structure of 31 sets of coded conditions. The design for the above said experiment comprises of a half replication of 25 (=16) factorial design plus 7 center points and 10 star points. These correspond to first 16 rows, the last 6 rows, and rows from 17 to 26, respectively, in the design plan shown. For half replicate, the addition point embraced to form a central composite design, a becomes 2(k-1)/4=2 The upper limitof the parameter is coded as 2; lower limit, as -2; and the coded values for intermediate values were calculated from the following relationship [14,15]:

[X.sub.i] = 2 (2X - ([X.sub.max] + [X.sub.min])) / ([X.sub.max] - [X.sub.max]) (2)

Where [X.sub.i] is the required coded value of a variable X. X is any value of the variable from [X.sub.min] to [X.sub.max]. The selected process parameters with their limits and notations are given in Table 1. All machining variables at the intermediate (0) level constitute the center points while the combination of each variable at either its lower value (-2) or its higher value (+2) with the other two parameters at the intermediate level constitute the star points [14,15].

3.Experimental Setup:

Jyoti DX200 CNC turning center machine tool used in the experiments with different nose radius coated carbide insert under dry conditions. It has a high degree of an accuracy and rigidity.

The dimension of the work piece specimen AL7075 T6 used in this study was dia 50 mm round bar and 100 mm in length. The chemical composition of Al7075-T6 aluminum alloy is shown in Table 2.

3.1. Work piece material, machine tool, cutting tool and measurement:

In this study, AL7075-T6 aluminum was used as the work piece material. The turning tests were carried out by using a Jyoti DX200 model CNC turning center that is equipped with a maximumspindle speed of 4000 rpm and a 12-kW drive motor. The cutting tool material selected for the machining trials was TiAlN coated carbide via a physical vapor deposition (PVD). Commercial grade inserts of Sandvik Coromant and PSBNR 2020 K12 mechanically tool holder were selected with tool geometry as follows corner radius 0.4mm, 0.6mm,0.8mm, 1 mm and 1.2mm. The vibration amplitude is measured by the A COCO-80 Real Time FFT Handheld data recorder Analyzer at three times runs to minimize the deviation. The average values of vibration amplitude the highest peak values were considered for analysis.

3.2. Cutting conditions and experimental design:

Cutting speed (Vc), feed rate (f), depth of cut (a) and cutting tool insert nose radius were considered as machining parameters. The values of cutting parameters were selected from the manufacturer's handbook recommended for the tested material. The cutting parameters and their levels are given in Table 3. Tests have been performed under dry cutting and was delivered to the interface of work piece-cutting tool.

3.3. Recording the response:

The vibration amplitude is measured with FFT analyzer (COCO 80). The acceleration amplitude is determined in the tool near to the tool insert. The data are acquired in the FFT analyzers and are tabulated to obtain the mathematical model (Table 3). Engineering Data Management (EDM) software received the digital vibration data form COCO-80 FFT Analyzer through the accelerometer. Figs. 1 and 2 represents the experimental data for the vibration signal waveform and spectrum obtained from the CoCo-FFT analyzer (Guide Manual 2009, 2004). The cutting conditions were: nose radius 1 mm; cutting speed 3500 rpm; feed rate 0.2 mm/rev; depth of cut 1 mm.

An accelerometer picks up with magnetic base one is attached to the turret station near cutting tool holder insert to sense the vibration. The signal absorbed by the accelerometer pick up is transferred to the FFT analyzer. The FFT analyzer is interfaced with a computer for vibration analysis in engineering data management software (EDM).

FFT analyzer and accelerometer setup is used for recording data, analysis and feedback.

A FFT analyzer (COCO 80), engineering data management analysis software and piezoelectric accelerometer (Model Number ABRO AB102-A, S/No AB1234) is used to measure the response of the acceleration. The accelerometer is used to collect vibration data generated by the cutting action of the work tool. The accelerator was mounted on the tool near to the tool insert. The data are acquired in the FFT analyzers and are tabulated to obtain the mathematical model (Table 5).

4. Development of Mathematical Model:

The quadratic polynomial, which relates response surface y and the process variable x under research, is


Where [[beta].sub.0] =constant, [[beta].sub.i] =linear term,[[beta].sub.ii] =quadratic term, and [[beta].sub.ij] =interaction term coefficient. The values of the coefficients of the polynomials were determined by the multiple regression method. Statistical softwares MiniTab16 and design expert software were used to calculate the values of these coefficients. As per this technique [18] second order mathematical model was developed by neglecting the insignificant coefficients. After determining the coefficients, the mathematical model is developed. The developed mathematical models are given as follows:

Acceleration amplitude


The adequacy of the model was tested using F and R ratio. According to ANOVA analysis, the calculated value of the F ratio of the model developed should not exceed the standard value of the F ratio for a desired level of confidence, i.e., 95 % and the calculated value of the R ratio of the model developed should exceed the standard tabulated value for the same confidence level. The model is acceptable only when these conditions are satisfied. From Table 4, it can be inferred that these conditions are satisfied. Hence, the developed model is adequate.

The normal probability plot of the residuals for Acceleration amplitude in Fig. 4 shows that the residuals lie reasonably close to a straight line, giving support that terms mentioned in the model are the only significant [18].


The mathematical model was used to predict tool Acceleration amplitude by substituting the respective values of the turning process parameters. The influence of the turning geometrical parameters and machining parameters on tool wear was analysed.

5.1 Main effect of machining parameter on tool Acceleration amplitude:

The direct effect of turning process parameters was studied by keeping all the machining parameters at the middle level. The parameter whose direct effect was excluded. Fig. 5 (a) shows the effect of, nose radius, cutting speed, cutting feed and depth of cut on Acceleration amplitude.

It can be seen From the Fig.5 (a), that as nose radius increases, Acceleration amplitude first rises to a peak value at nose radius of 0.8mm and the starts to decline. The reason for this decline of Acceleration amplitude with an increase of nose radius is due to the rise in the ploughing effect in the cutting zone. The ploughing effect leads to increasing more material side flow on the machined surface and also it provides smooth surface roughness [12].It can be seen from fig.5(b) that as cutting speed increases, the acceleration amplitude initially increases approaching a peak value at cutting speed of 2000rpm and then starts to decrease. The cutting speed has lesser influence on acceleration amplitude. It is explained from this figure that the acceleration amplitude decreases with the increase in cutting speed, machining turns out to be more adiabatic and the heat generated in the shear zone cannot be conducted away during the minimal span of time when the metal passes through the zone. Further it is identified that the rise in temperature softens the material leading to the grain boundary dislocation which in turn reduces the acceleration amplitude [9].

It can be seen from Fig. 5 (c), that as cutting feed increases, acceleration amplitude initially increase and approaches a value at a cutting feed rate of 0.04 mm/tooth and then begins to decreases. When operating aluminium at lower feed rates, which leads to the formation of a built-up edge, it will be generates the forced vibration, tears and galls on the machined surface. The feed rate produces effective results when combined with a large nose radius and higher cutting speed. It facilitates in removing the chip easily from cutting zone with the reduction of built up edge, chatter and cutting force [5].

From the Fig.5 (d), it can be inferred that increase in depth resulted in an increase of in acceleration amplitude on all levels. Higher the depth, higher contact length of the insert will get engaged which results in more vibration. Increase in depth of cut, the length of the contact area in the cutting length in the rotating direction is increased, which results in increased tool insert nose wear [9].

5.2 Optimization of acceleration amplitude:

The optimal selection of CNC turning process parameters should increase not only the function of cutting economics, but also the product quality and acceleration amplitude. In this work, optimum values of CNC turning process parameters are estimated by an optimization method. Therefore, the process parameters of CNC turning are decided in the standard optimization format that is solved by a numerical optimization algorithm. An objective function to be minimized is necessary to define the standard optimization problem. In CNC turning with different tool geometry acceleration amplitude, optimization problem can be expressed in the following:

Find: R, [V.sub.c], [f.sub.z], [a.sub.p]

Minimize: [] ([gamma], R, [V.sub.c], [f.sub.z], [a.sub.p])

With ranges of cutting parameters:

0.2mm [less than or equal to] [gamma] [less than or equal to] 1.2mm

2000rpm [less than or equal to] R [less than or equal to] 4000rpm

0.05mm/rev [less than or equal to] f [less than or equal to] 0.25mm/rev

0.5mm [less than or equal to] a [less than or equal to] 2.5mm (5)

Genetic algorithm (GA) solver, aglobal optimization technique, is used to solve the optimization problem resulted by Eq. (5). Genetic algorithm simulates the biological progression method. The solution of an optimization problem with genetic algorithm begins with a set of possible solutions or chromosomes that are randomly selected. The entire set of these chromosomes comprises a population. The chromosomes progress through numerous iterations or generations. Newer generations are produced employing the crossover and mutation method. Crossover comprises splitting two chromosomes and then joining one-half of each chromosome with the additional pair. Mutation includes tossing a sole bit of a chromosome. The chromosomes are then gauged using a definite fitness criteria and the best ones are reserved while the others are rejected. This procedure follows till one chromosome has the best fitness and is taken solution of the problem as the optimum [10,11].

The critical parameters of the Genetic algorithm are the size of the population, mutation rate and number of generations. In this work, population size of 20, Elit count 2, crossover fraction 0.8, mutation rate of 0.01, lower bound [-2 -2 -2 -2 -2], upper bound [2 2 2 2 2] and 100 generation are used [Matlab R2011]. Optimization history only up to 51 iterations is illustrated in Fig. 6.

Optimization problem in Eq. (5) is resolved without any constraint to examine the effect of numerous situations on optimum values of end mill process parameters. Fig.6. displays the results developed by running the Genetic algorithm (GA) solver for minimizing tool wear. The difference in the original curve is due to the search for the optimum solution.

From the fig.9 it is evident that the minimum tool wear occurs at 63rdgeneration and the value is 15.222142 mm/[sec.sup.2]. The Optimum values of the machining parameters is given as Nose radius - 0.6 mm

Cutting speed - 3500 rpm

Cutting Feed - 0.25 mm/rev

Depth of cut - 2 mm


In the present study response surface methodology and genetic algorithm have been utilized for determining optimum CNC turning cutting insert process parameter. This leads to minimum acceleration amplitude while turning Aluminum 7075-T6 with different tool insert nose radius. CNC turning process parameters such as nose radius, cutting speed, feed, depth of cut taken for conducting experiments. A regression model was developed for manipulating experimental measurements found from these acceleration amplitudes. The established RSM model was further coupled with an established genetic algorithm to find an optimum CNC turning process parameter projecting to the minimum acceleration amplitude value.

In addition to the results discussed above, the following conclusions can be summarized:

The acceleration amplitude of AL7075-T6 aluminum alloy can be computed effectively through the second-order quadratic model developed from this work. The direct and interactive effects of process parameters on acceleration amplitude within the range of investigation can be studied with ease from the central composite design.

The process parameters toward the desired acceleration amplitude that can be obtained from the mathematical model. A comparison is made between the predicted results and the experimental results. It was found that the deviation is well within the limit of 95% confidence level.

Acceleration amplitude is directly proportional to cutting feed rate and the axial depth of cut. The acceleration amplitude increases at low nose radius and decreases at high cutting speed. The nose radius, cutting speed and cutting feed are the dominant factors on the tool wear.

According to the CNC end milling process parameters employed in this research, the optimal process parameters for the minimal Acceleration amplitude are: Nose radius -0.6mm, cutting speed -3500rpm, cutting feed rate-0.25mm/rev, depth of cut -2mm. This work will provide an engineer who designs a machining center with a tool to predictthe Acceleration amplitude and also provide a guideline for industrial engineers to estimate the cutting performance of high-speed spindles during the design stage.


The author also wishes to thank CNC Precision industries, Coimbatore and special thanks to Mr. A. Sethupathy for technical assistance in machining.


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(1) M.Subramanian, (2) P.Janagarathinam, (3) T. Prakash, (4) V.S.Kaushik

(1) Professor, Department of Mechanical Engineering, SNS college of Technology, Coimbatore 641035, Tamil Nadu, India.

(2) Assistant Professor, Department of Mechanical Engineering, SNS college of Technology, Coimbatore 641035, Tamil Nadu, India.

(3) Associate Professor, Department of Mechanical Engineering, SNS college of Technology, Coimbatore 641035, Tamil Nadu, India.

(4) Assistant Professor, Department of Mechanical Engineering, SNS college of Technology, Coimbatore 641035, Tamil Nadu, India.

Received 28 February 2017; Accepted 22 March 2017; Available online 25 April 2017

Address For Correspondence: M. Subramanian, Professor, Department of Mechanical Engineering, SNS college of Technology, Coimbatore 641035, Tamil Nadu, India.

Mobile: +919942089517; E-mail:

Caption: Fig. 1: Waveform obtained from the COCO-80 real time FFT analyzer

Caption: Fig. 2: Spectrum obtained from the Coco-80 real time FFT analyzer

Caption: Fig. 3: A schematic diagram of the experimental set-uP

Caption: Fig. 4: Normal probability plot of residuals for Acceleration amplitude dat

Caption: Fig. 5: Main effect for response (Acceleration amplitude)

Caption: Fig. 6: Optimization history with generation for acceleration amplitude
Table 1: Factors and selected levels in turning experiments

Parameter            Units    Notation

Nose radius          Mm       R
Cutting speed        Rpm      [V.sub.c]
Cutting feed rate    mm/rev   [f.sub.z]
Axial depth of cut   Mm       [a.sub.p]

Parameter            Levels

                     -2     -1     0      1      2

Nose radius          0.4    0.6    0.8    1      1.2
Cutting speed        2000   2500   3000   3500   4000
Cutting feed rate    0.05   0.01   0.15   0.20   0.25
Axial depth of cut   0.5    1      1.5    2      2.5

Table 2: Chemical Composition of Al 7075--T6

Element       Al       Zn      Mg      Cu    Fe    Cr       Mn

Composition   87.1     5.1     2.1     1.2   Max   0.18     Max 0.3
%             - 91.4   - 6.1   - 2.9   - 2   0.5   - 0.28

Element       Ti    Si

Composition   Max   Max
%             0.2   0.4

Table 3: Experimental design-central composite design matrix

Trial No   Control factors     Response Acceleration amplitude

           R    Vc   fz   ap   Observed   Predicted   % of error
                               Value      value

1          -1   -1   -1   -1   9.7621     10.0704     3.0616
2          1    -1   -1   -1   35.9102    37.6722     4.6773
3          -1   1    -1   -1   27.2943    28.5350     4.3479
4          1    1    -1   -1   74.2954    71.8440     -3.4122
5          -1   -1   1    -1   4.0193     3.2652      -5.0960
6          1    -1   1    -1   21.9027    21.2970     -2.8440
7          -1   1    1    -1   19.9670    21.7298     8.1123
8          1    1    1    -1   54.2839    55.4688     2.1361
9          -1   -1   -1   1    23.5635    24.3874     3.3784
10         1    -1   -1   1    37.5470    35.9760     -4.3667
11         -1   1    -1   1    8.3927     8.1120      -3.4603
12         1    1    -1   1    33.7232    35.4078     4.7576
13         -1   -1   1    1    33.9172    35.4822     4.4106
14         1    -1   1    1    37.8109    37.5008     -0.8269
15         -1   1    1    1    18.9598    19.2068     1.2861
16         1    1    1    1    37.0489    36.9326     -0.3149
17         -2   0    0    0    2.0912     1.2836      -5.9191
18         2    0    0    0    44.7512    46.6112     3.9905
19         0    -2   0    0    12.9988    14.0380     5.4028
20         0    2    0    0    31.9215    31.9344     0.0405
21         0    0    -2   0    37.4267    39.5344     5.3313
22         0    0    2    0    32.8742    34.2540     4.0281
23         0    0    0    -2   37.6216    39.0038     3.5438
24         0    0    0    2    33.2001    34.7846     4.5552
25         0    0    0    0    38.1166    36.8942     -3.3132
26         0    0    0    0    35.8143    36.8942     2.9270
27         0    0    0    0    36.0904    36.8942     2.1786
28         0    0    0    0    36.1904    36.8942     1.9076
29         0    0    0    0    38.1166    36.8942     -3.3132
30         0    0    0    0    35.8143    36.8942     2.9270
31         0    0    0    0    38.1166    36.8942     -3.3132
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Author:Subramanian, P.; Janagarathinam, P.; Prakash, T.; Kaushik, V.S.
Publication:Advances in Natural and Applied Sciences
Article Type:Report
Geographic Code:9INDI
Date:Apr 1, 2017
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