International Journal of Mechanical ngineering and Technology (IJMT) Volume 9, Issue 1, January 018, pp. 64 63, Article ID: IJMT_09_01_067 Available online at http://www.iaeme.com/ijmt/issues.asp?jtype=ijmt&vtype=9&itype=1 ISSN Print: 0976-6340 and ISSN Online: 0976-6359 IAM Publication Scopus Indexed MATHMATICAL MODL DTMINATION FO SUFAC OUGHNSS DUING CNC ND MILLING OPATION ON 4CMO4 HADND STL Nexhat Qehaja, Fatlume Zhujani, Fitore Abdullahu* Faculty of Mechanical ngineering University of Prishtina, 1000 Prishtina, Kosovo * Corresponding Author mail: fitore.abdullahu@uni-pr.edu ABSTACT The most important measures of surface quality during the machining process is the average surface roughness (a), and it is mostly caused by many machining parameters, such as true rake angle and side cutting edge angle, cutting speed, feed rate, depth of cut, nose radius, machining time, material hardness, cutting fluid etc. This paper presents a study of development the surface roughness mathematical model during the end milling operation on hardened 4CrMo4 steel from 35 HC to 55 HC. The objective of this research is to analyze the effect of machining parameters on the surface roughness quality in CNC end milling. The milling parameters evaluated are spindle speed, feed rate, and depth of cut and workpiece material hardness. The experiment has been designed and carried out on the basis of a three level factorial design. The analysis of the results indicates that the optimal cutting parameters combination for good surface finish is high cutting speed and high depth of cut, as well as low feed rate and low material hardness. Key words: Cutting, Parameters, Milling, Hardness, Surface, oughness, Mathematical, Model Cite this Article: Nexhat Qehaja, Fatlume Zhujani, Fitore Abdullahu, Mathematical Model Determination for Surface oughness During CNC nd Milling Operation on 4CMO4 Hardened Steel, International Journal of Mechanical ngineering and Technology 9(1), 018, pp. 64 63. http://www.iaeme.com/ijmt/issues.asp?jtype=ijmt&vtype=9&itype=1 1. INTODUCTION Machining is one the major operation in manufacturing process in an industry to get finished goods. The quality of product is depends on the surface finish. To achieve optimum surface roughness with the constraint cost, time and available facility, the variables affecting surface finish need to studied. The machining variable speed, feed and depth of cut are the most influential machining parameters in milling operation. The other variables such as work piece material properties, tool wear, vibration, cutting fluid properties, are also affecting the surface http://www.iaeme.com/ijmt/index.asp 64 editor@iaeme.com
Mathematical Model Determination for Surface oughness During CNC nd Milling Operation on 4CMO4 Hardened Steel finish. The machining with end milling process is one the most widely used manufacturing process in an industry. The work reported for modelling of end milling process is mostly on machining parameters speed, feed and depth cut. It is also observed that conventional and advanced techniques and intelligent techniques are used for predicting the surface roughness [1]. The proposed methodology in the paper for modelling machining process using hardness of work piece material as input variable is a new approach in surface roughness modelling research []. The hardened work piece material selection for specific application is vital in industry. The main objective of using hardened die steel materials is to reduce as much as possible manufacturing time and cost so that surface roughness be at its lower value and with the aim of reducing finishing operation such as grinding, electrical discharge machining or manual polishing [3]. In order to get good surface quality, it is necessary to use optimization technique to find optimal machining parameters. This paper investigates the effect of four machining parameters on the quality of surface finish using SM (esponse Surface Methodology), multiple regression analyses and design of experiment (DO) method. The primary objective of this research is to develop a predictive mathematical relationship of the surface roughness for hardened Cr4Mo4 steel using HSV-C-4 flute carbide end mills in dry machining conditions, as a function of the cutting parameters such as cutting speed (m/min), feed rate (mm/rev), depth of cut (mm) and workpiece material hardness (HC).. SUFAC OUGHNSS AND ITS MASUMNT Surface oughness is a measurable surface characteristic quantifying high frequency deviations from an ideal surface. Usually measured in micrometers (μm), it is a subjective property incorporating appearance, smoothness, etc.[3]. It is usually described by the a - Arithmetic Average oughness. oughness averages are the most commonly used parameters because they provide a simple value for accept/reject decisions. Arithmetic average roughness, or a (formerly AA or CLA), is the arithmetic average height of roughness-component irregularities (peak heights and valleys) from the mean line, measured within the sampling cutoff length, L figure 1 [4]. Other common measures of surface roughness is q with the current term geometric average roughness for what was formerly called root-mean-square or MS. q is more sensitive to occasional highs and lows, making it a valuable complement to a. q is the geometric average height of roughness-component irregularities from the mean line measured within the sampling length, L. http://www.iaeme.com/ijmt/index.asp 65 editor@iaeme.com
Nexhat Qehaja, Fatlume Zhujani, Fitore Abdullahu Figure 1 Surface finish a Versus q [4] In general, a surface cannot be adequately described by its a or q values alone, since these are averages. Two surfaces could have the same roughness value, but quite different topographies. The process finish capability of a rough machining operation is about 0.05 mm and for finishing is about 0.005 mm. Note however that these values are affected by machining parameters and other factors. Measurement of surface roughness is usually accomplished through commercially available surface profilometers, the most common featuring a diamond stylus traveling over a surface. Additionally, it can also be observed directly through interferometry, either optical, Scanning-electron or Atomic-force microscopy. 3. DSIGN OF XPIMNT The experiment is performed to investigate the effect of one or more factors of process parameters on quality of surface finish. The parameters (factors) considered in this paper are cutting speed (v c ), feed rate (f),depth of cut (a) and hardness of workpiece material hardened at three levels (35; 45 and 55HC). The surface roughness was chosen as a target function (response, output). Since it is obvious that the effects of factors on the selected target function are nonlinear, an experiment with factors at three levels was set up (Table 1). A design matrix was constructed on the basis of the selected factors and factor levels (Table ). The selected design matrix was a full factorial design N= k +n 0 (k= 4- number of factors, n 0 = 8 number of additional tests for four factors) consisting of 4 rows of coded/natural factors, corresponding to the number of trials. This design provides a uniform distribution of experimental points within the selected experimental hyper-space and the experiment with high resolution. The factor ranges were chosen with different criteria for each factor, aiming at the widest possible range of values, in order to have a better utilization of the proposed models. At the http://www.iaeme.com/ijmt/index.asp 66 editor@iaeme.com
Mathematical Model Determination for Surface oughness During CNC nd Milling Operation on 4CMO4 Hardened Steel same time, the possibility of the mechanical system and manufacturer's recommendations are taken into account [5]. Machining conditions used in the experiment are shown in Table 1. All of the trials have been conducted on the same machine tool, with the same tool type and the same cutting conditions. 3.1. xperimental Setup Machine Tool: In the present work, a series of machining tests are carried out using CNC X.mill 900 KNUTH, P = 10 kw, speed range n = 8000 rpm, feed rate range: X=5-10000 mm/min, Y=5-10000 mm/min, Z = 5-1000 mm/min, Work table dimensions; X x Y x Z= 950 x 550 x 550.The machining processes are performed under dry conditions figure. Figure CNC X.mill 900 KNUTH Figure 3 Surface oughness Tester HADON, ST-610 Workpiece Material: 4CrMo4 steel for quenching and tempering according to DIN N 10083 hardened at three levels of hardness HC (35; 45 and 55), with dimensions L x B x H=300 x 10 x 50 mm. Heat treated at temperature 850-900 o C, cooled in the furnace to the temperature 450 o C and complete annealing the steel in the air. Its chemical composition is as follows:( 0.41-0.43)% C; (1.06-1.09%) Cr; (0.1-0.3%) Mo; (0.74-0.75)% Mn; 0.4-0.6% Si, (<0,034)S other components (Pb). Tensile: strength: 950-100 N/mm, Brinell hardness: 40-55 HB. Cutting Tools: xperiments were performed using commercially available HSV-C-4 flute Carbide nd Mills for Steel and High Temp. Alloys table 1. Table 1 Cutting tool data Cutter Diameter D 1 +.000" / -.00" Shank Diameter D (h6) Corner adius +.00" / -.00 Length of Cut L +.03" / -.000" Overall Length L1 +.06" / -.06 1 1.030 3 6 4 Flutes Surface oughness Measurement. The Centre line average (a) is commonly used for surface roughness measurement using HADON, ST-610 as shown in Figure 3. This device is a compact roughness measuring instrument for mobile use. http://www.iaeme.com/ijmt/index.asp 67 editor@iaeme.com
Nexhat Qehaja, Fatlume Zhujani, Fitore Abdullahu Other quipment s: Spectrometer Metorex Arc-met 930, Hardness meter Krautkramermic.10.DL. 3.. Selection of Levels for Process Variables In order to develop the surface roughness prediction model, four factors and three levels for each of them are selected. The selected process parameters for the experiment with their limits, units and notations are given in table. Table xperimental setup at three level factor. Cutting factors and their levels No. Factors Code level High level Middle level Low level 1 0-1 1 v c, m/min X 1 150 100 70 f, mm/rev X 0.08 0.05 0.03 3 a, mm X 3 1.5.1 3 4 HC X4 55 45 35 ntire experiment was carried out in the dry condition, during the turning process, and results are shown in table 3. Table 3 xperimental results of surface roughness Performance Coded factors Test No. measures X 0 X 1 X X 3 X 4 a(µm) 1 +1-1 -1-1 -1.057 +1-1 -1-1 1 7.384 3 +1-1 -1 1-1 3.185 4 +1-1 -1 1 1 6.16 5 +1-1 1-1 -1 5.418 6 +1-1 1-1 1 9.616 7 +1-1 1 1-1 3.84 8 +1-1 1 1 1 6.59 9 +1 1-1 -1-1 1.536 10 +1 1-1 -1 1 6.966 11 +1 1-1 1-1 3.855 1 +1 1-1 1 1 4.65 13 +1 1 1-1 -1 3.746 14 +1 1 1-1 1 8.589 15 +1 1 1 1-1 3.114 16 +1 1 1 1 1 5.588 17 +1 0 0 0 0 4.558 18 +1 0 0 0 0 6.053 19 +1 0 0 0 0 4.303 0 +1 0 0 0 0 5.031 1 +1 0 0 0 0 4.006 +1 0 0 0 0 5.43 3 +1 0 0 0 0 6.553 4 +1 0 0 0 0 5.345 4. GSSION BASD MODLING egression methods are among the first methods to be applied to the modeling of machining processes. Several machining processes, namely turning, milling, boring, and DM are investigated with these methods [6]. Furthermore, various aspects such as tool wear and tool condition monitoring, machinability, surface roughness and process cost estimation are analyzed. In several of these studies, the efficiency of a regression model is compared to that of soft computing methods, such as artificial neural networks (ANN). From the http://www.iaeme.com/ijmt/index.asp 68 editor@iaeme.com
Mathematical Model Determination for Surface oughness During CNC nd Milling Operation on 4CMO4 Hardened Steel aforementioned studies was concluded that, although regression methods exhibit their mathematical background and process a clear explanatory value, it is generally proven that that regression models can perform well when the relationships are almost linear[7], while the ANN give more accurate predictions also in complex, nonlinear case with a large number of variable [8]. Since multiple regression is used to determine the correlation between a criterion variable and a combination of predictor variables, the statistical multiple regression method is applied. It can be used to analyze data from any of the major quantitative research designs such as causal-comparative, correctional, and experimental. This method is also able to handle interval, ordinal, or categorical data and provide estimates both of the magnitude and statistical significance of the relationships between variables Therefore, multiple regression analysis will be useful to predict the criterion variable finish surface roughness via predictor variables such as feed rate, spindle speed, depth of cut and work piece material hardness [9]. This case study presents an example of using the SM methods for modeling of surface roughness of end milling process of hardened 4CrMo4 steel in dry machining. Obtaining the appropriate functional equations between the effects of the cutting process and adjustable parameters usually requires a large number of tests for different tool-workpiece configuration. The large number of experiments studies significantly increases the cost of experiment. A solution of this problem is mathematical and statistical tools for DO. Choosing the right tool remains at the knowledge of researcher, who must be aware of the benefits and limitations that arise from each potential method of approximation [10]. Among conventional DO techniques SM is widely used for machining process. xperiments based on SM technique relate to the determination of response surface based on general equation: Y=b 0 +b 1 x 1 + +b k x k +b1 x 1 x +b 13 x 1 x 3 + b k-1, k x k-1 x k +b 11 x 1 + +b kk x k (1) Generally, as proposed by many investigators, the tentative relationship between the machining responses and the machining variables for machining operations may take the nonlinear form [11,1]: = c v P f n a n () where c, p, m, n are constants to be predicted from the regression analysis using the experimental data. Four parameters were selected for this study: cutting speed (v c ), feed rate (f), depth of cut (a) and workpiece material hardness HC, therefore the q.() will appear as in the following: x y z a C vc f a H (3) where, a is arithmetic average roughness in (μm), v c - cutting speed in m/min, f - feed rate in mm/rev, a - depth of cut in mm and H-workpiece material hardness (HC), respectively C, x, y, z and δ are constants. Multiple linear regression models for surface roughness can be obtained by applying a logarithmic transformation that converts non-linear form of q. (3) into following linear mathematical form: http://www.iaeme.com/ijmt/index.asp 69 editor@iaeme.com
Nexhat Qehaja, Fatlume Zhujani, Fitore Abdullahu ln a lnc x lnv c y ln f z lna ln H (4) This form (4) can be linearized using the logarithmic transformation so that it takes the linearized form: Y p (5) 0x0 p1x1 px p3x3 p4x4 Where; Y = ln a ; X 0, X 1 = ln v c ; X = ln f; and X 3 = ln a, X 4 =lnh, respectively; y is the logarithmic value of surface roughness p 0, p 1, p, p 3, p 4, are regression coefficients to be estimated, x 0 is the unit vector, x 1, x, x 3,x 4, are the logarithmic values of cutting speed, feed rate, depth of cut, workpiece hardness and ε is the random error. The above equation in matrix form becomes: Y px (6) Thus, the least squares estimator of p is: ' 1 p ( X X ) X ' y (7) The fitted regression model is: Ý=X (8) The difference between the experimentally measured and the fitted values of response is: ε=y-ẏ (9) The regression analysis technique using least squares estimation was applied to compute the coefficients (p 0.p 1.p,p 3 and p 4 ) of the exponential model. For the analyzed example the final equation in terms of actual factors was determined, which determines the surface roughness from input factors, namely the machining parameters: a -0.15 0.36-0.106 1.706 0.0586 vc f a H (10) 4.1. Statistical Properties of the Model The analysis of the experimental data was performed to identify statistical significance for the parameters as cutting speed (Frv c =3.86), depth of cut (Fra=0.7), feed rate (Frf=14.64) and workpiece material hardness (Fr H =85.4) on the measured response roughness (a).the model was developed for 95% confidence level. The predictive mathematical model obtained (10) is adequate as it meet the condition[13]: s 0.0878016 F.970785955 F 3.57 (11) t s 0.0784718 Where; S n0 u1 y 0u n 1 n0 ( y ) 0u 0 u1 0.1949307, http://www.iaeme.com/ijmt/index.asp 630 editor@iaeme.com
Mathematical Model Determination for Surface oughness During CNC nd Milling Operation on 4CMO4 Hardened Steel respectively; s S f 0.1949307 0.0784718 7 (1) S S S 0.99736196, respectively; s s f 0.99736196 1 0.0878016 (13) N S Yeu Nbi 1.1876666 (14) u1 i0 k f f f N k 1 ( n0 1) 1 (15) F t =3.57 The value of F-distribution quantization table for; f (df 1 ) =1; f (df )=n o -1=7 and level of significance α=0.05 [14]. 5. SULTS AND DISCUSSION The obtained predictive mathematical model (10) shows the effect of four processing parameters on the predictive surface quality. According to presents 4 experimental results in table, it is observed that minimal value of surface roughness was obtained at cutting speed (150 m/min), feed rate (0,03 mm/rev), depth of cut (1.5 mm) work piece material hardness 35 HC (test No.9). Maximal value of surface roughness was registered at cutting speed (70 m/min), feed rate (0.08 mm/rev), depth of cut (1.5 mm) mm and material hardness 5 HC, (test No. 6). That means that good quality of surface roughness can be achieved at high speed and lower fed rate, depth of cut and work piece material hardness. 6. CONCLUSIONS Mathematical predictive models have become important for manufacturers to increase process efficiency and the quality of the produced parts. However, the direct implementation of existing performance predictive models for specific operations on the store floor is limited, as most of the models developed by the researchers are valid labs rather than the tried-and-tested store. In this case, surface roughness was studied by applying a full design of experiments on effective parameters that affect it. The investigations of this study indicate that work piece material hardness has maximum effect (1.706), followed by feed rate (0.33), cutting speed and depth of cut has minimum effect (0.101). By using analysis of variance for obtain the significant factors, it was distinguished that all main factors have significant effect on surface roughness except depth of cut. ACKNOWLDGMNTS http://www.iaeme.com/ijmt/index.asp 631 editor@iaeme.com
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