OPTIMIZATION OF CUTTING CONDITIONS FOR THE REDUCTION CUSP HEIGHT IN THE MILLING PROCESS

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1 OPTIMIZATION OF CUTTING CONDITIONS FOR THE REDUCTION CUSP HEIGHT IN THE MILLING PROCESS Abstract Ing. Jozef Stahovec Ing. Ladislav Kandráč Technical University of Košice Faculty of Mechanical Engineering Department of Technology and Materials Mäsiarska 74, Košice Slovak Republic The paper deals with a model for cusp height in the ball nose end milling process. The model for the mathematical prediction of the cusp height has been developed in terms of tool diameter, curvature of surface, axial and radial depth of cut. The application of the Design of Experiments technique by Taguchi method gives the process parameter s that lead to the minimum machining time and achieve a definite surface. Statistical software Minitab 16 was employed to process and evaluate of experimental data. Key words: milling, cutting conditions, cusp height, DOE. INTRODUCTION Shaped and sculptured surface are widely used in the design of complex product with moulds and dies features. These surfaces are often produced by 3 and 5-axis computer numerical control machine tools using ball nose end milling cutter. Chen et al. [1] presents the model, simulation and experimental verification of the scallop formation on the machined surface in the ball end milling process. The geometric shape and the dynamical change of the ball end cutting edges, path-interval scallop and feed-interval scallop are generated on the machined surface. Feng [2] states a new approach for the determination of efficient tool path in the machining of sculptured surfaces using 3-axis ball end nose milling. The objective is to keep the cusp height constant across the machined surface such that excess tool paths are minimized. Chuang [3] studies the cusp height dependent by the z- level depth and slope of the part surface. Kim [4] introduces a new approach of generating constant cusp height tool paths, he shows the suggested method, the deviation of cusp heights from an intended constant. Lee [5] expresses errors being estimated by comparing between the scallop heights of the offset curves and those of the tool paths. From the comparison, it is clear that the scallop heights are changed less than the given. Cusp height data of ball end nose milling from tab. 1 characterize the former and the latter. The factors which affect the surface finish in the ball nose end milling process are generally the cutting speed, feed rate, depth of cut and width of cut, etc. tab. 1 Cusp height data from ball nose end milling Type of surface Tool Cusp Source diameter height [mm] [mm] Concave surface 4 00 Chuang [3] Concave surface 9 06 Larigue [6] Convex and 5 91 Quinstat [7] concave surface Helicoidal surface Cao [8] Inclined surface 8 38 Iqbal [9] Plain surface Liu [10] Sculptured surface 6 04 Chen [1] Spherical surface 5 39 Mizugaki [11] Stamping dies López [12] CUSP HEIGHT In many milling operations, the cutting tool must perform step over and make several adjacent cuts to complete machining of any feature. As a result, a small cusp of material, called a cusp height, will remain between these cuts on the surrounding walls or on the machined surface if a ball nose end mill is used. The size of the step-over distance and the tool diameter will determine the cusp height between each step. Fig. 1 shows the generation the cusp height and base factors in this process. The data for experimental design is show in tab. 2. Fig. 1 Geometrical elements of machined surface To calculate theoretical cusp height: (1) To calculate effective diameter of ball nose end mill: (2) 244

2 Tab. 2 Experimental design matrix and results Control factors No. of Ex. a p [mm] a e [mm] Experimental Predicted Initial Improved Error model model , ,0777 0, , ,0756 0, , ,1012 0, , , , RESPONSE SURFACE METHOD Response surface method was used to establish the mathematical relationship between the response cusp height and the various machining parameters depth of cut, width of cut and radius of the work surface. Mathematical model based on the response surface of the second order was used to express effect of milling process on cusp height. Virtual machining was carried out in terms of the Taguchi L27 experimental design. Factors affecting the quality machined surface are show in Fig. 2. Taguchi designs are based on a fact that not all factors that cause variability can be controlled in practice and these uncontrollable factors are referred to as noise factors. Taguchi designs attempt to identify controllable factors (control factors) that minimize the effect of the noise factors. During experimentation, noise factors are manipulated to make variability occur and then to find optimal control factor settings that make the process or product robust, or resistant to variation from the noise factors. Fig. 3 shows the main effect plot form for milling of the variable shape of the machined surface. Basically, an increase in radial depth of cut makes the cusp height increase. Factors that affect the mean response are radial depth of cut, curvature of the machined surface and axial depth of cut shown in Fig. 3. Ball end mill Coating type Tool diameter D Tool edge geometry Machine tool Control Number of axis Precision Software Sculptured surface Definition Relationship Shape dimension Surface radius Input Process Milling sculptured surface Output Surface roughness Cusp height Cutting conditions Axial depth of cut ap Radial depth of cut ae Use of coolants Workpiece Machinability Microstructure Strenght Toughness Fig. 2 Factors affecting the quality of the product 245

3 Mean of Means Transfer inovácií 25/ ,07 0,07 Main Effects Plot for Means Data Means Fig. 3 Main effects plot for means by Taguchi The data given in the tab. 2 is analysed by using a software package MiniTab 16. The regression analysis and its coefficients are presented in tab. 3. Expressions in tab. 4 are used as the initial model and they include all the linear, square and interactions terms. The empirical equation for predicting the initial cusp height ch is: Response Table for means Level k[mm] ap[mm] ae[mm] ,07244 Delta Rank aims to determine whether a factor is significant; typically compare against an alpha of If the P- is lower than 0.05, then the factor is significant. Data from ANOVA are also used in the analysis of the regression and DOE. The initial model also indicates that the radius of the machined surface is insignificant factor for having less influence on cusp height. Tab. 4 Analysis of variance for cusp height Source DF Seq SS Adj SS Adj MS F P Regression ,43 0 Linear ,9 0 Square ,49 5 Interaction ,5 0,248 Res. Error Total Surface and contour plot of cusp height in Fig. 4 and 5 show the relation between two main factors, curvature of machined surface and a e which depend the cusp height resulting from milling. Surface Plot of vs ; Hold s 0,10 (3) Tab. 3 Estimated regression coefficients for ch Term Coef SE Coef T P Constant 0, , ,692 0,107 a e [mm] ,21 0 0, , ,203 5 a p [mm] ,548 0,138 * , ,558 9 a p [mm]*a p [mm] ,558 0,136 a e [mm]* , *a p [mm] -0,1671 0, ,566 0,134 S = PRESS = R-Sq = 85,04% R-Sq(pred) = 69,71% R-Sq(adj) = 79,52% R-Sq(adj) is indicating that our model can predict within 79,52 % accuracy. The empirical equation for predicting the improved cusp height ch is: (4) Analysis of variance (ANOVA) tab. 4 lists the sources of variation, their degrees of freedom, the total sum of squares, and the mean squares. The analysis of variance also includes the F-statistics and P-s. Use of these data is aimed to determine whether the predictors or factors are significantly related to the response. Use of the P 0,3 0,2 0,1 0,0 5 0,30 0,15 Fig. 4 Surface plot of cusp vs a e and k 0 0,75 0 1,25 Fig. 5 Contour plot of cusp vs a e and k The normal probability plot in Fig. 6 shows a clear pattern indicating that all the factors and their interaction given in tab. 3 are affecting the cusp height. The so called versus fits in Fig. 6 indicate that the maximum variation of - to, which shows the high correlation does exist between fitted and observed. Relations 1,50 1,5 Contour Plot of vs ; 1,75 < 0,08 0,08 0,10 > 0,

4 Frequency Cusp height Percent Transfer inovácií 25/ between various factors are shown in interaction plot for cusp height in Fig Normal Probability Plot Plots for Versus Fits The differences between measured and predicted responses cusp height for ball nose end milling process is illustrated in Fig. 9. 0, Fitted Value 0,08 0,08 6,0 4,5 Histogram Versus Order 3,0 1,5 0, Observation Order Fig. 6 plots for cusp height Experimental run 21 Variable ch measured ch predicted Interaction Plot for Data Means Fig. 7 Interaction plot for cusp height ANALYSIS FOR RESPONSE SURFACE OPTIMIZATION A desirability d means 0 d 1 and the of d increases as the "desirability" of the corresponding response increases. The factor settings with maximum desirability are considered to be the optimal parameter conditions. The optimization plot for surface roughness has been shown in Fig. 8. It is revealed that highest desirability could be obtained at mean curvature (0,2808 mm), mean depth of cut (626 mm) and low radial depth of cut ( mm). The goal was to minimize the cusp height (26 mm). The desirability of optimization has been calculated as 0 all the parameters are within their working range. Optimal D High Cur 000 Low Composite Desirability 000 Minimum y = 26 d = 000 Fig. 8 Optimization plot 0 0 [0,2808] [626] [0] Fig. 9 Comparison of measured and modeled s for the cusp height CONCLUSION Cusp height is the theoretical surface finish produced by successive tool paths made by a radius tool. Larger step over or a smaller cutter diameter produces a larger cusp height; i.e. a rougher finish. For the best surface finish, use the largest diameter tool possible at the lowest practical radial depth of cut. The use of today high-speed cutting technology makes it possible to increase federate and tooth feed without increasing machining time. The highest cusp height was achieved in joining circle. In finishing operations of sculptured surfaces by milling with 3 axis machines it is possible to achieve a better surface finish (roughness and cusp height) and a lower machining time using the traditional ball nose end mill. Advantage of RMS technique in comparison with Taguchi method is its possibility to model relationship between more factors and response variable not only in term of linear regression but also in square terms, as well as indicate the interaction among them see equation 3 and 4. References [1] CHEN J.-S., HUANG Y.-K., CHEN M.-S.: A study of the surface scallop generating mechanism in the ball-end milling process. (2005), International Journal of Machine Tools and Manufacture, Vol. 45, No. 9, pp ISSN [2] FENG H.-Y., HUIWEN L.: Constant scallopheight tool path generation for three-axis sculptured surface machining. (2002), Computer-Aided Design, Vol. 34, No. 9, pp ISSN [3] CHUANG C.-M., YAU H.-T.: A new approach to z-level contour machining of triangulated surface models using fillet endmills. (2005), 247

5 Computer Aided Design, Vol. 37, No. 10, pp ISSN [4] KIM T.: Constant cusp height tool paths as geodesic parallels on an abstract Riemannian manifold. (2007), Computer Aided Design, Vol. 39, No. 6, pp ISSN [5] LEE E.: Contour offset approach to spiral toolpath generation with constant scallop height. (2003), Computer Aided Design, Vol. 35, No. 6, pp ISSN [6] LARTIGUE C., THIEBAUT F., MAEKAWA T.: CNC tool path in terms of B-spline curves. (2001), Computer Aided Design, Vol. 33, No. 4, pp ISSN [7] QUINSAT Y., SABOURIN L., LARTIGUE C.: Surface topography in ball end milling process: Description of a 3D surface roughness parameter. (2008), Journal of Materials Processing Technology, Vol. 195, No. 1-3, pp ISSN [8] CAO L.-X., GONG H., LIU J.: The offset approach of machining free form surface: Part 1: Cylindrical cutter in five-axis NC machine tools. (2006), Journal of Materials Processing Technology, Vol. 174, No. 1-3, pp ISSN [9] IQBAL A., NING H., KHAN I., LIANG L., DAR N.U.: Modeling the effects of cutting parameters in MQL-employed finish hardmilling process using D-optimal method. (2008), Journal of Materials Processing Technology, Vol. 199, No. 1, pp ISSN [10] LIU N., LOFTUS M., WHITTEN A.: Surface finish visualisation in high speed, ball nose milling applications. (2005), International Journal of Machine Tools and Manufacture, Vol. 45, No. 10, pp ISSN [11] MIZUGAKI Y., KIKKAWA K., TERAI H., HAO M.: Theoretical estimation of machined surface profile based on cutting edge movement and tool orientation in ball-nosed end milling. (2003), CIRP Annals - Manufacturing Technology, Vol. 52, No. 1, pp ISSN [12] LÓPEZ DE LACALLE L.N., LAMIKIZ A., SÁNCHEZ J.A., ARANA J.L.: Improving the surface finish in high speed milling of stamping dies. (2002), Journal of Materials Processing Technology, Vol. 123, No. 2, pp ISSN Presented results have been achieved within 1/0500/12 VEGA Project: Research on Quality Improvement when Milling Formed Surfaces by Advanced Coated Tools, supported by Ministry of Education, Science, Research and Sports of Slovakia. 248