In this research paper, user-friendly and accurate mathematical model for estimating the cost of end-milling of AISI D2 tool steel using Polycrystalline Cubic Boron Nitride (PCBN) cutting tool inserts is developed. Initially, the different components of machining cost were identified, followed by establishment of equations to determine their values. Then, the required experimental and non-experimental data were collected and the bottom-up approach was adopted for evaluating the cost of machining corresponding to each of fifteen experimental runs. The Response Surface Methodology (RSM) was used to develop the model in which the cost of machining is given as a function of the machining parameters; cutting speed, feed per tooth, and depth of cut, and expressed in Ringgit Malaysia per cubic cm (RM per cm)3. Analysis of Variance (ANOVA) was utilized to check the adequacy of the developed model. The developed model was found to be statistically adequate

A.N., Mustafizul Karim

Amin, A. K. M. Nurul

Mohamed, Elhadie

English

The International Islamic University Malaysia Repository

978-1-4577-1884-7/11/$26.00 ©2011 IEEE Cost Model for End-Milling of AISI D2 Tool Steel   Mohamed Elhadie, A. N. Mustafizul Karim, A. K. M. Nurul Amin Department of Manufacturing and Materials Engineering International Islamic University Malaysia  Kuala Lumpur, Malaysia mhadie22@yahoo.com, mustafizul@iiu.edu.my, akamin@iiu.edu.my   Abstract—In this research paper, user-friendly and accurate mathematical model for estimating the cost of end-milling of AISI D2 tool steel using Polycrystalline Cubic Boron Nitride (PCBN) cutting tool inserts is developed. Initially, the different components of machining cost were identified, followed by establishment of equations to determine their values. Then, the required experimental and non-experimental data were collected and the bottom-up approach was adopted for evaluating the cost of machining corresponding to each of fifteen experimental runs. The Response Surface Methodology (RSM) was used to develop the model in which the cost of machining is given as a function of the machining parameters; cutting speed, feed per tooth, and depth of cut, and expressed in Ringgit Malaysia per cubic cm (RM per cm)3. Analysis of Variance (ANOVA) was utilized to check the adequacy of the developed model. The developed model was found to be statistically adequate.   Keywords—machining cost; cost modeling; end-milling; RSM; AISI D2 tool steel.  I. INTRODUCTION With the advancement of technology, the problems of cost estimation, cost analysis and cost control have assumed great dominance in economic and engineering decisions. These factors are highly critical for the continued success of a manufacturing enterprise [1]. Cost estimates have several significant uses such as: to provide information to be used in establishing the selling prices [2].  Development of reliable cost models to estimate the cost of room temperature machining of AISI D2 tool steel at different levels of machining parameters; cutting speed, feed, and depth of cut, is a useful endeavor. Having cost models enables determining which cost elements contribute most to the cost; i.e. it can identify cost drivers. With cost model it is possible to determine the conditions that minimize cost (cost optimization).  In this research paper, the bottom-up and parametric cost estimation techniques were merged to develop a rather new technique that is free from the limitations of the parent techniques and inherits their advantages. The bottom-up and parametric cost estimation techniques are the most common in practice. They are the two main techniques from which several other techniques branch out [3].  The cost models found in the literature that can be used for estimating the cost of a machining run are generally less user-friendly, and having less capability to answer some important questions, beside this, they do not combine easiness-of-use with accuracy. These problems, through merging the bottom-up and parametric techniques, and modeling the cost of machining as a function of a small number of parameters for which data can be obtained rather easily, are efficiently solved.   II. OVERVIEW OF PAST MACHINING COST MODELS The past models of machining cost are generally descriptive; that is, they describe the cost components found in machining operations. This characteristic causes two problems: firstly, the model will be consisting of parameters for some of which data is not easy to obtain. Secondly, it will be consisting of many input parameters. Thus, it is not user-friendly. For instance, George E. D. [4] presented the following cost model which can be used to calculate the cost of an end-milling operation:  TmttC0t)Ttoolt(1mt100)opOHW(1100)mOHM(1601uC ++++++=        (1)  Cu = total unit cost, $         M = machine cost (depreciation, and maintenance, etc), $/h OHm = machine overhead (power, proportional share of building, taxes, insurance, etc), %       W = labor rate for operator, $/h      Ct = tool cost, $ OHop = operator overhead rate, %      tm = machining time ttool = tool changing time      T = tool life  t0 = time elements that are independent of tool life   Obviously, this model is not user-friendly for finding the cost of a particular operation (or a run). It contains around ten input parameters for which the user has to find data. Besides containing many input parameters, data for some of these input parameters are not easily obtainable. For instance, any particular value of tool life is accompanied with a particular value of consumed power. Obtaining data of this pair is not readily easy. The model developed in this paper contains only three input parameters. The values for these parameters are chosen by the user (independent).     Similar models (to the one presented by George E. D.) were proposed by Robert C. C. et al. [2], Gavriel S. [5], Geoffrey B. and Winston A. K. [6], and others.  III. RESEARCH METHODOLOGY The methodology of this research can be outlined in form of the following activities:  • Establishment of equations to evaluate the cost of removing a unit volume of material (RM per cm3).  • Collection of all the data (experimental and non-experimental) required for evaluation of machining cost.  • Evaluation of machining cost considering 25% utilization.  • Use of RSM to model the cost of machining. ANOVA tables were used to check the adequacy of the developed model.  A. Establishment of Equations for Evaluating the Cost of Machining In this research paper, the cost of machining is made up by the following cost components: operator cost, VMC depreciation cost, VMC maintenance cost, cost of electricity consumed by the VMC, tool edge cost, tool edge changing cost, and setup, loading, unloading, and teardown (SLUT) cost [2, 4, 5, 6].  Machining cost has been determined in terms of cost required to remove a unit volume of material (RM per cm3). Rather than evaluating the cost per component, determination of cost per unit volume of removed material can be more appropriate approach. Machining cost was evaluated considering a utilization level of 25%. This level of utilization is used in process-based facilities (e.g. job-shops). To reduce the truncation error, a long period (a span of one year) of production has been chosen for the calculation of machining cost.  During production time, the following activities are carried out: machine setup, work-piece loading, material removing, tool changing, work-piece unloading, and machine teardown. At 25% utilization, the production time per working day is 120 minutes (8 * 60 * 0.25). Out of these 120 minutes, 15 are used for setup, loading, unloading, and teardown (SLUT). These 15 minutes are equivalent to 3.125% ((15 / (8 * 60)) * 100) of the working day. The remaining working time in a day at 25% utilization level is (120 - 15) = 105 minutes. These 105 minutes are equivalent to 21.875% (25% - 3.125%) of the 8-hours working day. These 105 minutes are used for material removing and tool changing only.  In the established equations, the cost per cm3 is obtained through dividing the yearly expense (RM) on a particular cost component by the yearly volume of removed material (cm3). Based on this, the equation established to calculate operator’s cost per cm3 is as follows: =yr3cmper Year  VMR/ yrRMper Year Salary  sOperator' 3cmRM 3cm per Cost Operator                                           (2)  The volume of material removed (VMR) per year is calculated as follows: ( )( )( )( ) +=min3cm MRR*min  LifeTool                             *min Time Changing Tool LifeTool / )yrminK *60*8*(250 yr3cm Year perVMR                                            (3)  K = 0.21875 (as elaborated above).  The VMC depreciation cost per cm3 is obtained by the following equations: =yr3cmper Year  VMR/yrRMAnnuity  VMC 3cmRM 3cm per Cost onDepreciati      VMC                     (4)  The Annuity is calculated as follows: 1))ni)/((1ni)  (1 (i *PAnnuity −++=                               (5)  P = initial expenses of the VMC        i = cost of capital           n = useful life of the VMC  The cost of electricity consumed by the VMC per cm3 is obtained by the following equation: =hr3cm MRR / hrRMper Hour  VMC by the Consumedy Electricit 3cmRM 3cm per Cost yElectricit     VMC                           (6)  The VMC maintenance cost per cm3 is obtained in a way similar to that of the operator’s cost per cm3; this is through dividing the yearly expense on maintenance by the VMR per year.      The tool edge cost per cm3 is given by the following equation:( ) ( )min3cm MRR*min  LifeTool / (RM)  EdgeToolper Cost  =3cmRM 3cm per Cost Edge Tool                    The tool edge changing cost per cm3 is given by the following equation: ( )( )+=minRM minper Cost   Machine minRM minper Cost Operator *min3cm MRR*min  LifeToolmin Time Changing  EdgeTool                                  3cmRM3cm per Cost Changing Edge Tool Operator cost per minute is given by the following equation:= Utilizati* 60 * 8 * 250/yrRMper Year Cost  sOperator'  minRM Minute per Cost Opertaor                       The machine cost per minute is given by the following equation: +=minRM per Minute VMCby  Consumedity   Electric          yrmin on Utilizati60 * 8 * 250per Year Cost  ce MaintenanVMCyrRMAnnuity  VMC                               minRM Minute per Cost Machine Finally, setup, loading, unloading, and teardown (SLUT) cost per cm3 is given by the following equation:( )( )( ) ( ) ++   MRR*min  LifeTool * (min) Time Changing  EdgeTool   LifeToolmin  K* 60 * 8 minper Cost   Machine minRM minper Cost Operator *min Time SLUT         3cmRM3cm per Cost Teardown and Unloading Loading, Setup,            (7)          (8)  yrmin on (9) +yrRM (10)  =min3cmminRM    (11) B. Data used for Evaluation of Machining CostThe data that were used to evaluate the cost of machining fall into two categories; experimental dataexperimental data. The non-experimental data are realistic assumptions and estimations. These data Tables 1 and 2.  Table I: The non-experimental data used for evaluating the cost of machining Item Operating days per year Operating hours per day Utilization Operator’s salary per year Initial expense of the VMC Useful life of the VMC  Cost of capital (%) Depreciation method Yearly expense on VMC maintenance Electricity tariff Price per edge of cutting tool Tool changing time Setup, loading, unloading, and teardown time  Table II: The experimental data used machining cost   C. Machining Cost Evaluated at 25%Machining cost was evaluated consideringlevel. The results are shown in Table          [7], and non-based on are shown in  Specification 250 8 of one shift  25% and 90% RM 33600  (RM 2800 * 12) RM 300000 15 years 5 Sinking fund RM 5000 RM 0.4 per kWh RM 15 5 minutes 15 minutes  for evaluation of    Utilization  25% utilization 3.    Table III: Machining cost evaluated at 25% utilization  The machining parameters and their values that are presented in Table 2 are the factors (input variables) in modeling the machining cost, while the machining cost values that apresented in the last column of Table 3 is the response IV. RESULTS AND DISCUSSIONThe Response Surface Methodology (RSM) developing the model. The software Design-Expert 6.0.8 was utilized for this purpose. In the developed modelcost is expressed in terms of the machining parametersspeed (v), feed (f), and depth of cut (d).   Analysis of variance (ANOVA) was used to test the adequacy of the developed model. The adequacy was verified at 95% confidence interval. ANOVA output includes statistics such as “Prob > F” and “lack of fit” values. These were used to examine the significance of the model and its terms. > F” value that is less than 0.05 generally indicates significance at 95% confidence interval. If it is greater than 0.05, this generally indicates insignificance. Various types of R2 were used to examine the prediction capability of the developed model. Higher values of R2 indicate that the model is capable of explaining higher percentages of variability in the response. The adequacy of the developed modelconfirmed by comparing the actual and predicted costs.  A. Formulation of Mathematical Model and Checking of Adequacy Model 1 was developed for estimating the cost of machining (RM per cm3) in room temperature endAISI D2 tool steel at 25% utilization using PCBN cutting tool inserts.  Log10(Machining Cost) = - 36.96332 + 1.10294 * 44.50876 * f + 3.35536 * d - 0.010668 * v2 + 44.22859 * 0.45071 * d2 - 48.70972 * f * d + 3.29433E-005 *  Model 1    re .  was used for , machining ; cutting “Prob  was  -milling of v + f2 - v3 The ANOVA output of Model indicates that this Model is statistically significant and fitting for exploring the design space at 95% confidence interval. Table IV: ANOVA output of Model 1  The “Prob > F” values of the Model and itswhich are “< 0.0001” and 0.9200, respectively, prove that the Model is statistically adequate.   All the terms of the model (except the term significant at the 95% confidence interval as indicated by their“Prob > F” values which are all less than 0.05. The term not significant, as indicated by its “Prob > F” value which is greater than 0.05. This term has been included in the Model because its removal adversely affects the adequacy of the model.  The "Pred R-Squared" of 0.9agreement with the "Adj R-Squared" of 0.9from each other); this indicates that there is no problem; neither with the data nor with the Model. value of 0.9895 indicates that the Model reas98.95% of the variability of the machining cost. The variation of the machining cost relative to the machining parameters is shown in Figure  1 (shown in Table 4)      “Lack-of-Fit” B2) are  B2 is 196 is in reasonable 756 (within 0.2 The “R-squared” onably explains  1.    Figure 1. Perturbation plot for machining cost By examining the equations that were established to calculate the values of the considered cost components, it can be seen that the cost of machining is influenced by three factors that vary with the machining parameters. These three factors are: tool life, material removal rate, and power consumption.   Tool life and material removal rate are located at the denominator of the cost components equations. Thus, as tool life and material removal rate increase, machining cost decreases. On the other hand, the cost of consumed power (RM per cm3) is a separate cost component that consists of the electricity cost per hour divided by material removal rate per hour. This cost component is added to the other components to obtain the cost of machining (RM per cm3). increase, the cost of machining increases, and viceeffect is opposite to the effect of tool life and material removal rate.  Generally, increase of cutting speed, tends to decrease the tool life, and this increases the cost of machining. On the other hand, as the cutting speed increases, material removal rate increases, this decreases the cost of machining. As cutting speed increases, the cost of consumed power might increase or decrease, thus, machining cost might decrease or increThese opposing effects result in a particular pattern of variation of machining cost relative to the machining parameters.  Machining cost, as demonstrated by Figure 1, increases as cutting speed increases. This continues up to a cutting speed of about 90 m/min, then, it decreases as cutting speed increases. Again, this continues up to a cutting speed of 130 m/min, then, it increases as cutting speed increases. The larger portion of the relation between machining cost and cutting speed is that machining cost decreases as cutting speed increases.   Thus, as it -versa. This ase.   Figure 1 indicates that the cost of feed and depth of cut increases. Machining cost, as demonstrated by Figure 1, appears to be very sensitive to cutting speed. Its sensitivity to the otless.  Figure 2 indicate that the interaction between feed and depth of cut is significant.   Figure 3 indicate that optimal values of machining cost are obtained when the feed and depth of cut are at their highest levels or close to them, while the cutting speed is kept constant at 110 m/min.   Figure 2. Response surface for machining costdepth of cut  Figure 3. Contour plot for machining costfeed  V. CONCLUSIONIn this research paper, usermathematical model to estimate the cost of endD2 tool steel using PCBN tool inserts is developed. This machining decreases as her two parameters is  vs. feed and   vs. depth of cut and  -friendly and accurate -milling AISI    model was developed based on 25% level of utilization. The ANOVA output indicated that the model is statistically adequate. For successful application of this model, it has to be used under the conditions that have been considered in developing it, such as the level of utilization, VMC initial expenses, operator’s salary, and so on. This model can be used in cost reduction programs, process selection, and establishment of selling prices.   REFERENCES  [1] Malstrom, E. M. (1984). Manufacturing Cost Engineering Handbook. Marcel Dekker, Inc. New York & Basel. [2] Crease, R. C., Adithan, M., & Pabla, B. S. (1992). Estimating and Costing for tthe Metal Manufacturing Industries. New York: Marcel Dekker, Inc.  [3] Toth, C. A. (2006). A Bottoms-Up Approach to Cost Estimation using Parametric Inputs. Master Dissertation, College of Engineering and Technology of Ohio University. [4] Dieter, G. E. (2000). Engineering Design: A Materials and Processing Approach (3rd Edn.). Singapore: Mcgraw-Hill. [5] Salvendy G. (2001). Handbook of Industrial Engineering. Canada: John Wiley & Sons, Inc. [6] Boothroyd, G., & Knight, W. A. (1989). Fundamentals of Machining and Machine Tools (2nd Edn.). New York: Marcel Dekker, Inc. [7] Lajis, M. A. (2009). Preheated Machining of Hardened Steel AISI D2 and Optimization of Parameters. Doctoral Dissertation, IIUM, Kuala Lumpur. [8] Esawi, A. M. K. & Ashby, M. F. (1998, May). Cost-Based Ranking for Manufacturing Process Selection. Proceedings of the Second International Conference on Integrated Design and Manufacturing in Mechanical Engineering, 4, 1001-1008. [9] Isakov, E. (2004). Engineering Formulas for Metal Cutting. New York: Industrial Press, Inc. [10] Jr., E. R. S. (1995). Precision Manufacturing Costing. New York: Marcel Dekker, Inc. [11] Safarah, N. Bt. Y. (2009). Cost Modeling for Preheated Machining of Difficult-to-Cut Materials. Final Year Project, IIUM, Kuala Lumpur. [12] Sullivan, W. G., Bontadelli, J. A., & Wicks, E. M. (2000). Engineering Economy (11th Edn.). New Jersy: Prentice-Hall, Inc.  

Cost Model for end-milling of AISI D2 tool steel

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Cost Model for end-milling of AISI D2 tool steel

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