Cost Model for End-Milling of AISI D2 Tool Steel

Transcription

1 Cos Model for End-Milling of AISI D2 Tool Seel Mohamed Elhadie, A. N. Musafizul Karim, A. K. M. Nurul A Deparmen of Manufacuring and Maerials Engineering Inernaional Islamic Universiy Malaysia Kuala Lumpur, Malaysia mhadie22@yahoo.com, musafizul@iiu.edu.my, aka@iiu.edu.my Absrac In his research paper, user-friendly and accurae mahemaical model for esimaing he cos of end-milling of AISI D2 ool seel using Polycrysalline Cubic Boron Niride (PCBN) cuing ool insers is developed. Iniially, he differen componens of machining cos were idenified, followed by esablishmen of equaions o deere heir values. Then, he required experimenal and non-experimenal daa were colleced and he boom-up approach was adoped for evaluaing he cos of machining corresponding o each of fifeen experimenal runs. The Response Surface Mehodology (RSM) was used o develop he model in which he cos of machining is given as a funcion of he machining parameers; cuing speed, feed per ooh, and deph of cu, and expressed in Ringgi Malaysia per cubic ( per ). Analysis of Variance (ANOVA) was uilized o check he adequacy of he developed model. The developed model was found o be saisically adequae. Keywords machining cos; cos modeling; endmilling; RSM; AISI D2 ool seel. I. INTRODUCTION Wih he advancemen of echnology, he problems of cos esimaion, cos analysis and cos conrol have assumed grea doance in economic and engineering decisions. These facors are highly criical for he coninued success of a manufacuring enerprise [1]. Cos esimaes have several significan uses such as: o provide informaion o be used in esablishing he selling prices [2]. Developmen of reliable cos models o esimae he cos of room emperaure machining of AISI D2 ool seel a differen levels of machining parameers; cuing speed, feed, and deph of cu, is a useful endeavor. Having cos models enables deering which cos elemens conribue mos o he cos; i.e. i can idenify cos drivers. Wih cos model i is possible o deere he condiions ha imize cos (cos opimizaion). In his research paper, he boom-up and parameric cos esimaion echniques were merged o develop a raher new echnique ha is free from he limiaions of he paren echniques and inheris heir advanages. The boom-up and parameric cos esimaion echniques are he mos common in pracice. They are he wo main echniques from which several oher echniques branch ou []. The cos models found in he lieraure ha can be used for esimaing he cos of a machining run are generally less userfriendly, and having less capabiliy o answer some imporan quesions, beside his, hey do no combine easiness-of-use wih accuracy. These problems, hrough merging he boomup and parameric echniques, and modeling he cos of machining as a funcion of a small number of parameers for which daa can be obained raher easily, are efficienly solved. II. OVERVIEW OF PAST MACHINING COST MODELS The pas models of machining cos are generally descripive; ha is, hey describe he cos componens found in machining operaions. This characerisic causes wo problems: firsly, he model will be consising of parameers for some of which daa is no easy o obain. Secondly, i will be consising of many inpu parameers. Thus, i is no userfriendly. For insance, George E. D. [4] presened he following cos model which can be used o calculae he cos of an end-milling operaion: 1 M(1 + OH ) W(1 + OH ) m op ool C u + m (1 + ) C T C u oal uni cos, $ M machine cos (depreciaion, and mainenance, ec), $/h OH m machine overhead (power, proporional share of building, axes, insurance, ec), % W labor rae for operaor, $/h C ool cos, $ OH op operaor overhead rae, % m machining ime ool ool changing ime T ool life 0 ime elemens ha are independen of ool life Obviously, his model is no user-friendly for finding he cos of a paricular operaion (or a run). I conains around en inpu parameers for which he user has o find daa. Besides conaining many inpu parameers, daa for some of hese inpu parameers are no easily obainable. For insance, any paricular value of ool life is accompanied wih a paricular value of consumed power. Obaining daa of his pair is no readily easy. The model developed in his paper conains only hree inpu parameers. The values for hese parameers are chosen by he user (independen). m T (1) /11/$ IEEE

2 Similar models (o he one presened by George E. D.) were proposed by Rober C. C. e al. [2], Gavriel S. [5], Geoffrey B. and Winson A. K. [6], and ohers. III. RESEARCH METHODOLOGY The mehodology of his research can be oulined in form of he following aciviies: Esablishmen of equaions o evaluae he cos of removing a uni volume of maerial ( per ). Collecion of all he daa (experimenal and nonexperimenal) required for evaluaion of machining cos. Evaluaion of machining cos considering 25% uilizaion. Use of RSM o model he cos of machining. ANOVA ables were used o check he adequacy of he developed model. A. Esablishmen of Equaions for Evaluaing he Cos of Machining In his research paper, he cos of machining is made up by he following cos componens: operaor cos, VMC depreciaion cos, VMC mainenance cos, cos of elecriciy consumed by he VMC, ool edge cos, ool edge changing cos, and seup, loading, unloading, and eardown (SLUT) cos [2, 4, 5, 6]. Machining cos has been deered in erms of cos required o remove a uni volume of maerial ( per ). Raher han evaluaing he cos per componen, deeraion of cos per uni volume of removed maerial can be more appropriae approach. Machining cos was evaluaed considering a uilizaion level of 25%. This level of uilizaion is used in process-based faciliies (e.g. job-shops). To reduce he runcaion error, a long period (a span of one year) of producion has been chosen for he calculaion of machining cos. During producion ime, he following aciviies are carried ou: machine seup, work-piece loading, maerial removing, ool changing, work-piece unloading, and machine eardown. A 25% uilizaion, he producion ime per working day is 120 ues (8 * 60 * 0.25). Ou of hese 120 ues, 15 are used for seup, loading, unloading, and eardown (SLUT). These 15 ues are equivalen o.125% ((15 / (8 * 60)) * 100) of he working day. The remaining working ime in a day a 25% uilizaion level is (120-15) 105 ues. These 105 ues are equivalen o % (25% -.125%) of he 8- hours working day. These 105 ues are used for maerial removing and ool changing only. In he esablished equaions, he cos per is obained hrough dividing he yearly expense () on a paricular cos componen by he yearly volume of removed maerial ( ). Based on his, he equaion esablished o calculae operaor s cos per is as follows: Operaor Cos per Operaor' s Salary per Year / VMR per Year The volume of maerial removed (VMR) per year is calculaed as follows: (250 * 8 * 60 * K ) / Tool Life VMR per Year (( Tool Life + Tool ChangingTime)( ) ) ( ) * MRR K (as elaboraed above). The VMC depreciaion cos per is obained by he following equaions: VMC Depreciaion Cos per VMC Annuiy / VMR per Year The Annuiy is calculaed as follows: n n Annuiy P * (i (1 + i) /((1 + i) 1)) (5) P iniial expenses of he VMC i cos of capial n useful life of he VMC The cos of elecriciy consumed by he VMC per is obained by he following equaion: VMCElecriciy Cos per Elecriciy Consumed by he VMC per Hour hr / MRR hr The VMC mainenance cos per is obained in a way similar o ha of he operaor s cos per ; his is hrough dividing he yearly expense on mainenance by he VMR per year. * (2) () (4) (6)

3 The ool edge cos per is given by he following equaion: Tool Edge Cos per ( Cos per Tool Edge ())/ Tool Life ( ) * MRR n The ool edge changing cos per is given by equaion: Tool Edge Changing Cos per Tool Edge Changing Time Tool Life ( ) * MRR ( ) + M Operaor Cos per Machine Cos per Operaor cos per ue is given by he following equaion: Operaor Cos per Minue Operaor' s Cos per Year / * 250*8* 60* Uilizai ion The machine cos per ue is given by he following equaion: VMC Annuiy Machine Cos per Minue + VMC Mainenance Cos per Year 250*8* 60 Uilizaion Elecriciy Consumed by VMC per Minue Finally, seup, loading, unloading, and eardown (SLUT) cos per is given by he following equaion: Seup, Loading, Unloadingand Teardown Cos per SLUT Time ( ) * Tool Life + Tool ( 8*60* K)( ) Operaor Cos per + Machine Cos per Edge Changing Time () *Tool Life ( ) * MRR (7) he following + (8) (9) (10) (11) B. Daa used for Evaluaion of Machining Cos The daa ha were used o evaluae he cos of machining fall ino wo caegories; experimenal daa [7], and non- daa are based on experimenal daa. The non-experimenal realisic assumpions and esimaions. s. These daa are shown in Tables 1 and 2. Table I: The non-experimenal daaa used for evaluaing he cos of machining Iem Operaing days per year Operaing hours per day Uilizaion Operaor s salary per year Iniial expense of he VMC Useful life of he VMC Cos of capial (%) Depreciaion mehod Yearly expense on VMC mainenance Elecriciy ariff Price per edge of cuing ool Tool changing ime Seup, loading, unloading, and eardown ime Specificaion of one shif 25% and 90% 600 ( 2800 * 12) years 5 Sinking fund per kwh 15 5 ues 15 ues Table II: The experimenal daa used for evaluaion of machining cos C. Machining Cos Evaluaed a 25% Uilizaion Machining cos was evaluaed considering 25% uilizaion level. The resuls are shown in Table.

4 Table III: Machining cos evaluaed a 25% uilizaion The ANOVA oupu of Model 1 (shown in Table 4) indicaes ha his Model is saisically significan and fiing for exploring he design space a 95% confidence inerval. Table IV: ANOVA oupu of Model 1 The machining parameers and heir values ha are presened in Table 2 are he facors (inpu variables) in modeling he machining cos, while he machining cos values ha are presened in he las column of Table is he response. IV. RESULTS AND DISCUSSION The Response Surface Mehodology (RSM) was used for developing he model. The sofware Design-Exper was uilized for his purpose. In he developed model, machining cos is expressed in erms of he machining parameers; cuing speed (v), feed (f), and deph of cu (d). Analysis of variance (ANOVA) was used o es he adequacy of he developed model. The adequacy was verified a 95% confidence inerval. ANOVA oupu includes saisics such as Prob > F and lack of fi values. These were used o exae he significance of he model and is erms. Prob > F value ha is less han 0.05 generally indicaes significance a 95% confidence inerval. If i is greaer han 0.05, his generally indicaes insignificance. Various ypes of R 2 were used o exae he predicion capabiliy of he developed model. Higher values of R 2 indicae ha he model is capable of explaining higher percenages of variabiliy in he response. The adequacy of he developedd model was confirmed by comparing he acual and prediced coss. A. Formulaion of Mahemaical Model and Checking of Adequacy Model 1 was developed for esimaing he cos of machining ( per ) in room emperaure end-milling of AISI D2 ool seel a 25% uilizaion using PCBN cuing ool insers. The Prob > F values of he Model and is Lack-of-Fi which are < and , respecively, prove ha he Model is saisically adequae. All he erms of he model (excep he erm B 2 ) are significan a he 95% confidence inerval as indicaed by heir Prob > F values which are all less han The erm B 2 is no significan, as indicaed by is Prob > F value which is greaer han This erm has been included in he Model because is removal adversely affecs he adequacy of he model. The "Pred R-Squared" of is in reasonable agreemen wih he "Adj R-Squared" of (wihin 0.2 from each oher); his indicaes ha here is no problem; neiher wih he daa nor wih he Model. The R-squared value of indicaes ha he Model reasonably explains 98.95% of he variabiliy of he machining cos. The variaion of he machining cos relaive o he machining parameers is shown in Figure 1. Log 10 (Machining Cos) * v * f * d * v * f * d * f * d +.294E-005 * v Model 1

5 Figure 1 indicaes ha he cos of machining decreases as feed and deph of cu increases. Machining cos, as demonsraed by Figure 1, appears o be very sensiive o cuing speed. Is sensiiviy o he oher wo parameers is less. Figure 2 indicae ha he ineracion beween feed and deph of cu is significan. Figure indicae ha opimal values of machining cos are obained when he feed and deph of cu are a heir highes levels or close o hem, while he cuing speed is kep consan a 110 m/. Figure 1. Perurbaion plo for machining cos By exaing he equaions ha were esablished o calculae he values of he considered cos componens, i can be seen ha he cos of machining is influenced by hree facors ha vary wih he machining parameers. These hree facors are: ool life, maerial removal rae, and power consumpion. Tool life and maerial removal rae are locaed a he denoaor of he cos componens equaions. Thus, as ool life and maerial removal rae increase, machining cos decreases. On he oher hand, he cos of consumed power ( per ) is a separae cos componen ha consiss of he elecriciy cos per hour divided by maerial removal rae per hour. This cos componen is added o he oher componens o obain he cos of machining ( per ). Thus, as i increase, he cos of machining increases, and vice-versa. This effec is opposie o he effec of ool life and maerial removal rae. Figure 2. Response surface for machining cos vs. feed and deph of cu Generally, increase of cuing speed, ends o decrease he ool life, and his increases he cos of machining. On he oher hand, as he cuing speed increases, maerial removal rae increases, his decreases he cos of machining. As cuing speed increases, he cos of consumed power migh increase or decrease, hus, machining cos migh decreasee or increase. These opposing effecs resul in a paricular paern of variaion of machining cos relaive o he machining parameers. Machining cos, as demonsraed by Figure 1, increases as cuing speed increases. This coninues up o a cuing speed of abou 90 m/, hen, i decreases as cuing speed increases. Again, his coninues up o a cuing speed of 10 m/, hen, i increases as cuing speed increases. The larger porion of he relaion beween machining cos and cuing speed is ha machining cos decreases as cuing speed increases. Figure. Conour plo for machining cos vs. deph of cu and feed V. CONCLUSION In his research paper, user-friendly and accurae mahemaical model o esimae he cos of end-milling AISI D2 ool seel using PCBN ool insers is developed. This

6 model was developed based on 25% level of uilizaion. The ANOVA oupu indicaed ha he model is saisically adequae. For successful applicaion of his model, i has o be used under he condiions ha have been considered in developing i, such as he level of uilizaion, VMC iniial expenses, operaor s salary, and so on. This model can be used in cos reducion programs, process selecion, and esablishmen of selling prices. REFERENCES [1] Malsrom, E. M. (1984). Manufacuring Cos Engineering Handbook. Marcel Dekker, Inc. New York & Basel. [2] Crease, R. C., Adihan, M., & Pabla, B. S. (1992). Esimaing and Cosing for he Meal Manufacuring Indusries. New York: Marcel Dekker, Inc. [] Toh, C. A. (2006). A Booms-Up Approach o Cos Esimaion using Parameric Inpus. Maser Disseraion, College of Engineering and Technology of Ohio Universiy. [4] Dieer, G. E. (2000). Engineering Design: A Maerials and Processing Approach ( rd Edn.). Singapore: Mcgraw-Hill. [5] Salvendy G. (2001). Handbook of Indusrial Engineering. Canada: John Wiley & Sons, Inc. [6] Boohroyd, G., & Knigh, W. A. (1989). Fundamenals of Machining and Machine Tools (2 nd Edn.). New York: Marcel Dekker, Inc. [7] Lajis, M. A. (2009). Preheaed Machining of Hardened Seel AISI D2 and Opimizaion of Parameers. Docoral Disseraion, IIUM, Kuala Lumpur. [8] Esawi, A. M. K. & Ashby, M. F. (1998, May). Cos-Based Ranking for Manufacuring Process Selecion. Proceedings of he Second Inernaional Conference on Inegraed Design and Manufacuring in Mechanical Engineering, 4, [9] Isakov, E. (2004). Engineering Formulas for Meal Cuing. New York: Indusrial Press, Inc. [10] Jr., E. R. S. (1995). Precision Manufacuring Cosing. New York: Marcel Dekker, Inc. [11] Safarah, N. B. Y. (2009). Cos Modeling for Preheaed Machining of Difficul-o-Cu Maerials. Final Year Projec, IIUM, Kuala Lumpur. [12] Sullivan, W. G., Bonadelli, J. A., & Wicks, E. M. (2000). Engineering Economy (11 h Edn.). New Jersy: Prenice-Hall, Inc.