SELECTION OF DRILL FOR DRILLING WITH HIGH PRESSURE COOLANT USING ENTROPY AND COPRAS MCDM METHOD

Transcription

1 U.P.B. Sci. Bull., Series D, Vol. 79, Iss. 4, 2017 ISSN SELECTION OF DRILL FOR DRILLING WITH HIGH PRESSURE COOLANT USING ENTROPY AND COPRAS MCDM METHOD Jelea STANOJKOVIĆ 1, Miroslav RADOVANOVIĆ 2 The selectio of drill for drillig holes i a cocrete material is a very importat task. I this paper the selectio of solid carbide drills for drillig holes i alumium alloys with high pressure coolat usig the multi-criteria decisio makig methodology is preseted. The multi-criteria decisio makig method is applied usig CORPAS method, while for determiig the weight coefficiets the etropy method is used. Based o the four criteria (cuttig speed, feed per revolutio, pressure coolat ad machiig time) four alteratives were raked, carbide drills from differet maufacturers (Iscar, Sadvik, Seco ad Keametal). Keywords: Etropy, COPRAS, multi-criteria decisio makig, solid carbide drill. 1. Itroductio Drillig is a machiig process for creatig holes i a solid material. The mai rotary motio i drillig is the ruig of a tool (drill). Secodary traslatioal movemet is carried out by a tool or workpiece. The mai movemet is defied by cuttig speed or umber of revolutios at the machie tool, ad supported by the movemet of feed rate [1]. The most importat factor affectig the process of drillig is the temperature that occurs i the cuttig zoe. Icreased temperatures i the cuttig zoe may lead to rapid tool wear ad the formatio of chips. [1]. I order to reduce wear ad icrease life of cuttig tool coolats are used. Drillig with high pressure coolat ( bars) is commoly -used i cases where the depth is three times larger tha the diameter of the drill [2]. The selectio of solid carbide drill for drillig with high pressure coolat ca be made easier usig a multi-criteria decisio makig methods. The methodology of multiple criteria decisio makig is based o the structurig problems ad makig decisios. Multi-criteria decisio makig methods help the decisio makers to choose the best solutio based o the give criteria. Decisiomakig cosists of the followig steps: defiig a problem, determiig the goal, determiig the criteria ad alteratives, rakig the alteratives based o the give criteria ad decisio makig [3]. 1 Faculty of Mechaical Egieerig, Uiversity of Niš, Serbia, staokovic@masfak.i.ac.rs 2 Faculty of Mechaical Egieerig, Uiversity of Niš, Serbia, mirado@masfak.i.ac.rs

2 200 Jelea Staoković, Miroslav Radovaović I this paper, for solvig the problem of selectio solid carbide drills with high pressure coolat the etropy method is applied for determiig weight coefficiets ad COPRAS method for determiig the best alterative based o the give criteria. 2. Etropy method Before applyig the etropy method for determiig weight coefficiets is ecessary to defie alteratives ad criteria for the selectio of solid carbide drill for drillig with high pressure coolat. Table 1 presets four alteratives, solid carbide drills from differet maufacturers (Iscar, Sadvik, Seco, Keametal) ad four criteria, cuttig speed, feed per revolutio, pressure coolat ad machiig time. The goal is to choose a drill for drillig holes with high pressure coolat, which has a maimum cuttig speed, feed per revolutio, pressure coolat ad miimal machiig time. Table 1 Alteratives ad criteria Alterative Criteria C 1-ma C 2-ma C 3-ma C 4-mi Solid carbide drills Cuttig speed (m/mi) Feed per rev. (mm/rev) Pressure coolat (bar) Machiig time (s) A 1 SCD-ACG5 (Iscar) A 2 R840 (Sadvik) A 3 SD205A (Seco) A 4 B285(Keametal) Determiig the weight coefficiets based o the defied criteria usig the etropy method is performed by applyig i four steps: Step 1: Determiig the elemets of of ormalized decisio matri, while the equatio (1) [2, 4]: i ri, i 1,..., m, 1,..., (1) i1 i Where: i is the performace of the i-th alterative i relatio to the -th criteria, m is a umber of alteratives ad is a umber of criteria. Based o the equatio (1) ormalized decisio makig matri is show i Table 2 Table 2 Normalized decisio makig matri Alterative C 1 C 2 C 3 C 4 A A A A

3 Selectio of drill for drillig [ ] pressure coolat usig etropy ad COPRAS MCDM meth. 201 Step 2: Quatity of iformatio cotaied i the ormalized decisio matri ad broadcast by criteria ca be measured as the value of etropy e usig the equatio (2) [2]: e k m ri ri i1 l (2) Where: k 1/ l m is a costat which esures that the value of the etropy moves withi the iterval 0 e 1, ad m is the umber of alteratives. For selectio of solid carbide drill with high pressure coolat m=4 ad costat k=0.721, the value of the etropy of ormalized decisio makig matri is show i Table 3. Table 3 Value of etropy Value of etropy C 1 C 2 C 3 C 4 e Step 3: Determiig the degree of deviatio d from the average level of the iformatio cotaied i the values which are the alteratives described usig the equatio (3) [2]: d 1 e, 1,..., (3) If the value of d for a give criterio is higher, the importace of criteria for a give decisio problem is bigger. The degree of deviatio for the selectio of solid carbide drill is show i Table 4. Table 4 Degree of deviatio Degree of deviatio C 1 C 2 C 3 C 4 d Step 4: Determiig the weight coefficiets by usig equatio (4) [2, 4]. d w (4) d 1 Weights coefficiets for selectio of solid carbide drill for drillig with high pressure coolat is show i Table 4. Table 5 Weights coefficiets Weights coefficiets C 1 C 2 C 3 C 4 w COPRAS method COPRAS (COmple PRoportioal ASsessmet) method was developed by researchers of Vilius Gedimias Techical Uiversity, Zavadskas ad Kaklauskas [5]. COPRAS method meas the rakig based o the relative importace (weight) of each alterative. By usig this method determied the best alterative (solutio),

4 202 Jelea Staoković, Miroslav Radovaović takig ito accout the positive ad egative-ideal-a ideal solutio. COPRAS method cosists of si steps: Step 1: Determiig the decisio makig matri (4) [2]: X i m m m2 Where: i is the performace of the i-th alterative i relatio to the -th criteria, m- a umber of alteratives ad -a umber of criteria. Based o the Table 1., a decisio matri is defied (5). Each row refers to oe alterative, ad each colum to oe criterio Step 2: Normalized decisio makig matri usig the equatio (1), from the equatio ormalized matri is show i Table 1. Step 3: Difficult ormalized decisio makig matri represets ormalized the multiplicatio of the ormalized matri elemets of the colum with the appropriate weight coefficiets usig equatio (6) [2, 6]: v r w (6) 1 2 m (4) X (5) i Difficult ormalized decisio makig matri for a selectio drill for drillig with high pressure coolat is show i Table 6. The weight coefficiets are w= ( , , , ) previously determied usig the etropy method. Table 6 Difficult ormalized decisio makig matri A A A A Step 4: Determiig the sums of difficult ormalized values of alterative to the maimum criteria usig the equatio (7) ad miimum criteria usig the equatio (8) [2,6]: S i i v i 1 (7)

5 Selectio of drill for drillig [ ] pressure coolat usig etropy ad COPRAS MCDM meth. 203 S i v i 1 Sums of difficult ormalized values for maimum ad miimum criteria are give i Table 7. Table 7 Sums of difficult ormalized values Alterative S +i S -i A A A A The values of S+i ad S-i show level of achievemet of the goals of each alterative. The higher value of S+I, the alterative is better, as the lower value of the S-i ad alterative is better. Step 5: Determiig of the relative sigificace of alteratives over the utility fuctio Qi usig the equatio 9 [7], Table 8. Smi Si i1 Qi Si m S mi S i i1 Si Where: i=1,,m i S-mi represet the miimum value of S-i. m Values of the utility fuctio Alterative Q i A A A A (8) (9) Table 8 Step 6: Determiig the coefficiet of efficiecy alterative Ui, usig the equatio (10) [2, 7]: Qi U 100% i (10) Qima ma Where Q i is the maimum value of the utility fuctio. Based o the coefficiet of efficiecy, rakig of alteratives is performed. Values coefficiet of efficiecy alterative is varyig from 0 to 100%. Efficiecy of alteratives for a selectio solid carbide drll for drillig with high pressure coolat is show i Table 9.

6 204 Jelea Staoković, Miroslav Radovaović Coefficiet of efficiecy ad rak Alterative Ui Rak A A A A Table 9 Base o the Table 9 the order of the alteratives is A3-A1-A2-A4, which meas that i the first place it is a alterative A3, solid carbide drill SD205 of maufacturer Seco. 4. Coclusio Drillig with high pressure coolat is a ew approach i machiig techology. The selectio of solid carbide drill for drillig with high pressure was carried out usig CORPAS multi-criteria decisio-makig method ad etropy method for determiig the weight coefficiets. Drill maufacturers (Iscar, Sadvik, Seco ad Keametal) were used as selectio alteratives, while the selectio criteria were: cuttig speed, feed per revolutio, pressure coolat ad machiig time. Base o the defied criteria ad alteratives the first choice is drill SD205 (Seco), the SCD-ACG5 (Iscar), R840 (Sadvik) ad fially B285 (Keametal). Ackowledgemet The paper is a part of the research doe withi the proect TR The authors would like to thak to the Miistry of Educatio ad Sciece, Republic of Serbia. R E F E R E N C E S [1]. H. Zoussef, H. El-Hofy, Machiig Techology, Machie Tools ad Operatios, CRC Press, Taylor ad Fracis Group, Boca Rato, Florida, USA, [2]. M. Madić, B. Nedić ad M. Radovaović, Busiess ad Egieerig Decisio Makig by Usig Multi-Criteria Decisio Makig Methods, Faculty of Egieerig, Uiversity of Kraguevac, [3]. S. Duraira, K. Sathiyasekar, M. Ilagkumara, Selectio of Alterate Fuel for Electrical Power Geeratio Usig Hybrid Multi Criteria Decisio Makig Techique, UPB Sci. Bull., Series C, vol. 78, o. 1, 2016, pp [4]. M. Milić, G. Župac, Subective Approach to the Determiatio of Criteria Weights Determiig the weight criteria, Military of Techical Courier, vol. 29, o. 2, 2012., pp [5]. E. K. Zavadskas, A. Kaklauskas, V. Sarka, The ew Method of multicriteria comple proportioal assessmet of proect, Techological ad Ecoomic Developmet of Ecoomy, vol. 1, o. 3, 1994, pp [6]. V. Podvezko, The Comparative Aalysis od MCDA methods SAW ad COPRAS, Egieerig Ecoomics, vol. 22, o. 2, 2011, pp [7]. S. H. Youlfai, N. Rezaeiiza, M. H. Aghdaie, E. K. Zavadskas, Quality Cotrol Maager Selectio Based o AHP COPRAS G Method: A Case i Ira, Ecoomic Research, vol. 25, o. 1, 2012, pp