ࡱ> fhe`M Lbjbj== mWW:lVVV$z,&,&,&P|&@'zM()()))---LLLLLLL$O QLV-----L1))"M111-)V)L1-L1128nG 6VH) ( :zz,&/ H HM0M*HCR/CRH1zzmachining costs in grinding Ante Pavi, Borislav Josipovi, Marijan Brozovi Prof.dr.sc. A. Pavi, Polytechnic of Karlovac, I. Meatrovia 10, 47000 Karlovac M.Sc. B. Josipovic, lecturer, Polytechnic of Karlovac, I. Meatrovia 10, 47000 Karlovac M. Brozovi, lecturer, Polytechnic of Karlovac, I. Meatrovia 10, 47000 Karlovac Keywords: machining costs, grinding, dressing of grinding wheels Abstract Grinding is a very important and often used fine machining operation of precise parts in production engineering. Thus, the machining costs are an essential estimate criterion for grinding process applicability. In this paper the structure of the grinding costs is given and an aproach to their calculating as a example of externally cylindrical longitudinal grinding is derived. 1. INTRODUCTION In modern automatized production the fine machining operations application and NNST technology principles are increasing. Besides an increasing introduction of fine machining operations like micromilling, fine hard machining etc., machining by grinding will remain an important and often irreplaceable fine machining approach in future. This especially refers to workpieces from materials which are difficult to machine. The criteria for a valuation of grinding process applicability are: (1) workpiece machined surface quality (roughnes, measure accuracy, surface integrity), (2) grinding wheel tool life, (3) machining costs and (4) grinding process efficiency. In the grinding process optimisation the intent is that machining costs will be lower, by correct choice of cutting data with keeping required machining quality. Externally cylindrical longitudinal grinding will be described. 2. machining costs in grinding Maschining costs per one workpiece (or one operation) in grinding, like in machining by cutting tools with defined cutting geometry, contain the workplace costs KPM and the tool (grinding wheel) costs KA, [1,2]:  EMBED Equation.2  (01) The workplace costs are determined by formula [3]:  EMBED Equation.2  (02) In previous the formula it is: KML workplace work price per minute (grinding machine + operator costs), Kn/min. tk piece time (min):  EMBED Equation.3  (03) tt machining time ( min), tp auxiliary time( min),  EMBED Equation.3  (04) where: L total machining length (mm), no workpiece rev. per minute (rpm), fa axial feed (mm/rev. of workpiece), aeuk total depth of cut for grinding (mm), ae depth of cut per one stroke (mm), k coefficent for spark machine time. After a certain machining time it comes to wearing out of the grinding wheel which for this reason loses one part of its volume Vst. Now, it is necessary to dress the grinding wheel work area, for example by one point diamond dresser. In dressing the grinding wheel loses also one part of its volume Vsd. Therefore, total lost volume Vs of grinding wheel is:  EMBED Equation.3  (05) Therefore, tool costs KA are contain the costs KV i. e. grinding wheel lost volume costs in grinding process, and also the costs Kd of grinding wheel dressing in which the costs of grinding wheel lost volume and work costs in dressing, which makes:  EMBED Equation.3  (06) Grinding wheel lost volume costs: KV (Kn/piece) per one workpiece are calculated by the formula:  EMBED Equation.3  (07) where: Vs - total grinding wheel losst volume per tool life, i.e. between two dressings (mm3/tool life), kw costs per one mm3 of grind. wheel volume (Kn/mm3), zT - workpiece number per one tool life. Grinding wheel dressing costs per one workpiece are calculated according to the formula [1]:  EMBED Equation.3  (08) where: KML - workplace work price per minute (grinding machine + operator costs), Kn/min, ted - grinding wheel dressing time based on one workpiece (min/dressing), Vsd - grinding wheel lost volume during one dressing (mm3/dressing) , Kwd - cutting tool e.g. diamond dresser purchase price (Kn), zTd - total number of dressings which the diamond dresser can endure (total dresser life). Specific volume of removed material in externally cylindrical longitudinal grinding is:  EMBED Equation.3  (mm3/s), (09) where: Do workpiece diameter (mm), ae depth of cut per one stroke (mm), vfa grinding wheel rate of feed in the direction of workpiece axis (mm/s). By increasing the specific volume of the removed material in grinding, the following results: decreasing the cutting time tt, decreasing number the workpieces mT that can be machined during one tool life, increasing the dressing time per one workpiece ted (s/workpiece), increasing the dressing costs Kd per one workpiece. Grinding wheel sketch for calculating the volume loss Vs is given in Figure 1. Figure 1. Grinding wheel sketch Simbols in Figure 1: Db grinding wheel external diameter, Do - grinding wheel boring diameter, as total depth of grinding wheel lost layer on account of grinding and dressing per one tool life, asb depth of grinding wheel worn layer on account of grinding, asp - depth of grinding wheel worn out layer on account of dressing, B grinding wheel width, Db1 grinding wheel external diameter after end wear in grinding, Db2 grinding wheel external diameter after dressing. Grinding wheel volume which was lost in grinding is smaller and is usually: Vs = (0.1 to 0.2)"Vsd . Grinding wheel depth for dressing usually ranges from asp = 0.05 to 0.08 mm. Depth of grinding wheel to worn out layer on account of grinding is: asb H" 0.15"asp mm. Total depth which is removed from grinding wheel is: as = asp+asb H" 0.065+0.065"0.15 H" 0.08 mm Grinding wheel volume lost in grinding process is, in Figure 1:  EMBED Equation.3  (10) Grinding wheel diameter after end wear in grinding is: Db1 = Db - 2asb Grinding wheel volume loss in dressing is:  EMBED Equation.3  (11) Grinding wheel diameter after dressing is: Db2 = Db1 - 2asp, or Db2 = Db - 2as Grinding wheel radius is: Rb = 0.5Db It is known that the grinding wheel minimal allowed radius of wear is: Rmin = 0.65Rb Grinding wheel total number of dressings up to total wear is:  EMBED Equation.3  (12) The costs in Kn per 1 mm3 of grinding wheel volume are given according to the formula:  EMBED Equation.3  (13) where: Cb grinding wheel purchase price (Kn), Vbe grinding wheel effective volume (mm3). Grinding wheel effective volume is: Vbe = Vb - Vbmin.  EMBED Equation.3  EMBED Equation.3  Using the relation Dbmin = 0,65Db (at total worn out grinding wheel) it is finally:  EMBED Equation.3  (14) Acordingly, volume Vb of new grinding wheel is used up about 58 %. Grinding wheel volume is:  EMBED Equation.3  (mm3) (15) 3. grinding wheel dressing Workpiece number zT which can be machined in one tool life (workpieces/tool life):  EMBED Equation.3  (16) where: Tb - tool (grinding wheel) life (min), tt - cutting time (min). Grinding wheel tool life depends on of the kind grinding operation, and is according to [4]: - externally cylindrical long. grinding with tool exit and externally radial grinding: 40 min - externally long. grinding without tool exit: 30 min - flat circumference grinding: 25 min - internally grinding, flat face grinding and profile grinding: 10 min Cutting data by dressing of grinding wheels [4,5,6]: - cutting speed: vcd = 15 do 20 m/s, - total depth of cut by dresing: aed uk = asp = 0.05 do 0.1 mm - dresser axial feed speed: vfad = 150 do 300 mm/min - dresser axial feed per rev. of the grinding wheel: fad = 0.05 do 0.15 (max. 0.2) mm/rev. - dressing depth of cut per one double stroke of the dresser: aed = 0.02 do 0.03 mm/d.h. - in rough dressing aed = 0.005 do 0.010 mm/d.h. - in fine dressing Remark: rough dressing is used at coarse grain size and fine dressing at fine grain grinding wheels. Dressing is performed with 1 to 2 double strokes at depth of cut aed, and than 2 to 3 double stokes are added (on account of smoothing of the grinding wheel) without radial feed i.e. aed = 0. Total depth of the layer removed from the grinding wheel is up to 0.08 mm. If are given the dresser feed speed vfad and grinding wheel cutting speed in dressing vcd are given, giving the grinding wheel rotation speed in dressing nbd, it is possible to calculate the dresser longitudinal feed fad (mm/rev. wheel):  EMBED Equation.3  (17) where: vf - feed speed (m/min), nb - grinding wheel rotation speed in dressing (rev/min):  EMBED Equation.3  (rev/min) (18) Total time needed for grinding wheel dressing ted contains grinding wheel dressing time td (cutting time) and auxiliary time tpd needed for one dressing:  EMBED Equation.3  (min) (19) Cutting time contains grinding wheel dressing time with longitudinal feed and grinding wheel smoothing time, and it will be calculated by the formula:  EMBED Equation.3  (min) (20) where: l1 = l2 H" 6 do 12 mm - entry / exit of the dresser, ndb - grinding wheel number during dressing (rev/min), fad - dresser axial feed (mm/rev. of grinding wheel), i - total number of dresser passes. For example, if dressing is performed with 2 double strokes and 2 double strokes for smoothing (at the same feed fad) are added, than it is: i = 2(2 + 2(2 = 8 strokes. Smoothing time is included in added strokes for smothing. Grinding wheel work area roughness:  EMBED Equation.3  (mm) (21) where: rd (mm) diamond dresser nose radius. 3. Practical example and results In machining operation of externally cylindrical longitudinal grinding of workpiece 60.2x145 to dimension 600.01x145, it is needed to calculate machining costs. Given data: Total depth of cut: aeuk = 0,1 mm (from workpiece) Workpiece number in batch: zos = 100 Workpiece material: 42CrMo4, 264 HB Grinding wheel: 2A46/2J6V35 - dimensions: DbxBxDo = 500x40x203 mm Grinding wheel purchase price: Cb = 1686.00 Kn Grinding wheel tool life: Tb = 40 min Machine tool: Externally cylindrical grind. machine Workplace price per hour: KML = 400.00 Kn/h Set-up-end time: tpz = 30 min/lot Auxiliary time: tp = 0.92 min Coefficient of added time: kd = 0.2 Total machining length: L = 145 + 8 = 153 mm Depth of cut per stroke: ae = 0.02 mm/hod Diamond dresser purchase price: Kwd = 650,00 Kn Total number of dressings (4 edges): zTd = 1600 k coefficent of spark machine time: k = 1,2 In this example the standard case of externally cylindrical grinding with tolerance measure is given. Total depth of cut is 0.2 mm in diameter. The values needed for calculating according to sources [5,6,7] were accepted, and afterwards this by using the given formula the requisted values were obtained. The results are given in Tables 1. and 2. Workplace costs calcul. data are given in Table 1. Table 1. Workplace costs calculate data ValuesCutting speed: vc (m/s)30AcceptedWorkpiece speed:vo (m/min)20AcceptedWorkpiece diameter: Do (mm)60.2GivenAxial feed of grinding wheel:fa fa = 0.4B (mm/rev) 16[6]Depth of cut: ae (mm/stroke)0.02[6]Total depth of cut:aeuk (mm)0.1GivenCutting time: tt (min)1.08Form. 04Piece time: tk (min/piece) 2.4Form. 03Workplace costs: KPM (Kn/piece)16.00Form. 11 Tool costs calculate data are given in Table 2: Table 2. Tool costs calculate data ValuesTotal depth of cut by grinding wheel dresing: asp (mm)0.07AcceptedDepth of grinding wheel worn out layer: asb= 0,15asp (mm)0.105[6,7]Total depth removed from grind. wheel:as= asb+asp (mm) 0.0805[6,7]Total lost volume of grinding wheel per tool life: Vs (mm3)659.72Form. 10Total number of dresings to total grinding wheel wear: ip 1086 Form. 12Grinding wheel volume loss in dressing: Vsd (mm3) 4397.4Form. 11Costs per one mm3 of grind. wheel volume: kw (Kn/mm3) 4410-5 Form. 13Grinding wheel vol.: Vb (mm3)6.56106 Form. 15Grinding wheel effective vol: Vbe = 0,58Vb (mm3)3.8106 [6,7]Workpiece number machined in one tool life: zT (pieces)37Form. 16Grinding wheel dressing speed: vcd (m/s)18AcceptedNumber of strokes in dressing i = 8 (4 rough + 4 fine)8AcceptedDressing time: td (min) 3.87Form. 20Total dressing time: ted (min) 4.37Form. 19Dressing costs: Kd (Kn/piece)0.857Form. 08Grinding wheel lost volume costs: KV (Kn/piece)0.00785Form. 07Total tool costs KA (Kn/piece)0.8586Form. 06 Total machining costs of the grinding: KO = KPM + KA = 16.00+0.8586 = 16.86 Kn/piece Total machining costs for batch: KOU = KOzos = 16.86100 = 1686.00 (Kn/batch) The histogram of the obtained results of machining costs is presented in Figure 2.  EMBED MSGraph.Chart.8 \s  Figure 2. Histogram of machining costs KPM  workplace costs, KA  tool costs It is possible to sum up that the calculation of the grinding machining costs is very difficult. The reason for this is specific grinding process affected by lot of influencing factors. The shares of individuel cost are similer to those in the machining methods performed with a geometrically defined edge, where share of the cutting tool costs is about 3 to 5 % in the total machining costs. 4. CONCLUSION Based on obtained results, it is possible to conclude the folloving: - in cutting tool costs the part of grinding wheel dressing costs are 99 % and grinding wheel lost volume costs are about 1 %. - in total machining costs of grinding operation, the workplace costs are about 95 %, and cutting tool costs about 5 %. - for the practical calculating of machining costs in grinding, it is needed to have many exact input data about grinding process, grinding wheel and diamond dresser. 5. REFERENCES [1] Fritz, A. H.; Schulze, G., 1998, Fertigungstechnik, Springer Verlag. [2] Cebalo, R., 2000, Obrada odvajanjem estica, own edition. [3] Knig, W.; Klocke, F., 1981, Fertigungsverfahren  Band 1, Drehen, Frsen, Bohren, VDI Verlag. [4] Velikanov, K.M., 1989, Ras eti ekonomi eskoj efektivnosti novoj tehniki, Maainostroenie. [5] Lochmann, K.: Fertigungstechnik (Formeln), 2001, Hanser Fachbuchverlag. [6] Tschtsch, H.: Praxiswissen Zerspantechnik, 1997, Vieweg Verlag. [7] Schnherr, H.: Spanende Fertigung, 2002, Oldenburg Verlag.     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