Considering Bearing Curves of Roughness on Face Mitled Surfaces ...

G, PETROPOALOS, C. PANDAZARAS,uDK 67e.8.057:62t.st4.2[l[l|--_-lI. STAMOS I II II ITC)tLIJU)r!tnIThe present contribution describes the statistical analysis <strong>of</strong> bearing (Abbott) curves <strong>of</strong> surfaceroughness prociuced by face milling <strong>of</strong> steel. <strong>Bearing</strong> curves parameters are found to closelycorrelate with feed rate and other surface texture parameters and to follow asymmetricaldistributions over milled surfaces, Furthermore, bearing curves cre modelled through Beta andP earson statistical systems.<strong>Considering</strong> <strong>Bearing</strong> <strong>Curves</strong> <strong>of</strong> <strong>Roughness</strong>on Face Mitled Surfaces <strong>of</strong> SteelKeywords: surface roughness, bearing curve and parameters, statistical distributions, Beta andPearson slstems, metal machining, face milling, corbon steels1. INTRODUCTIONMilling operations are among the most popularremoval processes in manufacturing industry.Especially, face milling is widely used in advancedmachine tools and systems (CNC, IMS etc), wherethere are high requirements for precise predictivemodels <strong>of</strong> basic machinability parameters. Such afactor is surface roughness seriously afflectingcomponents tribological performance [1-2].<strong>Roughness</strong> <strong>of</strong> engineering surfaces is expressed byvarious parameters, arithmetic and statistical. One <strong>of</strong>the latter is bearing area or Abbott curve; it providesrepresentation <strong>of</strong> the existing material in variousheights <strong>of</strong> the surface pr<strong>of</strong>ile and corresponds tocumulative probability <strong>of</strong> pr<strong>of</strong>ile amplitudedistribution. By virtue <strong>of</strong> being statistical, bearingcurves and corresponding parameters may describewell wear performance <strong>of</strong> surfaces under sliding andfeed surface contact models. On the other hand, theyare closely associated with the manufacturing processapplied and this is the reason why they areestablished in surface texture analysis in view <strong>of</strong> bothtribology and manufacturing science [3-4].In the present study the correlation between bearingparameters and cutting conditions is investigated inface milling <strong>of</strong> steel, as well as the relevant bearingcurves are represented and modelled via statisticalfunctions. Also, the statistical distributions <strong>of</strong> bearingG. Petropoulos,C. Pandazaras,L StomosDepctrtment <strong>of</strong> Mechanical and IndustrialEngineer ing, Univers ity <strong>of</strong> Thess alyPedion Areos, 38334 Volos, GREECEparameters over the milled surfaces are determined.The workpiece material was a Ck60 plain carbonsteel for different face milling designationsconsidered.2. EXPERIMENTAL PROCEDURE ANDANALYSISThe vertical knee type milling machine used is <strong>of</strong>medium size in very good working condition andpossessesufficient static and dynamic stiffness.Cubic specimens (40x40x40) mm' <strong>of</strong> Ck60 plainsteel were face milled.The cutting tools were sintered carbide P40 insertsmounted on a standardized five toothed millinqcutter <strong>of</strong> the following geometry:. diameter : 80mm. side angle : 60 "Special attention was paid for the tools to be keptsharp during the experiments.All experiments were carried out free <strong>of</strong> cutting fluid.Cutting conditions employed were: depth <strong>of</strong> cuta:0.5 mm, feed rate per tooth s, (0.16-0.60) mm rev' for z:I and (0.03-0..30) mm rev-' for z:5, cuttingspeed v (210) m min -'.The face milling configuration applied was that <strong>of</strong>approximate coincidence <strong>of</strong> cutter and workpiecegeometrical axes for two designations, namely onetooth (z:l) and five teeth (z:5) engagements.The paper wos published at Seventh YugoslavTribologt Conference YUTNB 2001Tribologt in industry, Volume23, No. 3&4, 2001.51

Surface texture measurements were carried outradialiy with respect to the cutter trace, as this is thedirection <strong>of</strong> chip thickness variation. A pr<strong>of</strong>ilometerwith a skidless pick-up was used. The cut <strong>of</strong>f length<strong>of</strong> the rolling filter was set at the range (0.8-2.0) mmdepending on feed rate value.The bearing ratio parameters considered were: Rtpzozand Rtpso%: representing the cross section <strong>of</strong> surfacematerial at the corresponding levels and they wereassessed through s<strong>of</strong>fware Talypr<strong>of</strong>. Analyticalbearing curves were calculated via Mathematica asintegrated functions <strong>of</strong> the Beta and Pearsonfunctions representing corresponding measuredroughness amplitude di stributions.The necessary statistical analysis <strong>of</strong> the results wasconducted via the commercial s<strong>of</strong>tware Statistica.Details on the interpretation and modelling <strong>of</strong>bearing curves according to Beta and Fisher-Pearsonfunctions are given elsewhere [5].3. RESULTS AND DISCUSSIONAs a general remark, roughness pr<strong>of</strong>iles in the case <strong>of</strong>the five toothed cutter, especially in the medium tohigh feed rate values, markedly deviate from theregular case appeared when cuttrng with one toothconsidering both shape and amplitude (Fig.1); also,r.vaviness is increased in the former case.An obvious explanation is that the significant threedimensional eccentricity <strong>of</strong> the cutter with z:5 isresponsible for this effect, as it induces vibration thatdeteriorates roughness amplitude and on the otherhand, successive teeth do not cut at the same depth orsome <strong>of</strong> them do not contribute at all to the surfacetopography; in consequence the generated pr<strong>of</strong>ilealthough periodic, is non regular compared to z:lt1l.4. CORRELATION OF BEARING RATIOPAII{METERSA very close correlation is revealed among bearingratio parameters and feed rate, Ru surface roughnessaverage and W. surface waviness average for the z:1cutter designation. Regarding z:5 cutter anincreasing trend is detected among bearing ratiosparameters and the aforementioned quantities,although correlation is fair but that was expectableowing to the very low feed rates and the smaller feedrate values range considered. Corresponding resultsare shown in Fies 2.3 and 4.35.030.025.0- 20.0t'15.010.0o Rtp20%1-aRtp507o,5.00.00 0.2 0.4 0.6 0.8s, [mm rev'l]Figure I a. Surface pr<strong>of</strong>ile machined with I toothedmill cutter (sr:0. I mm rev'' , v:2I0 m min-' )Figure 2a. Measurei Ro parameters for mill cutterwith I tooth against feed rate30.025.0A20.015.010.05.0AAo oo oooo Rtp20%a Rtp50%Figrre Ib. Surfoces pr<strong>of</strong>ile machined with 5 teethmill cutter (s,:0.1 mm reu-t, v:210 m min-t)0.00 0.1 0.2 0.3 0.4s, [mm rev't1Figure 2b. Measured R,, parameters for mill cutterwith 5 teeth againstfeed rate52 Tribolog,, in industry, Volume 23, No. 3&4' 2001.

35.030.025.0^ 20.0u15.010.05.0oAAoi; Rtpro* iia Rtp50% |0.00.0 1.0 2.0 3.0 4.0w. [um]Figure 3a. Measured R*for mill cutter with I toothversus roughness parameter Ro25.02 0.0F r s.o1 0.05.00.00.0 2.0 4.0 6.0 8.0Figure 3b,_ Measured R*for mill cutter with 5 teethversus roughness parameter Ro35.030.025.0o 20.0tr' 15.01n n5.0w' [Fm]Figure 4a. Measured R*Jbr mill cutter with I toothversus waviness parameter Wo30.025.020.015.010 05.06AAio o a ol-1IA0.0 lo0.0 5.0AooooR. [pm ]0.00.0 1.0 2.0 3.0 4.0aoow. [pmlFigure 4b. Measured R,<strong>of</strong>or mill cutter with 5 teethversus waviness porameter WnAAaoAAi1 0.0F Rtpro"/" Ii a Rtp507o lio Rtp20% 1,"Itp!%l5. DISTRIBUTION OF BEARING RATIOPARAMETERS OVER MILLED SURJACESThe distributions <strong>of</strong> bearing ratio parameters aremodelled after Fisher-Pearson statistical system <strong>of</strong>disturbances by 63J" form, see Fig. 5. This factindicates inhomogeneity <strong>of</strong> roughness ascharactertzed by bearing curves and is consistentwith relevant distributions <strong>of</strong> amplitude parametersR. and Rt t5l A possible explanation is thatroughness values are location dependent owing to thevariation <strong>of</strong> cutting force. The latter implies moreintense vibration and cutter run-out from the start <strong>of</strong>cut towards the cutting trace centre and vice versa.6. REPRESENTATION AND MODELLING OFBEARING CURVESIn Fig. 6 indicative results are presented formeasured curves in comparison to statisticalrepresentations (Fisher-Pearson and Beta functions).It is evident that there is a satisfactory agreementbetween experimental and calculated data. In thiswoy, bearing curves <strong>of</strong> face milled surfaces may bedescribed for ranges <strong>of</strong> cutting conditions byappropriate confrolling <strong>of</strong> the relevant statisticaldistributions parameters., - 1 A6t.a2'1.81.6o ,^E t.z.o4 0.8cG 0.60.40.2Figure 5a. Fisher -Pearson curve for Rp20(% to thewhole milled surfoce with mill cutter <strong>of</strong> I tooth'61A121EoI'gou€oo.Eloto+020Figure 5b. Fisher -Pearson curvefor R'020'% to thewhole milled surface with mill cutter oJ'5 teethTribolog,t in industry, Volume 230 No. 3&4 r 2001. 53