B. J. Griffiths R. J. Grieve Department of Manufacturing and Engineering Systems, Brunei University, England Modelling Complex Force Systems, Part 2: A Decomposition of the Pad Forces in Deep Drilling 1 Introduction This paper is a continuation of the earlier Part 1 paper [1] in which it was shown that the force system existing during a deep hole drilling operation was complex (see Fig. 1) and indeterminate using a single dynamometer approach. However, by using complementary dynamometers in conjunction with a force relationship to model the radial and tangential pad forces (Fig. 2) the system could be analyzed. As a result, the following forces were determined: (a) The cutting force system (PT PF PR) (b) The total force system at each pad (Rt, R2, ixR\, iiR2, HLRU ULRI) (c) The radial forces at each pad (Fm, FR2t Bm, BR2) In this paper the force model is developed further to analyze (1) the tangential pad forces and (2) the power and energy responsible for various actions of a deep drill. 2 Friction Coefficient (/tF) It has been shown in the earlier paper that the forces of the pads are made up of two sets of forces, namely, the friction and the burnishing forces as shown in Fig. 1. Also, these two separate actions of burnishing and rubbing are responsible for on average 37 percent of the torque force and hence energy expended in a deep drilling operation as shown by the torque and thrust diagram of Fig. 3. If the two sets of forces associated with these two actions can be separated it would be possible to determine the relative energies associated with the burnishing and hence surface integrity and the pad friction and hence hole accuracy and precision. To measure and separate the burnishing friction forces it is necessary to incorporate two sets of load cells into the pads. This would be particularly difficult because of the very small region of the pads over which burnishing occurs. An alternative approach which Would allow the pad forces to be analyzed further is to assume that conventional coulomb friction conditions exist at each pad over the portions not concerned with burnishing. This will allow the radial and tangential friction forces to be related by a coulomb type friction coefficient {nc) so that: ixc = FTI /FR i = FT2/FR2 (1) The values of this friction coefficient can be determined using the procedure prescribed in Appendix 1 where the torque and thrust dynamometer is used in conjunction with a special pilot bush which has a hardened surface and a bore surface finish equivalent to that of a deep drill hole. This dynamometer is shown in Fig. 4. Thus, during phase C of a deep drilling operation, frictional forces will be present over the full pad length, which are comparable to the friction forces present over part of the pad during normal deep drilling in phase E. Although the forces in these two cases will not be the same, the coulomb friction coefficient should be of a similar magnitude and it can be calculated using the following equation whose derivation is given in Appendix 1: lxc=M(h/d), (T*Ru/Tc), (PT/PR)) (2) 8 the ratio TR*,/TC is found from the torque and thrust dynamometer results by comparing the phase C forces produced by the dynamometer in conjunction with the hardened pilot bush and with the extended pilot bush as shown in Table 1 below: where the ratio TRl/Tc is calculated by the following: TRu/Tc= P h a s e [Cffardened~ CExtended\/[CExtended] (3) Figure 6(a) shows the variation of the pad components using the results described in the table. It is interesting that the variation with increase in feed follows the same trend indicated by the full dynamometer results given in Fig. 3. • the ratios h/d and PJ/PR are determined using the cutting forces dynamometer described in the first paper [1]. The resulting variation of the friction coefficient iic with feed is shown in Fig. 6(b). This coefficient is approximately half of the total friction coefficient (^) and it follows the same Table 1 Values of phase C torque using the different pilot bush configurations Phase C torque Hardened Pilot Bush Contributed by the Production Engineering Division for publication in the JOURNAL OF ENGINEERING FOR INDUSTRY. Manuscript received Sept. 1989; revised May 1992. Associate Technical Editor: S. O. Kapoor. Extended Pilot Bush MAY 1993, Vol. 1157 177 Journal of Engineering for Industry Copyright © 1993 by ASME Downloaded From: http://manufacturingscience.asmedigitalcollection.asme.org/ on 10/28/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use nv^. PR3 ^ BR3 ^ FR3 Fig. 1 Fig. 2 The total force system The force system with friction coefficients trend in that it decreases with increasing feed. T h e range is 0.07 < fic < 0.125 with the mean value at approximately 0.085. These values compare favorably with published values for lu- bricated steel on steel. Wright Baker [2] quote about 0.05-0.15 for boundary conditions. Bowden a n d T a b o r [3] give a range of 0.08 to 0.13 for standard cutting oils. It is also significant Nomenclature As per Part 1 of this paper, plus: C 5 , C6, C-i = constants given in E q . (12) r = drill radius TB = burnishing torque 1 7 8 / V o l . 115, MAY 1993 TRu TRl j3 /x = = = rubbing or friction torque rubbing torque when n o burnishing occurs burnishing coefficient friction coefficient Transactions of the ASME Downloaded From: http://manufacturingscience.asmedigitalcollection.asme.org/ on 10/28/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use O Fc + P B +P R U = P D o Workpiece. Pilot Bush. WTRU=TD Nm 50 /* i^ a0 005 01 0-15 0-2 mm/rev. 0 O05 Feed.lflr X0-1 Tp 0-15 0-2mm/rev. Feed.lfl- % % 100 100 Pc 80 80 60 60 40 40 20 20 •—- \ • TF Fig. 5 =5 0 005 0-1 0-15 0-2mm/rev. 0 0O5 Feed.lfl 0-1 0-15 Feed .If 1 BIAHeller. d=22mm. n = 1400revs/min. Material EN8. Fig. 3 Torque and thrust components Hi Thin Wall 3 ^ Drilling . Tube. Bush. f~TWkA Drilling Fig. 4 Pilot Table. The torque and thrust dynamometer Journal of Engineering for Industry 0-2mm/re Entry forces and phases that they show that for a low carbon steel the coefficient of friction falls with increasing load which agrees with the above trend shown in Fig. 6(b) since increasing feed means increasing pad force. The friction values also compare favorably with values given by Baier [4] for deep drilling. He investigated the coulomb friction coefficient using a simulated deep drilling operation where pads were pressed against a rotating bore in the presence of a flowing deep drilling oil but without burnishing. For practical values of force and speed he quotes a range of 0.06-0.1 which compares favorably with the range given above. From his results Baier concludes that mixed friction conditions exist which indicates there is a combination of metal to metal contact and hydrodynamic lubrication. 3 Burnishing Coefficient (/S) So far it has been shown that the frictional forces can be related by a coulomb coefficient. To allow the analysis to proceed it is necessary to model the burnishing forces and this can be done by assuming that there is a relationship between the tangential and radial burnishing forces at each pad which for convenience can be termed "the burnishing coefficient and represented by /3." This will not be a friction type relationship since the quickstop investigation [5] described in the first part of this paper [1] showed that the burnishing action is comparable to a high negative rake cutting process or an ironing process. The burnishing coefficient thus represents the ratio of two forces associated with plastic flow. Thus it can be assumed that: P = BT1 /BR i = BT1/BR2 (4) The friction and burnishing force systems acting on the pads will together equal the total or overall force system given by the following equation: R\,i = BR\t2 + FRIZ = Bnyp + FnVfc (5) Using these equations the drilling torque components can be analyzed. No attempt is made to analyze the thrust force components since the pad thrust is small in comparison to the total drilling thrust. If quantitative conclusions are to be reached as a result of this analysis, practical values of the coefficient 0 are needed. No values are available for deep drilling; however, in the quickMAY 1993, Vol. 115/179 Downloaded From: http://manufacturingscience.asmedigitalcollection.asme.org/ on 10/28/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use o/o r d = 22mm. n= 1400 revs/min. Matl. EN8. 100 80 TRU, 60 d=22mm. n=1400revs/min. Matl.ENB. 40 20 005 0-1 0-15 0-2 0-15 0-2 mm/rev. f- 0-15 \ \ 0-1 0'05 0-05 0-1 Feed.[fl- Fig. 6 Variation of the coulomb friction coefficient stop study the similarity between burnishing and high negative rake cutting was noted and cutting force ratios have been published for such tools. Two publications are relevant, both of which used high negative rake tools to simulate the cutting action of a single abrasive grit. Rubenstein et al [6] machined blocks of lead and aluminium at a very slow cutting speed of 1 in/min with 75 deg negative rake angle high speed steel tools. They present cutting force ratios which range from B = 0.313 to 0.667 and the average of all their tabulated results is 0.387. Unfortunately, they did not use conditions which allowed direct comparison with deep drilling but comparable values can be obtained by extrapolation. Extrapolation to a depth and width of cut indicated by the quickstop yields values of B = 0.30 and 0.71, respectively. These extrapolated values thus have the effect of widening the range of B values and therefore a mean 0.387 is still reasonable. This very low cutting speed used by Rubenstein et al suggests that their results may not represent cutting force ratios of more typical machining conditions. However, the cutting force results produced by Komanduri [7] for more typical grinding speeds are comparable to those of Rubenstein et al and therefore suggest that the results obtained from various slow speed machining are not unreasonable. Komanduri machined steel workpieces with 75 deg negative rake angle carbide tools at speeds from 600-1800 ft/min and found values of /3 from 0.250.4. Conditions are not directly comparable to those of deep drilling but extrapolation to typical values of depth and width of cut yield B values of 0.286 and 0.333, respectively. These ranges suggest a mean of approximately 0.320 which compares 1 8 0 / V o l , 115, MAY 1993 Fig. 7 Variation of burnishing and friction torque favorably with the mean of 0.387 obtained from the results of Rubenstein et al. The deep hole drilling analysis can now be continued and the value chosen for B is 0.35 which is the average of the Rubenstein et al and Komanduri results. It is most likely that the value of 8 will change with speed, and indeed both Rubenstein et al and Komanduri agree that 8 reduces with increasing width of cut (equivalent to the feed in deep hole drilling). However, for convenience of analysis and as a first order approximation a value of B is equal to 0.35 is assumed. 4 Friction and Burnishing Components of Torque Now that the friction and the burnishing coefficients have been defined it is possible to continue the model to determine the ratio of the torque forces. If the two sets of radial forces [i?i & R2 from Eq. (5)] are added, it can be shown using the method given in Appendix 2 that: TB/TD=TP/TD[l+(l/p-l/li)/(l/ii-llicy\ (6) TRu/TD=TP/TD-TB/TD (7) From these equations the curves in Fig. 7 were plotted using TP/TD, ixc values from above. The curves show that as: 0- '/* then TB-TP& TRu-0 Indeed B cannot be less than fi because it will result in negative values of TRu. Thus, the lower limit for B will be given by jt. At the other end of the B range the curves show that as: Transactions of the ASME Downloaded From: http://manufacturingscience.asmedigitalcollection.asme.org/ on 10/28/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use d =22 mm n = K00 revs/min f = 0-1 mm/rev. d = 22mm. Torque or Power n=UOOrevs/min. 1 I--' Matl.EN8. 01 Feed,! f I Fig. 8 0-15 Mat I. EN8. 6 = 0-35. 0-2mm/rev. - Variation of torque components 180 PAD /3—oo then TB & TRu — constants The two constants are not necessarily the same and the values are dependent upon feed. The effect of feed upon the friction torque ratio TRu/TD is seen to be much less than the effect on the burnishing torque ratios. This is not unreasonable since an increase in feed will dramatically increase the burnishing area but only slightly decrease the friction area. The curves in Fig. 8 show how the friction and burnishing torque ratios vary with speed over the range at /3 values suggested above. Results indicate the burnishing torque (TB) is generally greater than the rubbing torque. Taking a typical feed of 0.1 millimeters/rev, the pad torque is 37 percent of the total drilling torque of which 24 percent is due to burnishing and 13 percent due to friction. As the feed is increased the friction torque ratio increases whereas the burnishing torque ratio decreases. The ratios are given by: 90°PAD Fig. 9 18 ° pAD Torque component contributions then be entirely dependent upon the burnishing torque reduction. The only other person to have investigated the various torque components is Weber [8]. To separate the friction and burnishing components he first drilled a 50 millimeter diameter hole in C60 steel in the normal manner and then plugged the hole with a bar of the same material and redrilled. He concluded that no burnishing would be present during the second 0.35>TB/TD>0.16 drilling operation albeit the surface finish improved by 17 percent and that there was a negligible difference in the friction and area at the two pads between the two drillings. By simple 0.16>TRU/TD>0.09 subtraction of the two torque readings, the burnishing torque The friction range is 87 percent whereas the burnishing range and hence friction torque could be calculated. He found the is much larger at 19 percent. This is consistent with an increase burnishing torque to be 15 percent of the total torque and the in feed having a marked effect upon the burnishing area but friction torque 20 percent but this was for only one test. These only a small effect on the friction area. The ratio is changed values compare with 24 percent and 13 percent given here. with feed and suggests that the rate of change of the cutting Bearing in mind that the materials and'diameters were different and friction forces is greater than that of the burnishing forces. it is thought the differences can be accounted for by Weber's To observe the sensitivity of the friction and burnishing very different approach. ratios to changes in |3, the ratios have been calculated for the The diagram in Fig. 8 gives the average results found in this limiting values suggested above. The largest value was /3 = investigation. The proportions of the total drilling torque or 0.71 (extrapolating Rubenstein et al.'s results) and the smallest power (since the two are directly related) required for metal value was /3 = 0.25 (recorded by Komanduri). The effect of removal friction and burnishing are shown. Deep hole drilling these ranges is seen from the envelopes added to Fig. 8 except has three significant advantages which are: a high metal refor the lower feed rates the value of /3 does not seem to cause moval rate, the production of precision holes, and the unique a dramatic change in either ratio. It is of interest that both surface integrity. These three advantages can be linked to the Rubenstein and Komanduri report that j3 decreases as the width three "actions" of a deep drill namely metal removal at the of cut increases. The width of cut is equivalent to the feed rate cutting edge, friction at the pads and burnishing at the pads. in deep drilling which means that /3 decreases as the feed in- Thus, referring to Fig. 9, it can be said that on average 63 creases. This would have the effect of reducing the rate of percent of the power extended in deep drilling is responsible change of both ratios with feed so that they vary less. If this for the metal removal rate, 13 percent is responsible for the did occur then it is feasible that the friction ratio would not hole quality, and 24 percent is responsible for the unique survary with feed and the reduction in pad torque with feed would face integrity. Journal of Engineering for Industry MAY 1993, Vol. 115/181 Downloaded From: http://manufacturingscience.asmedigitalcollection.asme.org/ on 10/28/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use 5 The Individual Friction and Burnishing Forces at each Pad The friction and burnishing torque or energy components have been determined for the combined pads as 13 percent and 24 percent, respectively. These components can be subdivided further to determine the individual friction and burnishing forces at both pads. 5.1. Tangential Burnishing and Friction Forces ( B n 2 ) . If it is assumed that the tangential burnishing are directly related to area, the forces can be separated. At each revolution the drill moves forward a distance corresponding to the feed rate (/) and this will be shared by each pad in proportion to their angles. The angles are 85 and 182 deg from the cutting edge, so the included angle is 97 deg. The ratio of the burnishing tangential forces is given by: BT1:BT2::263:91 therefore Bn/BT2 = 263/97 = 2.71 so Bn = 0.73 (TB/r) = 0.175 (TD/r) BT2 = 0.21 {TB/r) = 0.065 (TD/r) Thus, the burnishing tangential forces divide into a ratio of 3:1 as shown in Fig. 9 which means that the lions share of the surface integrity is due to the 90 deg pad. For a typical feed of 0.1. mm/rev, TD = 23 Nm and r is equal to 11 mm thus: BT1,2 are equal to 366.6N, 135.21N 5.2 Tangential Friction Forces (Fn<2). The friction forces can be determined because the ratio of the total pad forces is known from the first paper [1] and the burnishing forces have been calculated in the previous section. First, the total tangential forces will be related by the previously determined pad ratios [1]: lxR{/nR2 = (BTl+FTX)/{BT2 + FT2) (10) Second, the friction forces will sum to the previously determined torque: TRu = 0.UTD = r(FTl+FT2) (11) Third, the tangential burnishing forces Bna have been determined above and are given in Eqs. (8) and (9). From these three sets of equations the friction forces can be found using the method described in Appendix 3: Fn = 0.058 {TD/r) FT2 = Q.Q12(TD/r) These have been added to the Fig. 10 diagram. For a typical feed of 0.1 mm/rev, TD = 23 Nm and r = 11 mm thus: FTia are equal to 121.3N, 150.5N. These friction results show that as a first order approximation the tangential forces are equal. The fact that these values are low supports the suggestion that the situation is hydrodynamic. 6 Concluding Remarks The model suggested for the solution of the complex force system of a deep drilling operation has allowed all the pad forces to be determined. In Part 1 of this two part paper the main conclusions were: • the 90 deg pad forces are 1.7 times greater than the 180 deg pad forces. • the pad tangential forces are 17 percent of the radial forces. • the pad axial forces are 17 percent of the tangential forces. 182/Vol. 115, MAY 1993 8 the pad radial indentation forces are 20 percent of the total pad force. 8 the pad radial friction forces are 80 percent of the total pad force. In this second part of the paper the basic model proposed in Part 1 has been extended to include a friction coefficient (ftc) relating the nonindentation forces at both pads and a burnishing coefficient (B) relating the indentation forces at both pads. Using the results from the deep drilling tests the percentage of the energy and power required for drilling is as follows: » 63 percent is expended at the cutting edge contributing to the high metal removal rates of a deep drilling operation. 8 24 percent is expended at the front of the pads during indentation and thus could be considered as the energy required to produce the unique surface integrity. 8 13 percent is expended over the nonindentation length of the pads and can be considered as contributing to the precision and stability of a deep drilling operation. In the last part of this paper the tangential friction and burnishing forces of both pads have been separated and the various components determined such that: 8 18 percent of the total drilling power is burnishing at the 90 deg pad (BTl) 8 6 percent of the total drilling power is friction at the 90 deg pad (FTl) 9 6 percent of the total drilling power is burnishing at the 180 deg pad (BT2) • 7 percent of the total drilling power is friction at the 180 deg pad (FT2) so that one can say approximately Fj\ = Fj-2 = BTI = Bn/3 therefore one can conclude that the major burnishing force occurs at the 90 deg pad and is three times larger than the other burnishing or friction forces. Thus the mathematical models proposed in these 2 papers have allowed a solution to the complex force system existing in a deep hole drilling operation. References 1 Griffiths, B. J., "Modelling Complex Manufacturing Force Systems, Part 1. The Cutting and Pad Forces in Deep Drilling," ASME JOURNAL OF ENGINEERING FOR INDUSTRY. 2 WrightBaker.H., 1969,Modem Workshop Technology, Part2, MacMillan Publishers. 3 Bowden, F. P., and Tabor, D., The Friction and Lubrication of Solids, Parts 1 and 2, Oxford University Press. 4 Baier, J., 1978, Messung Der Reibungsverhaltnisse an Den Stutzleisten von B.T.A. Tiefbohrwerkzeugen," Fachgesprache Zwischen Industrie und Hochschule, Universitat Dortmund, 23rd June. 5 Griffiths, B. J., 1986, "The Development of a Quickstop Device for use in Metal Cutting Hole Manufacturing Processes,'' The International Journal of Machine Tool Design and Research, Vol. 26, No. 2. pp. 191-203. 6 Rubenstein, C , Grossmann, F. K., and Koenigsberger, F., 1967, "Force Measurements during Cutting Tests with Single Point Tools Simulating the Action of a Single Abrasive Grit," Science and Technology of Industrial Diamonds, Proceedings of the International Diamond Conference, 1966, Vol. 1, Industrial Diamond Information Bureau, London, pp. 161-172. 7 Komanduri, R., 1971, "Some Aspects of Machining with Negative Rake Tools Simulating Grinding," International Journal of Machine Tool Design and Research, Vol. 11, pp. 223-233. 8 Weber, U., 1978, "Beitrag zur Messtechnischen Erfassung des Tiefbohrprozesses," Dr. Eng. Thesis, Universitat Dortmund, June. A P P E N D I X 1 Coulomb Friction Coefficient (/JLC). When drilling during phase C without burnishing, the friction forces will exist over the full length of both pads. In this situation, the equations for the friction coefficient calculation given in Appendix 3 of the previous paper can be used here where 7^* is substituted for TP & ixc for ^. Thus: Transactions of the ASME Downloaded From: http://manufacturingscience.asmedigitalcollection.asme.org/ on 10/28/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use (12) C5fi? + C 6 /*2-C 7 = 0 therefore where: TRu/TB=(l/p- 1 / M ) / ( 1 / | I - 1/^C) (13) But C5 = sin(a2 - «i)(sin «! - sin a2 - (2h T*Ru/dTc) 7> = r«„ + rB = rB(i + w i y sm(a2 - ai) + (cos a 2 - cos a{)/k) therefore C6 = (1 - cos(a 2 - aO)(sin <xx + sin a 2 ) + (cos(a 2 - ai) - 1) r P /r z ,=(i + r«„/7,B)rfl/rZ5 (cos a\ + cos a2)/k Substituting for TRu/TB from Eq. (13) above gives: C7 = 2ArLsin 2 (a2-a,)/c?r c TB/TD= TP/TD[l + ( ( 1 / 0 - l/ji)/(l//i +1//*))] where ai = 85 deg & a 2 = 182 deg. TRu/TD=TP/TD-TB/TD A P P E N D I X 2 A P P E N D I X Calculation of Burnishing and Friction Torque Ratio. From Fig. 4 of the first paper: Ri+R2-BRi+ Tangential Force (F n i 2 ) Equations. therefore (Bn (15) 3 From Eq. (10): BTI +FJ-\ = (Bf2 + Fj-2)R\/R2 FRi + BR2 + FR2 (fi + Fd/p = (F„ +FT2)/^+ (14) and +BT2)/p but (16) Taking the force situation at a typical feedrate of/ = 0 . 1 m m / rev the following four equations can be substituted into Eq. (16) to find the values of FTi and FT2: (a) from the previous paper: Tp = r(Fl+F2) Ri/R2=l.l and {b) from section 5.1 above: TRU = r (FTl + FT2) BTl = 0.175 TD/r and id) from section 5.1 above: TB = r(BTl+Br2) BT2 = 0.065 TD/r thus: (d) from Eq. (11) we get: TP/n=TRu/nc+TB/.p FT2 = 0.n{TD/r)-Fn substituting these four equations into Eq. (16) and rearranging gives: but Tp = TRU + TB therefore F-n =0.058 TD/r and TRu/n + TB/n = TRu/nc + TB/(3 therefore FT2 = 0.072 TD/r at a feed rate of 0.1 mm/rev. 7j!B(l/M-l//0 = 7i(l/|8-l//i) Change of Address Form for the Journal of Engineering for Industry If you are planning To Move, Please Notify The ASME-Order Dep't 22 Law Drive P.O. Box 2300 Fairfield, NJ 07007-2300 Don't Wait! Don't Miss An Issue! Allow Ample Time To Effect Change. Journal of Engineering for Industry Present Address-Affix Label or Copy Information from Label Print New Address Below Name Attention. Address City . State or Country. .Zip. MAY 1993, Vol. 1 1 5 / 1 8 3 Downloaded From: http://manufacturingscience.asmedigitalcollection.asme.org/ on 10/28/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use

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