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資源目錄里展示的全都有，所見即所得。下載后全都有,請放心下載。原稿可自行編輯修改=【QQ：401339828 或11970985 有疑問可加】 Journal of Materials Processing Technology 211 (2011) 141149Contents lists available at ScienceDirectJournal of Materials Processing Technologyjournal homepage: new in-feed centerless grinding technique using a surface grinderW. Xua, Y. WubaGraduate School, Akita Prefectural University, 84-4 Tsuchiya-ebinokuchi, Yurihonjo, Akita 015-0055, JapanbDepartment of Machine Intelligence and Systems Engineering, Akita Prefectural University, 84-4 Tsuchiya-ebinokuchi, Yurihonjo, Akita 015-0055, Japana r t i c l ei n f oArticle history:Received 15 April 2010Received in revised form15 September 2010Accepted 16 September 2010Keywords:Centerless grindingSurface grinderUltrasonic vibrationIn-feedRoundnessShoea b s t r a c tThis paper deals with the development of an alternative centerless grinding technique, i.e., in-feed cen-terless grinding based on a surface grinder. In this new method, a compact centerless grinding unit,composed of an ultrasonic elliptic-vibration shoe, a blade and their respective holders, is installed ontothe worktable of a surface grinder, and the in-feed centerless grinding operation is performed as arotating grinding wheel is fed in downward to the cylindrical workpiece held on the shoe and theblade. During grinding, the rotational speed of the workpiece is controlled by the ultrasonic elliptic-vibration of the shoe that is produced by bonding a piezoelectric ceramic device (PZT) on a metalelastic body (stainless steel, SUS304). A simulation method is proposed for clarifying the workpiecerounding process and predicting the workpiece roundness in this new centerless grinding, and theeffects of process parameters such as the eccentric angle, the wheel feed rate, the stock removal andthe workpiece rotational speed on the workpiece roundness were investigated by simulation followedby experimental confirmation. The obtained results indicate that: (1) the optimum eccentric angle isaround 6; (2) higher machining accuracy can be obtained under a lower grinding wheel feed rate,larger stock removal and faster workpiece rotational speed; (3) the workpiece roundness was improvedfrom an initial value of 19.90?m to a final one of 0.90?m after grinding under the optimal grindingconditions. 2010 Elsevier B.V. All rights reserved.1. IntroductionIn the manufacturing industry, for high accuracy and highproductivity machining of cylindrical components such as bear-ing raceways, silicon-ingots, pin-gauges and catheters, centerlessgrinding operations have been extensively carried out on spe-cialized centerless grinders. Two types of centerless grinders areavailable commercially; one is with a regulating wheel and theotherwithashoe,andtheyaredifferentfromeachotherinhowtheworkpiece is supported and how the workpiece rotational speedis controlled during grinding. Since the invention of the regu-lating wheel type centerless grinder by Heim in 1915 (Yonetsu,1966), much research has been devoted to enhance machiningaccuracy and efficiency. Rowe and Barash (1964) proposed a com-puter method for investigating the inherent accuracy of centerlessgrinding by taking into account the geometrical considerationsand the elastic deflexion of the machine. Further, Rowe et al.(1965) experimentally obtained the machining elasticity parame-ter.Hashimotoetal.(1982)analyzedtheproblemofsafemachiningoperation by discussing the friction-drive function of regulatingCorresponding author. Tel.: +81 184 272157; fax: +81 184 272165.E-mail addresses: d10s007akita-pu.ac.jp, (W. Xu).wheel. Miyashita et al. (1982) studied the deformation of con-tact area and built a dynamic model for selecting chatter freeconditions. Rowe and Bell (1986) experimentally investigated thehigh removal rate grinding process and optimized the grindingconditions. Wu et al. (1996) clarified the influence of grindingparameters on roundness error through a computer simulationmethod to optimize grinding conditions. Epureanu et al. (1997)analyzed the stability of grinding system through a linearizedmodel that described the formation and evolution of the patternon the ground surface. Guo et al. (1997) studied the geometri-cal rounding of above-center and below-center centerless grindingto assist in the selection of acceptable set-up conditions. Albizuriet al. (2007) proposed a novel method to reduce chatter vibra-tions by using actively controlled piezoelectric actuators. Krajniket al. (2008) developed an analytical mode that assists in efficientcenterless grinding system set-up for higher process flexibilityand productivity. Shoe type centerless grinding has also attractedattention from both industrial and academic researchers. Yang andZhang (1998) designed a flat vacuum-hydrostatic shoe to increasethe load capacity and stiffness for high precision applications ofshoe centerless grinding. Then Yang et al. (1999) and Zhang etal. (1999) analyzed the process stability in vacuum-hydrostaticshoe centerless grinding. In addition, Zhang et al. (2003) devel-oped a geometry model to predict the lobing generation in shoe0924-0136/$ see front matter 2010 Elsevier B.V. All rights reserved.doi:10.1016/j.jmatprotec.2010.09.009142W. Xu, Y. Wu / Journal of Materials Processing Technology 211 (2011) 141149Fig. 1. Three types of centerless grinding using a surface grinder: tangential-feed type (a), in-feed type (b) and through-feed type (c).centerless grinding and used the model for the analysis of grindingprocesses.From the viewpoint of production cost, the two types ofcenterless grinders are highly suitable for small-variety and large-volume production because the loading/unloading of workpiecesis extremely easy and fast. However, the centerless grinder isa special-purpose machine and relatively costly, putting it at adisadvantage for large-variety and small-volume production, thedemand for which has increased rapidly in recent years. As a solu-tion to this problem, one of the authors Wu et al. (2005) proposeda new centerless grinding technique that can be performed on asurface grinder (rather than a centerless grinder) previously. Thismethodisbasedontheconceptofultrasonicshoecenterlessgrind-ing developed by Wu et al. (2003, 2004). In the method, a compactunit consisting mainly of an ultrasonic elliptic-vibration shoe, ablade,andtheirrespectiveholdersisinstalledontheworktableofamultipurposesurfacegrinder.Thefunctionoftheultrasonicshoeistoholdthecylindricalworkpieceinconjunctionwiththeblade,andto control the workpiece rotational speed with the elliptic motionon its upper end-face.According to the relative motion of the workpiece to thegrinding wheel, three types of centerless grinding operations canbe performed in the proposed method as shown in Fig. 1: (a)tangential-feed type in which initially the grinding unit is locatedin the down-left side of the grinding wheel with a distance thatis large enough for loading the workpiece on the upper end faceof ultrasonic shoe, and then the workpiece is fed rightward alongthe tangential direction of the grinding wheel at a feed rate ofvf(Fig. 1(a) to perform the grinding action until the unit reaches thedown-right side of the grinding wheel with a distance that is largeenoughforunloadingthegroundworkpieceofftheultrasonicshoe;(b) in-feed type in which initially the grinding wheel is locatedabove the grinding unit with a distance that is large enough forloading the workpiece on the upper end face of ultrasonic shoe,and then the grinding wheel is fed downward in radial directioninto the workpiece at a feed rate ofvfr(Fig. 1(b) to perform thegrinding action until the required stock removal has been attained,and after a short period for “spark-out” the grinding wheel is liftedup from the ground workpiece with a distance that is large enoughto unloading the workpiece off the ultrasonic shoe; (c) through-feed type in which initially the grinding wheel is set at a givendistance from the upper end face of ultrasonic shoe (as shown inFig. 1(c), and then the workpiece is loaded on the loading guideand fed into the space between grinding wheel and ultrasonic shoealong its axial direction at a feed rate ofvfato perform the grindingaction until it loses the contact with the grinding wheel but beingsupported on the unloading guide for the subsequent unloading.Inourpreviousworks,simulationandexperimentalworkshavebeen conducted for the tangential-feed type (Xu et al., 2010). Theobtained results showed that the workpiece roundness can beFig. 2. Schematic illustration of in-feed centerless grinding using a surface grinder.W. Xu, Y. Wu / Journal of Materials Processing Technology 211 (2011) 141149143improved greatly from the initial value of 23.9?m to the final oneof 0.8?m, thus validating this new method. The objective of thepresent paper is to confirm the in-feed type of centerless grind-ing carried out on a surface grinder. For this purpose, a simulationmethod is proposed to clarify the workpiece rounding processand to investigate the effects of process parameters, such as theworkpiece eccentric angle, the grinding wheel feed rate, the stockremoval, and the workpiece rotational speed on the workpieceroundness. Then a series of grinding experiments are carried outto confirm the simulation results.2. Operation principle of in-feed centerless grinding usinga surface grinderFig. 2 shows the operation principle of in-feed centerless grind-ing using a surface grinder. A grinding unit, composed of anultrasonic elliptic-vibration shoe and its holder, a blade and itsholder,astopper,andabaseplate,isinstalledontotheworktableofa surface grinder at an angle of (hereafter called eccentric angle)(see Fig. 2(a). The workpiece is constrained between the blade, theshoeandthestopper.Asthegrindingwheelisfedinradialdirectionintotheworkpieceatfeedrateofvfr,anin-feedtypedown-grindingoperationisperformed,wheretheworkpieceisrotatedintheoppo-site direction to the wheel. As shown in Fig. 2(b), once the requiredstock removal has been attained, the wheel in-feed is stopped fol-lowed by a dwell for several seconds to allow “spark-out”. Duringgrinding, the workpiece rotational speed nwis controlled by theelliptic motion on the upper end-face of the shoe and the stop-per is used to prevent workpiece from jumping away the grindingarea. In addition, the blade is wedge-shaped with a tilt angle of ?(usually called blade angle) and the value of ? is in general set ataround 60in terms of the optimum workpiece rounding conditiondemonstrated by Harrison and Pearce (2004).In the grinding unit, the shoe is constructed by bonding a piezo-electric ceramic device (PZT) with two separated electrodes ontoa metal elastic body (stainless steel, SUS304). When two amplifiedalternating current (AC) signals (over 20kHz) with a phase differ-ence of , generated by a wave function generator, are applied tothe PZT, bending and longitudinal ultrasonic vibrations are excitedsimultaneously.Thesynthesisofthevibrationdisplacementsinthetwo directions creates an elliptic motion on the end-faces of themetal elastic body. Consequently, the workpiece rotation is con-trolled by the frictional force between the workpiece and the shoe,so that the peripheral speed of the workpiece is the same as thebending vibration speed on the shoe end-face. The workpiece rota-tional speed can be adjusted by changing the value of parameterssuch as the amplitude Vppand frequency f of the voltage appliedto the PZT, because the shoe bending vibration speed varies withthevariationoftheappliedvoltage(seeXuetal.,2009).Inaddition,a pre-load is applied to the shoe at its lower end-face in its longitu-dinal direction using a coil spring to prevent the PZT from breakingdue to resonance.3. Geometrical rounding analysisFig.3showsthegeometricalarrangementoftheshoe,theblade,the workpiece and the grinding wheel in an in-feed centerlessgrinding operation using a surface grinder after grinding for timet. At this moment, the eccentric angle and the workpiece radiusbecome (t) and ?(t), respectively, from their respective initial val-uesof0and?0.Inthemeantime,theworkpieceisheldbytheblade(with a tilt angle of ?) and the shoe at points B and C, respectively,and ground at point A by the grinding wheel rotating at the rota-tional speed of ngas the wheel is fed downward into the workpieceat a feed rate ofvfr.Fig. 3. Geometrical arrangements in in-feed centerless grinding using a surfacegrinder.3.1. Geometrical rounding modelingIn the simulation model (see Fig. 3), several assumptions aremade: (1) the workpiece is in constant contact with the blade andthe shoe at points B and C, respectively, during grinding; (2) thevibration of the entire machine is too small to be regarded, andno chatter occurs on the machine due to the ultrasonic elliptic-vibrationoftheshoe;(3)theworkpiecerotationalmotionisalwaysstable, and no variation of rotational speed occurs during grinding;(4) the wear of the grinding wheel is too small to be recognized,and the grinding wheel radius Rgis kept constant during grinding.Let a XY-coordinate system be located on the worktable. AnoptionalpointOontheworktableisdeterminedastheoriginofthecoordinate system. The X-axis is taken in the horizontal directionand the Y-axis in the vertical direction. Before grinding, the initialXY-coordinatesofthegrindingwheelcenterOg0andtheworkpiececenter Ow0are (XOg0, YOg0) and (XOw0, YOw0), respectively. Thus, theXY-coordinates of the initial blade contact point B (XB0, YB0) andthe shoe contact point C (XC0, YC0) can be obtained from the initialgeometrical arrangement, as follows:?XB0= XOw0 ?0sin?YB0= YOw0+ ?0cos?XC0= XOw0YC0= YOw0 ?0Then, the linear equations representing the blade end-face and theshoe upper end-face in this coordinate system can be written as:For the blade end-face:Y YB0= tan?(X XB0)(1)For the shoe upper end-face:Y YC0= 0(2)Substituting coordinates of point B and C into Eqs. (1) and (2),respectively, gives:PX + QY + R = 0(3)Y YOw0+ ?0= 0(4)whereP = tan?,Q = 1,R = YOw0+ ?0cos? tan?(XOw0?0sin?).During grinding, the coordinates of the workpiece centerOwtand the grinding wheel center Ogtwill vary as the material isremoved. Let the instantaneous workpiece radius in the directionparallel to the X-axis after grinding for time t be ?(t) (see Fig. 3).144W. Xu, Y. Wu / Journal of Materials Processing Technology 211 (2011) 141149At this moment, the workpiece radius at points A, B and C canbe expressed with ?(tTA), ?(tTB) and ?(tTC), respectively,where TA=?+2(t)/4?nw, TB=(?+2?)/4?nwand TC=3/4nware the time delays for points A, B and C. Since the ?(tTB) and?(tTC) are equal to the distances from the workpiece center Owtto the blade end-face and to the shoe upper end-face, respectively,they can be obtained from the geometrical arrangement in Fig. 3by using Eqs. (3) and (4) as follows:?(t TB) =|PXOw(t) + QYOw(t) + R|?P2+ Q2(5)?(t TC) = YOw(t) YOw0+ ?0(6)Solving Eqs. (5) and (6) simultaneously yields the XY-coordinatesof the workpiece center Owtat time t, as follows:XOw(t) =?P2+ Q2?(t TB) QYOw(t) RPYOw(t) = ?(t TC) + YOw0 ?0(7)In this moment, the XY-coordinates of the grinding wheel centerOgtare also obtained from the geometrical arrangement in Fig. 3as:?XOgt= XOg0= XOw0 (Rg+ ?0)sinYOgt= YOg0vfrt = YOw0+ (Rg+ ?0)cos vfrt(8)In addition, the following relationships are established from thegeometrical arrangement in Fig. 3.?XA(t) XOg(t)2+ YA(t) YOg(t)2= R2gYA(t) YOw(t) = cot(t)XA(t) XOw(t)(9)where:cot(t) =YOg(t) YOw(t)XOg(t) XOw(t)(10)Subsequently,theXY-coordinatesofpointAareobtainedasfollow-ing by re-arranging Eqs. (9) and (10).XA(t) =(V ?V2 4UW)2UYA(t) = cot (t)XA(t) XOw(t) + YOw(t)(11)whereU = 1 + cot2(t),V = 2cot(t)YOw(t) cot2(t)XOw(t) cot (t)YOg(t) XOg(t),W = X2Og(t) +cot(t)XOw(t) YOw(t) + YOg(t)2 R2gEventually,thework-piece radius ?(tTA) at the point A after grinding for time t iscalculated from the XY-coordinates of the workpiece center Owtand the grinding point A as follows:?(t TA) =?XA(t) XOw(t)2+ YA(t) YOw(t)2(12)Consequently,theapparentwheeldepthofcutwouldbe?=?(tTAT)?(tTA), where T is the time required for onerevolutionoftheworkpiece.Ifthegrindingsystemhasanidealstiff-ness, the true wheel depth of cut would be equal to the apparentone.However,thegrindingsystemwithstandstheelasticdeforma-tion caused by the grinding force during actual grinding. Rowe etal. introduced a dimensionless parameter called machining elastic-ity parameter k as a measure to indicate the elastic deformation ofcenterless grinding system, which is defined as a quotient betweenthe true depth of cut and the apparent depth of cut with Eq. (13)(Rowe and Barash, 1964; Marinescu et al., 2006).k =truewheeldepthofcutapparentwheeldepthofcut=?(13)Following Rowe et al.s consideration, the true wheel depth of cut? can be calculated as ? =k?in the current work, resulting in thatthe true workpiece radius at point A is:?(t TA) = ?(t TA T) k?(t TA T)?XA(t) XOw(t)2+ YA(t) YOw(t)2(14)However, the wheel depth of cut calculated using these equationsis less than zero occasionally. Obviously, this phenomenon wouldnot happen. Therefore, Eq. (14) should be modified as:?(t TA) = ?(t TA T) k(?(t TA T) ?XA(t) XOw(t)2+ YA(t) YOw(t)2)?(t TA) ?(t TA T)?(t TA) = ?(t TA T)?(t TA) ?(t TA T)(15)3.2. Determination of the machining elasticity parameterAs described above, the machining elasticity parameter kdepends on the stiffness of the grinding system. If the simulationresult is to be trusted, the value of k should be determined forthe given grinding system. For the tangential-feed type centerlessgrindingusingasurfacegrinder,themeasuringmethodofparame-ter k was proposed in our previous work (Xu et al., 2010). However,the proposed method is unsuitable for the in-feed type, since thereisasignificantdifferencebetweenthegeometricalarrangementsinthe two types. Therefore, an alternative method should be devel-oped for obtaining the machining elasticity parameter in in-feedtype. Rowe et al. (1965) proposed a method for the determinationof machining elasticity parameter k in conventional in-feed center-less grinding, in which a parameter proportional to the true wheeldepth of cut, i.e., the grinding power or the grinding force, during“feed-in” or “spark-out” stage is measured to obtain the parameterk. Following this methodology, in the current work an alternativeprocedure is proposed to determine the value of k for the in-feedtype centerless grinding based on a surface grinder as below.In spark-out, the apparent wheel depth of cut is removed justafterafewrevolutionsofworkpiece.Thedecreaserateofthewheeldepth of cut depends on the value of parameter k. If the apparentwheeldepthofcuthasavalueofa0atthecommencementofspark-out, the true depth of cut in the first half-revolution, ae1, and that inthesecondhalf-revolution,ae2,canbecalculatedwithEqs.(16)and(17), respectively, according to Rowe et al. (1965) and Marinescuet al. (2006).ae1= ka0(16)ae2= k(a0 ae1) = (1 k)ae1(17)Hence, the true depth of cut in the ith half-revolution, aei, can beobtained as:aei= k(a0 ae1 ae2 . aei1) = (1 k)i1ae1= .= (1 k)imaem(m = 1, 2, .,i)(18)Since the true depth of cut is proportional to the normal grindingforce Fnin general, the following relationship is obtained from Eq.(18):FniFnm=aeiaem= (1 k)im(19)Solving Eq. (19) yields:k = 1 e?(20)W. Xu, Y. Wu / Journal of Materials Processing Technology 211 (2011) 141149145Fig. 4. Schematic illustration of grinding force measurement method.whereeisthebaseofnaturallogarithmsand?=(lnFnilnFnm)/(im). Consequently, the value of k can bedetermined with Eq. (20) as long as the normal grinding forcesFniand Fnmafter spark-out for i and m revolutions have beenmeasured.Fig.4showsagrindingforcemeasurementmethodproposedforthecurrentwork.A3Ddynamometerisinstalledunderthegrindingunit to record the horizontal component Fxin the X-direction andthe vertical component Fyin the Y-direction of the grinding force.Thus, based on the geometrical arrangement shown in Fig. 4, thefollowing relationship is obtained:?Fncos + Ftsin = FyFnsin Ftcos = Fx(21)where Fnand Ftare the normal and tangential grinding forces,respecti