nd Intenational Confeence on Machiney, Mateials Engineeing, Chemical Engineeing and iotechnology (MMECE 015 Study on Ac Envelope Ginding Pocess of Revolving Cuved Suface Lingye Kong1, a,qiusheng Yan,b,Yongliang Qiu1,c and Tengxiong Qiu1,d 1 GuangDong Polytechnic of Industy and Commece, Guangzhou, China Guangdong Univesity of Technology, Guangzhou, China a konglingye@yeah.net, bqsyan@gdut.edu.cn Keywods: Ac ginding wheel, cuved suface, oughness unifomity, vaiable speed machining Abstact.To meet the pecision machining needs of axisymmetic evolving cuved suface, the ac envelope ginding technology fo cuved suface is studied so as to make a beakthough in the cuent pocess. The paticulaity of ac envelope ginding of cuved suface is analyzed. Though the analysis of the foming pocess of ginding cuved suface, the geometic model of the ginding wheel intefeing with the wokpiece duing the ac envelope ginding is established. Though the analysis of the moving distance of ginding point, the elationship between the effective moving distance, the adius of ac of ginding wheel, and the cuvatue adius of wokpiece is established. It is optimized and analyzed that the ginding point on the suface of ginding wheel has the maximum motion quantity to impove the wea esistance of ginding wheel. ased on the calculation of cuvatue of machined cuved suface, the change in feeding ate can be adjusted to ensue the unifom suface oughness of the cuved suface. It povides a theoetical basis fo the pactical application of Ac Envelope Ginding Method (AEGM fo cuved suface. Intoduction The typical pats with axisymmetic evolving cuved suface include the side plate of tie mold, mold coe of luminaie, olling wheel of olled tube, etc. It is chaacteized by the shape accuacy and suface oughness of cuved suface which has a decisive impact on poduct pefomance. Cuently, accoding to the equiements on mateial, shape and pecision and othe factos, the pocessing methods adopted fo the axisymmetic evolving cuved suface ae diffeent. Fo example, the ulta-pecision single point diamond tuning method can achieve the mio foming and pocessing of cuved suface via the ulta-pecision machine tool, but it is only limited to the pecision machining of coppe, aluminum, nickel and othe soft mold mateials, and it is difficult fo the pecision machining of hadening steel, high speed steel, had alloy and ceamic and othe supehad mold mateials. As fo the optical glass, ceamic and othe high-bittle mateials difficult fo pocessing, the pecision ginding, lapping and polishing methods ae mainly adopted to achieve pocessing[1]. Meanwhile, as fo the axisymmetic cuved suface with a small size, the compession molding method via mold, o diectly the single point diamond tuning method can be used[]. Fo lage cuved sufaces, the combination pocess method is often used. Fo example, the CNC machining is used to meet the accuacy equiements, and then the lapping and polishing ae adopted to meet the equiement of suface oughness. To meet the pecision machining need and the equiements of shape accuacy and suface accuacy of lage axisymmetic evolving cuved suface, the ginding pocess must be used. In this pape, based on the ac tajectoy envelope method, the ginding method by using a thick ginding wheel with a lage-diamete cicula section is poposed[3]. The featues of ac envelope ginding pocess of evolving cuved suface ae completely diffeent fom those of cylindes, planes and othe suface. Fo example, the contact state of suface between the ginding wheel and the wokpiece is changed, and the degee of ovelapping between the suface of ginding wheel and the machined suface is significantly educed, so the machining pocess has its own peculiaities, and many new poblems still need systematic study. This pape mainly analyzes the diffeences between cuved suface ginding, plane ginding and extenal ginding. ased on the envelope ginding method of ac 016. The authos - Published by Atlantis Pess 53
ginding wheel, the theoetical analysis is made on the movement of the ginding point on the suface of ginding wheel. And the paametes of ginding pocess ae optimized. Ac Envelope Ginding Method (AEGM fo Axisymmetic Revolving Cuved Suface Fom Fig.1, we know that the axisymmetic evolving cuved suface is fomed by a cuve (as geneatix otating aound the fixed axis. The cuved suface has the featues of an axisymmetic stuctue. To achieve pecise tajectoy envelope ginding of evolving cuved suface, the woking suface of an odinay ginding wheel is tued to ac evolving suface so as to avoid geometic intefeence between the ginding wheel and the wokpiece[4]. The machining method has the biggest advantages: with the change of ginding position of cuved suface, the ginding point on the ac suface of ginding wheel is moving; the ginding doesn't need the fixed point any longe, so moe abasive patices on the ginding wheel can paticipate in cutting, and the patial wea of ginding wheel can be educed and the sevice life of the ginding wheel can be impoved. On the othe hand, the cuve intepolation can be completed by contolling the two-axis linkage. So the motion contol of ginding wheel duing machining is simplified. Cutting Cutting Ploughing Rubbing Fig.1 Ac envelope ginding method Fig. Contact mode of envelope ginding method Analysis of Ac Envelope Ginding Pocess of Cuved Suface. Fo the AEGM, due to the pesence of cuvatue of the evolving cuved suface, the chaacteistics of envelope ginding pocess have geat changes compaed with those of cylindes, planes and othe suface. Fo example, the contact aea between the ginding wheel and the wokpiece suface becomes smalle, and the ovelapping between the suface of ginding wheel and wokpiece is significantly educed, so it shows diffeent machining pocesses and contol ules. It can be specificly summaized as follows: Contact mode Fo plane ginding o extenal and intenal ginding, the contact mode between the ginding wheel and the wokpiece suface is suface o line contact. Some abasive patices on the peiphey of ginding wheel mainly involve in ginding. And the est of abasive patices ae fo buffing on the machined suface, mainly playing a ole in ubbing and finishing. The fomed ginding suface is the esult of buffing by the ginding wheel fo seveal times, so the ginding efficiency is high, and the oughness of machined suface is low. Fo the ac envelope ginding of cuved suface, the point contact always exists between the ginding wheel (with the ac evolving suface and the cuved suface at any position. When moving to the next ginding position, the abasive patices which contacted with the suface of ginding wheel have been away fom the wokpiece. Theefoe, the abasive patices cannot continue the ginding, and the cuved suface fomed by ginding basically has no buffing pocess of plane ginding. Unde the same pocess conditions, the mateial pocessed by ac envelope cuve ginding has a low emoval ate, and a high suface oughness, as shown in Fig.. Theefoe, duing the ginding of wokpiece, the shape eo and wea value of the ginding wheel ae ovewitten to the same position on the wokpiece [5]. Fom the point of view of the wokpiece shape, the shape accuacy of the ac adius of the ginding wheel shall be ensued and the local wea shall be minimized. 54
x Wheel Z Envelop Fig.3 Residual height line Wokpiece Theoetical Residual Height of Machined Suface.Duing the ginding of evolving cuved suface, thee is a esidual height between the adjacent pocessing paths on the wokpiece. The value of esidual height depends on the otational speed, feeding ate of the wokpiece and othe motion elationships. Fig. 3 shows the calculation schematic of esidual height between the adjacent tajectoies of ginding wheel. P1 and P ae the two points on the cuved suface. When thei adjacent spacing is small, thei adius of cuvatue ρ can be appoximate to equal. Suppose that the cente distance f of adjacent pocessing tajectoies on the ginding wheel is, and the ac adius of the wheel is. Accoding to the geometic elationships in the figue, the esidual height R is as follows [3] : ( 4n ( 4n ( / / w w R = v v. (1 The adius of cuvatue in a diffeent position of the wokpiece is diffeent, so the value of esidual height is also diffeent, esulting in uneven suface oughness on the cuved suface of the entie wokpiece. Contolling the step pitch and feeding ate of ginding wheel is a solution to keep the value consistent. Movement of Ginding Point. Duing the envelope ginding of ac ginding wheel with cuved suface, the point contact always exists between the suface of ginding wheeland the cuved suface of the wokpiece. In ode to educe wheel wea, the contact length of ac section can be inceased to slow down the wheel wea and impove its shape etention, so as to ensue the shape accuacy of machined cuved suface and maintain a stable ginding pefomance. Depending on the change condition of cuvatue of machined cuved suface, the stuctual paametes of ginding wheel can be optimized to impove the effective utilization atio of the abasive patices, achieving unifom wea of the ginding wheel. Fist, it is necessay to study the effective ginding length of abasive patice on the suface of ginding wheel. Suppose that the geneatix of evolving cuved suface is a paabola ( z = ay. When the point A moves to the point, the included angle between the connecting line (between the cente of ac contou of the ginding wheel and the ginding point and the vetical axis is θ. Suppose that the cuvatue of the paabola at any point is q. The adius of cuvatue of any point on the evolving cuved suface is ρ n, and the distance between the ginding point and the cente of ginding wheel is R, as shown in Fig. 4. Accoding to the pinciple of diffeential geomety, fom point A to point, the ac length L paticipating in ginding on the peiphey of ginding wheel is as follows: θ y y a a a( y y1 L = dθ = dy = dy = /3 /3 1 + ( ay ( ( a ( a θ1 y1 y1 55
Z o Wheel Ld Tool path o o1 A F'(y θ incomplete ginding z=f(y Y Fig. 4 Calculation of effective ginding width Fig.5 Schematic of incomplete ginding of wokpiec Fom the above equation, when the adius of cuvatue ρ of the cuved suface inceases, the length of motion tajectoy of ginding point deceases. Meanwhile, when the adius of cuvatue of wokpiece is given, ty to choose a lage ac adius of cuvatue so as to incease the wea esistance of the ginding wheel. Howeve, fo the ginding wheel with a given width, if the ac adius of wheel is too lage, then the wokpiece may not be completely gound, as shown in the cicle in Fig. 5. When the wheel width is, and the ac cente of wheel is moved to the offset position of the cutte (R58, then the cuved suface can be completely gound. When the wheel width is 1, the ac adius of wheel is also less than the minimum of two adiuses of cuvatue on the cuved suface; since the width is small, the ac coss-section is shot, it will lead to incomplete ginding of the cuved suface. Theefoe it is necessay to study the elationship between the wheel width and the ac adius. As shown in Fig. 5, when the included angleθ 1 between the tangent line (at the edge of ac of wheel coss-section and the hoizontal plane is lage than the included angleθ between the tangent line (at the point with the maximum slope on the entie cuved suface of the wokpiece and the hoizontal plane, the complete ginding can be achieved. Theefoe, when θ1 θ, the incomplete ginding phenomenon does not occu. While θ = actgf ( y / Accoding to the geometic elationship, sin θ 1 = =, So, to ensue complete ginding, we have: acsin actgf ( y (3 In summay, in the entie ginding pocess of the cuved suface, the ac adius of ginding wheel must be as follows: 1 min = a (4 acsin actgf ( y Contact Ac Length.Fo the ginding of evolving cuved suface, due to the changes in suface cuvatue, fom the micoscopic point of view, the contact ac length and especially the contact aea ae also changed. When using AEGM, the changes in contact ac length cannot be ignoed.if the invese ginding method is used, then the contact ac length is [6,7] : vw fn dd s wa a w p lse = (1 + + ( (5 vs vs ds + dw Whee, vs ---- wheel speed (m/s, v w ---- wokpiece speed (m/min, fa ---- axial feed ate (mm/, nw ---- wokpiece otational speed (/min, d s ---- wheel diamete (mm, d w ---- wokpiece diamete (mm, a ---- ginding depth (mm p 56
The position of the ginding point contacting with the suface of ginding wheel is vaiational, so the values d s, d w, v s, v w in the fomula ae also vaiational, which means that the contact ac length is vaiational. Accoding to the stuctual paametes of olle die and the wheel size shown in Fig. 6, suppose that n w is 150/min, v s is 35m/s, wheel feeding ate V is 5mm/min, and ap is 0.0mm. The changes in contact ac length lse between the ginding wheel and cuved suface with the change of pocessing paametes ae calculated and analyzed, as listed in Table 1. The contact ac lengths at diffeent pats of the ginding wheel ae shown in Fig. 7. Fig.6 Wokpiece and wheel size Table1 Contact ac length at diffeent positions `N Vs(m/s Vw(m/s F(mm/s ds(mm dw(mm ap(mm lse(mm 1 33.46 0.94 0.083 38.88 10 0.0 1.3899 34.54 0.606 0.083 395. 79.06 0.0 1.1685 3 34.96 0.4718 0.083 400 60.1 0.0 1.036 4 34.385 0.5901 0.083 393.44 75.17 0.0 1.143 5 3.49 0.94 0.083 371.8 10 0.0 1.386 lse(mm.0 1.8 1.6 1.4 1. 1.0 0.8 0.6 0.4 0. 0.0 1 3 4 5 point Fig.7 The value of contact ac length Fig.8 Envelope contact width between wheel and wokpiece Thus, the contact ac length diffes due to the diffeent paametes. Accoding to the esults in the table, duing the ginding at the lowest point of the cuved suface, the contact ac length between the ginding wheel and the wokpiece is minimal and 5.5% smalle than the contact ac length on both ends. Futhemoe, when the ac adius R8 of ac section of ginding wheel is cetain and the cutting depth is 0.0mm, the envelope contact width L is also elated to the adius of cuvatue of the wokpiece, as shown in Fig. 8. The values soted by size ae L 58 > L 80 > L 110.4. Theefoe, the ginding at the lowest point in the middle has the best effect, while the ginding on two edges has the wost effect. Ginding with a Constant Removal Rate.In the foming pocess epesented by aspheical ginding, when the ginding adopts a constant feeding ate, the emoval amount (o envelope contact 57
width L of ginding wheel at diffeent pocessing points is diffeent due to the changes in the suface cuvatue, and the esidual height of the wokpiece suface is also diffeent, as shown in Fig. 9. The stess size of wheel changes accodingly, causing the diffeent cutte elieving amount, as well as the actual pocessing path inconsistent with the theoetical pocessing path [8]. Meanwhile, the oughness of machined suface also has geate diffeences. To this end, the Pofesso Shoji Kexiong of Tohoku Univesity fist poposed the idea of achieving the feeding with constant emoval amount by contolling the feeding ate of ginding wheel so as to educe the eos caused by feeding [9,10]. Accoding to the equation 1, the elationship between the feeding esidual height R and the feeding ate of ginding wheel with cuved suface by AEGM can be deduced: ( nw ( 4n 1/ ( ( 1 = { v / 4 / 4 1/ nw v nw + v ( [( v / w ] 1 v / 4 } 1/ [( ]. (6 Fom the above equation, / V > 0, duing the ginding of evolving cuved suface, in ode to ensue the unifom suface oughness of the entie cuved suface and the shape accuacy of the suface, the value of esidual height should be kept the same. When the ac adius of wheel section is constant, and the wokpiece speed n w is constant, whee the cuvatue adius inceases, the wheel feeding ate V should also be inceased; whee the cuvatue adius deceases, the wheel feeding ate should be minimized, as shown in Fig. 10. Accoding to this fomula, afte the wokpiece is sectionalized and an ideal value of oughness is given, the coesponding feeding ate at the appoximately equal adius of cuvatue can be obtained. Residual heightr /(mm 6.5x10-6 6.0x10-6 5.5x10-6 5.0x10-6 4.5x10-6 4.0x10-6 R80 R110.4 R58 Position 50 100 150 00 50 Fig.9 Residual height at diffeent positions Wheel feeding ate V /(mm/min 10 9 8 7 6 5 4 3 Radius of cuvatue of wokpieceρ/mm R=0.0001 mm, =31 mm, nw=60 /min Fig.10 Wheel feeding speed at diffeent positions Fom Fig. 9, we can know, in the case of constant feeding ate, if the adius of cuvatue of the cuved suface is R80, R140 and R58 espectively, then the feeding esidual height of ginding wheel is 0.0049μm, 0.004μm, and 0.0061μm accodingly. The volatility of esidual height on the entie cuved suface is 30.7%. The ate of change of suface oughness afte using a constant feeding ate is 35.06%. The suface oughness of each pat is R80: Ra0.36μm, R110.4: 0.3μm, and R58: 0.49μm, espectively. The change ule is almost the same with the ideal value of esidual height. Duing the ac envelope ginding, the use of vaiable-speed ginding (as shown in Fig. 10 can effectively educe the suface oughness. With the change of feeding ate of ginding wheel at diffeent pats of the cuved suface, thee may be a slight decline in the suface oughness, and the volatility of suface oughness is educed fom 35.06% to 11.33%,as shown in Fig. 11. 58
Roughness Ra(μm 0.50 0.48 0.46 0.44 0.4 0.40 0.38 0.36 0.34 0.3 0.30 WA40H6V Vaiable Constant R80 R110.4 R58 Radius fluctuationg atio(% 35 30 5 0 15 10 5 0 R Ra(constant Ra(vaiable categoy (Ginding ap0.01mm, total ginding thickness of 0.5mm Fig.11 Wheel feeding atevs.oughness Summay In this pape, the diffeences between the ginding of cuved suface and odinay ginding ae analyzed, including contact mode, esidual height, movement of ginding point, and contact ac length, etc. ased on the analysis of displacement distance of ginding point, the elationship between the ginding ac length, and ac adius of the ginding wheel as well as cuvatue adius of the wokpiece is obtained; meanwhile, the ange of ac adius of ginding wheel to pevent intefeence and incomplete ginding is solved. Though the calculation of contact ac length between the ginding wheel and the wokpiece, it can be obtained that the geate the cuvatue adius of the wokpiece is, the smalle the contact ac length and the contact aea ae. To ensue the consistent shape accuacy and suface oughness of the wokpiece, it is poposed to section the wokpiece, so the appopiate wheel feeding ate at diffeent adius of cuvatue can be obtained. Afte using the sectionalized vaiable-speed ginding, the volatility of oughness of entie cuved suface is educed to 11.33%. Refeences [1] J.Xie and J.Tamaki: Intenational Jounal of Machine Tools & Manufactue Vol. 48 (008, p. 1111-1119 [] J.S. Lee, M. Saeki, and T.Kuiyagawa: Intenational Jounal of the Koean Society of Pecision Engineeing Vol. 4 (003, p. 48-54 [3] Y.L.Kong, Q. S. Yan and J. H. Song: China Mechanical Engineeing Vol. 19 (008, p. 557-560 [4] T. Kuiyagawa, T. Tachibana, K. Syoji and Y. Moi: Tansactions of the Japan Society of Mechanical Enginees Vol. 63 (1997, p. 53-537 [5] K. Syoji: Ginding Technique (China Machine Pess, eijing 007 [6] J. X. Ren, R. K. Kang and X. K. Shi: Ginding Technology of Difficult-to-machine Mateials (National Defence Industy Pess, eijing 1999 [7] T. Kuiyagawa, K. Syoji and H. Ohshita: Jounal of Mateials Pocessing Technology Vol. 136 (003, p. 39-47 [8] Q. Liu, J. D. Yang, C. L. Tian and J. H. Liu: Optics and Pecision Engineeing Vol. 6 (006, p. 1048-1051 [9] M. Saeki, T. Kuiyagawa and K. Syoji: Jounal of the Japan Society fo Pecision Engineeing Vol. 68 (00, p. 1067-1071 [10] Y.. Guo, J. D. Yang and X. C. Liang: China Mechanical Engineeing Vol. 11 (000, p. 415-417 59