Design of a Composite Drive Shaft and its Coupling for Automotive Application

Transcription

1 Design of a Composie Drive Shaf and is Coupling for uomoive pplicaion M.R. Khoshravan,. Paykani * Deparmen of Mechanical ngineering, Parand Branch, Islamic zad Universiy Parand, Iran *[email protected] BSTRCT This paper presens a design mehod and a vibraion analysis of a carbon/epoxy composie drive shaf. The design of he composie drive shaf is divided ino wo main secions: Firs, he design of he composie shaf and second, he design of is coupling. Some parameers such as criical speed, saic orque, fiber orienaion and adhesive joins were sudied. Tsai-Hill failure crierion was implemened o conrol he rupure resisance of he composie shaf and hen is criical speed analysis and modal analysis were carried ou using NSYS. The behavior of maerials is considered nonlinear isoropic for adhesive, linear isoropic for meal and orhoropic for composie shaf. The resuls showed significan poins abou he appropriae design of composie drive shafs. The subsiuion of composie drive shaf has resuled in considerable weigh reducion abou 7% compared o convenional seel shaf. Furhermore, resuls revealed ha he orienaion of fibers had grea influence on he dynamic characerisics of he composie shaf. Keywords: Composie drive shaf; carbon/epoxy; design; modal analysis, naural frequency. 1. Inroducion Nowadays, composie maerials are used in large volume in various engineering srucures including spacecrafs, airplanes, auomobiles, boas, spors' equipmens, bridges and buildings. The widespread use of composie maerials in indusry is due o he excellen characerisics such as, specific srengh and specific hardness or srengh-weigh raio and hardness-weigh raio. The applicaion of composie maerials sared firs a he aerospace indusry in 1970s, bu nowadays afer only hree decades, i has been developed in mos indusries. Meanwhile, he auomoive indusry, considered as a pioneer in every counry, has been benefied from heproperies and characerisics of hese advanced maerials. long wih progress in echnology, meallic auomoive pars have been replaced by composie ones. Power ransmission drive shafs are used in many applicaions, including cooling owers, pumping ses, aerospace, srucures, and auomobiles. Drive shafs are usually made of solid or hollow ube of seel or aluminum [1]. For auomoive applicaions, he firs composie drive shaf was developed by he Spicer U-Join division of Dana Corporaion for Ford econoline van models in 1985 [].When he lengh of a seel drive shaf goes beyond 1500 mm, i is manufacured in wo pieces o increase he fundamenal naural frequency, which is inversely proporional o he square of he lengh and proporional o he square roo of he specific modulus. The naure of composies, wih heir higher specific elasic modulus, which in carbon/epoxy exceeds four imes ha of aluminum, enables he replacemen of he wo-piece meal shaf wih a single-componen composie shaf which resonaes a a higher roaional speed, and ulimaely mainains a higher margin of safey. composie drive shaf offers excellen vibraion damping, cabin comfor, reducion of wear on driverain componens and increases ire racion. In addiion, he use of single orque ubes reduces assembly ime, invenory cos, mainenance, and par complexiy [3]. Figure 1 shows a phoographic view of wo-piece seel and a one-piece composie drive shaf. Graphie/carbon/fiberglass/aluminum drive shaf ube was developed as a direc response o indusry demand for greaer performance and efficiency in ligh rucks, vans and high performance auomobiles. Since carbon fiber epoxy composie maerials have 86 Vol. 10, December 01

2 Design of a Composie Drive Shaf and is Coupling for uomoive pplicaion, M.R. Khoshravan / more han four imes specific siffness of seel or aluminum maerials, i is possible o manufacure composie drive shaf s in one-piece. The composie drive shaf has many benefis such as reduced weigh and less noise and vibraion [4]. (a) (b) Figure 1. Phoographic view of: a) wo-piece seel; b) one-piece composie drive shaf [5]. Numerous sudies have been carried ou o find ou he opimal design and analysis of composie drive shafs wih differen maerials and fibers orienaion. Pollard [5] sudied differen applicaions of composie drive shafs for auomoive indusry. He compared he advanages and disadvanages of hem a various condiions. Rasogi [6] implemened a F approach o design and analyze a composie drive shaf wih is couplings in differen condiions. Rangaswamy e al. [7] opimized and analyzed a one-piece composie drive shaf using geneic algorihm and NSYS. They found ha he use of composie maerials lead o he significan reducion in weigh compared o seel drive shaf. They also repored ha he fiber orienaion of a composie shaf srongly affecs he buckling orque. Kumar [8] performed an opimum design and analyzed a composie drive shaf for auomobile applicaion using a geneic algorihm approach. He opimized he design parameers wih he objecive of minimizing he weigh of he composie drive shaf. Chowdhuri e al. [9] replaced a wo-piece composie drive shaf by a one-piece seel shaf. They proposed wo differen designs consising of graphie/epoxy and aluminum wih graphie/epoxy. bu Talib e al. [3] implemened a finie elemen analysis o design composie drive shafs incorporaing carbon and glass fibers wihin an epoxy marix. configuraion of one layer of carbon epoxy and hree layers of glass epoxy was used. Their resuls showed ha he buckling srengh is he main concern over shear srengh in he drive shaf design. Badie e al. [10] conduced a finie elemen analysis o sudy effecs of design variables on he drive shaf criical mechanical characerisics and faigue resisance. They found ou ha sacking sequence has an obvious effec on he faigue resisance of he drive shaf. n efficien design of composie drive shaf could be achieved by selecing he proper variables, which can be idenified for safe srucure agains failure and o mee he performance requiremens. Since he lengh and ouer radius of drive shafs are limied due o spacing, he design variables include he inside radius, layers hickness, number of layers, fiber orienaion angle and layers sacking sequence. In he opimal design of he drive shaf hese variables are consrained by he laeral naural frequency, orsional vibraion, orsional srengh and orsional buckling. In he presen work an effor has been made o design a HM-Carbon/poxy composie drive shaf. onepiece composie drive shaf for rear wheel drive auomoive applicaion was designed and analyzed using NSYS sofware.. Design of a composie drive shaf Firs, he fibers are seleced o provide he bes siffness and srengh beside cos consideraion. I is misundersood ha carbon fiber shafs are oo siff. Indeed, wha we mean by oo siff, i is regarding he orsional siffness raher han he flexural siffness. I is a bes choice o use carbon fibers in all layers. Since he fiber orienaion angle, ha offers he maximum bending siffness which leads o he maximum bending naural frequency, is o place he fibers longiudinally a zero angle from he shaf axis. On he oher hand, he angle of ±45º orienaion realizes he maximum shear Journal of pplied Research and Technology 87

3 Design of a Composie Drive Shaf and is Coupling for uomoive pplicaion, M.R. Khoshravan / srengh and a 90º angle is he bes for buckling srengh [10]. The main goal design is o achieve he minimum weigh while adjusing he variables o mee a sufficien margin of safey, which is ranslaed in a criical speed (naural frequency) higher han he operaing speed (above 900 rpm), a criical orque higher han he ulimae ransmied orque and a nominal sress (he maximum a fiber direcion) less han he allowable sress afer applying any of he failure crieria like he maximum sress crieria (for example Tsai-Hill crieria). Due o he physical geomery (larger radius) of he drive shafs used in he menioned applicaions including auomoive applicaions, he shear srengh, which specifies he load carrying capaciy,i is of minor design imporance since he failure mode is dominaed by buckling herefore he main design facors are he bending naural frequency and he orsional buckling srengh, which are funcions of he longiudinal and hoop bending siffness, respecively [10]. The maerial properies of he drive shaf were analyzed wih classical laminaion heory (CLT). The variable of he laminae hickness has a big effec on he buckling srengh and sligh effec on bending naural frequency. From he properies of he composie maerials, a given fiber angles, he reduced siffness marix can be consruced. The expressions of he reduced siffness coefficiens Q ij in erms of engineering consans are as follows [3]: Q Q , Q, Q 66 1 G (1) where is he modulus of elasiciy, G is he modulus of rigidiy and is he Poisson s raio. The second sep is o consruc he exensional siffness marix []. This marix is he summaion of he producs of he ransformed reduced siffness marix [Q] of each layer and he hickness of his layer as [3]: N k [ ] [ Q] ( zk zk 1) () k 1 The marix is in (Pa. m) and he hickness of each ply is calculaed in reference o heir coordinae locaion in he laminae. The marix is used o calculae x and h, which are he average module in he axial and hoop direcions, respecively from [3]: x h 1 [ 1 [ ] ] (3) The HM-Carbon/poxy composie drive shaf was designed wih he objecive of minimizing he shaf weigh which is subjeced o he consrains such as orque ransmission, orsional buckling srengh capabiliies and naural bending frequency..1 Buckling orque Since he drive shaf is long, hin and hollow, here is a possibiliy for i o buckle. The expression of he criical buckling orque for hin-walled orhoropic ube is given as [3], 3 / 3 1/ 4 ( r )(0.7)[ xh ] Tcr (4) r Where r, is he mean radius and is he oal hickness. I is obvious ha he siffness modulus a hoop direcion ( h ) plays a big role in increasing he buckling resisance. The facor of safey is he raio of he buckling orque o he ulimae orque.. Laeral bending naural frequency The main poin ha aracs designers o use composie maerials in he drive shafs is ha hey make i possible o increase he lengh of he shaf. The relaionship beween shaf's lengh and he criical speed for boh ypes of drive shafs are shown in figure. I is eviden ha for a specific applicaion where he criical speed is abou 8000 rev/min, he longes possible seel shaf is 150 mm, while a composie one can have a lengh of 1650 mm [5]. 88 Vol. 10, December 01

4 Design of a Composie Drive Shaf and is Coupling for uomoive pplicaion, M.R. Khoshravan / f n 30 p r Ks (6) L where f n is he naural frequency, p is he firs naural frequency and, are properies of he seel shaf. Ks is given by he following equaion [8]: Figure. The effec of shaf lengh on criical speed [5] Criical speed of a shaf is obained hrough he following equaion: I I f ml N cr l (5) Where N cr is he criical speed and f is he bending frequency. Considering ha he naural frequency of a shaf according o he above equaion is inversely proporional o he square of shaf's lengh and is proporional o he square roo of Young's modulus, he convenional seel drive shafs are made of wo pieces o increase he naural frequency of he shaf, which resuls in overall increase in he weigh of he shaf. So, in order o increase he naural frequency, he lengh of shaf should be reduced or / raio should be increased. Despie he space limiaions ha confines ouer shaf diameer, he only way o increase he criical speed is o increase / raio (specific modulus) [7]. One of he ineresing properies of meals is ha alhough here is a clear difference in heir densiy, heir specific modulus is almos consan. By using fiber-reinforced composies, fiber orienaion arrangemen urns possible in he drive shaf; herefore, he bending modulus will be higher. lso heir relaive densiy is low resuling in he desirable specific modulus and an i increase in he criical speed [4]. The naural frequency of he drive shaf was obained hrough Timoshenko heory as he following equaion [8]: 1 p r fs 1 1 K L G s (7) where G is he modulus of rigidiy of seel shaf and f s is equal o for hollow cross secions. Then criical speed is obained in he following way [7]: N cr 60 f (8) n.3 Load carrying capaciy The composie drive shaf was designed o carry he orque wihou failure. The orsional srengh or he orque a which he shaf fails, is direcly relaed o he laminae shear srengh hrough T s rm l (9) where Ts is he failure orque, l is he in-plane shear srengh of he laminae, r m is he mean radius and is he hickness [3]..4 Tsai-Hill failure crierion By using Tsai-Hill failure crierion, i would be possible o calculae he dimension for failure. Wih he hickness of.03 millimeers and he applied loads, he 0 0 fibers will no be rupured. Wih he hickness of. millimeers and he applied loads, 0 he 90 fibers will no be rupured. Because of shaf s orsion, he buckling is negligible [1]. l l l lr r lr lr (10) Journal of pplied Research and Technology 89

5 Design of a Composie Drive Shaf and is Coupling for uomoive pplicaion, M.R. Khoshravan / Modal analysis of composie drive shaf using NSYS In his sudy, a finie elemen analysis was conduced using NSYS commercial sofware. The 3-D model was developed and a ypical meshing was generaed by using Shell 99 elemen. The drive shaf was fixed a boh ends and i was subjeced o orque in he middle. The orque ransmission capabiliy of he drive shaf was aken as 3000 N.m, he lengh and he ouer diameer here were considered as meers and 10 millimeers, respecively [1]. The shaf roaes a a consan speed abou is longiudinal axis. The shaf has a uniform, circular cross secion. The shaf was perfecly balanced, all damping and nonlinear effecs were excluded. The sress-srain relaionship for composie maerial is linear and elasic; hence, Hook s law is applicable for composie maerials. Since lamina is hin and no ou-of-plane loads were applied, i was considered as under he plane sress. Since he fiber volume of 60% is he sandard fiber volume fracion for mos indusries, i was seleced for composie drive shaf [11]. Table 1 shows he mechanical properies of each layer of he laminae. mong he various laminae configuraions, [±45] laminaes possess he highes shear modulus and are he primary laminae ype used in purely orsional applicaions [6]. To mee he minimum resonance frequency, he drive shaf mus have an adequae axial modulus and since he axial modulus of a [±45] laminae is raher low, 0 0 layer had o be added o he lay-up o improve he resonance frequency [10]. Regarding he design correlaions he appropriae fiber arrangemen of he composie drive shaf was obained as [90 / 0 / 45 ]. Figure 3 illusraes he domain of a finie elemen mesh. Once he finie elemen mesh and he layers were creaed, he orienaion of maerials was defined for he shell elemen and he layer maerials for each of hese elemens have been allocaed. The oher seps included placing he boundary condiions and selecing appropriae solvers. The drive shaf roaed a maximum speed so he design should include a criical frequency. If he drive shaf roaes a is naural frequency, i can be severely vibraed or even collapsed. The modal analysis was performed o find he naural frequencies in laeral direcions. 4 The mode shapes for all maerial combinaions were obained o heir corresponding criical speeds. number of fundamenal modes, all of hem criical frequencies, were obained. The dynamic analysis shows ha he firs naural frequency is Hz, and according o i he criical speed is equal o rpm, which is much more han he criical roaional speed of 4000 rpm. ccording o he equaions obained in he previous secion, naural frequency of a specific composie drive shaf is rpm. This value is very differen from he iniial one because some assumpions have been used for obaining naural frequency in Timoshenko heory [8]. Propery HM carbon/epoxy 11( Gpa ) 190 ( Gpa) 7.7 G 1( Gpa) c ( Mpa) 870 ( Mpa) 540 c 30 1( Mpa) 3 ( kg / m ) 1600 V f 0.6 Table 1. Mechanical properies for each Lamina of he laminae. Figure 3. The mesh configuraion of composie shaf. Figure 4 depics he deformaion rae change for composie drive shaf a he firs naural frequency. Figures 5 and 6 show he displacemen rae of 830 Vol. 10, December 01

6 Design of a Composie Drive Shaf and is Coupling for uomoive pplicaion, M.R. Khoshravan / composie drive shaf in differen direcions a firs mode. The naural frequencies of composie drive shaf are given in Table. Figure 6. The oal displacemen conour of composie shaf a firs mode. 3.1 ffec of fiber angle Figure 4. The deformaion form of composie shaf a firs mode. The fibers orienaion angle has a big effec on he naural frequency of he drive shaf. s we can se in figure 7, he fibers mus be oriened a zero degree o increase he naural frequency by increasing he modulus of elasiciy in he longiudinal direcion of he shaf. The drive shaf loses 38% of is naural frequency when he carbon fibers oriened in he hoop direcion a 90º insead of 0º. The cos facor plays a role in selecing only one layer of carbon/epoxy. The sacking sequence has no effec on he naural frequency since here is no load applied when defining he naural frequency. Figure 5. The displacemen rae of composie shaf in x-direcion a firs mode. Frequency number Frequency (Hz) Table. Naural frequencies of composie drive shaf. Figure 7. The effec of changing he carbon fiber orienaion angle in a drive shaf of sacking [90 / 0 / 45 ] on he naural frequency. 4 Journal of pplied Research and Technology 831

7 Design of a Composie Drive Shaf and is Coupling for uomoive pplicaion, M.R. Khoshravan / Design of adhesive joins in composie drive shafs The joins used for connecing composie maerials can be meallic or non-meallic. Seel faseners, due o he possibiliy of galvanic corrosion wih carbon-epoxy maerials, are mainly made of ianium or sainless seel. Oher alloys such as aluminum or seel can be used provided ha no conac wih he surface willoccurre. Joins were divided ino meal screws and rives. Non-meallic connecors were creaed from reinforced hermo se or hermoplasic resins. By using his connecion, srucural weigh reduces and corrosion problems disappear [1]. In his par, he hickness of he adhesive and he lengh of he adhesive bond were compued. Propery G Value.5 Gpa 1 Gpa e c 0.5 l Layers orienaion 45 mm [ 45/0 6 / 45] T Table 3. Mechanical properies of he adhesive [1]. Then, a finie elemen analysis of his ype of bond was performed using NSYS sofware. The "raldie" adhesive was used in his sudy. The following correlaions were used o calculae he required parameers [1]: max a m anh a (11) a Gl c Gee c Figure 8. Shear sress disribuion in he adhesive bond connecion. Where l is he lengh of adhesive bond. For obaining reasonable resuls he only possible way is o increase he value of e. so he hickness of he adhesive and he lengh of he adhesive bond were obained 1 millimeers and 4.5 cenimeers, respecively. The deails of he bond were given in able 3. For analysis, a F model was applied using he 3 - D linear solid elemens. suiable mesh for finie elemen modeling of adhesive layer was needed. The shear disribuion sress of he adhesive was demonsraed in figure 8. The applicaion of he appropriae adhesive, resuled in a decreased In he maximum shear sress in he adhesive a he edges of he connecion; however, if he sresses remain he same in he middle connecion, he sar of failure will depend on he relaive shear srengh values wihin he adhesive [6]. 4. The weigh comparison beween composie and seel drive shafs The enire vehicle drive shaf consiss of several roaing masses. bou 17-% of he power generaed by he engine was wased due o roaing mass of power rain sysem. Power was los because a lo of energy was needed o roae/ move heavy pars. This energy loss could be reduced by decreasing he amoun of roaing mass. In figure 9, a mass comparison beween seel and composie drive shafs has been done. The subsiuion of composie shaf has resuled in considerable weigh reducion abou 7% compared o convenional seel shaf. Due o an excessive weigh reducion he geomery would become slender which would lead o a large deflecion. 83 Vol. 10, December 01

8 Design of a Composie Drive Shaf and is Coupling for uomoive pplicaion, M.R. Khoshravan / Defleced roaing shaf would be prone o faigue failure. Faigue analysis of composie drive shaf was comprehensively performed by Badie e al. [10]. I was found ha, he sacking sequence has an effec on he faigue resisance. The bes sacking is o locae he layers of ±45 0 fiber orienaion angles ogeher and far near he inner face of he orque ube. In addiion, he cross-ply configuraion mus be locaed exposed o he ouside wih he senioriy of he 90 0 layer a he ouer face locaion Weigh Composie Seel Nomenclaure [] Siffness marix 66 h x G K L [N] r r m T e c shear siffness componen modulus of elasiciy average modulus in he hoop direcion average modulus in he axial direcion modulus of rigidiy orsional spring rae lengh force marix radius mean radius orque hickness Poisson s raio sress densiy dhesive hickness 5. Conclusions Figure 9. Mass comparison beween seel and composie shaf (Kg). In his paper a wo-piece seel drive shaf was considered o be replaced by a one-piece composie drive shaf. Is design procedure was sudied and along wih finie elemen analysis some imporan parameer were obained. The composie drive shaf made of high modulus carbon/epoxy mulilayered composies has been designed. Modal analysis was conduced o obain naural frequencies of he composie shaf. The effec of changing he carbon fiber orienaion angle on naural frequency was also sudied. The replacemen of composie maerials has resuled in considerable amoun of weigh reducion abou 7% when compared o convenional seel shaf. lso, he resuls showed ha he orienaion of fibers has grea influence on he dynamic characerisics of he composie shafs. References [1] D. Gay, S. V. Hoa, S. W. Tsai. Composie maerials: design and applicaion, CRC press, 004. [] P.K. Mallick, S. Newman. Composie maerials echnology. Hanser Publishers. pp , [3]. R. bu Talib,. li, M.. Badie and e al. Developing a hybrid, carbon/glass fiber-reinforced, epoxy composie auomoive drive shaf. Maer. & Des. Vol. 31, 010, pp [4] D.G. Lee, H.S. Kim, J.W. Kim, J.K. Kim. Design and manufacure of an auomoive hybrid aluminum/composie drive shaf. Compos. Sruc. Vol. 63, 004, pp [5]. Pollard. Polymer marix composie in drive line applicaions. GKN echnology, Wolverhampon, [6] N. Rasogi. Design of composie drive shafs for auomoive applicaions. Viseon Corporaion, S echnical paper series Journal of pplied Research and Technology 833

9 Design of a Composie Drive Shaf and is Coupling for uomoive pplicaion, M.R. Khoshravan / [7] T. Rangaswamy, S. Vijayrangan. Opimal sizing and sacking sequence of composie drive shafs. Maer. sci., Vol. 11, 005, India. [8].J. Kumar. Opimum design and analysis of a composie drive shaf for an auomobile. Maser's degree hesis, Deparmen of Mechanical ngineering, Belkinge Insiue of Technology, Sweden, 007. [9] M..K. Chowdhuri and R.. Hossain. Design analysis of an auomoive composie drive shaf. In. J. ng. and Tech., Vol., 010, pp [10] M.. Badie,. Mahdi,. M. S. Hamouda. n invesigaion ino hybrid carbon/glass fiber reinforced epoxy composie auomoive drive shaf.maer. & Des., Vol.3, 011, pp [11] D.G. Lee, N.P. Suh. xiomaic design and fabricaion of composie srucures: pplicaions in robos, machine ools, and auomobiles. Oxford Universiy Press, 006. [1] S. Pappada, R. Rameo. Sudy of a composie o meal ubular join. Deparmen of Maerials and Srucures ngineering, Technologies and Process, CTM, Ialy, Vol. 10, December 01