Elastohydrodynamic Lubrication Analysis of Journal Bearings Using CAD

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1 The 3d Intenational Confeence on Design Engineeing and Science, ICDES 1 Pilsen, Czech Repulic, August 31 Septeme 3, 1 Elastohydodynamic Luication Analysis of Jounal Beaings Using CAD Toshihio OZASA *1, Akia KINOSHITA *, Yuji HIROSE *3 and Masatoshi NIIZEKI * *1 Depatment of Mechanical Engineeing, Faculty of Engineeing, Osaka Electo-Communication Univesity 18-8 Hatsu-cho, Neyagawa-shi, Osaka , JAPAN ozasa@isc.osakac.ac.jp * Gaduate School of Osaka Electo-Communication Univesity, Now, PSG., Inc. *3 Gaduate School of Osaka Electo-Communication Univesity 18-8 Hatsu-cho, Neyagawa-shi, Osaka , JAPAN * Depatment of Electo-Mechanical Engineeing, Faculty of Engineeing, Osaka Electo-Communication Univesity 18-8 Hatsu-cho, Neyagawa-shi, Osaka , JAPAN niizeki@isc.osakac.ac.jp Astact In the calculation of the Elastohydodynamic Luication, EHL, of a jounal eaing, a compliance matix which expesses the elation etween defomation and oil film pessue on a eaing suface is necessay. Howeve, the deivation and pepaation of the compliance matix is a difficult task. In this study, a method of deiving the compliance matix using the stuctual analysis in a Thee Dimensional Compute Aided Design softwae, 3D-CAD, is descied and pefomed using CATIA V5. The EHL analysis of the con-od eaing using the compliance matix is pefomed unde the dynamic load of an engine and the defomations and oil film pessue distiutions on a eaing suface ae otained ove the engine cycle. The stess distiutions in the con-od ae studied using the stuctual analysis in the 3D-CAD. In this case, the pessue distiutions on the eaing suface ae used to calculate the ounday condition, namely the nodal foce distiutions on the eaing suface. Finally, the change of the maximum stess in the con-od unde the engine opeation is shown fo the design of the con-od. Keywods: elastohydodynamic luication, jounal eaing, compute aided design, stuctual analysis, compliance matix, stess analysis, con-od 1 Intoduction Defomation of eaings used unde high loading conditions like engines could not e neglected. Theefoe the Elastohydodynamic Luication, EHL, analysis of a jounal eaing is necessay and the study of EHL has een stated [1]. In the calculation of the EHL, a compliance matix which expesses the elation etween defomation and oil film pessue on a eaing suface is deived fom a stuctual analysis and impoves calculation efficiency []-[]. Howeve, the deivation and pepaation of the compliance matix take a lot of task. This is an ostacle to apply the EHL to design of a machine with dimensional changes. In these days, the design of a machine is pefomed using a Compute Aided Design, CAD, and a ecent CAD includes the function of a stuctual analysis. Theefoe in this study, a method of deiving the compliance matix using the stuctual analysis in a Thee Dimensional Compute Aided Design softwae, 3D-CAD, is descied and pefomed using CATIA V5. The EHL analysis of the con-od eaing using the compliance matix is pefomed unde the dynamic load of an engine and the defomations and oil film pessue distiutions on a eaing suface ae otained ove an engine cycle. The stess distiutions in the con-od ae studied using the stuctual analysis in the 3D-CAD. In this case, the pessue distiutions on the eaing suface ae used to calculate the ounday condition, namely the nodal foce distiutions on the eaing suface. Finally, the change of the maximum stess in the con-od unde the engine opeation is shown fo the design of the con-od. EHL of jounal eaings In a luication analysis, Reynolds equation is used []-[5], [7]. 1 3 h p 3 h p 1 hu h R 1R z 1 z R t whee h is cleaance [m], p is pessue [Pa], R is adius [m], t is time [s], U is velocity on a jounal suface [m/s], θ is eaing angle [ad], and μ is viscosity [Pa s]. Shae stess τ [Pa] is u at y h () y whee u [m/s] is velocity of oil at y [m] in oil film thickness. Fig. 1 Jounal eaing and EHL (1) 15

2 Figue 1 shows a jounal eaing with explanation of the EHL. W x and W y ae loads on ig end eaing in x and y diections, espectively [N]. In the case of a con-od, moment of foce on a small end y means of pessue, shae stess and Wx in ig end eaing is zeo.theefoe they do not any influence on load in the cylinde diection of an engine. The foce alances on a ig end eaing ae W x W y R pcos sin Rd dz, l R psin cos tan Rd dz l whee is eaing width [m], l is length etween centes of the ig and small ends [m],α is the angle etween cylinde and con-od axes. Oil film thickness etween a jounal and a eaing is descied as h R E xcos E ysin L E xsin E y cos (3) () whee is adius of the jounal [m], E x and E y ae eccenticities of a jounal cente in x and y diections [m] and L is deviation fom a cleaance cicle [m]. L can e teated as static defomation and is descied with a matix and vectos. C p L L (5) whee L is the deviation vecto fom a eaing cicle, C is compliance matix which expesses the elation etween elastic defomation on a eaing suface and oil film pessue distiution vecto p and L is the shape of eaing expessed y deviation fom the cleaance cicle. The [C] is deived fom stuctual analysis. Equations (1) and (3) ae numeically solved fo the egion of p> with the oil film thickness calculated fom Eqs. () and (5). Pessue in the citation is assumed to e zeo, p =. Figue shows calculation flow of the EHL. In the EHL analysis, the oil film thickness changes with elastic defomation. Theefoe calculation must e continued till convegence in elastic defomation and the EHL esults ae otained. Hydodynamic luication Defomation a eaing suface Compliance Oil film matix on pessue Convegence EHL esults Fig. Calculation flow of EHL using compliance matix 3 Compliance matix In many cases, a stuctue is analyzed with FEM. The elation etween foces and defomations in the stuctue is descied y line elation using vectos and matixes. F is a foce vecto on all nodes, is a defomation vecto in all nodes in a stuctue and K is a stiffness matix. The elation etween the foces and defomations of all nodes in the stuctue is When K F. () 1 D is defined as K D DF. (7) To make a compliance matix, a unit foce is applied on eaing suface [], [3]. D is the matix which expess the elation etween defomation of stuctue and foce on load points of a eaing suface in x and y coodinates and F is the foce vecto of node on a eaing suface in x and y diections. Defomation is expessed with ' D F δ. (8) When a unit foce is loaded in x diection at a node ' on a eaing suface, defomation is a column of the D coesponds to the unit load. When a unit foce is loaded in y diection at a node on the eaing suface, ' defomation is a column of the D coesponds to the unit load. The nodal points ae detemined y auto-mesh and change with evey calculation, so that they ae diffeent fom the calculation mesh of the luication analysis. Theefoe the defomation must accod to the calculation mesh of the luication y means of intepolations. δ is the defomation vecto on a eaing suface xyl in x and y diections accoding to the calculation mesh of luication deived with the intepolations of the δ which is the defomation vecto on a eaing suface selected fom the defomation vecto δ, D is the matix which expesses the elation etween defomation on the mesh points of luication and foce on load points of eaing suface in x and y coodinates. Defomation of luication mesh in x and y diections is expessed with D δ xyl F.(9) When ΔA is the matix which expess the aea of lod points on eaing suface, T 1 is the matix which tansfe adial foce to the foces in x and y diections, T is the tansfe matix which expesses the elation etween lod points and luication mesh on eaing suface, F is a adial foce vecto on eaing suface and E is unit matix, the following equations ae otained. T ΔAp F (1) δ D F D T F xyl D T T ΔA p 1 1, (11) In the aove equations, load points should e taken as 1

3 mesh points of luication, namely E T. When is eaged mean vecto of defomation and T is the tansfe matix of eaged mean of defomation on eaing suface in x and y diections, elative defomation of a eaing is E T xyl E T D T T ΔAp xyl 1. (1) When T is the tansfe matix of defomation on eaing suface fom x and y diections to adial diection, the compliance is expessed with T E T D T T ΔA C 1. (13) When δ is defomation in adial diection, the deviation vecto fom a eaing cicle is L L C pl δ. (1) This is Eq. (5). Figue 3 shows the flow chat of making the compliance using the 3D-CAD. In the pactice, the stuctue is con-od. Inside of the small end is fixed and the defomations of the suface of ig end eaing ae calculated in the 3D-CAD when 1 [N] is applied evey node on the eaing suface each in x o y diection. Figue shows the dimension of the con-od. Figue 5 (a) shows the stuctue model of the 3D-CAD. Figue 5 () shows the auto mesh model fo the stuctual analysis in which element size is aout 1 [mm]. in cicumfeence, in width and in diections is the nume of times of the stuctue analysis which is educed to e. Results The EHL analysis of the con-od eaing using the compliance matix is pefomed unde the dynamic load of an engine and the defomations and oil film pessue distiutions on a eaing suface ae otained ove the engine cycle. In the calculations, suction top dead cente is defined as cank angle of degees afte top dead cente, [ ATDC]. The stess distiutions in the con-od ae studied using the stuctual analysis in the 3D-CAD, CATIA V5, using the nodal foces on the eaing suface as the ounday condition. The nodal foce distiutions on the eaing suface ae deived fom the pessue distiutions otained fom the EHL analysis. Figues to 9 show the esults of engine speeds 1 [pm] to [pm] at 39 [ ATDC] when the maximum stess appeas y means of the explosion in the cylinde. In these figues, the defomation on the eaing suface is shown in (a), oil film pessue is shown in () and stess distiutions in the con-od is shown in (c). The loads on the con-od eaing ae shown in Tale CAD data Stuctual analysis in 3D-CAD A unit foce on evey mesh point on eaing suface Nume of mesh points on luicating suface diections 18 Fig. Dimensions of con-od [mm] Defomation data Intepolation: Defomation on eaing suface adjust to calculation mesh points Compliance matix Fig. 3 Flow of making a defomation-pessue matix, compliance matix, using stuctual analysis in Thee Dimensional Compute Aided Design Softwae The stuctue analysis was done with the mesh on the eaing suface which is 7 in cicumfeential diection and 11 in axial diection. The nume of times of the stuctue analysis is the nume of the mesh points in the luication analysis times in diections. In this case, it is 158Con-od is symmetical shape in left and ight and in font and ehind aout the od axis. The poduct of 37 (a) 3D-CAD data () FEM stuctual model Fig. 5Mesh on eaing suface Tale 1 Load on con-od eaing at 39 [ ATDC] Load Engine speed [pm] W x [kn] W y [kn]

4 Defomation [μm] (a) Defomation on eaing suface 8 Beaing angle () Oil film pessue 3 (c) Stess distiution of con-od Fig. EHL analysis and stuctual analysis at 39 ATDC unde engine speed of 1pm Defomation [μm] Pa (a) Defomation on eaing suface Beaing angle () Oil film pessue (c) Stess distiution of con-od Fig. 7 EHL analysis and stuctual analysis at 39 ATDC unde engine speed of pm 18

5 Defomation [μm] Pa (a) Defomation on eaing suface Fig. 8 EHL analysis and stuctual analysis at 39 ATDC unde engine speed of 3pm Defomation [μm] () Oil film pessue (c) Stess distiution of con-od Pa (a) Defomation on eaing suface Beaing angle () Oil film pessue 3 (c) Stess distiution of con-od Fig. 9 EHL analysis and stuctual analysis at 39 ATDC unde engine speed of pm 19

6 Wx, Wy [kn] σ max [MPa] Cank angle [ ATDC] (a) Beaing load Wx Wy Cank angle [ ATDC] () Maximum stess in con-od Fig. 1 Beaing load and maximum stess in con-od unde engine speed of pm Figue is the esult at 1 [pm]. As shown in (a), the load in the diection of con-od axis, W y, is high and maximum defomation is aout [μm]. As shown in (), the pessue is high in the diection of load and the peak pessues appea at oth ends in the eaing width. This is a peculia case in the EHL like as epoted in the past wok [7]. The oil film thickness in the oth ends is quite low. As shown in (c), the stess distiution in the con-od is quite high all ove the od. Figue 7 is the esult at [pm]. As shown in (), the peak pessue appeas at middle in the eaing width. As shown in (c), the stess distiution in the con-od is like as that at 1 [pm] ut slightly lowe. Figue 8 is the esult at 3 [pm]. As shown in (), the peak pessue appeas at middle in the eaing width. As shown in (c), the stess is slightly high in the left side of the od y means of ending. Figue 9 is the esult at [pm]. As shown in (c), the ending of the od is lage and the stess is quite high in the left side of od. The elation etween the EHL analysis and the stess analysis is claified and impotance of the elation could e undestood. Finally, the change of the maximum stess in the con-od unde the engine cycle at the [pm] is shown in Fig. 1 fo the design of the con-od. The engine is fequently opeated nea this speed in a usage. In this speed, the maximum stess in the con-od is highest nea 39 [ ATDC] ecause of the comustion in the cylinde. The highest maximum stess is lowe enough in compaison with the popety of steel mateials. and oil film pessue, is useful in the EHL analysis. The method of deiving the compliance matix using the stuctual analysis in the 3D-CAD is descied and is pefomed using CATIA V5. The EHL analysis of the con-od eaing using the compliance matix is pefomed unde the dynamic load of the engine. The defomations and oil film pessue distiutions on a eaing suface ae otained ove the engine cycle. The stess distiutions in the con-od ae studied using the stuctual analysis in the 3D-CAD. In this case, the pessue distiutions on the eaing suface ae used to calculate the ounday condition, namely the nodal foce distiutions on the eaing suface. Finally, the change of the maximum stess in the con-od unde the engine opeation is shown fo the design infomation. This method is confimed to e useful. This is ecause the stess analysis can e done with the pactical ounday conditions. Refeences [1] Fantino, B., Godet, M. and Fene, J., Dynamic Behio of an Elastic Connecting-Rod Beaing Theoetical Study, SAE Pape 8337, (1983). [] Goenka, P. K. and Oh, K. P., An Optimum Shot Beaing Theoy fo the Elastohydodynamic Solution of Jounal Beaings, Tansactions of the ASME, Jounal of Tiology, Vol. 18 (198), pp [3] Mclvo, J. D. C. and Fenne, D. N., Finite Element Analysis of Dynamically Loaded Flexile Jounal Beaings: Fist Newton-Raphson Method, Tansactions of the ASME, Jounal of Tiology, Vol. 111 (1989), pp [] Ozasa, T., Yamamoto, M, Noda, T., Mizutani, Y., Yamada, M and Toii, H., Elastohydodynamic Luication Analysis of Con-Rod Big-End Beaings- Expeimental Veification y Engine Test-, in Japanese, Poceedings of the Japan Society of Mechanical Enginees, No. 93-3, E, (1993), pp.5-7. [5] Ozasa, T., Noda, T. and Konomi, T. Elastohydodynamic Luication Model of Connecting Rod Big-End Beaing : Application to Real Engine s, Tansaction of the ASME jounal of Tiology, Vol. 119, (1997), pp [] Ozasa, T., Mass Conseving Elastohydodynamic Luication fo Con-Rod Beaings with an Oil Passage, in Japanese, Tansactions of the Japan Society of Mechanical Enginees, Vol. 8,, C(), pp [7] Ozasa, T., Suzuki, S., Noda, T. and Konomi, T. Elastohydodynamic Luication of Con-Rod Big- End Beaings: Compaison etween Theoy and Engine Test, Poceedings of the Intenational Tiology Confeence Yokohama 1995 (199), pp Received on Deceme 31, 13 Accepted on Feuay 7, 1 5 Conclusions The compliance matix, which expesses the elation etween elastic defomation on eaing suface 17