UNIVERSITY OF PITESTI SCIENTIFIC BULLETIN FACULTY OF MECHANICS AND TECHNOLOGY AUTOMOTIVE series, year XVII, no.1 ( 3 ) TORQUE CONVERTER MODELLING FOR ACCELERATION SIMULATION 1 Ciobotaru, Ticuşor *, 1 Vînturiş, Valentin, Caravan, Alexandru 1 Military Tecnical Academy, Romania, MOND, Romania * e-mail: cticusor4@yaoo.com KEYWORDS torque converter, modelling, simulation, ydrodynamic transmission ABSTRACT Simulation plays an important role in optimising te performances of te drive line of te off-road veicles. Te models of te engine, torque converter, transmission and running gear are assembled into a large model used for estimation of te veicle acceleration performances. Te paper presents a proposal for modelling of te torque converter dimensionless caracteristics using segmented continuous function taking as variable te inverse of te kinematic ratio. Tere are analysed te variants of te caracteristics offered by te literature as well as te implementation of te torque converter model into te veicle model. 1. INTRODUCTION Te simulation of te acceleration and of te tractive performances of veicles plays an important role in optimization of te driveline and running gear. Te accuracy of te simulation depends dramatically of te models used for engine and transmission. Usually, te steady state caracteristics of te engine are known from te tecnical specifications provided by te supplier in terms of variation of te effective power and torque versus engine speeds or, at least, te values of te maximum power and maximum torque and te speeds of te engine. Contrary, te tecnical specification of te transmission provide te only te ratios of te gearbox and, sometimes, te maximum torque ratio of te torque converter. Te modelling of te driveline imposes te Figure 1 Torque converter components usage of te torque converter caracteristics (te variation of te efficiency, torque ratio and absorbed torque versus slippage) (1). Te effort made for modelling te torque converter caracteristics ave focussed on te usage of cubic Spline for fitting data () and on te estimation of te torque converter caracteristics taking into account te geometry of te pump and turbine rotors (3), (4). Neverteless, te paper dealing wit te veicle performances or wit te analysis of te automatic transmissions include models based on te fitting of te torque caracteristics provided by te supplier (1), (6) or using appropriate tools implemented in specialized software suc as Dymola (7). 11
Very often, te designers ave to rougly estimate te longitudinal dynamics of te veicles for different configuration of te driveline based on commercial presentations of te engines and transmissions; suc presentations usually provide only te ratios of te gearbox and te maximum torque ratio of te torque converter.. DIMENSIONLESS CHARACTERISTICS OF TORQUE CONVERTER Te dimensionless caracteristic of te torque converter represents grapically te variation of te efficiency and torque transformation ratio versus te inverse of te speed ratio, defined as: nturbine nturbine =, [,1] ; K = (1) n n Figure presents a typical dimensionless caracteristic of torque converter (Allison TC-418)/ It may observe tat te efficiency curve presents two typical sections: 1. A parabolic sape crossing te origin.. A linear sape followed by an abrupt drop for ig values of te inverse of te speed ratio. impeller K K [ ] impeller Te evolution of te torque transformation ratio sows two sections too, te sapes being quasi-linear. Te two sections mentioned above correspond to te two stages of torque converter work: as torque converter and as ydro-coupler, respectively; te sifting between te two stages is automatic due to te release of te stator (see Figure 1 for te components of te torque converter) for K 1. Te efficiency of te torque converter is defined as te ratio of te output power by te input power: P input η =. () Poutput Using te following definitions: P = M ω ; P = M ω input impeller impeller output output output η [ ] [ ] as well as te relations (1), from te relation () finally results: η = K (3) η K Figure Typical torque converter dimensionless caracteristics 1 η 1 1
It is reasonable to model te efficiency curve according to te sapes of te two sections described above. Te following conditions apply in modelling te efficiency curve: A. Te curve must cross te origin: η () =. (4) B. Te maximum of te efficiency occurs for te value of te inverse of te speed ratio noted : 1 η ( ) =η ; (5) 1 d η ( ) d i = 1 =. (6) C. Te maximum value of te torque transformation ratio, noted K may be calculated using te relation (3): K η( ) = lim. (7) Imposing te conditions A and B, tree parameters may be calculated, wile using all te 3 conditions allows calculating 4 parameters. Consequently, it is possible to model te efficiency first section as a polynomial nd order or as polynomial 3 rd order, respectively; bot cases will be analysed furter. For te modelling of te efficiency as a nd order polynomial, te general form of te expression is: η ( ) = A ( ) + B ( ) + C, (8) and from te relation (4) results immediately: C =. Te relations (5) and (6) give te following simultaneous equations: A ( ) + B ( ) =η A ( 1) + B = 1 1 1 (9) Solving (9) wit respect to te parameters A and B permits to obtain te final expression of te efficiency: η 1 η ( ) = 1 1 (1) For te second case, considering te modelling as a 3 rd order polynomial, following similar steps of calculation, te final expression results: 3 ( ) ( K 1 1) ( 3 1 K 1) K 1 1 1 η = η + η + (11) Te typical values for te torque converters utilized for te ydrodynamic transmissions of eavy veicles are: 13
η =.84...88; =.8...86. 1 1 Te value of te maximum torque transformation ratio is provided by te torque converter producer and represents a key factor in selecting te appropriate type. For te ydro-coupler section te following linear relation is proposed: η ( ) =.95 (1) Finally, te all sections are described by one of te following functions: η 1 η ( ) = max,.95 ; (13) 1 1 η = η + η + 3 ( ) max ( K 1 1) ( 3 1 K 1) K,.95 1 1 1 (14) Te grapical representation of te actual curve and of te modelled curves is sown in Figure 3; it may observe tat for te normal region of te torque converter ( =...95 ) bot modelled curves provide an acceptable accuracy. η [ ] 1.9.8.7.6.5.4.3..1.1..3.4.5.6.7.8.9 1 i, ic, ic [ 1 ] Figure 3 Comparison of actual curve wit modelled curves Furter comparison is needed in order to conclude wat te best solution is. Te torque transformation ratio is calculated based on relation (3) in wic one of te relations (1) or (11) is inserted: K K η ( ) η = = 1 ( i) 1 1 3 K η 3 η K K = + + 1 1 1 1 ( i) 1 1 1 (15) (16) 14
Te grapical representation of te torque transformation ratio is presented in Figure 4. It results tat te nd order polynomial does not provide an accurate estimation of te maximum torque transformation ratio but te precision of te model is fully acceptable above =.. Contrary, te use of te 3 rd polynomial curve assure te accurate estimation of te maximum torque transformation ratio but te approximation becomes acceptable only above =.5. A detailed analysis of te modelling errors is grapically presented in Figure 5. error [%] 1 5 η [ ] K [ ].5.5 1.75 1.5 1.5 1.75 Actual curve nd order polynomial 3 rd order polynomial.5..4.6.8 1 [ ] Figure 4 Torque transformation ratio modelling 1 error [%] 5 K [ ] 5 nd order polynomial 3 rd order polynomial 1..4.6.8 1 1..4.6.8 1 [ ] [ ] Figure 5 Te estimation of te errors of modelling 3. ABSORPTION CHARACTERISTICS OF TORQUE CONVERTER Te torque converter absorbs te torque provided by te engine in variable amount depending on te slip between te impeller and te turbine. Te absorbed torque is calculated using te relation: n M impeller =. (17) Ki ( ) Te typical evolution of te absorption coefficient, noted K, is presented in Figure 6. Usually, te producers of torque converters provide only te value of stall absorption coefficient, noted K. In order to approximate te variation of te absorption coefficient, te K = K : following matematical expression is proposed based on te observation tat ( ) 5 i e K( ) = K + 1. (18) 15
Using te relation (18) te grap presented in Figure 6 as resulted. Te grap includes also te relative error due to te modelling. It may be empasised tat te relative errors are below % for inverse of speed ratio up to.4; te relative errors increase up to about 7% for.75, but increase dramatically at te edge of te ydrocoupling section. K [ ] 3 4 18 1 6 relative error..4.6.8 error [%] 1 5 5 1 15 [ ] Figure 6 Te absorption caracteristic of te torque converter K In order to better evaluate te accuracy of te modelling, te tractive caracteristics of a 14 tonnes veicle ave been calculated. Te powerpak includes a Diesel engine delivering 195 kw at 3 rpm and a planetary gear box wit 6 ratios for forward movement. Te metodology for calculating te tractive coefficient is detailed in (1), and te results are included into te grap presented in Figure 7. γ[ ].45.4.375.35.35.3.75.5.5..175.15.15.1.75.5.5 4 6 8 1 1 Figure 7 Tractive coefficient caracteristics V [kp] From Figure 7 results two main aspects wic are influenced by te errors due to te modelling of te torque caracteristics; te estimated speed for movement on slopes; 16
te setting of sifting speeds. Te first aspect is detailed in Figure 8; te resulted error is as ig as.5 kp representting about 5.1%. Tis error is inferior to tose of.375.35.35.3.75 estimation of te rolling.5 resistance or te driveline.5 efficiency. Consequently, te..5 5 7.5 1 1.5 15 V [kp] 17.5 modelling of te torque Figure 8 Detail for empasising te error in te estimation of te converter caracteristics does speed for climbing 15º slope not affect significantly te estimation of te speed te veicle can acieve climbing te slope. Te second relevant aspect regarding te influence of te torque converter caracteristics modelling refers to te estimation of te speeds for optimal sifting te ratio of te gear box. Te following sifting sequencing was adopted: 1 st stage wit torque converter (TC) working, ten te lock-up clutc is coupled end te next sift occurs at te speed wic corresponds to te nominal speed of te engine (3 rpm). Te process is detailed in Figure 9 wit empasis of te errors due te modelling of te torque converter modelling. It may conclude tat tese errors do not affect te acceleration process estimation of te veicle. For te stages 3 to 6, te tractive coefficient caracteristics presented in Figure 7 indicates tat is more economic to use only mecanical regime of te ydrodynamic transmission (te lock-up clutc remains coupled). 4. CONCLUSIONS.75.5.5.175.15.15.1.45.4 γ [ ].3. γ[ ] ΔV Sifting 1Mec-TC Sifting 1TC-1Mec Actual Based on te modelling Coupled Lock-Up Clutc.75 1 15 5 3 35 Te proposed modelling metod proposed use minimal data provided by te torque converter producers: te maximum torque transformation ratio and te stall absorption coefficient. Based on tese inputs, te proposed modelling metods allow te estimation of te efficiency, torque transformation ratio and absorption coefficient caracteristics. ΔV Sifting TC-Mec Figure 9 Sifting speed detailed V [kp] 17
Te estimation of te errors due to te modelling of te torque caracteristics as well as of te influences on te tractive coefficient caracteristics as demonstrated tat teir level is fully acceptable. Consequently, te proposed modelling is useful as a first estimation of te following aspects wic represent a real interest in design of powerpack and driveline of eavy veicles: estimation of te matcing of te engine and torque converter; estimation of te tractive coefficient caracteristics wic allow te cecking of te difficult movement situation suc as te motion on slopes; estimation of te acceleration performances of te veicle. Tus, te proposed metods may be applied to obtain first estimation of te veicle s performances witin te decision making process for adopting te appropriate configuration of te powerpack based on commercial data regarding te torque converter. REFERENCES (1) Ciobotaru T., Vînturiş, V., Oană M., Acceleration Process Of Te Tracked Veicle Wit Hydrodynamic Transmission, International Congress on Automotive and Transport Engineering, Brasov, Romania, October 7-9, CONAT 1, Braşov, Paper 15, 1 () Sandu C., Freeman J. S., Analysis of Veicle Subjective Performance and its Impact on Driving Simulation and Powertrain Design, Proc. of 14t Annual Ground Target Modeling and Validation (GTMV) Conf., Aug. 5-8, Hougton, USA, 3 (3) Sinya Kano S., Terasaka Y., Yano K., Prediction of Torque Converter Caracteristics by Fluid Flow Simulation, Komatsu Tecnical Report, VOL. 5, NO.154, 4 (4) Bărglăzan M., Dynamic Identification of a Hydrodynamic Torque Converter, U.P.B. Sci. Bull., Series D, Vol. 7, Iss. 4, 1 ISSN 1454-358, 1 (5) Stracan, P.J.,Reynaud F.P., Backstriim T.W., Te ydrodynamic modelling of torque converters, N&O JOERNAAL, APRIL, pp.1-8, 199 (6) Louca, L.S., Stein, J.L., Hulbert, G.M., and Rideout, D.G., Generating Proper Dynamic Models for Truck Mobility and Handling, Int. J. of Heavy Veicle Systems, v. 11(3-4), pp. 9-36, 3 (7) Hilding Elmqvist H. and oters, Realtime Simulation of Detailed Veicle and Powertrain Dynamics, SAE Paper 4-1-768, 4 18