PRELIMINARY SELECTION OF BASIC PARAMETERS OF DIFFERENT TORSIONAL VIBRATION DAMPERS INTENDED FOR USE IN MEDIUM-SPEED DIESEL ENGINES

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1 Ivan Filiović Dževad Bibić Aleksandar Milašinović Almir Blažević Adnan Pecar ISSN PRELIMINARY SELECTION OF BASIC PARAMETERS OF DIFFERENT TORSIONAL VIBRATION DAMPERS INTENDED FOR USE IN MEDIUM-SPEED DIESEL ENGINES Summary UDC 6.436: In the develoment and alication of highly dynamic mechanical systems, major roblems can arise from usually unwanted accomanying rocesses, such as torsional vibrations. The internal combustion engine is a tyical dynamic system with a high robability of fracture of a system art due to the effects of torsional vibrations. In engineering ractice, the IC engine crankshaft fracture due to torsional vibrations is revented by using additional devices that allow the transfer of critical vibration modes of the crankshaft out of the IC engine oerating range, or devices daming the resulting twist angle amlitudes. This aer resents a ossible aroach to defining arameters of torsional oscillatory systems of IC engines needed for a reliminary selection of basic arameters of various tyes of torsional vibration damers, such as the elastic damer, the balance weight damer and the dual mass flywheel. The roosed hysical and mathematical models and methods of defining the inut arameters were comared with exerimental results. Key words: torsional vibration damer, IC engine, balance weight damer, dual mass flywheel. Introduction Because of their secific way of work (cyclic energy machine), internal combustion (IC) engines roduce a variable torque at the crankshaft at all seeds. Variation of the torque is influenced by the engine design (number and osition of cylinders) and the maximum cylinder ressure. Taking the variation of the torque at the crankshaft [, 3, 0, ] and different crankshaft stiffness at different cross-sections [, 6, ] into consideration, the aearance of torsional vibration is inevitable. Besides to torsional vibration, the crankshaft is somewhat less exosed to flex and axial vibrations. If some resonant regimes are in the IC engine oerating range, torsional vibrations of the crankshaft ose a risk due to fatigue and ossible fracture of the crankshaft. The increase in secific IC engine energy arameters (ower, torque, in-cylinder ressure, etc.) due to the reduction in engine dimensions, or the number of cylinders, roduces greater unevenness of the torque at the engine crankshaft [9, ]. The analysis of torsional vibrations requires close attention, esecially when the IC TRANSACTIONS OF FAMENA XXXVI-3 (0) 79

2 I. Filiović, Dž. Bibić, A. Milašinović Preliminary Selection of Basic Parameters of Different A. Blažević, A. Pecar Torsional Vibration Damers Intended for Use engine works at critical resonant seeds. The emergence of critical resonant vibrations in the engine oerating range can be overcome in one of the two ways: by shifting the resonant regimes outside the IC engine oerating range, by introducing secial devices to reduce the vibration amlitude in the resonant regimes. The first mentioned method requires increasing the crankshaft stiffness while reducing the moment of inertia of all masses of the entire iston and connecting rod assembly. From the structural oint of view, this is ractically imossible. The second method, the introduction of secial devices called torsional vibration damers (TVDs) is realistic and extensively used. Torsional vibration damers used in IC engines differ in structure and working rinciles [, 3]. For road motor vehicles, viscous and elastic (rubber) damers were irrelaceable for a long eriod of time. They were more accetable because of their simlicity, cost and easier maintenance. Recently, there has been a trend of relacing the TVD as a searate unit with different variants of the dynamic absorber built in into the existing engine arts. So, torsional vibration absorbers are today already extensively develoed and used as incororated into the engine flywheel or the crankshaft balance weights [5, 8, 9]. This aer resents one ossible method of reliminary selection (evaluation) of damer arameters on the basis of dynamic absorbers, based on the modelling of torsional vibration rocesses. The final solutions must be exerimentally verified.. Torsional vibration damers for road vehicle engines By far the most commonly used TVD for road vehicle engines is the so-called elastic damer with a rubber elastic element. Such a damer is shown in Figure a. The damer is mounted on the crankshaft at the oosite side of the engine flywheel, where the largest twist angle amlitude occurs due to crankshaft vibrations (Fig. a). mass of inertia Connecting rod Crankshaft Carrier Elastic element Main mass Elastic element Mass of inertia viscoelastic element (ruber) Mass of inertia a) b) c) Fig. Three different TVDs for road vehicles IC engines TVD TVD TVD a) b) c) Fig. TVD mounting laces in IC engines Elastic damer with rubber as an elastic element is, in rincile, a searate unit mounted on one end of the engine crankshaft. The arameters determining the damer are highly non- 80 TRANSACTIONS OF FAMENA XXXVI-3 (0)

3 Preliminary Selection of Basic Parameters of Different Torsional Vibration Damers Intended for Use I. Filiović, Dž. Bibić, A. Milašinović A. Blažević, A. Pecar linear (stiffness, daming) and deend on the tye of elastic material, its dimensions, the twist angle and the temerature of elastic material, which varies deending on the engine oerating mode. The main disadvantage of the elastic damer is its reliability in oeration because the elastic element sticks to the metal (inertial mass of the hub). In order to increase reliability and eliminate the TVD as a searate element, vibration damers based on the rincile of dynamic absorbers have been recently develoed and incororated into the existing structural elements of IC engines. Thus the balance weight damer is successfully develoed [5] and built into the balance weight of the first crank web, see Figure b). If necessary, the balance weight damer can be mounted in more than one crankshaft balance weight. Similarly, the damer mounted in the IC engine flywheel [, 8, 9], the so-called dual mass flywheel (DMF), shown in Figure c), is develoed and shown in the IC engine resented in Figure c). The DMF has multile functions: it erforms vibration amlitude daming at critical engine seeds, balances the crankshaft angular velocity, rovides comfort to the driver when starting the vehicle from standstill, suorts the work of vehicle transmission and has imact on reducing engine noise. Because of the multile functions, and for the urose of achieving the desired effects, the DMF has a number of different structural designs (swing masses, different daming erformances, etc.) [8, 9], that will not be searately analyzed here. Here, the DMF is seen as a torsional vibration daming element. 3. Models for calculating amlitudes of torsional vibration system To analyze and study the TVD influence arameters, it is common to use the so-called hysical models of linear torsional vibration systems [, 7, 0], where all the rotating masses are reduced to the engine crankshaft rotation axis, under the condition of equal otential and kinetic energy of the real system and the hysical model. Alying this rincile, Figure 3 shows hysical models of torsional vibration systems for engines without a TVD (Fig. 3 a)), with an elastic TVD (Fig. 3b), with a balance weight damer mounted in the balance weight of the first crank web nearest to the first engine cylinder (Fig. 3c) and with a DMF (Fig. 3d). ulley TVD c 3 c c c 3 c 6 c 7 c c c 3 c 6 c TVD c a) c c) c c 3 c 6 c c c c 3 c 6 c c TVD b) 6 Fig. 3 Physical models of torsional vibration systems with different damers The movement of discs in the resented torsional vibration systems can be described mathematically by using the second order Lagrange equations [, 3]. By simlifying Lagrange's equations, the system of equations describing the vibration of an individual disk around the equilibrium osition (Figure 3), can be exressed as: where: I K C T(t) d) () 6 TRANSACTIONS OF FAMENA XXXVI-3 (0) 8

4 I. Filiović, Dž. Bibić, A. Milašinović Preliminary Selection of Basic Parameters of Different A. Blažević, A. Pecar Torsional Vibration Damers Intended for Use [I] the moment of inertia of the mass matrix [K] the internal and external daming matrix [C] the stiffness matrix {T(t)} the excitation matrix,, - the twist angle, seed and acceleration matrix. The general system of vibration equations () can be solved in several ways. Common methods are: the central difference method [] and the method of the harmonic analysis by introducing excitation (T(t)) in the form of Fourier's order, where solutions are obtained in the form of harmonic functions [, 3]. In engineering ractice, the most accetable method is still the last mentioned method, which is used in this aer too. Particularly sensitive inut data in this model are determined from the literature sources as follows: the moments of inertia of masses (θ i ) of comlex elements (connecting rod, crank web) are determined both exerimentally and numerically [, 3, 7, 0], the crankshaft stiffness (c i ), which is very sensitive because of the secific suort of crank ins at sliding bearings, is calculated by alying the finite element method and secific boundary conditions as described in [], the excitation amlitudes (T(t)), for each excitation order, are calculated by using the model described in [0], with corrections of some constants of the model, based on exerimental results, The internal (ε i ) and external (υ i ) daming coefficients are selected for a articular engine on the basis of the recommendations given in [, 3, 4], with some corrections based on exerimental results. The arameters for daming and stiffness of the elastic damer elements, shown in Figure, are not given within the above mentioned inut data for the mathematical model (). To successfully imlement the above model describing the torsional vibration movement of the engine crankshaft with its elements, two hysical engine models, shown in Figures 3a and 3b, are observed. For them, estimates of the crankshaft twist angles are made, and the results are comared with exerimental results. The IC engine is a four-stroke, 6- cylinder turbocharged diesel engine. Basic data about the engine are given in Table. Table Basic data about the IC engine Number of cylinders 6 Bore 5 mm Stroke 50 mm Engine ower / engine seed 84 kw/00 rm Maximum engine torque 890 Nm Firing order Moment of inertia of masses, Fig. 3a θ = 0,077 kg m, θ = θ 4 = θ 5 = θ 7 =0,47 kgm, θ 3 = θ 6 = 0,0835 kg m, θ 8 =,87 kg m Stiffness c = 4,3 0 6 Nm/rad, c =...= c 7 =,8 0 6 Nm/rad, c 8 = 4, 0 6 Nm/rad, Coefficient of external daming υ =...= υ 6 = Nms/rad Coefficient of internal daming ε, ε,..., ε 7 calculated according to [] 8 TRANSACTIONS OF FAMENA XXXVI-3 (0)

5 Preliminary Selection of Basic Parameters of Different Torsional Vibration Damers Intended for Use I. Filiović, Dž. Bibić, A. Milašinović A. Blažević, A. Pecar For the engine model shown in Figure a, calculations of torsional vibration amlitudes for the first mode and for the main excitation orders 6, 7.5, 9 and are made. The calculation results are shown in Figure 4. Along with these results, exerimental results are resented with an excellent agreement between exerimental and comutational results. The former are obtained by the method described in [4, ]. The agreement of comutational and exerimental results indicates that the model is roerly chosen and that the inut data are lausible. Given that the most sensitive element in the modelling rocess is the TVD, the confirmation of the chosen model for the calculation of torsional vibrations is made on the basis of the exerimental results obtained by measuring the engine with an elastic TVD, which has long been in use. The resented model of the engine with a TVD with a rubber elastic element is shown in Figure 3b. The arameters of the damer (ε and c ) are taken as a function of the relative twist angle between the masses (discs) (θ and θ ) and the rubber temerature [3]. The results are shown in Figure 5, where one can see a significant shift in the resonant oeration mode of the engine for the first mode of torsional vibration amlitudes and the excitation orders 4, 5 and 6, comared to the corresonding amlitudes for the engine without a TVD at resonant oerating mode. Vibration amlitude at ulley [ ] order/i Calculation Ex. 9 order/i 7.5 order/i 6 order/i Engine revolution [r..m] Fig. 4 Diagram of calculated and exerimentally obtained twist angles of the torsional vibration amlitudes at the ulley for the engine without a TVD Vibration amlitude at ulley [ ] Calculation Ex. 6 order/i 4.5 order/i Engine revolution [r..m] Fig. 5 Diagram of calculated and exerimentally obtained twist angles of the torsional vibration amlitudes at the ulley for the engine with.an elastic TVD The values of the torsional vibration amlitude at the end of the engine crankshaft oosite to the flywheel are below 0.5. The authors' exerience is that these values are, in terms of mechanical load acting on the IC engine crankshaft, within ermitted limits. Considering the nonlinear characteristics of rubber in articular, the agreement between the calculated and exerimental results is regarded as satisfactory, which means that the chosen TRANSACTIONS OF FAMENA XXXVI-3 (0) 83

6 I. Filiović, Dž. Bibić, A. Milašinović Preliminary Selection of Basic Parameters of Different A. Blažević, A. Pecar Torsional Vibration Damers Intended for Use model of the torsional vibration system is accetable for the analysis of torsional vibration arameters of the system with any damer. 4. Analysis of results 4.. Balance weight damer The main art of the research deals with the choice of arameters of the torsional vibration damer to be mounted on the engine crankshaft. The damer shown in Figure b reresents a kind of dynamic absorber built in the balance weight and mounted on the first crank web of the engine crankshaft oosite to the flywheel. The lace of mounting the TVD is shown in Figure b. The damer can be mounted in one or two balance weights, deending on the required inertial mass of the damer. The main condition to be fulfilled is the equality of mass moments of inertia of the disks θ =θ +θ, so that the balance of inertial forces and corresonding moments of the comlete engine can be maintained. This solution has fully eliminated the TVD as a searate entity, and the balance weight damer should rovide similar daming effects. The basic arameters of the new damer are: moment of inertia of the damer (θ ), torsional stiffness (c ) obtained from axial stiffness of srings distributed along the balance weight erimeter and internal daming defined by the internal daming coefficient (ε ). The internal daming coefficient (ε ) deends on the sliding bearings in which the inertial masses are moving (Fig. b). Quantities that define the reviously described damer in its character are: c f const, θ const, ε () When selecting the damer arameters, the model uses relative quantities c /c and θ /θ. The internal daming coefficient (ε ), which deends on the tye of bearings and comlete sliding surface, is considered a constant value. Its imact is commented on later. The hysical model of the torsional vibration system with a balance weight damer is shown in Figure 3c). It is necessary to modify the mathematical model described by the general equation () so it can be used for calculations with the balance weight damer. So, the vibration equations of mass (θ ) as they are used in the conventional engine model (Fig. 3a) θ ν ε ε 3 c c 3 T, (3) are relaced for the model with a balance weight damer (Fig. 3c) by two equations of the following form: θ c ν ε ε 3 ε c 3 c T, ε c 0 θ. (3b) The mathematical equations of the modified mathematical model are solved with varying relationshis c /c = and θ /θ = , which is, from the design oint of view, a ossibly realistic change of the arameters c and θ. The value of the internal daming coefficient is ket constant, 0 Nms / rad. The results of the maximum twist angle of the torsional vibration amlitudes for the first mode and 6 th order (A 6/I ) are shown in Figure 6, with Figure 6a showing the deendence (3a) 84 TRANSACTIONS OF FAMENA XXXVI-3 (0)

7 Preliminary Selection of Basic Parameters of Different Torsional Vibration Damers Intended for Use I. Filiović, Dž. Bibić, A. Milašinović A. Blažević, A. Pecar of A 6/I =f (c /c ) on θ /θ as a arameter, while Figure 6b shows the deendence of A 6/I =f (θ /θ ) on c /c as a arameter. As a comarative analysis of the results of the twist angle amlitudes at the first mode and 6 th order for the ulley of the engine without a damer (Fig. 4) and with an elastic damer (Fig. 5), Figure 6 clearly shows that with certain numbers of combinations of the relations c /c and θ /θ the same amlitude effect as in case of the engine with a conventional elastic TVD (A 6/I 0. ) can be achieved. This alies to the amlitude A 4.5/I too. The osition of the resonant vibration conditions both for the first mode and 6 th excitation order is different from the one resented in Figure 5 and it significantly deends on the relationshis c /c and θ /θ. A [ ] 6/I / = 0 Nms/rad A [ ] 6/I c/c = 0 Nms/rad Relation c /c Relation / Fig. 6 Diagram of twist angles of the torsional vibration amlitudes (A 6/I ) at the engine ulley (θ ) deending on the relative stiffness and relative moment of inertia of the inertial mass of the balance weight damer The effect of the relationshi c /c on the osition of the resonant vibration conditions is shown in Figure 7. The analysis also showed that the internal daming coefficient (ε ) of the damer minimally affects the osition of the resonant vibration. A [ ] 6/I 0.0 c/c / = 0,35 = 0 Nms/rad Engine revolution [r..m] Fig. 7 Diagram of twist angles of the torsional vibration amlitudes (A 6/I ) at the motor ulley (θ ) The influence of the damer daming effect (ε ) on the vibration amlitude (A 6/I ) is ositive, but it is not secifically analyzed here. TRANSACTIONS OF FAMENA XXXVI-3 (0) 85

8 I. Filiović, Dž. Bibić, A. Milašinović Preliminary Selection of Basic Parameters of Different A. Blažević, A. Pecar Torsional Vibration Damers Intended for Use 4.. Dual mass flywheel The design of a dual mass flywheel is shown in Figure c. In addition to torsional vibration amlitude daming, the DMF achieves other effects too that are suitable for the transmission of the vehicle and driver comfort. This aer analyzes the role of the DMF in the context of the torsional vibration amlitude daming, rimarily at the engine ulley (θ ). Figure c shows the mounting lace of the DMF on the IC engine crankshaft. The hysical model of the torsional vibration system with a DMF is given in Figure 3d. The mathematical model is the same as for the hysical models shown in Figures 3a and 3b. The requirement to analyze the influence of stiffness (c ) and the moment of inertia (θ ) of the DMF is to resect the equality of the moments of inertia of one mass (θ 8 ) and the DMF (θ 8 and θ ), θ 8 = θ 8 + θ. In this way, the degree of rotation unevenness of the engine crankshaft is ket. The values of stiffness (c ) and the inertial mass moment of inertia (θ ) are varied as relative quantities c /c = and θ /θ 8 = In this analysis, the internal daming coefficient (ε ), which deends on the design of the sliding elements of the srings and the inertial art of the DMF, is ket constant. The calculation results of the torsional vibration twist angle amlitudes for the first mode and 6 th excitation order (A 6/I ) at the engine ulley are shown in Figure / c/c A [ ] 6/I 0.0 A [ ] 6/I 0.0 = 0 Nms/rad = 0 Nms/rad Relation c /c Relation / 8 Fig. 8 Diagram of the torsional vibration twist angle amlitudes (A 6/I ) at the engine ulley In Figure 8a, the deendence of A 6/I =f (c /c ) on the ratio θ /θ 8 as a arameter is shown, while in Figure 8b the deendence of A 6/I =f (θ /θ 8 ) on the ratio c /c as a arameter is shown. The results shown in Figure 8 do not have the effect of the torsional vibration twist angle daming as this is the case with using the TVD shown in Figures a and b. This is exected due to the mounting osition of the DMF (Fig. c) and its multile functions. The increase in the torsional vibration amlitude daming effect can be achieved by introducing greater internal daming (ε ) and adding dangle masses. 5. Conclusions The aer resents a ossible aroach to a reliminary selection of basic arameters of different tyes of conventional and new designs of torsional vibration damers, and the effect of the arameters selected in this way on the critical torsional vibration twist angle amlitude at the ulley of medium seed diesel engine for road vehicles. 86 TRANSACTIONS OF FAMENA XXXVI-3 (0)

9 Preliminary Selection of Basic Parameters of Different Torsional Vibration Damers Intended for Use I. Filiović, Dž. Bibić, A. Milašinović A. Blažević, A. Pecar The choice of models (hysical and mathematical) and the roosed methods of defining the inut data on the torsional vibration system are convenient for engineering ractice considering good agreement between the calculated and exerimental results for the critical amlitude of the twist angles. These results are comared between engines without any significant internal daming and those showing significant internal daming (engine with an elastic TVD). The calculation results for the balance weight torsional vibration damer show that it can fully relace the elastic torsional vibration damer. Taking the design ossibilities into account and based on the torsional vibration twist angle amlitudes (A 6/I ), the inertial mass moment of inertia (θ ) and the corresonding sring stiffness (c ) can be chosen. Deending on the selected arameters (θ and c ), balance weight damers are mounted on one or two crank webs oosite to the engine flywheel. The effect of daming the critical twist angle amlitude in the case of using a DMF is slightly smaller than in cases in which other damers resented in this aer are used. In this case, however, the twist angle amlitudes of the engine ulley are reduced by more than 3 times. If additional structural details are introduced, the DMF can successfully relace the conventional torsional vibration damer. The resented method of choosing torsional vibration damer arameters is regarded as satisfactory for the so-called reliminary selection, esecially if engine arameters (moment of inertia, stiffness, daming and excitation) are not recisely defined. The final TVD design has to be confirmed exerimentally. REFERENCES [] Blažević A., Bibić Dž., Filiović I.: Function and Adotion of IC Engines Dual Mass Flywheel, I ut. Conference on accomlishments in Electrical and Mechanical Engineering and Information Technology - DEMI 0, , Banja Luka, 0. [] Filiović I.: Motori sa unutarnjim izgaranjem, dinamika i oscilacije, Mašinski fakultet Sarajevo, 007. [3] Filiović I., Določek V., Bibić Dž.: Modelling and the Analysis of Parameters in the Torsional- Oscillatory System Equivalent to the Diesel Engines in Heavy-Duty Vehicles, Journal of Mechanical Engineering vol. 5, no. /05 issue 488 (005) [4] Filiović I., Jankov R.: Modern aroach to measurement and analysis of the IC engines arameters, Proc. Int. Scientific Symosium Retracing the Puch Track, Ptuj, Slovenia, 00, [5] Gerhardt F., Fechler C., Lehmann S., Langeneckert H.: Internal Crankshaft Damer, 7 th LuK Symosium, aril 00., [6] Hafner E. K., Maass H.: Torsionsschwingungen in der Verbrennungskraftmaschine, Sringer Verlag, 985. [7] Hafner E. K.., Maass H.: Theorie der Triebwerksschwingungen der Verbrennungskraftmaschine, Sringer-Verlag, Wien-New York, 984. [8] Kooy A., Gillmann A., Jäckel J., Bosse M.: DMFW-Nothing New?, 7 th LuK Symosium, aril 00., [9] Kroll J., Kooy A., Seebacher R.: Torsional Vibration Daming for Future Engines, Schaeffler Symosium, 00. [0] Maass H., Klier H.: Kräfte, Momente und deren Ausgleich in der Verbrennungskraftmaschine, Sringer- Verlag, Wien-New York, 98. [] Milašinović A., Filiović I., Milovanović Z. Knežević D.: Determination of the Engine Torque of a Four Cylinder Four Stroke Diesel Engine on the Basis of Harmonic Analysis of the Crankshaft Angular Velocity, Transaction of FAMENA, Volume 35, No.4, Zagreb, 0, TRANSACTIONS OF FAMENA XXXVI-3 (0) 87

10 I. Filiović, Dž. Bibić, A. Milašinović Preliminary Selection of Basic Parameters of Different A. Blažević, A. Pecar Torsional Vibration Damers Intended for Use [] Milašinović A., Filiović I., Hribernik A.: Contribution to the Definition of the Torsional Stiffness of the Crankshaft of a Diesel Engine Used in Heavy-Duty Vehicles, Proc. ImechE, Part D, Journal of Automobile Engineering, Volume 3, Number 7/009, [3] Wilson W.K.: Practical Solution of Torsional Vibration Problems, Devices for Controlling Vibration (Volume Four), Chaman Hall, 968. [4] Wong Y., Lim T. C.: Prediction of Torsional Daming Coefficients in Recirocating Engine, Journal of Sound and Vibration, 38 (4), 000, Submitted: Acceted: Prof. dr Ivan Filiović Prof. dr Dževad Bibić Almir Blažević University of Sarajevo Mechanical Engineering Faculty Vilsonovo šetalište Sarajevo, BiH doc. dr Aleksandar Milašinović Unversity of Banja Luka Mechanical Egnineering Faculty Ul S. Steanovića Banja Luka, BiH Adnan Pecar Automotive Center - centar za vozila Sarajevo Vilsonovo šetalište Sarajevo, BiH 88 TRANSACTIONS OF FAMENA XXXVI-3 (0)