MULTIBODY ANALYSIS OF THE DESMODROMIC VALVE TRAIN OF THE DUCATI MOTOGP ENGINE

Transcription

1 MULTIBODY DYNAMICS 7, ECCOMAS Thematic Conference C.L. Bottasso, P. Masarati, L. Trainelli (eds.) Milano, Italy, 5 8 June 7 MULTIBODY ANALYSIS OF THE DESMODROMIC VALVE TRAIN OF THE DUCATI MOTOGP ENGINE David Moreno, Emiliano Mucchi, Giorgio Dalpiaz, and Alessandro Rivola Departamento de Ingenieria de Sistemas Industriales Universidad Miguel Hernández, Campus de Elche, Avda. de la Universidad s/n, Elche, Spain dmoreno@umh.es Department of Engineering University of Ferrara, Via Saragat, 44 Ferrara, Italy s: emiliano.mucchi@unife.it, giorgio.dalpiaz@unife.it DIEM University of Bologna, Viale Risorgimento, 46 Bologna, Italy alessandro.rivola@unibo.it Keywords: Desmodromic valve train, Motorcycle, Experimental validation. Abstract. This paper presents a preliminary study concerning a multibody model of the desmodromic valve train used in the Ducati MotoGP engines. The desmodromic mechanism has a positive cam that causes the dynamic effects to be partly different from common valve trains, where the valve spring plays an important role. The presented model includes only one camvalve mechanism. In a further step of the research, it will be possible to develop and expand the model by introducing the other cam-valve mechanisms and other mechanical parts that compose the system in order to obtain a complete model of the valve train. In the first part of this work, the generation of the cam profiles is explained. The second part is focused on the description of the multibody model employed for the dynamic simulations. Finally, the experimental validation is presented and discussed. The comparison between the numerical results and the experimental data is encouraging even if it shows that the effectiveness of the model is not completely achieved. Therefore, it will be necessary to improve the model by including the presence of other mechanical parts of the valvetrain, as well as other important dynamic effects as, for example, the link flexibility.

2 INTRODUCTION When a mechanism operates at a high speed, its dynamic behaviour is deeply affected by link elastic flexibility and mass distribution, as well as the effects of backlash and friction in joints. As a consequence, motion alterations may occur, causing mechanisms to fail in the proper execution of their tasks. High accelerations and dynamic stress levels may also produce early fatigue failures, and high levels of vibration and noise may arise. In the particular field of valve trains for high-performance engines, these dynamic effects are particularly important since they may cause serious functional troubles, such as jump and bounce phenomena. Thus, increasing attention is addressed to the elastodynamic analysis in order to predict the dynamic behaviour, forces and impacts, and to identify the causes of failures and poor performances. However, the papers on this topic generally concerns widely-used trains with closing springs. In this case, the valve spring plays an important role in the system dynamics and its accurate modelling is required. On the other hand, in the case of desmodromic valve trains (mechanisms with positive-drive cams) the dynamic effects are partly different, as studied in [] and []. + K C = J A? = I E J E L A H? A H K I J A H A C = J E L A H? A H 8 = L A I A = J 8 = L A D A Figure : (a) General view of the desmodromic valve train of Ducati motorbike engines with four valves per cylinder; (b) schematic of the cam mechanism driving a single valve. Some of the authors have already developed non-linear lumped-parameter models of the desmodromic valve train, Ref. [] and []. The aim of this paper is to present a different modelling approach based on a multibody code, namely LMS Virtual.Lab Motion [], integrated with user defined procedures implemented in Matlab and FORTRAN. An integrated multibody-fem model, will make it possible to study the dynamic behaviour of the timing system, considering the elasticity of the bodies and evaluating the stress, strain and vibrational states of the components under different operating conditions in a more accurate way. Attention will be addressed to the benefits and drawbacks of multibody approach with respect to lumped parameter models. DESCRIPTION OF THE DESMODROMIC VALVE TRAIN This work concerns the timing system of the fourcylinder L engine of Ducati racing motorbikes, having double overhead camshafts, desmodromic valve trains and four valves per

3 cylinder. This system is partially shown in the general view of Fig. (a): two camshafts with four conjugate cams each one are driven by a gear transmission; one camshaft drives the four intake valves and the other one the four exhaust valves. The schematic of the cam mechanism driving a single valve is shown in Fig. (b): the lobes of a conjugate cam are in contact with their respective rockers; these two rockers are then in contact with the adjuster located at the tip of the valve. Thus, it is possible to identify two parts of the mechanism, each one consisting of one cam lobe and its corresponding rocker. They give valve acceleration in positive and negative directions respectively, where the positive direction is considered to be the direction of the opening valve. Here the terms positive and negative cam disc/rocker are used; however, these links are commonly, but improperly, called opening and closing cam disc/rocker, respectively. With respect to the more widely-used trains with closing springs, the desmodromic trains make it possible to give higher valve accelerations, preventing the follower from jumping off the cam, without employing a very stiff closing spring; on the other hand, the mechanical complexity of the desmodromic system is justified only in high-speed engines with single-cylinder heads, such as Ducati engines. GENERATION OF THE DESMODROMIC CAM PROFILES This section is intended to describe the cam synthesis process, i.e. starting from the valve displacement law (Fig. left) and taking into account the geometry of the mechanism, the profiles of both cams will be obtained (Fig. right). It is worth noting that, in order to control the backslash as a function of the camshaft angle, each subsystem (positive and negative) was created following a different motion law. Both are shown in Fig. ; red for the positive subsystem and blue for the negative one. 9 6 Valve displacement [normalized] Figure : Cam generation process. Both cam profiles (positive and negative) are generated starting from the displacement laws shown in the graph on the left. 4 7 In order to tackle the generation problem, a specific multibody model is created. The cam synthesis is clearly a kinematic case. Therefore, the backslashes of the different links that compose the mechanism are not considered and a set of ideal constrains is used. The schematic of the model is depicted in Figure.

4 Figure : Multibody model employed for the CAM generation. As it is shown, the model inputs (depicted as joint drivers) are the imposed motion of the valve and the camshaft angle. The kinematic chain that links these inputs with the output, i.e. the profile of the CAM, consist of four bodies and 5 kinematic constrains. Although the structure of this chain is always the same, the bodies that compose it depend on the conjugate CAM to be generated. For each CAM, positive or negative, their corresponding rocker and adjuster are used. The active adjuster is bracketed to the valve through a bracket joint that constrains all the DOFs between both bodies. The valve is also linked to ground by means of a translational joint, which is driven so that the valve follows the desired displacement. The motion is then transmitted to the active rocker through a curve-to-curve joint. This kinematical joint defines a bilateral contact constraint between two curves, one on each body, in order to keep the tangent vectors parallel at the contact point. Slip is also allowed. The CAM body consists only of an axis system, which is used to reference the points that compose the profile of the CAM. A driven revolute joint is used in order to attach this body to ground. It is worth noting that the camshaft angle was properly synchronized with valve displacement. Finally, in order to relate the motion of the rocker with the CAM body, a specific tool from the Virtual.Lab Engine Library is used. It is called CAM Generator and allows to create a CAM profile by taking as input the motion of the follower and other parameters like the dwell radius 4

5 and the number of points of the profile. The result is a file containing the profile points. By means of the described model, the positive and negative cams were generated. This profiles will be used in the following sections to carry out dynamic simulations of the desmodromic system. 4 DYNAMIC SIMULATION 4. General description of the dynamic model This section describes the multibody model of the desmodromic valve train, which is being developed using LMS Virtual.Lab Motion. At this stage, only a single valve sub-system has been modelled in order to simplify the estimation of the model parameters. Figure 4 shows the schematic of this model, composed of eight rigid bodies and twelve massless parts. The latter, also called dummy bodies, will be used in a forthcoming flexible model as an interface to allow meshed parts to interact with the rest of the multibody model. The transmission that drives the camshaft has been neglected in order to focus the modelling process on the valve mechanism. Because of this, the model input is the angular speed of the camshaft, which is depicted in the schematic as Joint Driver. This input drives the revolute joint that links the camshaft with the dummy camshaft. Unlike the rest of the dummy bodies, which will be ignored for now, this one has a key role in the rigid model. It is introduced to be able to consider the camshaft bending compliance at the point where the CAM is placed. To do so, a linear bushing (i.e. a 6 DOF spring-damper) and a planar joint, both acting between the ground and the dummy body, are employed to model the camshaft stiffness in the XY plane. The driven revolute joint, on the other hand, constrains the relative angular motion between the dummy camshaft and the camshaft. Otherwise, if both elements were applied on the camshaft, the revolute joint would cancel the effect of the bushing. As shown in the schematic, both the positive and the negative rocker are related to the camshaft by means of specific CAM contact elements taken from the Virtual.Lab Motion Engine library. Therefore, the cam surface is modelled using a 5th order spline. For each cam in the simulation, this spline is used to determine the penetration depth, velocity and sliding velocity between the cam and the follower. These parameters are then used to generate the forces in the contact according to the following expressions: F N (x p ) = k x p + k x p + c p ẋ p (penetration) () F N (x p ) = k x p + k x p + c s ẋ p (separation) () F T = µf N () Where x p is the penetration depth, k and k are the linear and quadratic stiffness coefficients respectively, c p and c s are the penetration and separation damping coefficients and µ is the firction coefficient. Thus, the contact algorithm is capable of predicting valve float, since the cam and follower are allowed to separate and re-impact throughout the simulation. Moreover, the Coulomb friction is also taken into account by this contact element. The rocker-adjuster interaction is slightly different. In this case, unlike the former, the curvature radius of the parts that take part in the contact does not vary with time. Therefore, a simpler contact element, i.e. the sphere to revolved surface contact, is used in order to take advantage of this fact. This element allows to properly model the interaction between the cylindrical surface of the rocker (sphere) and the planar face of the adjuster (revolved surface). The contact force is 5

6 Figure 4: Scheme of the multibody model employed for the dynamic simulations. 6

7 based on the depth of penetration and the relative velocity normal to the contact surface, while friction forces are calculated based upon the relative velocities tangential to the surface. Both rockers are bracketed to the ground by means of the parallel combination of a linear bushing and a planar joint in order to take into account the compliance of the hubs in the XY plane. As it is shown in the schematic, between the rockers and the ground there are also bracket joints marked with an asterisk. These constrains, which remove all the relative DOFs between parts when they are active, allow to study the behaviour of the system when the compliance of the hubs is neglected. The same constraint is added between the ground and the dummy camshaft. The valve is divided into two different bodies, the valve stem and the valve-head. As it is represented in the schematic, they are connected by means of a spring-damper element and a translational joint. Thus, it is possible to introduce in the model the axial stiffness of the valve. However, it is worth noting that this configuration will be modified for the elastic model, where the entire valve will be a flexible part. The connection among the valve stem and the two parts that compose the adjuster is made through bracket joints. On the other hand, a nonlinear springdamper element is introduced between the valve-head and the ground in order to model the contact with the seat. Unlike the other spring-damper elements described above, this element is only active when the valve-head is in contact with the seat. 4. Hertzian stiffness As it will be shown in the last section, the initial configuration of the model did not work properly for high speeds. As an attempt to avoid this problem, it was introduced the Hertzian stiffness for both contacts adjuster-rocker. This stiffness was modeled according to the following equation: F Hertzian =.7E [ ( ɛ C + ɛ tanh.5 δ )] δ sign(δ) (4) ν ɛ Where E is the effective Young s modulus of the two surfaces involved in the contact, δ is the penetration, ɛ is the restitution coefficient, C is the compound radius of curvature of both surfaces at the current point of contact and ν ɛ is the transition velocity. 4. Model limitations The current multibody model present the following limitations with respect to the previous Simulink models developed by some of the authors: The Hertzian stiffness of both contacts CAM-rocker is not considered since the program does not allow to parameterize the stiffness as a function of the contact point. Because of this reason, a constant stiffness is used. At present it is being developed a subroutine to consider the Hertzian stiffness of this contacts. The Squeeze effect is not considered either because the CAM Contact element does not allow to take into account any force when there is no contact. Also in this case a subroutine will be introduced to consider this effect. 7

8 5 MODEL PARAMETERS The values of inertial parameters are computed automatically by the program. However, the rest of model parameters were preliminary evaluated on the basis of both literature data and previous Simulink models and subsequently adjusted in order to fit the experimental results. The following tables (Tables -5) summarize all the used parameters. Parameter Value X Stiffness Coefficient e8 N/m Y Stiffness Coefficient e8 N/m X Damping Coefficient 4 Kg/s Y Damping Coefficient 4 Kg/s Table : Linear bushing parameters: camshaft Parameter Value Stiffness Coefficient.4 N/m (deactivated) Damping Coefficient 56 Kg/s (deactivated) Table : Valve seat spring-damper Parameter Value Parameter Value Linear Stiffness e7 N/m Linear Stiffness.5e7 N/m Quad Stiffness Quad Stiffness Penetration Damping Kg/s Penetration Damping Kg/s Separation Damping Kg/s Separation Damping Kg/s Follower Radius mm Follower Radius 7.5 mm Transition Velocity. m/s Transition Velocity. m/s Friction Coefficient.6 Friction Coefficient.6 Table : Contact parameters: positive & negative CAM-rocker contacts Parameter Value Stiffness Coefficient e7 N/m Damping Coefficient Kg/s Transition Velocity. m/s Friction Coefficient.64 Restitution coefficient Parameter Value Stiffness Coefficient e7 N/m Damping Coefficient Kg/s Transition Velocity. m/s Friction Coefficient.64 Restitution coefficient Table 4: Contact parameters: positive & negative CAM-adjuster contacts 6 COMPARISON BETWEEN EXPERIMENTAL AND NUMERICAL RESULTS 6. Experimental set up Experimental tests were carried out on a test bench developed at the laboratory of Ducati Corse. The experimental apparatus includes a test stand, two cylinder heads pertaining to the These parameters were obtained from the validation of a single cam-valve mechanism without considering the transmission that drives it. For this reason, the values of model parameters are not definitively assessed. 8

9 Parameter Value Parameter Value X Stiffness Coefficient 4.e8 N/m X Stiffness Coefficient.8e8 N/m Y Stiffness Coefficient 4.e8 N/m Y Stiffness Coefficient.8e8 N/m X Damping Coefficient 6 Kg/s X Damping Coefficient 8 Kg/s Y Damping Coefficient 6 Kg/s Y Damping Coefficient 8 Kg/s Table 5: Linear bushing parameters: positive & negative rockers same bank, an electrically powered driveline to operate the camshafts, a lubrication circuit, and the measurement instrumentation. In particular, only the components required for the operation of the valve train were included into the system, that is, crankshaft, piston, cylinder, and connecting rod were excluded. As a result, no gas forces, combustion, or spurious vibrations occurred in the considered system. The system under test is clearly different from the real one: in particular, it is only a portion of the real valve train and it is worth noting that only the components required to operate the valve train are included in the test bench. The system response is therefore dissimilar from the actual one, i.e. the response of the motorbike engine system in working conditions. However, such differences, as well as the inclusion (or exclusion) of the forces due to compressed gases, do not compromise the validity of the experimental data as a tool for model validation. The small valve mass and its high velocity do not allow contact measurements; on the other hand, the high-frequency range and temperature do not suggest the use of proximity transducers. In addition, the valve motion measurements may be affected by vibration of the cylinder head; it is therefore necessary to measure the relative motion between the valve-head and its seat. For these reasons, a specific high-speed differential laser vibrometer was used for this experimental study: the Polytec High-Speed Vibrometer (HSV). Finally, the valve motion has to be referred to the camshaft position. To this purpose, the experimental apparatus includes an encoder which is placed on the camshaft. By means of the described test bench it possible to run either only one camshaft or both. The experimental results reported in this study are relative to tests performed on the timing system of the horizontal bank; in particular, only the intake camshaft was driven and, consequently, only four cam-valve mechanisms were operated. For the comparison of the results of the multibody model with the experimental measurements, the valve motion of the desmodromic mechanism closest to the driveline (named as first cam mechanism) has been employed in this work. In fact, since the multibody model refers to a single cam-valve mechanism, it seems reasonable to make use of the experimental motion of the first cam mechanism for the comparison with the numerical results due to the fact that the motion of this cam-valve mechanism is less affected than the others by the torsional and flexural behaviour the camshaft. 6. Results Next, the comparison with experimental data is presented. However, it is worth noting that due to the differences that exist between the multibody model and the experimental one (i.e. in the current multibody model there is only one valve mechanism and the transmission driving this mechanism is not taken into account), it is not possible to talk about a strict validation. It could be considered as a preliminary validation of the model. The following figures show the acceleration of the valve for different camshaft speeds. The curves in blue depict the experimental values while the red ones depict the numerical results. 9

10 Low regime Valve acceleration [normalised] Medium regime Valve acceleration [normalised] High regime Valve acceleration [normalised] Figure 5: Results without considering Hertzian stiffness.

11 Low regime Valve acceleration [normalised] Medium regime Valve acceleration [normalised] High regime Valve acceleration [normalised] Figure 6: Results considering Hertzian stiffness.

12 The only difference between both figures is the consideration of the Hertzian stiffness. The results obtained by neglecting it are presented in Fig. 5, while it is taken into account in Fig. 6. Both experimental and simulated results are overlapped in order to evaluate the the effectiveness of the developed multibody model. As shown in Fig. 5, the results are quite good for low speeds but they tend to get worse as the camshaft speed increases. In fact, for the low regime both curves, experimental and numerical, are quite similar. However, although the response of the model at the medium regime is acceptable, there are some peaks in the experimental signal that are not followed by the numerical model. Finally, at the high regime both curves are quite dissimilar and the frequency of the oscillations does not even match. On the other hand, at Fig.6 the response of the model is different. In this case, at the low and medium regimes, the presence of the Hertzian stiffness increases the frequency of the numerical response with respect to the experimental one and introduces several considerable peaks. However, at the high regime the numerical results are improved with respect to the former case only in the first phase of positive acceleration, but in general the frequency of the oscillations is higher than in the experimental signal. In the light of this results, it seems reasonable to suppose that taking into account the flexibility of the members of the mechanism could increase the effectiveness of the model above all for high speed regimes in which the elastodynamic behavior is more important. To this end, a flexible model is currently being developed in order to study its influence. Once this model is validated, it will be possible in a further study to add the other cam-valve mechanisms, the transmission driving the camshaft and the missing external forces in order to obtain a complete system model. 7 CONCLUSIONS In this paper, a simplified model of the desmodromic valve train of the Ducati MotoGP engine has been introduced. Instead of using the lumped parameter approach like the models previously presented by some of the authors, a multibody model has been developed and preliminary compared with experimental data. The presented model is composed of eight rigid bodies which are related by different kind of joints and by two kinds of contact forces that act between the pairs rocker-cam and rockeradjuster. Some parts of the real system have been neglected in order to simplify the modelling process of the valve mechanism. Particularly, there is only one valve mechanism and the driving transmission system is not taken into account. Although the presented results show that the model still needs to be improved, they are very encouraging considering the simplicity of this model. Taking into account the good behavior of the model at low regimes and its bad response at high speeds (Fig. 5), it is quite probably that the introduction of link flexibility will improve its response above all at high speeds. Therefore, it will be necessary, in a further study, to improve the model by including important dynamic effects as the link flexibility as well as the presence of other mechanical parts of the valve train. 8 ACKNOWLEDGEMENTS The work presented in this paper has been performed in the framework of the Marie Curie Host Fellowship EDSVS for early stage researchers. The author would like to thank the European Commission for the grant received. The authors wish to thank DucatiCorse for active

13 co-operation during the course of this research. Part of this project has been carried out within the Laboratorio di Acustica e Vibrazioni (LAV) which is supported by Regione Emilia Romagna - Assessorato Attivit Produttive, Sviluppo Economico, Piano telematico - Fondi Obiettivo (I). REFERENCES [] G. Dalpiaz and A. Rivola. A Non-Linear Elastodynamic Model of a Desmodromic Valve Train. Mechanism and Machine Theory, 5(), 55 56,. [] Rivola A.,Troncossi M., Dalpiaz G. and Carlini A. Elastodynamic analysis of the desmodromic valve train of a racing motorbike engine by means of a combined lumped/finite element model. Mechanical Systems and Signal Processing, ISSN: 888-7, (), 75 76, 7. [] LMS International. LMS Virtual.Lab 6A, 6. [4] Carlini A., Rivola A., Dalpiaz G., Maggiore A. Valve Motion Measurements on Motorbike Cylinder Heads using High Speed Laser Vibrometer. Proceedings of the 5th International Conference on Vibration Measurements by Laser Techniques: Advances and Applications, Ancona (Italy), ,. [5] Carlini Andrea. Studio di una Distribuzione Desmodromica: Progettazione Cinematica, Simulazione Elastodinamica e Verifica Sperimentale. Ph.D Thesis, Dottorato di Ricerca in Meccanica Applicata, University of Bologna,. [6] Fogli Federico. Analisi Multibody di una distribuzione desmodromica in ambiente LMS Virtual.Lab. Degree Thesis, University of Ferrara, 7. [7] R. R. Craig and M. C. C. Bampton. Coupling of substructures for dynamics analyses. AIAA Journal, 6(7), 9, 968.