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Modelling the Elastodynamic Behaviour of a Desmodromic Valve Train

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Modelling the Elastodynamic Behaviour of a Desmodromic Valve Train Modelling the Elastodynamic Behaviour of a Desmodromic Valve Train Alessandro RIVOLA (*), Andrea CARLINI (*), and Giorgio DALPIAZ (**) (*) DIEM - University of Bologna Viale Risorgimento, 2, I - 40136 Bologna, Italy e-mail: [email protected] (**) Dept. of Engineering, University of Ferrara Via Saragat, 1, I - 44100 Ferrara, Italy e-mail: [email protected] Abstract This paper deals with a lumped-parameter model of a motorbike engine’s desmodromic valve train. The model of such an uncommon cam system is developed and validated with the aid of experimental measurements carried out on a test bench which operates the cam mechanism by means of an electrically powered driveline. The model describes the mechanical system taking into account the mass distribution, the link elastic flexibility, and the presence of several non-linearities. The model parameter estimation is discussed and the effectiveness of the model is assessed by a comparison with experimental results. In addition, the model is employed to estimate the magnitude of contact forces and to predict the system behaviour as a consequence of changes in some design parameters; therefore, it may be used as a tool both in design optimisation and diagnostics. 1 Introduction train of a Ducati motorbike engine. Only works on widely-used trains with closing spring were found in Nowadays the study of the dynamic response of literature [7–9]; in those cases the valve spring plays flexible mechanisms operating at high speed is an important role in the system dynamics. becoming more and more important and several Conversely, in the case of desmodromic valve trains studies can be found in literature [1–4]. – i.e mechanisms with positive-drive cams – the As a matter of fact, the link elastic flexibility and dynamic effects are partly different, as shown in mass distribution, as well as the effects of [10–12] by the authors. backlashes and friction in joints, may affect the In order to get insight into the dynamics of such dynamic behaviour of the system so deeply that it an uncommon cam system, and to help the may fail to properly perform its task. In addition, development and validation of the elastodynamic high accelerations and dynamic stress may occur, model, valve motion measurements were retrieved causing early fatigue failure, and high vibration and from experimental tests carried out at the DIEM noise may arise [5–6]. Laboratory of the University of Bologna on In the specific field of valve trains for engines cooperation with Ducati [12]. During the test, the operating at very high speed, the above-mentioned camshaft was operated by means of an electrically dynamic effects are particularly important, since powered driveline. they may cause serious functional troubles, such as The model presented in this paper is a lumped- wear, fatigue loads and breakage of mechanical parameter model having twelve degrees of freedom components, jump and bounce phenomena of the (dofs). It describes the desmodromic train and the valve, and alteration of the engine’s fluid dynamics. driving mechanical transmission of the test bench, in Consequently increasing attention is addressed to order to employ the experimental results for model the elastodynamic analysis, as a tool for design assessment and validation. The model takes into optimisation and fault diagnostics as well as for the account the mass distribution, the elastic flexibility estimation of the actual dynamic forces, impacts, of all links (including the compliance of the and mechanism performances. driveline), and the presence of non-linearities. In this context, this paper presents a kineto- After the description of the mechanical system elastodynamic model of the desmodromic valve and its model, the measurement apparatus is Camshaft Timing Belt θ 0 Flywheel φ φ φ 2 3 1 Cylinder Head Timing Belt Intermediate Shaft φ 0 τ 1 Brushless Motor Figure 1: Schematic of the electrically powered driveline Figure 2: Schematic of the cam mechanism driving a single valve presented. Secondly, the paper compares the two camshafts (only one camshaft is shown in the numerical results to the experimental data in terms schematic of Fig. 1). Each camshaft has two of valve displacement and acceleration by using conjugate cams: one camshaft drives the two intake proper signal processing techniques. In addition, the valves and the other the two exhaust valves. importance of taking into account the stiffness Figure 2 shows the schematic of the cam variability of the rockers is pointed out. Finally, the mechanism driving a single valve: the discs of a model is employed to estimate the magnitude of conjugate cam are each in contact with a rocker; the contact forces and to predict the system behaviour two rockers are then in contact with the backlash as a consequence of changes in some design adjuster. It is therefore possible to identify two parts parameters. of the mechanism, each made up of one of the cam discs and the related rocker: one part gives valve positive acceleration, while the negative 2 The mechanical system acceleration is given to the valve by the other part of the mechanism (the positive direction is that of the This work deals with the timing system of the valve opening). twincylinder ‘L’ engines of Ducati racing motorbike A small helical spring is mounted around the which have double overhead camshafts, negative rocker pin and properly preloaded: its desmodromic valve trains and four valves per action is mainly needed during the dwell phase, cylinder [10, 11]. when separation of the cam discs from rockers takes As mentioned in the introduction, tests are place and, consequently, the contact between the carried out on an experimental test bench, where the valve-head and the seat might be lost. camshafts are moved by means an electrically powered driveline. The schematic of the driveline is shown in Fig. 1: it consists of a brushless motor 3 The elastodynamic model driving an intermediate shaft by means of a timing belt, and a second timing belt which moves the 3.1 Description of the model camshafts. The speed of the intermediate shaft is obtained by multiplying the motor velocity by the The mechanical system described above was ratio τ1 = 10/3. In order to reduce fluctuations of modelled with a twelve dofs lumped-parameter torque and velocity, the intermediate shaft is fitted model which describes the electrically powered with a flywheel. This shaft corresponds, in the driveline, the intake camshaft and the cam motorbike engine, to the shaft moved by the crank mechanism driving a single intake valve, namely the shaft with a gear transmission having ratio 1/2. The valve close to the camshaft pulley. The other cam second belt transmission, which reproduces the mechanism and the valve driven by the same engine belt loop, has ratio τ2 = 1/1 and drives the camshaft were not included in order to simplify the k ks ks k b1 12 23 b2 Js J J J 1 s2 s 3 0 φ φ φ φ θ 0 1 2 3 0 1 1 1 2 2 1 1 1 11 1 1 1 2 2 1 τ 1 1 τ δ 1 72 82 1 13 τ 1 1 τ 1 71 8 1 1 k 13 x 7 x 8 m7 m8 m3 x 3 k 7 k 8 k 34 x x 1 2 k 01 k 12 J J J 0 1 2 θ θ θ 01 2 δ 34 m 4 δ 46 x 4 k 45 k 46 k 5 x 6 m6 m5 k 6 k 26 x 5 δ 26 Figure 3: schematic of the lumped-parameter model model. However, this second mechanism is identical approximately introduced, assuming that this to the first one and theoretically moves in phase; the mechanism applies the same forces and torques to effects of the neglected mechanism are therefore the camshaft as the first one. In [10, 11] the authors presented models of the intermediate shaft between the flywheel and the desmodromic valve trains having eight dofs; in second pulley. those studies the speed of the camshafts was By means of the coordinate θ0, which represents assumed to be constant, that is, the dynamic the angular position of the pulley fitted on the intake behaviour of the mechanical transmission driving camshaft, the compliance of the second belt the camshafts was not considered. Actually, transmission is considered. The moment of inertia J0 experimental measurements carried out on the test is obtained by properly lumping the moment of bench, have shown that the oscillations of the inertia of the camshaft pulley together with the camshaft speed around the mean value are quite moment of inertia of a camshaft portion, the inertia important (up to ±10%). Therefore, the driveline of the exhaust camshaft, and the inertia of a portion moving the camshafts is taken into account in the of the timing belt. The torsional stiffness kb2 present work. represents the belt transmissions between the The model is developed with the aim to include intermediate shaft and the intake camshaft. all the important effects, as well as to get a rather The stiffness of both timing belts are not simple model. In particular, it takes into account the considered as constant during the simulation. In mass distribution, the elastic flexibility of all links fact, due to the effect of the dynamic loads, the belts (including the compliance of the driveline, the can release, causing the pre-load to be lost. bending and torsional compliance of the camshaft, The torsional compliance of the camshaft is and the variation of rocker stiffness as a function of taken into account by introducing the coordinates θ1 mechanism position), the damping effects, the and θ2, representing the angular displacements of variability of transmission ratios with mechanism the positive and negative cam discs, respectively.
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