# Desmodromic system

Nicolò Bozzato – nicolo.bozzato@studenti.unipd.it – Master Degree in Mechanical Engineering
updated on August 2017

## Introduction

The purpose of the project was to model and simulate the desmodromic system of a Ducati engine, in order to improve the performance.
The system was modeled in SolidWorks® and then imported in Adams for the analysis.

## Objectives

The objective of the study was to measure the acceleration of the valve and of the two rocker arms with two different profiles of the opening cam: the original one and the modified one.
The modified profile was conceived in order to change the valve lift trend and make it more “pushed”, to increase the engine rotation regime.

Fig. 1 – Cams

## The modelling problem

The profiles of the two cams (opening and closing lobes) were obtained with the metrology software ZEISS CALYPSO by Ph.D. Medeossi and Ing. Turchetto. The radiuses of the two rocker arms were obtained with the same technology, but not the complete shape of them: they were modeled in a simplified way, trying to be as close to the original profiles as possible.
For the sake of simplicity, the closing rocker arm was divided into two parts, an upper one and a lower one (with the same center of rotation).
A thickness of 5 mm and a density of 7850 kg/m³ was imposed to all the bodies. Given this value to the density, it was recognized that the calculated mass of the two rocker arms was similar to the real value, measured with a scale(14.9 g for opening rocker arm, 30.8 g for the closing one), proving the accuracy of the model.

Fig.2 – Models of the bodies

The portion of valve that was interesting for the analysis (opening shim, closing shim and part of the valve stem) was modeled in Adams as a composition of a box and a cylinder. In this case, the input was not the density but the mass, given by the constructor.
The centers of rotation of the cams were (obviously) coincident with themselves and with the origin of XY plane, while the positions of the centers of rotation of the rocker arms were given by the constructor.

## Simulations and analysis of results

After the implementation of the bodies into Adams, the creation of the connectors was performed: four revolute joint (one for each rotating body), a fixed joint between the two parts of the closing rocker arm and a translational joint for the valve, in order to constrain its movement in the y-direction.

 Body i Body j Type valve ground translational closing rocker arm (up) closing rocker arm (down) fixed closing cam ground revolute opening cam ground revolute closing rocker arm (up) ground revolute opening rocker arm ground revolute

Two rotational joint motions were imposed to the centers of rotation of the cams with the same runtime function: an angular velocity of 400 rad/s.
The Grubler count for the whole mechanism leads to: DOF = 6*6 – 5*4(R) – 5*1(T) -6*1(F) – 2(M) =3. The three DOF are related to the rotations of the two rockers and the translation of the valve. In the case we assume no clearance among bodies the Grubler DOF reduces to 0.
Four contacts were created: between the closing rocker arm and valve, opening rocker arm and valve, closing cam and closing rocker arm, opening cam and opening rocker arm.
To measure the angular acceleration of the rocker arms, a marker was added to each of the two arms. The displacement (lift), the velocity and the acceleration of the valve were measured in the center of mass of the valve.

### Original cam

The plot of the lift diagram obtained after the simulation is shown in the figure below:

Fig. 3 – Lift diagram

The maximum of this curve is 14 mm, reached at an angle of rotation of 192,5° of the opening cam. This maximum value must be unvaried for the new cam configuration because a greater value would cause damages.
The velocity and the acceleration of the valve are shown below:

Fig. 4 – Velocity and acceleration of the valve

The trend of this 3 diagrams (Fig.3 and Fig.4) is similar to those present in the literature [1], confirming the accuracy of the simulation. Finally, the angular accelerations of the rocker arms were calculated:

Fig. 5 – Angular acceleration of rocker arms

It is possible to observe that the two rocker arms have a specular diagram, with a trend similar to the acceleration of the valve. The negative and positive areas of these diagrams are due to the convention of the reference system.

### Modified cam

It was not possible to modify the cam in a considerable way: the maximum lift value must be 14 mm and the acceleration of the valve cannot exceed substantially from the diagram of Fig. 3. Furthermore, the occurrence of an undercut cam must be avoided [2]. Several trials were done before achieving this result.
A comparison between the two cams is shown in the figure below:

Fig. 6 – original (green) and modified cam (magenta)

All the previous measurements were repeated for this new type of cam.

Fig. 7 – comparison of the lift diagrams

The new cam “opens” the valve 3° earlier than the original one, and “closes” it 3° later.

Fig. 8 – Comparison between valve velocity and acceleration

Fig. 9 – Comparison between the acceleration of the rocker arms

The acceleration of the valve and of the rocker arms are bigger for the modified cam, but still in acceptable range.

## Conclusion

The modified cam, designed to change the lift diagram of the valve in order to improve the performance, gave good results in terms of velocity and acceleration of the valve and acceleration of rocker arms.
The next step is trying to create a more “aggressive” profile of the cam, in order to “expand the bell” of the lift diagram, without compromise the system.

## References

[1] M.Parini, “Analisi cinematica e cineto-statica delle ultime generazioni di distribuzione desmodromica Ducati”, M.Sc. Thesis, University of Bologna, 2012.

[2] A.Rivola, “Meccanismi con camme”, slides, University of Bologna. http://diem1.ing.unibo.it/mechmach/rivola/forli/mam_II/02Camme.pdf