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The Use of VALDYN in the Design of the Valvetrainand Timing Drive of the new

Ferrari V8 Engine

Abstract

A fully dynamic model of the cranktrain and timing drive of the Ferrari V8 engine was developedusing the computer program VALDYN with the objective of understanding the interactionsamongst the various components. The intent was to design the components to allow goodcontrol of the valve motion and the forces in the system. Results of a parametric study at lowengine speed and low power output are presented. The work provided a thorough understand-ing of the factors affecting the phenomenon of rattling noise in the gears of the timing drive.

Figure 1: Front engine view

Domenico NocetiFerrari

Maranello, Italy

Riccardo MeldolesiRicardo ConsultingEngineers Ltd, UK

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Introduction

The Ferrari philosophy is to use the most advanced technologies to design and develop sportcarswith a unique character. This is achieved utilising materials and design tools that were success-fully tested in the highly competitive world of Formula One. The Ricardo software VALDYN isalready a well established tool for the optimisation of valvetrains in Formula One engines [1].VALDYN has since proved a very valuable tool for the analysis of the whole timing drive. InFerrari the program was utilised for the optimisation of the new 3.5 litre V8 engine, for thesuccessor of the F 355, the Ferrari two seater, mid engined sportscar.

For the study of the engine, which is shown in Figure 1, three different models were developed:

� A fully detailed model of a single valvetrain, to simulate the valve dynamics (Figure 2)

� A simplified model of the whole timing drive, suitable for simulating the engine in conditionswhen the timing drive is not significantly influenced by the cranktrain, such as low speed, lowpower demand (Figure 3)

� A fully detailed model of the whole timing drive and cranktrain, to investigate any workingcondition of the model (Figure 4)

This paper presents the results of the parametric activity carried out with the second model for lightload, low speed, looking in particular at the behaviour of the first stage gear reduction.

Figure 2: Single Valvetrain Model

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Figure 3: Low Speed Model

Figure 4: Complete Model

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Background

The new Ferrari engine is an uprated version of the existing V8 used on the F 355 car. Theimprovement of engine performance, in terms of both power and driveability, was achieved byincreasing the engine displacement and introducing new features, including:

� Increased inlet and exhaust valve size� New intake and exhaust port geometry� New and more aggressive cam profiles� Variable geometry intake system� Variable exhaust valve timing

The adoption of more aggressive cam profiles and camshaft phase changing devices increasedthe torque required to drive the camshafts as well as their rotational inertia. At the same timethe use of materials and surface treatments suitable for the reduction of friction losses reducedthe damping in the system.

The choice of two stage reduction in the timing drive follows from the need for:

� High volumetric efficiency� High combustion efficiency

Which in turn dictates:

� Five valves per cylinder arranged radially in order to achieve a hemispherical shaped com-bustion chamber

� Small angle between inlet and exhaust valves� Direct attack valvetrain layout with hydraulic bucket tappet

Figure 5: First stage gear reduction

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Figure 6: Belt drive

This resulted in a very compact design of the cylinder head, giving a short distance between theaxis of the two overhead camshafts. The impossibility to accommodate large diameter pulleysfor the drive by the toothed timing belt made the adoption of a two stage reduction unavoidable.

The first motion reduction is achieved via three gears as displayed in Figure 5, one on thecrank nose and the other two in either side of it, to transmit the motion to the two cylinder rows.The gear ratio is 1.5.

The second stage is realised via two conventional toothed belts, one for each cylinder row. Thetotal gear ratio between crankshaft and camshafts being two and 3/2 being already imple-mented in the gear drive, the timing belt drive reduces the motion with a ratio of 4/3 (Figure 6).

This layout for the timing drive results in a very compact and stiff design, that contributes toachieving precise control of the valve event, ensuring high performance and low emissions.

The downside of this architecture is a cost increase and possibility of generating gear rattlenoise from the first stage reduction. The rattle noise would not be a problem on racing applica-tions, but it must be avoided on road cars.

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Other aspects considered in the design and development stage were:

� Reliability� Sound quality� Good refinement

With these objectives in mind a dynamic analysis of valvetrains and timing drive was carried outwith the purpose of verifying the design.

Identification of rattle

The rattle noise is caused by the torque reversals making the gears separate and impact.

The energy involved in the impact is transmitted to the gear supports with a broad frequencycontent, characteristic of impact events. The gearcase vibrates at its natural frequency, excitedby the different orders of the force on the gear supports.

The gearcase vibrations are then transformed into sound noise and radiated outward.

Modelling approach

The assumptions made during the modelling of the system to investigate the low speed condi-tions were:

� Camshaft mass concentrated into two masses representing the camshaft and the camshaftpulley-cam phaser assembly

� Simple model of the valvetrain, with constant linear stiffness of the hydraulic lash adjuster.The valve springs were modelled as a constant linear stiffness and the mass of the activecoils of the springs included into the valve mass

� The two exhaust valves of each cylinder were grouped together doubling mass, stiffnessand damping values of a single valve. This allowed the size of the model to be reduced. Theaccuracy of the predictions were not reduced by this simplification, since the camshaftswere simulated as infinitely stiff

� The same was done for the two side inlet valves, but the central one had to be modelledseparately, since its timing is offset with respect to the others

� Simplified modelling of the crankshaft with a two mass, single stiffness system, tuned to thecrankshaft natural frequency; this allows the crankshaft to react to the forces coming fromthe timing drive gears. One of the masses is concentrated on the crankshaft nose, where thetiming drive gear is located. The second crankshaft mass was moved at a constant angularvelocity to simulate the condition of light load, where the angular speed variation due tocylinder pressure and crankshaft torsional vibrations can be neglected

Apart from these simplifications, all the rest of the system was modelled in all its details [2]:

� The gear support stiffnesses were modelled, together with the tooth pressure angle, toothstiffness [3], tooth damping, gear assembly mass and polar inertia

� In addition, the gear backlash was modelled and used as a parameter in the parametricstudy

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� The timing belt was modelled using the specific VALDYN element that reacts with a forceonly when the timing belt is stretched

� The effect of the tensioner arm rotation on the timing belt tension was also implemented

� The belt tensioners were also fully modelled, including expansion spring, internal checkvalve, volume of the high pressure oil chamber, leaking passages and piston mass

Results

The analysis of the VALDYN results showed that, in the load conditions examined, the mainsource of excitation in the system comes from the valve actuation.Because the valvetrain is designed to run up to very high speeds, the valve spring loads re-quired to keep the valves under control are very high, needing to be greater than the inertiaforces on the valvetrain, that vary with the engine speed square.

As a consequence at low speeds, where the inertia relief is low, the cam to tappet contactforces are high over the whole opening cycle; this results in high friction and a requirement forconsiderable levels of torque to drive the camshafts. Figure 7 shows a plot of the torque todrive the inlet camshaft at 1800 rev/min;

The harmonic content of the camshaft torque when an infinite camshaft torsional stiffness isassumed, shows harmonics at multiples of four camshaft revolutions, as shown on Figure 8.

Figure 8: Harmonic content of camshaft driving torque at 1800 rev/min

Figure 7: Camshaft driving torque at 1800 rev/min

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The different harmonics excite the timing drive causing torsional vibrations of the system ac-cording to its natural modes. Figure 9 Shows the first two mode shapes of the timing drivetorsional vibrations, where one of the nodes is always close to the belt pulley driven by thecrankshaft via the gear reduction stage. This is because the cranktrain inertia is much greaterthan the one of the camshafts. For the way the vibrations occur, the mode that is more likely tocause gear rattle noise is the first mode, because this mode of vibration generates torquereversal on the gears.

Figure 9: Modes of vibration of the timing drive

As in the more familiar case of crankshaft torsional vibrations, when the engine speed varies,the different harmonics of the camshaft torque excite the timing drive that vibrate in a combina-tion of its natural modes. Generally the first mode prevails on the others in magnitude. Whenthe frequency of an excitation coincides with the natural frequency of the first mode, a peak inthe vibration amplitude is observed.

For timing drive systems the cam torque harmonics that have significant amplitudes are the12th, 8th and 4th; These, expressed in engine orders, become the 6th, 4th and 2nd, as dis-played in Figure 10.

First Mode Second Mode

Figure 10: Order plot of the Belt force in the tight span, right side

Sixth Order

Second Order

Fourth Order

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At the resonance speeds, energy is fed into the systems and it is dissipated into the timing beltand impacts when the backlashes present in the system close, particularly the ones in the firststage gear reduction.

This phenomenon is shown in Figure 11 a-d, that contains the results of the simulation at the6th order resonance speed of 1800 rev/min.

Figure 11a shows the time history of the force in the tight side of the drive to the first camshafts.

This gives alternate contacts between the gear teeth from the driving side (Figure 11b) to thetrailing side (Figure 11c).

The effect of these impacts can be detected into the gear support forces (Figure 11d) as highfrequency vibrations that can cause noise.

The effect of speed variation on the gear support forces can be seen in Figure 12 a-d:

� At 600 rev/min there is no resonance and the impacts are not severe

� At 1800 rev/min the 6th order is in resonance and energy is fed into the impacts

� At 2200 rev/min there is no resonance as the speed lays in between the two resonances ofthe 6th and 4th order and the impacts are less severe (see also figure 14)

� At 2800 rev/min there is the 4th order resonance and again the impacts are more severe

The result in terms of noise emission are displayed in Figure 13. These measurements weretaken with a close field microphone and setting large values for the gear backlash.

They show high noise at 1750 rev/min which is attributed to the 6th order resonance,a quietperiod between 2000 and 2500 rev/min and high noise from 2500 rev/min upwards.

In order to control the timing drive dynamics and the noise emissions, it is important to gain agood understanding of the system and the effect of the many design parameters of the wholevalve actuation system. This was done undertaking a parametric study with VALDYN.

Parametric study

The transmission of gear rattle noise outside the engine is mainly structural rather than air-borne. Therefore, the forces that excite the engine structure are an appropriate measure ofnoise level in the parametric study.It was decided to use the magnitude of the gear support forces instead of the tooth contactforces; this is because the latter had proved to be too nervous and too much influenced by thelevel of tooth damping to be reliable.

The parametric study was undertaken on the following parameters and features:

� Gear backlash� Gear inertia� Split gears� Belt tensioner� Belt pretension� Tooth stiffness� Valve springs� Camshaft damper

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Figure 11 a (top) to d (bottom): Generation of gear rattle

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Figure 12 a (top) to d (bottom): Time histories of gear support forces at variousspeeds

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Figure 13: Noise measurements (Close field microphone, high tooth backlash)

The results of the above parametric study were:

� Gear backlash

The backlash was set to three different values:

� 0 µm� 35 µm (baseline)� 80 µm

The results are shown in Figure 14. As it can be seen, the gear support force shows asignificant sensitivity to the backlash. It allows placement of a lower limit to the force levelachievable changing only the gear backlash. A higher limit is also set, as the rattle noise willarise inevitably as the backlash is increased.

The results for the baseline and the cases with zero tooth backlash will be shown in dashedlines in all the following graphs as a background reference

� Gear inertia

When thinking of a body hit with an hammer, it can be imagined that, leaving the impactvelocity constant, the impact energy will depend on the hammer size [5]; in the same way,the range of the gear support force is affected by the gear inertia. Figure 15 shows thatreducing the gear inertia reduces the gear support forces and vice versa.

A reduction in the gear inertia can be achieved by keeping it as narrow as possible andhaving lightening holes in the hub.

Tests at Ferrari though showed that fitting the gears with discs of high damping material likecopper or cast iron, can reduce the noise emission significantly, despite the increase in thegear inertia. It follows that the best solution is to make the gears the lightest possible andthen fit them with copper discs to increase their intrinsic damping.

� Split gears

A split gear is composed by two gears connected together by a torsional spring that has apreload, which allows the gear to operate avoiding or sensibly reducing the amount of con-tact in the back side of the teeth.

Pa(dB A)

1000

4000

3000

2000

2000 3000 4000 50001000Hz

RpmMeasured

0

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Figure 14: Effect of gear backlash Figure 15: Effect of gear inertia

� Belt tensioner

The belt tensioner is responsible for keeping the belt in tension and for this purpose has aspring that assures initial tension in the belt; this spring has relatively low stiffness, in orderto compensate the thermal expansion without varying the preload too much.

The tensioner also has a chamber filled with oil that has its own compressibility which isproportional to the volume of the high pressure chamber itself.

Reducing this volume, increases the stiffness of the drive and the resonance speeds as canbe seen on Figure 17. The figure also shows that the forces on the gear supports increaseas well and this is not wanted.

There is also a lower limit to the tensioner stiffness, because the lower the stiffness thehigher the amplitude of the vibrations; when the engine is running at full load and the crank-shaft torsional vibrations are significant this can create problems of cam timing accuracy.

� Belt pretension

The belt pretension was tested at two completely different levels:

� 125 N� 1250 N (baseline)

The first value allows the belt to go slack, whilst the second exclude any loss of tension in thebelt.

The results are shown in Figure 18, where it can be seen that the range of the gear supportforce is not affected very much.

Therefore it is advisable to keep the belt pretension at moderately low values in order not tooverload the belt and increase its life.

This results in a reduction of the support forces, as displayed in Figure 16.

The downside of this option is the increase in friction and in the cost of producing split gears.

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� Tooth stiffness

The tooth stiffness was set to two levels:

� 2.1 * 106 N/mm (baseline)� 1.5 * 106 N/mm

Usually increasing the compliance in the region close to the impact point reduces the peaksof the impact forces. In this case though, the simulations showed that the effect was negligi-ble.

� Valve springs

At low speed the valve actuation is the main excitation of the timing drive; hence, any reduc-tion in the spring load via an optimisation of their design and a reduction of the valvetrainmass results in a reduction in friction and in camshaft driving torque that is responsible forfeeding energy into the tooth impacts. Figure 19 shows what can be achieved reducing thetotal spring fitted force and the spring rate by 20%.

� Camshaft damper

The use of camshaft torsional vibration dampers is an option when other attempts to reducethe cam TVs have proved insufficient [6].

Camshaft dampers are unusual in these kind applications and represent an extra cost forthe engine. Their use though is possible and can be very effective.

In the Ferrari V8 the use of the damper was simulated (Figure 20). Its effect was to smoothaway all the peaks in the gear support forces.

Figure 16: Effect of split gears Figure 17: Effect of tensioner stiffness

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Figure 19: Effect of reduction inspring force

Figure 18: Effect of belt preload

Figure 20: Effect of camshaft damper

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References:

1 Guido di Paola, Ferrari racing team: �The use of VALDYN in the design of Formula 1valvetrains� - Proceedings of the 2nd Ricardo Software International User Conference, De-troit, 28 February 1997

2 Valdyn 2.0 user manual - Ricardo Consulting Engineers

3 MAAG Gear Company �Maag Gear Book� - ed 1990

4 William T. Thomson �Theory of vibrations with applications� ed Chapman and Hall, Fifthedition 1998

5 J. Derek Smith: �Gears and their vibrations� Macmillian Press Ltd. - 1983

6 Ker Wilson �Practical solution of torsional vibration problems�, Chapman and Hall, Thirdedition 1968

Conclusions

The use of VALDYN in the simulation of timing drive dynamics quantified the effect of thevarious design parameters on generating gear rattle noise.

From the analysis it emerged that the key point is to control the energy involved in the impactand this can be done by:

� Implementing a tight control on the value of gear backlash

� When dealing with gear inertia, making the gears as light as possible and then fitting themwith elements that increase their intrinsic damping.

� Adopting a split gear that can operate avoiding or sensibly reducing the amount of rattle; thisresults in a reduction of the support forces.

� Appropriately tuning the oil volume in the high pressure chamber of the belt tensioner.

� Setting the lowest possible values for valve spring fitted force and spring rate.

� Fitting a suitably tuned camshaft torsional vibration damper

The parameters that did not show significant effects on the generation of gear rattle noise were:

� Belt pretension level

� Tooth stiffness.

VALDYN has proved to be a very valuable tool for the concept study and the development ofthe engine. The results of the simulations allowed decisions to be made on the design anddevelopment of this new power unit at Ferrari.