TECHNICAL

Bad Vibrations

Winter testing on the latest batch of Formula 1 cars, fitted with the new-for-1997 rear impact absorbing structures, threw up an interesting vibration problem. While all the teams who experienced the problem have managed to solve it, it serves to illustrate a technical phenomenon that is well understood in the aerospace industry, but not so well understood in motor racing.

Rear wings have, until this year, been mounted on twin plates bolted to the gearbox. The plates support an aerofoil shaped cross beam, to the ends of which are bolted the rear wing endplates. The rear wing assembly is attached between the endplates. The new rear impact absorbing structure occupies the space used previously by the twin mounting plates, it did not take designers long to decide to mount the cross-beam direct to the conical impact structure.

The impact structure, looking like a reversed, similarly functioning nose cone, is very stiff and is attached rigidly to the rear of the gearbox case. The cross beam is bonded to it.

The teams that have experienced problems, and it is probably no coincidence that two of them have the Renault engine, have not been specific about the details, but it would appear that they have suffered cracking around the attachments of the cross beam to the wing endplates. Fortunately the cracks were detected in time and no catastrophic failures of the rear wing mountings occurred.

What happened, and why were two of the most technically competent teams in Formula 1 caught out? Firstly, it is necessary to go back to basics.

When any structural part of a racing car is designed, the loads it carries are determined and the resulting stresses and strains in the component are calculated - nowadays usually using F.E.A. Data acquisition has enabled the loads to be determined much more precisely than before. Steady state loads, for instance the cornering and braking loads on a suspension member, can quite easily be calculated from the geometry and confirmed by strain gauging the component during track testing. But it is generally not these loads that will cause a component to fail. It is the non-steady-state loads, caused by vibrations added on to the steady-state loads, that consume the fatigue life of the component, finally causing fatigue cracking and failure. These alternating loads are difficult to measure or predict. Experience of what works is built up over time and fatigue test cycles developed that enable the life of a component to be predicted and checked. A change to the excitation source or the response of the structure to that excitation and the bank of experience is useless.

Excitation - the input to a vibrating system - comes from many sources on a racecar, but ultimately they are powered by the engine - the only source of power in the whole system. The engine itself is a major source, with its reciprocating components and intermittent combustion. V-8 and V-10 engines are particularly difficult to balance - Honda even put a balance shaft in the Mugen-Honda V-10. One of the strongest modes is a lateral mode, at a frequency that is a function of the RPM - well into the 100's of cycles per second. Wheels and tyres, even perfectly balanced, produce vibrations. In the 70's tyre vibration was so strong drivers sometimes could not breathe while the car was in a corner! Brake squeal is a high frequency vibration. Aerodynamic turbulence, particularly vortex sheddings, generate alternating loads on any structure over which the turbulent air flows.

For modelling purposes, structures are treated as a series of mass-spring-damper systems. Depending on the level of complexity and the range of frequencies of interest, a racecar is made up of hundreds of mass-spring-dampers for modelling purposes. The number of modes in which it can vibrate is well into the hundreds as well. The masses and springs are reasonably straightforward to quantify, and so the frequency of the modes can be predicted with acceptable accuracy. The damping is much harder, and the damping determines the mode shape i.e. the range of frequencies and the peak amplitude of that mode. Damping comes from the inherent properties of the materials being deformed in the mode (rubber has high damping compared with steel for instance) but at the higher frequencies it is the joints between components that provide much of the damping. Movement between bolted components creates a friction force that absorbs energy. It is highly non-linear, frequency dependent and subject to the details of the joint - in other words: virtually unpredictable. Without damping a system will vibrate, when excited, at any of the modes' natural frequencies with a high amplitude, generating significant forces in the structure. Damping spreads out the modes' frequencies and reduces amplitude.

If the excitation is of large enough amplitude and its frequency coincides with the undamped, natural frequency of a major structural mode, the amplitude of the forces involved can result in failures in the structure. This is what happened in the new rear wing mountings.

Whether it was a new excitation frequency or increased amplitude in the new Renault engine, or whether it was the new rear wing mounting structure mode shape that induced the problem is not clear, but I suspect it was the latter as the new engine ran in last years Williams and Benettons during winter testing without problems.

One can only speculate as to the nature of the change that raised loads in some components until cracking occurred. However one can make a reasonable guess and it will serve to illustrate the type of problem that can strike the unwary. It is likely that the vibration mode involved was a lateral mode as a V-10 has a strong lateral vibration and the rear wing structure is not very stiff laterally. It is likely that the new rear impact structure is much stiffer than twin mounting plates.

Mounting structures will affect the structural deformation when vibrating in a possible mode. There may also be differences in the damping and hence amplitude, as well as natural frequency. The way the cross beam and wing elements are bolted to the endplates provides a lot of the structure's stiffness, and at the same time the loads induced in the joints when the whole system vibrates, are significant. It is likely that the cracks occurred near these joints.

To learn how to avoid the pitfalls of bad vibrations, one need only turn to the aircraft industry where unexpected failures and parts falling off are even more unwelcome than on racecars. No civil or military aircraft flies until it has been resonance tested. The whole structure in all of its main configurations, is excited through a sweep of frequencies (or with white noise) using electromagnetic or electrohydraulic exciters, and the response of he structure is measured with a multiplicity of accelerometers. Sophisticated analysis software calculates the mode shapes and can also graphically display how the structure vibrates, in slow motion, for each mode. Comparison with predictions allow any unexpected problems to be identified. If the structure is modified or additional parts hung onto the aircraft, such as under-wing stores, the tests are repeated.

Similar techniques are employed for road cars, with the principle aim being to locate the source of interior noise due to parts of the body shell vibrating. Everyone has experienced how different parts of a car boom or buzz depending on either engine speed, road speed or the texture of the road surface. Each noise is a mode.

However, resonance testing is a lengthy procedure and requires a fully representative structure for testing. It is one of the tests that keep aircraft on the ground for months after the first prototype is built. For a Formula 1 car those months do not exist. There simply is not time between first build and the first race to include thorough resonance testing. It is carried out on the track, with all new parts inspected carefully every time the car stops. 99% of the time this works well, but every once in a while, the effect of bad vibrations causes a problem.

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