Impulsive behaviour

Thursday, February 09, 2012

Tags :  camshafts

camshaftsThe Oxford English Dictionary rather politely defines a jerk as "a contemptibly foolish person", and in reality this is probably the definition that most non-engineers would give. However, and to its credit, a more formal definition and one which is perhaps more meaningful to the world of engineering, is that of "a quick, sharp sudden movement". But as engineers we prefer our definitions to be a little more exact, so a better description and one more readily applicable to the world of cams and cam profiles is the rate of change of acceleration. Reflecting the amount of impulsiveness of the forces in the valvetrain, and derived by differentiating the acceleration curve with respect to time, cam designers also generally list jerk alongside lift, velocity and acceleration.

In early automotive cam profiles when the design was a long and tedious process using trigonometrical tables (or, worse still, graphical methods), having derived the lift, velocity and approximate accelerations involved, no-one was particularly keen to go to the next step. Ploughing your way through endless polynomials and ensuring the boundary conditions were met for all, one could be forgiven for wishing to go to the next level. Nevertheless, many realised that the impulsive forces generated may have had a detrimental effect on their valvetrain but reasoned that with the relatively flexible valvetrains of the period there was little that could be done about it at the time. Even the late Keith Duckworth, designer of the Cosworth DFV, is reputed to have discounted many of the arguments over jerk and opted to go for constant acceleration designs (interspersed with high levels of jerk at their boundaries, presumably) in his early years. It is perhaps ironic that with comparatively flexible valvetrains, the need to control the rate of change of the forces and the excitation this can produce in the lift harmonics is more acute.

In recent times, when valve profile analysis is readily available at the touch of a button - after considerable effort in inputting the data, I might add - the emphasis is all about the 'smoothness' of the design. I well remember the late Professor Blair instructing me in the absolute necessity of smoothing the transition from one lift phase to another in any design intended for a race engine. According to the professor, the most critical time is often the transition from the initial valve ramp into the positive acceleration phase at the start of valve opening. Insufficient care and lack of smoothing in this zone can lead to higher acceleration peaks and substantially greater jerk for what amounts essentially to the same lift profile. Furthermore, even if the valvetrains are considerably stiffer, high jerks or impulsive forces inevitably lead to avoidable cam wear, pitting or scuffing.


camshafts-large

It is perhaps interesting that in many aftermarket cams, jerk does not appear to rate highly in the design procedure. With limitations on velocity (from the tappet diameter) and maximum acceleration, so long as jerk is within reasonable bounds then there are generally no grounds for concern. For direct-acting cams, levels like 0.01-0.02 mm/deg3 have been mentioned, but where pushrod arrangements are involved, maximum levels somewhere nearer half of these have been suggested. But as mentioned earlier, when Fourier analysis of the lift envelope is undertaken, undesirable valve motion caused by spring surge and other resonant effects can occur.

So while it may be advisable to ignore the jerk selling you the cam, the jerk that lies within it may not be quite so easy to avoid.

Fig. 1 - A sample camshaft

Written by John Coxon

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Would you care to expand this discussion with respect to roller followers/tappets?