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Who developed the Magic Formula Tyre Model widely used for the analysis of tire behavior?

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Effective mass continued...

Joe Walter’s latest column The tire’s place in fuel economy was an interesting article on a basic engineering principle that is often completely overlooked. As automotive design and engineering undergraduates in the 1960s, we analyzed a light, car-derived van for coast-down testing, including rolling resistance, and rotational inertia of the whole drivetrain back right to the pistons. Every time the transmission goes via a gear wheel set, the inertial effect of upstream components is squared.

By happy coincidence, in my Bachelors degree project on crash testing, I was able to use these exact data and principles to account for an unexplained non-linearity in crash decelerations across a range of test speeds from 4mph to 32mph performed on a van and three cars of the same model elsewhere. In 2016, this effect is still important, but little-applied in analyzing low-speed damage testing for insurance ratings.

Even in high-speed crashes with the gearbox in neutral, the rotational inertia effect of the tires, wheels and drive shafts is detectable: if the tire loses contact with the test track surface due to the vehicle pitching up, the energy is not absorbed in structural deformation. Such is the sophistication of crashworthiness engineering that even small effects can be seen, even if not explained or attributed by the team.

But back to the tire and wheel effects alone: in various roles I have found it difficult to get at validated data for moments of inertia (MoI) of either or both those components. Joe Walter’s students have made the most of the available facilities. The simplest method, trifilar suspension, which I have proposed on a number of occasions in industry, has been met with scepticism every time – as has the need even to know the difference in MoIs – and hence even getting CAD-derived values has been an uphill struggle. Without experimental validation (because CAD tire models in OEM use are rarely fully representative of detail construction), comparisons are not reliable, so I have been asked: why bother?

To me, it mattered not only in terms of total vehicle mass, rolling resistance and concomitant effects on fuel consumption and emissions, it also affects the energy required to be absorbed by the brakes by the several percent mentioned in the article – significant in dimensioning the rotors, friction surfaces and calipers or shoes for strength, stiffness and thermal requirements – and these have a spiralling secondary effect on vehicle mass, unsprung mass, and of course, rotor MoI.

The alternative recourse is to use traditional guestimating methods for early-stage vibration engineering, but applied to the wheel as a hollow cylindrical hub, spokes idealized as an equivalent disk, and a hollow cylindrical rim, plus the tire carcass as equivalent disks for the sidewalls and a thin cylinder for the belt and tread portion. Again, without experimental data, this was hardly going to produce credible comparisons.

Well, there is going to be at least one cohort of dynamics engineers out there who know why it matters and what to do about it.

April 6, 2016

 

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