Prediction of ply steer and conicity

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Various types of lateral forces arise during tire service. These side forces differ by several orders of magnitude depending on vehicle category and operating conditions. They consist of larger cornering forces, midsize camber thrust, and a seemingly minor residual influence comprised of two components – ply steer and conicity. These latter two forces are present even at zero slip and camber angles.

My vehicle dynamics students are often taken aback to hear that the apparently inconsequential ply steer and conicity forces receive a disproportionate share of industry attention from vehicle ride specialists. This is because both components occur in straight-ahead, free rolling motion on a level highway and cause steering wheel pull, mostly due to conicity, which is annoying to the driver. The magnitude of the resulting perturbation varies not only with wheel load and inflation pressure, but also with the direction of rotation of the tire. The resulting force may point toward or away from the vehicle centerline. Ply steer changes direction with clockwise or counter-clockwise motion, while conicity does not.

Nominally identical radial tires from the same manufacturer will have relatively large, but narrowly distributed, values of ply steer, and relatively small, but broadly distributed, values of conicity. Ply steer in a given tire design is a deterministic variable that can be predicted early during the tire development process using principles of composite material mechanics. Conicity, on the other hand, is a random factory variable caused by small variations in manufacturing tolerances – especially those arising during assembly of tire components. In 1961 Eric Gough and his Dunlop co-workers were the first to report measurements of ply steer (pseudo-slip angle) and conicity (pseudo-camber angle) and to discuss their effects on vehicle behavior. Specifically, conicity is primarily responsible for steering wheel pull (a torque at the handwheel), which is not only a nuisance but can be fatiguing to the driver. Ply steer causes so-called ‘dog tracking’ of a vehicle, which is generally not discernible to the driver.

During the 1970s the conicity force was the only tire parameter specified by OEMs in the USA in an attempt to control steering pull. Significant levels of pull can arise in a radial tire if the belt is slightly offset from the tread centerline. Thus, US OEMs had strict limits on conicity at that time and the tire manufacturers would mark their OE production with the direction of the conicity force. At the automobile assembly plant, the tires would be mounted on the front and rear axles such that these forces, left and right, would tend to cancel each other and minimize steering pull. In the replacement market, tire induced steering pull problems could be minimized by placing tires with large conicity values on the non-steering rear axle of an automobile.

During the 1980s, as front-wheel-drive vehicles fully penetrated the North American automotive fleet, it was observed that different brands of tires with the same level of conicity varied in pull behavior on the same vehicle. While conicity was a reasonably good predictor of tire induced steering pull, it was obviously not the total answer. In other words, it was necessary but not sufficient to have low levels of conicity to ensure that steering pull was not a problem on some vehicles, but not all.

By the early 1990s, the best predictor of steering pull seemed to be the net self-aligning torque, known as residual aligning torque (RAT), on front-axle tires. This aligning torque occurs at zero lateral force. RAT has two components – one due to ply steer and one due to conicity. Accordingly, the ply steer component (PRAT) is deterministic while the conicity component (CRAT) is random, but the latter is highly correlated with overall conicity.

To minimize net RAT, manufacturers in ride-sensitive markets measure conicity on tire uniformity machines in their factories for every OE tire, but selectively sample PRAT on cornering force machines (once its value has been set by vehicle suspension and tire design variables). The car companies provide specifications, unfortunately different for different manufacturers, for conicity and often PRAT to their tire suppliers. Thus, to this day, tire makers in ride-sensitive markets determine these properties for automobile, light truck and SUV tires shipped to their OEM customers.

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