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

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Air springs, hovercraft and tires

Air springs, also known as pneumatic springs or air bags, have surprising similarities with bias-ply tires with respect to construction, materials and functionality. Both are composed of rubber, fabric and one or more beads; both serve as pressurized vehicle suspension components providing isolation from road disturbances.

Geometrically, air springs and bias tires are defined as surfaces of revolution in their uncured and vulcanized states. Both are flexible fabric membranes undergoing large deformations. Such structures can be analyzed handily for internal stresses and deformation as pantographing networks of inextensible cords embedded in an incompressible rubber matrix. Both products are important, but neither of them dominate their respective markets. Nonetheless, many Class 8 trucks and most buses in the USA are fitted with air springs, although bias-ply aircraft and truck tires are extensively used worldwide.

Tires, in some sense, are rotating air springs. The first US patent for rubberized air springs was issued in 1847 to John Lewis for railroad cars and locomotives, the same year that R W Thomson published in Mechanics Magazine in the UK his results for horse-drawn carriage wheels equipped with pneumatic tires. Both concepts extolled the virtues of ‘riding on air’, but were not to be fully exploited until decades later.

Today, air springs are of two basic types: convoluted and rolling lobe, each featuring two plies of rubber and cord (at equal and opposite angles), and end plates for mounting purposes and air containment. Singly convoluted springs are often used as vibration isolators or load actuators. Doubly and triply convoluted versions resemble a stack of small tires lying on their sides and joined at the beads. The rolling lobe configuration, commercialized in the 1960s, is used mainly in heavy truck/bus suspensions. The lower end of the lobular assembly employs a contoured, concentric piston of aluminum or plastic over which the meniscus of the compliant sleeve moves up and down during jounce and rebound motions.

Vehicle suspensions allow tires to move about as needed to grip the road, leaving the chassis on a somewhat even keel to provide a comfortable ride. Steel springs commonly used in coil, leaf or torsion-bar configurations deliver a fixed spring rate, but can be modified to impart a slightly varying rate, as heavier axle loads require stiffer springs. Rolling lobe air springs, on the other hand, provide a widely variable, adjustable rate that can be changed automatically with load while maintaining constant ride height. This advantage of air springs is fully exploited in truck and bus suspensions where load variations fluctuate greatly. Despite that, OE passenger car fitments with air springs in the USA (1958-61) had a checkered history compared with heavy vehicles, showing poorer lateral stability and little improvement in automobile ride quality. Cost and complexity of compressors and height control valves and leaky air lines also contributed to the market failure. Nonetheless, so-called adaptive air suspensions are seeing limited use on upper-end automobiles, with ride height adjustment that can, for example, lower a chassis to reduce aerodynamic drag at high speeds, among other features.

Road shocks are partially absorbed by the relatively large excursions of vehicle suspension components. However, air and metal springs and, surprisingly, tires, all have poor damping characteristics. Thus, concurrent with the rise of the automobile early in the 20th century, shock absorbers (dampers) were developed as energy-absorbing adjuncts to car suspensions. George Westinghouse, the inventor of the railroad air brake, secured a patent in 1910 for an embodiment featuring oil and compressed air contained in dual telescopic tubes – today’s shock absorber. Various arrangements of these dampers and springs, some hydropneumatic, have since been used as vehicle suspension components.

Interestingly, when I joined Firestone decades ago, strategic planners in the company surmised that a possible long-term threat to replace the pneumatic tire could be a hovercraft vehicle supported by a cushion of low-pressure air. Invented in 1956 by Sir Christopher Cockerell, it seemed capable of traveling over land or water with air support only. Because of stability and lane control issues, only marine versions have had any success to date. Thus, it seems that pneumatic tires along with air springs in specific suspension applications will continue to meet our land-based transportation needs for smooth-riding vehicles.

 

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