Editorial Type:
Article Category: Research Article
 | 
Online Publication Date: 01 Sept 2006

Development of a Non-Pneumatic Wheel3

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Page Range: 150 – 169
DOI: 10.2346/1.2345642
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Abstract

The pneumatic tire has proven to be the dominant design for rolling transport since shortly after its invention by John Boyd Dunlop in 1888. This paper identifies four critical characteristics that led to the success of the pneumatic tire: low energy loss on rough surfaces, low vertical stiffness, low contact pressure, and low mass. A non-pneumatic structure is proposed that exhibits these four critical characteristics while breaking some of the most restrictive design constraints imposed by pneumatic mechanics. This structure consists of a circular beam composed of two inextensible membranes separated by a relatively low modulus elastic material. The beam is connected to a hub by thin elastic spokes. This structure forming an integrated tire∕wheel is called a Tweel™.

Keywords: non-pneumatic wheel; Tweel™
Copyright: The Tir Society
FIG. 1.
FIG. 1.

Rigid wheel impacting an obstacle.

FIG. 2.
FIG. 2.

Kinetic energy loss of a rigid wheel rolling over an obstacle. Note that a relative obstacle height (obstacle height divided by wheel radius) of 0.1 leads to a 23% loss in kinetic energy of the wheel.

FIG. 3.
FIG. 3.

Translational velocity of a simulated rigid cylinder and pneumatic tire rolling over an obstacle. Note that the rigid cylinder is very close to the analytical value computed. The pneumatic tire loses much less kinetic energy when rolling over an obstacle.

FIG. 4.
FIG. 4.

Fundamental load-carrying mechanics of wheels. Rigid wheels carry load by direct compression in the contact area, “bottom loaders.” Tensioned spoke wheels and pneumatic tires suspend the load from the arch of the wheel above the contact area due to reduction of spoke tension in the contact area, “top loaders.”

FIG. 5.
FIG. 5.

Typical load deflection curve of a pneumatic tire. The inflation pressure in this case is 0.2 MPa (2 bar). The curve follows a power law with an exponent slightly greater than one.

FIG. 6.
FIG. 6.

Typical stiffness curve for a pneumatic tire derived from Fig. 3. Note that the pneumatic tire acts as a stiffening or hardening spring, increasing stiffness with deflection.

FIG. 7.
FIG. 7.

Typical footprint of a pneumatic tire. Note that the total footprint area times the inflation pressure gives 87% of the tire load. Thus the contact pressure is approximately equal to the inflation pressure.

FIG. 8.
FIG. 8.

This non-pneumatic structure replaces the inflation pressure with a special beam that deforms almost entirely in shear. It consists of two inextensible membranes separated by a relatively low shear modulus elastic material and is called a “shear beam.”

FIG. 9.
FIG. 9.

Length of a shear beam deformed to a flat surface. Since the membranes on the inner and outer surface are inextensible, when flattened the material between the membranes must shear to accommodate the difference in membrane lengths. The shear strain can be calculated as a simple geometry problem.

FIG. 10.
FIG. 10.

A free-body diagram of an infinitesimal length of the shear beam. For simplicity, only the forces in the z direction are shown. The contact pressure p is assumed unknown.

FIG. 11.
FIG. 11.

The shear beam is connected to a hub by thin deformable spokes.

FIG. 12.
FIG. 12.

When loaded, the shear beam flattens in the contact area. The spokes in the contact area buckle and effectively carry no load. The wheel then acts as a “top loader.” The load is suspended from the top of the wheel by tension in the spokes.

FIG. 13.
FIG. 13.

The stiffness of the wheel is controlled by the spokes. The ring is effectively inextensible. When loaded the ring flattens and follows a shorter path than the original circle. The excess length must be accommodated. Weak spokes allow ring diameter growth and a short contact patch results, giving low stiffness. Stiff spokes restrain ring growth and force a longer contact patch, giving high stiffness. Contact pressure is independent of this mechanism.

FIG. 14.
FIG. 14.

Comparison of the load deflection behavior of a pneumatic tire and a Tweel™ of the same dimensions. Note that the two wheels have the same secant stiffness at about 0.011 M.

FIG. 15.
FIG. 15.

Comparison of the stiffness behavior of a pneumatic tire and a Tweel™ of the same overall dimensions. Note that the Tweel™ has about half the tangent stiffness of the pneumatic tire at the 0.011 M deflection that gave the same secant stiffness.

FIG. 16.
FIG. 16.

Translational velocity of a simulated pneumatic tire and a Tweel™ rolling over an obstacle. The pneumatic tire loses a little more translational velocity when rolling over an obstacle in this particular simulation. Both wheels have the same mass, moment of inertia, and secant stiffness at the loaded condition.

FIG. 17.
FIG. 17.

Progression of a rigid wheel rolling over an obstacle. (a) Just before striking the obstacle at point O. (b) Free-body diagram during the impact. (c) Just after striking the obstacle. (d) Wheel on top of the obstacle. (e) Wheel just before striking the ground at point P. (f) Wheel just after striking the ground.

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