For polyurethane treaded wheels, the prominent mode of failure is the bond between the tread and hub. While numerous factors can create such a failure, the predominant mechanism leading to bond failure is excessive heat in the bond region. Caster Concepts (CCI) has developed a model that predicts failure in polyurethane-treaded wheels based on the operating conditions of the wheel (load speed, ambient temperature, and so on). This formula provides a better understanding of polyurethane tires and how they react in different applications.
Polyurethane tires generate heat from the hysteresis of the urethane when it is cyclically deformed under load. This energy generation is related to the load and speed of the wheel as well as the physical characteristics – diameter, width, and tire thickness. The energy generated is absorbed by the wheel core or expelled through convective heat loss. When the energy absorbed is summed together with the energy lost to convection, they equal the energy generated by the cyclic deformation. This equation results in a first order differential equation that can predict the final temperature the wheel will reach.
When solving for the wheel failure prediction equation, two unknown parameters were needed from testing. The first was the convective heat transfer coefficient, hA, and the second was dependent on the urethane material used. It is called the material heat generation coefficient, kHG, for short. These unknowns were solved for during testing at CCI.
Where v is the velocity of the wheel in miles per hour, R is the radius of the wheel, L is the load on the wheel in pounds, s is the tire thickness in inches, w is the tire width in inches, TAMB is the ambient temperature of the surroundings in degrees F, T∞ is the steady state temperature of the wheel in degrees F.
To verify the equation, testing was done on various wheel sizes and polyurethanes. The failure prediction equation predicts steady state temperature of the wheel accurately, within 5%, for a given speed, load, and wheel size.
The prediction equation does begin to break down when the tire deflection under load exceeds 10%. Once 10% deflection is reached, the heat generation begins to change and grows exponentially, so the wheels become more likely to fail.
The variations in the failure prediction equation, between theoretical and actual results, can be attributed to many different factors. Precision error in all of the computer sensors and equipment is listed at 0.05%. Force load cell resolution is approximately 111 N (25 lb). The positioning of the IR sensor could also give a fluctuation in temperature readings of about ±2°C. There is also some contributable human error in reading the temperature profile graphs, approximated at ±1°C.
The final temperature of the wheel can be predicted from a given speed and load. This temperature can be compared to the failure temperature to determine if the polyurethane tire will withstand the applied load and speed. The equation will predict the final temperature within 5%. This equation can also be applied to wheels of different diameters and widths.
The equation is only valid for thin-tread polyurethane tires. When the tread becomes thick—greater than 0.02 m (0.75 in.)—the heat becomes trapped in the urethane due to its insulating properties, and the wheel does not follow the lumped capacitive model.
The predictive failure model can be useful for determining the correct wheel and urethane tire combination for specific applications without the need for testing. With the formula developed, only a few baseline tests are needed to develop the kHG for any urethane. Once a baseline kHG is developed, the formula can be used as a quality control tool to monitor tire/bond performance. Since kHG is affected by the bond strength, a poor bond will yield a higher kHG, which can then be compared to the baseline. Variations in the urethane stoichiometry will also affect the kHG and the performance of a wheel.
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