A DEEPER LOOK
A DEEPER LOOK: WHERE THE WHEEL MEETS THE RAIL
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rains are the most efficient means of ground transportation ever developed for moving large volumes of heavy materials. Loaded railcars in North America can weigh up to 143 tons. On a given railcar this weight is distributed among its eight wheels, giving a wheel load of about 18 tons. The amazing efficiency of trains derives in large part from the low rolling resistance of hard steel wheels on hard steel rails, even under such heavy loads. Figure 1 is a schematic drawing of a loaded railway wheel pressing onto a rail. The highest demand in the steel of the wheel and rail is concentrated in the vicinity of the contact. Under 18-ton wheel loads, the demand is high enough to generate dangerous fatigue defects during use, even in the best quality wheel and rail steels. A full fatigue cycle occurs in loaded wheels with each revolution. A full fatigue cycle occurs in rail with each loaded wheel passage. Let’s take a deeper 12 Railway Track & Structures // January 2024
look at the demand placed on the steel where the wheel meets the rail. Where a wheel and rail meet in contact, the steel in both components deforms resulting in contact over an area rather than at a single point—much like pressing the tips of your index fingers together. This area of contact between a lightly worn wheel and a lightly worn rail can be quite small—around 0.3 square inches. In such a case, the average surface pressure between a fully loaded wheel and a rail is nearly 120,000 pounds per square inch (psi). In reality, however, the distribution of surface pressure between a wheel and rail is not uniform. The pressure is zero-valued around the edges of the contact area and maximal at the center of contact—roughly 140,000 psi at its peak. Given that the yield strength of modern wheel and rail steels is roughly 110,000 psi, how is it possible that wheels and rails last as long as they do in a heavy axle load
railway?! Before jumping into the details, there is some interesting historical background to consider. The German physicist Heinrich Rudolph Hertz is credited as being the first person to derive a complete mathematical description for the region of contact between elastic solids. (This is the same Hertz who proved the existence of electromagnetic waves and for whom the frequency unit, cycles per second, is named.) At the time, Hertz was a postdoctoral researcher studying the optics of glass lenses that were stacked on one another. He determined that the glass deformed locally where the lenses made contact, which he believed measurably affected the results of his experiments. Over a winter holiday break at his lab, the 23-year-old Hertz completed a mathematical analysis of his lens contact problem and resolved the issues he was having in his tests. Hertz published the solutions that he rtands.com
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By Gary T. Fry, Ph.D., P.E.