Posts Tagged ‘belt tension’

The Two T’s of the Euler-Eytelwein Formula

Sunday, May 14th, 2017

    Last time we introduced some of the variables in the Euler-Eytelwein Formula, an equation used to examine the amount of friction present in pulley-belt assemblies.   Today we’ll explore its two tension-denoting variables, T1 and T2.

   Here again is the Euler-Eytelwin Formula,where, T1 and  T2 are belt tensions on either side of a pulley,

T1 = T2 × eθ)

    T1 is known as the tight side tension of the assembly because, as its name implies, the side of the belt containing this tension is tight, and that is so due to its role in transmitting mechanical power between the driving and driven pulleys.   T2 is the slack side tension because on its side of the pulley no mechanical power is transmitted, therefore it’s slack–it’s just going along for the ride between the driving and driven pulleys.

   Due to these different roles, the tension in T1 is greater than it is in T2.

The Two T’s of the Euler-Eytelwein Formula

The Two T’s of the Euler-Eytelwein Formula

    In the illustration above, tension forces T1 and T2 are shown moving in the same direction, because the force that keeps the belt taught around the pulley moves outward and away from the center of the pulley.

    According to the Euler-Eytelwein Formula, T1 is equal to a combination of factors:  tension T2 ; the friction that exists between the belt and pulley, denoted as μ; and how much of the belt is in contact with the pulley, namely θ.

    We’ll get into those remaining variables next time.

Copyright 2017 – Philip J. O’Keefe, PE

Engineering Expert Witness Blog

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A First Look at the Euler-Eytelwein Formula

Friday, May 5th, 2017

    Last time we introduced the Pulley Speed Ratio Formula, a Formula which assumes a certain amount of friction in a pulley-belt assembly in order to work.   Today we’ll introduce another Formula, one which oversees how friction comes into play between belts and pulleys, the Euler-Eytelwein Formula.   It’s a Formula developed by two pioneers of engineering introduced in an earlier blog, Leonhard Euler and Johann Albert Eytelwein.

    Here again is the Pulley Speed Ratio Formula,

D1 × N1 = D2 × N2

where, D1 is the diameter of the driving pulley and D2 the diameter of the driven pulley. The pulleys’ rotational speeds are represented by N1 and N2.

   This equation works when it operates under the assumption that friction between the belt and pulleys is, like Goldilock’s preferred bed, “just so.”   Meaning, friction present is high enough so the belt doesn’t slip, yet loose enough so as not to bring the performance of a rotating piece of machinery to a grinding halt.

    Ideally, you want no slippage between belt and pulleys, but the only way for that to happen is if you have perfect friction between their surfaces—something that will never happen because there’s always some degree of slippage.   So how do we design a pulley-belt system to maximize friction and minimize slip?

    Before we get into that, we must first gain an understanding of how friction comes into play between belts and pulleys.   To do so we’ll use the famous Euler-Eytelwein Formula, shown here,

A First Look at the Euler-Eytelwein Formula

A First Look at the Euler-Eytelwein Formula

   

where, T1 and  T2 are belt tensions on either side of a pulley.

    We’ll continue our exploration of the Euler-Eytelwein Formula next time when we discuss the significance of its two sources of tension.

Copyright 2017 – Philip J. O’Keefe, PE

Engineering Expert Witness Blog

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