Last time we introduced a scenario involving a hydroponics plant powered by a gas engine and multiple pulleys. Connecting the pulleys is a flat leather belt. Today we’ll take a step further towards determining what width that belt needs to be to maximize power transmission efficiency. We’ll begin by revisiting the two T’s of the angle of wrap.
We must start by calculating Euler-Eytelwein Formula, which is presented here again,
e^{(μ} (1)^{θ)}We determined last time that the coefficient of friction, μ, between the two interfacing materials of the belt and pulley are, respectively, leather and cast iron, which results in a factor of 0.3. The other factor shown as a exponent of
You’ll note that this π, the other, α, which is less familiar. The unnamed variable α is used as shorthand notation in equation (2), to make it shorter and more manageable. It has no particular significance other than the fact that it is equal to,
D) ÷_{1} – D_{2} 2x) (3)If we didn’t use this shorthand notation for
D) _{1} – D_{2}÷ 2x))) × (π ÷ 180) (3a)That’s a lot of parentheses! Next week we’ll get into some trigonometry when we discuss the diameters of the pulleys, which will allow us to solve for
Copyright 2017 – Philip J. O’Keefe, PE Engineering Expert Witness Blog ____________________________________ |