## Posts Tagged ‘belt width’

### Optimizing Belt Width in a Pulley-Belt Assembly

Friday, September 15th, 2017
 It’s been awhile since we began our discussion of a pulley-belt assembly operating within a hydroponics plant, and we’ve solved for a lot variables and derived many equations along the way.   Today we’ll tackle the two remaining variables,  T1 , the belt’s tight side tension, and T2 , its loose side tension, and we’ll determine exactly what belt width will optimize power transmission within our system.   Optimizing Belt Width in a Pulley-Belt Assembly        Last time we converted mechanical power, P, from horsepower into foot-pounds per second and the belt’s velocity, V, into feet per second in order to get things into terms we can work with.   We then inserted these values into the mechanical power formula to get, 2,200 foot pounds per second = (T1 – T2) × 3.93 feet/second               (1)    This equation will allow us to solve for T1 and T2, and from there we’ll develop a value for the optimum belt width.    Previously, we determined from the Euler-Eytelwein Formula that, T1 = 2.38T2                                                                                     (2)    Substituting equation (2) into equation (1), we get, 2,200 foot pounds per second = (2.38T2  – T2) × 3.93 feet/second      (3)    Reducing this equation with algebra we arrive at, T2 = 405.65 pounds                                                                         (4)    We can now insert equation (4) into equation (2) and calculate T1, T1 = 2.38 × 405.65 pounds                                                               (5) T1 = 965.44 pounds                                                                         (6)      T1 is maximum tension in the belt, specified by the manufacturer to be 300 pounds per inch of width, which makes the minimum width belt to be used to optimize power transmission within our  pulley-belt assembly, w = T1 ÷ 300 pounds per inch                                                           (7) w = 965.44 pounds ÷ 300 pounds per inch                                         (8) w = 3.22 inches                                                                                (9)    We can use a belt of minimum width of 3.22 inches to safely transmit 4 horsepower from the engine to the pump without incurring breakage and slippage along the belt, thereby optimizing power transmission within our assembly.   If we used a narrower belt, breaking and slippage would occur.   If we used a wider belt, an unnecessary expense would be incurred.    Next time we’ll begin a discussion on flywheels as they apply to rotating machinery like gasoline and steam engines.   Copyright 2017 – Philip J. O’Keefe, PE Engineering Expert Witness Blog ____________________________________

### Another Specialized Application of the Euler-Eyelewein Formula

Tuesday, June 13th, 2017
 Last week we saw how friction coefficients as used in the Euler-Eyelewein Formula, can be highly specific to a specialized application, U.S. Navy ship capstans.   In fact, many diverse industries benefit from aspects of the Euler-Eytelwein Formula.   Today we’ll introduce another engineering application of the Formula, exploring its use within the irrigation system of a hydroponics plant. Another Specialized Application of the Euler-Eyelewein Formula         Pumps conveying water are an indispensable part of a hydroponics plant.   In the schematic shown here they are portrayed by the symbol ⊗.     In our simplified scenario to be presented next week, these pumps are powered by a mechanical power transmission system, each consisting of two pulleys and a belt.   One pulley is connected to a water pump, the other pulley to a gasoline engine.   A belts runs between the pulleys to deliver mechanical power from the engine to the pump.     The width of the belts is a key component in an efficiently running hydroponics plant.   We’ll see how and why that’s so next time.   Copyright 2017 – Philip J. O’Keefe, PE Engineering Expert Witness Blog ____________________________________