## Pulleys

Shaft 1 Connecting belt r If

V-belt

Shaft 1 Connecting belt

Driver pulley

FIGURE 6.1. Parts of a V-belt system.

Driven pulley

Shaft 2

Pulley crass section

Driver pulley

### FIGURE 6.1. Parts of a V-belt system.

the diameter of the driver pulley times the speed of the driver pulley is equal to the diameter of the driven pulley times the speed of the driven pulley. Expressed mathematically the pulley equation is:

where D = Diameter of a pulley; N = Pulley speed in revolutions per minute.

This statement is true because the linear speed (feet per minute) of the belt remains constant. If we identify D1 as the diameter of the driver pulley and D2 as the diameter of the driven pulley, we can determine the speed of the driven pulley by rearranging the pulley equation.

Using the example problem:

10.0 in x 100 rpm

When you understand the pulley equation, you should be able to state with confidence that when the driven pulley is smaller than the driver, the speed will increase, and when the driven pulley is larger than the driver is, the speed will decrease. Thus by visual inspection and intuitive reasoning you should be able to tell if a pulley drive train will increase or decrease the speed. To determine the actual amount of change, use the pulley equation.

One application of this principle is represented in the fan drive in Figure 6.2. Large ventilation fans of this type are commonly used in greenhouses, livestock buildings, and other agricultural applications.

Problem: Assume that you have a fan and an electric motor, but no pulleys. The fan is designed to operate at 500 rpm, and the electric motor operates at 1725 rpm. What sizes of pulleys will be needed to operate the fan?

Solution: First, intuitive reasoning tells us that a large change in speed will require a large difference in pulley diameters. Second, we know that the pulley equation

FIGURE 6.2. Determining unknown pulley size.

includes four variables, and at this point we only know two, the pulley speeds. To find a solution we must select one of the pulley sizes and then determine the other.

We could begin by selecting a pulley for the fan, but because the fan speed (driven) is less than the motor speed (driver), we know that the pulley on the motor will be smaller than the pulley on the fan. If we selected a pulley for the fan that is too small, the calculated pulley size for the electric motor may be smaller than what is physically possible. Therefore, begin by selecting the pulley size for the electric motor, and then calculate the required pulley size for the fan. If we select a 2.5-in pulley for the motor, then the size of the fan pulley can be determined by rearranging the pulley equation:

N2 500 rpm 8

Because pulleys are manufactured with diameters in increments of fractions of an inch, an 8 and 5/8-in pulley probably would be used.

Note that the ratios of the pulley diameters, D2/D1, will be equal to the ratios of the pulley speeds, N1/N2 = 3.45. Thus, if for any reason the 2.5-in pulley for the motor is not available, any combination of pulley diameters with a ratio of 3.45 (or approximately 3.5) will provide the correct speed. For example, pulleys with diameters of 8.625 and 2.5 or 17.25 and 5.0 or 34.5 and 10.0 will produce the same change in speed. This ratio of two pulleys is called the speed ratio and it will be discussed in more detail later in this chapter.