Faces come in many shapes and sizes. You might have a round face or maybe an oval-shaped face. You could have a square face or even a rectangular face. Based on the shape of your face, a particular hair style might suit you better. When you get to a certain age, and your eyesight starts to change, the width of your face will determine the size of the frames you will need for those pesky reading glasses that you suddenly require. Gears have faces, too. They also come in many sizes and shapes.
The face width of a gear is the length of the gear tooth perpendicular to the line of action as detailed in Figure 1.
With a spur gear, the face is the area at which the rolling action of the gear mesh occurs. As such, the face width contributes significantly to the maximum allowable torque capacity. For metric spur gears, the recommended face width is equal to ten times the module. For a module 2.5 spur gear, this would be 25 millimeters. The minimum recommended face width for a spur gear is 2.5 times the tooth height. This minimum value is set in order to prevent premature failure of the gear at the tooth root. For a module 2.5 spur gear, this minimum value would be 14 millimeters.
In order to design a gear with sufficient bending strength, the transmitted tangential force at the working pitch circle, Ft, is not to exceed the allowable tangential force at the working pitch circle, Ftlim, that is calculated taking into account the allowable bending stress at the root.
where Ftlim is calculated by:
In this equation mn is the normal module and b is the face width. Thus, the gear strength can be increased by either increasing the module or by increasing the face width. This relationship is linear. This means that a 20 percent increase in face width will increase the torque capacity 20 percent, and an increase in the face width of 125 percent will increase the torque capacity by 125 percent.
For a helical gear, there is a face width and an effective face width. The face width as measured on a spur gear is not applicable to a helical gear. Since the face width is measured perpendicular to the line of action, the effective face width is the distance along the tooth face (Figure 2). The calculation for effective face width is,
The effective face width increases as the helix angle increases. As the effective face width increases, the bending strength torque also increases. Thus, using a helical gear in place of a spur gear allows the designer to increase the torque capacity of a gear pair without increasing the width of the design window. However, since the pitch diameter increases as the helix angle increases, the gear diameter window does need to increase.
For straight tooth gear racks, the face width is measured in the same manner as a spur gear. For helical gear racks, the face width is measured in the same manner as a helical gear.
For bevel gears, the face width is measured along the gear tooth from the heel to the toe (Figure 3). The face width of a bevel gear is limited by the distance from the toe to the pitch apex. The distance from the pitch apex to the crown along the tooth face is known as the cone distance. The face width of a bevel gear should always be less than either 1/3 of the cone distance or 10 times the module. If the face width exceeds these values, then the tooth at the toe end becomes too thin to be functional.
For worm gears, the face width is measured at the pitch line. If the worm gear tooth is tapered after the pitch line, then the face width is measured as shown in the left image in Figure 4. If the worm gear tooth is tapered below the pitch line, then the face width is measured as shown in the right image in Figure 4. Although a worm gear is similar to a helical gear in geometry, the lead angle of a worm gear is too small to impact the bending strength torque.
The characteristic of face width exists for every type of gear. It is an important input into the calculation of bending strength, torque capacity, and, in certain designs, can allow for a stronger gear inside the same design envelope. When designing a gear system, be certain to account for the limitations of the face width of your gears.
