What is a spur gear?

Gearing 101: A primer on a type of cylindrical gear with straight teeth that are cut parallel to the axis of rotation.

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What is a spur gear? A spur gear is a type of cylindrical gear with straight teeth that are cut parallel to the axis of rotation. They are the simplest and most common type of element in mechanical drive systems.

Spur gears transmit power and motion between two parallel shafts. In order to do so, both the pitch and the pressure angle of both gears must be the same. Spur gears can increase or decrease the speed and torque of the rotating shaft depending on the sizing and arrangement of the gears.

The teeth of a spur gear are cut using a gear hobbing machine or a gear shaping machine. Spur gears can be produced from various materials, including steel, brass, bronze, or plastic, and depending on the application, they can be hardened based on the requirements for strength and durability.

A spur gear is the simplest and most common type of element in mechanical drive systems. (Courtesy: KHK USA)

The geometry of a spur gear is defined by several parameters. Figure 1 shows the location of various critical dimensions of a spur gear. Table 1 details the calculations for these same dimensions.

Figure 1: The meshing of profile shifted gears.
( a = 20, z1 = 12, z2 = 24, x1 = +0.6, x2 = +0.36 )

The first value needed to produce a spur gear is the pitch. In the metric system, this is known as the module. As the value of the module increases, the size of the gear tooth increases. In the English standard system, the pitch of a spur gear is known as the diametral pitch (DP). It represents the number of teeth that are found on a gear with a one-inch reference diameter.

The pressure angle is the angle between the line of action of the gears and the tangent to the pitch circle. It determines the contact between the teeth of the gears and affects the load-carrying capacity and efficiency of the gears. For English system spur gears, the typical values for pressure angle are 20 degrees and 14 degrees 30 minutes. For metric spur gears, the pressure angle is typically 20 degrees.

The number of teeth for each gear is chosen by the end-user based on the speed ratio that is desired for the application. In this example, the desired speed ratio is 1:2.

Table 1 details the calculations for a pair of spur gears with a profile shift coefficient. This gear tooth modification factor is not typically applied, but is sometimes used to manipulate the center distance of a spur gear pair. When the value is set to zero for both gears, they are considered to be standard spur gears.

Table 1: The Calculations for Profile Shifted Spur Gears A standard spur gear is, as seen here, a profile shifted gear with 0 coefficient of shift; that is x1 = x2 = 0.

Most industrial spur gears are produced with an involute tooth form. This shape is easy to produce with hobbing tools and allows for a smooth meshing of the gear teeth.

When the profile shift coefficients are set to zero, the working pressure angle and the reference pressure angle are equal. If there is a profile shift coefficient on one or both of the gears, a detailed calculation needs to be performed to determine the working pressure angle.

If there is a profile shift coefficient being used on either gear, then a center distance modification factor needs to be calculated. However, if the profile shift coefficients are both zero, then the center distance of a pair of spur gears is equal to one half of the sum of each gear’s reference diameter. The reference diameter of a spur gear is also known as the pitch diameter. 

The addendum of a spur gear tooth is the radial distance between the pitch circle and the tooth tip. Correspondingly, the dedendum is the radial distance between the pitch circle and the tooth root. The sum of the addendum and the dedendum determines the total tooth height.

The tip diameter of a spur gear is also known as the outer diameter or the outside diameter. For standard spur gears, the tip diameter is equal to the reference diameter plus two addendums.

Although not shown in Table 1, the value for backlash is important for spur gears. This value measures the distance between mating gear teeth when they are not in contact. It is necessary to have a minimum amount of backlash in order for the gear teeth to mesh properly and for lubricant to engage with the gears at their point of contact.   

The design of spur gears involves determining the pitch diameter, module, pressure angle, addendum, dedendum, and backlash. These factors are dependent on the desired gear ratio, power transmission requirements, and the design of the mechanical system. Spur gears will only transmit power between parallel shafts. As the gears rotate, the teeth engage and transmit torque from the driving gear to the driven gear. The direction of rotation of the driven gear is always opposite to that of the driving gear, and the speed of the driven gear is determined by the gear ratio.

Spur gears are one of the most commonly used elements in mechanical systems because they are simple in design, efficient in operation, and cost-effective. Understanding the technical definitions and design principles of spur gears is essential for anyone working with mechanical systems.  

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is general manager of KHK USA Inc, a subsidiary of Kohara Gear Industry with a 24-year history of working in the industrial automation industry. He is skilled in assisting engineers with the selection of power-transmission components for use in industrial equipment and automation. Dengel is a member of PTDA and designated as an intern engineer by the state of New York. He is a graduate of Hofstra University with a Bachelor’s of Science in Structural Engineering.