What is a bevel gear?

Gearing 101: A primer on straight tooth bevel gearing.

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What is a bevel gear? A bevel gear is a type of conically shaped gear that has octoidal teeth.  The gear teeth of a bevel gear mesh with the teeth of a mating bevel gear, forming a bevel gear pair. They are a type of machine element commonly found in applications that require a change in direction and speed.

Bevel gears are used with bevel pinions to create mechanical systems that change speed and torque primarily in perpendicular shaft applications. When the bevel gear and the bevel pinion have the same number of teeth, they are called miter gears. For any straight tooth bevel gear combination, the mating pinion and the bevel gear must be the same pitch, and the same pressure angle. In addition, the pinion gear must be produced with a pitch angle that when added to the pitch angle of the bevel gear is equal to the reference cone angle. The reference cone angle is commonly known as the shaft angle. Figure 1 details this relationship.

Figure 1: The reference cone angle of a bevel gear.

A bevel gear can have straight teeth or spiral teeth. This article only covers straight tooth bevel gearing. The teeth of straight bevel gears are readily identifiable as they would come together at the intersection of the shaft axes if extended. Straight bevel gears can be grouped into two styles. One style is the Gleason type and the other is the standard type.

Gleason type bevel gears are designed specifically as profile shifted gears. The bevel pinion is positively shifted, and the bevel gear is negatively shifted. This is done in order to better distribute the gear strength within the pair. As miter gears are equal, there isn’t any shifting of Gleason miter gears. Another difference in the Gleason type bevel gearing is that the tooth tip and root clearance are designed to be parallel. With the face cone of the gear blank machined parallel to the root cone of the mating gear, the possibility of fillet interference is eliminated.

Standard type bevel gears do not have any profile shift and do exhibit some weakness when the number of teeth on the pinion is small relative to the number of teeth on the mating bevel gear. (Figure 2)

Figure 2: Dimensions and angles of bevel gears.

The teeth of a bevel gear are generated using a specialized cutter on a bevel generating machine. The cutter machines a section of the bevel gear and then indexes. The number of teeth produced by each cutter is limited as the cutter radius needs to account for the number of teeth on the mating bevel gear and the required shaft angle. Bevel gears can be produced from various materials, including steel, brass, bronze, or plastic and, depending on the application, they can be hardened for strength and durability.

The geometry of a bevel gear is defined by several parameters. The primary considerations of the bevel gear are the outer diameter, the mounting distance, the cone distance, and the length through the bore. 

Table 1 details the calculations for a Gleason type bevel gear pair. Table 2 details the calculations for a standard type bevel gear pair.

Table 1: The calculations of straight bevel gears of the Gleason system.
Table 2: The calculations for standard straight bevel gears.

The first value needed to produce a bevel 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 helical 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. In the English system, gears typically have values for pressure angle of 20 degrees or 14 degrees 30 minutes. For metric gears, the pressure angle is typically 20 degrees.

The number of teeth for the pinion is chosen by the end-user based on the speed ratio that is desired for the application and an understanding that values of less than 12 teeth is not practical for power transmission. The speed ratio of a singular pinion engaged with a bevel gear is simply the number of teeth on the bevel gear divided by the number of the number of teeth on the pinion. Speed ratios for straight bevel pairs are limited by the size of the bevel gear and the pitch angles. As such, they are limited in practice to ratios of 6:1 or less.

The addendum of a bevel gear tooth is the linear distance between the pitch radius and the tooth tip measured at the heel of the bevel gear tooth. Correspondingly, the dedendum is the linear distance between the pitch radius and the tooth root. The sum of the addendum and the dedendum determines the total tooth height.

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

The design of a bevel gear involves determining the pitch, pressure angle, shaft angle, mounting distance, and backlash. These factors are dependent on the desired speed ratio, power transmission requirements, and the design of the mechanical system. Bevel gears will only transmit power between non-parallel axes. When the pinion is used as the driver, the pinion rotates; the teeth engage, and torque is transmitted from the pinion to the bevel gear, resulting in a reduction in speed but an increase in torque. When the bevel gear is used as the driver, the bevel gear rotates; the teeth engage, and torque is transmitted from the bevel gear to the pinion, resulting is an increase in speed but a decrease in output torque. This is a significant drawback if you are using bevel gearing in a speed increaser.

Bevel gears are a commonly used element in mechanical systems where a change in direction and speed is required because they are simple in design, efficient in operation, and cost-effective. Understanding the technical definitions and design principles of bevel gearing 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.