What is a spiral bevel gear?

Gearing 101: A primer on spiral tooth bevel gearing and how they’re designed.

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

Spiral bevel gears are used with spiral bevel pinions to create mechanical systems that change speed and torque primarily in perpendicular shaft applications. When the spiral bevel gear and the spiral bevel pinion have the same number of teeth, they are called spiral miter gears. For any spiral tooth spiral bevel gear combination, the mating pinion and the spiral bevel gear must be the same pitch, the same pressure angle, the same spiral angle, but opposite spiral direction. 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 spiral bevel gears.

A bevel gear can have straight teeth or spiral teeth. This article only covers spiral tooth bevel gearing. The teeth of spiral bevel gears are readily identifiable, as they are curved in nature and taper toward the intersection of the shaft axes. Spiral bevel gears can be grouped into two styles. One style is the Gleason type, and the other is the standard type.

Gleason type spiral bevel gears are designed specifically as profile shifted gears. The spiral bevel pinion is positively shifted, and the spiral 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. The tooth profile of a Gleason spiral bevel gear has the tooth depth h = 1.888m; tip and root clearance c = 0.188m; and working depth hw = 1.700m.             

Standard type spiral 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 spiral bevel gear.

Spiral bevel gears are used with spiral bevel pinions to create mechanical systems which change speed and torque primarily in perpendicular shaft applications.

The teeth of a spiral bevel gear are generated using a specialized cutter on a spiral bevel generating machine. The cutting tool machines a section of the spiral 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 spiral bevel gear and the required shaft angle. Spiral bevel gears can be produced from various materials; however, carbon or alloy steels are typically used. Softer materials including brass, bronze, or plastic are not suitable for the production of spiral bevel gearing. 

The geometry of a spiral bevel gear is defined by several parameters. The primary considerations of the spiral 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 spiral bevel gear pair.

Table 1: The calculations for spiral bevel gears in the Gleason system.

The first value needed to produce a spiral 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 spiral bevel gear is simply the number of teeth on the spiral bevel gear divided by the number of the number of teeth on the pinion. Speed ratios for straight spiral bevel pairs are limited by the size of the spiral bevel gear and the pitch angles. As such, they are limited in practice to ratios of 6:1 or less.

The addendum of a spiral bevel gear tooth is the linear distance between the pitch radius and the tooth tip measured at the heel of the spiral 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.

Figure 2: Dimensions and angles of bevel gears.

Although not shown in Table 1, the value for backlash is very important for spiral bevel gear pairs. This value measures the distance between the spiral pinion gear teeth and the spiral 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 spiral bevel gear and spiral bevel pinion at their point of contact.

The design of a spiral 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. Spiral 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 spiral bevel gear resulting in a reduction in speed, but an increase in torque. When the spiral bevel gear is used as the driver, the spiral bevel gear rotates, the teeth engage, and transmits torque from the spiral bevel gear to the pinion, resulting in an increase in speed but a decrease in output torque. This is a significant drawback if you are using spiral bevel gearing in a speed increaser.

Spiral 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. Due to the continuous tooth engagement, they are ideal for high-speed and high-torque applications.  Understanding the technical definitions and design principles of spiral 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.