Bevel gears are gears designed to transmit motion between intersecting axes. Perpendicular arrangements are most common, but bevel gears can be manufactured for nearly any angle. The teeth bearing surface of the gear, or surface pitch, is conically shaped or tapered.

Miter gears are bevel gears manufactured in a 1:1 ratio, with the same number of teeth on mating gears and with perpendicular axes.

The axes of the gears intersect at point 0. Image credit: Wikimedia

Video credit: drizzo95 / CC BY 3.0

Types of Bevel and Miter Gears

Teeth alignment of bevel gears include straight, spiral, hypoid and crown configurations.

Dimension Specifications

Gears mate via teeth with very specific geometry. Pitch is a measure of tooth spacing and is expressed in several ways.

Diametral pitch (DP) is the ratio of the number of teeth to the pitch diameter of a gear; a higher DP therefore indicates finer tooth spacing. It is easily calculated by the formula DP= (N+2) ÷ OD, where N is the number of teeth, and OD represents the circumferential measurement.

Circular pitch (CP) is a direct measurement of the distance from one tooth center to the adjacent tooth center. It can be measured by the formula CP= Π ÷ DP.

Module (M) is a typical gear discipline and is a measurement of the size and teeth number of the gear. Gears measured in inches earn 'English module' distinction to prevent confusion. M = OD ÷ N

Pressure angle is the angle of tooth drive action, or the angle between the line of force between meshing teeth and the tangent to the pitch circle at the point of mesh. Typical pressure angles are 14.5° or 20°.

Helix angle is the angle at which the gear teeth are aligned compared to the axis.

Selection tip: Gears must have the same pitch and pressure angle in order to mesh. In addition, spiral bevel and hypoid bevel gears must be of opposite-hand teeth orientation to mesh.

Gear vernacular identified Image credit: QTC Gears

Helix vernacular identified Image credit: Wikimedia

Mounting Specifications

Consider the gear center, bore diameter and shaft diameter. The gear center can be bored or an integral shaft. The bore diameter is the diameter of the center hole. The shaft diameter is the diameter of the shaft for gears with an integral shaft. Bevel gears can be mounted on a hub or shaft. A hub is a cylindrical projection on one side of a bevel gear, often for the provision of a screw or other shaft attachment mechanism. Hubless gears are typically attached via press fit, adhesive or internal keyway.

Shaft mounting choices include the following:

Application Requirements

Application requirements should be considered with the workload and environment of the gear set in mind.

• Power, velocity and torque consistency and output peaks of the gear drive so the gear meets mechanical requirements.
• Inertia of the gear through acceleration and deceleration. Heavier gears can be harder to stop or reverse.
• Precision requirement of gear, including gear pitch, shaft diameter, pressure angle and tooth layout.
• Handedness (left or right teeth angles) for spiral and hypoid bevel gears.
• Gear lubrication requirements. Some gears require lubrication for smooth, temperate operation.
• Mounting requirements. Application may limit the gear's shaft positioning.
• Noise limitation. Commercial applications may value a smooth, quietly meshing gear.
• Corrosive environments. Gears exposed to weather or chemicals should be especially hardened or protected.
• Temperature exposure. Some gears may warp or become brittle in the face of extreme temperatures.
• Vibration and shock resistance. Heavy machine loads or backlash, the deliberate surplus space in the circular pitch, may jostle gearing.
• Operation disruption resistance. It may be necessary for some gear sets to function despite missing teeth or misalignment.

Materials

Gear composition is determined by application, including the gear's service, rotation speed, accuracy and more. 

• Cast iron provides durability and ease of manufacture.
• Alloy steel provides superior durability and corrosion resistance. Minerals may be added to the alloy to further harden the gear.
• Cast steel provides easier fabrication, strong working loads and vibration resistance.
• Carbon steels are inexpensive and strong, but are susceptible to corrosion.
• Aluminum is used when low gear inertia with some resiliency is required.
• Brass is inexpensive, easy to mold and corrosion resistant.
• Copper is easily shaped, conductive and corrosion resistant. The gear's strength would increase if bronzed.
• Plastic is inexpensive, corrosion resistant, quiet operationally and can overcome missing teeth or misalignment. Plastic is less robust than metal and is vulnerable to temperature changes and chemicals. Acetal, delrin, nylon, and polycarbonate plastics are common.
• Other material types like wood may be suitable for individual applications.

Resources

Stahl Gear - Bevel

Wikipedia - Bevel gear

How Stuff Works - Gears