Gear Design

A gear schematic showing the major dimensions.


The action of two gear teeth making contact.


That portion of a gear tooth that extends from the pitch circle to the outside diameter.

Conjugate Tooth Pairs

Two gear teeth are conjugate if they produce uniform motion as they roll together. This is equivalent to saying that one tooth form generates the other as they move. For gears with parallel axes of rotation, the involute profile is most widely used since it has a constant normal load resultant throughout its arc of action and is relatively insensitive to centre distance between the gears. Hypoid gearing is used in most RWD applications since it transmits power for perpendicular, non-intersecting axes. The hypoid gears used in most automotive applications are not involute tooth pairs and the geometry of the gear teeth is not defined on the print. The machine settings used to form the gears are specified instead. The geometric complexity of hypoid gears has historically made it difficult to determine from dimensional checks if the gears would produce noise.

Contact Ratio

The total or modified contact ratio is usually expressed as a function of the transverse/profile and the face/axialcontact ratios. The contact ratio is the average number of pairs of teeth in contact between two gears. This number can never be less than one for uniform motion gears. The use of helical gears for parallel axis gearing increases the contact ratio and helps distribute the load among more than one tooth pair.


The depth, or that portion of a gear tooth from the pitch circle to root circle of gear.


For a gear pair that is accurately machined and with roller bearings the efficiency is likely to be 95 to 96%.

Face Width

This is dependent on the torque that is being transmitted, but as a rough rule of thumb:


The lead of a helical gear tooth is the axial advance resulting from one full revolution of the helix on the cylinder. A spur gear is a special case of helical gear where the lead is infinite. The helix angle is called the spiral angle on hypoid gears.


The best way is to spray oil directly at the point of meshing. The oil is then collected in a sump and from here picked up by the pump. However, where the load is lower one of the gears may dip into the oil. This does lead to greater loss through oil whirl. For gears that are only used intermittently then a grease may be applied to the gears at service intervals.


In practice, gear teeth are designed to accommodate manufacturing errors, misalignments and deflections of gear teeth, supporting bearings and housings, etc. A modification to the theoretical profile and lead is generally specified to optimize conjugate action at the design loads. The modification to the lead also includes a slight crown in the axial direction to avoid high localized stress at the edge of the gear teeth.


This is the pitch circle diameter divided by the number of teeth. For a gear pair the module must be the same.

The addendum, dedendum and depth of the gear teeth are directly related to the Module.

Addendum, A = Module, M
Dedendum, B = 1.25 M
Tooth Depth = A + B = 2.25 M


Pitch is the distance between the teeth on a gear. A fine pitch gear has many small teeth and a coarse pitch gear has fewer, larger teeth. An interesting observation is that the stiffness of a gear tooth is not related to the pitch.

Pitch Circle

The pitch circle is the effective working circle of a gear which would be obtained if a pair of gears were replaced with disks that transmitted the same motion in the same package space through contact friction. The hypoid gears used in conventional axles do not have a true pitch circle since both sliding and rolling occurs at the teeth and the gears could not be replaced with frictional disks.

Pressure Angle

This is the angle made by the tangent to the gears at the point of contact. If this is not defined then 20° is a good assumption.


The gear tooth profile is the line which defines the tooth shape in a cross-section of the gear perpendicular to the plane of rotation. The profile of a parallel axis gear is an involute (an involute is a spiral generated by a point on a string as it is unwound from a roll).

Gear profile error results in the generation of gear noise at subharmonics of the fundamental gear meshing frequency.

Transmission Error

This is the difference between the actual position of the output gear and the position it would occupy if the gear drive were perfect. This is usually expressed as angular displacement and may be shown as linear displacement at the pitch point. TE is the primary excitation of gear noise and is dependent on load.

Velocity Ratio

This is a ratio between the number of teeth in the larger gear to the number of teeth in the small pinion gear.

See also: Bevel Gear, Gear Cutter, Gear Mesh Frequency, Gear Noise, Gear Oil, Gears, Mesh, Spur Gear, Worm, Worm Gear.

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Subjects: Mechanical Engineering