Design of Gears

In this tutorial, you will be introduced to Gear systems and their types. You will become acquainted with the common terminology associated with gears and see the gear shapes commonly found in mechanical systems.


  1. What are Gears?
  2. Which Gears to use?
  3. Terminology of a Gear
  4. What is a Module?
  5. What is Backlash?
  6. Standard Systems for Gear Tooth
  7. Why do Gear Teeth Fail?
  8. Application of Gears

What are Gears?

Gears are rotating machine components with grooves cut into them to serve as teeth, which mesh with another gear to transmit torque between two shafts. Geared devices find applications where there is a requirement to change the speed, torque, or even the direction of the power being transmitted.

  • Gears create a Mechanical Advantage when used in pairs of different sizes and are classified as Simple Machines.
  • Multiple meshing gears work synchronously and are called a gear train or a transmission system.
  • Depending on the shape of the gear, one can increase or decrease speed, change directions of rotation, connect non-parallel shafts and even convert between rectilinear and rotary motion.

Which Gears to use?

Gears are classified into external and internal types depending on the arrangement of gears in the assembly. Generally, gears can be classified into four major groups, spur gears, helical gears, bevel gears, and worm gears.
Here, we see some common types of gears

some common types of gears
  • Spur Gears are designed to transmit power through parallel shafts. Their teeth are parallel to the axis of the shaft. They tend to be noisier as they act on a single line of contact. In mesh, the role of contact from one tooth before engaging the other.
  • Helical gears have teeth that are at an angle to the shaft, unlike a spur gear. This angle, called the helix angle can be between 12°–20°. Helical gears have more than one tooth in contact when in operation and can thus carry far more load than a spur gear. They can have right-handed or left-handed teeth. They however produce thrust forces in the application and require proper thrust bearing to compensate.
  • A Herringbone gear is a helical gear with different kinds of teeth on the face with no gap in between them. Usually very small in size, they are suited for high shock and vibration applications. However, they are often difficult to manufacture.
  • Bevel gears are commonly used to transmit power between shafts intersecting at a 90-degree angle. A common application is the differential of a car. They are costly and are not able to transmit much torque.
  • Worm gears transmit power through shafts that are non-parallel and non-intersecting. They produce thrust load and are good for high shock load application. They have very low efficiency and are used in low power applications.


Terminology of a Gear

The gear tooth is usually involute or cycloidal, as they satisfy the law of gearing, which states that the common normal to the tooth profile at the point of contact should always pass through a fixed point, called the pitch point, to obtain the constant velocity ratio. The terminology of gear includes various storms unique to gears which help define the characteristics of a gear.
The following figure shows the major gear terminology.

major gear terminology
  • The Pinion is the smaller of the two mating gears, while the larger one is simply called the gear.
  • The Velocity ratio, or the speed ratio, is the angular velocity of the driving gear to the angular velocity of the driven gear.
  • The Pitch circle is the curve of intersection of the pitch surface, which are imaginary planes, cylinders, or cones that roll together when slipping. It is an imaginary circle that rolls without slipping with the pitch circle of a mating gear.
  • The base circle is the imaginary circle from which the involute curve of the profile is generated. They are tangent at the pressure lines.
  • The top land is the top surface of the gear tooth, while the bottom land is the surface of the gear between the flanks of the teeth.
  • The Addendum circle is an imaginary circle that traces the top of the gear teeth in the cross-section, while the dedendum circle borders the bottom of the spaces between in the cross-section.
  • Face width is the width of the teeth along the parallel axis.
  • The pressure angle is the angle made by the line of action with the common tangent to the pitch circles. It is often referred to as the angle of obliquity.
  • Line of action is the common tangent between the two base circles of the mating gear. This line serves to be the direction in which force is transmitted from the driving gear to the driven gear.
  • Contact Ratio is defined as the number of teeth that are engaged simultaneously. For continuous transfer of power, the contact ratio must be more than 1 to ensure that at least one pair of teeth are always in contact.

What is a Module?

A module of a gear is the unit of size that describes how large or small a gear is. A pair of gears can only mesh correctly if the module for both the gears is the same. It is defined as the ratio of the pitch circle diameter (d) to the number of teeth (z).
m = d/z
The Diametrical Pitch is the reciprocal of the module and is represented by P. It is defined as the ratio of the number of teeth (z) to the pitch circle diameter (d).
P = z/d = 1/m

What is Backlash?

When two mating gears are produced such that tooth spaces are equal to tooth thickness at the reference diameter, then there will not be any clearances in between teeth that are getting engaged with each other. The gears will be jammed even from the slightest eccentricity. This results in a small play between the mating surfaces and is called the backlash.

  • Backlash refers to the angle that the output shaft of a gearhead can rotate without the input shaft rotates.
  • Backlash can become a serious issue in controlling endpoint motion, due to the limited resolution of sensing the gearhead output shaft angle using an encoder that is attached to the shaft.
  • Backlash increases with the number of gear stages. Gear types like harmonic drives are designed for near-zero backlash. Usually by using flexible materials.
  • At lower power outputs, backlash results in inaccurate calculations due to the small errors introduced at each change of direction. At larger outputs, backlash results in large shocks throughout the system.

Standard Systems for Gear Tooth

An involute is a curve traced by any point on a line as the line rolls without slipping of the circle. All standard systems prescribe involute profiles for gear tooth because they satisfy the law of gearing at any center-to-center distance. All involute gears at a given module or pressure angle are completely interchangeable. There are three standard systems for the shape of the gear teeth.
The figure shows the standard Gear Tooth Systems

standard Gear Tooth Systems
  • 14.5° Full Depth Involute System – The system comprises straight sides except for fillet arcs. Usually, the interference occurs when the number of teeth on the pinion is less than 23. This system is used for gears with a very large number of teeth.
  • 20° Full Depth Involute System – The system comprises straight sides except for fillet arcs, like the previous one. Usually, the interference occurs when the number of teeth on the pinion is less than 17. This system is widely used in practice. It has minimal risk of undercutting and minimum interference. It works with minimum noise and vibration.
  • 20° Stub Involute System – The gears in this system have shorter addendum and shorter dedendum. The portion of the toot which interferes is removed. Stub teeth are stronger than full-length teeth as they have a smaller moment arm. They have a lower production cost. The major drawback is the reduced contact ratio.


Why do Gear Teeth Fail?

There exist two major modes of gear tooth failures – breakage of the tooth due to static and dynamic loads and surface destruction. The breakage of the tooth can be avoided by adjusting the parameter of the gear design, such as the module and the face width. The principal types of gear tooth wear are given below.

  • Abrasive wear results when foreign particles such as dirt, rust, weld spatter or metallic debris enter the meshing area and scratch the tooth surface. Remedies for this include oil filters, increasing surface hardness, and the use of high viscosity oils.
  • Corrosive Wear is caused due to corrosive elements such as extreme pressure additives in oils. They attack the surface of the tooth resulting in uniform wear throughout the affected surface. Selecting the proper additives is important to prevent this wear.
  • Initial Pitting is a localized phenomenon identified by small pits at the surface. It is a result of surface irregularities and misalignment. To prevent this, one requires precision machining and proper adjustment of the teeth alignment.
  • Destructive Pitting is a result of surface fatigue failure, occurring when the load exceeds the surface endurance strength. It is characterized by pits that continue to grow once formed, resulting in the complete wearing away of the tooth. The surface endurance can be increased by increasing the surface hardness.
  • When there is an inadequate supply of the lubricant, there is an excess of the frictional forces developed resulting in heating of the meshing teeth. Scoring is the phenomenon resulting from alternate welding and shearing at the high spots. The rate of wear is very high in this case.

Application of Gears

Gears are effective forms of power transmission and find widespread application in all industries and many components. Gears are reliable, efficient and an economic form of power transfer and can be easily manufactured to suit requirements. In case of failure, they can be easily interchanged. This makes gears an important and efficient element in modern machinery.

  • Spur gears are used in Clocks, Pumps, Watering systems, Household appliances, Clothes washing and drying machines, Power plants, Material handling systems, the Aerospace and aircraft industry, and the Railways and trains sector.
  • Helical Gears have similar applications as Spur gears but are used for applications involving larger speed criteria.
  • Bevel gears are used in clockworks and Differentials for vehicles and hand drills.
  • Worm gears are used in instruments, Lifts and elevators, Material handling systems, and Automobile steering systems.
  • Rack and Pinions are used for weighing scales, railways and trains, steering systems, and also machineries like Drawing and Planning machines.

Key Points to Remember

Here is the list of key points we need to remember about “Design of gears”.

  • Gears are machine components that serve to transfer power including the variation of torque, speed changes, or simply changes in the direction of the power.
  • Spur gears, Helical gears, Bevel gears, and worm gears are among the most common gear shapes found in mechanical systems.
  • The module is the basic unit that defines the shape and size of the module. Two gears can only mate if they have the same module.
  • Backlash refers to the free movement between meshing teeth where the gear rotates without any transfer of power.
  • There are three standard systems for the shape of the gear teeth – 14.5° Full Depth Involute System, 20° Full Depth Involute System, and 20° Stub Involute System.
  • The pressure angle or the angle of obliquity is the angle made by the line of action with the common tangent to the pitch circles.
  • Gears fail due to either static or dynamic loading or due to surface destruction.

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Manish Bhojasia - Founder & CTO at Sanfoundry
Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He lives in Bangalore, and focuses on development of Linux Kernel, SAN Technologies, Advanced C, Data Structures & Alogrithms. Stay connected with him at LinkedIn.

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