Design of Gear

By Mohit Uniyal|Updated : June 20th, 2022

The design of Gear is one of the greatest and oldest inventions in history. It was invented in the 17th century B.C. at that time it have been used by one of the Greek Inventors in clocks and water wheels. The various types of sketches and designs of gears of this time have been found in history. At that time, gear was defined as the direction of rotation opposite when one gear wheel drives the other gear wheel.

There are various mechanical drives like chain drive, belt drive, and gear drive. In the list of mechanical drives, gear is one of the most suitable for transmitting mechanical power from one shaft to another. In this article, we have seen the detail about gears, their purpose and requirement, and the design of gears.

Table of Content

What is the Design of Gear?

Gear is defined as a toothed element that is used for transmitting rotary motion from one shaft to another with a constant velocity ratio. The concept of gear is come from the friction wheels, to increase the friction and avoid slipping between the wheels proper teeth are cut over it. The profile of the tooth should follow the law of gearing, then only we can say it as gear. General involute and cycloidal profiles are most used and suitable for gear.

A combination of two or more gears, which are arranged in such a way that power is transmitted from a driving shaft to the driven shaft, is known as a gear train. The gear train consists of the main driver known as the pinion, the main drive known as the gear, intermediate gear, and some in some cases arms. ​As the gear has the advantage that there is no slip condition, it is used in the application where accurate and precise motion is required like watches, lathe machines, etc. 

Forces Analysis in Design of Gear

As far as concerns the design of gear the first thing that comes into the picture what are the forces acting on the gear tooth. According to the gear tooth profile type, gears have a different tooth profile. As the mashing gear starts rotating and transferring the power and torque force are applied normally to the face and shank of the gear, according to their tooth profile the resultant forces are resolved into two components at a pitch point.

  1. Tangetial components Ft
  2. Radial components Fr

In the design of gears, we have to consider the following assumptions:

  • As the point of contact moves, the magnitude of the resultant force Fn changes. This effect is neglected in the analysis. ​
  • It is assumed that only one pair of teeth takes the entire load. At times there are two pairs, which are simultaneously in contact and share the load. This aspect is neglected in the analysis. ​
  • The analysis is valid under static conditions, i.e., when the gears are running at very low velocities. In practice, there is a dynamic force, in addition, to force due to power transmission. The effect of this dynamic force is neglected in the analysis.

The tangential force responsible for transmitting the torque is given by

Ft  = (2 Mt)/d 


Mt = [60 * 106 (kW)]/n    

The radial force or separating force is given by

F= Ft tanα

The resultant force normal to the surface is given by 

FN = Ft/cosα


  • Mt = Torque transmitted by gears
  • α = Pressure angle
  • d = Dimeter of gear
  • n  = Speed of rotation (rpm)

Stress Analysis in Design of Gear

While doing design analysis of spur gear, we consider the teeth of gear as a cantilever beam. As we see that two forces acting on the tooth, the radial component results in the compressive stress and tangential components result in the bending stress in the gear tooth, as the magnitude of radial force is less than that of the tangential component. Therefore we considered only bending moment while doing the stress analysis in the design of gear.

In stress analysis of the design of gear following assumptions have to be considered:

  • The effect of the radial component (Fr), which induces compressive stresses, is neglected.
  • It is assumed that the tangential component (Ft) is uniformly distributed over the face width of the gear. This is possible when the gears are rigid and accurately machined.
  • The effect of stress concentration is neglected.
  • It is assumed that at any time, only one pair of teeth is in contact ​and takes the total load.

The beam strength of the gear tooth is given by the equation:

Ft = m b σb Y

Y = t2/(6 h m)

S≥ m b σb Y

S≥ Ft ……………(For the safe design of gears)


  • Sb= Beam strength of gear tooth (N)
  • σb = Permissible bending stress (N/mm2)
  • m = Module of gear
  • b = Width of gear tooth
  • Y  = Lewis form factor
  • h  = Effective length of gear tooth
  • t  = Thickness of gear tooth 

For the safe design of gears beam strength of the gear is should be greater than  or equal to the tangential force applied to the gear


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FAQs on Design of Gear

  • The following are the advantages of gear drive:

    • It is a positive drive.
    • Velocity remains constant.
    • Provisions for changing velocity ratios can be made with the help of the gearbox.
    • It is very highly efficient if proper lubrication is provided.
    • We can archive variable speed ratios.
    • It provides the required torque-speed combination.
    • It is compact in construction.
  • The following are the disadvantages of gear drive.

    • They are not suitable when shafts are distant.
    • At high speeds noise and vibration happens.
    • It requires lubrication for smooth running and high efficiency.
    • Only predetermine gear ratio can be achieved.
    • Not suitable when distance between the shaft is more.
    • Conjugate tooth profile required for mashing of gear.
  • Apart from bending stress, gear can be failed due to failure of its surface. The failures after the design of gear are:

    • Abrasive wear - It is due to the impurities present in the lubricating oil such as dirt, rust, weld spatter or metallic debris roughening the gear surface.
    • Corrosive wear - Due to improper lubrication and moisture, corrosive element, and foreign material are present in the lubrication.
    • Scoring - ​Scoring is a stick-slip phenomenon, in which alternate welding and shearing take place rapidly at the high spots.
    • Pitting - It is a type of fatigue failure, when the load on the gear tooth exceeds the limits of surface endurance strength of the material, pitting failure will occur.
  • The gears can be classified as follow:

    a. Parallel shaft

    1. Spur gear.
    2. Spur rack and pinion gear.
    3. Helical spur gear.
    4. Double helical gear.
    5. Herringbone gear.

    b. Intersecting shaft

    1. Zero bevel gear.
    2. Spiral bevel gear.

    c. Skew shaft (non-parallel, Non-intersecting shaft)

    1. Cross helical gear.
    2. Worm gear.
    3. Hypoid gear.


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