Support for gear design

KHK offers following gear design help.

Click here for Gear technical reference
This detailed gear design material allows access to all commonly known gear technical data.
gear technical reference

Click here for Automated drawing of custom gears
Variety of gear drawings can be made by simply inputting parameters.
(spur gears, helical gears, internal gears, rack and pinion, bevel gears, worm gear etc)

Click here for Automated drawing of gears with secondary operations and their strength calculations
Use it by entering a KHK part number in the gray colored middle column on a stock gears page.
(At present, the secondary operations are limited to the features supported in the standard stock gears.)
strength calculation

Various elements of gear design and the conditions for determining elements

For design of gears, determine elements such as size, tooth shape, pitch, number of teeth, amount of profile shift, material, need for heat treating and/or grinding, choice for kind of tooth surface finish, amount of backlash, helix angle, helix direction, method of mounting on shaft, precision class, etc., the production process and the method of lubrication.

The main conditions for determining these elements are listed below:

– Dimensional considerations – mainly related to space restrictions of the machine design

  1. Center distance of the shafts
    Normally gears matching the center distance between the shafts is used, but there are occasions when profile shifting is used.
  2. Available space for mounting gears
    The decisions on tooth widths and outside diameters are affected by this. Normally various elements of mechanism within the interior of the machine are placed to utilize space efficiently. Therefore, these tooth widths and outside diameters can be restricted by the machine’s design itself.

– Amount and direction of force considerations – mainly related to the required performance of gears

  1. The amount of force transmission and the required strength of gears
    Chiefly conditions affecting bending and tooth surface strengths which are determined by material, pitch, pressure angle, profile shifting amount, tooth width, heat treating methods, etc.
  2. Direction of force transmission
    Affects the decision of tooth helix direction and type of gears (e.g. use of racks for linear motion).
  3. Desired speed ratio
    Determined by the choices of numbers of teeth.

– Usage and handling considerations

  1. Durability of gears
    Since it is mostly determined by the bending and tooth surface strengths, it influences the decision on material, pitch, pressure angle, profile shifting amount, tooth width, heat treating methods, etc. Also it affects the lubrication method.
  2. Related to the weight and maintainability
    Determines mainly the size, form, material (specific gravity), and method of shaft attachment.
  3. Related to noise and vibration
    Affects the decisions chiefly on precision grade, need for tooth grinding, use of crowning or end relief,
    material, amount of backlash and lubrication method.
  4. Related to shock at start and stop time
    Related to gear strength so that it is influenced by material, pitch, pressure angle, profile shifting amount, tooth width, heat treating methods, etc. It is also affected by the amount of backlash.

– Conditions concerning the manufacturing and economy

  1. Ease of production and possible utilization of available production facilities.
    Influenced by manufacturing method, size and many other elements.
  2. Manufacturing cost
    Affects choices of material, use of gear grinding, surface finish, precision class, etc.

– Environmental conditions of gear usage

  1. Temperature and humidity
    Influences the selection of material, kind of surface treatment, etc.
  2. Cleanliness and sanitary considerations
    Determines material, type of surface treatment, lubrication method, etc.

Basic knowledge of the mechanical design of gears


Like other professions, mechanical design requires certain knowledge. In fact, you may need a wide range of knowledge. Some of basic areas of knowledge of mechanical design are shown below.

The Machine element

The machine element falls roughly into four elements :

1) Fixing element
2) Transmission element
3) Sealing element
4) Fluid element

In this section we will explain gears, one of transmission elements.

Among transmission elements, gears are used to transmit power when the distance between two axes is relatively short.
The types of tooth curves for gearing include involute tooth and cycloid tooth. The cycloid tooth has some advantages, but not used currently because of the difficulty in shaping. Therefore, the involute tooth is mainly used of the  tooth curves of gearing. If the necessary effectiveness and loads are not large, you can also use pins.

Gearing falls roughly into the following five categories :

a) Spur gear
b) Helical gear
c) Bevel gear
d) Screw gear
e) Worm and worm wheel

Involute function
When the pressure angle α of the optional point P’ on the involute curve is shown,

θ = tan α° – α (rad)

So, if α is 20°,

θ = tan20° – 0.3490 = 0.01490 (rad)

The formula above is expressed as θ = inv α, and is used to calculate tooth thickness.

Below is the formula for gearing. A pressure angle of 20° is the JIS standard.

m (module) : tooth size (mm)
P0 : pitch diameter (mm)
Dk : tip diameter (mm)
Z : number of tooth
Ca : center distance (mm)

In this case,

m = P0 / Z

m becomes bigger as the number of tooth is fewer.


dk = (Z + 2) m

Thus, the tooth tip is 1*m from pitch diameter, and 1.25*m to the tooth bottom.

The bottoms of intermeshing gears interfere, so the minimum number of teeth is :

Zg = 2 / (sin αc)2
(αc is tool pressure angle)

When αc is 20°, Zg becomes 17.

The interference of tooth bottoms of gears is called “undercut”. Any slight undercut is normal and the minimum number of teeth is 14.

Simplified design method for gear

When setting center distance Ca and speed ratio, the outline of the module is also set based on transmitting power. Choose a module from the list of JIS standard modules.

Choose the number of teeth for the small pinion (minimum is 14), and determine the number of teeth of the big gear by the speed ratio. Generally, when the number of teeth of small pinion is even, big gear should also be even. Similarly, when the number of teeth of small pinion is odd, big gear should also be odd.

Calculate the pitch diameter, and adjust the number of teeth until the sum of half of each pitch diameter matches the speed ratio. Adjust center distance or speed ratio in the case of slight difference. Finally, calculate strength of gear teeth and ensure that the outlined module has no problems. That is quite difficult work, but the design support software made by gear manufacturers may help you.

Gear cutting
Gear cutting is roughly divided into two methods : the generating method and the forming method. In the generating method, involute tooth is shaped by rack type or pinion type cutter based on the principal of an involute curve. Gears with any number of teeth can be processed accurately if the module and pressure angle of the tool are determined. Nowadays gears are processed by the generating method. In the forming method, the gear is cut by a plain milling machine, using disc shaped gear cutter that matches the gear tooth groove. This method is hardly used because one type of gear cutter can process only one type of gear. In the generating method, two types of machine tool are mainly used : pinion cutter or rack cutter type gear shaping machines, and hob machines which uses screw-like cutter with a reference rack.

Recently, some gears are mass-produced using sintered metal, but metal die manufacturing requires special knowledge.

When the distance between two axes is long, timing belt drives with gear-shaped pulleys are recommended because they are more silent and stable when compared to chain drive.

You need to choose timing belts and pulleys from commercial items according to designing conditions as shown below :

  1. Machine type
  2. Transmitting power (rated output of motors)
  3. Extent of load variation
  4. Operating hours per day
  5. Rotation speed of small pulley
  6. Speed ratio (big pulley / small pulley)
  7. Tentative distance between two axes
  8. Operating conditions (temperature, humidity)

Please choose timing belts and pulleys according to the condition above.

At first you may choose them by yourself several times, then try using selection support software made by manufacturer.

Related links :
Design of Plastic Gears – A page of Gear Technical Reference
齿轮设计 – 中文页