# Gear (cogwheel)

A gear (or cogwheel) it is the main element in a transmission system, in which teeth are cut around cylindrical or cone shaped surfaces with equal spacing; or in the case of a cogwheel, inserted teeth (called cogs). By meshing a pair of these elements, they are used to transmit rotations and forces from the driving shaft to the driven shaft.

For efficient transfer of speed and power, gears should conform perfectly to the designed profile and dimensions. Misalignments and gear runout will result in vibrations, chatter, noise, and loss of power.

A gear tooth is formed by portions of a pair of opposed involutes. By far, the involute tooth profile is most preferred in gears. A clear understanding of the various terminologies associated with gears is extremely important before an attempt is made to learn about inspection and measurement of gears. The following are some of the key terminologies associated with gears.

## Gear terminology

Base circle
It is the circle from which the involute form is generated. Only the base circle of a gear is fixed and unalterable.

Outside circle
It marks the maximum diameter of the gear up to which the involute form is extended. It is also called the addendum circle. In addition, it is the diameter of the blank from which the gear is cut out.

Pitch circle
It is the imaginary circle on which lies the centers of the pitch cylinders of two mating gears.

Root circle
It is the circle corresponding to the minimum diameter of the gear profile. However, the involute profile is limited only up to the base circle of a spur gear.

It is the radial distance between the addendum circle and the pitch circle.

Dedendum
It is the radial distance between the pitch circle and the root circle.

Face
The portion of tooth lying between the addendum circle and the pitch circle is called the face.

Flank
The portion of tooth lying between the pitch circle and the dedendum circle is called the flank.

Circular pitch
It is the distance between corresponding points of adjacent teeth measured along the pitch circle.

Diametrical pitch
It is expressed as the number of teeth per unit diameter of the pitch circle.

Module
It is simply the metric standard for pitch. It is the linear distance (in millimetres) that each tooth of the gear would occupy if the gear teeth were spaced along the pitch diameter. Accordingly, if the pitch circle diameter of the gear is D and the number of teeth is N, then the module m is given by D/N and is expressed in millimetres.

Base pitch
It is the distance measured around the base circle from the origin of the involute on the tooth to the origin of a similar involute on the next tooth. Base pitch = Base circumference/Number of teeth.

## Gear manufacturing

The gears (gear teeth) are generally made by one of the following two methods:

1. reproducing method, in which the cutting tool is formed involve cutter, which forms the gear teeth profiles by reproducing the shape of the cutter itself. In this method, each tooth space is cut independently of the other tooth spaces;
2. generating method, in which the cutting tool (hob) forms the profiles of several teeth simultaneously during constant relative motion of the tool and blank.

The various sources of errors in the gear made by reproducing method be due to incorrect profile on the cutting tool, and incorrect positioning the tool in relation to the work and incorrect indexing of the blank.

The sources of error when gears are made by generating method are: errors in the manufacture of the cutting tool, and errors in positioning the tool in relation to the work and errors in the relative motion of the tool and blank during the generating operation.

## Types of gear

Gears can be classified by shape as involute, cycloidal and trochoidal gears. Also, they can be classified by shaft positions as parallel shaft gears, intersecting shaft gears, and non-parallel and non-intersecting shaft gears.

## Gear errors

From a metrological point of view, the major types of errors are as follows:

1. Gear blank runout errors
2. Gear tooth profile errors
3. Gear tooth errors
4. Pitch errors
5. Runout errors
7. Assembly errors

### Gear blank runout errors

Gear machining is done on the gear blank, which may be a cast or a forged part. The blank would have undergone preliminary machining on its outside diameter (OD) and the two faces. The blank may have radial runout on its OD surface due to errors in the preliminary machining.

In addition, it may have excessive face runout. Unless these two runouts are within prescribed limits, it is not possible to meet the tolerance requirements at later stages of gear manufacture.

### Gear tooth profile errors

These errors are caused by the deviation of the actual tooth profile from the ideal tooth profile. Excessive profile error will result in either friction between the mating teeth or backlash, depending on whether it is on the positive or negative side.

### Gear tooth errors

This type of error can take the form of either tooth thickness error or tooth alignment error. The tooth thickness measured along the pitch circle may have a large amount of error. On the other hand, the locus of a point on the machined gear teeth may not follow an ideal trace or path. This results in a loss in alignment of the gear.

### Pitch errors

Errors in pitch cannot be tolerated, especially when the gear transmission system is expected to provide a high degree of positional accuracy for a machine slide or axis. Pitch error can be either single pitch error or accumulated pitch error. Single pitch error is the error in actual measured pitch value between adjacent teeth. Accumulated pitch error is the difference between theoretical summation over any number of teeth intervals and summation of actual pitch measurement over the same interval.

Pitch and index errors are both caused by three things: problem with machine 1001s, cuttillg tool problems and gear blank and mounting errors.

### Runout errors

This type of error refers to the runout of the pitch circle. Runout is a characteristic of gear quality that results in an effective center distance variation. As long as the runout doesn’t cause loss of backlash, it won’t hurt the function of the gear, which is to transmit smooth motion under load from one shaft to another. However, runout does result in accumulated pitch variation, and this causes non-uniform motion, which does affect the function of the gears. Runout is a radial phenomenon, while accumulated pitch variation is a tangential characteristic that causes transmission error, vibrations, noise, and reduces the life of the gears and bearings. This error creeps in due to inaccuracies in the cutting arbour and tooling system. It is also possible to have a gear with accumulated pitch variation, but little or no runout.

In fact, runout affects, every other characteristic of gear quality, such as involute or tooth form, index or pitch variation, lead or tooth alignment variation, and noise and vibration. It is quite common for one to have problems trying to meet specifications for index or pitch variation when the cause is actually runout. The various measures of gear quality are not independent parameters. They are influenced by runout.