# Spur Gear Design

Mechanical engineers working in transmission field would often have to decide upon kind of gears they have to use. Although this task has become a matter of selection of gear based on standards, it is also important to know what goes behind this. In this video tutorial you will learn how to design a pair of spur gears for mechanical strength, surface resistance and fluctuating load.

The video lecture is described below in detail## AGMA Standard of Gear Design

A designed gear should meet following design criteria conforming to AGMA standards. It should have

- Enough mechanical strength to withstand force transmitted
- Enough surface resistance to overcome pitting failure
- Enough dynamic resistance to carry fluctuating loads

## Design Inputs and Outputs in Gear Design

Following figure shows design inputs and outputs of a gear design

Fig.1 Input and output parameters for a gear design |

Fig.2 A general spur gear nomenclatures |

## Design for space constrains

The designed gear system should fit within a space limit. So the designer could say if he sums pitch diameters of the mating gears, it should be less than or equal to allowable space limit as shown in figure below.

Fig.3 Space constrain of gear design |

## Determination of Number of Teeth - Interference

Here we will understand how to determine number of teeth on both the gears. To do this we have to assume number of teeth on one gear(T1), say the smaller gear. Now using the relation given below we can determine number of teeth on other gear,T2.

So we got number of teeth on both the gears, but one should also check for a phenomenon called interference if gear system has to have a smooth operation. Interference happens when gear teeth has got profile below base circle. This will result high noise and material removal problem. This phenomenon is shown in following figure.Fig.4 A pair of gear teeth under interference |

Fig.5 Flow chart to determine number of teeth on each gears |

## Design for Mechanical Strength - Lewis Equation

Now the major parameter remaining in gear design is width of the gear teeth, b. This is determined by checking whether maximum bending stress induced by tangential component of transmitted load, Ft at the root of gear is greater than allowable stress. As we know power transmitted,P and pitch line velocity V of the gear Ft can be determined using following relation.

Here we consider gear tooth like a cantilever which is under static equilibrium. Gear forces and detailed geometry of the tooth is shown in figure below.Fig.6 Gear tooth under load |

## A More Realistic Approach - AGMA Strength Equation

When a pair of gear rotates we often hear noise from this, this is due to collision happening between gear teeth due to small clearance in between them. Such collisions will raise load on the gear more than the previously calculated value. This effect is incorporated in dynamic loading loading factor, Kv value of which is a function of pitch line velocity.

At root of the gear there could be fatigue failure due to stress concentration effect. Effect of which is incorporated in a factor called Kf value of which is more than 1.

There will be factors to check for overload (Ko) and load distribution on gear tooth (Km). While incorporating all these factors Lewis stregth equation will be modified like this

The above equation can also be represented in an alternating form (AGMA Strength equation) like shown below Where J is Using above equation we can solve for value of b, so we have obtained all the output parameters required for gear design. But such a gear does not guarantee a peacefull operation unless it does not a have enough surface resistance.## Design for surface resistance

Usually failure happens in gears due to lack of surface resistance, this is also known as pitting failure. Here when 2 mating surfaces come in contact under a specified load a contact stress is developed at contact area and surfaces get deformed. A simple case of contact stress development is depicted below, where 2 cylinders come in contact under a load F.

Fig.7 Surface deformation and development of surface stress due to load applied |