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Why is contact ratio important ?

From Stephane Baleon, posted 10/07/2019

What is contact ratio ?

When rotating two gears meshed against each others, the load goes through the teeth. There must be at least a tooth pair in contact, if not two at the same time.

The contact ratio represents the average number of teeth meshing at the same time. If only one tooth is in contact 50% of the time, and two teeth during the other 50%, then the contact ratio is 1.5.

This contact ratio is applicable to spur gears, helix gears, straight bevel gears or spiral bevel gears. It is an important parameter when designing a pair of gears.

Contact ratio also refers to the ratio of the length of the arc of contact (blue line) to the circular pitch (orange line).

contact ratio on spur gears

When it comes to spur gears with spiral or helix angle, it is required to add an overlap contact ratio to the calculation which is the facewidth divided by the normal pitch of the gear.

For bevel gears contact ratio calculation, we use its virtual spur gears and the same formula as for a regular spur gear.

The benefits of high contact ratio

Having multiple teeth in contact means the load is shared, improving the operational life of the gear.

The load being shared, the average stiffness of the gear is higher. Higher stiffness means less deflection of the teeth or better transmission accuracy. Transmission errors are the source of noise in a gear train.

An other very important parameter is not just the average stiffness of the gear mesh but also the stiffness variation that can lead to noise. Higher contact ratio will reduce the stiffness variation and reduce noise.

contact ratio on spur gears

So having a high contact ratio will:
- improve stiffness
- reduce noise
- better operation life
- higher load carrying capacity

However, special care to accuracy needs to be taken. As a matter of fact, increasing contact ratio means the gear pair will be less compliant with slight geometry errors and good accuracy is required in order to avoid an increase in noise. Trying to reduce noise by increasing contact ratio and not looking at accuracy can actually work the other way around and produce noisier gears!

How to increase contact ratio

A large number of teeth on both gears will raise the contact ratio.

If you are able to customize your gears then introducing a negative profile shift modification while increasing the number of teeth and keeping the center distance will give you an increased contact ratio and the same gear ratio.

Here is an exemple with a 200 teeth gear pair in contact. The contact ratio between these two spur gears is 1.91. As a note, meshing two spur gears with 100 teeth will give a contact ratio of 1.85, still high.

200 teeth spur gears meshing

To show you how you can keep the same ratio and increase the contact ratio of the mesh, here are few values keeping the same center distance:

- pinion 25 teeth / gear 50 teeth / module 1 / ratio 2:1 / contact ratio 1.68
- pinion 50 teeth / gear 100 teeth / module 0.5 / ratio 2:1 / contact ratio 1.80
- pinion 83 teeth / gear 166 teeth / module 0.3 / ratio 2:1 / contact ratio 1.86

To keep the center distance the same while increasing the contact ratio and without profile modification you need to reduce the module.

If you want to go this route, you will see that Adamant Precision can provide spur gears with modules as low as 0.3. Have a look at the spur gears selector and see for yourself.

If you are using spur gears or straight bevel gears then switching to helix or spiral gears will definitly improve the contact ratio.

helix and spiral spur bevel gears

Adamant Precision is able to help, providing you with spiral gears. Spur gears can replaced by helix gears and bevel gears can be replaced by spiral bevel gears.

The contact ratio will be much higher, but be aware that an additional axial load is generated due to this helix angle. Adamant can help you through the component selection of our gears catalogue.

Impact of center distance on contact ratio

As seen, you can affect the contact ratio by changing your gear design. But other parameters will affect the contact ratio and you need to be aware of them to avoid potential operation issues in your mechanism.

Variation of center distance: It seems obvious, but increasing the center distance of the gears will reduce the contact ratio. The center distance is affected by few things:

- Gear profile accuracy
- Gear radial and face runout after assembly
- Bearing runout
- Positional errors in the assembly
- Thermal expantion

For a strong design, it is recommanded to calculate the contact ratio for both minimum and maximum center distance based on the criteria above. Adamant Precision can give you guidelines for your gears design.

If you have any questions regarding this article, please get in touch.


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