Gear Box Design

It is a free selection. Anyway, you have some considerations before starting the distribution.

Firstly, in the first stage, it is good to have a big ratio because the pinion is going to be little and because of this, its tangential speed is going to decrease and with it, the noise of this stage (the principal cause of noise in a gearbox is the first stage).

It is good to have a big ratio in the last stage because the diameter of the last wheel is going to grow, and with this diameter, the torque resistance (the teeth in this wheel are going to support lower tangential efforts).

For the second stage ratio there is no considerations. Only think that it is good to have not very big differences between the steps. In 3 stages gearbox second stage ratio could be a little bit lower than the first and the last one stage.

Thanks for your reply it was very useful..

but does the gear ratio distribution effect the performance or life of the Gearbox ?

Of course. The ratio distribution is going to have a big influence in the gearbox life and in its noise.

Madrid's original response of "free choice" is correct, and the choice of largest ratio for first stage is valid. Another consideration: if you can distribute the wear, life improves. One approach is to use ratios with few (or no) common multiples, so that a given tooth sequentially engages with many [or all] valleys on the mating gear, taking many revolutions to return to its initial position. When I worked at a manufacturer of electromechanical timers with plastic gears, we routinely used prime numbers of teeth if we had an opportunity to do so. We had the advantage of being able to use whatever pitch or module we pleased, including non-standards like a 27.3 pitch: when you're wire EDM'ing the tool, you are freed from the need to obtain hobs and similar tools. This is wonderful when you need to offer many ratios but with gear / pinion pairs on the same centers.

Out on a limb here, but could certain gear tooth counts and the ratio of the other gear on same shaft (ie same rpm) as well as ratio to mating gear have something to do with exciting harmonics? Especialy if you have straight cut teeth, as apposed to helical cut which will reduce noise by reducing vibration. A good point was made that the first stage supplies most of the noise. To support this in an unformal way I am disecting a Minolta copier (big one) for motors and optical switches as well as drive train. There are many gear sets in there on most of them the first stage is either helical cut teath with a large ratio, the rest of the sets being smaller steps typicaly. The other first stage gears are worm gears, these inherently create large speed reductions. This depends alot on what you are making.

A cement mixer drive, or a gear drive for an electric ultra light RC plane? Also consider how the torque increases through the stages and the gear tooth stresses created. Will heat be an issue? What material(s) do you plan on using? Are those materials compatible?

Ron is correct. But not only is important to choose no common multiples gears, it is important too to have enough teeth number in each pinion. It is normal to see in a lot of gearboxes pinions with 8, 7 or 6 teeth. Remember that the theoric lower limit for this number is 14. It is true that if you increase the clearance this number can be lower, but the endurance is going to be very much lower too, and you have always the risk to increase the noise.

Having helical teeth is the noise is going to decrease, of course. Firstly, you are going to increase the engagement coefficient and you are going to have a softly contact in the beginning of the engagement. But remember that they are more expensive and, if you don´t reach an egagement coefficient of, at least, 2.3, normally it is not going to be interesting. To increase this factor in helical gears, normally is enough to increase the gear width, but you must be careful with it because the price is going to be increased too.

Perhaps it could be interesting to change the geometry in the sides of the teeth and to have tip relief, but this considerations need a lot of particular study for each case. No one of them have a really good theoric aproximation and normally each calculated relation need to be tested to be sure of its real functioning.

In addition to all previous interesting comments did you take a look at the following adress?
GlobalSpec.com > Mechanical Components > Power Transmission > Gears > Metric Gears > Learn More

many manufacturers of gears can give you for free a precalculation of the best efficient stage ratio distribution including bearing selection.

they can propose at shipper price standard gears coming fom their standard gear boxes.