The main reason for using reduction on a rack and pinion system is to allow the smaller motors to be used and keep the recommended motor to load inertia ratio below 10:1 and in some cases below 5:1. This of course depends on the weight of the gantry and the type of operation, Plasma, Routing, Milling etc.
If you want to obtain certain feed and acceleration rates for a given gantry mass then these calculations are important. Often the best bet is to use the highest reduction you can and still maintain your target top feed rate.
Al.
CNC, Mechatronics Integration and Custom Machine Design
“Logic will get you from A to B. Imagination will take you everywhere.”
Albert E.