
Calculation is (very) simple:
Stepper motors I used have a resolution of 200 steps/revolution. We want to obtain a precision in full step mode of 1/10 mm. This is more than enough to mill balsa ribs and various parts for your models. To get enough torque and have sufficient precision when the machine is milling we cannot use a direct drive system, so we must select a gear ratio for the machine I have selected a 4:1 ratio. This obtained with a set of toothed pulleys A 10 teeth pulley mounted on the stepper motor drives a 40 teeth pulley using a closed belt. The pitch for the pulleys (and belt) is 5 mm. All carriages are also driven with a 5 mm pitch belt on all the axes with 16 teeth pulleys . This finally gives a precision of 0.1mm/step. I guess some of you want some explanations? Just read the next part. This is not rocket science. Only basic maths! Explanations: Each carriage is driven by a 16 teeth pulley with a 5mm pitch. When this pulley makes a full revolution (360 degrees) the displacement is number of teeth x pitch => 16 x 5 = 80 mm. In other words the carriage will move 80 mm when the pulley makes a full revolution. As we have a gear ration of 1:4 on the stepper motor, when the motor makes a full revolution the displacement of the carriage will be 80 mm /gear ratio => 80/4 = 20 mm. Finally the stepper motor has a resolution of 200 step/revolution or 1.8 deg/step. As a full revolution of the motor produces a displacement of 20 mm, one step will produce a displacement of 20/200 =0.1mm. The CNC 3AX driver board I use has a half step mode, which gives a theoretical precision of 0.05 mm (20/400). Taking into account the backlash effects on the carriages, the final precision should be around 1/10 mm, which is already very good for the required use.


Closed belts dimensioning It's a bit more complex to calculate the length of the closed belts used for the stepper motors If you build a machine identical to mine, you will need 330 mm closed belts (pitch 5mm) with 40 teeth pulleys ( primitive Ø 63.66 mm) and 10 teeth pulleys ( primitive Ø 15.92 mm) Distance between centres is 99.5 mm. It is also necessary to have a system of tension for the belts to obtain a correct adjustment. On my machine, the clamp holes for the motors are oblong. This makes it possible to move a little the motors to obtain a correct tension of the belts. If you change the values above, you will have to make your own calculations. Here are the formulas:
TIP: You can request free catalogs from HPC Europe They contain all kinds of formulas of calculation and useful abacuses to dimension the elements of your machine.

