The present article proposes to show the mathematical design of a spindle and the speed that it requires, using mathematical formulas, to carry out the extrusion process of recycled PETG or HDPE plastic. Speed control in this process is of great importance because the quality of the filament to be obtained will depend on it. The study will be simulated on spindles and casing that are 3640 and 3890 mm long respectively and made of AISI 4140 steel. The spindle casing has 3 types of band resistors, which vary their temperature according to the material to be used: PETG plastic or HDPE plastic. Each band type resistor is found in each section that the spindle has; the screw has 3 stages called the feeding zone, the compression zone, and the dosing zone. The production capacity is 40 kg /h of PETG or HDPE plastic filament 3 mm thick. In conclusion, the present method consists of the mathemati...