Delta / Kossel Stepper Motor Calculator

RELEASE V1.0


INPUTS

SPEEDS and SETTINGS





Power Supply Voltage (usually 12 or 24)
Desired Max Travel Speed (effector, mm/sec)
Driver Current, Motor Amps

PHYSICAL CHARACTERISTICS

YOUR PRINTER
Pully Teeth
Belt Pitch in mm
Max Rod Angle, at approx. 10mm from an edge opposite a tower

MOTOR DATA SHEET
Steps per Rev (200 for 1.8°, 400 for 0.9°)
Inductance in mH
Motor Rated Current (From data sheet, NOT driver setting)
Motor Rated Holding Torque in Nm


OUTPUTS

INTERMEDIATE CALCULATIONS

Max Belt Speed mm/sec
Max Motor Revs/Sec
Peak Back EMF from Inductance
Peak Back EMF from rotation (approximated)

FINAL OUTPUTS


Sum of Back EMF (approx.)
Torque Ratio at Maximum Speed
Effective Torque at Maximum Speed


NOTES

This calculator is intended to help selection of Stepper Motors for Delta / Kossel 3D printers. The formulas and information on which it is based (and the initial values) are derived from: https://duet3d.com/wiki/Choosing_stepper_motors

Torque Ratio over 100 is 'good'. It means there is 'headroom' in the system. Of course, there will never be more torque at speed than holding torque. Torque Ratio under 100% may be OK, it depends on how much torque is really needed to move your printer vs. how much torque is available from the motors.

Since Voltage and Resistance of the stepper motor are not part of this calculator, it is worth noting that you should avoid motors with rated voltage (or product of rated current and phase resistance) > 4V or inductance > 4mH.

The input fields can be pre-set via URL arguments:

Hint: Data Sheets may have N.cm, In-OZ, Kg.m, etc. Be certain that you convert to Nm.

Hint: Set the rod angle to 45° and the belt speed will equal the input desired speed, useful for calculating cartesian printers.

A couple of specific examples:
Filastruder USA stock of E3D suggested 0.9 axis motor Calculator for that motor
Sparkfun USA stock of a 0.9 stepper. Calculator for that motor