Deriving steps per mm for an LVE system

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Abstract

Modification of off-the-shelf fused filament fabrication (FFF) 3D printers with a syringe pump, used as a large volume extruder (LVE) is a common method for the creation of low-cost laboratory 3D bioprinters. Open-source syringe pumps with accompanying firmware exist, however they require researchers to choose accurate control of the syringe pump over rich control over the 3D printer system. The combination of open-source syringe pump hardware controlled with 3D printer electronics and firmware gives the best of both worlds, however this firmware is not designed to control fluids, consequently some parameters may need to be calculated differently. FFF printer firmware (such as RepRapFirmware) uses E-steps-per-mm to translate the movement of the stepper motor into the extrusion of filament pre-nozzle. This method finds the value of this parameter for a bioprinter with a bowden-tube based LVE.

Steps

Take measurements

0.1.

Take the following measurements:

Finding the thread's lead

Most lead screws are single start, and the one recommended in the MOST OSSP is single start, this means that the lead (the distance the carriage travels with one rotation of the lead screw) is equal to the pitch (the distance between the crests of the thread).

If you are using a multi-start lead screw the following formula should be used to calculate the thread's lead:

Deriving the revolutions per mm

The ratio between the syringe and the Bowden tube can be calculated as follows:

Where is the distance travelled by the syringe plunger, is the resultant distance the gel travels through the bowden tube, is the internal radius of the syringe, and is the internal radius of the bowden tube.The ratio between the motor and the syringe is equal to the ratio between the motor and the linear distance travelled by the syringe plunger is: From this we know, when l_s = lead, the ratio between the lead screw and the Bowden tube, is: This makes the revolutions per mm:

Finding the E-Steps-per-mm

Multiply the motor steps by the micro-stepping by the length of filament produced through thr bowden tube with one revolution of the stepper motor