# Peristaltic pump development

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The custom three-roller pump, its first-order displacement model and the strict distinction between motor command resolution and delivered-volume accuracy.

In brief

The custom three-roller pump, its first-order displacement model and the strict distinction between motor command resolution and delivered-volume accuracy.

**Custom pump architecture.** Original CAD from the supplied pump package. Geometry supports the first-order model; delivery performance requires gravimetric calibration. [I03]

## Explanation

A three-roller rotor compresses a flexible tube. Advancing the compression moves liquid while the liquid remains inside the replaceable tube. The motor provides a precise command, but only calibration determines the volume that actually exits the tube.

## Documented design

 |
 Parameter | v2 design value | Classification

 | Pump type | three-roller peristaltic | design architecture
 | Tube | 3.2 mm ID / 6.4 mm OD silicone | design specification
 | Nominal channel radius | 18 mm | CAD specification
 | Drive | NEMA 17, 1.8° full step, direct drive | component specification
 | Command mode | 1/16 microstepping | firmware design
 | Housing | PETG prototype geometry | CAD specification
 | System channels | four independent pump modules | system design

## First-order model

 P-1 A t = π d i 2 4 A_t=\frac{\pi d_i^2}{4} A t ​ = 4 π d i 2 ​ ​ Nominal undeformed internal tube area.

**Explanation**Tube area is calculated from its internal diameter.

 P-2 V r e v , i d e a l = A t L e f f N e V_{\mathrm{rev,ideal}}=A_tL_{\mathrm{eff}}N_e V rev , ideal ​ = A t ​ L eff ​ N e ​ Ideal displacement per rotor revolution using an effective displaced length Leff and displacement-event count Ne.

**Explanation**Ideal volume per turn is tube area multiplied by the effective squeezed length and the number of displacement events.

With d i = 3.2 mm, L eff = 25 mm and N e = 3, the report model gives A t ≈ 8.04 mm² and V rev,ideal ≈ 0.603 mL/rev.

 P-3 V r e v , m e a s = η v V r e v , i d e a l V_{\mathrm{rev,meas}}=\eta_vV_{\mathrm{rev,ideal}} V rev , meas ​ = η v ​ V rev , ideal ​ Measured displacement represented by a fitted volumetric-efficiency term. ηv may depend on speed, pressure, tube and age.

**Explanation**The ideal volume is corrected by an efficiency measured on the real pump.

 P-4 Q = V r e v , m e a s   n Q=V_{\mathrm{rev,meas}}\,n Q = V rev , meas ​ n Mean flow at rotor speed n in r e v   m i n − 1 \mathrm{rev\,min^{-1}} rev mi n − 1 .

**Explanation**Flow equals delivered volume per turn multiplied by turns per minute.

## Motor-command increment

 P-5 N μ s t e p / r e v = 360 ∘ 1.8 ∘   16 = 3200 N_{\mu\mathrm{step/rev}}=\frac{360^\circ}{1.8^\circ}\,16=3200 N μ step/rev ​ = 1. 8 ∘ 36 0 ∘ ​ 16 = 3200 Microstep commands per direct-drive rotor revolution.

**Explanation**Motor step angle and microstepping determine how many commands produce one rotor revolution.

 P-6 Δ V c m d , n o m = 0.603   m L 3200 ≈ 0.188   μ L / c o m m a n d \Delta V_{\mathrm{cmd,nom}}=\frac{0.603\ \mathrm{mL}}{3200}\approx0.188\ \mathrm{\mu L/command} Δ V cmd , nom ​ = 3200 0.603   mL ​ ≈ 0.188   μ L/command Nominal geometric displacement assigned to one command.

**Explanation**Nominal volume per command is the measured volume per revolution divided by commands per revolution.

 **Engineering note**

0.188 µL per microstep is not accuracy, repeatability, minimum dose or experimentally resolved liquid volume.

## Why calibration is mandatory

Tube recovery, occlusion, viscosity, suction head, outlet pressure, roller geometry, motor torque, microstep non-linearity and tube wear all alter delivered volume. Peristaltic-pump modelling and published multi-channel systems therefore use physical calibration rather than geometry alone. [R18] [R19]

## Progress classification

The pump geometry and four-channel module are substantial v2 engineering progress. The supplied report documents CAD, component selection and the analytical model. No traceable FlavoRotor gravimetric dataset accompanies the report, so delivered-volume performance remains unclaimed until CR-PMP-001 is published.

## FlavoRotor design provenance

The system-specific configuration on this page is traced to the supplied FlavoRotor engineering records. [I02] [I03]

## CAD documentation

**Roller and tube path.** Internal CAD record. [I03]

**Exploded pump assembly.** Internal CAD record showing serviceable components. [I03]

## References

- [I02] FlavoRotor project team (2026). FlavoRotor v2.0 system architecture. *Internal engineering design report*.
- [I03] FlavoRotor project team (2026). FlavoRotor peristaltic pump technical record. *Internal engineering record*.
- [R18] Formato, Gaetano; Romano, Raffaele; Formato, Andrea; Sorvari, Joonas; Koiranen, Tuomas; Pellegrino, Arcangelo; Villecco, Francesco (2019). Fluid–Structure Interaction Modeling Applied to Peristaltic Pump Flow Simulations. *Machines*. https://doi.org/10.3390/machines7030050
- [R19] Buchhorn, Michael; Akkoc, Gun Deniz; Dworschak, Dominik (2025). An open-source peristaltic pump with multiple independent channels for laboratory automation. *Digital Discovery*. https://doi.org/10.1039/D5DD00157A