# Gravimetric pump calibration

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A complete channel-specific procedure for converting motor commands into measured liquid volume with uncertainty and drift.

In brief

A complete channel-specific procedure for converting motor commands into measured liquid volume with uncertainty and drift.

## Principle

Each pump dispenses into a vessel on a calibrated balance. Mass gain is converted to volume using fluid density at the measured temperature. The test is repeated across channel, dose, speed, tube condition and hydraulic head.

 C-1 V i = m a f t e r , i − m b e f o r e , i ρ ( T ) V_i=\frac{m_{\mathrm{after},i}-m_{\mathrm{before},i}}{\rho(T)} V i ​ = ρ ( T ) m after , i ​ − m before , i ​ ​ Delivered volume for repetition i.

**Explanation**The mass gained by the receiving vessel is converted into liquid volume using density at the measured temperature.

 C-2 Q i = V i Δ t i Q_i=\frac{V_i}{\Delta t_i} Q i ​ = Δ t i ​ V i ​ ​ Mean flow for repetition i.

**Explanation**Mean flow is delivered volume divided by run time.

The gravimetric chain follows traceable liquid-volume and uncertainty principles: balance performance, test-liquid density, evaporation, timing, repeatability and calibration state are recorded. Large published peristaltic-pump datasets show why repeated measurements and drift analysis are necessary, but their performance values are not transferred to FlavoRotor. [R37] [R38] [R47]

## Test matrix

 |
 Factor | Levels

 | Channel | 1, 2, 3, 4
 | Rotor speed | 5, 15, 30 and 60 rev/min
 | Commanded dose | 0.5, 1, 2, 5 and 10 mL
 | Repetitions | minimum 20 per primary condition
 | Fluid | deionised water and each representative stock class
 | Tube state | new, mid-life and replacement threshold
 | Hydraulic condition | minimum, nominal and maximum inlet head; installed outlet path
 | Direction | forward; reverse purge characterised separately

## Calibration statistics

 C-3 V ˉ = 1 N ∑ i = 1 N V i \bar V=\frac{1}{N}\sum_{i=1}^{N}V_i V ˉ = N 1 ​ i = 1 ∑ N ​ V i ​ Mean delivered volume.

**Explanation**The arithmetic mean combines all repeated delivery measurements.

 C-4 b i a s = V ˉ − V s e t \mathrm{bias}=\bar V-V_{\mathrm{set}} bias = V ˉ − V set ​ Absolute systematic error at a test point.

**Explanation**Bias is the difference between the mean delivered volume and the requested volume.

 C-5 C V = 100   s V ˉ \mathrm{CV}=100\,\frac{s}{\bar V} CV = 100 V ˉ s ​ Coefficient of variation for repeatability.

**Explanation**The coefficient of variation expresses repeatability spread as a percentage of the mean.

 C-6 R M S E = 1 N ∑ i = 1 N ( V i − V s e t ) 2 \mathrm{RMSE}=\sqrt{\frac{1}{N}\sum_{i=1}^{N}\left(V_i-V_{\mathrm{set}}\right)^2} RMSE = N 1 ​ i = 1 ∑ N ​ ( V i ​ − V set ​ ) 2

 ​ Combined deviation from the requested volume. **Explanation**RMSE combines all deviations from the requested volume into one error value.

Repeatability, bias, residual analysis and method precision are reported using declared statistical procedures rather than a single R² value. [R46] [R50]

## Channel model

 C-7 V ^ j = a j N c m d + b j \hat V_j=a_jN_{\mathrm{cmd}}+b_j V ^ j ​ = a j ​ N cmd ​ + b j ​ First candidate model for channel j; residuals determine whether speed, pressure or nonlinear terms are required.

**Explanation**The first calibration model links command count to delivered volume; residuals show whether a more complex model is needed.

## Predefined engineering acceptance gates

 |
 Metric | Gate for initial reservoir dosing

 | Relative bias | ≤ ±3% for doses ≥1 mL within the declared range
 | Repeatability | CV ≤2% for doses ≥1 mL
 | Channel model | residual structure absent and R² reported, not used alone
 | Drift | ≤5% before recalibration or tube replacement
 | Cross-channel contamination | none detected above method limit
 | Backflow/siphon | no uncontrolled transfer in the installed hydraulic range

These are FlavoRotor acceptance criteria, not claimed achieved performance. Published multi-channel pump data guide the method but are not copied as FlavoRotor results. [R19]

## FlavoRotor design provenance

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

## References

- [I03] FlavoRotor project team (2026). FlavoRotor peristaltic pump technical record. *Internal engineering record*.
- [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
- [R37] Bean, Vern E.; Espina, Pedro I.; Wright, John D.; Sheckels, Sherry D.; Johnson, Aaron N. (2006). NIST Calibration Services for Liquid Volume. *NIST Special Publication 250-72*. https://doi.org/10.6028/NIST.SP.250-72
- [R38] Joint Committee for Guides in Metrology (2008). Evaluation of measurement data — Guide to the expression of uncertainty in measurement. *JCGM 100:2008*. https://doi.org/10.59161/JCGM100-2008E
- [R46] Heckert, N. Alan; Filliben, James J.; Croarkin, C. M.; Hembree, B.; Guthrie, William F.; Tobias, P.; Prinz, J. (2002). NIST/SEMATECH e-Handbook of Statistical Methods. *NIST Handbook 151*.
- [R47] Privitera, Davide; Mecocci, Alessandro; Bartolini, Sandro (2025). Extensive Dataset for Peristaltic Pump Accuracy Enhancement in Pharmaceutical Environments. *Scientific Data, 12, 1618*. https://doi.org/10.1038/s41597-025-05902-z
- [R50] International Organization for Standardization (2025). ISO 5725-2:2025 Accuracy (trueness and precision) of measurement methods and results — Part 2: Basic method for the determination of repeatability and reproducibility of a standard measurement method. *ISO*.