{"@context":"https://schema.org","@type":"TechArticle","id":"PR-PMP-001","slug":"pump-calibration","canonical_url":"https://flavorotor.com/research/pump-calibration","machine_readable_url":"https://flavorotor.com/research/data/chapters/pump-calibration.json","markdown_url":"https://flavorotor.com/research/markdown/pump-calibration","title":"Gravimetric pump calibration","description":"A complete channel-specific procedure for converting motor commands into measured liquid volume with uncertainty and drift.","chapter":"Nutrient dosing","version":"1.1","updated":"2026-07-26","table_of_contents":[{"id":"principle","label":"Principle"},{"id":"matrix","label":"Test matrix"},{"id":"statistics","label":"Calibration statistics"},{"id":"model","label":"Channel model"},{"id":"acceptance","label":"Predefined engineering acceptance gates"},{"id":"provenance","label":"FlavoRotor design provenance"}],"html":"<section aria-label=\"Article summary\" class=\"fr-article-summary\"><div><span>In brief</span><p>A complete channel-specific procedure for converting motor commands into measured liquid volume with uncertainty and drift.</p></div></section><h2 id=\"principle\">Principle</h2>\n<p>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.</p>\n<div class=\"equation\"><div class=\"equation-label\">C-1</div><div class=\"equation-text\">V<sub>i</sub> = (m<sub>after,i</sub> − m<sub>before,i</sub>) / ρ(T)</div><div class=\"equation-desc\">Delivered volume for repetition i.</div></div>\n<div class=\"equation\"><div class=\"equation-label\">C-2</div><div class=\"equation-text\">Q<sub>i</sub> = V<sub>i</sub> / Δt<sub>i</sub></div><div class=\"equation-desc\">Mean flow for repetition i.</div></div>\n<p>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. <button aria-label=\"Open source record R37\" class=\"research-source-trigger\" data-research-source=\"R37\" type=\"button\">[R37]</button> <button aria-label=\"Open source record R38\" class=\"research-source-trigger\" data-research-source=\"R38\" type=\"button\">[R38]</button> <button aria-label=\"Open source record R47\" class=\"research-source-trigger\" data-research-source=\"R47\" type=\"button\">[R47]</button></p>\n<h2 id=\"matrix\">Test matrix</h2>\n<div class=\"table-wrap\"><table><thead><tr><th>Factor</th><th>Levels</th></tr></thead><tbody><tr><td>Channel</td><td>1, 2, 3, 4</td></tr><tr><td>Rotor speed</td><td>5, 15, 30 and 60 rev/min</td></tr><tr><td>Commanded dose</td><td>0.5, 1, 2, 5 and 10 mL</td></tr><tr><td>Repetitions</td><td>minimum 20 per primary condition</td></tr><tr><td>Fluid</td><td>deionised water and each representative stock class</td></tr><tr><td>Tube state</td><td>new, mid-life and replacement threshold</td></tr><tr><td>Hydraulic condition</td><td>minimum, nominal and maximum inlet head; installed outlet path</td></tr><tr><td>Direction</td><td>forward; reverse purge characterised separately</td></tr></tbody></table></div>\n<h2 id=\"statistics\">Calibration statistics</h2>\n<div class=\"equation\"><div class=\"equation-label\">C-3</div><div class=\"equation-text\">V̄ = (1/N) ΣV<sub>i</sub></div><div class=\"equation-desc\">Mean delivered volume.</div></div>\n<div class=\"equation\"><div class=\"equation-label\">C-4</div><div class=\"equation-text\">bias = V̄ − V<sub>set</sub></div><div class=\"equation-desc\">Absolute systematic error at a test point.</div></div>\n<div class=\"equation\"><div class=\"equation-label\">C-5</div><div class=\"equation-text\">CV = 100 · s / V̄</div><div class=\"equation-desc\">Coefficient of variation for repeatability.</div></div>\n<div class=\"equation\"><div class=\"equation-label\">C-6</div><div class=\"equation-text\">RMSE = √[(1/N)Σ(V<sub>i</sub> − V<sub>set</sub>)²]</div><div class=\"equation-desc\">Combined deviation from the requested volume.</div></div>\n<p>Repeatability, bias, residual analysis and method precision are reported using declared statistical procedures rather than a single R² value. <button aria-label=\"Open source record R46\" class=\"research-source-trigger\" data-research-source=\"R46\" type=\"button\">[R46]</button> <button aria-label=\"Open source record R50\" class=\"research-source-trigger\" data-research-source=\"R50\" type=\"button\">[R50]</button></p>\n<h2 id=\"model\">Channel model</h2>\n<div class=\"equation\"><div class=\"equation-label\">C-7</div><div class=\"equation-text\">V̂<sub>j</sub> = a<sub>j</sub>N<sub>cmd</sub> + b<sub>j</sub></div><div class=\"equation-desc\">First candidate model for channel j; residuals determine whether speed, pressure or nonlinear terms are required.</div></div>\n<h2 id=\"acceptance\">Predefined engineering acceptance gates</h2>\n<div class=\"table-wrap\"><table><thead><tr><th>Metric</th><th>Gate for initial reservoir dosing</th></tr></thead><tbody><tr><td>Relative bias</td><td>≤ ±3% for doses ≥1 mL within the declared range</td></tr><tr><td>Repeatability</td><td>CV ≤2% for doses ≥1 mL</td></tr><tr><td>Channel model</td><td>residual structure absent and R² reported, not used alone</td></tr><tr><td>Drift</td><td>≤5% before recalibration or tube replacement</td></tr><tr><td>Cross-channel contamination</td><td>none detected above method limit</td></tr><tr><td>Backflow/siphon</td><td>no uncontrolled transfer in the installed hydraulic range</td></tr></tbody></table></div>\n<p>These are FlavoRotor acceptance criteria, not claimed achieved performance. Published multi-channel pump data guide the method but are not copied as FlavoRotor results. <button aria-label=\"Open source record R19\" class=\"research-source-trigger\" data-research-source=\"R19\" type=\"button\">[R19]</button></p>\n<h2 id=\"provenance\">FlavoRotor design provenance</h2><p>The system-specific configuration on this page is traced to the supplied FlavoRotor engineering records. <button aria-label=\"Open source record I03\" class=\"research-source-trigger\" data-research-source=\"I03\" type=\"button\">[I03]</button></p>","text":"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 after,i − m before,i ) / ρ(T) Delivered volume for repetition i. C-2 Q i = V i / Δt i Mean flow for repetition i. 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 V̄ = (1/N) ΣV i Mean delivered volume. C-4 bias = V̄ − V set Absolute systematic error at a test point. C-5 CV = 100 · s / V̄ Coefficient of variation for repeatability. C-6 RMSE = √[(1/N)Σ(V i − V set )²] Combined deviation from the requested volume. 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 V̂ j = a j N cmd + b j First candidate model for channel j; residuals determine whether speed, pressure or nonlinear terms are required. 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]","source_ids":["I03","R19","R37","R38","R46","R47","R50"],"visuals":[],"sources":[{"id":"I03","authors":"FlavoRotor project team","year":2026,"title":"FlavoRotor peristaltic pump technical record","publication":"Internal engineering record","doi":null,"url":"/research/peristaltic-pump","source_type":"internal primary record","relevance":"Documents CAD geometry, components, first-order equations, four-channel integration and the proposed calibration protocol.","verification":"Derived from the original FlavoRotor pump engineering package","verified_on":"2026-07-26","verification_status":"INTERNAL PRIMARY RECORD","verified_against":"Original internal project file and extracted media"},{"id":"R19","authors":"Buchhorn, Michael; Akkoc, Gun Deniz; Dworschak, Dominik","year":2025,"title":"An open-source peristaltic pump with multiple independent channels for laboratory automation","publication":"Digital Discovery","doi":"10.1039/D5DD00157A","source_type":"peer-reviewed engineering research","relevance":"Provides a relevant multi-channel open-source pump architecture and a measured calibration methodology.","verification":"Publisher metadata and full text checked 2026-07-26","url":"https://doi.org/10.1039/D5DD00157A","verified_on":"2026-07-26","verification_status":"DOI METADATA CHECKED","verified_against":"Publisher, DOI landing page, PubMed or official repository where available"},{"id":"R37","authors":"Bean, Vern E.; Espina, Pedro I.; Wright, John D.; Sheckels, Sherry D.; Johnson, Aaron N.","year":2006,"title":"NIST Calibration Services for Liquid Volume","publication":"NIST Special Publication 250-72","doi":"10.6028/NIST.SP.250-72","source_type":"official metrology publication","relevance":"Provides traceable liquid-volume calibration concepts relevant to gravimetric pump calibration and uncertainty.","verification":"Official NIST metadata checked 2026-07-26","url":"https://doi.org/10.6028/NIST.SP.250-72","verified_on":"2026-07-26","verification_status":"DOI METADATA CHECKED","verified_against":"Publisher, DOI landing page, PubMed or official repository where available"},{"id":"R38","authors":"Joint Committee for Guides in Metrology","year":2008,"title":"Evaluation of measurement data — Guide to the expression of uncertainty in measurement","publication":"JCGM 100:2008","doi":"10.59161/JCGM100-2008E","source_type":"international metrology guide","relevance":"Defines the framework for measurement models, standard uncertainty, combined uncertainty and expanded uncertainty.","verification":"Official BIPM/JCGM record checked 2026-07-26","url":"https://doi.org/10.59161/JCGM100-2008E","verified_on":"2026-07-26","verification_status":"DOI METADATA CHECKED","verified_against":"Publisher, DOI landing page, PubMed or official repository where available"},{"id":"R46","authors":"Heckert, N. Alan; Filliben, James J.; Croarkin, C. M.; Hembree, B.; Guthrie, William F.; Tobias, P.; Prinz, J.","year":2002,"title":"NIST/SEMATECH e-Handbook of Statistical Methods","publication":"NIST Handbook 151","doi":null,"url":"https://www.nist.gov/publications/handbook-151-nistsematech-e-handbook-statistical-methods","source_type":"official statistical handbook","relevance":"Supports calibration regression, residual analysis, experimental design and statistical process control.","verification":"Official NIST publication record checked 2026-07-26","verified_on":"2026-07-26","verification_status":"OFFICIAL RECORD CHECKED","verified_against":"Named official institution record"},{"id":"R47","authors":"Privitera, Davide; Mecocci, Alessandro; Bartolini, Sandro","year":2025,"title":"Extensive Dataset for Peristaltic Pump Accuracy Enhancement in Pharmaceutical Environments","publication":"Scientific Data, 12, 1618","doi":"10.1038/s41597-025-05902-z","source_type":"peer-reviewed data descriptor","relevance":"Supports repeated gravimetric characterisation, drift monitoring and data-driven compensation for peristaltic dosing.","verification":"Publisher and PubMed metadata checked 2026-07-26","url":"https://doi.org/10.1038/s41597-025-05902-z","verified_on":"2026-07-26","verification_status":"DOI METADATA CHECKED","verified_against":"Publisher, DOI landing page, PubMed or official repository where available"},{"id":"R50","authors":"International Organization for Standardization","year":2025,"title":"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","publication":"ISO","doi":null,"url":"https://www.iso.org/standard/90054.html","source_type":"international standard","relevance":"Supports estimation of repeatability and reproducibility of measurement methods.","verification":"Official ISO record checked 2026-07-26; ISO 5725-2:2025 is the current published edition.","verified_on":"2026-07-26","verification_status":"OFFICIAL RECORD CHECKED","verified_against":"Official ISO catalogue record"}]}
