{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,22]],"date-time":"2026-09-22T11:06:05Z","timestamp":1790075165327,"version":"4.0.1"},"reference-count":37,"publisher":"MDPI AG","issue":"18","license":[{"start":{"date-parts":[[2026,9,21]],"date-time":"2026-09-21T00:00:00Z","timestamp":1789948800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>This paper presents a method for the dynamic characterisation of load cells and force transducers designed to be straightforward to implement and based on instrumentation commonly used in structural dynamics testing. Impact hammers simultaneously provide an impulsive force to the sensor under test and measure the actual input to estimate the frequency response function. The bandwidth of the sensor is evaluated using an analytical single- or multi-degree-of-freedom frequency-domain model that is fitted to the experimental frequency response function using a Non-Linear Least-Squares approach. This paper provides guidelines for selecting the model complexity and the fitting frequency range and demonstrates the procedure on an experimental strain-gauge load cell. For the investigated transducer, the identified first natural frequency was 481.4 Hz, resulting in bandwidths of 47.9 Hz, 105.1 Hz, and 154.2 Hz for allowable deviations from the static sensitivity of 1%, 5%, and 10%, respectively. Moreover, for the single-degree-of-freedom case, the effect of masses added under operating conditions is modelled, with a worst-case relative error below 1% in the prediction of the natural frequency for the validation measurements, thus enabling the actual bandwidth to be estimated.<\/jats:p>","DOI":"10.3390\/s26185972","type":"journal-article","created":{"date-parts":[[2026,9,22]],"date-time":"2026-09-22T10:21:48Z","timestamp":1790072508000},"page":"5972","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Model-Based Approach for Dynamic Characterisation of Force Transducers with Impact Hammers"],"prefix":"10.3390","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0187-942X","authenticated-orcid":false,"given":"Gianmarco","family":"Battista","sequence":"first","affiliation":[{"name":"Department of Engineering for Industrial Systems and Technologies, University of Parma, 43124 Parma, Italy"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"methodology","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"},{"role":"data-curation","vocabulary":"credit"},{"role":"software","vocabulary":"credit"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3256-2158","authenticated-orcid":false,"given":"Stefano","family":"Pavoni","sequence":"additional","affiliation":[{"name":"Department of Engineering for Industrial Systems and Technologies, University of Parma, 43124 Parma, Italy"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"data-curation","vocabulary":"credit"},{"role":"methodology","vocabulary":"credit"},{"role":"writing-original-draft","vocabulary":"credit"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6390-3704","authenticated-orcid":false,"given":"Francescantonio","family":"Luc\u00e0","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Politecnico di Milano, Via La Masa, 34, 20156 Milan, Italy"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"writing-review-editing","vocabulary":"credit"},{"role":"software","vocabulary":"credit"},{"role":"visualization","vocabulary":"credit"},{"role":"validation","vocabulary":"credit"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8625-0822","authenticated-orcid":false,"given":"Marta","family":"Berardengo","sequence":"additional","affiliation":[{"name":"Department of Mechanical, Energy, Management and Transportation Engineering, University of Genova, 16145 Genova, Italy"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"conceptualization","vocabulary":"credit"},{"role":"methodology","vocabulary":"credit"},{"role":"data-curation","vocabulary":"credit"},{"role":"investigation","vocabulary":"credit"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9864-6728","authenticated-orcid":false,"given":"Marcello","family":"Vanali","sequence":"additional","affiliation":[{"name":"Department of Engineering for Industrial Systems and Technologies, University of Parma, 43124 Parma, Italy"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"conceptualization","vocabulary":"credit"},{"role":"methodology","vocabulary":"credit"},{"role":"software","vocabulary":"credit"},{"role":"supervision","vocabulary":"credit"},{"role":"funding-acquisition","vocabulary":"credit"}]}],"member":"1968","published-online":{"date-parts":[[2026,9,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"113789","DOI":"10.1016\/j.measurement.2023.113789","article-title":"Development of a differential load cell negating inertial force","volume":"223","author":"Kim","year":"2023","journal-title":"Measurement"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"114151","DOI":"10.1016\/j.measurement.2024.114151","article-title":"A six-axis force and torque sensor consisting of compliant mechanisms and full-bridge strain gauges","volume":"226","author":"Wang","year":"2024","journal-title":"Measurement"},{"key":"ref_3","unstructured":"(2011). 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