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<p>Accurate, traceable force calibration remains a challenge for microtribometers because of lateral/normal cross-talk and operating-point dependence bias in conventional procedures. We present a traceable force calibration (TFC) that solves the full 2 × 2 calibration matrix (<i>C</i><sub>1</sub>-<i>C</i><sub>4</sub>) from angle-resolved loading using a diamagnetic-levitation spring with a microbalance as an SI-traceable force standard. A known load is applied while the cantilever is tilted through multiple angles; linear slopes Δ<i>V</i><sub>x,z</sub>/Δ<i>F</i><sub>1</sub> at each angle provide sufficient equations to recover <i>C</i> without neglecting cross-talk. Using 18 angles, TFC yields stable coefficients <i>C</i><sub>1</sub> =  − 746.98 ± 0.01 μN/V and <i>C</i><sub>4</sub> =  − 737.17 ± 0.45 μN/V, with small cross-terms <i>C</i><sub>2</sub> = 3.372 ± 0.003 μN/V and <i>C</i><sub>3</sub> =  − 45.14 ± 0.63 μN/V. Subsampling shows convergence with only 3–4 angles, and a ± 1° reference-angle bias changes <i>C</i><sub>1</sub> and <i>C</i><sub>4</sub> by ≤ 1.01% and ≤ 0.49%, respectively. Compared head-to-head with the diamagnetic-levitation force-calibration (DLFC) route, TFC produces <i>C</i><sub>1</sub> values invariant to angle choice, whereas DLFC yields set-point (<i>V</i><sub>z</sub>)-dependent results and larger scatter (<i>e.g.</i>, <i>C</i><sub>1</sub> =  − 758 ± 41 μN/V). TFC thus offers a compact, low-uncertainty, SI-traceable workflow that quantifies cross-talk and delivers reliable calibration over micro- to milli-newton forces, enabling high-precision, reproducible microtribometry.</p>

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Traceable Force Calibration (TFC) for Microtribometers via Diamagnetic Levitation and Microbalance

  • 期刊论文

  • 发表日期：

    2025年12月1日

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  • Zitong Huang,
  • Tianci Chen,
  • Yijiang Wang,
  • Qingrui Song,
  • Kun Liu,
  • Jiaxin Ye

摘要

Accurate, traceable force calibration remains a challenge for microtribometers because of lateral/normal cross-talk and operating-point dependence bias in conventional procedures. We present a traceable force calibration (TFC) that solves the full 2 × 2 calibration matrix (C1-C4) from angle-resolved loading using a diamagnetic-levitation spring with a microbalance as an SI-traceable force standard. A known load is applied while the cantilever is tilted through multiple angles; linear slopes ΔVx,z/ΔF1 at each angle provide sufficient equations to recover C without neglecting cross-talk. Using 18 angles, TFC yields stable coefficients C1 =  − 746.98 ± 0.01 μN/V and C4 =  − 737.17 ± 0.45 μN/V, with small cross-terms C2 = 3.372 ± 0.003 μN/V and C3 =  − 45.14 ± 0.63 μN/V. Subsampling shows convergence with only 3–4 angles, and a ± 1° reference-angle bias changes C1 and C4 by ≤ 1.01% and ≤ 0.49%, respectively. Compared head-to-head with the diamagnetic-levitation force-calibration (DLFC) route, TFC produces C1 values invariant to angle choice, whereas DLFC yields set-point (Vz)-dependent results and larger scatter (e.g., C1 =  − 758 ± 41 μN/V). TFC thus offers a compact, low-uncertainty, SI-traceable workflow that quantifies cross-talk and delivers reliable calibration over micro- to milli-newton forces, enabling high-precision, reproducible microtribometry.