Yelong Zheng

Micron-scale high-stiffness doubly clamped beams are core structures in micro- and nanodevices such as accelerometers and gyroscopes. Owing to their small size and high natural frequency, they play an important role in the development of microelectromechanical systems. However, the relatively high uncertainty of existing measurement methods presents significant challenges for elastic-parameter measurement. This study proposes a method for measuring the elastic parameters of micron-scale high-stiffness doubly clamped beams. A parallelogram flexure hinge combined with a precision balance is introduced to measure the equivalent stiffness, while piezoelectric ceramic excitation is used to induce microbeam vibration and determine the equivalent mass and damping coefficient. The proposed method enables the equivalent stiffness, equivalent mass, and damping coefficient to be obtained within a unified measurement framework, while providing SI traceability and good measurement repeatability. Based on the simulation and experimental results, the measured equivalent stiffness, equivalent mass, and damping coefficient of the micron-scale high-stiffness doubly clamped beam were 21 309 N m ⁻¹ , 0.023 mg, and 0.002 kg s ⁻¹ , respectively, with corresponding relative standard uncertainties of 2.1%, 8.6%, and 4.1%.

Slope parameters are widely used in linear measurement and calibration to characterize key metrological quantities. However, the Guide to the Expression of Uncertainty in Measurement (GUM) does not provide an explicit procedure for evaluating the uncertainty of slope parameters that are implicitly determined from linear fitting when both variables carry measurement uncertainty. In this work, the slope is formulated as a measurand within the GUM framework, and an implicit measurement model is established based on the optimality conditions of the fitting process. Sensitivity coefficients are derived through implicit differentiation, enabling uncertainty propagation from the input quantities to the slope parameter within a GUM-consistent framework. To validate the proposed framework, stiffness calibration experiments based on a flexure hinge mechanism were conducted, where stiffness was represented by the slope of the force–displacement relationship. The uncertainty evaluation results were compared with those obtained using Ordinary Least Squares, York regression, and the Monte Carlo method. The results show that the proposed framework yields uncertainty estimates that are consistent with Monte Carlo simulations while exhibiting systematic differences from conventional regression-based approaches due to differences in uncertainty propagation mechanisms. Additional experiments over a stiffness range from 20 to 100 N m − 1 further demonstrate the applicability and stability of the proposed framework under different stiffness conditions. The proposed framework provides a metrologically interpretable uncertainty evaluation approach for slope parameters implicitly determined in linear measurement models.

The precise evaluation of micro-thrusters is critical for the success of advanced space missions, necessitating highly accurate and reliable calibration methods for pendulum-based thrust stands. This paper proposes a gravity-based calibration method that generates a precise and continuously adjustable gravitational torque by rotating an eccentric mass rod mounted directly on the pendulum. This approach enables equivalent calibration forces based on a clear physical principle, effectively overcoming key limitations of existing techniques, including complex traceability chains and susceptibility to installation errors. A key innovation is the use of a weighing bridge method to accurately determine the rod's mass moment, effectively bypassing the difficult direct measurement of its center-of-mass offset and ensuring a short traceability chain to the SI system. Experimental validation on a compound pendulum thrust stand demonstrates outstanding performance, including a wide calibration range (0–2858.3 μN), and high resolution (better than 0.1 μN). The method achieves a low relative expanded uncertainty of 0.396% (K=2) at 50 μN and better than 2.0% across the 1–300 μN range. Cross-comparison with an electromagnetic coil calibration device shows a deviation of only 0.46%. The proposed rotating rod calibration method provides a simple, high-precision, non-contact solution for advanced thrust stands.

Accurate monitoring of the horizontal tilt is essential to suppress low-frequency noise in the measurement system of micro-thrust—a requirement for spacebased gravitational wave measurements. Unfortunately, the sensitivity of modern inclinometers is fundamentally limited by the noise floors of their physical and electronic components.To overcome these limitations is a new inclinometer design which consists of a gravitational compound pendulum and a displacement sensor that reach ultrahigh sensitivity. Our inclinometer implements a mechanical amplification mode of a quasi-zero stiffness system.By critically coupling the pendulum’s gravitational restoring moment with the stiffness of a flexure pivot, the system efficiently transforms minute tilt angles into measurable displacements. Theoretical modelling clarifies the mechanics of this angular amplification and guides our strategy for regulating the gravitational restoring moment.Experimental characterization demonstrates a resolution of 0.87 nrad over a 0–109 µrad range, the tunable amplification factor can be increased to exceeding 160 and the nonlinearity error as low as 1.18%. This compact and versatile design provides a strong motivation to deploy ultra-precision tilt measurement on advanced metrology and adaptive devices.

Micro thrusters play a crucial role in satellite orbit correction and attitude control. Given their low thrust, reducing the stiffness of the thrust stand is often required to enhance resolution. However, since the thrust typically ranges from micronewtons to several millinewtons, a thrust stand with fixed stiffness is insufficient to meet the demands. The trade-off between high resolution and wide range remains a key challenge in ground testing of thruster. Therefore, an efficient stiffness adjustment method is proposed by introducing the negative restoring moment of extension spring. Tests show that the stiffness of the stand can be continuously adjusted from 19.71 to 1.28 N/m. The models of nonlinearity and fixed-end offset of spring are established to evaluate their impact on the results. Performance validation using electrostatic force show that the thrust stand achieves a resolution better than 0.5 μN while extending the range to 3346.4 μN. The thrust of the micro-Hall thruster was tested at various flow and discharge voltages based on this thrust stand. The uncertainty evaluation of the stand shows that the expanded uncertainty is better than 2.0% when thrust is 73.55 μN. This study is significant for optimizing the resolution and range of force sensors.