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An Instrument for Micro-Newton Force Measurement with Uncertainty in E-5
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摘要: 微牛级力值的测量技术广泛应用于空间探测、生物材料分析与微纳制造等领域的研究。基于静电力天平原理，设计并搭建了一套用于微牛级力值测量的装置，针对前期研究中测量装置的铅垂向刚度过大和圆柱形电容器同轴度对准误差较大的问题，通过优化设计四边形柔性枢轴的结构降低了系统在铅垂向的刚度，提升了静电力天平的力值分辨力，并基于圆柱形电容器的电容特性实现了对内、外电极同轴度的校准。经过实验测量，设计的微牛级力值计量装置具备了将100 μN力值的测量不确定度控制在E-5量级的能力。此项研究成果将为微牛级力值测量基准装置的建立和微牛级力值量传方法的研究做出重要贡献。Abstract: Micro-newton force measurement technology, extensively employed in the domains of space exploration, bio-materials analysis, and micro-nano manufacturing, plays a pivotal role. This study presents a device constructed based on the principle of electrostatic force balance, aimed at measuring micro-newton force values. Addressing the issues encountered in preliminary research, such as excessive stiffness in the vertical direction and significant alignment error of cylindrical capacitors, structural optimization of quadrilateral flexible pivots was undertaken to diminish system stiffness vertically, thereby enhancing the force resolution of the electrostatic force balance. Additionally, calibration of the concentricity of the inner and outer electrodes was achieved based on the capacitance characteristics of cylindrical capacitors. Experimental assessments revealed that the devised micro-newton force measurement device adeptly confines the measurement uncertainty of 100 μN force values to the E-5 level. The outcomes of this research are poised to significantly contribute to the establishment of micro-newton force measurement standard devices and further research on micro-newton force measurement methodologies.
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图 1 静电力天平测量装置简图
Figure 1. Schematic of the electrostatic force balance measurement device
图 2 静电力天平装置中四边形柔性枢轴结构三维图
Figure 2. 3D diagram of quadrilateral flexible pivots structure in the electrostatic force balance device
图 3 内、外电极径向偏移量和倾斜角对电容梯度的影响
Figure 3. Influence of radial offset and tilt angle of inner and outer electrodes on capacitance gradient
图 5 激光干涉仪与电容电桥的稳定性实验结果
Figure 5. Experimental results on the stability of laser interferometer and capacitance bridge
图 7 电容梯度的分散性与重复性实验结果
Figure 7. Experimental results on dispersion and repeatability of capacitance gradient measurements
图 8 静电力天平的刚度测量结果
Figure 8. Measurement results of stiffness in the designed electrostatic force balance
图 9 力值测量实验中电压控制模式和相应的位移变化
Figure 9. Voltage-controlled mode and corresponding displacement variation in force measurement experiment
表 1 10 mg砝码质量与重力加速度的校准结果
Table 1. Calibration results of 10 mg weight with gravitational acceleration
砝码质量 重力加速度 重力值 10.0019 mg 9.8012 m/s2 98.0306 μN 
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表 2 10 mg砝码力值测量不确定度
Table 2. Uncertainty budget in the measurement of 10 mg weight force
不确定度来源 类别 不确定度分量 电容电桥 B 5.00E-7 激光干涉仪 B 1.00E-8 电压源 B 2.50E-5 力值分辨力 B 7.20E-6 电容梯度重复性 A 1.72E-5 同轴度 B 1.25E-5 力值重复性 A 6.24E-5 10 mg砝码力值测量的合成标准不确定度（k=1） 7.09E-5
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