Optimization of Electrostatic Force System Based on Newton Interpolation Method

Abstract

The measurements of micro/nanoforces are of great importance in both science and engineering. We developed a traceable system for micro/nanoforces based on electrostatic force using two electrodes. Noises (creep, ground vibration, and airflow) are one of the limitations for force resolution. The forces are distorted by noise and cannot be measured accurately. Although ABA method can be used to eliminate linear creep, it is invalid for nonlinear noise. In this paper, a new method known as the Newton interpolation method (NIM) has been adopted in capacitance gradient and the calibration of cantilever stiffness to reduce the effect of nonlinear noise. The results show that the capacitance gradient, with a relative standard deviation of 0.004%, is stable and has good repeatability. The stiffness of cantilever was measured using electrostatic force. The typical value of stiffness ranged from 5.1 to 48 N/m. The relative standard deviation was small, i.e., less than 0.6% owing to Newton interpolation method. These results show that our system is very stable and repeatable. This research may assist in the designing of force measurement systems based on electrostatic force.

Micro-force sensing techniques and traceable reference forces: a review

“…The sensitivity of cylindrical sensors is decided by the ratio of the radii of the two electrodes. The closer the ratio is to 1, the higher the sensitivity [54]; further, it has nothing to do with the length of the electrode. A capacitive force sensor is an effective way to measure micro forces from millinewton to piconewton levels [1].…”

“…Air damping was introduced for the first time in the cylindrical capacitor, which increased the damping ratio from 0.0005 to 0.1 and improved both the response time and anti-jamming capability [154]. The differential method [16] and Newton interpolation method [54] were adopted to reduce uncertainty due to non-linear low-frequency noise. It was proved that the facility could measure and trace microforces on the order 10 −7 N within a 2% combined relative standard uncertainty through the comparisons to milligram weights calibrated using kilogram subdivision.…”

Torsion balance-based system for high-precision force measurement in horizontal plane: part II. Static and dynamic improvement

“…However, in many situations, the drift is non-linear and by running the ABA sequence measurements the errors could still remain in the measured signal. In case of the apparatus presented in this paper, we used another alternative known as the Newton's polynomial interpolation (NPI) for estimation of the non-linear drift [23,24]. Equation (3) describes the calculation method of the NPI: Using the NPI as equation ( 3) describes, the drift values at the time where forces is applied could be estimated as figure 6 shows.…”

A New Approach to Newton-Type Polynomial Interpolation with Parameters

“…In order to obtain better repaired results, iele's rational interpolation was combined with Newton-iele rational interpolation to repair damaged images. In [25], the Newton interpolation method was adopted in capacitance gradient and the calibration of cantilever stiffness. Based on polynomial approximation of local surface, Rahman et al [5] presented a novel local patch descriptor which is invariant to the changes in viewpoint, scale, orientation, and illumination.…”