The scalar triangulation and ranging (STAR) method is a magnetic method based on magnetic gradient tensor invariants. Due to the asphericity parameter, there are distance error and direction error in the STAR method. There have been studies to compensate the direction error, but the distance error has not been compensated. This paper proposes a new STAR method (NSM) that uses an iterative method to compensate both the direction error and the distance error. Considering the convenience and feasibility of the operation, previous researchers analyzed the detection accuracy of the magnetic method by the detection error of the magnetic target on a latitude trajectory. But different latitude trajectories will lead to different analysis results. In order to analyze the influence of motion trajectory on the detection error, the omnidirectional magnetic detection model (OMDM) is established. Based on the OMDM, the warp trajectory that accurately measures the detection accuracy is found. Simulation results show that NSW reduces the localization error of the STAR method, Lv-STAR method, and Wang-STAR method by 87.5%, 58.8%, and 12.5%, respectively. Both simulation and experimental results show that when comparing and analyzing the detection accuracy of the magnetic method, the results obtained by a latitude trajectory are one-sided, but a warp trajectory is both operable and accurate.

Vibration isolators are a key technology in ultra-precision machining and ultra-precision measurements. The increasing performance requirements of magnetic vibration isolation systems (MVISs) continue to demand improvements in the accuracy on which these devices are modeled. However, a serious constraint exists in designing MVISs, as high stiffnesses will be introduced by nonlinear force-displacement characteristics. The traditional analytic magnetic charge model assumes that the relative magnetic permeability $\mu_r$ = 1, which causes the accuracy of the magnetic analytic model of the MVIS to decrease. To solve this defect, low-stiffness MVISs are designed by using the 3D analytic magnetic charge model while considering the variations of the operating point. The optimized parameters of the MVIS are then obtained by combining the genetic algorithm. The feasibility of the proposed analytical charge method is verified from the results of experimental measurements and finite element methods. The results of this paper provide a powerful tool for the design of a high performance MVIS and provide important support for the ultimate goal of ultra-precision machining and measurements.

Distributed Magnetic Sensor System (DMSS) can measure vector magnetic field and magnetic gradient tensor (MGT) and is widely used in magnetoencephalography, geological exploration, magnetic navigation, magnetic positioning, and other fields. The posture and position of the magnetic sensor are the key factors that affect measurement accuracy. For the first time, using a magnetic shielding room (MSR) and a composite coil that can switch between uniform and gradient fields in situ, a new correction method for various errors is proposed to reduce vector measurement errors. In addition, sensor position deviation can also lead to MGT calculation errors. This paper establishes a compensation model by using the magnetic field gradient formula. The simulation results show that the average calibration errors of the posture and position of the magnetic sensor are 0.08% and 0.53%, respectively, and the measurement error of the MGT is reduced by four times. Experimental results in the MSR show that the measurement error of the vector magnetic field is reduced by two orders of magnitude and that of the MGT by one order of magnitude. Therefore, the new calibration method can effectively enhance the measurement accuracy of the DMSS.

In order to overcome the shortcomings of the traditional magnetic absolute linear displacement sensors in which cables affect the flexibility and measurement range in linear motor transmission systems, this paper proposes a novel cable-free moving magnetic grid-type long-range absolute displacement sensor. The sensor consists of a magnetic grid and a signal acquisition board. The magnetic grid is a moving component that contains two rows of permanent magnet arrays, one for relative displacement measurement and the other for the displacement interval code. The signal acquisition board is a fixed component that uses n groups of two-row Hall sensor arrays for continuous absolute displacement measurement. The principle of the sensor using the 2D magnetic field signal for the relative displacement measurement is analyzed, and a measurement method based on Hall sensor arrays for coding and absolute displacement detection over n cycles is proposed. Finally, a sensor prototype is fabricated and the experiments are performed. The experimental results show that the measurement resolution of the sensor is 5 μm, and the measurement accuracy is ±14.8 μm within the measurement range of 0–98.3 mm. The proposed sensor can realize continuous absolute displacement measurement over multiple cycles without cable binding.

This paper presents the design and realization of a three degrees of freedom (DOFs) displacement measurement system composed of Hall sensors, which is built for the XYθz displacement measurement of the short stroke stage of the reticle stage of lithography. The measurement system consists of three pairs of permanent magnets mounted on the same plane on the short stroke stage along the Y, Y, X directions, and three single axis Hall sensors correspondingly mounted on the frame of the reticle stage. The emphasis is placed on the decoupling and magnetic field fitting of the three DOFs measurement system. The model of the measurement system is illustrated, and the XY positions and θ_Z rotation of the short stroke stage can be obtained by decoupling the sensor outputs. A magnetic field fitting by an elliptic function-based compensation method is proposed. The practical field intensity of a permanent magnet at a certain plane height can be substituted for the output voltage of a Hall sensors, which can be expressed by the elliptic function through experimental data as the crucial issue to calculate the three DOFs displacement. Experimental results of the Hall sensor displacement measurement system are presented to validate the proposed three DOFs measurement system.