Experimental characterisation of a combined LVDT position sensor and voice-coil actuator for gravitational wave detectors

Abstract

A detailed characterisation of a combined Linear Variable Differential Transformer (LVDT) position sensor and voice-coil (VC) actuator designed for seismic isolation systems in gravitational wave detectors is presented. A dedicated experimental setup and a FEMM-based finite-element simulation framework were developed to measure and model a representative ETpathfinder Type-A LVDT+VC assembly. The setup employs a precision translation stage and balance to quantify LVDT displacement response and VC force output under controlled conditions. We found good agreement between experiment and simulation: the measured LVDT response was determined with an uncertainty of 0.5% and differed by only 1.3% from the FEMM model prediction, demonstrating high linearity over a +/- 5 mm range. In addition, the VC force measurements agreed within the total uncertainty: the maximum normalised force was determined with a precision of 2.3% and matched the simulated value with only a 0.6% discrepancy. These results validate the combined sensor-actuator design and our measurement methodology. The demonstrated linear response and stable actuation confirm that this LVDT+VC device can be used for low-frequency suspension control. Our framework therefore provides a validated tool to optimise existing sensor and actuator designs and to study novel prototypes for next-generation gravitational wave detectors.

Figures (13)

• Figure 1: A schematic of a combined LVDT+VC system with all parts and their dimensions indicated.
• Figure 2: Type-A LVDT+VC assembly installed in a seismic isolation stage of ETpathfinder ETpathfinderTDR. Left: clear view of the fixed, counter-wound secondary coils. Right: primary coil and permanent-magnet housing, illustrating the radial clearance between the primary and secondary coils that accommodates residual transverse suspension motion.
• Figure 3: Drawing of the measurement setup at the University of Antwerp, capable of characterising both LVDT sensors and VC actuators. A 3D view (left) and front view (right) provide an overview with all major components indicated.
• Figure 4: Measurement of the normalised LVDT output (left) and linearity (right) in a $\pm 5$ mm range (step size 0.5 mm) with the oscilloscope (pre-amplification), compared to FEMM simulations. The primary coil is excited with 9 V (data) and 20 mA (simulation) 10 kHz sine wave. The data points are fitted with a linear polynomial in $[-3,-1]$ mm and $[1,3]$ mm to extract the LVDT response and plot the linearity.
• Figure 5: Measurement of the normalised LVDT output (left) and linearity (right) in a $\pm 5$ mm range (step size 0.5 mm) with the DAQ system (post-amplification), compared to FEMM simulations scaled with the electronics gain factor. The primary coil is excited with a 0.1 V (data) and 20 mA (simulation) 10 kHz sine wave. The data points are fitted with a linear polynomial within $[-1,1]$ mm to extract the LVDT response and plot the linearity.