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Design and optimisation of linear variable differential transformers and voice coil actuators using finite element analysis: a methodical approach to enhance sensor response and actuation force

Kumar Akhil Kukkadapu, Hans Van Haevermaet, Wim Beaumont, Nick van Remortel

Abstract

This study introduces a systematic and optimised methodology for designing Linear Variable Differential Transformer (LVDT) sensors and Voice Coil (VC) actuators, tailored for high-precision applications such as gravitational wave detectors and particle accelerators. Unlike prior studies, which focus primarily on industrial-grade LVDT design frameworks or isolated parameter studies, this work addresses the specific challenges of achieving both enhanced sensor response and actuation force within strict geometric and thermal constraints. Using a custom-developed simulation pipeline based on Finite Element Method Magnetics (FEMM), we evaluate the effects of key parameters such as coil dimensions, radial gaps, and coil wire diameter on performance metrics such as response and linearity. The novelty of this work lies in its systematic exploration of design trade-offs, such as maximising performance while minimising heat dissipation, and its applicability to high-precision environments. In this work, we focus in particular on the combination of the LVDT and VC functionalities in one unified sensor-and-actuator system designed for gravitational wave detectors. In addition, the methodology and simulation results are validated with experimental measurements of an optimised design. This work represents a significant advance over existing methodologies by offering a structured, scalable design process.

Design and optimisation of linear variable differential transformers and voice coil actuators using finite element analysis: a methodical approach to enhance sensor response and actuation force

Abstract

This study introduces a systematic and optimised methodology for designing Linear Variable Differential Transformer (LVDT) sensors and Voice Coil (VC) actuators, tailored for high-precision applications such as gravitational wave detectors and particle accelerators. Unlike prior studies, which focus primarily on industrial-grade LVDT design frameworks or isolated parameter studies, this work addresses the specific challenges of achieving both enhanced sensor response and actuation force within strict geometric and thermal constraints. Using a custom-developed simulation pipeline based on Finite Element Method Magnetics (FEMM), we evaluate the effects of key parameters such as coil dimensions, radial gaps, and coil wire diameter on performance metrics such as response and linearity. The novelty of this work lies in its systematic exploration of design trade-offs, such as maximising performance while minimising heat dissipation, and its applicability to high-precision environments. In this work, we focus in particular on the combination of the LVDT and VC functionalities in one unified sensor-and-actuator system designed for gravitational wave detectors. In addition, the methodology and simulation results are validated with experimental measurements of an optimised design. This work represents a significant advance over existing methodologies by offering a structured, scalable design process.
Paper Structure (12 sections, 9 equations, 17 figures, 3 tables)

This paper contains 12 sections, 9 equations, 17 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Simulation framework
  3. Methodology
  4. Simulation studies
  5. Secondary coil design
  6. Primary coil design
  7. Magnet dimensions
  8. Coil wire design
  9. Experimental validation
  10. LVDT characterisation
  11. VC characterisation
  12. Conclusions

Figures (17)

  • Figure 1: Example of an integrated LVDT+VC assembly installed in a seismic isolation stage of ETpathfinder ETpathfinderTDR. (a) Alignment of the moving primary coil relative to the fixed counter-wound secondary coils. (b) A view of the primary coil and magnet housing, showing the difference in primary and secondary coil radii to allow for residual transverse motion in the suspension. Both views illustrate the efficient design that enables simultaneous position sensing and actuation.
  • Figure 2: Axisymmetric FEMM simulation results for the integrated LVDT+VC system. (a) complete overview of the implemented model indicating the airspace volumes and different mesh sizes; (b) LVDT sensing mode with the primary coil excited at 10 kHz; (c) VC actuation mode with a DC current applied to the secondary coil, showing the resulting magnetic field distribution interacting with the permanent magnet to produce actuation force. Colour shading indicates magnetic flux density while contour lines show the field lines linking primary and secondary coils. These results illustrate the distinct flux paths in sensing versus actuation.
  • Figure 3: A drawing of a combined LVDT+VC system with all geometric design parameters indicated.
  • Figure 4: Effect of $\rm D_s$ on LVDT performance when the response is fitted within a $\pm 1$ mm range. (a) response (V/mmA) increases slightly as $\rm D_s$ decreases, due to stronger mutual coupling. (b) linearity degrades with reduced $\rm D_s$ beyond a $\pm 2$ mm displacement.
  • Figure 5: Influence of $\rm D_s$ on VC actuation force and stability with constant magnet dimensions. (a) variation of $\rm F_{max}$ for different $\rm D_s$ values. (b) corresponding change in VC force stability. Increasing $\rm D_s$ slightly reduces the maximum available force while marginally improving stability.
  • ...and 12 more figures