Abstract:To address the issues in absolute linear displacement measurement where dual-track structures require a large installation space, amplitudephase matching errors among multiple sensing channels tend to accumulate, and induced signal amplitude and signal-to-noise ratio are insufficient under compact installation conditions, a design scheme for a single-track absolute linear time-grating displacement sensor based on multi-frequency magnetic field coupling is proposed. The sensor integrates coarse and fine measurement units within the same track space, employs a dual-turn combined excitation coil structure to enhance the normal magnetic flux density within the installation air gap, and realizes absolute displacement calculation through time-division excitation of the coarse and fine code tracks, grounding of the non-working code track, and heterodyne frequency-downconversion processing. First, a transient magnetic field coupling model of planar coils is established, and the magnetic field distribution characteristics of different coil structures are evaluated using the average normal magnetic flux density, magnetic field standard deviation, and normalized uniformity index. Subsequently, a sensor model is constructed based on the principle of relatively prime pole-pair numbers, and periodic errors caused by unequal amplitudes, spatial quadrature deviations, and magnetic field harmonics are analyzed. Finally, finite element simulations and prototype experiments are conducted to verify and evaluate sensor performance. Simulation results show that, compared with the conventional time-grating excitation coil structure, the dual-turn combined excitation coil structure increases the average normal magnetic flux density by 21.26%, which is beneficial for increasing the signal amplitude and improving the signal-to-noise ratio. Experimental results demonstrate that the sensor can achieve absolute displacement measurement within an effective measuring range of 206.4 mm, with a resolution of approximately 0.17 μm. Under the optimal installation air gap of 0.5 mm, the peak-to-peak error within one pole pair is 5.63 μm, and the full-scale peak-to-peak error is 6.42 μm. Featuring a compact structure, fewer sensing channels, and strong engineering practicality, the sensor provides a novel and practical solution for miniaturized high-precision absolute linear displacement measurement.