Aiming at the problem that traditional displacement sensors do not balance both long range and high precision， a new displacement measurement method combining the time-grating principle with the magnetoresistive effect based on a spherical array was proposed. The orthogonally changing magnetic field was constructed by using spatial orthogonal excitation windings， and the magnetic field was accurately constraint-controlled by the spatial periodic sensing structure. The mapping relationship between magnetoresistance and displacement was established by using induction windings to pick up the change in the magnetic field， which revealed the displacement sensing mechanism. The model parameters were optimized by electromagnetic simulation， the sensor prototype was developed， the experimental platform was built， and the measurement error experiments of the sensor were conducted. The experimental results show that the sensor has a measurement error of ±9.4 μm and a resolution of 0.1 μm within the 512 mm measurement range. Micrometer scale measurement accuracy is realized using the millimeter scale sensing unit， which greatly reduces the manufacturing difficulty of the sensor. Furthermore， the measurement range can be increased with the requirements of the applications， and its high resolution measurement can be achieved without the interpolation technology. It can be used in harsh environments such as strong oil pollution conditions， which promises the significant academic value and engineering application value.

spherical array;time-grating sensors;magnetic field constraint;Linear displacement