We obtain improved constraints on the coupling constants of axion-like particles to nucleons from a recently performed Casimir-less experiment .
For this purpose , the differential force between a Au-coated sphere and either Au or Si sectors of a rotating disc , arising due to two-axion exchange , is calculated .
Over a wide region of axion masses from 1.7 \times 10 ^ { -3 } eV to 0.9 eV the obtained constraints are stronger up to a factor of 60 than the previously known ones following from the Cavendish-type experiment and measurements of the effective Casimir pressure .