Can the use of Permalloy to make the core of the electromagnet significantly increase the suction force?

Not necessarily.

The magnetic force F of the magnet is the product of the magnetic field magnetic induction intensity gradient deltaB and the magnetic moment m, F=deltaB*m.

The purpose of adding an iron core to the solenoid coil is to make the magnetic field generated by the solenoid magnetize the magnetic material of the iron core to increase its magnetic moment. The magnetic moment of the helix is ​​m1=NIS, the magnetic moment of the iron core is the volume component of its magnetic field intensity M m2=MV, and the magnetic field intensity M of the magnetic material is the magnetic field intensity H of the solenoid multiplied by the magnetic permeability u of the magnetic material, and the magnetic permeability is the product of the relative magnetic permeability u0 of the vacuum and the relative magnetic permeability ur of the magnetic material (i.e. u=u0*ur).

Finally, F=(m1+m2)*deltaB=(NIS+Mv)*deltaB=(NIS+uo*ur*H*v)*deltaB. The relative magnetic permeability ur of Permalloy is indeed very high. If the current in the solenoid is very small, that is, the magnetic field intensity H generated by the solenoid is very small and has not yet reached the saturation of Permalloy, its suction will indeed increase; but the saturation magnetic induction intensity of Permalloy is low, and the magnetic field generated by the solenoid reaches 7000A/m, which can basically magnetize it to saturation, and its suction will not continue to increase.

Therefore, your answer is not necessarily. When the current of the solenoid is small and has not yet saturated the magnetic core, its suction can be increased; but if the current is large and saturates it, a magnetic material with high saturation magnetic induction intensity and high relative magnetic permeability should be selected.