Motor die-cast rotor non-grain-oriented VS grain-oriented

If the material is non-grain-oriented, the path of least resistance for the magnetic flux varies widely from point to point across the sheet: in one place it may go left-to-right across the sheet surface, in another top-to-bottom, and in still another through the sheet. Other points may be anywhere and everywhere in between.

If the material is grain-oriented, the material is aligned such that there is a significant reduction in the energy requirement for passing flux in one direction relative to any other.

Most machines work best with a uniform flux distribution at all points of the airgap surface: this is achieved by stacking both stator and rotor using non-grain-oriented laminations in any arrangement. However, for a grain-oriented material, each lamination has to be rotated by some angle with respect to the one above and below it in the stack (think of it like a spiral staircase).

Regardless of how the winding is made for the rotor (form wound, bar and ring, or die-cast), it is the STACKING process for the core steel that affects grain orientation.

As to skewing BOTH stator and rotor ... why? It is a more costly and complex manufacturing process to produce a skewed core vs an unskewed one, regardless whether the skew is in the rotor or stator. Once the skew is begun, there is no real cost difference between a full slot skew and a fractional slot skew.

If you really want to skew both, though - opt for a half-slot skew in one direction in the rotor, and a half-slot skew in the opposite direction for the stator. Note that this means there is only ONE way to assemble rotor and stator together - with the skews opposing. (With the full slot skew on either rotor or stator and an unskewed opposite piece, the rotor can be inserted from either end of the stator with the same effect.)