Your centroidal axis occurs where your cross-sectional area is balanced above and below the line. The neutral axis occurs where the sum of the forces acting on the cross-section are balanced, based on a linear varying strain - zero at the neutral axis, and at its maximum at the extremities of the section.

Is the centroid always the neutral axis?

The neutral axis always passes through the centroid of area of a beam's cross-section, but its inclination α (see Fig. 15.12(b)) to the x axis depends on the form of the applied loading and the geometrical properties of the beam's cross-section.

What is the difference between neutral axis and principal axis?

The strongest axis of any cross section is called major principal axis. ... The failure due to bending starts and prolongs from weakest axis of any cross section. The neutral axis is an axis at which the strain is zero under the application of bending forces on a bending element.