Does increasing the size of an axial substituent always result in higher relative strain energies for the axial conformation

There is no need to increase the size of the axial substituent, since the strain energy in the axial conformation increases. This is why, sometimes, the size of the substituent increases, where the length of the bond between the carbon atom and the substituent increases, however, the deformation energy of the axial conformation does not increase.

It is not necessary that the increase in the axial substituent size always enhances the strain energy for the axial conformation. In certain cases, the size of substituent increases due to which the bond length between the carbon and substituent also enhances.

In this case, the relative strain energies for axial conformation does not increases. The example is iodocyclohexane.