  Nuclear rings are excellent laboratories for studying intense star formation.
We present results from a study of nuclear star-forming rings in five nearby
normal galaxies from the Star Formation in Radio Survey (SFRS) and four local
LIRGs from the Great Observatories All-sky LIRG Survey (GOALS) at sub-kpc
resolutions using VLA high-frequency radio continuum observations. We find that
nuclear ring star formation (NRSF) contributes 49 - 60\% of the total star
formation of the LIRGs, compared to 7 - 40\% for the normal galaxies. We
characterize a total of 58 individual star-forming regions in these rings, and
find that with measured sizes of 10 - 200 pc, NRSF regions in the LIRGs have
SFR and $\Sigma_\mathrm{SFR}$ up to 1.7 M$_\odot$yr$^{-1}$ and 402
M$_\odot$yr$^{-1}$kpc$^{-2}$, respectively, which are about 10 times higher
than NRSF regions in the normal galaxies with similar sizes, and comparable to
lensed high-$z$ star-forming regions. At $\sim 100 - 300$ pc scales, we
estimate low contributions ($< 50\%$) of thermal free-free emission to total
radio continuum emission at 33 GHz in the NRSF regions in the LIRGs, but large
variations possibly exist at smaller physical scales. Finally, using archival
sub-kpc resolution CO (J=1-0) data of nuclear rings in the normal galaxies and
NGC 7469 (LIRG), we find a large scatter in gas depletion times at similar
molecular gas surface densities, which tentatively points to a multi-modal star
formation relation on sub-kpc scales.
