Proper affine actions on semisimple Lie algebras

For any noncompact semisimple real Lie group $G$, we construct a group of affine transformations of its Lie algebra $\mathfrak{g}$ whose linear part is Zariski-dense in $\mathrm{Ad}G$ and which is free, nonabelian and acts properly discontinuously on $\mathfrak{g}$.