The production of $chi_b$ mesons in proton-proton collisions is studied using a data sample collected by the LHCb detector, at centre-of-mass energies of $sqrt{s}=7$ and $8$ TeV and corresponding to an integrated luminosity of 3.0 fb$^{-1}$. The $chi
_b$ mesons are identified through their decays to $Upsilon(1S)gamma$ and $Upsilon(2S)gamma$ using photons that converted to $e^+e^-$ pairs in the detector. The relative prompt production rate of $chi_{b1}(1P)$ and $chi_{b2}(1P)$ mesons is measured as a function of the $Upsilon(1S)$ transverse momentum in the $chi_b$ rapidity range $2.0<y<4.5$. A precise measurement of the $chi_b(3P)$ mass is also performed. Assuming a mass splitting between the $chi_{b1}(3P)$ and the $chi_{b2}(3P)$ states of 10.5 MeV/$c^2$, the measured mass of the $chi_{b1}(3P)$ meson is $ m(chi_{b1}(3P))= 10515.7^{+2.2}_{-3.9}(stat) ^{+1.5}_{-2.1}(syst) MeV/c^2.$
