A mathematical modeling approach to determine fluid film thickness on the vane tip in a vane pump transmission is developed. The transmission is based on a double-acting vane pump with an additional output shaft coupled to a floating ring. Owing to the floating ring design, the internal viscous friction helps to drive the output shaft, whereas the friction is turned into heat in a conventional vane pump. To study the mechanical efficiency, it is crucial to investigate the fluid film thickness between the vane tip and the ring inner surface. The modeling approach in this study takes the interactions between vane radial motion and chamber pressure dynamics into consideration, without using a computational fluid dynamics approach. The lubrication on the vane tip is considered as elasto-hydrodynamic lubrication and the fluid film thickness calculation is based on the Hooke lubrication diagram. Results show that the developed simulation model is capable of revealing the fluid film thickness change and vane radial motion in different operation regions. Sensitivity studies of several parameters on the minimum fluid film thickness are also presented.