Mobile robots that are required to climb inclined ferromagnetic surfaces typically employ magnetic wheels. In order to design magnetic wheels and to properly size the permanent magnet as magnetizing source without the need for finite element analyses, a model that predicts the attractive magnetic force is necessary. In this paper, an analytical force model is derived by estimating the reluctance between the wheel and the surface. A magnetic circuit is constructed, incorporating the leakage flux from the side of the wheel. The model is validated against the results from finite element analyses and measurements from a test rig and a wheel prototype. Within the limitations of the model, it can adequately predict the force and can be used for initial design of magnetic wheels.
