Analytical model of magnetic field distribution in the air-gap of quartz flexible accelerometer

As common high precision inertial sensors, quartz flexible accelerometers have wide application prospect in many circumstances such as low cost inertial navigation systems. In order to quickly evaluate magnetic field distribution in air-gap of these accelerometers and provide an insightful knowledge for design optimization, we introduced an analytical method based on scalar magnetic potential to describe their magnetic behaviour. Some related Laplace and Poison equations are solved by separating variables and the parameters of the solutions are calculated by a set of linear vector equations considering boundary conditions. Magnetic field computed with the proposed analytical method is proved effective through finite element method and some preliminary experiments, additionally, the scale factor estimated can be validated by the gravitational field roll-over test.