Authors B.M. Petrov, D.E. Titova
Month, Year 05, 2016 @en
Index UDC 537.868.3; 621.37
Abstract The majority of the rotation measurement devices can be differentiated into the optical one, which based on Sagnac effect, and MEMS-gyros, using mainly the effect of Coriolis force. The former are mainly used in aviation and space due to their high sensitivity, while the latter are in most cases simpler in production and cost-effective, what meets the requirements in such spheres as robotics, navigation systems of vehicles and mobile devices. Now the investigations in the sphere are devoted to minimizing the sizes of optical gyros and increasing the sensibility of the MEMS devices. In the article the influence of the dielectric loss of the dielectric a rotating spherical resonator is filled with on the shape of the frequency characteristic of the resonator is studied. That allows analysing the new resonant method of resonator rotation rate measurement using resonators frequency characteristic. The method allows implementing electromagnetic field of radio-frequency band, what gives a possibility of increasing the precision of the rotation rate measurement and decreasing geometrical dimension of gyroscopes. For that purpose, the boundary task of excitation of rotating spherical resonator filled with dielectric with EMR sources is set up and solved rigorously using covariant relations of electrodynamics. The definition of rotating electric and magnetic Debye potentials are introduced, which meet the equations equal to wave equations. The Debye potentials allow to split electromagnetic field into the E-field and H-field. Homogeneous boundary conditions on the perfectly conducting surface of the metal for the tangential components of the electric field vectors lead to the solution of the boundary problem of the second order for the electric Debye potential, and for the H-filed – to the solution of the boundary problem of the first order for the magnetic Debye potential. Solutions of the wave equations are get as the expand in systems of electric and magnetic Markov functions defined for the Riemann space and expanded into spherical functions series. The Debye potentials of the primary field (the EM-field excited) are defined as for the free space, while for the secondary field they are expanded into spherical functions systems with coefficients defined by the boundary conditions. The solutions for the Debye potentials for the total fields of electric and magnetic oscillations are got this way. Rotation leads to the split of the eigen resonant frequencies of the resonator and emerging of the new resonant frequencies. Every eigen frequency of the resonator “at rest” is split into 2N new eigen frequencies inside the rotating resonator, shifted relative to each other by the rotation rate, where N is the number of mode. This results from the influence of the equivalent gravitational field on the EM-field of isometric harmonics which traverse along the direction of rotation and on the direction opposite to it. This allows measuring of the resonator rotation rate as the difference between Nth eigen resonant “rotation” frequency and the “rest” frequency of the resonator for the given EM-oscillation mode in the resonator, divided by . Another way is to measure the shortest distance between two neighboring resonant frequencies on the frequency characteristics of the cavity. In the article the results of the calculations of the frequency characteristics of the dielectric filled rotating spherical resonator excited with electric vibrator are got for dielectric of different parameters. The results are described and analyzed. It is shown that the rotation rate measurement uncertainty and the relative shift of the resonant “rotation” frequencies is defined by the loss tangent of the dielectric the resonator is filled with. In order to increase the Q-factor of the cavity and the precision of the rotation rate measurement it is suggested to opt for dielectrics with low loos tangent.

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Keywords Spherical resonator; gyroscope; dielectric loss; rotation rate; loss tangent
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