時計用ステップモーターの出力トルクについて

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Stepping motor has been employed for time piece as the transducer which converts an electrical time signal into an angular displacement. In this paper, the mathematical expression of the output torque of the stepping motor is introduced for the design of the motor. The output torque is devided into motor torque and index torque. The motor torque means the one induced through the magnetic field by coil carrent, and the index torque means the one induced through the magnetic field by rotor magnet it self. (1) By applying the magnetic circuit theory, the expression of the motor torque is deduced as follows; M_m=(πJ_0ρ^2hsn 1)/(2a) (1) where Jo is the permanent magnetization of the rotor magnet, ρ the radius of the rotor, hs the thickness of the stator, a the radius of the stator hole, n the number of windings, I the coil current. (2) The expression of the index torque of the stepping motor which has two semicircular notches in the stator hole is deduced by combining the dimensional analysis and the finite element method, as follows; M_i=(J^2_0ρ^r^2hs)/(μ_ra^4) (2) where μ_r is the recoil permeability of the magnet and r the radius of the notches. α≒1.7 is determined experimentally. (3) Introducing the deviated area S from the circular shape of the stator hole into the expression (2), the similar expression of the index torque corresponding to the other shapes of the stator hole is obtained as follows; M_i=(βJ^2_0ρ^4Shs)/(μ_ra^4) The above expression is ascertained by the numerical calculation using the finite element method about the motor with the various shapes of the stator hole. β≒0.5 is determined experimentally.
社団法人日本時計学会の論文
1983-06-25

時計用ステップモーターの出力トルクについて

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