The paper deals with the finite element analysis of a simple and reliable speed transducer -the AC tachogenerator II. FIELD-CIRCUIT-ROTATING MOTION MODEL with rotor of solid conductor type. The coupling between the field equations, circuit equations and the rotor motion is A. Mathematical model. considered in the numerical computation of eddy currents and The finite element analysis of the electromagnetic field is global quantities that characterize the transducer operation. based on a 2D model in the plane xOy of laminations, Fig. 1. The diffusion of the electromagnetic field in the rotor, the speed The main unknown of the mathematical model -the magnetic -output voltage dependence, the power losses in the rotor and vector potential A[0, 0, A(x,y,t)], satisfies the equation: the power delivered by the 50 Hz supply source to the field winding of the transducer are evaluated for three rotor types: homogeneous copper or magnetic nonlinear steel rotors and a curl[(1/t) curlA] -(v x curlA)/p + (aA/at)/p = J (1) rotor consisting in a copper cup around a magnetic steel cylinder. The sensitivity of the transducer output voltage with The vector quantity J in equation (1) regroups the current respect the magnetic properties of the rotor and the airgap . X value is analyzed. The linearity of the output voltage -speed ade J2(t)= /2.J2.sin(ot±p2) in the field winding,. 2, characteristic of the tachogenerator when the field winding is and J2(t)in2J2si(elet±p2), si the output winding. The 400 Hz supplied and the upper limit of speed measurement is second term in the left side of the equation represent the very low in comparison with the synchronous speed is studied. densities of eddy currents generated by motion in the solid conductor rotor of resistivity p, and the third term, the eddy currents generated by time variation of the magnetic field. I. INTRODUCTION The vector quantity v is the local value ofrotor velocity. The rotor of the AC tachogenerator in Fig. 1
is of solidThe values of the voltage U1 supplying the field winding, conductor type [1] and the two distributed windings, ninety the operation frequency f = w/2 and the impedance of electric degrees shifted, are placed in the slots of the stator apparatus for the output voltage Ue measurement are input magnetic core, laminations made. The field winding, colored data of the numerical model. Adding to the numerical model in red in Fig. 1, is supplied by an AC voltage source and the of the electromagnetic field the equations of the circuit model output voltage of the transducer is measured at the terminals of the tachogenerator, Fig. 2, the three scalar unknowns A(x, of the output winding, cyan colored. y, t), J1(t) and J2(t) can be evaluated.The two materials of the unslotted rotor of the studied tachogenerator are the copper and the magnetic non-linear steel. Output If no rotor motion, the total magnetic flux generated in the Volage Field Outputwindng U output winding by field winding and by rotor eddy currents is winding winding null. When the rotor moves, the valu...
