John R. Brauer

Alternative dynamic electromechanical models of magnetic actuators containing eddy currents

Two methods of modeling electromechanical performance of magnetic actuators are compared when eddy currents are present. While a coupled dynamic electromagnetic/structural model accurately analyzes eddy current effects, a systems model based on parametric magnetostatic finite element analysis is often needed and is derived for the first time to include eddy current effects. The two methods are applied to the Bessho solenoid actuator and compared with measured electromechanical performance. In addition, a simple estimator of the effects of eddy currents on actuator closing times is presented and verified.

3D coupled electromagnetic and structural finite element analysis of motional eddy current problems

A finite element technique is described that fully couples structural and electromagnetic analysis in the time domain. One finite element model,with both linear and nonlinear structural and electromagnetic material properties, is solved in two or three dimensions. Displacements computed versus time for the TEAM12 eddy current 3D problem and for a nonlinear axisymmetric solenoid are shown to agree closely with measurements. >

AC contactor motion computed with coupled electromagnetic and structural finite elements

An alternating current relay contactor is analyzed using coupled electromagnetic and structural finite elements, The structural finite elements include a nonlinear spring for the relay contact arms. The electromagnetic finite elements include 2D nonlinear elements for the steel laminations and aluminum shading ring, as well as 1D and 0D elements for the voltage-driven coil windings and end-turn inductance. The computed current and motion of the actuator are in good agreement with measurements.

Coupled nonlinear electromagnetic and structural finite element analysis of an actuator excited by an electric circuit

A finite element technique is described that allows arbitrary electric circuits to be included in a fully coupled structural and electromagnetic nonlinear transient analysis. Displacements computed versus time for a typical solenoid actuator are shown to be compatible with available measurements and with simple circuit theory for a voltage excitation. Current waveforms are shown to be affected by friction occurring when the armature rebounds. >

Surface integrals on 3D and 2D finite element models for skin effect excitations and open boundaries

Surface integrals on three-dimensional finite-element models can be used to excite currents in conductors with skin effects and to approximate open boundaries. In both cases the surface integrals are shown to be inhomogeneous Neumann boundary integrals which do not increase matrix bandwidth or destroy its symmetry. To excite total conductor currents in skin effect problems, inhomogeneous Neumann excitations are used. To represent open boundaries, the surface integrals are transformed into asymptotic boundary conditions. Example analyses include a 3-D railgun with transient skin effects, a 2-D air core electromagnet with open boundaries, and three-phase AC bus bars having both closed and open boundaries. Results for the electromagnetic agree with theory within two parts per million. >

Magnetic torque or force calculation by direct differentiation of finite element coenergy

A vector-potential finite-element method for calculating magnetic force or torque by direct analytic differentiation of coenergy is derived and applied to two- and three-dimensional actuators. The results are shown to agree well with calculations using the conventional difference between coenergies at two positions and with experimental measurements. Another method of force calculation, Maxwells stress tensor, is also derived by differentiating the coenergy, resulting in a formula that is applicable on the surface of nonlinear materials. >

Adaptive time-stepping in nonlinear transient electromagnetic finite element analysis

Time-step size is automatically adapted to enable efficient convergence in nonlinear transient electromagnetic finite element computations. The adaptive time-stepping takes into account both induced eddy currents and the nonlinear reluctance matrix due to saturable B-H curves. The new algorithm is shown to obtain results that agree with fixed time-step methods, but with savings in computing time of up to 90%.

Finite-element computation of nonlinear magnetic diffusion and its effects when coupled to electrical, mechanical, and hydraulic systems

Finite elements are used to compute eddy currents and magnetic diffusion times in steel cylinders with nonlinear B--H curves. Computations are made of diffusion times versus current in a typical axisymmetric magnetic actuator, showing good agreement with recently published approximate analytical formulas. The computed nonlinear diffusion times are then used to derive an equivalent resistor that is used in a model of an electrohydraulic system. The diffusion time causes delays in the coupled mechanical and hydraulic responses.

Polyphase induction motor performance computed directly by finite elements

Finite element analysis is used to directly compute torques and currents of an induction motor, without need for any equivalent circuit. The AC voltages are applied by means of 0D and 1D finite elements, and the fields and related parameters are computed by nonlinear transient finite element analysis with adaptive time stepping. Equations are derived that allow balanced polyphase motors to be analyzed at any speed without rotating the rotor finite elements, and for torque to be computed directly from power loss. Computed torques and currents of a typical highly saturated polyphase motor with closed rotor bars are shown to agree quite well with measurements.

Finite element analysis of Hall effect and magnetoresistance

This paper shows that the finite element method can be used to compute Hall voltages and electric fields, magnetoresistance, and current flow patterns. The computed Hall voltage is reduced (up to 54%) when the semiconductor geometry is changed from a narrow rod to a wide rod and when the sense electrodes are made of nonzero size. Both two-dimensional and three-dimensional geometries are analyzed. >