In most AC/DC interfaces, the Force Calculation feature can be used to compute forces and torques using Maxwell stress tensor. In electric field and current interfaces, the force is calculated by integrating
In the Magnetic and Electric Fields interface, both expressions (
Equation 3-8 and
Equation 3-9) are included.
E is the electric field,
D the electric displacement,
H the magnetic field,
B the magnetic flux density, and
n1 the outward normal from the object (Material 1).
where ∂Ω represents the domain boundary. The torque is computed as
where r0 is a point on the axis of rotation. For a theoretical discussion about the stress tensor, see
Electromagnetic Forces.
The Lorentz force is defined as
F = J × B. The Lorentz force is very accurate for electromagnetic force calculations in electrically conducting domains. The Lorentz force variables
<name>.FLtz<component> are available both in domains and on boundaries (in the case of surface currents).
In the Rotating Machinery, Magnetic interface, in addition to the
Force Calculation feature, the
Arkkio Torque Calculation feature based on Arkkio’s method is available. Arkkio’s method is a variant of the Maxwell stress tensor method, specifically useful in modeling rotating machines where the thin air gap separates rotating parts. In this case, the normal
n1 of the air gap can be defined as the radial outward unit vector. Arkkio’s method computes the torque as
where Fϕ is the azimuthal force density;
Br,
Bϕ are the radial and azimuthal magnetic flux density, respectively;
rA is the distance from the rotation center;
nsec is the number of sectors. Different from surface integral
Equation 3-11 used in Maxwell stress tensor method, the torque expression for Arkkio’s method (
Equation 3-12) is a volume integral on the domain
Ω, yielding a less mesh-dependent result.