1. Figure 1 shows a cross-section through a limited angle rotary actuator used in fly-by-wire
system. The actuator consists of a permanent magnet rotor and a pair of series connected
coils wound onto a toroidal core. It is important to note that the conductors on the outside
edge of the core are merely return conductors (so called end-windings) that play no role in
generating torque. The only conductors which interact with the permanent magnet field and
hence generate torque are those within the core.
The axial length of the actuator (i.e. length into the plane of the paper) is 30mm. The various
dimensions shown in Figure 1 include some that are specific to each student which are shown
in red text in the table in Appendix 1. Each individual coil has TURNS_ON_COIL turns. The
particular grade of magnet is MAGNET_GRADE.
The airgap magnetic field is given by the simplified, but well-established, relationship:

1 +

is the effective magnetic which for this device includes both the mechanical clearance
gap and the coil thickness, i.e. = + ℎ . The remanence of the permanent
, is an intrinsic material property which is specific to a particular grade of magnet.
a) By researching manufacturer’s on-line data sheets / catalogue, find the room temperature
(20°C or 25°C depending on manufacturer) value of the permanent magnet remanence
for the manufacturer and grade specified against your name in Appendix A. Some
manufacturers specify typical / nominal and minimum values. For this assignment, please
use the typical / nominal values.
b) Calculate the airgap magnetic flux density for your grade of magnet at room temperature.
c) The torque produced by the actuator for a current of PART ii CURRENT.
d) Find a method for calculating the moment of inertia of the rotor and hence calculates its
moment of inertia assuming that both the core and the magnet has a density of 8000 kgm-3.
(Hint: You can think of the rotor as a circular rotor with two circle segments removed).
e) If the load has a LOAD_MOMENT_OF_INERTIA and the friction is FRICTION, calculate the
time taken for the rotor to move through ANGLE_EXCURSION from standstill (you may
assume that during this excursion, the rotor magnet remains entirely within the span of the
stator coil).