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221 | Salman & Mohammed & Mohammed
J = a · EME (3)
F=J×B (4)
The symbol (J) represents eddy current density, while (s ) is
used to denote the electrical conductivity of the material. By
using the material’s permeability (µ) and magnetic field inte
nsity (H) to calculate the magnetic flux density (B).
The power dissipated in the eddy current braking system
is a crucial parameter [16].
Fig. 1. Illustrates the operational principle of the PMECB Pin = (Ieddy)2R
(5)
hind PMECB is explored, including the equations determining The power output of the braking system represents the energy
braking force and design details. The impact of various perma- absorbed to slow down a moving object.
nent magnet configurations, magnet strengths, and brake plate
designs on braking performance and efficiency was investi- Pout = T · ? (6)
gated in a study [10]. [11] to study and forecast the behavior
of PMECB systems. The many benefits of PMECB systems The symbol (T) represents braking torque, while (?) refers to
make them desirable for various applications, as stated by rotational speed. The efficiency of the eddy current braking
researchers’ study [12]. Researchers explored new ways to system is the ratio of output power to input power, which can
optimize deceleration profiles through hybrid braking systems be calculated using a specific equation [17]:
that combine PMECB with other technologies [13].
?= Pout (7)
This paper examines a model of an eddy current braking sys- pin
tem using FEM. This modeling study aims to demonstrate
the effectiveness of PMECB in producing braking force, dis- III. DESIGN CONSIDERATIONS AND
sipating energy, and enhancing overall braking performance. SIMULATION
The findings from this study will be used to support further
research in this area. Choosing the right permanent magnet type is crucial for creat-
ing an efficient PMECB system. The magnets used directly
II. FORMULAS FOR THE PMECB SYSTEM IN affect the strength of the magnetic field, which in turn im-
MATHEMATICS pacts the braking force produced by the system. Proper selec-
tion of magnet materials is essential when designing efficient
The PMECB system’s mathematical formulations are derived PMECB systems. Neodymium Iron Boron, Samarium Cobalt,
from electromagnetic principles and Maxwell’s equations [14], and Ferrite (Ceramic) are commonly used magnet materials
providing information on braking forces and energy dissipa- for PMECB applications [18]. The arrangement of permanent
tion. According to Faraday’s law, a changing magnetic field magnets in the PMECB system is crucial in determining the
passing through a conductor creates an electromotive force distribution of magnetic fields and the effectiveness of the
(EMF) in a closed loop braking force. The magnet must be positioned correctly to
distribute force evenly and optimize energy conversion. Sim-
EMF = - dF (1) ulation software like FEA tools allows designers to develop
dt virtual models of efficient and reliable PMECB systems us-
ing critical simulation and optimization methods [19]. These
where EMF is the induced voltage, (dF) is the magnetic flux models demonstrate the interaction between magnets, con-
linked with the material, and (dt) is the period. The braking ductors, and magnetic fields, displaying information on force
force (F) produced by the interplay of induced eddy currents distribution and eddy current effects. Table I displays the
and the magnetic field can be estimated as follows [15] design aspects of PMECB. Numerical simulations can predict
braking system behavior and analyze the effects of conductive
B = µH (2) materials. Simulation and analysis of the braking system are
