Definition of Series Magnetic Circuit
Definition: A series magnetic circuit is defined as a magnetic pathway composed of multiple sections with varying dimensions and materials, all carrying the same magnetic field. Consider a circular coil or solenoid with distinct dimensional parameters, as illustrated in the figure below:
Series Magnetic Circuit Analysis
A current I flows through a solenoid with N turns wound around one section of a circular coil, inducing a flux Φ in the core.
- a₁, a₂, a₃: Cross-sectional areas of the solenoid sections
- l₁, l₂, l₃: Lengths of the three serially connected coil sections with different dimensions
- μᵣ₁, μᵣ₂, μᵣ₃: Relative permeabilities of the circular coil materials
- a₉, l₉: Area and length of the air gap (assuming ag denotes air gap area)
The total reluctance (S) of the magnetic circuit is:
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- Sectionalize the magnetic circuit into distinct parts.
- Determine flux density (B) for each section using B =ϕ/a, where ϕ is flux (Weber) and a is cross-sectional area (m²).
- Calculate magnetizing force (H) using H=B/(μ0μr), where:
- B is flux density (Wb/m²),
- μ0= 4π×10−7 (absolute permeability),
- μr is relative permeability (provided or derived from the B-H curve if unknown).
- Multiply each H value(e.g., H1, H2, H3, Hg) by the corresponding section length (l1, l2, l3, lg).
- Sum all products of H×l to obtain the total MMF:Total MMF= H1l1 + H2l2 + H3l3 + Hglg)
B-H curve for the various material like cast iron, cast steel and sheet steel is shown in the above figure.
