Q2Electrical Machine Design

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Q.2. What is a Cruciform Core? Design a cruciform core for a 125 kVA, 50 Hz, single phase oil immersed core type transformer. Assume flux density as 1.23 T. Take emf per turn as 17V.

Answer 1

What is a cruciform core: a cruciform (cross-shaped, stepped) core is a transformer core cross-section built from two (or more) different-width strips of lamination stacked to form a stepped, approximately cross-shaped profile, rather than a simple rectangle. Since the core must fit inside a circular (or near-circular) cylindrical winding, a plain rectangular core cross-section wastes a significant amount of the available circular window area; using a 2-stepped (cruciform) or multi-stepped cross-section allows the core to occupy a substantially larger fraction of the circumscribing circle's area (typically improving the space utilization factor from about 0.5 for a simple rectangle/square to about 0.6-0.7 for cruciform designs), reducing the winding mean-length-per-turn (and hence copper cost and loss) for a given required iron area.

Step 1 — determine required net iron area Ai from the given emf per turn:

E_{t} = 4.44 f B_{m} A_{i} \Rightarrow A_{i} = \frac{E _{t}}{4.44 f B _{m}} = \frac{17}{4.44 \times 50 \times 1.23} = \frac{17}{273.06} \approx 0.06226 m^{2} = 622.6 cm^{2}

Step 2 — relate net iron area to the circumscribing circle diameter for a cruciform core: for a standard 2-stepped cruciform core, the net iron area is related to the circumscribing circle diameter d by the approximate empirical relation Ai ≈ 0.62d² (accounting for both the stacking factor and the cruciform geometry's space utilization), commonly used in transformer design texts for a 2-stepped cruciform section:

d = \frac{A _{i}}{0.62} = \frac{0.06226}{0.62} = 0.1004 \approx 0.317 m = 317 mm

Step 3 — determine the cruciform core step widths (standard 2-stepped proportions): for a 2-stepped cruciform core, the standard proportions (derived from maximizing the inscribed cross area within the circle) give the main (widest) limb width a ≈ 0.85d and the second step width b ≈ 0.53d:

a \approx 0.85 d = 0.85 \times 317 \approx 269 mm, b \approx 0.53 d = 0.53 \times 317 \approx 168 mm

These dimensions define the two lamination strip widths to be stacked to form the cruciform cross-section: the wider strip (a) forms the main horizontal/vertical arms of the cross, and the narrower strip (b) forms the additional stepped corner sections, together approximating a circular cross-section within the d=317mm circumscribing circle while providing the calculated net iron area of approximately 622.6 cm² (after accounting for the stacking factor already embedded in the 0.62 coefficient used above), which is required to support the specified 17V per turn at Bm=1.23T for this 125 kVA, 50 Hz single-phase oil-immersed core-type transformer design.

Why cruciform rather than a simpler square or rectangular core: although a simple square-core cross-section is easier to manufacture (requiring only a single lamination width), it wastes considerably more of the available circular winding-window area (space utilization factor around 0.5) than a cruciform design (around 0.6-0.62), meaning that for the same required net iron area, a square-core design would need a larger circumscribing circle diameter, and hence a larger, more expensive coil (winding conductor length scales with the mean turn length, which increases with core diameter). This is precisely why the cruciform (or further multi-stepped) cross-section is the standard choice for medium and large oil-immersed core-type transformers such as this 125 kVA unit, where the resulting savings in winding copper (and the corresponding reduction in copper loss and cost) justify the modestly greater manufacturing complexity of stacking two different lamination widths rather than one uniform width.

Q2Electrical Machine Design

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