in construction of a transformer cruciform core has more advantage than a square shaped .if we use a circular core it will be much more advantageous.
Venkata, as you have pointed out, a cruciform cross-section is advantageous than a square one. Assuming a circular winding, the length of one turn is proportional to the perimeter of the circumscribing circle of the core sectional area. Less perimeter means less conductor material, less losses. Thus, with a given core sectional area, as the number of core steps are increased, the perimeter keeps reducing, but follows an inverted exponential nature. This means that as the number of steps is increased, the rate of further reduction reduces such that one needs infinite steps to achieve the lowest perimeter, which is for a perfect circle. On the other hand, a large number of steps implies a large variety of core widths which have to be assembled in sequence to form a circle. Since assembly is still manual in large transformers, there must exist finite visible distinction between step sizes to prevent human error in picking the wrong strip width. Using large number of steps on a small core area will again reduce the dimensional difference between strip widths, making assembly difficult. Thus, the number of steps is practically limited (to about 17), depending on the actual diameter of the core.
In core manufacturing, the stamping used are made from thin sheet of CRGO etc. material, to reduce the manufacturing cost of cutting and assembling, for small rating, the same size(width) cutting dai is used, and then all stamping put together to form the core, as core size(cross section) is small, though winding is made circular as possible, by using insulator filler in gap if required. For large core(cross section) different width stamping are cut, and put to gather in such a way(stare case), that the shape should be near to circular, with small step. as the winding be circular coil, as resultant force of magnetic fiend by current flowing, in circular coil would be uniform and would be more stable.
Circular shape consumes more core material,and it ivokes more cost and more chance of leakage current.So,to prevent all those things a staire case square shape core is used rather than a circular type.
- For small rating transformer, square core is used for reasons cited. (ease of manufacturing - cost.)
- For large ratings transformer (distribution transformer and up), the forces acting upon the windings in case of short circuit are so high, that the windings need to be circular. (else the transformer would blow apart during short circuit.) As a result, circular cores are used.
Not just circular core, by which I assume you mean cylindrical shape, but also that cylindrical core bent in a circle (toroidal core), are in fact used in some applications. I would agree that cost is a deterrent, but sometimes cost is not a big issue.
Cylindrical cores are commonly used in those internal AM (medium wave and short wave) antennas in radios, and toroid transformers are not uncommon in audio equipment, for instance, for power transformers and chokes.
http://www.purevoltindia.com/toroidal-round-transformer.html
Venkata, as you have pointed out, a cruciform cross-section is advantageous than a square one. Assuming a circular winding, the length of one turn is proportional to the perimeter of the circumscribing circle of the core sectional area. Less perimeter means less conductor material, less losses. Thus, with a given core sectional area, as the number of core steps are increased, the perimeter keeps reducing, but follows an inverted exponential nature. This means that as the number of steps is increased, the rate of further reduction reduces such that one needs infinite steps to achieve the lowest perimeter, which is for a perfect circle. On the other hand, a large number of steps implies a large variety of core widths which have to be assembled in sequence to form a circle. Since assembly is still manual in large transformers, there must exist finite visible distinction between step sizes to prevent human error in picking the wrong strip width. Using large number of steps on a small core area will again reduce the dimensional difference between strip widths, making assembly difficult. Thus, the number of steps is practically limited (to about 17), depending on the actual diameter of the core.
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