Yes, it should be iron core (laminated). Look quality of transformer! Each laminat should be isolated with thin layer of laquier. Look wires isolation, it should be very good (multi-layer laquier + special insulating fabrics on wires). Copper wires not aluminium. Good made transformers when assembled at full load, should not have noise caused by magnetostricion.
Use some thermal protection for windings to protect windings wires. At high temp this will turn off transformer.
For copper wires calc use max 2,5A/mm².
Some raw calc for EI core (inner core section 75mm x 100mm) around 5,6KW, primary windings should have (220V) 150 turns of 2,15mm diameter wire, and secundar winding should have 12 turns of 7mm diameter wire, for 100A of current. The iron core will be saturated with around 40% at full load, which is good, you will get lower temperature. Also because you use bigger EI core, you have more space for wire isolations.
You need only one secundar 18V-0-18V, and you dont need three secundars. Current and voltage are regulated on primary side.
Also use strong rectification diodes, always more stronger then is needed. Mount diodes on good heatsink, and ensure good ventilation of device internal parts, maybe additional FAN as support.
It does not hurt to add voltage and current meter of secundar section, with temperature of transformer windings, all on separated 7-seg LED displays on device case. Current can be measured with CT (Current transformer) or Hall sensor.
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