Delta-delta Transformer Voltage Problems

I Have A Three Phase Delta-delta 480vac To 240vac Transformer. This Transformers Has Me Concerned Due To The Voltage Readings To Ground. This Transformer Feeds A 3 Wire 240vac Panel.

When We Read Phase To Phase It Reads 240vac. I Measured Phase A To Ground And Read 10vac. Phase B To Ground Was 240vac, And Phase C To Ground Was 240vac. Phase A Increased To 120vac While Phase C Decreased To 120vac. We Used Two Meters And Witnessed Simultaneous Voltage Change On Those Two Phases.

These Connect Numerous Loads Which Do Not Seem To Be Effected By The Voltage Fluctuating. Once In Awhile The Machines Blows An Incoming Fuse, But Does Not Trip The Breaker.

I Know That This Is An Ungrounded Delta-delta Transformer. Do I Need To Ground One Phase Of The Secondary? Is It Possible That The Transformer Is Breaking Down?

P.s. We Are Only Using Single Phase 240vac Loads And Three Phase 240vac From This Panel I Mentioned Above.

Thanks For Suggestions