A trans-sonic drill was a type of drill used for mining pergium.
In 2375, Yanas Tigan asked Miles O'Brien if he could take a look at a malfunctioning trans-sonic drill which nobody else on her staff was able to repair. Her son, Janel Tigan protested that while O'Brien was an engineer, he was not a mining engineer; while her daughter Ezri Dax protested that O'Brien needed to rest, but O'Brien assured them he felt fine.
O'Brien was able to determine that the problem was in the secondary input transtator, discovering that the drill required a 52-J, but was equipped with a 52-L. (DS9: "Prodigal Daughter")
According to the script "The drill is a large piece of equipment about the size of a mini-van. There's a beam emitter at one end, which is used for cutting into the ore."