break one's back vs knuckle down

break one's back and knuckle down both are verbs.

Word	Noun	Adjective	Verb	Adverb
break one's back	No	No	Yes	No
knuckle down	No	No	Yes	No

As verbs, break one's back and knuckle down are synonyms defined as:

Other synonyms of break one's back include buckle down, slave.

break one's back (verb)	knuckle down (verb)
work very hard, like a slave	work very hard, like a slave