ax to grind vs on the brain

ax to grind

noun
  • A grudge or grievance, with implications of confrontation. 

  • A proposition or point of view to advocate, especially motivated by self-interest. 

on the brain

prep
  • Obsessively in mind. 

How often have the words ax to grind and on the brain occurred in a corpus of books? (source: Google Ngram Viewer )