ax to grind vs compulsion

ax to grind

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

  • A grudge or grievance, with implications of confrontation. 

compulsion

noun
  • An irrational need or irresistible urge to perform some action, often despite negative consequences. 

  • The use of authority, influence, or other power to force (compel) a person or persons to act. 

  • The lawful use of violence (i.e. by the administration). 

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