have an axe to grind表达"另有企图"的带自私或强烈意见的行为。
The study should be conducted by a firm that has no axe to grind.
These local politicians have always got an axe to grind. You know they’re hiding something from you.
have an axe to grind指某人的行为别有用心、另有企图，不像表面上看起来那么简单，有点中文的“黄鼠狼给鸡拜年”味道。
You think she offered you the job because you are the most qualified applicant? Don't be naïve. She obviously has an axe to grind. She wants your dad to owe her a big one so that she can ask for his "help" in the future.