Oil pump rotor

An oil pump rotor assembly comprising:

• an inner rotor having “n” external teeth;
• and
• an outer rotor having (n+1) internal teeth which are engageable with the external teeth,
• wherein each of the tooth profiles of the inner rotor is formed such that the tip profile thereof is formed using an epicycloid curve which is formed by rolling a first circumscribed-rolling circle along a base circle without slip, and the tooth space profile thereof is formed using a hypocycloid curve which is formed by rolling a first inscribed-rolling circle along the base circle without slip, and each of the tooth profiles of the outer rotor is formed such that the tooth space profile thereof is formed using an epicycloid curve which is formed by rolling a second circumscribed-rolling circle along a base circle without slip, and the tip profile thereof is formed using a hypocycloid curve which is formed by rolling a second inscribed-rolling circle along the base circle without slip, and
• wherein the inner rotor and the outer rotor are formed such that the following equations are satisfied:
• øB=øBi;
• øDo=øDi·(n+1)/n+t·(n+1)/(n+2);
• and
• øi Ao=øAi+t/(n+2),
• where øDi is the diameter of the base circle of the inner rotor, øAi is the diameter of the first circumscribed-rolling circle, øBi is the diameter of the first inscribed-rolling circle, øDo is the diameter of the base circle of the outer rotor, øAo is the diameter of the second circumscribed-rolling circle, øBo is the diameter of the second inscribed-rolling circle, and t (≠0) is gap between the tooth tip of the inner rotor and the tooth tip of the outer rotor.