The contact force of internal-meshing gear compressor between gears directly affects the choice of gears' materials

friction power and operating reliability. Linear-elastic theory was employed to set up two different mathematical models with or without consideration of the gap between the cylinder and the outer gear

respectively. The present models were more simple than finite element method and could obtain the relationship between the contact force and the rotate angle. In particular

calculating results could guide and optimize the design of profiles. The research result shows the gap will influence the magnitude and variation of the contact force. The contact force calculated with the gap model is almost 10 times higher than that with the non-gap one. The gap model is close to the actual situation and is recommended in the design of this type of compressors.