Wrap of cylinder and its effect on main features of rotary vane compressor for automobile air conditioning system

The rotary vane compressor has been used in the automobile air conditioning system. One of the key factors of its design is the wrap of its cylinder. From the working principle of this type of compressor, it is explained in mathematics why the wrap is composed of four parts: arc of circle, main curve, and two segments of transit curves, and the conditions that the wrap needs to satisfy are derived simultaneously. At the same conditions, we compared to the gas force Fp, contact force Fnc of the blade head, the force acting on rotor by blades, and the suction volume Vs for three kinds of main curves. The wrap composed of trigonometric function can form the biggest value of Vs, while the least suction volume Vs will be reached as the cubic polynomial is taken. The wrap composed of trigonometric function forms the biggest absolute value of the gas force Fp and the middle peak value of the force acting on rotor by blades, while the least absolute value of the gas force Fp and the biggest contact force Fnc of blade head will be reached as the cubic polynomial is taken. The force acting on the rotor by blades takes the biggest peak value if the main curve is the ellipse curve. The frequency of the force acting on the rotor by blades is the same as the number of blades at the range of the crank angle from 0 to 180°.