Roots type fluid machine

A roots type fluid machine comprising:

• a housing;
• a rotor chamber formed by the housing;
• a suction port formed in the housing;
• a discharge port formed in the housing;
• a pair of rotary shafts rotatably arranged in parallel to each other in the rotor chamber;
• a pair of rotors, plane symmetrical to each other, each rotor being fixed on one of the rotary shafts for rotation therewith in the rotor chamber and respectively having a number n of lobe portions with an apex end and valley portions with a bottom end for engaging each other, wherein the lobe portions of each rotor are located on imaginary lines extending radially from an axis of the associated rotary shaft at an angular spacing apart respectively,
• a fluid chamber defined by the outer surfaces of the rotors and the inner surface of the rotor chamber, and in which fluid is caused to flow in through the suction port and discharged out through the discharge port by rotating the rotors,
• wherein the outer surface of each one of the rotors is generated by rotating an outline of the rotor around and moving the outline in the direction of the axis of the associated rotary shaft, the outline of the rotor extending from each apex end of the lobe portion to the bottom end of the valley portion through a first transition point and a second transition point thereon, the outline of the rotor including an arc extending from the apex end of the lobe portion to the first transition point and having a radius R and a center located on the imaginary line, an involute curve extending continuously from the first transition point to the second transition point and formed by an imaginary base circle having a radius r and a center located on the axis of the rotary shaft, and an envelope curve with an arc having a radius R extending continuously from the second transition point to the bottom end of the valley portion,
• wherein the number n of the lobe portions is four or more, and a torsional angle β of the lobe portions is over 360/n degrees, and
• wherein the axes of the rotary shafts are spaced away from each other at a distance L, and the diameter r of the circle meets a condition of r<nL/(π2+4n2)1/2 and the radius R of the arc meets the condition R<πr/2n.