Optimized helix angle rotors for Roots-style supercharger

A rotor for a Roots-type blower comprising a housing defining first and second transversely overlapping cylindrical chambers, said housing including a first end wall defining an inlet port, and a second end wall, said housing defining an outlet port formed at an intersection of said first and second chambers, and adjacent said second end wall;

• said blower including first and second meshed, lobed rotors disposed, respectively, in said first and second chambers;
• each rotor including a plurality N of lobes, each lobe having first and second axially facing end surfaces sealingly cooperating with said first and second end walls, respectively, and a top land sealingly cooperating with said cylindrical chambers, each lobe having its first and second axially facing end surfaces defining a twist angle, and each lobe defining a helix angle;
• said rotor characterized by:
• said twist angle for said lobe is a maximum ideal twist angle that is a function, partially, of said number N of lobes on said rotor;
• and
• said helix angle for each lobe is a function of said twist angle and an axial length between said first and second axially facing end surfaces of said lobe, said rotor including a Lead, wherein said Lead is a function of said maximum ideal twist angle and said axial length, said helix angle being determined in accordance with the equation:
• Helix Angle (HA)=(108/π*arctan (PD/Lead)),
• wherein PD is the pitch diameter of the lobe.

A Roots-type blower comprising:

• a housing defining first and second transversely overlapping cylindrical chambers, said housing including a first end wall defining an inlet port having an inlet pressure and an outlet port formed at an intersection of said first and second chambers and adjacent to a second end wall;
• and
• first and second meshed, lobed rotors disposed, respectively, in said first and second chambers, each rotor including a plurality N of lobes, each lobe having first and second axially facing end surfaces sealingly cooperating with said first and second end walls, respectively, and a top land sealingly cooperating with said cylindrical chambers, said lobes defining a control volume of fluid having an inlet seal time, a transfer seal time, and a total seal time that is a sum of the inlet and transfer seal times, each lobe having its first and second axially facing end surfaces defining a twist angle that is a function, partially, of said number N of lobes on said rotor, a maximum ideal twist angle being the largest possible twist angle for each rotor lobe without opening a leak path from the outlet port to the inlet port, wherein when the twist angle is a maximum ideal twist angle, the total seal time is a total maximum seal time and the transfer seal time is zero, and when the twist angle is less than the maximum ideal twist angle, the total seal time is a total optimized seal time and the transfer seal time is greater than zero, but the total maximum seal time and the total optimized seal time are substantially constant.