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A mathematical model is proposed to calculate the coordinates of
the rotorprofile and simulate the meshing process of the dry
vacuum pump. Four basic curves, circular-arc, conjugate curve
to the circular-arc, extendedinvolute curve, and extended
cycloid curve, commonly used by the industry are included in
the proposed mathematical model . According to theory of
gearing , we can establish the meshing mechanism simulation of
two rotors and find the mathematical model of conjugate curves
of basic curves by using theory of conjugate. Since rotors of
the vacuum pump are synchronized by the timing gears
attached to the end of the rotating shafts , the meshing
rotors do not contact each other at any moment . Therefore
, the conventional tooth contact analysis technique is not
suitable for simulating the meshing process.A numerical
algorithm is developed to calculates the profile coordinates,
the contact points , the gap distance variation , the volume
variation of the carry-over, and volume enclosed between the
rotors and the chamber of the housing. A modified tooth contact
analysis which permit small gaps between the meshing rotors is
proposed to calculate the quasi-contact line. A reverse
engineering process for the rotor profile is also proposed to
study the existing design. Finally the drawing software Autocad
could be applied to verify the accuracy of the proposed
mathematical model and the numerical algorithm values will
help us to analyse the characteristic of the dry vacuum
pump. The results of the thesis can be applied to develop new
dry vacuum pump.
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