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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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