Conductance calculation of channels in laminar gas flow regime at an arbitrary pressure difference

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Mathematical model of oil free claw vacuum pump is presented. The model is based on energy balance differential equations of thermodynamic system of variable mass working body. Using the equations of coordinates transformation and contact line of rotors continuity condition, equations for geometry of сlaw pump working chamber on condition of rotors point connection are obtained. To evaluate the leakage through the rotor mechanism channels, their existence graphs are plotted and geometric parameters of the channels depending on rotors position are determined.As a result of modeling, dependence of pressure and temperature in suction and compression-discharge chambers on rotation angle at different rotary speeds and on different inlet pressures and relationship between pumping speed and inlet pressure are obtained.The comparison between calculated values and experimental data obtained for one-stage claw pump with identical rotors is carried out. The maximal difference between the calculated and experimental values does not exceed 15 %. The developed mathematical model is recommended for analysis of influence of rotors geometry on the working process parameters and pumping characteristics of an oil free claw pump. SUMMARY L A ∆ α δ RR δ S1 δ S2 δ RS R S FIGURE 1: Main dimensions of a claw vacuum pump.

Section: Calculation Of Leakage Through Slot Channelsmentioning

confidence: 99%

The working process of an oil‐free claw vacuum pump

Raykov¹,

Salikeev²,

Бурмистров³

et al. 2017

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“…At pressures higher than 10 kPa the influence of wall velocity on mass rate is slight that is why methods of conductance calculation [14][15][16] are used in this range.…”

Section: Leakage and Heat Exchangementioning

confidence: 99%

“…The temperatures of the scroll elements are determined with the help of the other mathematical model [15] based on the finite-element method. The initial data for calculation of temperature fields are pressures and temperatures in each chamber of the pump determined with the help of mathematical model presented above and temperature distribution on the surfaces of the working elements.…”

Section: Temperature Field and Deformations Modelmentioning

confidence: 99%

Mathematical model of working process of oil free scroll vacuum pump

Бурмистров¹,

Salikeev²,

Raykov³

et al. 2017

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Summary A mathematical model of oil free scroll machine working in vacuum conditions is considered. Differential equations and main assumptions in the model are presented. Four types of control volumes are specified. The model takes into consideration heat exchange between the pump working elements, change of clearances due to thermal deformations, and mobility of the scroll element wall in calculation of leakage. The comparison of the calculated values of the pumping speed with experimental values obtained at different rotation speed of the driveshaft is carried out.

“…In viscous flow regime the conductance of the channels 1, 2 is calculated according to the relationships [4,5]…”

Section: Problem Formulationmentioning

confidence: 99%

Conductance Calculation Of Slot Channels with Variable Cross Section

Бурмистров¹,

Salikeev²,

Bronshtein³

et al. 2015

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The range of operation pressures of non‐contact vacuum pumps may reach six decades, and flow regime in slot channels of the rotor mechanism may vary from molecular flow to viscous flow. This article is a continuation of a series of authors‘ publications dedicated to the development of a method which makes it possible to calculate promptly the conductance of slot channels with complex contoured geometry with the minimal clearance at a certain point along gas flow direction for all three gas flow regimes: molecular, transient and viscous. The numerical solution of the differential equations system (equations of motion, energy, continuity and state) is used for calculation of mass flow rate in transient gas flow regime. On the basis of the numerical calculation results the relationship is obtained which represents a smooth joining of the data for molecular and viscous flow regimes. Verification of the model and the obtained relationship is carried out by comparison of numerical calculation results of gas mass flow rate and conductance with experimental data obtained by blowing‐through of slot channels. The maximal deviation of calculation according to the obtained relationship from the experiment does not exceed 14%, the average uncertainty being less than 8%, which makes it possible to recommend it for practical application in transient flow regime.