Analysis of a Two Wrap Meso Scale Scroll Pump

Abstract

The scroll pump is an interesting positive displacement pump. One scroll in the form of an Archimedes spiral moves with respect to another, similarly shaped stationary scroll, forming a peristaltic pumping action. The moving scroll traces an orbital path but is maintained at a constant angular orientation. Pockets of gas are forced along the fixed scroll from its periphery, eventually reaching the center where the gas is discharged. A model of a multi-wrap scroll pump was created and applied to predict pumping performance. Meso-scale scroll pumps have been proposed for use as roughing pumps in mobile, sampling mass spectrometer systems. The main objective of the present analysis is to obtain estimates of a scroll pump's performance, taking into account the effect of manufacturing tolerances, in order to determine if the meso scale scroll pump will meet the necessarily small power and volume requirements associated with mobile, sampling mass spectrometer systems. The analysis involves developing the governing equations for the pump in terms of several operating parameters, taking into account the leaks to and from the trapped gasses as they are displaced to the discharge port. The power and volume required for pumping tasks is also obtained in terms of the operating parameters and pump size. Performance evaluations such as power and volume per unit of pumped gas upflow are obtained. Nomenclature a-radius of an Archimedes spiral (m) P(φ)-pressure ratio at φ b-real positive number (m) P E-exhaust pressure ratio C LE-end leak conductance (l/s) P G-geometric pressure ratio C LSC-edge leak conductance (l/s) Q-power for pump (W) d-gap distance between the scrolls (m) r-orbit radius (m) f D-operating frequency (Hz) R-radius of the scroll (m) F N-normal force (N) T-temperature of the gas (K) H-height of the scroll (m) v f-linear slip velocity (m/s) k-Boltzmann's constant (J/K) V T (φ)-tapped volume at φ (l) L-scroll segment length (m) V TI-inlet trapped volume (l) m-mass of a gas molecule (kg) α-transmission probability n-number density (#/m 3) δ-thickness of the scroll walls (m) n E-exhaust number density (#/m 3) φ-orbit angle (rad) n I-inlet number density (#/m 3) µ k-coefficient of kinetic friction N-number of scroll wraps N T (θ)-number density flow (#/s)

Mathematical model of working process of oil free scroll vacuum pump

“…The most part of such studies involves development of mathematical models of a scroll mechanism working in regime of a scroll compressor [1][2][3][4][5]. Scroll vacuum pumps studies [6][7][8] are considerably fewer.…”

An analytical method for calculating forces and torques in oil-free scroll vacuum pumps and compressors

“…насос вакуумный спиральный (нвсп) -новейшее средство получения безмасляного среднего и низкого вакуума. большое количество патентов и публикаций ведущих зарубежных производителей, например [2][3][4][5], посвященных, как профилям спиралей и способам изоляции рабочего объема от подшипниковых узлов, так и приводным механизмам, подтверждают интерес исследователей и производителей к нвсп.…”

“…Осевая сила давления газа на спиральный элемент определяется выражением (3) здесь предполагается, что давление в объеме всасывания равно P вх , и это же давление действует на торцевой диск с тыльной стороны. Площадь окна нагнетания не учитывается.…”