An analytical model to describe the compression in turbomolecular pumps and roots blowers

Abstract

An analytical model is presented, useful in practice, for calculating and analysing the compression curves of classical turbomolecular pumps, wide range turbomolecular pumps and Roots blowers. It is demonstrated that the model, primarily proposed for classical turbomolecular pumps, can be applied to wide range turbomolecular pumps and Roots blowers as well. The model is based on an ordinary differential equation for the pressure as a function of position inside the pump. Solving the differential equation makes it possible both to calculate the compression curves for a finite gas throughput (Q > 0) and for zero gas throughput. A hypothesis is posed holding that the compression curve for zero gas throughput can be derived from a compression curve for a finite gas throughput, e.g., Q = 1 sccm in the case of turbomolecular pumps. In the case of Roots blowers a proposal is made how to describe the backleakage phenomenon quantitatively. For each type of vacuum pump mentioned above the comparison with experimental data shows that the model provides an excellent qualitative and quantitative reproduction of the observed phenomena in the whole relevant pressure range, i.e., perfect agreement over more than five pressure decades is achieved.