A valid method of gas foil bearing parameter estimation: A model anchored on experimental data

Abstract

Gas foil bearings are a smart green technology and suitable for the next generation of small turbo machinery e.g. turbochargers, micro gas turbines, range extenders and compressors of fuel cells. A combination of low power loss, high speed operation and the omission of an oil system are the major advantages. To enable access to this technology, it is essential to evaluate critical speeds and onset speeds of subharmonic vibration of the rotor system in the first design stage. Hence, robust and valid models are necessary, which correctly describe the fluid structure interaction between the lubrication film and the elastic bearing structure. In the past three decades several experimental and numerical investigations of bearing parameters have been published. But the number of sophisticated models is small and there is still a lack of validation towards experimental works. To make it easy for designers dealing with this issue, the bearing parameters are often linearised about certain operating points. In this paper a method for calculating linearised bearing parameters (stiffness and damping) of gas foil bearing is presented. Experimental data are used for validation of the model. The linearised stiffness and damping values are calculated using a perturbation method. The pressure field is coupled with a two-dimensional plate model, while the non-linear bump structure is simplified by a link-spring model. It includes Coulomb friction effects inside the elastic corrugated structure and captures the interaction between the single bumps. For solving the separated perturbed Reynolds equation a static stiffness is used for the 0. order equation (stationary case) and a dynamic stiffness is applied for 1. order equation (dynamic case). Therefore, an additional dynamic structural model is applied to calculate the dynamic stiffness. The results depend on the load level and friction state of each bump. Different case studies including the impact of clearance, frictional contacts and the comparison of a linear and non-linear structure are carried out for infinitesimal perturbations. The results show, that the linear structure underestimates main and cross-coupling effects. The impact of the clearance is notable, while the impact of the overall frictional contacts is small due to relatively small loadings. The infinitely small perturbation model is adapted to the experimental setup by using a superposition of two resulting bearing parameters identifications of two total loadings including shaker forces. Due to this adaptation a good correlation with the experimental results of the bearing parameters is achieved.

Keywords

Gas foil bearing parameter identification non-linear structure friction

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