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This article presents a new approach in which the explicit finite element method (EFEM) and the discrete element method (DEM) are coupled to investigate dynamics of flexible rotor systems supported by deep-groove ball bearings. In this investigation, DEM is used to develop the bearing (dynamic motion) model in which all of the components of the bearing (i.e., inner and outer race, balls, and cage) have 6 degrees of freedom. The flexible shaft is modeled with a full 3D elastic formulation using the EFEM rather than the reduced form, which implements component mode synthesis. The EFEM and DEM were combined to investigate the dynamics of flexible shaft rotor systems supported by ball bearings. Rotor and inner races of the bearings are fully coupled such that both translation and rotation of the flexible rotor are transmitted to the bearings. At each time step, the translational motion and rotation/tilt angle of the rotor cross section at the location of an inner race are applied to the inner race of the bearing. The resulting reaction forces and moments calculated in the dynamic bearing model are in turn applied to the nodes of the shaft. The combined model is used to investigate the motions of the inner races and the resulting reaction forces and moments from the supporting bearings due to an applied load on the shaft. In the current coupled modeling approach, the deformation of the shaft affects the internal components of the bearing by altering the orientation of the inner race, which results in ball spin and slip.

The objective of this experimental investigation was to design and develop a high speed turbocharger test rig (TTR) in order to critically examine the whirl and frictional characteristics of floating ring and ball bearing turbochargers. In order to achieve the objective, a high speed TTR was designed and developed with the capability of reaching speeds in excess of 100,000 rpm and was equipped with speed and displacement sensors to obtain the necessary results for comparison between the two turbocharger models. The TTR was used to compare and contrast the whirl and friction characteristics of two identical turbochargers differing only by the support structure of the rotor system: one containing a floating ring bearing turbocharger (FRBT) and the other a ball bearing turbocharger (BBT). The TTR is driven by an industrial compressor powered by a six cylinder 14 liter diesel engine. This configuration closely resembles turbocharger operation with an actual engine and was able to operate in both nominal and extreme operating conditions. A pair of displacement sensors was installed to measure the whirl of the rotor near the end of the compressor. Whirl results indicated that the BBT was significantly more rigid and stable than the FRBT. Waterfall plots were used to compare the frequency response of the two turbochargers over the full range of operating speeds. The majority of motion for the BBT was the whirl of the synchronous excitation due to a negligible inherent imbalance with some larger motions caused by vibrational modes. The whirl of the FRBT consists of not only the synchronous motion but also subsynchronous motions as a result of oil film instabilities throughout the entire operating range of speeds. The TTR was also used to compare frictional losses within the bearings. A study of the run-down times after the pressurized air supply was removed indicated that the BBT has significantly lower frictional losses under all operating conditions tested.

The objective of this investigation was to determine the effect of housing support on bearing performance and dynamics. In order to achieve the objective, an existing dynamic bearing model (DBM) was coupled with flexible housing model to include the effect of support structure on bearing dynamics and performance. The DBM is based on the discrete element method, in which the bearing components are assumed to be rigid. To achieve the coupling, a novel algorithm was developed to detect contact conditions between the housing support and bearing outer race and then calculate contact forces based on the penalty method. It should be noted that although commercial finite element (FE) software such as abaqus is available to model flexible housings, combining these codes with a bearing model is quite difficult since the data transfer between the two model packages is time-consuming. So, a three-dimensional (3D) explicit finite element method (EFEM) was developed to model the bearing support structure for both linear elastic and nonlinear inelastic elastomeric materials. The constitutive relationship for elastomeric material is based on an eight chain model, which captures hyperelastic behavior of rubber for large strains. The viscoelastic property is modeled by using the generalized Maxwell-element rheological model to exhibit rate-dependent behaviors, such as creep and hysteresis on cyclic loading. The results of this investigation illustrate that elastomeric material as expected has large damping to reduce vibration and absorb energy, which leads to a reduction in ball–race contact forces and friction. A parametric study confirmed that the viscoelastic stress (VS) contributes significantly to the performance of the material, and without proper amount of viscoelasticity it loses its advantage in vibration reduction and exhibits linear elastic material characteristics. As expected, it is also demonstrated that housing supports made of linear elastic material provide minimal damping and rely on the bearing friction to dissipate energy. A study of housing support geometry demonstrates that bearing support plays a large role on the dynamic performance of the bearing. Motion of bearing outer race is closely related to the geometry and symmetry of the housing.

The objectives of this investigation were to develop a coupled dynamic model for turbocharger ball bearing rotor systems, correlate the simulated shaft motion with experimental results, and analyze the corresponding bearing dynamics. A high-speed turbocharger test rig was designed and developed in order to measure the dynamic response of a rotor under various operating conditions. Displacement sensors were used to record shaft motion over a range of operating speeds. To achieve the objectives of the analytical investigation, a discrete element angular contact ball bearing cartridge model was coupled with an explicit finite element shaft to simulate the dynamics of the turbocharger test rig. The bearing cartridge consists of a common outer ring, a pair of split inner races, and a row of balls on each end of the cartridge. The dynamic cartridge model utilizes the discrete element method in which each of the bearing components (i.e., races, balls, and cages) has six degrees-of-freedom. The rotor is modeled using the explicit finite element method. The cartridge and rotor models are coupled such that the motion of the flexible rotor is transmitted to the inner races of the cartridge with the corresponding reaction forces and moments from the bearings being applied to the rotor. The coupled rotor–cartridge model was used to investigate the shaft motion and bearing dynamics as the system traverses critical speeds. A comparison of the analytical and experimental shaft motion results resulted in minimal correlation but showed similarity through the critical speeds. The cartridge model allowed for thorough investigation of bearing component dynamics. Effects of ball material properties were found to have a significant impact on turbocharger rotor and bearing dynamics.