Behnam Ghalamchi

Simple and Versatile Dynamic Model of Spherical Roller Bearing

Rolling element bearings are essential components of rotating machinery. The spherical roller bearing (SRB) is one variant witnessing increasing use because it is self-aligning and can support high loads. It is becoming increasingly important to understand how the SRB responds dynamically under a variety of conditions. This study introduces a computationally efficient, three-degree-of-freedom, SRB model that was developed to predict the transient dynamic behaviors of a rotor-SRB system. In the model, bearing forces and deflections were calculated as a function of contact deformation and bearing geometry parameters according to the nonlinear Hertzian contact theory. The results reveal how some of the more important parameters, such as diametral clearance, the number of rollers, and osculation number, influence ultimate bearing performance. One pair of calculations looked at bearing displacement with respect to time for two separate arrangements of the caged side-by-side roller arrays, when they are aligned and when they are staggered. As theory suggests, significantly lower displacement variations were predicted for the staggered arrangement. Following model verification, a numerical simulation was carried out successfully for a full rotor-bearing system to demonstrate the application of this newly developed SRB model in a typical real world analysis.

Modeling and Dynamic Analysis of Spherical Roller Bearing with Localized Defects: Analytical Formulation to Calculate Defect Depth and Stiffness

Since spherical roller bearings can carry high load in both axial and radial direction, they are increasingly used in industrial machineries and it is becoming important to understand the dynamic behavior of SRBs, especially when they are affected by internal imperfections. This paper introduces a dynamic model for an SRB that includes an inner and outer race surface defect. The proposed model shows the behavior of the bearing as a function of defect location and size. The new dynamic model describes the contact forces between bearing rolling elements and race surfaces as nonlinear Hertzian contact deformations, taking radial clearance into account. Two defect cases were simulated: an elliptical surface on the inner and outer races. In elliptical surface concavity, it is assumed that roller-to-race-surface contact is continuous as each roller passes over the defect. Contact stiffness in the defect area varies as a function of the defect contact geometry. Compared to measurement data, the results obtained using the simulation are highly accurate.

Twice-Running-Speed Resonances of a Paper Machine Tube Roll Supported by Spherical Roller Bearings: Analysis and Comparison With Experiments

Imperfections in a rotor-bearing system may cause undesirable subcritical resonances occurring when the rotating speed of the rotor is a fraction of the natural frequency of the system. These resonances arise partly from rotor imperfections and partly from bearing imperfections. This study demonstrates that the subcritical twice-running-speed vibrations originating from bearing waviness may be investigated by combining a simplified rotor model with a detailed bearing model, using a finite element method. The rotor-bearing system under investigation is a roller test rig consisting of the tube roll of a paper machine supported by spherical roller bearings. The bearing waviness from the second to the fourth orders is emulated as accurately as possible in the finite element model. This is achieved by measuring the waviness of the real bearings and then incorporating the measurement results into a simulation model. The tube roll of the test rig is modeled as a symmetric tube, neglecting the effects of the uneven mass and stiffness distribution of the roll. The contact between the rotor and the bearings is described using nonlinear Hertzian contact theory. The subcritical responses of the system are studied by means of time integration, and the results are converted into the frequency domain using fast Fourier transformation. The results of the analysis are compared with the measurement results for the subcritical responses of the roll. The agreement between the simulation and experimental results of the studied system can be observed even though rotor imperfections are not considered.© 2014 ASME

Dynamic Model of Spherical Roller Bearing

Rolling element bearings are essential machine elements in the rotating machinery. Extensive research has been conducted to study the dynamics of ball bearings, while studies related to spherical roller bearings are short-shrifted. On the other hand, the number of industrial applications that utilize spherical roller bearings has been increasing constantly. This is due to self-aligning nature and high-load capacity of spherical roller bearings. Typical applications are paper machines, steel rolling, marine equipment, geared transmissions and modern high power wind turbines. This study introduces a three-degree-of-freedom spherical roller bearing model that is computationally efficient, and it is designed to be used in the transient simulations of complete rotor-bearing systems. In the proposed model, the bearing forces are calculated as a function of contact deformation and bearing geometry parameters according to the non-linear Hertzian contact theory. In the numerical results, the important bearing design parameters such as diametral clearance, number of rollers and osculation are studied. Existence of varying compliance (VC) vibrations and the capability of the proposed model in the transient simulations of rotor-bearing systems are demonstrated. The bearing model is verified by using commercial bearing analysis software. Future improvements and model extension possibilities are also discussed.Copyright

Design of a 400 KW Gas Turbine Prototype

Decentralized power and heat generation is a growing trend throughout the world. In smaller applications, electrical power output less than few megawatts, reciprocating engines have dominated the market. In recent years, small sized gas turbines have emerged as challengers for the reciprocating engines. The small gas turbines have a growing share of the decentralized energy market, which itself is rapidly growing. Hence, improvements in small gas turbine efficiency have a significant impact from the economic and environmental perspective.In this paper, the design of a high efficiency 400 kW gas turbine prototype is described and discussed. The prototype is a two-spool, recuperated and intercooled gas turbine where both spools comprise of a radial compressor and turbine, a permanent magnet electric generator, an axial and two radial active magnetic bearings and two safety bearings.The prototype design was divided into five categories and each of the categories are discussed. The categories were: the process design, the turbomachinery design, the generator and electrical design, bearing design and rotor dynamic analysis, and mechanical design. The design of recuperator, intercooler, and combustion chamber were outsourced. Hence, they are not discussed in this paper.The prototype design process showed the readiness of the chosen technological selections, as well it showed that the type of machine under discussion can be designed and manufactured.© 2016 ASME

Spherical Roller Bearing Simulation Model with Localized Defects

Since Spherical Roller Bearings (SRBs) have high load capacity and are self-aligning, they are seeing increasing use in the rotating machinery. Typical applications are paper machines, steel rolling, marine equipment, geared transmissions and modern high power wind turbines. Therefore, it is becoming increasingly important to study the dynamic behavior of SRBs and know the excitations caused by internal imperfections. Extensive research has been conducted to study the dynamics of ball bearings, while studies related to spherical roller bearings are short-shrifted. In this paper a three degree of freedom dynamic model of spherical roller bearing that takes into account the inner and outer race surface defects is introduced. In the model, bearing forces and deflections are calculated as a function of contact deformation and bearing geometry parameters according to nonlinear Hertzian contact theory; taking radial clearance into account. Two defect cases are simulated: an elliptical surface concavity on the inner race, and an elliptical surface concavity on the outer race. In case of elliptical surface concavity, it is assumed that the contact between the roller and inner and outer races is continuous as each bearing roller passes over the defect, and contact stiffness in the defect area varies as a function of the defect’s contact geometry. The equations of motion were solved numerically. Simulation results demonstrate that the SRB model is sufficiently accurate for typical rotor bearing systems. Numerical results also show that each local defect excites vibration at a frequencies corresponding to the bearing defect frequencies, and thus, makes it possible to identify the location of the defect (i.e. inner or outer race) from the simulated frequency spectrum. Numerical simulation is carried out successfully for a full rotor-bearing system to demonstrate the application of developed SRB model in a real world analysis. Finally, simulation results are verified and compared to measured data obtained from an equivalent rotor bearing system with a predefined local defect. Comparison shows a good agreement between the simulated and measured results.