Bifurcation analysis of rotor/bearing system using third-order journal bearing stiffness and damping coefficients

Hydrodynamic journal bearings are used in many applications which involve high speeds and loads. However, they are susceptible to oil whirl instability, which may cause bearing failure. In this work, a flexible Jeffcott rotor supported by two identical journal bearings is used to investigate the stability and bifurcations of rotor bearing system. Since a closed form for the finite bearing forces is not exist, nonlinear bearing stiffness and damping coefficients are used to represent the bearing forces. The bearing forces are approximated to the third order using Taylor expansion, and infinitesimal perturbation method is used to evaluate the nonlinear bearing coefficients. The mesh sensitivity on the bearing coefficients is investigated. Then, the equations of motion based on bearing coefficients are used to investigate the dynamics and stability of the rotor-bearing system. The effect of rotor stiffness ratio and applied load on the Hopf bifurcation stability and limit cycle continuation of the system are investigated. The results of this work show that evaluating the bearing forces using Taylor’s expansion up to the third-order bearing coefficients can be used to profoundly investigate the rich dynamics of rotor-bearing systems.

Centrifugal Compressor Stage Efficiency and Rotor Stiffness Augmentation via Artificial Neural Networks

Centrifugal compressor stages with high rotor stiffness (i.e. impeller hub-to-outer-diameter ratio) may represent a crucial element to cope with tight rotordynamic requirements and constraints that are needed for certain applications. On the other hand, high-stiffness has a detrimental effect on the aerodynamic performance. Thus, an accurate design and optimization are required to minimize the performance gap with respect to low-stiffness stages. This paper shows a redesign and optimization procedure of a centrifugal compressor stage aimed at increasing the impeller stiffness while keeping high aerodynamic performance. Two different optimization steps are employed to consider a wide design space while keeping the computational cost as low as possible. At first the attention is focused on the impeller only, then the diffuser and the return channel are taken into account. The multi-objective and multi-operating point optimization makes use of artificial neural networks (ANNs) as a surrogate model to obtain the response surfaces. RANS calculations are carried out using the TRAF code and are employed to create the training dataset. Once the ANN has been trained, an optimization strategy is used to find the constrained optimum geometries for the impeller and the static components. The optimized high-stiffness stage is finally compared to the low-stiffness one to assess its applicability.

Bifurcation Analysis of Rotor/Bearing System using Third Order Journal Bearings Stiffness and Damping Coefficients

Journal bearings have many applications in industry due to its high load carrying capacity. In addition proper design of journal bearings enables safe operation at very high speeds. However, they are susceptible to oil whirl instability which may cause bearing failure. The fluid film pressure distribution inside the journal bearing is described by Reynolds equation. Many studies had been done to approximate the bearing performance using first order bearing coefficients. Although this analysis is stable for evaluating the threshold speed but it is insensitive to limit cycles above the threshold speed. Mush literature show that above the threshold speed, subcritical or supercritical bifurcations may be observed. Therefore, the aim of the present paper is to evaluate the third order bearing coefficients for a finite length journal bearing using finite perturbation method. The values of these coefficients are evaluated using infinitesimal perturbation analysis. These values are used to investigate the bifurcation stability of flexible Jeffcott rotor supported by two symmetric journal bearings. The effect of rotor stiffness ratio on the bifurcation stability of the system is investigated. The results of this work show that the third order parameters can be used to evaluate the type of bifurcation above the threshold speed.

Adaptation of an Existing Impeller Design to Large Bore Requirements: Aerodynamic Considerations

Multistage process centrifugal compressor applications with single shaft rotors supported by only two bearings are quite common. It is sometimes desirable to operate impellers at higher rotational speeds, resulting in relatively compact and cost-effective machines. Such high-speed rotors can, however, pose rotordynamic challenges, and therefore require larger shaft or impeller bore diameters to increase rotor stiffness and rotordynamic stability. This work explores aerodynamically favorable ways to adapt an existing standard bore impeller design to large bore requirements. First, the stage aerodynamic performance and flow range implications of increasing bore diameter are discussed using meanline modeling and vector diagram arguments. Some strategies for adapting a standard bore design to large bore variant are then presented. Attempts are made to identify and clarify technical limitations to the degree of adaptability of an existing impeller to large bore requirements. Finally, a CFD-backed case study on a large-bore adaptation of a particular stage is presented to clarify practical considerations.

Dynamic Characteristics of Rotor System With Additional Constraint due to Rub-Impact

Not only excitation force but also additional constraint will be induced to the rotor system by the rubbing effects. The latter can lead to the change of rotor stiffness and damping, which affects the dynamic characteristics of the rotor further. The paper investigates the effects of the additional constraint on the rotor’s natural characteristics and response through theoretical modeling and experiment testing. The results reveal that the stiffness enhancement caused by the additional constraint will increase the rotor’s resonance speed and widen the resonance interval and the unstable contact region, however the influence of the damping is opposite. Meantime, the characteristics of constraint stiffness are different for different rub-impact states, which has different effects on the rotor’s response characteristics. For annular rubbing, constraint stiffness is constant, which will not change rotor response characteristics. However, for partial rubbing, constraint stiffness is time-varying and non-smooth, resulting in the super-harmonic components in frequency domain and rotor’s quasi-periodic motion. The conclusions are also confirmed by the experimental results. Obtained numerical and experimental results can help to understand some phenomena in the rotating machinery and could be further used for improving of more complicated models for dynamical design and enhancement of aircraft engines.

Study on Rub-Impact Dynamical Behavior of An Asymmetrical Rotor-Bearing with Variable Ratio of Stiffness

A rub-impact mathematic model of an Asymmetrical rotor-bearing with nonlinear oil film force is built in the paper. The bifurcation diagrams of the response were given following the changing of ratio of stiffness. We analyzed the bifurcation and the chaos character of an Asymmetrical rotor-bearing with operating rotor stiffness changing, then we get the dynamical character and the law when the rubbing happen. The nonlinear dynamic behaviors of the system were studied by using the numerical value integral and Poincare mapping methods. By analysis the process of rub-impact, it is so complex and many low frequencies with large amplitude are in the range of 0.3~0.6 X. The way of period-chaos-period and the phenomena of diverging backward whirl are discovered when the rubbing happen. These results provide important theoretical references for the safety operation of generating sets and the exact identification of the faults in rotating machinery.

Using Cross-Coupling Effects for Suppression of Contact Severity

In this paper the influence of cross-coupling effects on the rubbing-related dynamics of rotor/stator systems is investigated. The model considered in this paper is a 4-dof rotor/stator system which takes into account the dynamics of the stator and the deformation on the contact surface as well as the cross-coupling effects. The stability of the synchronous full annular rub solution of the model is first analyzed. Then, the cross-coupling effects on the stability of the system at different system parameters are studied. It is found that the cross-coupling effects of the rotor stiffness as well as those of the stator damping and stiffness will benefit the synchronous full annular rubs while the cross-coupling damping of the rotor will reduced the stability domain of the response and lead the system to a response with a heavier rubbing

Study on the Stiffness Loss and its Affecting Factors of the Spline Joint Used in Rotor Systems

The spline joint is a kind of widely used joint structures in the rotor system. Its discontinuous mechanical characteristics results from the contact surface. The surface will slide and deform when the spool deforms. As a consequence, the joint stiffness is always smaller than that of the integral configuration. This affects the rotor stiffness distribution and the rotor dynamics further. The objective of this study is to investigate the stiffness mechanical characteristics of the spline joint and their affecting factors. Based on the characteristics of structure and mechanical state, a spline joint stiffness mechanical model is built to explain the stiffness loss and its affecting factors. The cylindrical coordinate contact model is used to describe the contact of the cylindrical centering surface. And then a spline joint simulation model, taking the characteristics of the contact into account, is built by the nonlinear finite element method. At last, in the static stiffness experiment, the displacement of the spline joints is measured in different assembling and loading conditions. The results show that, the linear and angular stiffness loss of spline joint is significant and has a close relationship with the load and assembling condition. The study shows the effectiveness in controlling the mechanical properties of the rotor with spline joints by carefully adjusting structural design, load and assembling parameters.

Nonlinear Dynamic Analysis of Rub-Impact Rotor System under Different Parameters

Nonlinear dynamic-behavior analysis of rotor system under different parameters is presented. The derivation of nonlinear dynamic equations under the action of rub-impact force is set up basing on Jeffcott model, and the system bifurcation characteristics and influences has been investigated under the ratio of operating angular velocity and the rotor’ natural angular velocity influence by numerical analysis. Bifurcation and dynamical behaviors of nonlinear of system with the changes of argument (that is the ratio of operating angular velocity and the rotor’ natural angular velocity) under several specific parameters are analyzed. The results show that the ratio, rotor eccentricity and rotor stiffness have great effect on the dynamical behaviors of nonlinear system.