Amplitude Of Unbalance Response Research Articles

A Numerical Investigation of the Effects of Groove Texture on the Dynamics of a Water-Lubricated Bearing–Rotor System

This paper aims to investigate the combined effects of working condition and structural parameters of groove texture on the dynamic characteristics, stability and unbalance response of a water-lubricated hydrodynamic bearing–rotor system to avoid instability and excessive vibration of the rotor. The Navier–Stokes equation, standard K-ε model with enhanced wall treatment and Zwart–Gerber–Belamri cavitation model are considered using the commercial software Fluent to calculate the stiffness and damping coefficients of a groove-textured, water-lubricated bearing based on the dynamic mesh method; the critical mass to express the stability and the unbalance response solved by the fourth order Runge–Kutta method of the rotor are calculated based on dynamic equations. The results indicate that shallower and longer groove textures can improve the direct stiffness along the load direction kyy, weaken the stiffness in the orthogonal direction kxx, improve stability and decrease the unbalance response amplitude of the water-lubricated bearing–rotor system at a greater rotational speed and smaller eccentricity ratio; however, the impact of grooves on damping parameters is not as great as it is on stiffness—there exists an optimum groove width to achieve a best dynamic performance.

Rotordynamic Characteristics Analysis for an aero-engine Low Pressure Rotor Rig Test Model

3D whole engine finite element model of a low pressure rotor rig test model is established in this paper. Rotorynamic characteristics are mainly analysed with three models, which include rotor model with static stiffness, rotor model with dynamic stiffness, and whole engine model. The calculation results were compared and discussed deeply. Rotordynamic characteristics of rotor model with static stiffness are similar with the rotor model with dynamic stiffness, but the latter may have additional resonance peaks caused by dynamic stiffness. Whole engine model, which can capture the modes of casing and coupling vibration between stator and rotor, may have more critical speeds than rotor model only. The unbalance response amplitude and phase angle of the whole engine model are different with the only rotor model, in the values and distributions of the peaks. The result of rotor model with dynamic stiffness is closed to the whole engine model than the rotor model with static stiffness. The peak values of the whole engine model are smaller than the only rotor model. Rotordynamic characteristics with whole engine model are more accurate than rotor model only, so it necessary to analyse rotordynamic characteristics with whole engine model in detail design stage.

Dynamics of polymer and polymer composite rotors – An operator based finite element approach

This paper presents a differential time operator based approach to obtain equations of motion of a generally viscoelastic rotor–shaft after discretizing the shaft continuum with finite beam elements. The equations of motion are utilized to study dynamic behaviour of a generic viscoelastic composite rotor–shaft comprising of viscoelastic reinforcing fibres in a viscoelastic matrix. Anelastic Displacement Field model (ADF), a time-domain material model, is used to represent the viscoelastic constitutive relationships. The model parameters are extracted by a Genetic Algorithm based optimisation procedure from frequency-dependent values of storage and loss modulii. For an example the composite rotor is assumed to be made by reinforcing unidirectional long graphite fibres in a PVC (Poly-Vinyl-Chloride) matrix. The equations of motion are used for numerical simulation as well as comparison of stability limit of spin speed and unbalance response amplitude at the disc of two rotor–shaft systems, one made of pure PVC and the other made by reinforcing graphite fibres in the PVC matrix. It is concluded that reinforcement of long fibre, enhances the stability limit of spin speed as well as the first natural frequency in comparison with those of rotor–shaft made of pure PVC.

Influences of bearing housing nonconcentricity on vibration characteristics of rolling element bearing–rotor system

A rotor–cylindrical roller bearing system is investigated in this paper. The applied loads and moments acting on the bearings due to the bearing housing nonconcentricity are calculated by analyzing mechanics and deformation of the bearing. Taking the effect of nonconcentricity of bearing housings into consideration, an analytical vibration model for the rotor–bearing system is developed by modifying the transfer matrix method. Afterwards, this vibration model is applied in a rotor–bearing system example and the numerical solution of the model is carried out for analyzing the effects of nonconcentricity of the bearing housings on the system vibration characteristics. By simulation, some dynamic curves of the rotor–bearing system are obtained. It is found that the natural frequencies, the amplitude of unbalance response, and the position of the peak amplitude of the system vary with the increase of degree of misalignment between two bearing housings.

Analysis of Unbalanced Response for Coupled Double-Rotor Spindle System of High Speed Grinder

This study was focused on the theoretical modeling and numerical simulation about the unbalanced response for coupled double-rotor spindle system of high speed grinder. Based on the rotor dynamics, a theoretical model was established using the transfer matrix method. The moment balance equations, and the transition matrix, the state vector, field matrix of coupled double-rotor spindle system of high speed grinder were analyzed and calculated. The numerical results showed that the amplitude of unbalance response increased by the same multiple as that of the amount of unbalance at different locations and at different speeds. Furthermore, the position most sensitive to the unbalance was the front end of rotor 2, followed by the middle and back end of rotor 2. Rotor 2 was especially sensitive to unbalance. Moreover, the vibration amplitudes of the front end, front and back bearings of rotor 1 increased in response to unbalanced increase of rotate speed. The vibration amplitude abruptly increased at 17500r/min corresponding to first-order critical speed.

Influence of unbalanced response of ultra-high speed grinder spindle on dynamic performance

This study was focused on the theoretical modelling and numerical simulation about the unbalanced response of spindle system of ultra-high speed grinder. Based on the rotor dynamics, a theoretical model was established using the transfer matrix method. The moment balance equations, and the transition matrix, the state vector, field matrix of spindle system of ultra-high speed grinder were analysed and calculated. The results showed that the amplitude of unbalance response increased by the same multiple as that of the amount of unbalance at different locations and at different speeds. Furthermore, the first order amplitude increased first and then decreased, and the maximum unbalance was located at the middle of the rotor; second order amplitude decreased first and then increased, and the maximum unbalance was located at the front end of the spindle; the third order amplitude decreased first and then increased, and the maximum unbalance was located at the back end of the spindle.

Mathematical Model of Unbalanced Response of Spindle System of Ultra-High Speed Grinder

This study was focused on the theoretical modeling and numerical simulation about the unbalanced response of spindle system of ultra-high speed grinder. Based on the rotor dynamics, a theoretical model was established using the transfer matrix method. The moment balance equations, and the transition matrix, the state vector, field matrix of spindle system of ultra-high speed grinder were analyzed and calculated. The results showed that the amplitude of unbalance response increased by the same multiple as that of the amount of unbalance at different locations and at different speeds. Furthermore, the first order amplitude increased first and then decreased, and the maximum unbalance was located at the middle of the rotor; second order amplitude decreased first and then increased, and the maximum unbalance was located at the front end of the spindle; the third order amplitude decreased first and then increased, and the maximum unbalance was located at the back end of the spindle.

Reduced model of a rotor-shaft system using modified SEREP

A modified System Equivalent Reduction Expansion Process (SEREP) is reported to reduce large linear system-equations of motion, which also include gyroscopic effect, internal and external damping. The process is employed on equations of motion written in state-space and utilizes both right and left eigenvectors of the original system unlike only the former in conventional SEREP approach. Numerical example with a finite element model representing multi-disc rotor-shaft-bearing-dynamics shows effectiveness of the process. Nice agreement of Campbell diagrams, FRF plots and unbalance response amplitude between reduced and original systems show usefulness of the reduction process.