Transmissibility Analysis of a Regenerated Rotor System

The aim of this paper is to represents a dynamic behavior of rotor bearing system wirth simply supported beam for three different position disc. rotating machinery such as compressors, turbines, pumps, jet engines, turtobo chargers, etc. are subject to vibrations. rotating machines are operated in very high speed and they are subjected to some unbalance force due to vibration from that machine pass to the foundation of machine.so the analysis of the dynamics parameter of rotor it is important to determine force transmissibility, natural frequency, critical speed and amplitudes of rotor system. Keywords: force transmissibility, vibration, critical speed, rotor bearing system etc.

Negative potential energy content analysis in cracked rotors whirl response

Appearance of transverse cracks in rotor systems mainly affects their stiffness content. The stability of such systems at steady-state running is usually analyzed by using the Floquet’s theory. Accordingly, the instability zones of rotational speeds are dominated by negative stiffness content in the whirl response in the vicinity of critical rotational speeds. Consequently, an effective stiffness measure is introduced here to analyze the effect of the crack and the unbalance force vector orientation on the intensity of negative potential and stiffness content in the whirl response. The effective stiffness expression is obtained from the direct integration of the equations of motion of the considered cracked rotor system. The proposed effective stiffness measure is applied for steady-state and transient operations using the Jeffcott rotor model with open and breathing crack models. The intensity of negative potential and stiffness content in the numerical and experimental whirl responses is found to be critically depending on the propagation level of the crack and the unbalance force vector orientation. Therefore, this can be proposed as a crack detection tool in cracked rotor systems that either exhibit recurrent passage through the critical rotational speeds or steady-state running.

Negative Potential Energy Content Analysis in Cracked Rotors Whirl Response

Appearance of fatigue cracks in rotor systems mainly affects their stiffness content. The stability of such systems at steady-state running is usually analyzed by using the Floquet’s theory. Accordingly, the instability zones of rotational speeds are dominated by negative stiffness content in the whirl response in the vicinity of critical rotational speeds. Consequently, an effective stiffness measure is introduced here to analyze the effect of the crack and the unbalance force vector orientation on the intensity of negative potential and stiffness content in the whirl response. The effective stiffness expression is obtained from the direct integration of the equations of motion of the considered cracked rotor system. The proposed effective stiffness measure is applied for steady-state and transient operations using the Jeffcott rotor model with open and breathing crack models. The intensity of negative potential and stiffness content in the numerical and experimental whirl responses is found to be critically depending on the propagation level of the crack and the unbalance force vector orientation. Therefore, this can be proposed as a crack detection tool in cracked rotor systems that either exhibit recurrent passage through the critical rotational speeds or steady-state running.

Vibration Mechanism and Compensation Strategy of Magnetic Suspension Rotor System under Unbalanced Magnetic Pull

The existing imbalance compensation strategies for magnetic suspension motors mainly focus on the mass unbalance force, ignoring the effects of the unbalanced magnet pull (UMP). This paper studied the vibration mechanism and compensation strategy of magnetic suspended permanent magnet synchronous motor (PMSM) under the influence of UMP. Firstly, an analytical model of the flux density was established based on equivalent magnetic circuit method, then the analytical expressions of UMP was deduced by Maxwell stress tensor method. Furthermore, an unbalanced compensation method based on hypothetical reference frame (HRF) transformation was proposed. The stability of the closed-loop system with compensation was analyzed based on the complex-coefficients theory. The proposed model and compensation strategy were verified by the simulations and experiments. The results indicate that the proposed compensation strategy can achieve effective suppression of the magnetic rotor vibration.

Non-Uniform Three-Dimensional Pulsating Heat Pipe for Anti-Gravity High-Flux Applications

This study proposes a novel high-flux pulsating heat pipe that can lift the major constraint of the conventional pulsating heat pipe (PHP) which is unable to function properly upon anti-gravity operations. The proposed PHP introduces additional unbalance force via uneven tube diameter/geometry in the adiabatic sections to tailor the problem in anti-gravity operation. The design contains a three-dimensional configuration circuitry with compact arrangement tubes on the evaporator and condenser. Through this design, the non-uniform three-dimensional pulsating heat pipe (3D-PHP) manipulates the uneven inner diameters of the adiabatic sections to form uneven vapor/liquid distributions in the adiabatic sections to yield a unitary flow pattern that is able to withstand a much higher input power. The present PHP uses methanol as working fluid, with 38% volumetric filling ratio, and has a high-flux of 22.9 W/cm2 and a low the thermal resistance ratio (Ranti-gravity/Rgravity-assisted) of 1.05 when the input power is 800 W. Both the heat flux and thermal resistance ratio for the proposed design are far better than the existing literature.

Dynamic analysis of rotor-bearing system by considering the transverse crack on rotor

In this study, a new improved theoretical model of rotorbearing system has been presented to analyse the behaviour of the system due to the transverse crack on the rotor. Firstly, a mathematical model of the system with a transverse crack on rotor has been developed. In the modelling, the rotor is taken as Timoshenko beam and the unbalance force also included, which vary with rotating speed. The rotor is supported by two healthy deep groove ball bearing at both ends. The contact between balls and races of the bearings is considered as nonlinear spring, whose stiffness is obtained by Hertzian contact deformation theory. After the modelling of the rotor, the equation of motion has been derived which represents the dynamic behaviour of the system. Bifurcation diagrams are used to investigate the influence of depth and size of the crack on the dynamic behaviour of rotor ball-bearings system. Results indicate that if the depth and size of the crack increase the system becomes highly chaotic and unstable.

Effect of Angular Acceleration and Unbalance Force Orientation on the Backward Whirl in Cracked Rotors

Rotors have wide applications in several aerospace and industrial heavy-duty systems. In most of these applications, the rotating system reaches its steady state operational speed after the passage through at least one of its critical rotational speeds. In real-life applications, the probable appearance of a residual slight unbalance in the system could cause an elevation in vibration amplitudes at the critical rotational speeds. Accordingly, propagation of cracks in rotating shafts usually influences the level of these vibration amplitudes during start-up and cost-down operations. For such rotating systems, the critical whirl speeds are usually associated with forward and backward whirl responses where it has been always assumed that the backward whirl zone should precede the forward whirl zone. Here, two configurations of cracked rotor-disk systems are considered to study the effect of the angular acceleration and the unbalance force vector orientation with respect to the crack opening direction on the whirl response at the backward whirl zone of rotational speeds. The obtained numerical simulation results are verified through a robust experimental testing for system startup operations. The backward whirl zone is found here to appear immediately after the passage through the critical forward whirl rotational speed. The onset of the backward whirl is also found to be associated with a sharp drop in vibration whirl amplitudes. This backward whirl zone is found to be significantly affected by the unbalance force angle vector orientation and the shaft angular acceleration. More importantly, this zone of backward whirl orbits is not found to be preceding the critical forward whirl zone for the considered cracked shaft-disk configurations.

Negative Effective Stiffness Content in Cracked Rotors

The appearance of cracks in rotor systems affects the whirl response in the neighborhood of the critical whirl rotational speeds. The combined effect of the crack depth and the unbalance force vector angle orientation with respect to the crack opening direction on the effective stiffness content of the cracked rotor system in the neighborhood of the critical rotational speed is addressed here. The effective stiffness expression of the cracked system can be obtained from the direct integration of the equations of motion of the cracked rotor system. The cracked rotor equations of motion can be expressed by the Jeffcott rotor or the finite element models. The appearance of cracks in rotor systems converts them into parametrically excited dynamical systems with time-periodic stiffness components. The interaction between the time-periodic stiffness and the external periodic forcing function of the unbalance force significantly alters the effective stiffness content in the system at both transient and steady state operations. For wide range of crack depths and unbalance force vector angles, the effective stiffness has been found to be of negative values. This means that the cracked rotor system tends to have more resistance to deflect towards the center of its whirl orbit and less resistance to deflect away under the unbalance force excitation effect. Consequently, in the negative stiffness content zone of the unbalance force vector angles, the cracked rotor system tends to exhibit a sharp growth in the vibration whirl amplitudes. However, for positive effective stiffness values, the shaft has more resistance to deflect away from its whirl orbit center. Therefore, the cracked rotor system is at higher risk of failure in the negative effective stiffness zone of unbalance force vector angles than the positive effective stiffness zone of these angles.

Effect of Unbalance Force Vector Orientation on the Whirl Response of Cracked Rotors

The combined effect of a crack with unbalanced force vector orientation in cracked rotor-bearing-disk systems on the values and locations of critical whirl amplitudes is numerically and experimentally investigated here for starting up operations. The time-periodic equations of motion of the cracked system are formulated according to the finite element (FE) time-varying stiffness matrix. The whirl response during the passage through the critical whirl speed zone is obtained via numerical simulation for different angles of the unbalance force vector. It is found that the variations in the angle of unbalance force vector with respect to the crack opening direction significantly alters the peak values of the critical whirl amplitudes and their corresponding critical whirl speeds. Consequently, the critical speeds of the cracked rotor are found to be either shifted to higher or lower values depending on the unbalance force vector orientation. In addition, the peak whirl amplitudes are found to exhibit significant elevation in some zones of unbalance force angles whereas significant reduction is observed in the remaining zones compared with the crack-free case. One of the important findings is that there exists a specific value of the unbalance force angle at which the critical whirl vibration is nearly eliminated in the cracked system compared with the crack-free case. These all significant numerical and experimental observations can be employed for crack damage detection in rotor systems.

Application of the Proper Orthogonal Decomposition Method for Cracked Rotors

The application of the proper orthogonal decomposition (POD) method to the vibration response of a cracked rotor system is investigated. The covariance matrices of the horizontal and vertical whirl amplitudes are formulated based on the numerical and experimental whirl response data for the considered cracked rotor system. Accordingly, the POD is directly applied to the obtained covariance matrices where the proper orthogonal values (POVs), and the proper orthogonal modes (POMs) are obtained for various crack depths, unbalance force vector angles, and rotational speeds. It is observed that both POVs and their corresponding POMs are highly sensitive to the appearance of the crack and the unbalance force angle direction in the neighborhoods of the critical rotational speeds. The sensitivity zones of the POVs and POMs to the crack propagation are found to be coinciding with the unstable zones found by the Floquet's theory of the considered cracked system.