Campbell Diagram Research Articles

Whirling frequencies of rotor systems using ANSYS APDL

Whirling is one important type of vibrations that may cause fatigue failure to a rotor system. The whirling natural frequencies of the system depend very much on the stiffness, damping, mass and constraints imposed to the system. In this study, a modal analysis for whirling type vibration has been conducted on rotor systems using finite element method software of ANSYS APDL to determine the whirling frequencies of the rotor systems. Two cases of rotor system have been considered: a simple shaft with rigid bearing and a disc-shaft system with rigid bearing. Through the second case, the work is validated by comparing the system whirling frequency with past work. Further, through the second case also, parametric studies were conducted to investigate the impact of variation of shaft diameter, bearing and disk parameters on the vibration characteristics of the rotor system. Campbell diagrams have been generated to provide the difference in whirling frequencies of the rotor systems with respect to spin speeds while providing the critical speeds of the rotor system. It was found that in the first case, the Campbell diagram generated followed the supposed theoretical form while the results in the second case agreed well with past results. The parametric studies conducted showed that the several modes of whirling natural frequency depended on the shaft diameter, location of the disc and the mass of the disc.

Modal analysis strategy and nonlinear dynamic characteristics of complicated aero-engine dual-rotor system with rub-impact

This paper aims to gain insight into the nonlinear modal characteristics and the possible influence of the modes on the responses for the practical dual-rotor system with rub-impact in aero-engine. The finite solid element method combined with a constraint stiffness model produced by rub-impact is introduced to build the governing equation of the complicated nonlinear dual-rotor system. In order to deal with the efficiency and numerical divergence in the process of solving the nonlinear modes of this large-scale nonlinear system, an analysis strategy is proposed by integrating a two-layer reduction technique into the harmonic balance method. The effectiveness of the analysis strategy is validated by applying to a simple rotor system, which can easily obtain the theoretical result. Based on the modeling method and analysis strategy, the modal characteristics of an aero-engine dual-rotor system with rub-impact are revealed. The results show that the modal frequency of the dual-rotor system increases when rub-impact occurs and has the feature of interval, which allows us to obtain the critical speeds of the rubbing system by traditional Campbell diagram. The rotation direction is an important factor since it can not only affect the gyroscopic effect but also change the friction effect of the rub-impact. It is found that the modal frequencies of the counter-rotation dual-rotor are less than those of co-rotation condition. More importantly, the forward modes of the counter-rotation dual-rotor may be instable when rub-impact occurs at a certain rotor, while the corresponding modes under the co-rotation condition are always stable. Furthermore, by analyzing the rubbing response of the dual-rotor, it is found that the modal characteristics have an important influence on rotor’s response. The instable forward modes existing in the counter-rotation dual-rotor may lead to the divergence of the response when passing the corresponding critical speed.

Deformation and vibration analysis of compressor rotor blades based on fluid-structure coupling

Under the influence of aerodynamic and rotational load, deformation and vibration could occur to rotor blades of axial compressor, which may cause fatigue fracture, and threaten the exist of tip clearance because it is the assurance of operation safety by separating the rotor from the case. The overall performance will be deteriorated by the change of blade shape due to the deformation and vibration. Three different materials, titanium alloy, aluminum alloy and stainless steel are compared quantitatively under various operating conditions by fluid-structure coupling method. First the CFD method is validated by experimental data, the obtained pressure distribution on blade surface is exerted to the structure as boundary condition, then deformation characteristic and the corresponding maximum equivalent stresses are analyzed, at last vibration modal is analyzed and resonance points, the main reason for the vibration-induced failure, are predicted by Campbell diagrams. The results show that deformation increases with rotation speed and outlet pressure; the aluminum alloy has the largest deformation of the three materials. The equivalent stress of the blade is mainly caused by rotation, large stress regions are often near the blade root. The tip clearance of rotor blades can be reduced by deformation in the radial direction, for titanium and aluminum alloy blade, the maximum stretched length of blade at 100% rotation can account for 30% of the designed tip clearance. Centrifugal loading is the main reason for the increase of natural frequency while the increased amplitude with rotation speed is extremely small compared to the first order natural frequency.

Effective Rotordynamics Analysis of High Speed Machine Tool Spindle – Bearing System

The work is focused on computation of high speed rotor bearing system using XLrotor. The spindle-bearing system which is considered as the most significant component of machine tool, due to its dynamic behavior at varying speeds affects machining productivity and quality. Therefore at design and development stage it is necessary to know the dynamic forces acting on rotor model that causes resonance. The XLrotor advanced computational method is adopted for analysis to assess, investigate and evaluate the performance of spindle- bearing system. The XLrotor tool performs effectively the complete rotordynamic analysis which determines Undamped Critical Speeds (UCS), Campbell diagrams, Imbalance Response and Load on Bearings at Imbalance. For rotor model, the balance correction masses and locations is calculated from measured vibration signature and balancing is carried out for spindle – bearing system as part of corrective measure using XLrotor.

A comparative dynamic analysis of rotor involving three engineering materials applying finite element analysis (FEA) simulation

The purpose of this study is to facilitate engineering applications and allied researches by presenting a detailed comparative picture based on dynamic analysis of Jeffcott rotor, diameter 32 mm for three materials, namely low carbon steel, SAE1045, and SAE5120 employing finite element analysis simulation software, ANSYS. The authors covered modal, harmonic response, and transient analyses along with natural frequencies and whirling speeds at different modes. Resonance occurrence speeds are also analyzed using the Campbell diagram. The harmonic response is investigated, with added material (0.1 kg) on the disc, to reveal the stresses and deformation. Transient analysis is performed with time-varying loads to work out stresses. FEA is carried out to estimate critical speeds for these three materials. The result highlights that SAE5120 exhibits the least resonance with a high value of natural frequency. Similarly, Campbell diagrams reveal no instabilities with a majority of critical speeds at the backward whirl, thus modal-based analysis confirms the superiority of SAE5120. Stress analysis involving harmonic responses also supports SAE5120 as the stress values are very high for both SAE1045 and SAE5120. The transient analysis involving equivalent, principal, and shear stresses supports the above results. The study compares and establishes the overall usefulness of SAE5120 for rotor applications among three materials.

ВЛИЯНИЕ ГАЗА В ЗАЗОРАХ ЛАБИРИНТНЫХ УПЛОТНЕНИЙ НА ДИНАМИЧЕСКОЕ СОСТОЯНИЕ РОТОРА

When transporting natural gas over long distances, it is necessary to build gas compressor stations that compensate for the gas energy losses due to friction. The uninterrupted supply of natural gas to consumers depends on their reliability. Current trends in increasing power with a simultaneous decrease structure stiffness leads to the occurrence of previously unpredictable oscillations of the compressor rotor. The article describes the main causes of compressor rotor vibrations and some methods of dealing with them. Due to the limitations of the considered phenomena with this methods, the article proposes the use multiphysics modeling of gas and structure interaction using the 2FSI approach. Simulation performed for a simplified labyrinthseal compressor rotor model. To solve the problem, the ANSYS software product was chosen, which implements the 2FSI method. The calculations were carried out on a high-performance computing complex PNRPU. For the model structure, an analysis of natural frequencies is performed and a Campbell diagram is constructed. The trajectories analysis of a point on shaft rotation axis at different rotation frequencies of the rotor is carried out. The influence of the imbalance on the dynamics of the system is noted. Further, the results of numerical modeling of the structure taking into account gas dynamics are presented and the results comparison by dynamic modeling of the structure is carried out. To identify the factors influencing the rotor dynamics, taking into account gas dynamics, numerical calculations were carried out with various options for taking into account the effect of gravity and imbalance.

The Evaluation of Structural Safety of Impeller Using FEM Simulation

As modern industries are highly being developed, it is required that mechanical parts have to be manufactured with a high precision. In order to have precise parts, error-free designs have to be done before manufacturing with accuracy. For this intention being fulfilled, a mechanical analysis is essential for design proof. Nowadays, FEM simulation is a popular tool for verifying a machine design. In this paper, an impeller, being utilized in a compressor or an oil mixer as an actuator, is studied for an evaluation. The purpose of this study is to present a safety of an impeller for a proof of its mechanical stability. A static analysis for stress, strain, and deformation within a regular usage is examined. This simulation test shows 357.26×106 Pa for maximum equivalent stress and 0.207mm for total deformation. A fatigue test is carried to provide durability and its result shows that minimum safety factor is 3.2889, which guarantees that it runs without a fatigue failure in 106 cycles. The natural frequencies for the impeller is ranged from 228.09Hz to 1,253.6Hz for the 1st to the 6th mode. Total deformations at these natural frequencies are shown from 6.84mm to 12.631mm. Furthermore, Campbell diagram reveals that a critical speed is not found throughout regular rotational speeds. From the test results for the analysis, this paper concludes that the suggested impeller is proved for its mechanical safety and good to utilize at industries.

The effect of estimating chest wall compliance on the work of breathing during exercise as determined via the modified Campbell diagram.

The modified Campbell diagram provides one of the most comprehensive assessments of the work of breathing (Wb) during exercise, wherein the resistive and elastic work of inspiration and expiration are quantified. Importantly, a necessary step in constructing the modified Campbell diagram is to obtain a value for chest wall compliance (CCW). To date, it remains unknown whether estimating or directly measuring CCW impacts the Wb, as determined by the modified Campbell diagram. Therefore, the purpose of this study was to evaluate whether the components of the Wb differ when the modified Campbell diagram is constructed using an estimated versus measured value of CCW. Forty-two participants (n = 26 men, 16 women) performed graded exercise to volitional exhaustion on a cycle ergometer. CCW was measured directly at rest via quasistatic relaxation. Estimated values of CCW were taken from prior literature. The measured value of CCW was greater than that obtained via estimation (214 ± 52 mL/cmH2O vs. 189 ± 18 mL/cmH2O; P < 0.05). At modest-to-high minute ventilations (i.e., 50-200 L/min), the inspiratory elastic Wb was greater and expiratory resistive Wb was lower, when modified Campbell diagrams were constructed using estimated compared with measured values of CCW (P = 0.001). These differences were however small and never exceeded ±5%. Thus, although our findings demonstrate that estimating CCW has a measurable impact on the determination of the Wb, its effect appears relatively small within a cohort of healthy adults during graded exercise.

Nonlinear Analysis of Rod Fastened Rotor under Nonuniform Contact Stiffness

Rod fastened rotor is widely used in gas turbine, aero engine, and other occasions. The bending stiffness of the contact interface directly affects the stable operation of the rotor. Dynamic model of the rod fastened rotor-bearing system has been established considering nonuniform stiffness of interface. The motion equation of this system has been deduced from Lagrange’s equations. The linear dynamic characteristics of this rotor has been investigated, such as Campbell diagram, critical speed, and formation, and the nonlinear characteristics of this system, such as chaos and bifurcation, has been investigated too. The result shows that “bistable state” characteristic appeared on the rod fastened rotor system; that is, there are two critical speeds for each order, and they are all positive precession critical speed, and the amplitude response to the lower critical speed is much larger than that its counterparts to the higher critical speed. In terms of nonlinear characteristics, the rod fastened bearing system has experienced periodic 1 motion, multiple periodic motion, quasi-periodic motion, periodic 1 motion, and chaotic motion successively.

Experimental Analysis of Noise Characteristics of Electric Agricultural Utility Terrain Vehicle Gearbox

Noise and vibration measurement tests have been performed to analyze the source of noise in a utility terrain vehicle (UTV) gearbox to improve its quality. For accurate analysis of gearbox noise source, the effects of other test equipment should be separated from the gearbox noise results. In this study, the noise source of the gearbox was investigated through noise and vibration tests of the gearbox and dynamometer. Noise and vibration were measured during gearbox and dynamometer run-up tests. Dominant noise types were identified through order tracking analysis of the test results. Some types of noise were identified in the Campbell diagram. By separating the effect of the inverter and dynamometer noise, it was confirmed that the 6.39th-, 12.78th-, 14th-, and 28th-order components were the sources of noise generated by the gearbox. Dominant order components caused by the gearbox were identified. These components are expected to be used as excitation sources for the optimization of noise reduction in electric UTV gearboxes.

Crack growth simulation in 13th row of compressor blades under foreign object damage and resonant vibration condition

In this study, the cracks growth rate in the 13th row of the T56 compressor blades was studied to investigate their fatigue life. For this purpose, the centrifugal and aerodynamic forces on the blade were calculated and then the resulting stress field was obtained by using finite element method. Then, the critical points of stress were determined and the initial semi-elliptical cracks were modeled at these points. After modeling of the initial crack, the stress intensity factor on the crack front was calculated by ANSYS software. Furthermore, the number of required cycles for the crack growth and blade fracture were calculated by applying Paris law to a certain value. After crack growth at this stage, a crack with new length was also modeled at the same point and all the mentioned stages for its growth, were repeated. In this paper, the modal analysis of the blade was conducted and normal frequencies with possible stimulation on compressor velocity were determined by Campbell Diagram. After determining the stress field at resonant frequency, all stages of crack growth were repeated under these conditions to calculate the fatigue life.

Numerical Study for Comparison of Pseudo Modal and Direct Method in Predicting Critical Speed of Coaxial Dual Rotor System

Machines with high speed rotation, high power, and lighter weight are the challenge in design of modern rotation machinery. In analysis of coaxial dual rotor system, the problem leads to a multi-degree of freedom system (1multi-DOF). The resulting equation of motion cannot be solved analytically. For multi-DOF system, numerical method has to be implemented. In this study, the equations of motion of co-axial dual rotor system was solved numericallyusing MATLAB programming language. This study compares the result of two methods used: the pseudo-modal method and the direct method, with the aim of getting the most effective method in predicting critical rotational speedby plotting Campbell diagram. It was foundthat the difference in the value of critical speeds between Pseudo Modal and the Direct Method is 0%-9,56% for the first 6 lowest frequencies and 0.09%-3.58% for the first 8 lowest frequencies.

Design and Dynamic Analysis of a Compact 10 MW Medium Speed Gearbox for Offshore Wind Turbines

Abstract This paper deals with the design of a compact gearbox for the DTU 10 MW reference offshore wind turbine. An innovative gearbox concept consisting of a fixed planetary stage and a differential compound epicyclic stage is proposed. Power splitting and compound epicyclic transmission technologies are employed, which can effectively reduce the gearbox size. The power transmission principle of the gearbox is described and power distribution ratios in two transfer paths are calculated via the geometrical and mechanical relationships among the gearbox components. The gearbox is designed based on the design loads and fatigue criteria by referring to relevant international standards. A high-fidelity drivetrain numerical model is established by means of a multi-body system (MBS) approach. Then, the power distribution ratios in two transfer paths are compared between the simulation results and the design values with a good agreement. Resonance analysis of the drivetrain model is conducted by means of the Campbell diagram and energy distribution of components, and the results show that no severe resonance phenomena appear in this drivetrain model. Additionally, the load-sharing behavior of the gearbox model is assessed under different environmental conditions, and the results indicate that the compact gearbox has a good load-sharing performance. Such a compact gearbox design, which fulfills all the design requirements for offshore applications, could be a good alternative for offshore wind turbines.

A novel methodology for analyzing modal dynamics of multi-rotor wind turbines

A multi-rotor wind turbine (MRWT) is accepted as a novel solution in reducing the rotor size without decreasing the energy harvesting capability compared to a single-rotor wind turbine (SRWT). However, there is no systematic methodology available for obtaining the modal properties of MRWTs. This paper presents a novel methodology and systematic modeling method of modal dynamics with comprehensive numerical simulations and analyses of MRWTs. In the methodology, Coleman transformation is employed to convert the nonlinear time-variant dynamics formulation of a MRWT into a set of linear time-invariant dynamic equations. Using HAWC2 and HAWCStab2 a method to establishing high-fidelity linear time-invariant dynamic models is presented. The structural modal dynamics of a tri-rotor wind turbine is systematically investigated by using modal analysis theory and interpreting the rotor speed-dependent dynamics visualized in a Campbell diagram. The investigation shows that rotor modes on a MRWT have similar behavior as for a SRWT and that low torsional stiffness of the rotor attachment point affects the first flapwise backward whirling modes by decreasing the corresponding natural frequencies. Moreover, the low torsional stiffness results in a delayed splitting of the asymmetric flapwise rotor modes. The simulations and analyses result verified the proposed dynamic modeling method. The major contributions in this paper provide the essential insights and guidance in the design of MRWTs but also for SRWT with slender towers.

Dynamic Analysis of Low-Pressure Steam Turbine Last Stage Fir-Tree Root Blade

Abstract In the present study, the dynamic behavior of the last stage low-pressure steam turbine blade with fir-tree root at different conditions of blade root flank faces and their interfaces with rotor groove have been analyzed. Modal analysis has been done using a finite element approach to evaluate natural frequencies and evaluation of Campbell diagram generated under these conditions. For this, both healthy and defective blade have been taken. Since the variable crack size of fir-tree root flank has been taken, the excitation pattern has been evaluated due to stiffness variation of the cracked blade. This analysis provides the basis of excitation pattern of cracked blades due to inherent character and critical stressed zone. The outcome of this study forms the guidelines and checks during the fitting of blades in rotor assembly and its checks during health audit, overhaul, overspeed balancing test, and frequency turning.

Development of Pump-Drive Turbine Module with Hydrostatic Bearing for Supercritical CO2 Power Cycle Application

The turbomachinery used in the sCO2 power cycle requires a high stable rotor-bearing system because they are usually designed to operate in extremely high-pressure and temperature conditions. In this paper, we present a pump-drive turbine module applying hydrostatic bearing using liquid CO2 as the lubricant for a 250 kW supercritical CO2 power cycle. This design is quite favorable because stable operation is possible due to the high stiffness and damping of the hydrostatic bearing, and the oil purity system is not necessary when using liquid CO2 as the lubricant. The pump-drive turbine module was designed to operate at 21,000 rpm with the rated power of 143 kW. The high-pressure liquid CO2 was supplied to the bearing, and the orifice restrictor was used for the flow control device. We selected the orifice diameter providing the maximum bearing stiffness and also conducted a rotordynamic performance prediction based on the designed pump-drive turbine module. The predicted Campbell diagram indicates that a wide range of operation is possible because there is no critical speed below the rated speed. In addition, an operation test was conducted for the manufactured pump-drive turbine module in the supercritical CO2 cycle test loop. During the operation, the pressurized CO2 of the 70 bar was supplied to the bearing for the lubrication and the shaft vibration was monitored. The successful operation was possible up to the rated speed and the test results showed that shaft vibration is controlled at the level of 2 μm for the entire speed range.

High-frequency unsteady flow near the tip in a transonic fan rotor with a small clearance

This research presents a half-annulus simulation of a wide-chord transonic fan rotor to investigate a high-frequency unsteady flow phenomenon near the tip region. The evolution and underlying mechanism of the unsteady flow are revealed. And the results show the dominant frequency of flow to be about 1.356fBPF. The periodic low-speed region originating from the tip causes a blockage after passing the shock wave. Part of the low-speed region bypasses the leading edge of the adjacent blade to enter the next passage, and another part moves downstream along the pressure side, causing separation fluctuations near the suction side. By decomposing the pressure, the propagation pattern of the pressure upstream, downstream, and on the blade surface is revealed. Through the visualization method, the vortex structure in the passage is clearly displayed. A C-shaped vortex tube and two branches with opposite directions form a vortex unit, which propagates downstream along the pressure side. Because the flow and blade frequencies are very close, the potential coupling vibration risks are discussed using the Campbell diagram.

Wind turbine stability: Comparison of state-of-the-art aeroelastic simulation tools

As rotor diameters and blade flexibility are increasing, current and future generation wind turbines are more susceptible to aeroelastic instabilities. It is thus important to know the prediction capabilities of state-of-the-art simulation tools in regards of the onset of aeroelastic instability. This article presents results of a code-to-code comparison of five different simulation codes using a representative wind turbine model. It is shown that the models are in good agreement in terms of isolated structural dynamics and steady state aeroelastics. The more complex the test cases become, the more significant are the differences in the results. In the final step of comparison, the aeroelastic stability limit is determined through a run-away analysis. The instability onset is predicted at different wind speeds and the underlying mechanisms differ between the tools. A Campbell diagram is used to correlate the findings of time domain simulation tools with those of a linear analysis in the frequency domain.

Modal Analysis of a Quad-Rotor Wind Turbine

Unlike Single-Rotor wind turbines, stability analysis of Multi-Rotor wind turbines is still in its initial stages. This paper presents the modal analysis of a Quad-Rotor wind turbine and identifies the new modes or possible instability modes that are otherwise not present on a Single-Rotor wind turbine. Multi-Blade Coordinate transformation scheme is adapted to a Quad-Rotor wind turbine to write the system’s equation of motion in fixed-reference frame followed by Eigenvalue analysis to determine the natural frequencies and mode shapes of the Quad-Rotor wind turbine. A Campbell diagram of the Quad-Rotor wind turbine is presented. Results indicate that the Quad-Rotor turbine is soft-soft to the first tower modes (fore-aft, side-side, and torsion). Furthermore, the modes with low natural frequency other than the tower modes are a combination of tower, boom, and blade modes. Therefore, due to the presence of blade modes, the modal frequency of these modes increases or decreases with increasing rotor speed due to centrifugal stiffening.

Reverse Trigger Phenotypes in Acute Respiratory Distress Syndrome.

Rationale: Reverse triggering is an underexplored form of dyssynchrony with important clinical implications in patients with acute respiratory distress syndrome.Objectives: This retrospective study identified reverse trigger phenotypes and characterized their impacts on Vt and transpulmonary pressure.Methods: Fifty-five patients with acute respiratory distress syndrome on pressure-regulated ventilator modes were included. Four phenotypes of reverse triggering with and without breath stacking and their impact on lung inflation and deflation were investigated.Measurements and Main Results: Inflation volumes, respiratory muscle pressure generation, and transpulmonary pressures were determined and phenotypes differentiated using Campbell diagrams of respiratory activity. Reverse triggering was detected in 25 patients, 15 with associated breath stacking, and 13 with stable reverse triggering consistent with respiratory entrainment. Phenotypes were associated with variable levels of inspiratory effort (mean 4-10 cm H2O per phenotype). Early reverse triggering with early expiratory relaxation increased Vts (88 [64-113] ml) and inspiratory transpulmonary pressures (3 [2-3] cm H2O) compared with passive breaths. Early reverse triggering with delayed expiratory relaxation increased Vts (128 [86-170] ml) and increased inspiratory and mean-expiratory transpulmonary pressure (7 [5-9] cm H2O and 5 [4-6] cm H2O). Mid-cycle reverse triggering (initiation during inflation and maximal effort during deflation) increased Vt (51 [38-64] ml), increased inspiratory and mean-expiratory transpulmonary pressure (3 [2-4] cm H2O and 3 [2-3] cm H2O), and caused incomplete exhalation. Late reverse triggering (occurring exclusively during exhalation) increased mean expiratory transpulmonary pressure (2 [1-2] cm H2O) and caused incomplete exhalation. Breath stacking resulted in large delivered volumes (176 [155-197] ml).Conclusions: Reverse triggering causes variable physiological effects, depending on the phenotype. Differentiation of phenotype effects may be important to understand the clinical impacts of these events.