Thermal Bow Research Articles

Design equations for thermal bowing and composite degree of concrete sandwich panels

Concrete sandwich panels (CSPs) are oftentimes subjected to extreme exterior temperatures, causing thermal gradients between inner and outer surfaces, and eventually bowing. In addition, the composite degree (kp) of CSPs has been conventionally estimated using methods that require costly and time-consuming experimental tests or rigorous numerical models. The lack of research and understanding on the effects of kp and bowing oftentimes result in overly conservative and uneconomic design, particularly for partially composite (PC) panels. This study develops simple design equations for thermal bowing and kp in CSPs based on a comprehensive parametric study using a transient thermal-structural coupled finite element (FE) model developed earlier by the authors. Key parameters considered are span (L); connector configuration, material, and reinforcement ratio; wythe and insulation thicknesses; concrete strength and thermal differential (ΔT) on both sides. In panels with L larger than 13 m, particularly those featuring steel and CFRP truss connectors and subjected to temperature gradients (ΔT) higher than 30 °C, bowing was larger than the deflection serviceability limit of L/360. Cracking in concrete wythes and yielding of steel connectors were also observed and were mainly dependent on ΔT and kp. Two existing theoretical models were evaluated using results of the parametric analysis and were found to overestimate thermal bow, particularly for panels with low kp. A proposed bowing model is presented which incorporates the effects of composite degree and yields much better predictions than these from literature.

Influence of geometrical design on the cooling process of double annular turbine section

The article describes the issue of gas turbine cooling after operation. Due to natural convection, an asymmetric temperature distribution occurs in the double annulus, which has a significant effect on the thermal bow of the rotor. At the same time, the desire to minimize radial clearances as this brings the advantage of higher engine efficiency is nowadays essential. On the other hand, it also requires the ability to understand and predict the cooling transient to avoid critical failures during engine restart. Based on a real engine, an experimental facility was designed to represent a simplified double annulus flow path in a section of the turbine flow path. Experimental measurements were performed and a computational model of natural convective flow during gas turbine cooling was developed. The time dependence of the temperature fields was observed and compared with computational model. Furthermore, the dependence of the temperature differences between the upper and lower double annulus was presented. The computational study is carried out with different geometrical setups, which were also validated by experimental measurements. It is shown that the thermal gradient of the rotor due to natural convection can be significantly affected by the choice of geometry and other constraints in this region. The results of the study showed several options to mitigate the rotor bow of a gas turbine. The applicability of the results may have a significant influence on the design and development of gas turbines nowadays.

Finite Element Analysis of Bent Rotors

Abstract The rotating components of a gas turbine engine are typically designed around a perfectly straight centerline. In spite of advanced manufacturing technology and the conviction of the human eye, straightness is virtually impossible to achieve during manufacturing and assembly. High-tech metrology can quantify ever so slight centerline deviations along the unconstrained rotor assembly which are called bends. Related phenomena are rotor bow and thermal bow, the latter of which is normally due to asymmetric cooling after engine shutdown. Yet, bent and bowed rotors differ from one another in that bends are permanent deviations from the centerline of the unconstrained rotor, whereas rotor bow is temporary, typically elastic, and observed in the mounted, and, therefore, constrained rotor assembly. Greater complexity is introduced with the realization that a bent rotor can additionally be subject to rotor bow. The presence of bends leads to force and moment distributions along the rotating structure that can have significant dynamic implications for even very small bends. In opposition to unbalance loads, which increase with rotor speed, the rotating excitation of a bent rotor remains constant. The equations of motion (EOM) of a bent rotor are well defined in the literature. However, the analysis is usually confined to simplified cases where said centerline deviations at the bearing supports are zero. For realistic rotor applications, this is not the case and additional static analysis is required to obtain the proper dynamic load distribution along the rotor. In this paper, the finite element method (FEM) is used to analyze bent rotors within an MSC NASTRAN v2021 work-flow that can address rotor models of any complexity. The proposed approach can also account for static, compliant, and greatly featured support structures that communicate with the rotor model via its common, and potentially misaligned, bearing supports. Angular and lateral offsets are explored in three different scenarios of two rotor configurations: scenarios 1 and 2 introduce a simply bent rotor, along which synchronous force and moment distributions are computed (due to its intrinsic deviations) to subsequently excite the bent rotor dynamically. While scenario 1 requires an initial static analysis with enforced displacements to accomplish this task, the equivalent dynamic excitation of scenario 2 can be computed directly due to perfect bearing alignment. In scenario 3, the complexity of the rotor bend is increased to four angular kinks and four lateral offsets to suggest the deployment of this method in combination with high-tech metrology equipment that can produce a large number of such measurements via automated probing or scanning technologies. In a final step, the bent rotor is augmented with unbalances and compared to its nominal counterpart to deliver the motivation for this method and its value to the turbomachinery community. All results of scenarios 1, 2, and 3 are verified against an experimentally validated transfer matrix method (TMM).

Transient rotordynamic thermal bow (Morton effect) modeling in flexure-pivot tilting pad bearing systems

The Morton effect (ME) is a thermally induced rotodynamic instability problem frequently reported in the fluid film bearing system. The temperature difference across the journal circumference may cause large spiral, synchronous vibration. Earlier ME modeling approaches rarely focus on the flexure-pivot bearing (FPB), significantly disproportionate to its wide application. Hereby, the transient ME prediction algorithm is proposed based on a high-fidelity thermo-elasto-hydrodynamic FPB model. A hybrid finite element analysis is adopted to evaluate the entire rotor thermal bow profile including the rotor midspan. The algorithm is benchmarked with experiments and applied to a realistic compressor model. Simulations confirm the proneness of the FPB system to the ME instability, and reveal the ME sensitivity to the bearing-rotor configuration and operation conditions.

An Unconventional Method for the Diagnosis and Study of Generator Rotor Thermal Bows

Abstract The rotor thermal sensitivity often affects the dynamic behavior of power unit generators. Owing to this phenomenon, increments of field current and other process parameters that are related to it may cause a shaft thermal bow and significant changes in the synchronous vibration. This symptom can also be caused by many other common malfunctions that affect rotating machines. Therefore, diagnostic techniques aimed at identifying the actual fault are very useful for optimizing maintenance activities. The thermal sensitivity of generator rotors can be deemed as a fault because it is commonly caused by a local deterioration of the winding insulation as well as by jamming phenomena between conductors and rotor slots, caused by friction forces due to the different thermal expansions of these components. This paper shows the results obtained by applying a diagnostic method, based on multiple linear regression models, which has been developed for the analysis of generator vibrations caused by thermal sensitivity. Nevertheless, nonlinear relationships between vibration and process parameters have also been taken into account. The capabilities of this diagnostic technique have been validated using the analysis of experimental data collected in a power plant. The results of this investigation are shown and discussed in the paper.

Analysis of Muara Tawar CCPP Block 1 Steam Turbine Vibration

Condition monitoring of steam turbine enables early detection of faults and avoid unexpected breakdowns. Vibration analysis has gained much attention in the field of condition monitoring because of its accuracy in detecting faults and its ability for proper diagnosis of the faults. Muara Tawar CCPP block 1 has a steam turbine generator with a capacity of 215 MW. Steam turbine roll after inspection shows high vibration occurs on bearing 1. This study aims to find the cause of this high vibration and provide recommendations to avoids such symptoms. The vibration data used in the analysis are obtained from vibration analyzer tools associated with vibration monitoring systems. It is found that the amplitude of vibration at rotational speed frequency (1X) increased and phase angle changes at a constant speed. The vibration level at the coast down is higher than the observed vibration level at run-up. There is a shift in the position of critical speed which indicates a change of rotor stiffness. It is concluded that the high vibration is likely by a thermal bow on the rotor. The thermal rotor bow is caused by a light partial rubbing between rotor and labyrinth seal on the stator.

Squeeze Film Damper Suppression of Thermal Bow-Morton Effect Instability

Abstract The Morton effect (ME) is a synchronous vibration problem in turbomachinery caused by the nonuniform viscous heating around the journal circumference, and its resultant thermal bow (TB) and ensuing synchronous vibration. This paper treats the unconventional application of the SFD for the mitigation of ME-induced vibration. Installing a properly designed squeeze film damper (SFD) may change the rotor's critical speed location, damping, and deflection shape, and thereby suppress the vibration caused by the ME. The effectiveness of the SFD on suppressing the ME is tested via linear and nonlinear simulation studies employing a three-dimensional (3D) thermohydrodynamic (THD) tilting pad journal bearing (TJPB), and a flexible, Euler beam rotor model. The example rotor model is for a compressor that experimentally exhibited an unacceptable vibration level along with significant journal differential heating near 8000 rpm. The SFD model includes fluid inertia and is installed on the nondrive end bearing location where the asymmetric viscous heating of the journal is highest. The influence of SFD cage stiffness is evaluated.

Prediction of the thermal bow of rotor based on the measured displacement and temperature

The thermal bow of the rotor occurs in the cooling process after the shutdown of the aeroengine. The deflection of the bowed rotor is the primary concern of the research on this problem. The objective of this work is to propose a method to predict the bow shape of the rotor with the measured temperature and displacement in a rotor thermal bow experiment. The experiment was introduced and the variations of the measured temperature and displacement were analyzed. A series of polynomial function was proposed to model the bowed shape of the rotor. The measured temperature and displacement were taken into considered in the constraint equations, with which the coefficients in the polynomial function were obtained. The bow shapes of the rotor at different time in the experiments were analyzed. Results showed that the maximum deflection of the rotor was much greater than the measured displacement at the sections near the rotor support. The forced cooling could reduce the thermal deflection of the rotor quickly. The analysis of the different cases of experiment indicated that the proposed method could predict the bow shape of the rotor with the measured temperature and displacement.

Case study on Detecting Rub Issue on Compressor

This case is a vibration issue on a Recycle Gas Compressor. The Machinery Diagnostics Engineer was requested on site to collect only steady state data using a multichannel data collector. When Unit was running at full load condition, vibration at Compressor suddenly increased and exceeded Alert setpoint. Operation at this condition is unsafe and can result in serious unit damage.
 This case study is designed to outline how the high vibration issue was successfully diagnosed based on a very limited set of information - only steady state data collection, the root cause for the high vibration found and correction actions were recommended and applied.
 The source of high vibration was considered as rotor unbalance, appeared due to material build up at the rotor. It was the initial issue, lead the Rubbing symptom in the compressor seals and the rotor thermal bow.
 A compressor rotor inspection was recommended. Signs of significant rubs were found. The compressor rotor was replaced. Vibration level at Unit Startup was well below OEM setpoints.

Characteristics of oil film nonlinearity in bearings and its effects in rotor balancing

Since unbalance is inherent to any rotating machine, and some effects like coupling misalignment and thermal bow, which are not taken into account in pre-balancing, can lead to changes in unbalance distribution, in-field rotor balancing is sometimes a necessary action. Traditionally, the influence coefficients method has been used as the main balancing procedure, and due to the low accessibility in assembled rotating machinery, generally only the journal displacements inside hydrodynamic bearings are available for the balancing procedure. However, influence coefficients method assumes linearity of rotor response and it is known that hydrodynamic bearings can sometimes present a strong nonlinear relationship between bearing forces and journal displacements, making balancing difficult or even impossible. Otherwise, the bearing housing vibrations are directly proportional to the bearing forces and are independent of the journal displacements, therefore avoiding problems related to oil film nonlinearities. This paper proposes the use of bearing housing accelerations as influence coefficients and verifies experimentally that balancing can be successful also in highly nonlinear oil film bearing conditions. First, the oil film nonlinear characteristics are introduced by means of a simple analytical model. Then, different behaviors have been experimentally investigated by means of a test rig rotor supported by three hydrodynamic bearings, designed to enhance oil film nonlinear effects. Nonlinear effects are quantified through deviations with respect to linear behavior and development of higher harmonics in the response of the oil film. It is shown that these effects can seriously affect the possibility of balancing with the use of influence coefficients. Finally, it has been verified experimentally that balancing with the use of bearing housing acceleration to calculate influence coefficients was successful, as expected.

A new computational method for predicting the thermal bow of a rotor

In a heavy-duty gas turbine, when hot rotor is left cooled in standstill condition, thermal bow occurs due to natural convection, which may result in high vibrations in a subsequent restart. Usually, a turning gear is immediately started after shutdown of gas turbine to slowly roll and uniformly cool the rotor in order to prevent thermal bow, which is called turning gear operation. The minimum turning time and the acceptable temperature of wheel space are two important indexes of turning gear operation, and their determination highly depends on accurate prediction of thermal bow. This paper proposes an analytical method to predict the thermal bow behavior of rotors with complex structures and investigates the effect of turning time on thermal bow. First, the general form of analytical solution of rotor thermal bow is derived and validated through both finite element analysis and experiments. Then the analytical solution is applied in a heavy-duty gas turbine to predict the most severe thermal bow behavior of the rotor with no turning gear in operation before standstill. Finally, the effect of turning time on thermal bow is investigated, and the indexes to achieve acceptable thermal bow are discussed. Results show that the shape of thermal bow of the gas turbine rotor is close to the first-order mode shape; the peak of the most severe thermal bow reaches 0.7 mm after 3.8 h of cooling and the decrease of thermal bow is much slower than the increase. Besides, the maximum thermal bow of the rotor due to insufficient turning gear operation presents an exponential decay with turning time and lies in linear relationship with the temperature of the same location. These two relationships help determine the minimum turning time and acceptable temperature of wheel space to attain an acceptable bow and thus have practical significance to develop and optimize turning gear operations.

Tilting pad gas bearing induced thermal bow- rotor instability (Morton effect)

Abstract The Morton effect ME is a thermally induced, rotordynamic instability, which is frequently reported in overhung machines supported with oil-lubricated bearings. Synchronous journal whirling results in an uneven viscous shearing of the lubricant film and temperature variation around the journal circumference. This bends the shaft and under certain conditions causes increasing synchronous vibration. Previous research focused solely on oil-lubricated bearings. A transient, high-fidelity ME methodology is presented to expand the scope to tilting pad gas bearing (TPGB) systems. Three dimensional finite element models are established to predict the rotor and bearing temperature and dynamic responses in the time domain. Simulations indicate that the ME can occur in the TPGB systems and may be sensitive to imbalance and overhung mass.

A Review of the Rotordynamic Thermally Induced Synchronous Instability (Morton) Effect

The Morton effect (ME) is a thermally induced instability problem that most commonly appears in rotating shafts with large overhung masses and supported by fluid-film bearings. The time-varying thermal bow, due to the asymmetric journal temperature distribution, may cause intolerable synchronous vibrations that exhibit a hysteresis behavior with respect to rotor speed. First discovered by Morton in the 1970s and theoretically analyzed by Keogh and Morton in the 1990s, the ME is still not fully understood by industry and academia experts. Traditional rotordynamic analysis generally fails to predict the potential existence of ME-induced instability in the design stage or troubleshooting process, and the induced excessive rotor vibrations cannot be effectively suppressed through conventional balancing, due to the continuous fluctuation of vibration amplitude and phase angle. In recent years, a fast growing number of case studies of ME have sparked academic interest in analyzing the causes and solutions of ME, and engineers have moved from an initial trial and error approach to more research inspired modification of the rotor and bearing. To facilitate the understanding of ME, the current review is intended to give the most comprehensive summary of ME in terms of symptoms, causes, prediction theories, and solutions. Published case studies in the past are also analyzed for ME diagnosis based on both the conventional view of critical speed, separation margin (SM), and the more recent view of the rotor thermal bow and instability speed band shifting. Although no universal solutions of ME are reported academically and industrially, recommendations to help avoid the ME are proposed based on both theoretical predictions and case studies.

A Review of Morton Effect: From Theory to Industrial Practice

ABSTRACTThe Morton effect (ME) is known to cause spiral vibrations of rotors supported by fluid lubricant bearings when there is significant differential heating at rotor journals. The root cause of ME is accumulative asymmetric heating brought on by the viscous shearing effect of the bearing lubricant, mainly during synchronous vibrations. The thermal nature of the cause together with the symptoms of spiral vibrations make ME a thermal-induced instability. This article provides an in-depth review of the ME. It starts with a general introduction and assessment of the significance of ME, noting its widespread nature. Subsequently, key findings are introduced about general ME mechanisms, including the important relationship between journal orbits and the hot spot. The circumstances and typical symptoms of ME-induced instability are summarized and followed by a discussion of the critical issues to be tackled in both the theoretical analysis and the experimental techniques regarding ME phenomenon. Lastly, this article includes a discussion about the inconsistencies found in the literature regarding topics such as the excitation models for the thermal bow.

Analysis of Rotor Thermal Bow and Vibration Response in Gas Turbine

Analysis of Rotor Thermal Bow and Vibration Response in Gas Turbine

Double Overhung Disk and Parameter Effect on Rotordynamic Synchronous Instability—Morton Effect—Part I: Theory and Modeling Approach

The Morton effect (ME) is a thermally induced instability problem that most commonly appears in rotating shafts with large overhung masses, outboard of the bearing span. The time-varying thermal bow due to the asymmetric journal temperature distribution may cause intolerable synchronous vibrations that exhibit a hysteresis behavior with respect to rotor speed. The fully nonlinear transient method designed for the ME prediction, in general, overhung rotors is proposed with the capability to perform the thermoelastohydrodynamic analysis for all the bearings and model the rotor thermal bow at both overhung ends with equivalent distributed unbalances. The more accurate nonlinear, coupled, double overhung approach is shown to provide significantly different response prediction relative to the more approximate linear method based using bearing coefficients and the single-overhung method, which assumes that the ME on both rotor ends can be decoupled. The flexibility of the bearing pad and pivot is investigated to demonstrate that the pivot flexibility can significantly affect the rotordynamics and ME, while the rigid pad model is generally a good approximation.

Rotordynamic Morton Effect Simulation With Transient, Thermal Shaft Bow

The Morton effect (ME) is characterized by an asymmetric journal temperature distribution, slowly varying thermal bow and intolerable synchronous vibration levels. The conventional mass imbalance model is replaced by a more accurate thermal shaft bow model. Rotor permanent bow and disk skew are synchronous excitation sources and are incorporated in the dynamic model to investigate their influence on the ME. A hybrid beam/solid element finite element shaft model is utilized to provide improved accuracy for predicting the rotor thermal bow and expansion, with practical computation time. ME is shown to be induced by initial shaft bow and disk skew. The conventional mass imbalance approach is shown to have some limitations.

Three-Dimensional Thermohydrodynamic Morton Effect Analysis—Part II: Parametric Studies

This paper presents simulation results corresponding with the theoretical Morton effect model explained in Part I, where the 3D finite element models of bearing, shaft, and fluid film are adopted. In addition, it explains how thermal bow induced imbalance force develops in the spinning journal with time and how the vibration level is affected by the thermal bow vector. Shaft asymmetric thermal expansion induced by nonuniform journal heating is simulated, which is one of the unique contributions of this research. The effect of changes in: (1) thermal boundary condition around the pad, (2) lubricant supply temperature, (3) initial mechanical imbalance, (4) pivot stiffness, (5) film clearance, and (6) pad material are studied. Cooling the pad and the lubricant, using a pad with a low thermal expansion coefficient, soft pivot, and reducing the initial imbalance are found to be the best remedies for the thermal induced synchronous rotor instability problem.

Quantitative Research on the Stability of the Rubbing Rotor System with Thermal Bow

Quantitative Research on the Stability of the Rubbing Rotor System with Thermal Bow

Thermal elongation of sandwich panels

Sandwich cladding panels with two thin metal faces separated by a lightweight core are well-established cladding products. There have been several instances recently in which the thermal elongation or contraction of sandwich panels has been cited as a possible cause of leakage or local damage in a roof. Historically, the industry has always designed sandwich panels for proper combinations of conventional loading together with a temperature gradient across the panel. This temperature gradient gives rise to ‘thermal bow' which can cause stresses of the same order of magnitude as those from wind or snow load. As a result of this, designers have generally dismissed longitudinal thermal movements from consideration because it is argued that they are taken out by ‘thermal bow' rather than by linear expansion or contraction. Conversely, it is not unusual for roofing and cladding ‘experts' to argue either that thermal bow has little influence on longitudinal thermal movements or that, although it may help in the summer case, it can be of no benefit when the panels try to contract in winter. Surprisingly, there does not appear to have been any previous attempt to determine the actual thermal expansion or contraction of multi-span sandwich panels and appropriate calculation procedures are described for the first time in this study. Perhaps unsurprisingly, it transpires that neither side is correct. Thermal bow results in a significant reduction of longitudinal temperature movements, but it does not eliminate them completely. The formal calculations are not trivial, but it is possible to make a relatively simple estimate of the movements arising in a long panel which has several approximately equal spans.