Bearing Reaction Forces Research Articles

A Failure Analysis of the Long-Term Overturning Stability of Concrete Continuous Single-Column Pier Bridges Considering Creep and Overloaded Vehicles

Several single-column pier girder bridges have been involved in overturning accidents, resulting in significant economic losses and casualties, thus necessitating a risk assessment of the overturning stability. To date, the effect of structural degradation due to concrete creep on the long-term stability of bridges has not been demonstrated. In this study, a full-scale nonlinear analysis of the lateral overturning process of a collapsed concrete box girder based on the explicit dynamic finite element method (EFEM) was conducted to verify the reliability of the numerical method. An EFEM model incorporating concrete creep was developed to demonstrate the effect of structural degradation on the long-term stability of bridges. The synthesis overturning axis method (SOAM) was proposed to evaluate the long-term overturning stability of concrete continuous bridges, aiming to address the deficiencies in existing methods, particularly for curved bridges, and was compared with conventional methods. The results show that the variations in bearing reaction forces between curved and straight bridges under creep and self-weight are minimal, staying within 2%. An increase in the creep terminal coefficient results in the opposite trend in the ultimate vehicle weight of curved bridges and straight bridges, but fluctuations remain within 2%, indicating that long-term creep has a limited effect on the overall overturning stability. A failure analysis of 20 single-column pier bridges reveals significant differences in the ultimate vehicle weight between the rigid overturning axis method (ROAM) and folded overturning axis method (FOAM), with error ranges of −14.2% to 567.4% and −99.1% to −32.1%, respectively. The SOAM results have the smallest error range compared to those of the EFEM, with an error range of −38.8% to 33.9%. Despite these errors, the SOAM demonstrates a significant improvement in characterizing the trend and assessment accuracy of the overall overturning stability of single-column pier bridges.

Research on Bridge Integrity Assessment and Early Warning Monitoring Methods Based on Bearing Reaction Force

Traditional bridge monitoring and damage identification techniques typically rely on full-bridge coverage of sensors, such as displacement or strain sensors. However, this approach proves economically unfeasible for the vast numbers of small- and medium-span continuous beam bridges. In response to the need for rapid damage identification and integrity assessment of continuous beam bridges, a novel bridge safety monitoring method relying solely on bearing reaction forces is proposed. Firstly, the analytical expressions for the bearing reaction influence lines of a three-span continuous beam bridge under damage conditions were derived. Secondly, a rapid structural damage localization method based on the bearing reaction influence lines was proposed. Finally, feasibility and applicability were confirmed through numerical simulations and experimental validation. Additionally, the discussion includes the implementation of the warning classification and threshold setting using data from bearing force monitoring. The research demonstrates that utilizing a limited amount of bearing reaction force information can not only identify damage areas in a “non-full-coverage” manner, but also facilitates early warning and the integrity assessment of bridges. In the future, there is potential for large-scale application in medium- and small-span continuous beam bridges.

Analysis of the effect of maneuvering overload on the reaction force of the main shaft bearing in aero-engine

In order to study the effects of maneuvering overload on the main shaft bearing (abbreviation: bearing) reaction force in an aero-engine, a bending-torsion coupling dynamic model of the dual rotor system under maneuvering overload was established. Combined with the output parameters of the system model, the bearing reaction force analysis model was established. The maneuvering overload parameters are input into system model. Newmark-β and Newton-raphson methods are used to obtain the bearing reaction force response, and the change laws of bearing reaction force under the different maneuvering overloads are analyzed. The results show that gravity will make the transient response of bearing reaction force offset, and maneuvering overload will make the offset shift. Maneuvering overload will cause bearing to produce a circumferential asymmetric reaction force. For bearing 1, the additional gyroscopic torque in maneuvering overload has a significant effect on the dynamic eccentricity, resulting in a larger offset of reaction force of y direction. For bearings 3 and 4, reaction force of x direction has a larger offset. Under the influence of bent-torsional coupling, the combined frequencies of base frequencies of rotational speed appear in the reaction force spectrum diagram.

Classification and Mechanical Behaviors of Inner Concave Cable-Arch Structure with V-Shape Web Struts

The inner concave cable-arch structures with V-shape web struts were classified, and single-tensioning construction method and multiple-tensioning construction method for continuous cable-arch structures were described. The optimization of pretension for multiple-tensioning construction method was carried out. FE models of cable-arch structures including the single-tensioning models and the multiple-tensioning models were created. The mechanical behaviors including stress ratios, stiffness, horizontal bearing reaction force and structural stability of the two kinds of models were compared. The results show that the pretension does not significantly influence the maximum resultant displacement, horizontal bearing reaction force, and stability of the singletensioning cable-arch structures. With pretension increasing the stress ratios can be reduced. The stress ratios and stiffness decrease with the increasing of the rise-to-span ratio, and horizontal bearing reaction force slightly decreases, but structural stability has no obvious changing rules. There is no difference in mechanical behaviors between two types of cable-arch structures with the rise-to-span ratio of 0.2, it is recommended to use the singletensioning construction method. However, the mechanical behaviors of multiple-tensioning type are generally better than that of single-tensioning type with the rise-to-span ratio of 0.3 and 0.4. It is necessary to consider the cost of construction and mechanical behaviors to determine its tensioning construction method.

Study of the Hull Structural Deformation Calculation Using the Matrix Displacement Method and Its Influence on the Shaft Alignment

The analysis of the influence of hull deformation on shaft alignment is predominately conducted using the finite element method (FEM), which is time-consuming, labor-intensive, and challenging to use for iterative hull design optimization. In this paper, hull deformation is separated into two parts—global deformation and local deformation, simplified to a single-span beam model and a grillage beam model, respectively—then solved using the matrix displacement method (MDM). Compared to FEM, the proposed method has a small calculation error, proving its correctness, while the calculation time is greatly reduced. The proposed method has been used to calculate the hull deformation of a ship under various conditions and evaluate its influence on shaft alignment. The results indicate that under certain conditions, the bearing reaction forces are constant, whereas the bearing pressure changes as a consequence of the change in shaft-to-bearing angle. The comparison between local rotation and shaft-to-bearing angle reveals that bearings in various positions follow distinct laws. We suggest that the shaft-to-bearing angle be used as an additional parameter in the evaluation of shaft alignment calculations. Moreover, when optimizing bearing pressure, bearings in different positions are affected differently by global and local deformation, and their optimization priorities are distinct.

Measurement of bearing reaction force by distributed strain variation

Bearing is a crucial transmission component of aero-engines under high-speed and heavy-load conditions. To design a roller bearing with high loading capacity and reliability, it is essential to focus on the relationship between the external load state (reaction force) and the internal load distribution (load distribution). Therefore, a measurement method for bearing reaction force using load distribution and radial basis function neural network is presented in this study. Unlike conventional static reaction force measurement methods, both the direction and magnitude of the reaction force are considered in the proposed method without modifications to bearing. First, an experimental system is designed to investigate the load distribution in a roller bearing under different reaction forces using strain variation measurements. Then, a finite element analysis is conducted, and simulation results of the strain variations at three interested points match well with the experimental measurements. Finally, a radial basis function neural network with strong nonlinear fitting ability is applied to construct the mapping relationship between strain variation and reaction force. The results demonstrate that the proposed method can predict the reaction force with high accuracy based on the strain variation at three measuring points.

The role of gear layout and meshing phase for whine noise reduction in ordinary geartrains

Whine noise is one of major concern within geared system dynamics. The time-varying bearing forces are transmitted to the gearbox case, which coupled with the whole system assembly provokes an undesired noise emission. The paper proposes an analytical formulation able to forecast the main overall direction and magnitude of bearing reaction forces on idler gear when the geartrain works under quasi-static condition. Moreover, a parametric study is conducted by evaluating the influence of geartrain layout, the meshing phase shift and the amplitudes of meshing forces. Finally, numerical experiments are performed in order to evaluate discrepancies and similarities when the inertial effects become relevant.

Stability Analysis of the Surrounding Rock-Lining Structure in Deep-Buried Hydraulic Tunnels Having Seepage Effect

To clarify the factors affecting the stability of deep-buried hydraulic tunnels containing pore water, the elastoplastic theory and the Mogi-Coulomb strength criterion were used to derive the analytical solutions of stress on the surrounding rock-lining structure, tunnel wall displacement, and plastic zone radius in surrounding rock under different operating conditions. During this process, the seepage effect and surrounding rock-lining interaction were considered. The influencing rules of seepage action, intermediate principal stress coefficient, lining permeability coefficient, and lining thickness on the stability of the surrounding rock-lining structure were investigated in depth. The results show that the seepage effect significantly changed the stress distributions in the lining structure and surrounding rock, reduced the bearing reaction force, and lowered the tunnel stability. The bearing reaction force was decreased considerably from the intermediate principal stress, and the plastic zone radius in the surrounding rock and the tunnel wall displacement was obviously reduced. Moreover, the bearing reaction force was reduced, and the plastic zone radius in the surrounding rock and the tunnel wall displacement was increased with the decrease of the lining permeability coefficient. With increasing the lining thickness, the bearing reaction force was enhanced, and an apparent restriction on the development of plastic zone in the surrounding rock appeared at the beginning, but the restriction effect weakened subsequently. This research can theoretically provide references for analyzing the stability of hydraulic tunnels containing pore water.

Optimization of the cable forces of completed cable-stayed bridges with differential evolution method

Long-span cable-stayed bridges have been massively erected worldwide in recent decades, and reasonable cable forces play an essential role in achieving the desired configurations of completed bridges. In the current research, a differential evolution (DE) algorithm is adopted to optimize the cable forces considering the counterweight. An asymmetrical cable-stayed bridge is taken as a case study, and the numerical model of the bridge is established with the OpenSees platform. The cable sag effect and geometric nonlinearity are considered in the numerical model. The weighted total bending energy of the girder and pylons is taken as the objective function of the optimization problem. In addition, the constraints of the cable forces, the range and magnitude of the counterweight, and the bearing reaction forces at the transition and auxiliary piers are considered. The numerical results reveal that the proposed framework is efficient and stable for optimizing the cable forces, and several optimum solutions can be obtained. In addition, the performance of the proposed optimum algorithm is less sensitive to the values of the initial parameters (feasible regions and population size). Moreover, the proposed algorithm automatically determines the control parameters (scaling factor and crossover rate) of the DE method, which makes it easy to use in practical engineering. In addition, the proposed algorithm can be used to optimize the cable forces in the final stage and the construction stages.

Numerical study on existing RC circular section members under unequal impact collision

Traffic accidents and derailed train-related incidents have occurred more often than ever in recent years, resulting in some economic damage and casualties. Reinforced concrete (RC) constructions often involve derailed train and vehicle accidents. Rarely are such side collisions studied in previous studies. To do this, high-fidelity simulation-based finite-element (FE) models are created in this paper to accurately simulate the collision of circular RC members with a derailed train. The reinforced concrete member structure is common in high-speed railway stations. The impact energy of the impact body is significant, causing structural member failure. It analyses the dynamic behavior of reinforced concrete members under unequal span impact loads. Numerical implementations of impact issues are discussed from the perspective of geometric, contact, and material properties. The reliability and precision of the ABAQUS code to solve impact issues are verified by comparing failure modes, impact, and deflection time history experimental outputs. By analysing the impact response characteristics, used the control variables to study the failure process and mode (including the characteristics of impact and reaction forces, deflection time history curve, impact force–deflection curve, and bearing reaction force–deflection curve). The reinforcement ratio, impact velocity, concrete strength, and slenderness ratio significantly affect shear crack pattern and development. Changes in impact velocity and slenderness ratio also affect member failure modes.

Response-based bridge deck limit state considering component-level failure under extreme wave

Coastal bridges are crucial components of transportation systems; however, they are susceptible to increasing failure risk from extreme waves due to climate change scenarios. Previously, most of the studies focused on the extreme wave forces on the bridge superstructure, while the effects of the overturning moment, bearing constraints, and local damage were seldom discussed. This research conducts an in-depth investigation on the wave-bridge interaction to explore the structural limit state of the coastal bridges subjected to extreme waves considering component failure. Firstly, a three-dimensional (3D) Computational Fluid Dynamics (CFD) model is established and validated to simulate the wave-bridge interaction under various wave scenarios. To lend confidence to the CFD model, laboratory experiments are conducted to improve and validate the simulation results. Subsequently, based on the numerical results, wave force prediction methods are proposed by considering the solitary wave characteristics. Accordingly, the time histories of wave forces are imported into a spatial Finite Element (FE) model of the investigated bridge FE model to compute dynamic structural responses, including bearing reaction forces, bridge displacements, and bearing working states. Then, based on the dynamic structural response, a novel structural limit state incorporating component damage is developed to prevent bearing damages under the wave impacts and corresponding structural demand is parametrically studied and quantified with different wave parameters. Such a study could help optimal and robust designs of coastal bridges and modifications of existing ones.

Application of Deep Reinforcement Learning to Predict Shaft Deformation Considering Hull Deformation of Medium-Sized Oil/Chemical Tanker

The enlargement of ships has increased the relative hull deformation owing to draft changes. Moreover, design changes such as an increased propeller diameter and pitch changes have occurred to compensate for the reduction in the engine revolution and consequent ship speed. In terms of propulsion shaft alignment, as the load of the stern tube support bearing increases, an uneven load distribution occurs between the shaft support bearings, leading to stern accidents. To prevent such accidents and to ensure shaft system stability, a shaft system design technique is required in which the shaft deformation resulting from the hull deformation is considered. Based on the measurement data of a medium-sized oil/chemical tanker, this study presents a novel approach to predicting the shaft deformation following stern hull deformation through inverse analysis using deep reinforcement learning, as opposed to traditional prediction techniques. The main bearing reaction force, which was difficult to reflect in previous studies, was predicted with high accuracy by comparing it with the measured value, and reasonable shaft deformation could be derived according to the hull deformation. The deep reinforcement learning technique in this study is expected to be expandable for predicting the dynamic behavior of the shaft of an operating vessel.

Bidirectional LSTM-Based Soft Sensor for Rotor Displacement Trajectory Estimation

Constant rotor system monitoring enables timely control and maintenance actions that decrease the likelihood of severe malfunctions and end product quality deficits. Soft sensors represent a promising branch of solutions enhancing rotor system monitoring. A soft sensor can substitute a malfunctioning physical sensor and provide estimates of a quantity that is difficult to measure. This research demonstrates a soft sensor based on bidirectional long short-term memory (LSTM), and a training procedure for rotor system monitoring at high sampling frequency and varied operating conditions. This study adopts a large rotor and bearing vibration dataset. The soft sensor accurately estimates lateral displacement trajectories of the rotor from the bearing reaction forces over a large range of constant rotating speeds and constant support stiffnesses. The mean absolute error (MAE) of the LSTM-based soft sensor is 0.0063 mm over the test trajectories in the complete operating condition space. The soft sensor performance is shown to decrease significantly to a MAE of 0.0442 mm, if the training dataset is limited in the rotating speed range.

Reaction force of ship stern bearing in hull large deformation based on stochastic theory

A theoretical calculation model for ship stern bearings with large hull deformation is established and validated theoretically and experimentally. A hull simulation model is established to calculate hull deformations corresponding to the reaction force of stern bearings under multi-factor and multi-operating conditions. The results show that in the condition of wave load, hull deformation shows randomness; the aft stern tube bearing load obeys the Gaussian distribution and its value increases significantly compared with the load under static, and the probability of aft stern tube bearing load greater than 1 is 65.7%. The influence laws and levels between hull deformation and bearing reaction force are revealed, and suggestions for ship stern bearing specifications are proffered accordingly.

Dynamical response of the shaft-bearing system of marine propeller shaft with velocity-dependent friction

The appropriate assessment of dynamical response of the marine propeller shaft is essential to enable optional power delivery to propeller and to minimize friction of supporting bearings. Abnormal shaft vibration induced by the interaction of water-lubricated stern bearings seriously affect the reliability of marine propulsion system during ships’ navigation. An applicable numerical model regarding dynamical response of the shaft-bearing system considering velocity-friction interaction is proposed. The cooperative Newton-Raphson & Newmark-β iterative method is applied to solve this nonlinear model with velocity-dependent friction. To capture the nature of shaft-bearing interaction, the dynamical response of shaft relative velocity, bearing reaction force and dynamic friction coefficient with various model parameters are obtained. The influence of rotational speed, stick factor and slip factor regarding velocity-dependent friction on the dynamical response is discussed with data comparison in detail. The residual force defined in theoretical basis is also analyzed for each Case to certificate the reliability of the numerical calculation. A comparison of the Poincaré surface between present work and previous reference is conducted to validate the applicability of the proposed frictional model. The optimized design for marine propeller shaft and water-lubricated stern bearings is thus realized based on the adjustment of material friction properties.

Effects of Shaft Shape Errors on the Dynamic Characteristics of a Rotor-Bearing System

Effects of shaft shape errors are studied on dynamic characteristics of a rotor-bearing system. Stability characteristics of the cylindrical journal bearing are studied. It is shown that the rotating speed at which the oil whip occurs increases when the shape errors exit. And, there is a threshold speed of the bearing with shaft shape errors; before the speed is increased to the threshold, orbits of the center of the journal decrease, and when the speed exceeds the threshold, the orbits increase dramatically and oil whip appears. Furthermore, the quantitative relationship between shaft shape errors and bearing reaction forces of the rotor-bearing system is obtained, which is verified by experiments using rotors with different machining precisions. In order to reduce computing time, variational principle is applied when solving Reynolds’ equation.

Modal Analysis of Rail Transit Gearbox

Modal analysis is an important method to study the dynamic properties of structures. In order to explore the effect of prestress on the dynamic characteristics of rail transit gearboxes, in this paper, a three-dimensional solid model of the rail transit gearbox was established, and the bearing reaction force of the transmission system was obtained by multi-body dynamics method. Considering the force transmitted by transmission system through the bearing seat to the case, the prestressed modal analysis of the rail transit gearbox casing was conducted by utilizing a finite element method, and the prestressed modal of the case was obtained. The modal parameters of the model were compared with the model of the case without prestress. The results manifested that the prestress has a significant on the modal characteristics of the gearbox casing, and the prestress of gearbox casing should be taken into account when conduct modal analysis.

Application of gain-scheduled vibration control to nonlinear journal-bearing supported rotor

Bearing reaction forces are commonly approximated by linear coefficients at a given rotational speed, although they are, in reality, considerably nonlinear in some situations. Therefore, a precise numerical simulation is highly desirable before experimental tests, usually resorting to integration of classical Reynolds equation, a well-known numerically time consuming. Due to faults or unusual demands, controllers can be applied to avoid failure. However, control action changes the machine dynamic behavior. This paper investigates the performance of a faster simulation method using a high order Taylor force approximation, by means of nonlinear coefficients, in situations that differs from the one in which the force was originally identified. This is accomplished using the force generated by a gain-scheduled static H∞ controller. The proposed controller aims to stabilize fluid-induced instability and attenuate unbalance vibration at critical speed of a journal bearing supported rotor. A polynomial fit is applied to express the hydrodynamic bearings coefficients according to rotor rotational speed. The resultant polynomial system is then used in linear matrix inequalities from a two-stage method in order to synthetize a controller linearly dependent on rotational speed. Furthermore, the control efficiency is verified under the influence of bearing nonlinearities. The numerical simulations were compared with experimental data measured in a laboratory test rig. The results reveal that the control is effective in reduce vibration amplitudes especially in critical speed and fluid induced instability, and that the nonlinear coefficients are promising for approximating journal motion for both uncontrolled and controlled systems.

Research on the Dynamics and Variable Characteristics of a Double-Swash-Plate Hydraulic Axial Piston Pump With Port Valves

Axial piston pumps with port valves are widely used in applications that require high pressure and high power. In the present research, a new type of double-swash-plate hydraulic axial piston pump (DSPHAPP) with port valves is presented. The structure and working principle of the pump are discussed, and the balance characteristics of the pump are analyzed. A mathematical model of the pump flow distribution mechanism considering the leakage is established, based on which the effects of centrifugal forces acting on the port valves, working pressure, and rotational speed on the flow distribution characteristics are studied. A new method of varying the displacement of the pump that changes the phase relation of the two swash plates is proposed, and the principle and regulating characteristics of the variable method are studied. A detailed analysis of the forces and moments acting on the cylinder and the bearing reaction forces is presented. Finally, the relationship between volumetric efficiency and working pressure, and rotational speed and variable angle, is presented. It is revealed through an analysis that the working principle of the pump is feasible, and that the variable method can meet the requirements of varying the displacement of the pump. The characteristics of static balance and dynamic balance of the double-swashplate pump have the advantage of reducing vibration and noise. The research results also show that the reasonable matching of the working pressure and rotational speed can increase the pump's working performance to its optimum level.

The Cause of Premature Wind Turbine Bearing Failures: Overloading or Underloading?

ABSTRACTThough the premature failures of wind turbine gearboxes are often attributed to bearing fatigue from overloading, there is compelling evidence that wear from underloading is a significant contributor. Here we attempt to gain insight into the relative contributions of over- and underloading by assessing planet bearing reaction forces from the Gearbox Reliability Collaborative (GRC) standard gearbox within a typical utility-scale wind turbine under realistic conditions. The results demonstrate that non-torque load sharing by the planetary stage increases and decreases planet bearing reaction forces at different locations within each rotor cycle regardless of wind speed. Planet bearing reaction forces exceeded the fatigue limit at wind speeds above 12 m/s and fell below the minimum load rating at wind speeds below 7 m/s. Based on analyses of published wind spectra from 10 U.S. sites, the expected fatigue life of the planet bearings ranged from 42 to 529 years even after accounting for non-torque load sharing. At the same 10 sites, planet bearings were underloaded (below 2% of the dynamic load rating) once per rotor cycle 40–70% of the time. Underloaded bearings are susceptible to surface damage when suddenly exposed to common transient events, such as yaw, wind gusts, braking, and grid faults. The resulting surface damage can initiate premature failure via wear (e.g., micropitting) or by reducing bearing fatigue life. The results suggest that carrier bearing clearance, non-torque load sharing, and planet bearing underloading are significant contributors to the premature failures of wind turbine planet bearings.