Dynamic Load Factor Research Articles

Quantifying the impact of subgrade stiffness on the railway dynamic load factor using instrumented wheelset and MRail measurements

Quantifying the impact of subgrade stiffness on the railway dynamic load factor using instrumented wheelset and MRail measurements

Quantifying the impact of rail longitudinal level changes on dynamic load magnitudes through instrumented wheelset measurements

Track geometry significantly influences train-track dynamic interactions, primarily due to irregularities at the wheel-rail interface. These irregularities generate dynamic load excitations, leading to defects and damage. This study evaluates how track surface profile longitudinal level vertical changes affect vertical wheel-to-rail loads, quantified by the dynamic load factor ( ϕ ), due to the importance of ϕ in track design. A limitation of the existing studies is their focus on instrumented sections and numerical modellings without considering different track structures. This study conducted dynamic load measurements using two instrumented wheelsets (IWS) over a 340 km section operated by a North American Class 1 freight railway in the Canadian Prairies under various track structures and train speeds. Rail surface longitudinal level measurements were obtained as routine measurements through a track geometry car. The paper presents statistical distributions of rail longitudinal level across different track structures and evaluates two widely used and recently developed ϕ equations within the context of North American freight railways to quantify the impact of rail longitudinal level (i.e. profile) changes on dynamic load magnitudes. The study also evaluates regulated threshold values by considering observed trends in the measured data, which aims to quantify and compare these values with our current understanding.

Investigation on the propagation of uncertainties of a timber floor under human excitation

Due to the characteristics of high stiffness-weight ratio, timber floors are prone to annoying vibrations under human excitation. Given the natural origin of timber, its mechanical properties exhibit significant variability. The randomness inherent in human excitation cannot be overlooked during structural dynamic analysis. Consequently, the adoption of a stochastic approach is imperative for attaining reliable serviceability evaluation results. However, current research on human-induced vibrations in the timber floor, accounting for this randomness, remains inadequate. In this paper, an experimental investigation is conducted on the dynamic properties and human-induced responses of a timber floor composed of glued laminated timber and oriented strand board. A finite element model is developed and subsequently validated for accuracy in terms of modal properties and dynamic responses. The probability density evolution method is introduced for stochastic analysis, which demonstrates that both the natural frequency and dynamic responses of the floor exhibit considerable variability when uncertainty factors are considered. The Kullback–Leibler divergence indices are used to assess the impact of each uncertain variable quantitatively. The results indicate that the longitudinal elastic modulus has the greatest influence on the natural frequency, while the first dynamic load factor, αz1, exerts the most significant impact on dynamic responses. Notably, both material mechanical properties and load model parameters contribute to the uncertainty of dynamic responses, with the influence of the load model parameters being significantly greater than that of material mechanical properties.

Vision-based survey method for extraordinary loads on buildings

The statistical modeling of extraordinary loads on buildings has been stagnant for decades due to the laborious and error-prone nature of existing survey methods, such as questionnaires and verbal inquiries. This study proposes a new vision-based survey method for collecting extraordinary load data by automatically analyzing surveillance videos. For this purpose, a crowd head tracking framework is developed that integrates crowd head detection and reidentification models based on convolutional neural networks to obtain head trajectories of the crowd in the survey area. The crowd head trajectories are then analyzed to extract crowd quantity and velocities, which are the essential factors for extraordinary loads. For survey areas with frequent crowd movements during temporary events, the equivalent dynamic load factor can be further estimated using crowd velocity to consider dynamic effects. A crowd quantity investigation experiment and a crowd walking experiment are conducted to validate the proposed survey method. The experimental results prove that the proposed survey method is effective and accurate in collecting load data and reasonable in considering dynamic effects during extraordinary events. The proposed survey method is easy to deploy and has the potential to collect substantial and reliable extraordinary load data for determining design load on buildings.

Dynamic Load Analysis of Mine-Truck Using Multibody Dynamic Analysis Method

Abstract: Vehicle load distributed on front & rear axle assembly during various working conditions is one of the most important factors influencing working performance and service life of drive axle assembly. The dynamic load on axle assembly is higher compared to the rated load because of variations in vehicle speed and road surface conditions. Early failure of structural components is caused because of higher dynamic reaction forces due to uneven road profiles. The dynamic load calculation of axle assembly is presented in this paper for a Mine-truck with various road conditions and vehicle speeds. The road load conditions consist of grade, bump & path hole. Mine-truck with payload capacities of 63 Ton is considered for the study. The behaviour of vertical force is calculated for different vehicle speeds (3 - 12 km/hr.) of the machine on the front & rear axle assembly during running conditions. Multi-body dynamic Analysis tool ADAMS is used for this study. ADAMS helps to study the dynamics of moving parts and load distribution throughout mechanical systems during motion. The Mine-truck3D model was created with the help of computer-aided design (CAD) software. Major units of Mine trucks are considered to prepare 3D models like Cabin-engine mass, Bucket, front axle assembly, rear Axle assembly & tires. Multi-body vehicle models are prepared in simulation software ADAMS by importing 3D models prepared by computer-aided design (CAD) software. This provides guidelines for selecting dynamic load factors while designing structural parts of the vehicle.

VERIFICATION OF LAMINATE COMPOSITEPLATE SIMULATION UNDER COMBINED LOADINGS THERMALSTRESSES

This study deals with thermal cyclic loading phenomena of plates which were fabricated from composite materials (woven roving fiber glass + polyester) were exposed to (75 C°) temperature gradient thermal shock for ten times in different stage of conditioning times due to the effect of thermal fatigue using the method of Levy solution and compared these results with both results from experimental published work and (ANSYS Ver. 9) program. A composite laminate plate with fiber volume fraction (υf =25.076%) is selected in this study and applying the combined loadings like bending moment (Mo), and in-plane force (Nxx) beside the effect of thermal fatigue. It involves multi theoretical and finite element fields; but the theoretical one contains the derived equation of stresses distribution and evaluating the normal deflection of a middle point for dynamic analysis applying different boundary conditions for heating and cooling. The main present numerical results for a composite plate with (80%) fiber volume fraction claim that the relative reduction in normal deflection and dynamic load factor are (78.593%) and (9.421%) during cooling to (-15 respectively.

3D Size-Dependent Dynamic Instability Analysis of FG Cylindrical Microshells Subjected to Combinations of Periodic Axial Compression and External Pressure Using a Hermitian C2 Finite Layer Method Based on the Consistent Couple Stress Theory.

This work develops a three-dimensional (3D) weak formulation, based on the consistent couple stress theory (CCST), for analyzing the size-dependent dynamic instability behavior of simply-supported, functionally graded (FG) cylindrical microshells that are subjected to combinations of periodic axial compression and external pressure. In our formulation, the microshells are artificially divided into nl layers. The displacement components of each individual layer are selected as the primary variables, which are expanded as a double Fourier series in the in-plane domain and are interpolated with Hermitian C2 polynomials in the thickness direction. Incorporating the layer-wise displacement models into our weak formulation, we develop a Hermitian C2 finite layer method (FLM) for addressing the current issue. The accuracy and the convergence rate of our Hermitian C2 FLM are validated by comparing the solutions it produces with the accurate two-dimensional solutions of critical loads and critical pressures of FG cylindrical macroshells and single-walled carbon nanotubes, which were reported in the literature. The numerical results show the effects of the material length-scale parameter, the inhomogeneity index, the radius-to-thickness and length-to-radius ratios, the load magnitude ratio, and the static and dynamic load factors on the first principal and first secondary instability regions of parametric resonance of simply-supported FG cylindrical microshells are significant.

Extrapolating specification-level dynamic load factors for bridge performance analysis using deflection measurements during ambient traffic excitations

Field-measured dynamic load factors (DLFs) are underutilized for bridge health assessment. Bridge practitioners often face confusion when comparing field-measured DLFs to specification design values owing to significant DLF variations across different traffic load levels. However, mathematical relations or methods correlating bridge DLFs and load levels are lacking. To address this challenge, this study proposes practical methods for determining specification-level DLFs using field-deflection measurements during ambient traffic excitations. Deflections from a continuous rigid-frame bridge over six months were measured, and DLFs were computed using hourly maximal total deflections and their corresponding static deflections. Two approaches were developed and validated to extrapolate the specification-level DLF using field-measured DLFs of low load levels. Extrapolated DLFs from both methods illustrated a noticeable downward trend in DLFs relative to load levels. Both methods yielded consistent results, falling within the range of 0.03–0.09, equivalent to the design DLF value of 0.05 for the bridge under study. No significant temporal-dependent changes in extrapolated DLFs were evident, indicating that bridge performance and pavement roughness met design expectations and did not deteriorate significantly. This study provides an alternative data-driven approach that utilizes field-measured DLFs to assess the health condition of bridges.

Mine pressure behavior law of isolated island working face under extremely close goaf in shallow coal seam

In order to study the mining pressure characteristics of the shallow buried coal seam with the same silo working face under the very close mining void zone and the overlying coal rock body, the theoretical analysis is used to determine whether the open-cutting eye bearing layer belongs to the mining under the very close mining void zone or not, based on the numerical simulation of FLAC3D and on-site measurement of the working resistance at the end of the cycle of the working face's hydraulic bracket, It is proposed to divide the mining stress of the working face based on the advancing length of the working face, that is, the high-pressure zone, the transition zone and the low-pressure zone. The results of the study show that: FLAC3D software was used to analyze the stress intensity of the “C” island working face when it was mined back to 50 m, 100 m, 150 m, and 180 m (one time “square”), and the simulation results were imported into the Origin software, which was used to analyze the stress intensity of the working face. The simulation results were imported into Origin software, and the influence range of mining stress was divided into four areas: high-stress area, stress transition area, low-stress area, and "square" stress concentration area. According to the on-site measurement of the working resistance at the end of hydraulic support cycle, the initial pressure step of the working face under the overlying coal rock body is 48.9–55.7 m, with the peak value of 38 MPa, the cycle pressure step is 9.0–23.3 m, with the peak value of 36 MPa, and the dynamic load factor of the working face is 1.14–1.16; relative to the overlying coal rock body, the average decrease of the cycle pressure step is nearly 10% and the average increase of dynamic load factor is 1.14–1.16; compared with that under the overlying coal rock body, the average decrease of the cycle pressure step is nearly 10% and the average increase of dynamic load factor is 1.14–1.16. Compared with the overlying coal rock body, the average decrease of the cycle pressure step under the overlying mining zone is nearly 10%, the average increase of the dynamic load factor is 20%, and there is no obvious regularity and periodicity in the direction of strike, and the working face is divided into three parts along the direction of strike: high-pressure zone, transition zone, and low-pressure zone. Therefore, in the process of mining under the overlying coal rock body, we should strengthen the roadway peripheral rock support and roof and floor management, which is of guiding significance to the mining of similar working faces and mine safety production.

Meshing characteristics and dynamic characteristics of planetary transmission system with new tooth-type flexible ring gear

As one of the important components of the planetary transmission system, dynamic meshing characteristics of ring gear directly affect the performance of planetary transmission system load sharing and dynamic load factor. With the help of the flexibility of ring gear, the planetary gear system with flexible ring gear (FRG) can compensate for the uneven transmission torque of each branch caused by the machining error and installation error and improve the system's load sharing and dynamic load performance. An L-shaped FRG was developed in Italy to improve the traditional ring gear and was used in the latest AW101 helicopter with good feedback. By increasing the ring flexibility, the load distribution between planetary gears is more uniform, and the load-sharing performance of the system is significantly improved. Tooth wear and fracture caused by uneven load distribution can be improved. However, the structure has problems such as unbalanced loading, strength weakening, and stress concentration. In this article, the FRG's meshing and structural characteristics are analyzed in detail by constructing the parametric finite element model. Differences, advantages, and disadvantages of FRG and traditional ring gear are compared. A new type of tooth-type FRG is proposed. It has excellent structural flexibility meshing characteristics of tooth surface and avoids generating stress concentration. It improves the planetary gear train's load-sharing performance and overcomes tooth surface unbalanced loading and large amplitude fluctuation of loaded transmission errors.

Enhancing vehicle wheel suspension test equipment through Taguchi method for optimization

The study demonstrates a significant advancement in vehicle suspension testing by utilizing the Taguchi method for optimization. The suspension system determines a vehicle’s performance, directly affecting ride comfort, handling, and safety. The research presented in this study highlights a potentially effective method for enhancing suspension testing. The research systematically investigates the complex network of factors influencing suspension behavior using the Taguchi method, a robust optimization technique. The analysis includes examining road surface conditions, passenger weight variations, and tire pressure fluctuations. The objective is to design a suspension system that provides both comfort and stability without making any concessions, regardless of the obstacles encountered on the road. The car utilized for this research is an Altis sedan equipped with tires with a 205/55 R16 profile. The study’s findings indicate that factor A, which represents embankment height, significantly impacts 56 % of road irregularity management and the maintenance of a stable driving experience. The dynamic load factor (Factor D) contributes significantly to the vehicle’s overall stability and ride quality, accounting for 43 % in different scenarios. Based on the given framework, it can be observed that the variables B (tire pressure) and C (passenger weight) significantly influence suspension vibration, resulting in a reduction of below 0.1 %. While the research results presented here only cover a subset of automobiles, the methodology employed can be used to deal with similar problems in other vehicles.

Three-Dimensional Electromagnetic and Structural Analysis of Disruptions in the COMPASS Upgrade Vacuum Vessel

Structural analyses of disruptions and the electromagnetic (EM) analyses to support them typically use symmetry to produce a manageable model size. Nonaxisymmetric halo loads require larger analysis models. In this paper, the results of transient EM analyses of halo strikes during a vertical displacement event are presented. The plasma motions and halo characteristics are prescribed based on analyses performed by the Institute of Plasma Physics of the Czech Republic. The time transient EM solution provides loads to a full three-dimensional transient dynamic analysis of the vacuum vessel. The responses to large lateral halo loads are altered and mitigated by the mode responses of the vessel. Dynamic load factors are computed for specific locations in the vessel and supports.

Surrogate models for dynamic load factor and ductility ratio in blast response determination

In this article, the blast response of structures by the Single Degree of Freedom (SDOF) method is revisited. The existing literature in which the Biggs’ chart is used to determine the ductility ratio is examined in detail. The numerical method determines the SDOF response by considering the elastic perfectly plastic behaviour of the structure. The numerical values of the ductility ratio in various plastic Dynamic Load Factors (DLF) in each td/T ratio are collected. Such verifiable data can represent the whole chart in the elastic and plastic regions. The only available implicit formula suitable for sharp pulses is tested. It is shown that substantial inaccuracy exists in the formula. Since the error in the existing formula is up to 100%, an alternative formula is suggested to reduce the error. The new nonlinear surrogate model describes the chart by introducing 3 regions. In each region, an approximate formula is developed. The model computes the ductility ratio with less than 2% error. The newly suggested functions are nonlinear quadratic types and have been developed by using high-order polynomial optimization. In the numerical example, the result of the new surrogate model is commented on in comparison with SDOF and FEM. It is shown that it can be used in the computational design of protective structures without using Biggs’ chart. It is concluded that similar surrogate models can be developed for unsymmetrical blast pulses.

Dynamic load factor of concrete defects in hammer loading

The most reliable way to check the safety of elements against the spalling of concrete defects is to apply a load of sufficient magnitude. Nevertheless, the determination of a sufficiently large load is qualitative and based on the technician’s intuition. Additionally, the response to impact loading is not the same as that to static loading. It would be useful to evaluate the response to a dynamic loading from an equivalent static loading. This paper investigates the dynamic load factor (DLF), defined as the ratio of the dynamic and static responses, adopting the response of a beam under impact loading and numerical analyses for more complex structures. Numerical results show that the most important variable in estimating the DLF is the ratio of the load time to the natural period of the first vibration mode. The DLF for displacements neglecting vibration damping can be estimated with sufficient accuracy in an undamped one-degree system. However, the DLF for stresses with damping, which is important for safety checks, is difficult to estimate. Nevertheless, its lower limit can be evaluated using the DLF of the undamped one-degree system. Although the risk of spalling is not considered to be high for defects with a first-order natural frequency exceeding 1000 Hz, a large load is likely to be applied by hammering. It is recommended not to hit hard to avoid excessive load during inspection.

Verification of damped bipedal inverted pendulum model against kinematic and kinetic data of human walking on rigid-level ground

In this study, kinematic and kinetic data for 14 test subjects walking on a treadmill were recorded to verify a damped bipedal inverted pendulum (DBIP) model. The verification aim was for the DBIP model to match the step frequency and first harmonic dynamic load factor (DLF1) extracted from the measured data, as these are key parameters of interest in civil engineering applications. The verification was conducted in several phases. First, kinematic data from 39 markers attached to the human body were used to get the trajectory of body’s centre of mass (BCoM). This trajectory, in conjunction with the vertical and longitudinal ground reaction forces (GRFs) were then used to plot the leg force – leg length relationship. Linear curve fitting yielded the spring stiffness and spring length parameters. These parameters, together with the body mass and damping coefficient, were fed into the DBIP model to identify initial conditions for the motion of BCoM leading to the stable periodic gait. For the 14 test subjects, the model produced excellent agreement with the measured step frequency and DLF1, while relative error for the walking speed was between -12.6% and 2.0%. The simulated waveform of the vertical BCoM displacement was found to match the measured signal well. In addition, match between simulated and measured GRF profiles was satisfactory except for one test subject. Regression functions have been established for estimating model parameters, based on which step-by-step procedures have then been proposed for modelling a pedestrian within the population. The results suggest that the DBIP succeeds in modelling pedestrians walking on rigid level surfaces. In the next step the model should be considered for modelling pedestrians on vibrating civil engineering structures.

Evaluation of compliant walking locomotion models for civil engineering applications

This study aims to evaluate the suitability of the spring-loaded inverted pendulum (SLIP) model and three of its upgrades for modelling pedestrians in civil engineering applications. Model equations in Cartesian coordinates have been derived for the four SLIP-based models and they have been presented in ready-to-use format. The input parameter space that produces the stable periodic gait has been identified and relevant gait parameters (step frequency, average speed, and dynamic load factor) have then been evaluated against the measured parameter space characterising the pedestrian population. The results indicate that the original SLIP model has multiple drawbacks. Adding roller feet was found to increase the estimates of average walking speed when compared with the SLIP model. Adding damping brings more substantial benefits of improved coverage of the step frequency and dynamic load factor parameter space. Dimensional analysis was found to be a useful means of modelling a new pedestrian having either a new body mass or leg length. In summary, the analysis suggests that inclusion of leg damping in the model is crucial for achieving realistic estimates of the step frequency and dynamic load factor, while modelling foot geometry brings improved estimates of the walking speed.

Static and Dynamic Stability Analyses of Functionally Graded Beam with Inclined Cracks

The focus of this paper is to examine the static and dynamic instabilities of functionally graded beam that contains multiple inclined cracks under the influence of an axial force comprising both static and time-varying harmonic components. The elasticity modulus and mass density of the functionally graded beam are assumed to vary exponentially along its thickness direction. Local stiffness matrix model-based finite element analysis (FEA) is conducted to determine the bending stiffness and tensile stiffness of the section with a crack, and the coupled effect of tensile and bending loadings. Two-node beam elements with three degrees-of-freedom per node are utilized. By combining the Euler–Bernoulli beam theory with Lagrange method, we derive the governing equations that describe the static and dynamic instabilities of a functionally graded beam with multiple inclined cracks. These equations can be solved as eigenvalue problems to obtain the natural frequency and static critical buckling load of the beam. Furthermore, to investigate the dynamic instability of the system, we use the Bolotin method to determine the boundary between the regions of instability and stability based on the same governing equations. By adopting this approach, the study comprehensively investigates the impacts of crack position, inclination angle, and length, as well as elasticity modulus ratio, static and dynamic load factors on both static and dynamic stabilities of a cracked functionally graded beam to gain valuable insights into the stability and performance of cracked functionally graded structures.

The impact of periodic axial loads on nonlinear dynamic instability behavior of Inconel 625 pipes

In various engineering fields like aerospace and aircraft structures or marine and offshore platforms, constitutive material of critical components should be made of specific materials that can work properly in the required workspace. Such materials must have excellent properties such as high mechanical strength as well as great resistance to corrosion, oxidation, and creep. Inconel 625 is a superalloy that is chosen as constitutive material of critical components due to its great abilities. On the other hand, since investigating Inconel 625 pipe has not been done yet, different mechanical characteristics of using structures made of Inconel 625 should be assessed. Additionally, doing so would be necessary to gather information for current industrial affairs and also future investigations. Therefore, the nonlinear dynamic instability response of axially loaded Inconel 625 pipes is investigated in the current article. The pipe structure is modeled via the Donnell shell theory and nonlinear von Kármán theory. The motion equations of pipes are established by applying the Hamiltonian approach. Then, in order to alter the nonlinear derived partial differential equations into the Mathieu-Hill equation, both Navier's solution and Airy stress function are implemented. Additionally, the amplitudes of steady-state oscillation of the Inconel 625 pipe are determined by employing Bolotin's method. Eventually, the impacts of various effective parameters on the nonlinear dynamic behaviors of Inconel 625 pipes are evaluated. The results indicate static and dynamic load factors possess a remarkable effect on instability exciting areas and steady-state vibration amplitudes of pipe. Moreover, the dynamic instability response of the pipe is dependent on the radius-to-thickness and length-to-radius ratios, and also how the ratios are affected depends on the wave number.

Modeling and analysis of dynamic load factor in a fail-safe crane mechanism equipped with a hydraulic equalizing cylinder

In the design and manufacturing of sensitive crane mechanisms, in particular, those utilized in nuclear facilities, safety is of utmost importance. A few designs are based on a hydraulic equalizing cylinder where the purpose is mainly to dampen the dynamic load factor generated by the sudden failure of the wire rope system. To the best of the authors' knowledge, design equations and engineering models for such an intricate dynamic mechanism are not reported anywhere in the literature. Toward achieving this goal, a model is proposed for the dynamic behavior of a hydraulic equalizing cylinder when coupled to a single-failure-proof cross-reeved crane hoist. The constitutive equations involve the time-dependent incompressible Navier-Stokes equations. These equations are coupled with the dynamics of the lower block and the elastic wire rope. A nonlinear second-order ordinary differential equation is obtained, which is solved analytically. This yields a closed-form relation for the dynamic load factor. The validity of the new model is investigated using experimental studies, which are presented in this work. The normalized root mean square error for the dynamic load factor obtained by the model compares favorably to the experimental results, where the maximum observed error is 3.9 percent. The results confirm that the current model can be used as a design equation by practitioners.

Body Motion Sensor Analysis of Human-Induced Dynamic Load Factor (DLF) for Normal Walks on Slender Transparent Floors

Modern constructions are often characterized by the presence of slender and aesthetically fascinating components and assemblies. For pedestrian systems in particular, such constructions are notoriously associated with possible vibration issues, and thus require special calculations. When these slender systems are made of structural glass, additional effects due to transparency may also affect human behaviours and motions. In this paper, based on a single body motion, a microelectromechanical system (MEMS) sensor in the body’s centre of mass (CoM) is introduced, an extended, original experimental investigation is presented, and human-induced effects on slender transparent floors are discussed. Major attention is given to the well-known dynamic load factor (DLF) induced by a single pedestrian’s normal walk; a fixed walking rate is assigned, and different substructures (with major variations in their structural dynamic parameters) are taken into account. A discussion of experimental results is proposed for rigid reinforced concrete (RC), and a laboratory contrast system (SLAB#1), which is used as a reference for the analysis of DLF trends on relatively light and flexible transparent glass flooring systems (SLAB#2 and SLAB#3). It is shown that structural frequency and mass, but also possibly transparency, can affect human motion and result in a quantitative modification of measured DLF values, especially for the first and second harmonics of vertical force components.