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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

Experimental Evaluation of Wheel-Rail Interaction

Radmehr, Ahmad 14 January 2021 (has links)
This study provides a detailed experimental evaluation of wheel-rail interaction for railroad vehicles, using the Virginia Tech Federal Railroad Administration (VT-FRA) Roller Rig. Various contact dynamics that emulate field application of railroad wheels on tracks are set up on the rig under precise, highly-controlled and repeatable conditions. For each setup, the longitudinal and lateral traction (creep) forces are measured for different percent creepages, wheel loads, and angles of attack. The tests are performed using quarter-scaled wheels with different profiles, one cylindrical and the other AAR-1B with a 1:20 taper. Beyond the contact forces, the wheel wear and the deposition of worn materials are measured and estimated as a function of time using a micron-precision laser optics measurement device. The change in traction versus amount of worn material at the contact surface is analyzed and related to wheel-rail friction. It is determined that the accumulation of the worn material at the contact surface, which appears as a fine gray powder, acts as a friction modifier that increases friction. The friction (traction) increase occurs asymptotically. Initially, it increases rapidly with time (and worn material accumulation) and eventually reaches a plateau that defines the maximum friction (traction) at a stable rate. It is estimated that the maximum is reached when the running surface is saturated with the worn material. Prior to the saturation, the friction increases directly with an increasing amount of deposited material. The material that accumulates naturally at the surface—hence, referred to as "natural third-body layer"—is estimated to be a ferrous oxide. It has an opposite effect from the Top of Rail (ToR) friction modifiers that are deposited onto the rail surface to reduce friction in a controlled manner. Additionally, the results of the study indicate that longitudinal traction decreases nonlinearly with increasing angle of attack (AoA), while lateral traction increases, also nonlinearly. The AoA is varied from -2.0 to 2.0 degrees, representing a right- and left-hand curve. Lateral traction increases at a high rate with increasing AoA between 0.0 – 0.5 degrees, and increases at a slow rate beyond 0.5 degree. Similarly, longitudinal traction reduces at a high rate for smaller AoA and at a slower rate for larger AoA. For the tapered wheel, an offset in lateral forces is observed for a right-hand curve versus a left-hand curve. The wheel taper generates a lateral traction that is present at all times. In one direction, it adds to the lateral traction due to the AoA, while in the opposite direction, it subtracts from it, resulting in unequal lateral traction for the same AoA in a right-hand versus a left-hand curve. The change in traction with changing wheel load is nearly linear under steady state conditions. Increasing the wheel load increases both longitudinal and lateral tractions linearly. This is attributed to the friction-like behavior of longitudinal and lateral tractions. An attempt is made to measure the contact shape with wheel load using pressure-sensitive films with various degrees of sensitivity. Additionally, the mathematical modeling of the wheel-roller contact in both pure steel-to-steel contact and in the presence of pressure-sensitive films is presented. The modeling results are in good agreement with the measurements, indicating that the pressure-sensitive films have a measurable effect on the shape and contact patch pressure distribution, as compared with steel-to-steel. / Doctor of Philosophy / This study provides a detailed experimental evaluation of wheel-rail interaction for railroad vehicles, using the Virginia Tech Federal Railroad Administration (VT-FRA) Roller Rig. Better understanding the dynamics and mechanics of wheel-rail interaction would significantly contribute to the development of technologies, materials, and operational methods that can further improve fuel efficiency, and reduce wheel and rail wear. Considering that the railroads are the backbone of cargo and passenger transportation and are critical to economic well-being, the results of this study are expected to contribute to the betterment of society. An attempt is made to emulate the field application of railroad wheels on tracks on the rig under precise, highly-controlled and repeatable conditions. For each set up, the contact forces are measured for different parameters, such as wheel loads. Beyond the contact forces, the wheel profile degradation and the deposition of worn materials are measured and estimated as a function of time using a micron-precision laser optics measurement device. It is determined that the accumulation of the worn material at the contact surface, which appears as a fine gray powder, increases contact forces. The effect of wheel load on contact forces is almost linear. Additionally, the results of the study indicate that the yaw angle between the wheel and the roller (AoA) changes the contact forces direction, which has a higher rate of change for a small AoA such as 0.0 – 0.5 degrees, compared to a larger AoA. An attempt is made to measure the contact shape with wheel load and AoA using pressure-sensitive films with various degrees of sensitivity. Additionally, the mathematical modeling of the wheel-roller contact in both pure steel-steel contact and in the presence of pressure-sensitive films is presented. As expected, both the model and test result indicate that the presence of a film at the contact surface changes both the dimensions and pressure distribution at the contact patch. Quantifying the distortion that occurs as a result of the pressure-sensitive film allows for a better assessment of the pressure distribution measurements that are made with the films in order to potentially discount the resulting distortions.
2

State of the Art Roller Rig for Precise Evaluation of Wheel-Rail Contact Mechanics and Dynamics

Meymand, Sajjad Zeinoddini 25 January 2016 (has links)
The focus of this study is on the development of a state-of-the-art single-wheel roller rig for studying contact mechanics and dynamics in railroad applications. The use of indoor-based simulation tools has become a mainstay in vehicle testing for the automotive and railroad industries. In contrast to field-testing, roller rigs offer a controlled laboratory environment that can provide a successful path for obtaining data on the mechanics and dynamics of railway systems for a variety of operating conditions. The idea to develop a laboratory test rig started from the observation that there is a need for better-developed testing fixtures capable of accurately explaining the complex physics of wheel-rail contact toward designing faster, safer, and more efficient railway systems. A review of current roller rigs indicated that many desired functional requirements for studying contact mechanics currently are not available. Thus, the Virginia Tech Railway Technologies Laboratory (RTL) has embarked on a mission to develop a state-of-the-art testing facility that will allow experimental testing of contact mechanics in a dynamic, controlled, and consistent manner. VT roller rig will allow for closely replicating the boundary conditions of railroad wheel-rail contact via actively controlling all the wheel-rail interface degrees of freedom: cant angle, angle of attack, and lateral displacement. Two sophisticated independent drivelines are configured to precisely control the rotational speed of the wheels, and therefore their relative slip or creepage. A novel force measurement system, suitable for steel on steel contact, is configured to precisely measure the contact forces and moments at the contact patch. The control architecture is developed based on the SynqNet data acquisition system offered by Kollmorgen, the motors supplier. SynqNet provides a unified communication protocol between actuators, drives, and data acquisition system, hence eliminating data conversion among them. Various design analysis indicates that the rig successfully meets the set requirements: additional accuracy in measurements, and better control on the design of experiments. The test results show that the rig is capable of conducting various contact mechanics studies aimed for advancing the existing art. Beyond developing the experimental testing fixture for studying contact mechanics, this study provides a comprehensive review of the contact models. It discusses the simplifying assumptions for developing the models, compares the models functionality, and highlights the open areas that require further experimental and theoretical research. In addition, a multi-body dynamic model of the entire rig, using software package SIMPACK, is developed for conducting modal analysis of the rig and evaluating the performance of the rig's components. A MATLAB routine is also developed that provides a benchmark for developing creep curves from measurements of the rig and comparing them with existing creep curves. / Ph. D.
3

Design and Development of Force Control and Automation System for the VT-FRA Roller Rig

Dixit, Jay Kailash 13 August 2018 (has links)
This study discusses the design of a force control strategy for reducing force disturbances in the Virginia Tech – Federal Railroad Administration (VT-FRA) Roller Rig. The VT-FRA Roller Rig is a state-of-the-art roller Rig for studying contact mechanics. It consists of a 0.2m diameter wheel and a 1m diameter roller in vertical configuration, which replicates the wheel-rail contact in a 1/4th scale. The Rig has two 19.4 kW servo motors for powering the rotational bodies and six heavy-duty servo linear actuators that control other boundary conditions. The Rig was operationalized successfully with all degrees of freedom working in the default position feedback control. During the Rig's commissioning, this approach was found to result in vertical force fluctuations that are larger than desired. Since the vertical force affects the longitudinal and lateral traction between the wheel and roller, keeping the fluctuations to a minimum provides a better test condition. Testing and data analysis revealed the issue to be in the control method. The relative position of the wheel and roller was being controlled instead of controlling the forces between them. The latter is a far more challenging control setup because it requires a faster dynamic response and full knowledge of forces at the interface. Additionally, force control could result in dynamic instability more readily than position control. Multiple methods for force control are explored and documented. The most satisfactory solution is found in a cascaded loop force/position controller. The closed loop system is tested for stability and performance at various load, speed, and creepage conditions. The results indicate that the controller is able to reduce the standard deviation of vertical force fluctuations at the wheel-rail contact by a factor of four. In terms of power of the vertical force fluctuations, this corresponds to a 12 dB reduction with the force control when compared with the previous control method. This study also explores the possibility of automating the tests in order to enable running a larger number of tests in a shorter period of time. A multi-thread software is developed in C++ for executing a user-defined position, velocity, or force vs. time trajectory, and for recording the data automatically. The software also provides continuous monitoring, and performs a safe shutdown if a fault is detected. An intuitive GUI is provided for constant data polling and ease of user operation. The code is modular in order to accommodate future modifications and additions for various testing needs. The engineering upgrades included in this study, together with the baseline testing, complete the commissioning of the VT-FRA Roller Rig. With unparalleled parameter control and testing repeatability, the VT-FRA Roller Rig holds the promise of being used successfully for various contact mechanics needs that may arise in the railroad industry. / MS / Roller Rigs have seen widespread use around the world for research and development of railway vehicles. These test rigs are specialized machinery that provide the means to test a particular aspect of railroading in a controlled environment, allowing for thorough parametric analyses which aid in the design and development of railroad vehicles. One such test rig is the Virginia Tech – Federal Railroad Administration (VT-FRA) Roller Rig, located at the Railway Technologies Laboratory in Blacksburg, Virginia. It is a state-of-the-art test rig which is developed with the objective of providing a controlled test environment for studying railway contact mechanics. A good understanding of the wheel/rail contact is critical to railroad engineering, and this problem has been the subject of research for about a century now. Several compelling mathematical models have been proposed, but the experimental verification of those theories has proven to be difficult. Traditionally, field testing data has been utilized for comparison with prediction from the models. However, field tests are plagued by a low level of noise control and the inability to carry out sophisticated parametric analyses. VT-FRA Roller Rig holds the promise to fill this gap with its sophisticated electro-mechanical design and high precision instrumentation. The VT-FRA Roller Rig replicates the wheel-rail contact in a 1 /4 th scale by utilizing the INRETS scaling strategy. The locomotive wheel is replicated by a 0.2m diameter wheel and the tangent track is replicated by a 1m diameter roller. The relative size difference ensures that the contact distortion effects from the use of roller are kept to a minimum. The wheel and the roller are arranged in a vertical configuration, and are independently powered by two 19.4 kW servo motors. This enables the VT-FRA Roller Rig to achieve a precise creepage control of up to 0.1%. VT-FRA Roller Rig also has six heavy-duty servo linear actuators which are responsible for controlling four boundary conditions: cant angle, angle of attack, lateral displacement and vertical load. A sophisticated six-axis contact force-moment measurement system allows for precise measurements with a high dynamic bandwidth. The Rig was operationalized successfully with all degrees of freedom working in the default position feedback control. During the Rig’s commissioning, this approach was found to result in force fluctuations that were larger than desired. Since the vertical force affects the longitudinal and lateral traction between the wheel and roller, keeping the fluctuations to a minimum provides a better test condition. Testing and data analysis revealed the issue to be in the control method. The relative position of the wheel and roller was being controlled instead of controlling the forces between them. This study documents the development process of a reliable force control methodology for the VTFRA Roller Rig. Force control is a far more challenging control problem when compared to position control because it requires a faster dynamic response and full knowledge of forces at the interface. Additionally, force control could result in dynamic instability more readily than position control. Multiple methods for force control were implemented on the VT-FRA Roller Rig. Satisfactory solution is achieved with the complicated cascaded loop force/position controller, and the stability and performance of the control system is ensured by a slew of tests at various operating conditions. This study also explores the possibility of automating the tests in order to enable running a larger number of tests in a shorter period of time. A multi-thread software is developed in C++ for executing a user-defined position, velocity, or force vs. time trajectory, and for recording the data automatically. The software also provides continuous monitoring, and performs a safe shutdown if a fault is detected. An intuitive GUI is provided for constant data polling and ease of user operation. The code is modular in order to accommodate future modifications and additions for various testing needs. The engineering upgrades included in this study, together with the baseline testing, complete the commissioning of the VT-FRA Roller Rig. With unparalleled parameter control and testing repeatability, the VT-FRA Roller Rig holds the promise of being used successfully for various contact mechanics needs that may arise in the railroad industry.
4

Dynamic Modelling of the KTH Roller Rig / Dynamisk Modellering av KTH Rullriggen

Fraschini, Daniele Mario January 2021 (has links)
The Rail Vehicle Research group at Kungliga Tekniska Högskolan (KTH) is on the path to design and build a scaled test rig called roller rig for research and educational purposes. A roller rig is a device simulating the track with rollers on which the test subject (a wheelset, bogie or even a full vehicle) canbe placed.This thesis report is part of a bigger project involving several team members and it explores the applicability of track irregularities on a scaled roller rig by means of computer simulations. A scaled roller rig model, capable of simulating track irregularities, is generated using the multibody simulation softwareSIMPACK. Track irregularity data, represented as Power Spectral Densities (PSD), are applied to the model created. The model created and implementation of track irregularities are assessed in order to validate the modelling steps.Comparison with a reference vehicle model is carried out to verify if results obtained on the test rig are representative of a vehicle running on track, taking into account roller rig intrinsic errors. Results obtained aim to support the design of the roller rig’s mechanical components from a dynamical standpoint. / Forskargruppen spårfordon på Kungliga Tekniska Högskolan (KTH) arbetar med att designa och bygga en nedskalerad testrigg, en så kallad rullrigg, iforsknings- och utbildningssyfte. En rullrigg är en apparat avsedd att efterlikna järnvägsspåret med hjälp av cylinderhjul, på vilken testsubjektet (hjulaxel, boggi eller ett helt fordon) kan placeras.Denna rapport är en del av ett större projekt som involverar ett flertal gruppmedlemmar och undersöker tillämpligheten av spårlägesfel på en nedskalerad rullrigg med hjälp av simulationer. En nedskalerad rullrigg, kapabel att återskapa spårlägesfel, genereras med flerkroppsdynamik mjukvaran SIMPACK. Data för spårlägesfel, representerade med spektraltätheter (PSD), appliceras på den skapade modellen. Modellen samt implementering av spårlägesfelen bedöms sedan för att validera modelleringens steg.Jämförelse med en referensfordonsmodell genomförs för att verifiera att erhållna resultat från testriggen är representativ för ett verkligt spårfordon, med hänsyn tagen till rullriggens inneboende fel. Erhållna resultat syftar till att stödja utformningen av rullriggens mekaniska komponenter från ett dynamiskt perspektiv.
5

Accurate Wheel-rail Dynamic Measurement using a Scaled Roller Rig

Kothari, Karan 08 August 2018 (has links)
The primary purpose of this study is to perform accurate dynamic measurements on a scaled roller rig designed and constructed by Virginia Tech and the Federal Railroad Administration (VT-FRA Roller Rig). The study also aims at determining the effect of naturally generated third-body layer deposits (because of the wear of the wheel and/or roller) on creep or traction forces. The wheel-rail contact forces, also referred to as traction forces, are critical for all aspects of rail dynamics. These forces are quite complex and they have been the subject of several decades of research, both in experiments and modeling. The primary intent of the VT-FRA Roller Rig is to provide an experimental environment for more accurate testing and evaluation of some of the models currently in existence, as well as evaluate new hypothesis and theories that cannot be verified on other roller rigs available worldwide. The Rig consists of a wheel and roller in a vertical configuration that allows for closely replicating the boundary conditions of railroad wheel-rail contact via actively controlling all the wheel-rail interface degrees of freedom: angle of attack, cant angle, normal load and lateral displacement, including flanging. The Rig has two sophisticated independent drivelines to precisely control the rotational speed of the wheels, and therefore their relative slip or creepage. The Rig benefits from a novel force measurement system, suitable for steel on steel contact, to precisely measure the contact forces and moments at the wheel-rail contact. Experimental studies are conducted on the VT ��" FRA Roller Rig that involved varying the angle of attack, wheel and rail surface lubricity condition (i.e., wet vs. dry rail), and wheel wear, to study their effect on wheel-rail contact mechanics and dynamics. The wheel-rail contact is in between a one-fourth scale AAR-1B locomotive wheel and a roller machined to US-136 rail profile. A quantitative assessment of the creep-creepage measurements, which is an important metric to evaluate the wheel-rail contact mechanics and dynamics, is presented. A MATLAB routine is developed to generate the creep-creepage curves from measurements conducted as part of a broad experimental study. The shape of the contact patch and its pressure distribution have been discussed. An attempt is made to apply the results to full-scale wheels and flat rails. The research results will help in the development of better simulation models for non-Hertzian contact and non-linear creep theories for wheel-rail contact problems that require further research to more accurately represent the wheel-rail interaction. / MS / Rail vehicles are supported, steered, accelerated, and decelerated by contact forces acting in extremely small wheel-rail contact areas. The behavior of these forces is quite complex and a broad interdisciplinary research is needed to understand and optimize the contact mechanics and dynamics problem. Key industry issues, such as control of Rolling Contact Fatigue (RCF), maximizing wheelset mileages, and minimizing the impact of rolling stock on the infrastructure, are directly related to the interaction at the wheel-rail contact. The Rig consists of a wheel and roller in a vertical configuration that allows for closely replicating the boundary conditions of railroad wheel-rail contact via actively controlling all the wheel-rail interface degrees of freedom: angle of attack, cant angle, normal load and lateral displacement, including flanging. The Rig has two sophisticated independent drivelines to precisely control the rotational speed of the wheels, and therefore their relative slip or creepage. The Rig benefits from a novel force measurement system, suitable for steel on steel contact, to precisely measure the contact forces and moments at the wheel-rail contact. The primary purpose of this study is to perform accurate dynamic measurements on a scaled roller rig designed and constructed by Virginia Tech and the Federal Railroad Administration (VT-FRA Roller Rig). Experimental studies are conducted on the VT – FRA Roller Rig that involved varying the angle of attack, the wheel and rail surface lubricity condition (i.e., wet vs. dry rail), and the wheel wear to study their effects on wheel-rail contact mechanics and dynamics. The wheel-rail contact is in between a one-fourth scale AAR-1B locomotive wheel and a roller machined to US-136 rail profile. A quantitative assessment of the creep-creepage measurements, which is an important metric to evaluate the wheel-rail contact mechanics and dynamics, is presented. A MATLAB routine is developed to generate the creep-creepage curves from measurements conducted as part of a broad experimental study. The shape of the contact patch and its pressure distribution have been discussed. An attempt is made to apply the results to full-scale wheels and flat rails. The research results will help in the development of better simulation models for non-Hertzian contact and non-linear creep theories for wheel-rail contact problems that require further research to more accurately represent the wheel-rail interaction.
6

A Statistical Approach to Modeling Wheel-Rail Contact Dynamics

Hosseini, SayedMohammad 12 January 2021 (has links)
The wheel-rail contact mechanics and dynamics that are of great importance to the railroad industry are evaluated by applying statistical methods to the large volume of data that is collected on the VT-FRA state-of-the-art roller rig. The intent is to use the statistical principles to highlight the relative importance of various factors that exist in practice to longitudinal and lateral tractions and to develop parametric models that can be used for predicting traction in conditions beyond those tested on the rig. The experiment-based models are intended to be an alternative to the classical traction-creepage models that have been available for decades. Various experiments are conducted in different settings on the VT-FRA Roller Rig at the Center for Vehicle Systems and Safety at Virginia Tech to study the relationship between the traction forces and the wheel-rail contact variables. The experimental data is used to entertain parametric and non-parametric statistical models that efficiently capture this relationship. The study starts with single regression models and investigates the main effects of wheel load, creepage, and the angle of attack on the longitudinal and lateral traction forces. The assumptions of the classical linear regression model are carefully assessed and, in the case of non-linearities, different transformations are applied to the explanatory variables to find the closest functional form that captures the relationship between the response and the explanatory variables. The analysis is then extended to multiple models in which interaction among the explanatory variables is evaluated using model selection approaches. The developed models are then compared with their non-parametric counterparts, such as support vector regression, in terms of "goodness of fit," out-of-sample performance, and the distribution of predictions. / Master of Science / The interaction between the wheel and rail plays an important role in the dynamic behavior of railway vehicles. The wheel-rail contact has been extensively studied through analytical models, and measuring the contact forces is among the most important outcomes of such models. However, these models typically fall short when it comes to addressing the practical problems at hand. With the development of a high-precision test rig—called the VT-FRA Roller Rig, at the Center for Vehicle Systems and Safety (CVeSS)—there is an increased opportunity to tackle the same problems from an entirely different perspective, i.e. through statistical modeling of experimental data. Various experiments are conducted in different settings that represent railroad operating conditions on the VT-FRA Roller Rig, in order to study the relationship between wheel-rail traction and the variables affecting such forces. The experimental data is used to develop parametric and non-parametric statistical models that efficiently capture this relationship. The study starts with single regression models and investigates the main effects of wheel load, creepage, and the angle of attack on the longitudinal and lateral traction forces. The analysis is then extended to multiple models, and the existence of interactions among the explanatory variables is examined using model selection approaches. The developed models are then compared with their non-parametric counterparts, such as support vector regression, in terms of "goodness of fit," out-of-sample performance, and the distribution of the predictions. The study develops regression models that are able to accurately explain the relationship between traction forces, wheel load, creepage, and the angle of attack.
7

Electromechanical Design and Development of the Virginia Tech Roller Rig Testing Facility for Wheel-rail Contact Mechanics and Dynamics

Hosseinipour, Milad 28 September 2016 (has links)
The electromechanical design and development of a sophisticated roller rig testing facility at the Railway Technologies Laboratory (RTL) of Virginia Polytechnic and State University (VT) is presented. The VT Roller Rig is intended for studying the complex dynamics and mechanics at the wheel-rail interface of railway vehicles in a controlled laboratory environment. Such measurements require excellent powering and driving architecture, high-performance motion control, accurate measurements, and relatively noise-free data acquisition systems. It is critical to accurately control the relative dynamics and positioning of rotating bodies to emulate field conditions. To measure the contact forces and moments, special care must be taken to ensure any noise, such as mechanical vibration, electrical crosstalk, and electromagnetic interference (EMI) are kept to a minimum. This document describes the steps towards design and development of all electromechanical subsystems of the VT Roller Rig, including the powertrain, power electronics, motion control systems, sensors, data acquisition units, safety and monitoring circuits, and general practices followed for satisfying the local and international codes of practice. The VT Roller Rig is comprised of a wheel and a roller in a vertical configuration that simulate the single-wheel/rail interaction in one-fourth scale. The roller is five times larger than the scaled wheel to keep the contact patch distortion that is inevitable with a roller rig to a minimum. This setup is driven by two independent AC servo motors that control the velocity of the wheel and roller using state-of-the-art motion control technologies. Six linear actuators allow for adjusting the simulated load, wheel angle of attack, rail cant, and lateral position of the wheel on the rail. All motion controls are performed using digital servo drives, manufactured by Kollmorgen, VA, USA. A number of sensors measure the contact patch parameters including force, torque, displacement, rotation, speed, acceleration, and contact patch geometry. A unified communication protocol between the actuators and sensors minimizes data conversion time, which allows for servo update rates of up to 48kHz. This provides an unmatched bandwidth for performing various dynamics, vibrations, and transient tests, as well as static steady-state conditions. The VT Roller Rig has been debugged and commissioned successfully. The hardware and software components are tested both individually and within the system. The VT Roller Rig can control the creepage within 0.3RPM of the commanded value, while actively controlling the relative position of the rotating bodies with an unprecedented level of accuracy, no more than 16nm of the target location. The contact force measurement dynamometers can dynamically capture the contact forces to within 13.6N accuracy, for up to 10kN. The instantaneous torque in each driveline can be measured with better than 6.1Nm resolution. The VT Roller Rig Motion Programming Interface (MPI) is highly flexible for both programmers and non-programmers. All common motion control algorithms in the servo motion industry have been successfully implemented on the Rig. The VT Roller Rig MPI accepts third party motion algorithms in C, C++, and any .Net language. It successfully communicates with other design and analytics software such as Matlab, Simulink, and LabVIEW for performing custom-designed routines. It also provides the infrastructure for linking the Rig's hardware with commercial multibody dynamics software such as Simpack, NUCARS, and Vampire, which is a milestone for hardware-in-the-loop testing of railroad systems. / Ph. D.

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