In order to ensure safe travel, railway vehicles must be stable under every condition along the track. Thus, a vehicle can be certified for operation only when it can fulfil certain criteria related to the ride stability. The stability of the vehicle is highly dependent on the wheel-rail friction coefficient: higher friction results in worse ride. So, to ensure a good evaluation of the stability, the friction should be high enough during tests. The same applies to the risk of wheel flange climbing. At the present time, the wheel-rail friction can not be measured directly but there are different procedures utilized to ensure that the conditions are suitable for testing the stability of the vehicle. In this study an algorithm is proposed to estimate the wheel-rail friction coefficient by using quantities which can be measured in reality. The algorithm is tried out in computer simulations. The algorithm has two parts: in Part 1 the friction coefficient is proposed to be equal to the ratio of the total creep force divided by the normal force; in Part 2 the total creep and spin creep are estimated to observe their correlation to the estimated friction. The contact angle in Part 1 is estimated by a contact point function. In the simulations, different conditions are tried. There are four horizontal radii: tangent track, R1300m, R1000m, and R400m. Three friction coefficients are used: 0.5, 0.4 and 0.3. In addition to this, track irregularities are included. A single vehicle is simulated in two modes: capable and incapable of passive radial steering. The track irregularities caused high values of the proposed estimated friction coefficient. The values in some instances were close or equal to the input friction coefficient of the simulation. Thus, if the highest values of the estimated friction were taken over a certain distance or time, the friction of the simulation could be approximated. In most cases, the total creep was following the trend of the estimated friction. The total creep and spin creep were used as a quality factor to determine how close the estimated friction was to the simulation’s friction. In this study when the total creep was greater than 0.006 and the spin creep was less than 1.0 m-1, the estimated friction was close to the input friction. The closeness was dependent on the simulation’s friction. Higher input friction resulted in larger deviation compared to lower friction. A sensitivity analysis has been performed by deliberately introducing errors in the position of the contact point and the angle of attack. The analysis shows that the errors are not critical when the contact point is close to the tread circle. When the contact point is close to the flange, a good measurement of the wheel profile and the contact point position required to obtain accurate results. On the other hand, the errors affect the friction estimate for high spin and low total creepage. These results are discarded by the algorithm, the influence of the errors is minimized.

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Transit operators are increasingly interested in improving efficiency, reliability, and performance of commuter trains while reducing their operating costs. In this context, the application of optimal control theory to the problem of train control can help towards achieving some of these objectives. However, the traction and braking systems of commuter trains often exhibit significant time delays, making the control of commuter trains highly challenging. Previous literature on optimal train control ignores delays in actuation due to the inherent difficulty present in the optimal control, and in general, the control, of input-delay systems. In this thesis, optimal control of a commuter train is presented under two cases: (i) equal, and (ii) unequal time delays in the train traction and braking commands. The solution approach uses the economic model predictive control framework, which involves formulating and solving numerical optimization problems to achieve minimum mixed energy-time optimal control in discretized spatial and time domains. The optimization problems are re-solved repeatedly along the track for the remainder of the trip, using the latest sensor measurements. This would essentially establish a feedback mechanism in the control to improve robustness to modelling errors. A key feature of the proposed methods is that they are model-based controllers, they explicitly incorporate model information, including time delays, in controller synthesis hence avoiding performance degradation and potential instability. To address the issue of input-delays, the well-established predictor approach is used to compensate for input-delays. The case of equal traction-braking delays is treated in discretized spatial domain, which uses an already developed convex approximation to the optimization problem. The use of the convex approximation allows for robust and rapid computation of the optimal control solution. The non-equal traction-braking delays scenario is formulated in time domain, leading to a nonconvex optimization problem. An alternative formulation for minimum-time optimal control problems is presented for delay-free systems that simplifies the solution of minimum-time optimal control problems compared to conventional minimum-time optimal control formulations. This formulation along with the predictor approach is used to help solve the train optimal control problem in the case of non-equal traction-braking delays. The non-equal traction-braking delay controller is compared with the equal traction-braking delay controller by insertion of an artificial delay to make the shorter delays equal to the longer delay. Results of numerical simulations demonstrate the validity and effectiveness of the proposed controllers. / Thesis / Master of Applied Science (MASc)

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.