Abstract:Application of the Nadal Limit to the prediction of wheel climb derailment is presented along with the effect of pertinent geometric and material parameters.Conditions which contribute to this climb include wheelset angle of attack, contact angle, friction and saturation surface properties, and lateral and vertical wheel loads. The Nadal limit is accurate for high angle of attack conditions, as the wheelset rolls forward in quasi-static steady motion leading to a flange climbing scenario. A detailed study is m… Show more
“…Many researchers [7][8][9][10] find it primitive and unable to take into account many factors affecting the safety of railway vehicles. Numerous attempts have been made to correct Nadal's formula with the aim of clarifying it [11][12][13][14][15][16][17][18][19][20][21][22][23][24]. However, derailments of locomotives and railway cars continue to occur quite regularly [25].…”
Section: Discussion Of the Results Of Studying The Safety Factor Agaimentioning
confidence: 99%
“…An attempt to improve Nadal's formula is also made in [13]. The refinement is based on taking into account the influence of the longitudinal contact force of creep and the angle of the wheel approaching the rail.…”
Section: проведено моделирование схода колеса железнодорожного экипажmentioning
“…Many researchers [7][8][9][10] find it primitive and unable to take into account many factors affecting the safety of railway vehicles. Numerous attempts have been made to correct Nadal's formula with the aim of clarifying it [11][12][13][14][15][16][17][18][19][20][21][22][23][24]. However, derailments of locomotives and railway cars continue to occur quite regularly [25].…”
Section: Discussion Of the Results Of Studying The Safety Factor Agaimentioning
confidence: 99%
“…An attempt to improve Nadal's formula is also made in [13]. The refinement is based on taking into account the influence of the longitudinal contact force of creep and the angle of the wheel approaching the rail.…”
Section: проведено моделирование схода колеса железнодорожного экипажmentioning
“…The mechanism of generation and development of this trace is not studied sufficiently yet and needs additional researches [18]. Besides, according to this paper, friction coefficient in the contact zone of the wheel and rail reaches 0.5 and more at derailments.…”
At present, Nadal's formula is used for prediction of derailment that contains a limited number of parameters. Besides, insufficient study of laws of variation of the noted parameters and ignorance of the influence of other parameters on the derailment complicate solution of the problem. The sliding distance and the relative sliding velocity are the most sensitive factors contributing to the destruction of the third body. Moreover, increased friction coefficient between the steering surfaces of the wheel and rail promotes climbing of a wheel on the rail and derailment. Dependences of the main parameters, influencing the destruction of the third body, the sliding distance and the relative sliding velocity on the rail track curvature, and difference of diameters of wheels of the wheelset and the non-roundness of one of the wheels of the wheelset are shown in the work. The methods for estimation of the third body destruction degree and consideration in Nadal's formula of the additional criterion of impossibility of the wheel rolling on the contact point of the wheel and rail steering surfaces, containing a value of this contact point advancing, which in turn depends on the angle of attack, are proposed.
“…[27][28][29][30][31][32][33][34][35][36] Other investigations have attempted to extend or correct Nadal's derivation, [37][38][39] and some recent investigations have recognized the importance of the wheelset orientation as well as the movement of the contact point. 3,26,[40][41][42][43][44][45][46][47][48] It is the purpose of this investigation to shed light on and reinforce the importance of taking into account the wheelset orientation as well as to demonstrate that, for a wheelset in contact with a tangent track at three distinct points, the system configuration can be fully defined given the wheelset angle of attack. It is the hopes of the authors that the analysis presented in this paper will be used to determine important derailment parameters and to fully understand the wheel climb derailment initiation problem.…”
Section: Motivation Background and Scopementioning
confidence: 99%
“…Wheel climb derailments can occur at low speeds and without any indication to the vehicle operator, and therefore, have been the target of numerous investigations. 1–7 These investigations have produced derailment criteria, which aim to measure the risk of and prevent such derailments. Figure 1.Wheelset angle of attack.…”
In previous research, a set of nonlinear algebraic kinematic constraint equations were developed that describe the configuration of a wheelset in contact with a track at two distinct points. In such a case of two points of contact, a simplified wheelset model that has the lateral displacement and angle of attack as the independent variables can be developed. In the current investigation, this approach is extended to the new case of a wheelset in contact with a tangent track at three distinct points. The solution of this three-point contact problem requires specifying the wheelset angle of attack only. This wheelset configuration is significant in derailment investigations because it is a possible configuration at the initiation of a wheel climb derailment. In order to study this wheel climb initiation configuration, a set of nonlinear kinematic constraint equations is developed as a function of the wheelset angle of attack and solved for the unknown system coordinates and contact surface parameters using an iterative Newton-Raphson algorithm. The wheelset angle of attack during wheel climb derailments can be determined forensically at the derailment site, making this approach of practical significance. It is shown in this investigation that the system configuration can be fully defined for wheel climb derailment initiation, which allows for the investigation of various derailment parameters such as the wheel-rail contact angle. It is then reinforced in this study that the wheelset flange angle, which is the angle between the tangent to the wheel surface at the contact point and the wheelset axle, is not representative of the wheel-rail contact angle, which is the angle between the tangent to the contact surfaces and the lateral common tangent to the two railheads; this distinction can only be demonstrated through full definition of the system configuration that accounts for the wheelset roll angle. This investigation therefore calls into question the Nadal L=V derailment limit as well as any investigation that chooses to neglect the wheelset orientation or the effect of such orientation on the wheel/rail contact geometry. This new formulation is validated and supported using a three-dimensional fully nonlinear unconstrained multibody system wheel climb derailment model recently proposed in a previous study. Using this model, new results demonstrate that initiation of the wheel climb motion is correctly predicted using proper geometry definitions in the derailment criteria, whereas previous results demonstrated such motion was not correctly predicted using the geometry definitions used by Nadal. This investigation is not intended as a derailment criteria proposal, but rather as support and rationalization for the use of correct contact geometry in derailment investigations. This investigation reiterates the important result that the Nadal L=V derailment limit is not conservative, and demonstrates that, with proper formulation, more accurate and justifiable derailment criteria can be developed.
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