Analysis of the Nonlinear Dynamics of a Railway Vehicle Wheelset

Law, E. Harry; Brand, R. S.

doi:10.1115/1.3426645

Cited by 20 publications

(5 citation statements)

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“…Therefore, the subsequent studies by Law and Brand [8], Hedrick and Arslan [9], and many other researchers extended the linear models to include the nonlinear factors of the vehicle systems, such as the wheel/rail contact geometry, creep forces, and suspension elements. The bifurcation theory provides the dynamic behavior of nonlinear systems when the system parameters change and plays an important role in the analysis of nonlinear system.…”

Section: Mathematical Problems In Engineeringmentioning

confidence: 99%

Numerical Investigation into the Critical Speed and Frequency of the Hunting Motion in Railway Vehicle System

Sun

Chi

Cai

et al. 2019

Mathematical Problems in Engineering

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The critical speed and hunting frequency are two basic research objects of vehicle system dynamics and have a significant influence on the dynamic performance. A lateral dynamic model with 17 degrees of freedom was established in this study to investigate the critical speed and hunting frequency of a high-speed railway vehicle. The nonlinearities of wheel/rail contact geometry, creep forces, and yaw damper were all considered. A heuristic nonlinear creep model was employed to estimate the contact force between the wheel and the rail. The Maxwell model, which covers the influence of the stiffness characteristic, is used to simulate the yaw damper. To reflect the blow-off of the yaw damper, the damping coefficient is described by stages. Based on the mathematical model, the combined effects of vehicle parameters on the critical speed in the straight line and hunting frequency of the wheelset were investigated innovatively. The novel phenomenon that the hunting frequency exhibits a sudden increase from a smaller value to a larger value when the blow-off of the yaw damper occurs was discovered during the calculations. The extents to which various parameters affect the critical speed and hunting frequency are clear on the basis of the numerical results. Moreover, all of the parameter values were divided into three sections to determine the sensitive range for the critical speed and hunting frequency. The results show that the first section of values plays the decisive role on both the critical speed and the hunting frequency for all parameters analyzed. The investigation in this paper enriches the study of hunting stability and gives some ideas to probably solve the abnormal vibrations during the actual operation.

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Section: Mathematical Problems In Engineeringmentioning

confidence: 99%

Numerical Investigation into the Critical Speed and Frequency of the Hunting Motion in Railway Vehicle System

Sun

Chi

Cai

et al. 2019

Mathematical Problems in Engineering

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“…We can solve the linear critical speed according to (16) and Hurwitz criterion [17][18][19][20]33], hereinafter referred to as and cr . With parameters in Table 1…”

Section: Asymptotic Domain Of Railway Wheelset By Metelitsyn's Theoremmentioning

confidence: 99%

“…They also investigated the influence of parameters on linear critical speed [18]. He et al used Hurwitz criterion and SQP algorithm to solve the nonlinear optimization stability problem of car [19]; see also the study by Law and Brand [20]. As for the nonlinear critical speed, it refers to the nonlinear bifurcation theory.…”

Section: Introductionmentioning

confidence: 99%

Analysis of the Gyroscopic Stability of the Wheelset

Dong

Zeng

et al. 2014

Shock and Vibration

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The wheelset of the railway vehicle is a rotor which itself has gyroscopic effect. Nowadays, the rolling stock has entered the era of high speed, and the wheel rotates faster than in the past. The influence of gyroscopic effect on stability is little understood. Metelitsyn’s inequality theorem for asymptotic stability has some advantages to analyze this problem although this method is sufficient but not necessary condition. Based on its deduction, the extremal eigenvalues criterion and compared with Routh-Hurwitz criterion, both are applied to solve the critical value of speed. Further, according to the instability criterion, gyroscopic contributory ratio is derived to study how the role the gyroscopic effect plays in stability. Moreover, the effect of gyroscopic matrix or gyroscopic terms pitch rotor inertia Iy on stability coefficient is investigated. The results show that Iy is a key factor to wheelset gyroscopic stability. The gyroscopic effect becomes significant, and the stability increases with increasing Iy. The results also indicate that the critical value of speed solved by Metelitsyn theorem is more conservative than the one it solved by Hurwitz criterion, which proves that Metelitsyn inequality theorem for asymptotic stability is a sufficient but not necessary condition in the way of attaining the numerical simulation result. Finally, the test for the influence of gyroscopic effect on stability needs to be further studied.

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“…Usually, a compromise between the two sets of nonlinearities is arrived at when a mathematical model of the motion of a train or a wheelset is derived. Using this latter approach, De Pater [10] Brann [3], Cooperrider [9], Law and Brand [23], Wickens [32,33] and others have obtained numerical and analytical solutions to the problems of a single wheelset or a truck. For a survey up to 1974, see [24], and for more recent work, see De Pater [11].…”

Section: Introductionmentioning

confidence: 99%

“…The averaging method [2,8] consists in finding a co-ordinate transformation so that after averaging, the equations become much less complicated and are therefore easily integrated. We note that recently, the above techniques have been employed in [3,9,10,23] and in [13,16,26] to determine the limit cycle of wheelsets and trucks.…”

Section: Introductionmentioning

confidence: 99%

On the application of a numerical algorithm for Hopf bifuraction to the hunting of a wheelset

Huilgol¹,

Janus²,

Lohe³

et al. 1984

J. Aust. Math. Soc. Series B, Appl. Math

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The main ideas of Hopf bifurcation theory and its relevance to the development of periodic motions of an autonomous system depending on a parameter are presented, and an algorithm for the computation of the orbits is described. It is then shown that a model system for the motion of a wheelset can be cast in the form amenable to Hopf bifurcation theory. Numerical results for the period and amplitudes of the lateral and yaw motions are obtained in terms of the forward speed of the wheelset, and the wheel-rail profile parameters It is found that the period of oscillation decreases while the lateral and yaw motion amplitudes increase as the forward speed increases, for any given rail and wheel profile. While the effect of wheel curvature on the lateral motions seems to be non-existent, its effect on the yaw motion amplitude and the period is to increase them very slightly as the wheel profile changes from a conical to a curved profile. On the other hand, the effect of rail curvature on the lateral amplitude, for instance, is significant; the larger the curvature the smaller the amplitude for a given forward speed.

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Analysis of the Nonlinear Dynamics of a Railway Vehicle Wheelset

Cited by 20 publications

References 0 publications

Numerical Investigation into the Critical Speed and Frequency of the Hunting Motion in Railway Vehicle System

Numerical Investigation into the Critical Speed and Frequency of the Hunting Motion in Railway Vehicle System

Analysis of the Gyroscopic Stability of the Wheelset

On the application of a numerical algorithm for Hopf bifuraction to the hunting of a wheelset

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