Abstract
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.
Highlights
Dynamic stability problem of railway vehicle has been studied since hunting motion phenomenon was discovered by Stephenson from the United Kingdom 100 years ago [1]
Hurwitz criterion is the sufficient and necessary condition for all eigenvalues having negative part and the result VCM < Vcr proves that Metelitsyn theorem is the sufficient but not necessary condition for asymptotic stability
We derive the critical value of V and gyroscopic contributory ratio of wheelset equation with Metelitsyn inequality theorem
Summary
Dynamic stability problem of railway vehicle has been studied since hunting motion phenomenon was discovered by Stephenson from the United Kingdom 100 years ago [1]. Sedighi and Shirazi proposed equivalent functions method for complex nonlinearities to analyze the limit cycle of wheelset based on Yang and Ahmadian’s asymptotic method, where the Hopf bifurcation point is solved by Hurwitz criterion [17] They investigated the influence of parameters on linear critical speed [18]. It is not the traditional linear critical speed that we focus on, but it is the value solved by Metelitsyn’s criterion and the derived gyroscopic effect analysis that we investigate in this paper
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