By Alan Wickens

Basics of Rail motor vehicle Dynamics lays a starting place for the layout of rail automobiles in line with the mechanics of wheel-rail interplay as defined by means of the equations of movement. the writer advances uncomplicated versions to explain specific demanding situations and exhibit cutting edge structures whereas utilizing analytical experiences to envision novel layout options. instead of targeting a "typical" set of parameters, the e-book discusses the problems linked to the full variety of parameters to be had, focusing on the configuration and parametric layout of the bogie in terms of steerage, dynamic reaction, and balance. this can be an exceptional reference for designers and researchers concerned car improvement.

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**Sample text**

6 Heuristic approximations The analysis by Vermeulen and Johnson [31] is valid for arbitrary creepages but not for spin, and represented a simple way of accounting for creep saturation. It was, therefore, useful for dynamics analysis. Shen et al [44] proposed an extension to the method of Vermeulen and Johnson which includes the effects of spin. If the resultant of the creep forces calculated from (20) and (21) is TL then the effect of creep saturation is represented by if T ≤ 3µΝ if T > 3µΝ ⎧⎛ T L ⎞ 1 ⎛ T L ⎞ 2 1 ⎛ T L ⎞ 3 ⎫ ⎪ ⎪ ⎟− ⎜ ⎟ + ⎜ ⎟ ⎬ T = µN ⎨⎜ µ µ µ 3 27 N N N ⎠ ⎝ ⎠ ⎝ ⎠ ⎪ ⎪⎩⎝ ⎭ T = µN (30) (31) and then the longitudinal and lateral forces from (20) and (21) are reduced by the ratio T/TL.

10 Two point contact between wheel and rail. 1 Elasticity and friction So far, the size of the contact patch has been assumed to be small compared with the dimensions of the wheelset. However, the forces acting between wheel and rail depend on their elastic interaction in the vicinity of the contact patch, as well as the effects of friction. A comprehensive treatment of contact mechanics is given in [19]. 2 Laws of friction Laws of friction were postulated by Leonardo da Vinci, Amontons and Coulomb.

5 An approximate theory for arbitrary creepages An alternative to the complete numerical solution of the problem is the approximate and faster approach given by Kalker’s simplified theory [35] which is implemented in the computer program FASTSIM. 11 Typical relationships between creep forces and creepages and spin. 45 m, Rr = 149 mm, Rw = 271 mm. then substitution in (11) and (12) would give for the area of adhesion ∂σ x γ 1 ω 3 y = − ∂x f f (25) EQUATIONS OF MOTION 39 ∂σ y ∂x = γ 2 ω3 x + f f (26) These equations are approximated by ∂σ x γ 1 ω3 y = − ∂x f1 f3 ∂σ y ∂x = (27) γ 2 ω3 x + f2 f3 (28) where f1, f2 and f3 are determined so as to obtain results which agree with linear theory for small creepages.