The wheel-rail interface is fundamental to explain the dynamic running behavior of a railway vehicle. It must therefore be understood and among the parameters by which it is characterized, the one called “equivalent conicity ” plays an essential role since it allows optimal appreciation of wheel-rail contact on tangent track and on large-radius curves.
輪軌接觸是解釋鐵道車輛動力學特性的基礎，因此必須理解，而且在其特征參數中，等效錐度是本質的，可以理想地評估直線和大半進曲線上的輪軌接觸。
As the term equivalent conicity is used in a number of standard documents, including UIC leaflets, ISO standards and European standards, there needs to be an unambiguous way of determining it.
在不少標準文檔，包括UIC標準，ISO標準以及歐洲標準，都用到了名詞等效錐度，因此明確地定義它。
The purpose of this leaflet is to propose a method for determining equivalent conicity which can be applied in the context of standards documents.
本標準的目的在于推薦一種確定等效錐度的方法，并可用于標準文檔。
This leaflet does not define limits for the equivalent coniciity and gives no tolerance for the shape of the railhead and the wheel profile to obtain acceptable results with the conicity.
本標準沒有規定等效錐度的限度，
2-Symbols, principles and definition符號，原理和定義
2.1-Symbols 符號
х displacement of wheelset in the longitudinal of the track
輪對在鋼軌上的縱向位移
y displacement of wheelset in the lateral direction of the track
輪對在鋼軌上的橫向位移
ψ angle of movement in the x-y-plane
x-y平面上的運動角
e distance between contact points (approximately 1500 mm for standard gauge)
接觸點跨距（標準軌距約1.5m）
λ wave length
波長
r0 radius of wheels when the wheelset is centred on the track
輪對位于軌道中心車輪半徑
r1 rolling radius of right-hand wheel
右側車輪滾動半徑
r2 rolling radius of left-hand wheel
左側車輪滾動半徑
r mean rolling radius of both wheels
車輪名義滾動半徑
Δr difference of rolling-radii between right-hand and left-hand wheels
右側和左側車輪滾動半徑差
R local radius of wheel path
車輪路徑的局部半徑
ds curve length of path corresponding to angle dψ
dψ角對應的曲線長
tan γe equivalent conicity
等效錐度
tan γa inclination of wheel and rail profiles in contact point
接觸點位置車輛和鋼軌外形的傾角
ŷ amplitude of wave
波幅
yem y-displacement, where Δr = 0
y-位移，Δr = 0時
yemin, yemax corresponding ymin and ymax displacements for a certain wave
波形對應的ymin和ymax位移
v speed of forward movement of vehicle
車輛前進速度
2.2-Principles and definition 原理和定義
The kinematic movement of a free wheelset, which no inertia, running on a track, is described by the following differential equation:
軌道上自由輪對的運動以下面微分方程描述：
Without limiting the conclusions concerning calculation of the equivalent conicity, the speed of forward movement V of the vehicle can be assumed to be constant for the purposes of this study, such that
為了研究起見車輛前進速度假設為常數，不會限制涉及等效錐度計算的結論，于是
Hence:
因此：
以及
The differential equation becomes:
微分方程變為：
In the case of a wheelset whose wheels have a conical profile of angle γ：
若輪對的車輪外形為γ角的錐形：
The differential equation then becomes:
于是微分防程改寫為：
a second-order differential equation with constant coefficients whose solution is a sinewave with a wavelength of λ:
常系數二階微分方程的解是波長λ的正弦波：
When the wheels do not have a conical profile, linearisation methods can be used so that the linear differential equation can still be applied by replacing tanγ with tanγe , which is called the “equivalent conicity”.
如果車輪外形不是錐形，可以采用線性化方法，在微分方程中以tanγe取代tanγ進行線性化，tanγe稱作等效錐度。
By definition, the equivalent conicity is equal to the tangent tan γe.of the cone angle of a wheelset with coned wheels whose lateral movement has the same kinematic wavelength as the given wheelset (but only on tangent track and on large-radius curves).
等效錐度定義為與給定輪對橫向運動波長相同的錐形車輪輪對的車輪的錐度角正切。
3-Method of determination 定義方法
3.1-General principles 基本原理
The following assumptions are used:
- both the wheel and the rail are considered rigid,
-a theoretical wheel is symmetrical in revolution,
-a theoretical rail is straight and is represented by a single profile,
-a real rail is defined by at least 11 profiles regularly spaded apart over a 100m section of line; the conicity is obtained by taking the average of these individual coniciyies, the standard deviation of which should also be indicated,
-the wheel does not penetrate into the rail: only point contacts are considered,
-no account is taken of an axle’s roll (rotation about an axis longitudinal to the track) as the wheelset moves laterally on the track,
-at the point of contact, the planes tangent to the rail and to the wheel are parallel.
NB: a real wheel can be defined using an average profile determined by taking the average of 4sections of the wheel locater 90degree apart.
注：實際車輪取車輪90o分布的四個斷面外形的平均。...
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