UIC519_等效锥度全译文
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- UIC519_等效锥度全译文1-Purpose 目的
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.
轮轨接触是解释铁道车辆动力学特性的基础，因此必须理解，而且在其特征参数中，等效锥度是本质的，可以理想地评估直线和大半进曲线上的轮轨接触。
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.
在不少标准文档，包括UIC标准，ISO标准以及欧洲标准，都用到了名词等效锥度，因此明确地定义它。
The purpose of this leaflet is to propose a method for determining equivalent conicity which can be applied in the context of standards documents.
本标准的目的在于推荐一种确定等效锥度的方法，并可用于标准文档。
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.
本标准没有规定等效锥度的限度，
2-Symbols, principles and definition符号，原理和定义
2.1-Symbols 符号
х displacement of wheelset in the longitudinal of the track
轮对在钢轨上的纵向位移
y displacement of wheelset in the lateral direction of the track
轮对在钢轨上的横向位移
ψ angle of movement in the x-y-plane
x-y平面上的运动角
e distance between contact points (approximately 1500 mm for standard gauge)
接触点跨距（标准轨距约1.5m）
λ wave length
波长
r0 radius of wheels when the wheelset is centred on the track
轮对位于轨道中心车轮半径
r1 rolling radius of right-hand wheel
右侧车轮滚动半径
r2 rolling radius of left-hand wheel
左侧车轮滚动半径
r mean rolling radius of both wheels
车轮名义滚动半径
Δr difference of rolling-radii between right-hand and left-hand wheels
右侧和左侧车轮滚动半径差
R local radius of wheel path
车轮路径的局部半径
ds curve length of path corresponding to angle dψ
dψ角对应的曲线长
tan γe equivalent conicity
等效锥度
tan γa inclination of wheel and rail profiles in contact point
接触点位置车辆和钢轨外形的倾角
ŷ amplitude of wave
波幅
yem y-displacement, where Δr = 0
y-位移，Δr = 0时
yemin, yemax corresponding ymin and ymax displacements for a certain wave
波形对应的ymin和ymax位移
v speed of forward movement of vehicle
车辆前进速度
2.2-Principles and definition 原理和定义
The kinematic movement of a free wheelset, which no inertia, running on a track, is described by the following differential equation:
轨道上自由轮对的运动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
为了研究起见车辆前进速度假设为常数，不会限制涉及等效锥度计算的结论，于是
Hence:
因此：
以及
The differential equation becomes:
微分方程变为：
In the case of a wheelset whose wheels have a conical profile of angle γ：
若轮对的车轮外形为γ角的锥形：
The differential equation then becomes:
于是微分防程改写为：
a second-order differential equation with constant coefficients whose solution is a sinewave with a wavelength of λ:
常系数二阶微分方程的解是波长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”.
如果车轮外形不是锥形，可以采用线性化方法，在微分方程中以tanγe取代tanγ进行线性化，tanγe称作等效锥度。
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).
等效锥度定义为与给定轮对横向运动波长相同的锥形车轮轮对的车轮的锥度角正切。
3-Method of determination 定义方法
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.
假设如下：
-车轮和钢轨都是刚性的；
-理论上车轮旋转时对称的；
-理论上钢轨是直且可以用单一外形表示；
-实际钢轨要在100m以上的线路上至少用11个固定分布的外形来定义，锥度取这些锥度的平均值，标准差应说明；
-车轮不能侵入钢轨：只考虑一点接触；
-当轮对在轨道上横移时，不考虑轴的侧滚（绕着与轨道一致的纵向轴）
-在接触点，钢轨与车轮的切平面互相平行
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：实际车轮取车轮90o分布的四个断面外形的平均。...
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