变速器设计-外文翻译

变速器设计-外文翻译（通用3篇）

变速器设计-外文翻译篇1

Helwan University ABSTRACT Dynamic modeling of the gear vibration is a useful tool to study the vibration response of a geared system under various gear parameters and operating conditions.An improved understanding of vibration signal is required for early detection of incipient gear failure to achieve high reliability.However, the aim of this work is to make use of a 6-degree-of-freedom gear dynamic model including localized tooth defect for early detection of gear failure.The model consists of a gear pair, two shafts, two inertias representing load and prime mover and bearings.The model incorporates the effects of time-varying mesh stiffness and damping, backlash, excitation due to gear errors and modifications.The results indicate that the simulated signal shows that as the defect size increases the amplitude of the acceleration signal increases.The crest factor and kurtosis values of the simulated signal increase as the fault increases.Though the crest factor and kurtosis values give similar trends, kurtosis is a better indicator as compared to crest factor.KEYWORDS：Vibration acceleration, system modeling, Crest Factor, Kurtosis value, defect size, gear meshing, pinion, gear NOMENCLATURE JD，J1，J2，JL

Drive motor, pinion, gear, and load mass moment of inertia

Nagwa Abd-elhalim, Nabil Hammed, Magdy Abdel-hady，Shawki Abouel-Seoud and Eid S.Mohamed

replacement decision in a suitable time.m1，mMasses of pinion and gear.TD

Driving motor torque.TL

Load torque.第 1 页

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TF1，TFFriction torque.C1，C2

Viscous damping coefficient of pinion and gear bearing.Cm

Gear mesh damping.Gear mesh stiffness.Km

K1，K2

Pinion and gear shaft stiffness.4

The variance square.N

The number of samples.f

The defect width in face direction.Unit width Hertzian stiffness.KhD，1，2，L Angular displacement of drive motor, pinion, gear and load.D，1，2，L Angular velocity of drive motor, pinion, gear and load.，，， Angular acceleration of drive motor, pinion, gear and load.D12LINTRODUCTION Much of the past research in the dynamic modeling area has concluded that an essential solution to the problem is to use a comprehensive computer modeling and simulation tool to aid the transmission design and experiments.These have been two major obstacles to such an approach:(1)Progress in understanding of the basic gear rattle phenomenon has been limited and slow.This is because the engine-clutch-transmission system involves some strong nonlinearities including gear backlash, multi-valued springs, dry friction, hysteresis, and the like.(2)The gear rattle is a system problem and not only problem of gear teeth.Even through the research and industrial community has discussed the difficulties in varies stages of the problem, yet no thorough frame work covering the entire investigation process of such problem currently exists.This is largely due o the complexity of the power train system, which

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may make a computer analysis tool inefficient, in particularly when many different elements and clearances are encountered(e.g., gears, bearings, splines, synchronizers, and clutch)[1-3].A comprehensive review of mathematical models used in gear dynamics, published before 1986, has been presented by [4].In this review, gear dynamic models without defects have been discussed.In the past few years, researchers have been working on the gear dynamic models which include defects like pitting, spalling, crack and broken tooth.A single-degree-of-freedom model is used which include the e4ffects of variable mesh stiffness, damping, gear errors, profile modifications and backlash.The effect of time-varying meshing damping is also included in this case, The solution is obtained by using the harmonic balance methods.A method of calculated the optimum profile modification has been proposed in order to obtain a zero vibration of the gear pair [5-7].They also proposed a linear approximate equation to mode the gear pair by using a single-degree-of freedom model Gear rattle vibration is a undesirable vibration for passenger cars and light trucks equipped with manual transmissions.Unlike automatic transmissions, manual transmission do not have the high viscous damping inherent to a hydrodynamic torque converter to suppress the impacting of gear teeth oscillating through their gear backlash.Therefore a significant level of vibration an be produced by the gear rattle and transmitted both inside the passenger compartment and outside the vehicle.Gear rattle, idle shake, and other vibration generated in the automobile driveline have become an important concern to automobile manufactures in their pursuit of an increased level of perception of high vibration quality.The torsional vibration o driveline is a major source of gear rattle vibration.The manual transmission produces gear rattle by the impacting of gear oscillating through their gear backlash.The impact collisions are transmitted to the transmission housing via shafts and bearings [8].The gear pair dynamic models including defects have been done by [9].The study

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suggests that little work has been done on modeling of gear vibration with defect and an accurate analytical procedure to predict gear vibrations in the presence of local tooth fault has yet to be developed.However, the purpose of this paper is to develop a multidegree-of-freedom nonlinear model for a gear pair that can be used to study the effect of lateral-torsional vibration coupling on vibration response in the presence of localized tooth defect.A typical fault signal is assumed to be impulsive in nature because of the way it is generated.The simulation artificially introduced pitting in gears in multi-stage automotive transmission gearbox at different operation conditions(load, speed, etc).The processing of simulated and experimental signals is also introduced.SIGNAL-PROCESSING TECHNIQUE Among various signal-processing techniques, crest factor and kurtosis analysis have been used for analyzing the whole vibration signal for the early detection of fault.In this section, crest factor and kurtosis value have been explained.MATHEMATICAL MODEL FORMULATION

Helical gears are almost always used in automotive transmissions.The meshing stiffness of a helical tooth pair is time-varying [10], and was modeled as a series of suggested spur gears so that the simulation techniques for spur gears can be applied.where M is Module(mm), b is Face width(mm),  is pressure angle(deg),  is helix angle(deg)and D1 is pitch diameter(mm).Fig.2 shows the equivalent gear system in the first gear-shift, where the main parameters for the gear system of Fiat-131 gearbox and the equivalent gear system in the first gear-shift are also shown in the figures.第 4 页

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汽车变速箱动态建模轮齿局部缺陷的早期检测

Nagwa Abd-elhalim, Nabil Hammed, Magdy Abdel-hady，Shawki Abouel-Seoud and Eid S.Mohamed

阿勒旺大学

摘要

在研究齿轮系统中各种齿轮参数的振动响应和操作条件时，齿轮振动的动态建模是一个非常有用的工具。对早期的齿轮检测提出了一种改进理解的振动信号，但还没达到高的可靠性。但是，这项工作的目的是利用一个6自由度的齿轮动力学模型对齿轮轮齿缺陷故障的早期检测。该模型包括一对齿轮副、两个轴、两个惯性负载、动力传动装置和轴承。由于齿轮的误差和变动，该模型被采用时受到时变啮合刚度、阻尼、反弹和励磁的影响。模拟信号显示的结果表明，随着缺陷尺寸的增加加速度信号的振幅增加。模拟信号的波峰因素和峰值随着缺陷的增加而增加。虽然波峰因素和峰值做同样的趋势，但和波峰因素相比峰值是一个比较好的指标。关键词：振动加速度、系统建模、波峰因素、峰值、缺陷大小、齿轮啮合、齿轮专业术语

JD，J1，J2，JL

驱动电机、小齿轮、大齿轮和负载在一定时间内的惯性矩 m1，m

1大齿轮、小齿轮的模数 TD

发动机驱动转矩 TL

负载力矩 TF1，TF摩擦力矩

C1，C2

齿轮、轴承的粘滞阻尼系数

齿轮啮合阻尼

齿轮啮合刚度 Km

K1，K齿轮、齿轮轴的刚度



平方差

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样本数量

宽度方向的缺陷

单位宽度的刚度 KhD，1，2，L

驱动电机、小齿轮、大齿轮和负载的角位移 D，1，2，L

驱动电机、小齿轮、大齿轮和负载的角速度

，，，

驱动电机、小齿轮、大齿轮和负载的角加速度 D12L引言

在大多数过去的动态建模研究领域中，解决问题的重要办法是全面使用计算机建模和仿真工具来辅助变速器的设计和实验。这种方法有两种主要的障碍：（1）对齿轮传动中噪声基本认识的进展是有限的和缓慢的。这是因为发动机离合器传动系统中包括齿轮侧隙、多值弹簧、非线性滞后等等。（2）齿轮发出的噪声是一个系统问题，并不是齿轮的唯一问题。既使是工业研究领域已经讨论了这个问题在不同阶段所出现的不同问题，但并没有彻底覆盖工作的框架，整个研究过程中的问题依然存在。这主要是由于列车电力系统的复杂性，可能导致你的计算机的分析工具效率不高，尤其是工作中遇到许多不同的因素和间隙（例如：齿轮、轴承、花键、同步器和离合器）。

在1986年出版之前，对齿轮动力学中提出的齿轮动态建模进行了审查。这次审查中，对不存在齿轮缺陷的齿轮动力学模型进行了讨论。在过去的几年里，研究人员对齿轮的动态模型缺陷进行了研究，其中包括点蚀、剥落、裂缝和齿轮折断等。

单自由度系统模型中，对啮合刚度的影响包括4个方面的因素，阻尼、齿轮误差、轮廓变动和齿侧间隙，时变啮合阻尼效应也包含在这种情况中。解决问题的方法是利用谐波平衡的方法。为了实现齿轮副的零振动，提出了一种最优化的计算方法。他们还利用齿轮副单自由度模型提出了一个近似的线性方程模型。

齿轮噪声振动是轿车和轻型货车手动变速箱中的不良振动。不同于自动变速箱的是，手动变速箱没有一个固有的高粘性阻尼液力变矩器以制止通过齿轮侧隙造成的齿轮摆动的影响。因此，无论是在车厢内外由齿轮振动和传动产生的噪声，对车

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辆振动的影响都非常大。随着人们对汽车高性能振动的追求，齿轮松动、振动以及其他汽车传动系产生的噪声已成为人们关注的重点。传动系统中的扭转振动是齿轮振动的一种主要噪声来源。手动变速箱产生的齿轮噪声是由于齿轮受到齿轮间隙振动的影响。通过轴和轴承把碰撞产生的影响传输到变速箱壳体。

对齿轮副的动态模型缺陷的研究结果表明，对齿轮副动态模型缺陷已做了大量工作，用准确的分析方法对齿轮振动的检测在当时轮齿故障方面还没得到发展。然而，本研究的目的是建立一个多自由度非线性模型用于研究，结果表明轮齿局部缺陷的扭转振动是耦合振动的响应。由于他的产生一个典型的故障信号被假设为自然的脉冲信号。在不同操作条件下（负荷、转速等），模拟人工对多级汽车变速器齿轮缺陷进行了介绍。同时也对信号的仿真和实验处理进行了介绍。信号处理技术

在各种各样的信号处理技术中，波峰因素、峰值已用于分析整个振动信号的早期故障。在本节中，波峰因素和峰值已被解释。数学模型

汽车变速器中的齿轮大都是斜齿圆柱齿轮。被视为一系列齿轮仿真技术适用于螺旋状的轮齿时变啮合刚度。式中m是模数(毫米),b齿面宽(毫米),是压力角(度),是螺旋角(度)，D1是直径(毫米)。图2的数据显示了等效齿轮系统在齿轮变动中变速箱齿轮系统的主要参数。

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交通运输外文翻译外文文献篇2

S.Oppe 关键字：后果;目的;描述;限制;关注;事故分析;可能性

摘要：交通事故的统计数字，尤其国家一级的数据对监控和预测事故的发展，积极或消极检测事故的发展，以及对定义安全目标和评估工业安全特别有益。事故分析是应用非常有限的分析，是前瞻性分析和回顾性分析，能够对新开发的交通安全系统和特殊过程的安全措施进行评价。目前迫切需要一个将实时事故分析与研究相结合的行为。将自动检测和视频录制相结合的研究交通事故的科研论文会比较容易接受。这种类型的研究最终会对交通理念有个完善的认识。

1．简介

本文主要是基于个人的经验，研究有关交通安全、安全分析以及事故分析等在研究中的作用。由这些经验推导出的哲学思考就像通过研究和统计得出的实践观点。而这些调查数字已经在其他地方发表了。

在缺少直接观察的事故中，许多方法论问题的产生，导致不能直接测试对结果持续讨论。通过看事故视频来讨论是富有成效的。事实证明，用来解释事故的大部分有关信息就是事故中缺少的记录。深入研究还无法回忆起所有的必要的用来测试有关事故发生的假设数据。尤其是车-车相撞发生的车祸，这是在荷兰城市道路交叉口录制的视频，一辆从岔路驶来的汽车与主干路的汽车相撞，下列问题可以问：为什么汽车来自次干路上，突然加速后又几乎停止，撞上了在左侧主路的一辆汽车呢？为什么没有注意到正在驶来的车？是不是因为两车从右边驶来，司机因为前面的交叉为他们提供了可能性而斤斤计较？难道他向左看过，但他认为停在拐角处的绿色货车能让他停下来？当然，交通状况并不复杂。目前这个事故中没有骑自行车或行人在拥挤路口分散他的注意。如果停着的绿色车能够在五分钟内消失，这两辆车可能就不会相撞。在事故发生的相关条件下，几乎不可能观察下一个交通行为，因为交通事故是不可预见的。由于新的视频设备和自动检测事故设备的不断发展，如在收集数据方面不需要很高的成本就能变得越来越逼真。必要的增加数据类型也能更好的解释交通中存在的危险因素。关于事故分析的可能性和限制性的问题是不容易回答的，我们不能确切的分析交通事故。因为事故分析涵盖了每一个活动中的不同背景，并根据不同的信息来源范围来补充资料，特别是收集事故的数据，背景资料等，我们首先要看看在交通安全领域的活动周期然后再回答事故分析的可能性与限制。这些行为主要是与交通系统的安全管理有关，有些则是相关的研究活动。

应该用下面的步骤来加以区分： ——检测交通安全问题；

——描述问题和它的主要特征； ——分析其原因分析和改进建议； ——选择和执行安全措施； ——评价所采取的措施。

虽然这个周期可以由同一人或一群人做出来，而问题在每个阶段（政治/管理或科学）都有不同的背景。我们用事故分析来描述这一阶段。做这个决定是重要的。很多关于分析结果的方法的讨论由于忽视之间的区别而成为徒劳的。政治家或道路管理人员对道路的个别事故不是很留意。他们对事故的看法往往都是一视同仁，因为总的结果比整个事故中的每个人的因素重要。因此，每次事故看做一个个体，之间相互协调就会达成安全的结果。

研究人员研究事故发生时一连串事件中每个人的兴趣。希望从中得到关于每次事故的详细信息并能发现其发生的原因和有关的条件。政治家们希望只是因为细节决定行动。在最高一级事故总数减少。信息的主要来源是国家数据库及其统计学处理系统。对他来说，统计意外数字及其统计的波动来进行事故分析。这适用于事故分析中的交通安全领域。因此，我们将首先描述了事故的这些方面。2．事故的性质和它们的统计特性

事故基本概念是意外，不管是其发生的原因还是引起事故出现的过程。两个简单的假设通常是来描述交通事故的形成过程：

-事故发生的概率与以往发生的事故之间是独立；-事故发生在时间上是同性质的

如果这两个假设成立，那么事故是泊松分布。第一个假设与大多数的批判不符。事故是罕见的事件，因此不会受到以前事故的影响。在某些情况下，有一个直接的因果链（例如，大量的车开到一起）这一系列的事故被认为是一个个体事故但包含许多的车。这个假设并不适用于统计人员伤亡。伤亡人数往往与同一事故有关，因此，独立性假设不成立。第二个假设乍一看似乎不太容易理解。穿越空间或在不同地点发生的的事故同样具有可能性。然而，假设需要很长一段时间并且没有缓缴期。其性质是根据理论的假设。如果其短时间内能成立，那么它也适用于长时间，因为泊松分布变量的总和，即使他们的泊松率是不同的，但也属于泊松分布。对于这些时期的总和泊松率则等于为这些地方的泊松率的总和。假设与一个真正的情况相比较计数，无论是从一两个结果还是总情况来看都有一个基本情况比较符合。

例如，对比在一年中特定的一天例如下一天，下一个星期的一天发生的交通事故。如果条件是相同的（同一时间，交通情况相同，同样的天气条件等），那么由此产生的意外数字是相同的泊松过程的结果。这一假设可以通过估算进行测试的两个观测值的基础上（估计是两个值的平均值）的速度参数。概率理论能够

考虑到这两个观察值的平均，用于计算的平等假设的可能性。这是一个相当强大的统计过程。泊松假设是研究了很多次，来获得证据支持。它已经应用于许多情况，数的差异表明在安全性的差异然后确定是否发生意外。这一程序的主要目的是检测在安全分歧。这可能是一个时间上的差异，或不同的地方或不同的条件。这种差异可以指导改进的过程。由于主要关注的是，以减少意外的发生，这种分析可能导致对治疗中最有前途的领域。为这样一个测试应用程序的必要条件是，那意外的数字进行比较是大到足以证明存在的分歧。在许多地方情况下，一个应用程序是不可能的。事故黑点分析往往阻碍了这一限制，例如，如果应用这种测试，找出事故是否在特定的位置数是高于平均水平。该程序的描述，也可以使用，如果发生意外乃根据数的特点找到有前途的安全目标。不仅聚集，而且还与分类泊松假设成立，而意外数字可以相互测试的泊松假设的基础。这种测试是相当麻烦的，因为每个特定的情况下，每一个不同的泊松参数，即，对所有可能结果的概率必须计算应用测试。然后，泊松分布近似为正态分布，均值和方差等于泊松参数。一旦均值和方差的正态分布，给出了所有的测试可以改写了标准零均值和

方差的正态分布条件。没有任何更多的必要计算，但测试统计，需要利用表绘制。3.行车安全政策事故统计的应用

分析那些假设的基础上描述的测试程序的类型及其优点。这种应用最好的例子是为一个国家或地区进行超过一年的安全监测，用事故的总体数据（最终的特定类型，如死亡事故）与前几年的数据相比较。根据数年的事故序列，能够分析出它的发展趋势，并大致预测以后几年的事故数量。一旦建立了这样一种趋势，那么在误差范围内未来一年或几年都可以预见。从一个给定趋势的偏差也可以进行预测新的事件。最有名的是斯米德在1949年进行的分析。我们将讨论这个事故类型分析更详细的内容。

1、该测试应用推广到高阶分类。Foldvary和Lane（1974），在衡量强制佩戴安全带的效果，谁是最早应用于值的4路表高阶相互作用的总卡方分配的。

2、测试不局限于总体影响，但卡方值就可以分解模型内子假说。另外，在双向表，卡方总可以分解成零件表互动的作用。对1的优势。和2。比以前的情况是，这对许多相互关联的（子）表和相应的智广场卡方检验是由大量分析，取而代之的是一个一卡方的确切划分。

3、投入更多关注的是参数估计。例如，在卡方分割使人们有可能以测试有关行参数的线性或二次限制或趋势的不连续性。

4、分析的单位是从数到广义加权计数。这对于道路安全分析，那里一段时间，道路使用者的数量，地点或公里数的车辆往往是必要的修正有利。最后一个选项是没有发现在许多统计软件包。安徒生1977年给出了一个用于道路双向安全分析表的例子。工资保障运动的一个计算机程序。这一级没有说明事故原因分

析。它会尝试检测安全问题需要特别注意。所需的基本信息包括事故数字，来形容不安全总额，暴露的数据来计算风险，并找到一个高风险的情况下或（团体）道路使用者。

4.事故分析研究目的

交通安全的研究是有关的事故及其后果的发生。因此，人们可能会说，研究对象是意外。然而研究人员的兴趣较少集中在这个最后的结果本身，而是多在进程更多的结果（或不结果）的事故。因此，最好是把作为他的研究对象，在流量的重要事件。一个在交通意外的过程，结果是，该实际发生是由研究者未落观测研究的主要问题。

调查一宗交通意外，他将努力重建了间接来源的事件，如涉及的道路使用者，所提供的资料或目击者有关情况，车辆，道路和司机的特点。因此这不是科学独特的，也有一个间接的研究对象的研究更多的例子。但是，第二个困难是，该研究的对象不能被诱发。有系统的控制实验手段研究只对问题方面的可能，而不是问题本身。

间接观察和缺乏系统的控制组合使调查人员很难发现在什么情况下造成事故的因素。虽然研究人员主要是在事故处理领导有兴趣，他几乎完全信息的后果，它的产品，意外。此外，事故背景是复杂的。一般来说，可分为以下几个方面：

-考虑到交通系统，交通量和组成国家，道路使用者，他们的速度，天气条件下，路面情况，车辆，道路使用者和他们的相互作用的演习，意外可以或无法预防。

-由于发生事故，也对这样的速度和车辆质量的因素，大量的不同，碰撞角度，对道路使用者和他们的脆弱性，影响等位置的保护，伤害是严重或或多或少物质损失是多还是少可观。虽然这些方面不能独立研究从理论的角度看，它也从由此产生的结果的优势，区分交通情况有潜在危险的数字，是由有一个意外的可能性，在这种潜在的危险局势，给定一个特定事故。

这个概念框架是对风险的关于个别道路使用者，以及上级的决定控制器的决定制定的一般基础。在风险的数学公式，我们需要一个明确的概率空间的介绍，基本事件（的情况），可能导致事故组成，每个类型的事件的概率，最终收在一次事故中，最后的具体成果，损失，鉴于事故的类型。

另一种方法是看事故特征组合，然后找出关键因素。这种类型的事故分析是通过分析事故的共组或子群来开展。事故本身是一个研究的单位，但也要研究道路因素：道路位置，道路设计（如一个弯道）等。

原文出处：SWOV institute for road safety research Leidschendam（会议记录），记录者，S.Oppe.POSSIBILITIES AND LIMITATIONS OF ACCIDENT

ANALYSIS

S.Oppe Keyword：Consequences;purposes;describe;Limitations;concerned;Accident Analysis;possibilities Abstraet：Accident statistics, especially collected at a national level are particularly useful for the description, monitoring and prognosis of accident developments, the detection of positive and negative safety developments, the definition of safety targets and the(product)evaluation of long term and large scale safety measures.The application of accident analysis is strongly limited for problem analysis, prospective and retrospective safety analysis on newly developed traffic systems or safety measures, as well as for(process)evaluation of special short term and small scale safety measures.There is an urgent need for the analysis of accidents in real time, in combination with background behavioural research.Automatic incident detection, combined with video recording of accidents may soon result in financially acceptable research.This type of research may eventually lead to a better understanding of the concept of risk in traffic and to well-established theories.1.Introduction.This paper is primarily based on personal experience concerning traffic safety, safety research and the role of accidents analysis in this research.These experiences resulted in rather philosophical opinions as well as more practical viewpoints on research methodology and statistical analysis.A number of these findings are published already elsewhere.From this lack of direct observation of accidents, a number of methodological problems arise, leading to continuous discussions about the interpretation of findings that cannot be tested directly.For a fruitful discussion of these methodological problems it is very informative to look at a real accident on video.It then turns out that most of the relevant information used to explain the accident will be missing in the accident record.In-depth studies also cannot recollect all the data that is necessary in order to test hypotheses about the occurrence of the accident.For a particular car-car accident, that was recorded on video at an urban intersection in the Netherlands, between a car coming from a minor road, colliding with a car on the major road, the following questions could be asked:Why did the driver of the car coming from the minor road, suddenly accelerate after coming almost to a stop and hit the side of the car from the left at the main road? Why was the approaching car not noticed? Was it because the driver was preoccupied with the two cars coming from the right and the gap before them that offered him the possibility to cross? Did he look left before, but was his view possibly blocked by the green van parked at the corner? Certainly the traffic situation was not complicated.At the moment of the accident there were no 5

bicyclists or pedestrians present to distract his attention at the regularly overcrowded intersection.The parked green van disappeared within five minutes, the two other cars that may have been important left without a trace.It is hardly possible to observe traffic behaviour under the most relevant condition of an accident occurring, because accidents are very rare events, given the large number of trips.Given the new video equipment and the recent developments in automatic incident and accident detection, it becomes more and more realistic to collect such data at not too high costs.Additional to this type of data that is most essential for a good understanding of the risk increasing factors in traffic, it also important to look at normal traffic behaviour as a reference base.The question about the possibilities and limitations of accident analysis is not lightly answered.We cannot speak unambiguously about accident analysis.Accident analysis covers a whole range of activities, each originating from a different background and based on different sources of information: national data banks, additional information from other sources, specially collected accident data, behavioural background data etc.To answer the question about the possibilities and limitations, we first have to look at the cycle of activities in the area of traffic safety.Some of these activities are mainly concerned with the safety management of the traffic system, some others are primarily research activities.The following steps should be distinguished:description of the problem and its main characteristics;selection and implementation of safety measures;the probability of an accident to occur is independent from the occurrence of previous accidents;-the occurrence of accidents is homogeneous in time.If these two assumptions hold, then accidents are Poisson distributed.The first assumption does not meet much criticism.Accidents are rare events and therefore not easily influenced by previous accidents.In some cases where there is a direct causal chain(e.g., when a number of cars run into each other)the series of accidents may be regarded as one complicated accident with many cars involved.The assumption does not apply to casualties.Casualties are often related to the same accident and therefore the independency assumption does not hold.The second assumption seems less obvious at first sight.The occurrence of accidents through time or on different locations are not equally likely.However, the assumption need not hold over long time periods.It is a rather theoretical assumption in its nature.If it holds for short periods of time, then it also holds for long periods, because the sum of Poisson distributed variables, even if their Poisson rates are different, is also Poisson distributed.The Poisson rate for the sum of these periods is then equal to the sum of the Poisson rates for these parts.The assumption that really counts for a comparison of(composite)situations, is whether two outcomes from an aggregation of situations in time and/or space, have a comparable mix of basic situations.E.g., the comparison of the number of accidents on one particular day of the year, as compared to another day(the next day, or the same day of the next week etc.).If the conditions are assumed to be the same(same duration, same mix of traffic and situations, same weather conditions etc.)then the resulting numbers of accidents are the outcomes of the same Poisson process.This assumption can be tested by estimating the rate parameter on the basis of the two observed values(the estimate being the average of the two values).Probability theory can be used to compute the likelihood of the equality assumption, given the two observations and their mean.This statistical procedure is rather powerful.The Poisson assumption is investigated many times and turns out to be supported by a vast body of empirical evidence.It has been applied in numerous situations to find out whether differences in observed numbers of accidents suggest real differences in safety.The main purpose of this procedure is to detect differences in safety.This may be a difference over time, or between different places or between different conditions.Such differences may guide the process of improvement.Because the main concern is to reduce the 7

number of accidents, such an analysis may lead to the most promising areas for treatment.A necessary condition for the application of such a test is, that the numbers of accidents to be compared are large enough to show existing differences.In many local cases an application is not possible.Accident black-spot analysis is often hindered by this limitation, e.g., if such a test is applied to find out whether the number of accidents at a particular location is higher than average.The procedure described can also be used if the accidents are classified according to a number of characteristics to find promising safety targets.Not only with aggregation, but also with disaggregation the Poisson assumption holds, and the accident numbers can be tested against each other on the basis of the Poisson assumptions.Such a test is rather cumbersome, because for each particular case, i.e.for each different Poisson parameter, the probabilities for all possible outcomes must be computed to apply the test.In practice, this is not necessary when the numbers are large.Then the Poisson distribution can be approximated by a Normal distribution, with mean and variance equal to the Poisson parameter.Once the mean value and the variance of a Normal distribution are given, all tests can be rephrased in terms of the standard Normal distribution with zero mean and variance one.No computations are necessary any more, but test statistics can be drawn from tables.3.The use of accident statistics for traffic safety policy.The testing procedure described has its merits for those types of analysis that are based on the assumptions mentioned.The best example of such an application is the monitoring of safety for a country or region over a year, using the total number of accidents(eventually of a particular type, such as fatal accidents), in order to compare this number with the outcome of the year before.If sequences of accidents are given over several years, then trends in the developments can be detected and accident numbers predicted for following years.Once such a trend is established, then the value for the next year or years can be predicted, together with its error bounds.Deviations from a given trend can also be tested afterwards, and new actions planned.The most famous one is carried out by Smeed 1949.We will discuss this type of accident analysis in more detail later.1.The application of the Chi-square test for interaction is generalised to higher order classifications.Foldvary and Lane(1974), in measuring the effect of compulsory wearing of seat belts, were among the first who applied the partitioning of the total Chi-square in values for the higher order interactions of four-way tables.2.Tests are not restricted to overall effects, but Chi-square values can be decomposed regarding sub-hypotheses within the model.Also in the two-way table, the total Chisquare can be decomposed into interaction effects of part tables.The advantage of 1.and 2.over previous situations is, that large numbers of Chi-square tests on many interrelated(sub)tables and

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2006年9月13日

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