利用只装有车轮速度传感器的制动防抱死系统做路面情况鉴定【中英文WORD】【中文2390字】.zip
共 页 第 页装订线【中文【中文 2390 字】字】利用只装有车轮速度传感器的制动防抱死系统做路面情况鉴定利用只装有车轮速度传感器的制动防抱死系统做路面情况鉴定摘要摘要:制动防抱死系统(ABS),是目前在汽车上得到广泛使用的设备。为了降低制造成本,并利用现有可用的技术,标准 ABS 系统仅使用车轮速度传感器检测车轮转速,这是不能够直接获取控制单元需要的车轮滑移率,但可以利用计算所得的车轮角速度和估计的车速间的关系来计算参考滑移率。因此,道路摩擦系数,它决定了车辆在紧急刹车时的减速度,是一个估算汽车速度的重要参数。本文分析了在不同路面情况下模拟紧急制动时车轮的加速度,并选择一对特殊的点来确定车轮加速曲线在每个不同的操纵情况下,比如路面情况,制动扭矩和车轮的垂直载荷。它是建立在每个用试点做出的针对不同路面的曲线明显不同于其他路面。因此,不同的路面可以用这些点来区分,这些点反映了他们所代表的路面情况。分析假设只有车轮速度传感器是可利用的仪器并且道路附着情况可以在紧急制动的开始初期阶段确定。关键字关键字:制动防抱死系统(ABS);路面情况鉴定;车轮角加速;轮胎特性介绍介绍 对制动防抱死系统(ABS)来说,道路附着情况是最重要的因素之一。标准 ABS系统可以在制动时确定道路附着情况,并且确定道路摩擦力是高(沥青路面)、或低(雪、冰路面),然后由控制单元激活相应的逻辑控制系统。只有车轮速度传感器在标准ABS 系统中可以确定路面情况,不需要其他需要传感器的帮助。道路情况鉴定是当前汽车控制研究领域的一个热门主题,但研究人员通常采用额外的除车轮速度传感器以外的可用的设备来测量汽车运动及其他国家参数来持续监测道路状况。但是标准ABS 系统只需要在制动初期阶段确定道路状况,并获得路面信息,以确定其控制单元的必需操作。显然,标准 ABS 系统不要求太精确的鉴定,因此只需要较少的仪器和费用。但是,这种道路情况鉴定方法并不明确。本文正是研究在标准 ABS 系统下的道路情况鉴定方法。分析的依据是通过测量车轮角速度所得的车轮角加速度。因为轮胎与路面在不同路面上的磨擦特性不同,所以,,在不同道路表面上车轮制动时的反应也不同,因此车轮制动反应研究必须包括路面附着信息。所以我们模拟车轮制动情况,并在车轮加速曲线上选择两个典型数据作为标准来区分不同的路面。并讨论了测量中的不确定因素的影响。共 页 第 页装订线1 建模建模 四分之一的汽车模型(表 1)使用的是 Dugoff 轮胎模型。轮胎滑动摩擦力的最大值(即附着系数)对不同的路面是不同的,如干燥沥青路面 0.8-0.9,湿沥青路面0.5-0.7,积雪路面约 0.2%,冰面 0.1。此外,当滑移率从零开始增大时,摩擦系数随之增加的速度是不同的。特别是在冰雪路面上的摩擦系数增加速度远低于在沥青路面上。在路面摩擦系数达到最大前控制单元对路面情况作反映之时,这一特点是很重要的。当摩擦系数接近最大值时,控制单元开始调节制动压力。一般而言,摩擦系数随着滑移率增加的速度在沥青路面上至少是在雪或冰路面上的两倍。为了反映此差异,在沥青路面上的曲线的初始阶段的斜率应该为雪地路面上的两倍。如果此差异更大,以此假设得出的结果将会更加可信。图一 四分之一汽车模型 一阶制动模型为:dTp/dt=(Tp-Tb)/(1)其中 TP 是施加的制动扭矩,Tb 是.实际的制动扭矩,是制动常量。2 结果和讨论结果和讨论 四分之一汽车模型的满载重量是 400 公斤。最大的制动扭矩为 1000nm,在理论上可以产生足够的车辆减速度为 1g。在雪地路面上(0.2),最大的地面制动扭矩是 200nm,所以若施加制动扭矩超过 200nm,车轮将抱死。在湿沥青路面上(0.5),最大的地面制动扭矩是 500nm,所以车路将在施加制动扭矩超过 500nm 时抱死。图二表示的是在湿沥青路面(0.5)和雪地路面(0.2)上不同制动扭矩下的车轮减速度曲线。在每种情况下,施加的制动扭矩都高到足以抱死车轮。在任何路面条件下,增加制动扭矩都导致车轮减速度快速增大,并使滑移率增大。在雪地路面上,当制动扭矩很大时,车轮速度降低比在沥青路面上更快。因此当道路上有雪覆盖时,该系统可以很容易判断出。但是,当制动扭矩不是很高但足以引起车轮抱死时,车轮减速的过程就类似于在沥青面上,控制单元就不能判断出遇到的是何种路面。这时需要作进一步分析。共 页 第 页装订线 -雪地路面 湿沥青路面 图二:在沥青路面和雪地路面上不同制动扭矩下的车轮减速度。在图 2 上的每一条减速度曲线上都可以用两个点来描述该曲线。第一个是减速度在 0.05s 时,另一个是减速度达到 50 rad/s2 时。(制动从 0 时开始)我们提到的这些是加速度时间曲线确定的标准用这些点做出曲线定义为加速度时间曲线。图三是最大地面的制动力矩为 900,700,500 和 200 时,在沥青路面(0.9,0.7 和 0.5)和雪地路面(0.2)上做出的加速时间曲线。曲线之间没有相交表明加速度时间曲线确定的标准符合特殊的路面情况或最大的地面制动力矩。前面的分析是假设的一辆满载汽车。如果车轮垂直载荷变化,车轮运动情况也会有所不同,所以会产生不同的加速度时间曲线。图四中是半载的车轮在沥青路面(0.9和 0.5)和雪地路面(0.5)上做出的三条加速度时间曲线和满载时的曲线。他们的最大地面制动力矩为 450,250 和 100Nm。假设一条加速度时间曲线是在车轮局部负荷即在半载和满载之间在沥青路面(0.9)上做出的那么它将位于制动力矩为 900NM 和450NM 的曲线之间,那么部分负荷曲线将与制动力矩 700nm 和 500nm 的曲线相似。因此,加速度时间曲线的标准不符合的路面情况但符合最大地面制动力矩。由此可以看出,车轮反映取决于施加的制动扭矩和道路摩擦潜力(地面制动力矩)。如果车轮负载变化并不大,如轿车,满载的车重不等于空载车重的两倍,这时在沥青路面和雪地路面上的加速度时间曲线无论在任何操作情况下都将不会相交。在这种情况下,可以用加速度时间曲线的标准来分辨出沥青路面和雪地路面。共 页 第 页装订线图三:在四中路面情况下的车轮加速度时间曲线t:时间 在 0.05s 时 a:加速度 在-50rad/s2图四:满载和半载情况下的车轮加速度时间曲线t:时间 在 0.05s 时 a:加速度 在-50rad/s23 结论结论 本文分析了车轮加速度与路面情况以及车轮负荷之间的关系。建议采用的车轮加速时间标准,可以用一个带有控制单元的车轮速度传感器来测出。可以反映出由路面情况和车轮负载决定的道路摩擦潜力。对轿车来说,,标准甚至可以确定路面情况,即确定车轮是与沥青路面还是雪地路面相接触。Road Identification for Anti-Lock Brake Systems Equipped with Only Wheel Speed SensorsAbstract:Anti-lock brake systems(ABS)are now widely used on motor vehicles.To reduce cost and to use currently available technologies,standard ABS uses only wheel speed sensors to detect wheel angular velocities,which is not enough to directly obtain wheel slip rations needed by the control unit,but can be used to calculate reference slip ratios with measured wheel angular velocities and the estimated vehicle speed.Therefore,the road friction coefficient,which determines the vehicle deceleration during severe braking,is an important parameter in estimating vehicle speed.This paper analyzes wheel acceleration responses in simulations of severe braking on different road surfaces and selects a pair of specific points to identify the wheel acceleration curve for each operating condition,such as road surface,pedal-braking torque and wheel vertical load.It was found that the curve using the selected points for each road surface clearly differs from that of the other road surface.Therefore,different road surfaces can be distinguished with these selected points which represent their corresponding road surfaces.The analysis assumes that only wheel speed sensors are available as hardware and that the road cohesion condition can be determined in the initial part of the severe braking process.Key words:anti-lock brake systems(ABS);road identification;wheel angular acceleration;tire characteristics IntroductionFor anti-lock brake systems(ABS),the road cohesion condition is one of the most important factors.Standard ABS can identify road cohesion conditions while braking and decide whether the road friction is high(asphalt)or low(snow,ice),so that the control unit activates the corresponding control logic.Only wheel speed sensors are available in standard ABS to identify the road conditions,with no other sensors needed.Road identification research is currently a popular topic in automotive control,but researchers usually assume extra equipment is available for measuring vehicle motion and other state parameters besides wheel speed sensors,to continuously monitor the road condition.But standard ABS only needs to identify road conditions during the initial braking period,and then obtain road information to ensure necessary operations of the control unit.Obviously,the standard ABS demands less strict identification,therefore less hardware and cost.However,the method to identify the conditions is not obvious.This paper investigates the road identification method for the standard ABS configuration.The analysis is based on the wheel angular acceleration,which is acquired from the measured wheel angular speed.Since tire-road friction characteristics differ on different road surfaces,the wheel responses while braking on different surfaces are also different,so the wheel responses must contain road cohesion information.Therefore,we simulated braking situations and then chose two typical values on the wheel acceleration curve as criteria to distinguish between different road surfaces.Influence of uncertainties in the measurements is also discussed.1 ModelingA one quarter vehicle model(Fig.1)is used with the Dugoff tire model.The peak values of the tire slip-friction curve(i.e.,cohesion coefficient)are different for different road surfaces,such as dry asphalt 0.8-0.9,wet asphalt 0.5-0.7,snow about 0.2 and ice about 0.1.Furthermore,when the slip ratio increases above zero,the friction coefficient increases at a different rate.This is especially true for the increase of the friction coefficients on snow or ice which are much lower than on asphalt.This feature is important since the control unit makes decisions about road conditions before the friction coefficient reaches a maximum.Once the friction coefficient is close to the maximum,the control unit starts to regulate the braking pressure.Generally,the friction coefficient rate of increase with the increasing slip ratio on asphalt is at least double that on snow or ice.To reflect this difference,the initial slope of the characteristic curve on asphalt was assumed to be twice that of snow.If the difference is even greater,the results using the assumption will be even more effective.Fig.1 one quarter vehicle model A first-order braking model is given by:dTp/dt=(Tp-Tb)/(1)where Tp is the pedal-braking torque,Tb is the actual braking torque,and is the brake constant.2 Results and DiscussionFull load for the quarter-vehicle model is 400 kg.The maximum pedal-braking torque is 1000Nm,which is theoretically enough to produce a vehicle deceleration of 1g.On snow(0.2),the maximum ground-braking torque is 200Nm so if the pedal-braking torque is over 200Nm,the wheel will lock.On wet asphalt(0.5),the maximum ground-braking torque is 500Nm so the wheel will lock at a pedal-braking torque higher than 500Nm.Wheel acceleration curves are shown in Fig.2 for braking on wet asphalt(0.5)and snow(0.2)using different pedal-braking torques.In each case,the pedal-braking torque is high enough to lock the wheel.On either road surface,increasing the pedal-braking torque cause the wheel to decelerate more rapidly and the slip ratio to increase.On snow,when the pedal-braking torque is very,the wheel decelerate much more rapidly than on asphalt,so the system can easily judge when the road is covered with snow.However,when the pedal-braking torque is not very high but enough to cause lockup,the wheel deceleration process may resemble that on asphalt,the control unit may not be able to decide which type of road surface has been encountered.This case needs further analysis.-Snow Wet asphaltFig.2 Wheel acceleration for different pedal braking torques on wet asphalt and snowEach acceleration curve in Fig.2 can be described with two points on the curve.One is the acceleration at the time 0.05s,and the other is the time when the acceleration reaches 50 rad/s2.(Braking starts at time 0.)We refer to these as the acceleration-time criteria and the curve defined by these points is referred to as the acceleration-time curve.Acceleration-time curves for asphalt(0.9,0.7,and 0.5)and snow(0.2)are drawn in Fig.3 for maximum ground-braking torques of 900,700,500,and 200 Nm.None of the curves intersect which means the acceleration time criteria corresponds to a particular road surface or maximum ground braking torque.The previous analysis assumed a fully-loaded vehicle.If the wheel vertical load changes,the wheel will behave differently which will result in different acceleration-time curves.Three acceleration-time curves for a half-loaded wheel on asphalt(0.9 and 0.5)and snow(0.5)are shown in Fig.4 with the full-load curves.Their maximum ground braking torque are 450,250,and 100 Nm.Assuming that the acceleration-time curve for a wheel with a partial load between“full”and“half”on asphalt(0.9)will be located between the curves for braking torque of 900 Nm and 450Nm,then a partial load curve would be similar to the curve for braking torque of 700Nm and 500Nm.Therefore,the acceleration-time criteria do not correspond to the road surface,but to the maximum ground braking torque.It is physically reasonable that the wheel response depends on the difference between the pedal-braking torque and the road friction potential(ground-braking Torque),In cases where the wheel load does not vary greatly,such as in passenger cars,the full load of a car may not be double the load of empty car,then the acceleration-time curves for asphalt and snow will always be separated for any operating conditions.In such cases,asphalt and snow can be distinguished by the acceleration-time criterion.3 ConclusionsThis paper analyzes the relationships between the wheel load.The proposed wheel acceleration-time criteria,which can be measured by a control unit with wheel speed sensors,can reflect the road friction potential resulting from the road surface and wheel load.For passenger cars,the criteria can even determine the road conditions,whether the wheel is in contact with asphalt or snow.
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共 页 第 页装订线【中文【中文 2390 字】字】利用只装有车轮速度传感器的制动防抱死系统做路面情况鉴定利用只装有车轮速度传感器的制动防抱死系统做路面情况鉴定摘要摘要:制动防抱死系统(ABS),是目前在汽车上得到广泛使用的设备。为了降低制造成本,并利用现有可用的技术,标准 ABS 系统仅使用车轮速度传感器检测车轮转速,这是不能够直接获取控制单元需要的车轮滑移率,但可以利用计算所得的车轮角速度和估计的车速间的关系来计算参考滑移率。因此,道路摩擦系数,它决定了车辆在紧急刹车时的减速度,是一个估算汽车速度的重要参数。本文分析了在不同路面情况下模拟紧急制动时车轮的加速度,并选择一对特殊的点来确定车轮加速曲线在每个不同的操纵情况下,比如路面情况,制动扭矩和车轮的垂直载荷。它是建立在每个用试点做出的针对不同路面的曲线明显不同于其他路面。因此,不同的路面可以用这些点来区分,这些点反映了他们所代表的路面情况。分析假设只有车轮速度传感器是可利用的仪器并且道路附着情况可以在紧急制动的开始初期阶段确定。关键字关键字:制动防抱死系统(ABS);路面情况鉴定;车轮角加速;轮胎特性介绍介绍 对制动防抱死系统(ABS)来说,道路附着情况是最重要的因素之一。标准 ABS系统可以在制动时确定道路附着情况,并且确定道路摩擦力是高(沥青路面)、或低(雪、冰路面),然后由控制单元激活相应的逻辑控制系统。只有车轮速度传感器在标准ABS 系统中可以确定路面情况,不需要其他需要传感器的帮助。道路情况鉴定是当前汽车控制研究领域的一个热门主题,但研究人员通常采用额外的除车轮速度传感器以外的可用的设备来测量汽车运动及其他国家参数来持续监测道路状况。但是标准ABS 系统只需要在制动初期阶段确定道路状况,并获得路面信息,以确定其控制单元的必需操作。显然,标准 ABS 系统不要求太精确的鉴定,因此只需要较少的仪器和费用。但是,这种道路情况鉴定方法并不明确。本文正是研究在标准 ABS 系统下的道路情况鉴定方法。分析的依据是通过测量车轮角速度所得的车轮角加速度。因为轮胎与路面在不同路面上的磨擦特性不同,所以,,在不同道路表面上车轮制动时的反应也不同,因此车轮制动反应研究必须包括路面附着信息。所以我们模拟车轮制动情况,并在车轮加速曲线上选择两个典型数据作为标准来区分不同的路面。并讨论了测量中的不确定因素的影响。共 页 第 页装订线1 建模建模 四分之一的汽车模型(表 1)使用的是 Dugoff 轮胎模型。轮胎滑动摩擦力的最大值(即附着系数)对不同的路面是不同的,如干燥沥青路面 0.8-0.9,湿沥青路面0.5-0.7,积雪路面约 0.2%,冰面 0.1。此外,当滑移率从零开始增大时,摩擦系数随之增加的速度是不同的。特别是在冰雪路面上的摩擦系数增加速度远低于在沥青路面上。在路面摩擦系数达到最大前控制单元对路面情况作反映之时,这一特点是很重要的。当摩擦系数接近最大值时,控制单元开始调节制动压力。一般而言,摩擦系数随着滑移率增加的速度在沥青路面上至少是在雪或冰路面上的两倍。为了反映此差异,在沥青路面上的曲线的初始阶段的斜率应该为雪地路面上的两倍。如果此差异更大,以此假设得出的结果将会更加可信。图一 四分之一汽车模型 一阶制动模型为:dTp/dt=(Tp-Tb)/(1)其中 TP 是施加的制动扭矩,Tb 是.实际的制动扭矩,是制动常量。2 结果和讨论结果和讨论 四分之一汽车模型的满载重量是 400 公斤。最大的制动扭矩为 1000nm,在理论上可以产生足够的车辆减速度为 1g。在雪地路面上(0.2),最大的地面制动扭矩是 200nm,所以若施加制动扭矩超过 200nm,车轮将抱死。在湿沥青路面上(0.5),最大的地面制动扭矩是 500nm,所以车路将在施加制动扭矩超过 500nm 时抱死。图二表示的是在湿沥青路面(0.5)和雪地路面(0.2)上不同制动扭矩下的车轮减速度曲线。在每种情况下,施加的制动扭矩都高到足以抱死车轮。在任何路面条件下,增加制动扭矩都导致车轮减速度快速增大,并使滑移率增大。在雪地路面上,当制动扭矩很大时,车轮速度降低比在沥青路面上更快。因此当道路上有雪覆盖时,该系统可以很容易判断出。但是,当制动扭矩不是很高但足以引起车轮抱死时,车轮减速的过程就类似于在沥青面上,控制单元就不能判断出遇到的是何种路面。这时需要作进一步分析。共 页 第 页装订线 -雪地路面 湿沥青路面 图二:在沥青路面和雪地路面上不同制动扭矩下的车轮减速度。在图 2 上的每一条减速度曲线上都可以用两个点来描述该曲线。第一个是减速度在 0.05s 时,另一个是减速度达到 50 rad/s2 时。(制动从 0 时开始)我们提到的这些是加速度时间曲线确定的标准用这些点做出曲线定义为加速度时间曲线。图三是最大地面的制动力矩为 900,700,500 和 200 时,在沥青路面(0.9,0.7 和 0.5)和雪地路面(0.2)上做出的加速时间曲线。曲线之间没有相交表明加速度时间曲线确定的标准符合特殊的路面情况或最大的地面制动力矩。前面的分析是假设的一辆满载汽车。如果车轮垂直载荷变化,车轮运动情况也会有所不同,所以会产生不同的加速度时间曲线。图四中是半载的车轮在沥青路面(0.9和 0.5)和雪地路面(0.5)上做出的三条加速度时间曲线和满载时的曲线。他们的最大地面制动力矩为 450,250 和 100Nm。假设一条加速度时间曲线是在车轮局部负荷即在半载和满载之间在沥青路面(0.9)上做出的那么它将位于制动力矩为 900NM 和450NM 的曲线之间,那么部分负荷曲线将与制动力矩 700nm 和 500nm 的曲线相似。因此,加速度时间曲线的标准不符合的路面情况但符合最大地面制动力矩。由此可以看出,车轮反映取决于施加的制动扭矩和道路摩擦潜力(地面制动力矩)。如果车轮负载变化并不大,如轿车,满载的车重不等于空载车重的两倍,这时在沥青路面和雪地路面上的加速度时间曲线无论在任何操作情况下都将不会相交。在这种情况下,可以用加速度时间曲线的标准来分辨出沥青路面和雪地路面。共 页 第 页装订线图三:在四中路面情况下的车轮加速度时间曲线t:时间 在 0.05s 时 a:加速度 在-50rad/s2图四:满载和半载情况下的车轮加速度时间曲线t:时间 在 0.05s 时 a:加速度 在-50rad/s23 结论结论 本文分析了车轮加速度与路面情况以及车轮负荷之间的关系。建议采用的车轮加速时间标准,可以用一个带有控制单元的车轮速度传感器来测出。可以反映出由路面情况和车轮负载决定的道路摩擦潜力。对轿车来说,,标准甚至可以确定路面情况,即确定车轮是与沥青路面还是雪地路面相接触。Road Identification for Anti-Lock Brake Systems Equipped with Only Wheel Speed SensorsAbstract:Anti-lock brake systems(ABS)are now widely used on motor vehicles.To reduce cost and to use currently available technologies,standard ABS uses only wheel speed sensors to detect wheel angular velocities,which is not enough to directly obtain wheel slip rations needed by the control unit,but can be used to calculate reference slip ratios with measured wheel angular velocities and the estimated vehicle speed.Therefore,the road friction coefficient,which determines the vehicle deceleration during severe braking,is an important parameter in estimating vehicle speed.This paper analyzes wheel acceleration responses in simulations of severe braking on different road surfaces and selects a pair of specific points to identify the wheel acceleration curve for each operating condition,such as road surface,pedal-braking torque and wheel vertical load.It was found that the curve using the selected points for each road surface clearly differs from that of the other road surface.Therefore,different road surfaces can be distinguished with these selected points which represent their corresponding road surfaces.The analysis assumes that only wheel speed sensors are available as hardware and that the road cohesion condition can be determined in the initial part of the severe braking process.Key words:anti-lock brake systems(ABS);road identification;wheel angular acceleration;tire characteristics IntroductionFor anti-lock brake systems(ABS),the road cohesion condition is one of the most important factors.Standard ABS can identify road cohesion conditions while braking and decide whether the road friction is high(asphalt)or low(snow,ice),so that the control unit activates the corresponding control logic.Only wheel speed sensors are available in standard ABS to identify the road conditions,with no other sensors needed.Road identification research is currently a popular topic in automotive control,but researchers usually assume extra equipment is available for measuring vehicle motion and other state parameters besides wheel speed sensors,to continuously monitor the road condition.But standard ABS only needs to identify road conditions during the initial braking period,and then obtain road information to ensure necessary operations of the control unit.Obviously,the standard ABS demands less strict identification,therefore less hardware and cost.However,the method to identify the conditions is not obvious.This paper investigates the road identification method for the standard ABS configuration.The analysis is based on the wheel angular acceleration,which is acquired from the measured wheel angular speed.Since tire-road friction characteristics differ on different road surfaces,the wheel responses while braking on different surfaces are also different,so the wheel responses must contain road cohesion information.Therefore,we simulated braking situations and then chose two typical values on the wheel acceleration curve as criteria to distinguish between different road surfaces.Influence of uncertainties in the measurements is also discussed.1 ModelingA one quarter vehicle model(Fig.1)is used with the Dugoff tire model.The peak values of the tire slip-friction curve(i.e.,cohesion coefficient)are different for different road surfaces,such as dry asphalt 0.8-0.9,wet asphalt 0.5-0.7,snow about 0.2 and ice about 0.1.Furthermore,when the slip ratio increases above zero,the friction coefficient increases at a different rate.This is especially true for the increase of the friction coefficients on snow or ice which are much lower than on asphalt.This feature is important since the control unit makes decisions about road conditions before the friction coefficient reaches a maximum.Once the friction coefficient is close to the maximum,the control unit starts to regulate the braking pressure.Generally,the friction coefficient rate of increase with the increasing slip ratio on asphalt is at least double that on snow or ice.To reflect this difference,the initial slope of the characteristic curve on asphalt was assumed to be twice that of snow.If the difference is even greater,the results using the assumption will be even more effective.Fig.1 one quarter vehicle model A first-order braking model is given by:dTp/dt=(Tp-Tb)/(1)where Tp is the pedal-braking torque,Tb is the actual braking torque,and is the brake constant.2 Results and DiscussionFull load for the quarter-vehicle model is 400 kg.The maximum pedal-braking torque is 1000Nm,which is theoretically enough to produce a vehicle deceleration of 1g.On snow(0.2),the maximum ground-braking torque is 200Nm so if the pedal-braking torque is over 200Nm,the wheel will lock.On wet asphalt(0.5),the maximum ground-braking torque is 500Nm so the wheel will lock at a pedal-braking torque higher than 500Nm.Wheel acceleration curves are shown in Fig.2 for braking on wet asphalt(0.5)and snow(0.2)using different pedal-braking torques.In each case,the pedal-braking torque is high enough to lock the wheel.On either road surface,increasing the pedal-braking torque cause the wheel to decelerate more rapidly and the slip ratio to increase.On snow,when the pedal-braking torque is very,the wheel decelerate much more rapidly than on asphalt,so the system can easily judge when the road is covered with snow.However,when the pedal-braking torque is not very high but enough to cause lockup,the wheel deceleration process may resemble that on asphalt,the control unit may not be able to decide which type of road surface has been encountered.This case needs further analysis.-Snow Wet asphaltFig.2 Wheel acceleration for different pedal braking torques on wet asphalt and snowEach acceleration curve in Fig.2 can be described with two points on the curve.One is the acceleration at the time 0.05s,and the other is the time when the acceleration reaches 50 rad/s2.(Braking starts at time 0.)We refer to these as the acceleration-time criteria and the curve defined by these points is referred to as the acceleration-time curve.Acceleration-time curves for asphalt(0.9,0.7,and 0.5)and snow(0.2)are drawn in Fig.3 for maximum ground-braking torques of 900,700,500,and 200 Nm.None of the curves intersect which means the acceleration time criteria corresponds to a particular road surface or maximum ground braking torque.The previous analysis assumed a fully-loaded vehicle.If the wheel vertical load changes,the wheel will behave differently which will result in different acceleration-time curves.Three acceleration-time curves for a half-loaded wheel on asphalt(0.9 and 0.5)and snow(0.5)are shown in Fig.4 with the full-load curves.Their maximum ground braking torque are 450,250,and 100 Nm.Assuming that the acceleration-time curve for a wheel with a partial load between“full”and“half”on asphalt(0.9)will be located between the curves for braking torque of 900 Nm and 450Nm,then a partial load curve would be similar to the curve for braking torque of 700Nm and 500Nm.Therefore,the acceleration-time criteria do not correspond to the road surface,but to the maximum ground braking torque.It is physically reasonable that the wheel response depends on the difference between the pedal-braking torque and the road friction potential(ground-braking Torque),In cases where the wheel load does not vary greatly,such as in passenger cars,the full load of a car may not be double the load of empty car,then the acceleration-time curves for asphalt and snow will always be separated for any operating conditions.In such cases,asphalt and snow can be distinguished by the acceleration-time criterion.3 ConclusionsThis paper analyzes the relationships between the wheel load.The proposed wheel acceleration-time criteria,which can be measured by a control unit with wheel speed sensors,can reflect the road friction potential resulting from the road surface and wheel load.For passenger cars,the criteria can even determine the road conditions,whether the wheel is in contact with asphalt or snow.
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