Inertia and Losses
This is a general discussion about inertia and losses in a vehicle and / or dynamometer application.
Inertia is the term used to describe the resistance of a mass to changes in motion (speed). This mass can be a vehicle traveling down a road, steel drums rotating on a shaft or a motor generating torque to simulate inertia.
Inertia (total mass), torque (rotational force) and deceleration rate (change in speed over change in time) are linearly related. Torque = Inertia * Acceleration. If the deceleration doubles, the total torque must have doubled (assuming the inertia stayed the same). If the inertia suddenly drops by half, the deceleration rate will double (assuming the torque stayed the same). This simple picture gets rather muddy when all the torque (forces) working on a machine (or vehicle) is not known (or measured). The general assumption is that the only thing stopping a vehicle or dynamometer is brake torque. This is not the case; there are many other forces at work causing deceleration...
Dynamometer losses:
Bearings. These usually display a linearly increasing loss with
increasing speed. This loss will also change with temperature (as lubricants change viscosity and bearing preload changes due to heating).
Windage. The windage losses from the inertia disks can be substantial.
The more disk faces exposed to free air, the more windage losses will be experienced. These losses increase exponentially with speed.
Drive motor. DC motors have a different coast torque when the field is
energized than when the field is turned off. This small torque difference may be noticeable when running with a very light inertia (keep this in mind when viewing the inertia specification from the DC motor manufacturer, this inertia will be specified with the motor field de-energized. During operation, the field will be energized).
Vehicle losses:
Tires. This loss increases with increasing decel rates. When wheel
lock-up occurs, ALL the stopping energy is absorbed by the tires. The
heat buildup in tires is directly caused by frictional losses in the tires. Losses are always converted to heat. Many tire coupled, road wheel type machines use drag force (the tangential axle force) and wheel speed sensors to determine (and account for) tire losses accurately.
Bearings, seals. This loss usually displays a linearly increasing loss with
increasing speed (compared to the other losses, this one is negligible).
Windage. This loss increases exponentially with speed. This is the most
significant loss at high speeds (when a vehicle is traveling at full speed (flat out), all the engine horse power is used overcoming windage, if engine power is lost, the vehicle will initially decelerate at a rate equivalent to the wheel torque level the engine was supplying (but with NO measured brake torque)).
Drive line. This loss is very hard to quantify. Also known as engine
braking, this torque WILL appear in the drive wheel's torque transducer and may be easily mistaken as brake torque. Wheel torque transducers DO NOT measure brake torque. They measure wheel torque. To truly measure brake torque would require an instrumented rotor, reactionary load cell on the caliper or rotating torque cell in the drive shafts. In the confines of modern vehicle wheel wells, anything other than wheel torque transducers are impractical. Also, the driveline can provide extra energy for the brakes to absorb, both at low speeds due to engine idle and in the case of driver input (two footed driving).
Grade. Stopping a vehicle on an upward slope requires less work than
stopping on a level surface. This makes the vehicle appear as if it got lighter. Grade can be a difficult thing to measure. Decel and downward grade appear to be the same physical property to a decel transducer. Inclination transducers incorporating a gyro are available, but the calculating the total energy added or absorbed by grade changes during a braking event, using data from a multi-axis inclinometer, is not a trivial task.
Torque spread. When analyzing the vehicle data, keep in mind the
overall vehicle decel observed is the result of ALL the brakes on the vehicle. It is difficult to determine the amount of work a single brake has done when only total work is known. The coefficient of friction is a constantly changing value across all wheels/brakes on the vehicle. This moves the work done around to different areas. Energy spread across all wheels is also dependent on cornering, road surface changes, and general road conditions.
Using the above information, the following can be deduced:
The brakes never see the total, specified mass / inertia (unless done on
a machine using inertia simulation with loss compensation enabled). If the brake is applied with the pressure set to zero, the machine / vehicle is going to stop anyway (with no brake torque). For example, if the brake torque is such that the machine will stop in half the time that the machine / vehicle coast down would normally take, then the brake saw only half of the test mass / inertia.
On a dynamometer, the brake sees more inertia on high decel stops
than light decel stops. The faster the machine is decelerated, the less time the losses have to help the machine slow down. In a vehicle, the higher the decel, the wheel/brake sees more inertia but more and more of the kinetic energy is transferred to the tire tread.
Comparing test results (temperature profiles, stop times, stop distances, etc.) from one machine to another assumes the losses of both machines are the same.
If external energy is applied (or removed) from the system during a stop (upward/downward grade, DC motor still on, transmission shifts, motor idle torque, etc.), inertia will be difficult to quantify. If there is brake torque and no change in speed over time (drag stops), this will calculate as infinite inertia.
has addressed many of the issues in the above article to account for the effects of losses. These include the AIV and Inertia simulation systems.
See Vehicle modeling for a general paper on brake testing.
See Mathematical formulas for more information regarding the actual calculations.
-------------------------------------------------- ------------------------------ 惯性和损失
-------------------------------------------------- ------------------------------ 在车辆和/或测功机应用的惯性和损失，这是一个一般性讨论。
转动惯量是一个术语，用来描述在运动中的变化（速度）的质量的电阻。这种大规模的，可以在车辆行驶的道路，钢鼓的旋转轴或电动机产生的转矩来模拟惯性。 惯量（总质量），扭矩（旋转力）和减速率（变化的速度超过时间的变化）是线性相关的。扭矩=惯性加速度。如果减速加倍，总扭矩必须增加了一倍（假设的惯量保持不变）。如果惯性突然下降了一半，减速率将增加一倍（假设扭矩保持不变）。这个简单的图片变得相当泥泞，当所有的一台机器上工作（或车辆）的扭矩（力）不知道（或测量）。一般的假设是，唯一停止车辆或测功机是制动力矩。这是不是这样，还有许多其他的工作而导致减速力量...
测力计的损失：
路轴承。这些通常显示随着速度的增加线性增加亏损。这种损失也将随温度的改变（如改变润滑油的粘度和轴承预紧力的变化，由于加热）。
路风阻。从惯性磁盘的风阻损失是巨大的。面接触到自由的空气，更多的风阻损失将经历更多的磁盘。这些损失成倍增加的速度。
路驱动电机。直流电动机有一个不同的海岸转矩，当该字段被激励时，该字段是关闭的。这个小扭矩差运行时可能会出现明显在操作过程中，该字段将是一个很轻的惯量（观看时的惯性规范直流电动机制造商，这种惯性将指定与电机领域断电，记住这一点。通电）。 车辆损失： 路轮胎。这种损失增加减速率的增加。当车轮的锁定发生时，所有的停止能量被吸收的轮胎。直接造成热量积聚在轮胎在轮胎的摩擦损失。损失总是转化为热能。许多轮胎耦合道路轮型机使用拖曳力（切向轴力）和轮速传感器来确定（账户）轮胎损失准确。
路轴承，密封件。这一损失通常会显示线性增加的损失随着速度的增加（相对于其他方面的损失，这一个可以忽略不计）。
路风阻。这种损失成倍增加的速度。在高速行驶时（当车辆行驶在全速（平出），所有的发动机马力用于克服风阻，如果发动机功率丢失，这是最显着的损失，车辆开始减速的速率相当于到车轮扭矩水平的发动机供应（但没有测得的制动力矩））。
路车道线。这种损失是很难量化的。也被称为发动机制动，扭矩将出现在驱动轮的扭矩传感器，并可以很容易误认为制动转矩。车轮扭矩传感器，不要测量制动转矩。他们测量车轮扭矩。要真正衡量制动力矩将需要检测转子，反动负载上的的卡尺或传动轴的旋转扭矩细胞的细胞。在现代化的车轮井的局限，车轮扭矩传感器以外的任何东西是不切实际的。另外，动力传动系统可以提供额外的能量吸收的刹车，在低速时，由于发动机的怠速，在驱动器输入（两个左脚驾驶）的情况下。 路级。停止一个向上的斜坡上的车辆需要较少的工作比停在一个水平面上。这使得车辆的出现，就好像它变得更轻。等级可以衡量一件很难的事情。减速和向下级减速换能器是相同的物理性质。倾角传感器装有陀螺仪是可用的，但，计算级制动事件期间的变化，采用了数据从一个多双轴倾角，增加或吸收的总能量是不是一个简单的任务。
路扭矩传播。分析车辆数据时，请记住车辆的整体减速观察的结果是所有车辆的刹车。这是很难确定一个单一的制动器已经做大量的工作时，只有总的工作被称为。摩擦系数在所有车轮/制动器的车辆上是一个不断变化的价值。这会将周围不同领域所做的工作。能源遍布所有车轮也是依赖于转弯，路面的变化，路况一般。 使用上述信息，可以推导出以下：
路刹车从来没有看到，其中指定的质量/惯性（除非做了一台机器上使用惯量模拟与损失补偿功能）。如果制动器已被施加的压力设置为零，机器/车辆停止无论如何（没有制动转矩）。例如，如果是这样，机器将停止在半机/车辆滑行的时间，通常会采取制动转矩，则制动只看到了一半的测试质量/惯性。
路测力计，制动看到惯性减速停止高光比减速停止。更快的机器，被减速的损失，以帮助机器慢下来的时间就越少。在车辆减速较高，车轮/制动看到更多的转动惯量，但越来越多的动能转移到轮胎胎面。
试验结果相比较（温度廓线，停止时间，停止距离，等）从一台机器到另一假定两台机器的损失是相同的。
如果外部施加能量（或删除）从系统停止期间（向上/向下的级，直流电动机，变速器换档，电动机的空载转矩等），转动惯量将是难以量化。如果有制动力矩的速度随着时间的推移（拖累停止）并没有改变，这将计算为无穷大的惯性。已解决了许多的问题，考虑到上述文章中
的亏损的影响。这些措施包括禽流感和惯量模拟系统。 见车辆造型一般纸张制动测试。
请参阅更多有关实际计算的数学公式。
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