Polymorphic Uncertainty of Friction

在机械工程领域，摩擦是无处不在的。它是能量损失和磨损的根本原因。另一个令人担忧的问题是与舒适性相关的摩擦诱发振动的发生。最突出的例子是NVH现象，如刹车尖叫，德国汽车业和学术界正在花费大量资金对其进行调查，以确定其原因和潜在的影响因素。为此，进行了许多专门的测量，并使用了不同复杂程度的模型。所有这些测量和模型都有一个共同的特点，即摩擦系数，即切向力与法向力的比率，对系统的稳定性具有决定性的影响。要将宏观模型中的摩擦系数参数化，必须进行测量。在这种情况下，通常使用随时间和各种加载过程的平均值。正如测量所显示的那样，摩擦系数实际上不是恒定的，而是在各种时间尺度上受到由边界层中的复杂过程引起的高度动力学的影响。因此，将摩擦系数作为一个稳态参数，甚至作为一个常量来处理，这是一个重大的简化。摩擦系数的大变异性导致所考虑的模型的稳定极限的相应的变化。这种现象是在现实世界中观察到的，在现实世界中，尖叫似乎具有一种不确定的行为。这表明在摩擦系数的建模中存在不确定性。由于各种类型的不确定性(变异性、不完备性和不精确性)，整个问题是一个多态不确定性的问题，拟议的项目重点是摩擦系数的建模，考虑了不确定性的各种原因。对申请者研究所多年来对制动系统中摩擦现象的研究所获得的原始数据进行评估，并根据其不确定性属性进行分类。借助这些发现，将通过多态不确定性模型来开发对摩擦系数的适当描述。具体地说，这指的是方程的结构(例如，微分方程组的阶数)，以及对外部参数的依赖(例如，法向力、相对速度)。摩擦系数的不确定性模型将基于刹车尖叫的最小模型在频率和时间域中进行测试。将强调相关依赖对稳定的影响。这项技术应成为今后工作的基础，因为它将有助于在相对较少的测量应用的基础上，获得关于摩擦引起的不稳定性的相关性和发生频率的统计上可靠的陈述。

In the fields of mechanical engineering, friction is ubiquitous. It is a fundamental cause of energy loss and wear. Another concern is the occurrence of comfort-relevant friction induced vibrations. Prominent examples of this are NVH phenomena such as brake squeal, which is being investigated at great expense by the German automotive industry and academia, to determine its causes and potential influencing factors.For this purpose, numerous specialized measurements are performed, and models of varying complexity are used. All of these measurements and models have the common trait that the coefficient of friction, defined as the ratio of the tangential force and normal force, has a decisive influence on the systems stability. To parameterize the friction coefficient in macroscopic models, measurements must be performed. In this case, often an average over time and over various loading procedures is used. As the measurements reveal, the coefficient of friction is in reality not constant, but is subject to a high degree of dynamics on various time scales, caused by complex processes in the boundary layer. A treatment of the coefficient of friction as a steady-state parameter, or even as a constant, is thus a major reduction.The large variability of the coefficient of friction causes a corresponding variance in the stability limits of the models considered. This phenomenon is observed in the real world, where squealing seems to have a non-deterministic behavior. This suggests uncertainties in the modeling of the friction coefficient. Due to the various types of uncertainty (variability, incompleteness and inaccuracy), the entire problem is a matter of polymorphic uncertainty.The proposed project focuses on the modeling of the friction coefficient, taking into account the various causes of uncertainty. Selections of raw data obtained at the applicants institute throughout many years of research on friction phenomena in brake systems will be evaluated and classified with respect to its uncertainty properties.With the aid of these findings, appropriate descriptions of the coefficient of friction will be developed by means of polymorphic uncertainty models. In particular, this refers to the structure of the equations (for example, order of the system of differential equations), and the dependencies on external parameters (for example, normal force, relative speed). The uncertainty model of the friction coefficient will be tested based on minimal models of brake squeal in both the frequency and time domains. The impact of relevant dependencies on stability will be emphasized. This technique should be a basis for future work, as it will facilitate the attainment of statistically reliable statements regarding the relevance and frequency of occurrence of friction induced instabilities, based on relatively few measurement applications.