Dr.-Ing. Michael Klein, INTES GmbH, GERMANY

Virtual product development for brakes systems are widely accepted and used in industry. Using simulations in an early design stage reduces time to market, saves costs and improves the physical behavior of the brake system. But it is often neglected that many parameters are subject to uncertainties. Identification of parameters with uncertainties and an efficient integrated method to take them into account by brake system simulation are necessary.

Parameters of brake systems could be classified in two main categories. Application parameters and design parameters. The application parameters are e.g. brake pressure and rotation speed. The influence of the designer on these parameters is very limited, because they vary during application in a wide range. These parameters must be examined by sampling in their entire value range by simulation. Design parameters, like the shape, materials and the realization of all connections are based on decisions during the development of a brake system. Although precise decisions have been made, the parameters are uncertain. E.g. the component geometries vary in the production process and the material, especially the brake pad material, is not always exactly the same.

Measurements during production and during application deliver information about the distribution of the values of uncertain parameters. The task of simulation is to take into account those uncertainties for the calculation of sensitivities with respect to NVH behavior. However, the computational effort for such additional information should be kept as small as possible. The solution for maximum efficiency is the integration of the uncertainty analysis into the FEA software.

Solver integrated methods for this challenging task are available in the high-performance solver PERMAS. The evaluation is based on stability maps that contain the uncertainties. Advanced methods with control of the covered analyses reduce the effort to the possible minimum.

An example of CEA with several uncertain parameters shows the practical application of the advanced options of loop control. The mathematical benefits are used for the industry oriented numerical example to show the effectiveness of the approach.