For the quantitative investigation of surface properties such as elasticity, friction and wear by atomic force microscopy (AFM), a quantitative determination of the forces acting on the probe during its motion along the sample surface is essential. In this article, a fully parameterized finite element model for V-shaped cantilevers is presented and the three-dimensional mechanical deformations of the AFM cantilever are investigated. Force constants and detection angles for tip displacements in the three spatial directions are calculated for widely used cantilevers. The limits of linearity according to Hook's law are studied. It is found that the AFM contact cantilevers investigated here show a linear bending behavior for tip displacements within a range below approx. 10 nm in lateral directions and 100 nm in the normal direction. Displacements within this range are typical for many AFM applications including force modulation techniques. For higher loads as used e.g. for surface modification, a significant deviation from linear behavior is observed.
In this paper a new method for an automated shape optimization of dynamically loaded components in mechanical systems is presented. The optimization is carried out by means of the results of a durability analysis based on finite elements. Load time histories, which are necessary for durability analyses, are derived from a multibody simulation. The whole optimization loop, which is an iterative procedure, incorporates all these gradual analysis steps and is implemented by the authors in a straightforward, batch-oriented manner using wellknown standard software. Since the whole process involves several different analysis types, such as multibody system simulation and durability analysis, the resulting setup is rather complex. Furthermore, the reader may not be familiar with all the terms arising within the context of every single analysis domain. Therefore, some essential aspects of each of the stages involved in the process are explained to provide the reader with the necessary background. In the following, the required software setup as well as the implementation are described. Finally, an academic example is discussed to illustrate and clearly outline the potential of this method.Key words shape optimization, multibody systems, durability analysis, fatigue, lightweight construction, virtual prototyping IntroductionIn the past years the significance of computer aided engineering (CAE) methods in the development processes of various products has increased considerably. The strong demand for shorter development processes induces the need to reduce physical prototyping and testing by replacing it with virtual prototyping by means of CAE methods. Finite element methods (FEM) and multibody system simulation (MBS), for example, play a major role in many fields of industrial production, research and development. Especially in the field of structural mechanics, these techniques are established and used extensively.Although computer-based optimization methods for an application in structural mechanics have been available for several years, they are not very popular. There are several reasons for this:1. Modelling for computer-based optimization is often complex and time-consuming 2. Optimization results and quality strongly depend on boundary conditions and load cases 3. Optimized models are sometimes difficult to interpret and/or produce in realityIn this paper, points one and two, with regard to the special case of dynamically loaded structural components, which are critical in terms of durability, are addressed. Components in dynamic mechanical systems such as parts of a gear are sometimes subject to time-varying loads, which are often stochastic. When lightweight construction is desired, normally questions concerning durability arise. This is especially true for components where failure of these components leads to safety issues. Therefore, the design process of such components always implies durability investigations such as testing, analytical calculations and/or computer-based durability analysis (DA).In ...
Computer aided engineering has gained increasing significance in product development processes and research in recent years. Simulation techniques and CAE methods are becoming more and more significant as strategic success factors.While the finite element method and multibody system simulation are state-of-the-art in many fields of application, structural optimisation methods are not so widely used. Although much progress in development has been achieved in recent years, their successful application is often still timeconsuming and sometimes not even possible. Further research work and development is necessary to improve both the capabilities of structural optimisation methods and their usability.The research work presented in this paper is a contribution towards producing an integrated structural optimisation process, introducing a new shape optimisation approach. The new process allows an integrated investigation of dynamically loaded parts in complex mechanical systems and a straightforward optimisation with respect to fatigue. Coupling effects between optimisation operations and system dynamics are fully covered. Finite element analysis (FEA), multibody system simulation (MBS), fatigue analysis and shape optimisation are tied together into a fully automated process. The whole optimisation loop, which is an iterative procedure, incorporates all these analysis steps and is implemented in a straightforward, batch-oriented manner using well-known standard software.Since the whole process involves several different analysis types, the resulting setup is rather complex and the reader may not be familiar with all the terms arising within the context. Therefore, some essential aspects of each of the stages involved in the process are explained, to provide the reader with important concepts. An academic example is discussed in depth, to illustrate and clearly outline the potential of this method. The results clearly show the importance of covering fatigue aspects in shape optimisation problems of parts in dynamic systems. In particular, the interaction between the dynamic properties of the part and the overall system, as well as its implications on the optimisation process are demonstrated.Finally, a more complex application, namely the optimisation of a passenger car suspension arm, is presented. This example demonstrates the applicability and feasibility of the optimisation process for real world problems.
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