Design and optimization of a general planar zero free length spring Delissen, Arnoud A.T.M.; Radaelli, Giuseppe; Herder, Just L. AbstractA zero free length (ZFL) spring is a spring with special properties, which is commonly used in static balancing. Existing methods to create ZFL springs all have their specific drawbacks, which rises to the need of a new method to create such a spring. A method is proposed to design planar ZFL springs with specified stiffness (250-750 N/m) within a certain range (up to 20 mm of displacement). Geometric non-linearities of a curved leaf spring are exploited by changing its shape. The shape is determined by a non-linear least squares algorithm, minimizing the force residuals from a non-linear numerical analysis. Constraints are introduced to help in preventing the spring from intersecting itself during deformation. For three types of springs with different boundary conditions, designs are found with characteristic shapes and maximum force errors less than 1%. A trend is observed between spring size, maximum stress and desired stiffness. New type of ZFL springs can now be designed, which can not only be used in existing applications, but also enables the use of ZFL springs in micro mechanisms. KeywordsZero free length spring; null-length spring; ideal spring; curved flexure; shape optimization; desired forcedisplacement List of variables (in order of appearance)Reaction/spring force Spring stiffness Displacement 0

A great deal of engineering effort is focused on changing mechanical material properties by creating microstructural architectures instead of modifying chemical composition. This results in meta-materials, which can exhibit properties not found in natural materials and can be tuned to the needs of the user. To change Poisson's ratio and Young's modulus, many current designs exploit mechanisms and hinges to obtain the desired behavior. However, this can lead to nonlinear material properties and anisotropy, especially for large strains. In this work, we propose a new material design that makes use of curved leaf springs in a planar lattice. First, analytical ideal springs are employed to establish sufficient conditions for linear elasticity, isotropy, and a zero Poisson's ratio. Additionally, Young's modulus is directly related to the spring stiffness. Second, a design method from the literature is employed to obtain a spring, closely matching the desired properties. Next, numerical simulations of larger lattices show that the expectations hold, and a feasible material design is presented with an in-plane Young's modulus error of only 2% and Poisson's ratio of 2.78×10−3. These properties are isotropic and linear up to compressive and tensile strains of 0.12. The manufacturability and validity of the numerical model is shown by a prototype.

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In many engineering applications, the dynamic frequency response of systems is of high importance. In this paper, we focus on limiting the extreme values in frequency response functions, which occur at the eigenfrequencies of the system, better known as resonant peaks. Within an optimization, merely sampling the frequency range and limiting the maximum values result in high computational effort. Additionally, the sensitivities of this method are not complete, since only information about the resonance peak amplitude is included. The design dependence with respect to the frequency of the extreme value is missed, thus hampering the convergence. To overcome these difficulties, we propose a constraint which can efficiently and accurately limit resonant peaks in a frequency response function. It has a close relation with eigenfrequency maximization; however, in that case, the amplitudes of the frequency response are unconstrained. In order to keep the computational time low, efficient implementation of this constraint is studied using reduced-order models based on modal truncation and modal truncation augmentation. Furthermore, approximated sensitivities are investigated, resulting in a large computational gain, while still yielding very accurate sensitivities and designs with almost equivalent performance compared with the non-approximated case. Conditions are established for the accuracy and computational efficiency of the proposed methods, depending on the number of peaks to be limited, numbers of inputs and outputs, and whether or not the system input and output are collocated.

The design of high-performance mechatronic systems is very challenging, as it requires delicate balancing of system dynamics, the controller, and their closed-loop interaction. Topology optimization provides an automated way to obtain systems with superior performance, although extension to simultaneous optimization of both topology and controller has been limited. To allow for topology optimization of mechatronic systems for closed-loop performance, stability, and disturbance rejection (i.e. modulus margin), we introduce local approximations of the Nyquist curve using circles. These circular approximations enable simple geometrical constraints on the shape of the Nyquist curve, which is used to characterize the closed-loop performance. Additionally, a computationally efficient robust formulation is proposed for topology optimization of dynamic systems. Based on approximation of eigenmodes for perturbed designs, their dynamics can be described with sufficient accuracy for optimization, while preventing the usual threefold increase of additional computational effort. The designs optimized using the integrated approach have significantly better performance (up to 350% in terms of bandwidth) than sequentially optimized systems, where eigenfrequencies are first maximized and then the controller is tuned. The proposed approach enables new directions of integrated (topology) optimization, with effective control over the Nyquist curve and efficient implementation of the robust formulation.