Research Papers

J. Mech. Des. 2013;135(3):031001-031001-11. doi:10.1115/1.4023322.

An earlier study introduced the concept of piezoelectric energy-harvesting skin (EHS) to harvest energy by attaching thin piezoelectric patches onto a vibrating skin. This paper presents a methodology for the optimum design of EHS with the use of an efficient topology optimization method referred to as the hybrid cellular automaton (HCA) algorithm. The design domain of the piezoelectric material is discretized into cellular automata (CA), and the response of each CA is measured using high-fidelity finite-element analysis of a vibrating structure. The CA properties are parameterized using nonlinear interpolation functions that follow the principles of the SIMP model. The HCA algorithm finds the optimal densities and polarizing directions at each CA that maximize the output power from the EHS. The performance of this approach is demonstrated for the optimal design of EHS in two real-world case studies.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2013;135(3):031002-031002-14. doi:10.1115/1.4023280.

This paper presents a methodology to provide the cumulative failure distribution (CDF) for degrading, uncertain, and dynamic systems. The uniqueness and novelty of the methodology is that long service time over which degradation occurs has been augmented with much shorter cycle time over which there is uncertainty in the system dynamics due to uncertain design variables. The significance of the proposed methodology is that it sets the foundation for setting realistic life-cycle management policies for dynamic systems. The methodology first replaces the implicit mechanistic model with a simple explicit meta-model with the help of design of experiments and singular value decomposition, then transforms the dynamic, time variant, probabilistic problem into a sequence of time invariant steady-state probability problems using cycle-time performance measures and discrete service time, and finally, builds the CDF as the summation of the incremental service-time failure probabilities over the planned life time. For multiple failure modes and multiple discrete service times, set theory establishes a sequence of true incremental failure regions. A practical implementation of the theory requires only two contiguous service-times. Probabilities may be evaluated by any convenient method, such as Monte Carlo and the first-order reliability method. Error analysis provides ways to control errors with regards to probability calculations and meta-model fitting. A case study of a common servo-control mechanism shows that the new methodology is sufficiently fast for design purposes and sufficiently accurate for engineering applications.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2013;135(3):031003-031003-11. doi:10.1115/1.4023157.

The constraint-based design of flexure mechanisms requires a qualitative and quantitative understanding of the constraint characteristics of flexure elements that serve as constraints. This paper presents the constraint characterization of a uniform and symmetric cross-section, slender, spatial beam—a basic flexure element commonly used in three-dimensional flexure mechanisms. The constraint characteristics of interest, namely stiffness and error motions, are determined from the nonlinear load–displacement relations at the beam end. Appropriate assumptions are made while formulating the strain and strain energy expressions for the spatial beam to retain relevant geometric nonlinearities. Using the principle of virtual work, nonlinear beam governing equations are derived and subsequently solved for general end loads. The resulting nonlinear load–displacement relations capture the constraint characteristics of the spatial beam in a compact, closed-form, and parametric manner. This constraint model is shown to be accurate using nonlinear finite element analysis, within a load and displacement range of practical interest. The utility of this model lies in the physical and analytical insight that it offers into the constraint behavior of a spatial beam flexure, its use in design and optimization of 3D flexure mechanism geometries, and its elucidation of fundamental performance tradeoffs in flexure mechanism design.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2013;135(3):031004-031004-16. doi:10.1115/1.4023282.

To avoid failures in the marketplace, the control of the risks in product innovation and the reduction of the innovation cycles require fast and valid assessments from customers. An interactive genetic algorithm (IGA) is proposed for eliciting users' perceptions about the shape of a product, in order to stimulate creativity and to identify design trends. Interactive users' assessment tests are conducted on virtual products to capture and analyze users' responses. The IGA is interfaced with Computer Aided Design (CAD) software (CATIA V5) to create sets of parameterized designs in real time, which are presented iteratively by a graphical interface to the users for evaluation. After a description of the IGA, a study on the convergence of the IGA is presented. The convergence varies, according to the tuning parameters of the algorithm and the size of the design problem. An experiment was carried out with a set of 45 users on the application case, a dashboard, put forward by Renault. The implementation of the perceptive tests and the analysis of the results are described using hierarchical ascendant classification (HAC) and multivariate analysis. This paper shows how the results of tests using IGA can be used to elicit user perception and to detect design trends.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2013;135(3):031005-031005-14. doi:10.1115/1.4023279.

A self-aligning coupling is used as a vehicle to show that the Tolerance-Map (T-Map) mathematical model for geometric tolerances can distinguish between related and unrelated actual mating envelopes as described in the ASME/ISO standards. The coupling example illustrates how T-Maps (Patent No. 6963824) may be used for tolerance assignment during design of assemblies that contain non-congruent features in contact. Both worst-case and statistical measures are obtained for the variation in alignment of the axes of the two engaged parts of the coupling in terms of the tolerances. The statistical study is limited to contributions from the geometry of toleranced features and their tolerance-zones. Although contributions from characteristics of manufacturing machinery are presumed to be uniform, the method described in the paper is robust enough to include different types of manufacturing bias in the future. An important result is that any misalignment in the coupling depends only on tolerances, not on any dimension of the coupling.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2013;135(3):031006-031006-13. doi:10.1115/1.4023484.

This work presents a methodology for discovering structure in design repository databases, toward the ultimate goal of stimulating designers through design-by-analogy. Using a Bayesian model combined with latent semantic analysis (LSA) for discovering structural form in data, an exploration of inherent structural forms, based on the content and similarity of design data, is undertaken to gain useful insights into the nature of the design space. In this work, the approach is applied to uncover structure in the U.S. patent database. More specifically, the functional content and surface content of the patents are processed and mapped separately, yielding structures that have the potential to develop a better understanding of the functional and surface similarity of patents. Structures created with this methodology yield spaces of patents that are meaningfully arranged into labeled clusters, and labeled regions, based on their functional similarity or surface content similarity. Examples show that cross-domain associations and transfer of knowledge based on functional similarity can be extracted from the function based structures, and even from the surface content based structures as well. The comparison of different structural form types is shown to yield different insights into the arrangement of the space, the interrelationships between the patents, and the information within the patents that is attended to—enabling multiple representations of the same space to be easily accessible for design inspiration purposes. In addition, the placement of a design problem in the space effectively points to the most relevant cluster of patents in the space as an effective starting point of stimulation. These results provide a basis for automated discovery of cross-domain analogy, among other implications for creating a computational design stimulation tool.

Commentary by Dr. Valentin Fuster

Technical Briefs

J. Mech. Des. 2013;135(3):034501-034501-8. doi:10.1115/1.4023327.

Iterative algorithms are widely applied in reliability analysis and design optimization. Nevertheless, phenomena of failed convergence, such as periodic oscillation, bifurcation, and chaos, are oftentimes observed in iterative procedures of solving some nonlinear problems. In the present paper, the essential causes of numerical instabilities including periodic oscillation and chaos of iterative solutions are revealed by the eigenvalue-based stability analysis of iterative schemes. To understand and control these instabilities, the stability transformation method (STM), which is capable of tackling numerical instabilities of iterative algorithms in reliability analysis and design optimization, is proposed. Finally, several benchmark examples of convergence control of PMA (performance measure approach) for probabilistic analysis and the SORA (sequential optimization and reliability assessment) for reliability-based design optimization (RBDO) are presented. The observations from the benchmark examples indicate that the STM is a promising approach to achieve convergence control for iterative algorithms in reliability analysis and design optimization.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2013;135(3):034502-034502-5. doi:10.1115/1.4023326.

This work focuses on the design, development, and testing of an inexpensive, low-profile, cartwheel flexure mechanism for torque measurement. It has been designed primarily for use in a rehabilitation and diagnostics instrument for the treatment of ankle injuries. The sensor is manufactured rapidly and at low-cost using an Omax™ abrasive waterjet machine. Strain gauges are bonded to the flexure beams to measure applied strain using a full wheatstone bridge circuit. Displacement, force, and torque are then calculated from the measured circuit voltage; power and velocity can also be determined if required by the application. Experimental results show that there exists a linear relationship between applied torque and output voltage of the wheatstone bridge for the nested cartwheel flexure design. Furthermore, results of preliminary tests of an ankle rehabilitation device show that it fulfills a need not currently satisfied by current rehabilitation and diagnostic technology in physical medicine and rehabilitation.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2013;135(3):034503-034503-5. doi:10.1115/1.4023281.

A type of modified-hourglass worm gear drive, frequently called type-II worm gearing for short, has various favorable meshing features. Its sole shortcoming is the undercutting of the worm wheel. By adopting a slight modification, this problem can be overcome due to the removal of a part of one subconjugate area containing the curvature interference limit line. To measure how effectively the undercutting is avoided, a strategy to determine the meshing point in the most severe condition is proposed for a type-II worm drive. The strategy presented consists of two steps. The first step is to establish a system of nonlinear equations in five variables in accordance with the theory of gearing. The second step is to solve the system of nonlinear equations by a numerical iteration method to ascertain the meshing point required. A numerical example is presented to verify the validity and feasibility of the proposed scheme.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2013;135(3):034504-034504-8. doi:10.1115/1.4023324.

Straight bevel gears are widely used in the plant of large-sized power generation when the gears have large size. The purpose of this study is to manufacture the large-sized straight bevel gears with equi-depth teeth on a multitasking machine. The manufacturing method has the advantages of arbitrary modification of the tooth surface and machining of the part without the tooth surface. For this study, first, the mathematical model of straight bevel gears by complementary crown gears considering manufacture on multitasking machine is proposed, and the tooth contact pattern and transmission errors of these straight bevel gears with modified tooth surfaces are analyzed in order to clarify the meshing and contact of these gears. Next, the numerical coordinates on the tooth surfaces of the bevel gears are calculated and the tooth profiles are modeled using a 3D-Computer-Aided Design (CAD) system. Five-axis control machines were utilized. The gear-work was machined by a swarf cutting using a coated carbide end mill. After rough cutting, the gear-work was heat-treated, and it was finished based on a Computer-Aided Manufacturing (CAM) process through the calculated numerical coordinates. The pinion was also machined similarly. The real tooth surfaces were measured using a coordinate measuring machine and the tooth flank form errors were detected using the measured coordinates. As a result, the obtained tooth flank form errors were small. In addition, the tooth contact pattern of the manufactured large-sized straight bevel gears was compared with those of tooth contact analysis. The data showed good agreement.

Topics: Machinery , Gears , Cutting
Commentary by Dr. Valentin Fuster

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