Showing papers in "Journal of Mechanical Design in 2011"

On the benefits and pitfalls of analogies for innovative design : Ideation performance based on analogical distance, commonness, and modality of examples

Abstract: Drawing inspiration from examples by analogy can be a powerful tool for innovative design during conceptual ideation but also carries the risk of negative design outcomes (e.g., design fixation), depending on key properties of examples. Understanding these properties is critical for effectively harnessing the power of analogy. The current research explores how variations in analogical distance, commonness, and representation modality influence the effects of examples on conceptual ideation. Senior-level engineering students generated solution concepts for an engineering design problem with or without provided examples drawn from the U.S. Patent database. Examples were crossed by analogical distance (near-field vs. far-field), commonness (more vs. less-common), and modality (picture vs. text). A control group that received no examples was included for comparison. Effects were examined on a mixture of ideation process and product variables. Our results show positive effects of far-field and less-common examples on novelty and variability in quality of solution concepts. These effects are not modulated by modality. However, detailed analyses of process variables suggest divergent inspiration pathways for far-field vs. less-common examples. Additionally, the combination of far-field, less-common examples resulted in more novel concepts than in the control group. These findings suggest guidelines for the effective design and implementation of design-by-analogy methods, particularly a focus on far-field, less-common examples during the ideation process. © 2011 American Society of Mechanical Engineers.

An Experimental Study of Group Idea Generation Techniques: Understanding the Roles of Idea Representation and Viewing Methods

Abstract: Advances in innovation processes are critically important as economic and business landscapes evolve. There are many concept generation techniques that can assist a designer in the initial phases of design. Unfortunately, few studies have examined these techniques that can provide evidence to suggest which techniques should be preferred or how to implement them in an optimal way. This study systematically investigates the underlying factors of four common and well-documented techniques: brainsketching, gallery, 6-3-5, and C-sketch. These techniques are resolved into their key parameters, and a rigorous factorial experiment is performed to understand how the key parameters affect the outcomes of the techniques. The factors chosen for this study with undergraduate mechanical engineers include how concepts are displayed to participants (all are viewed at once or subsets are exchanged between participants, i.e., "rotational viewing") and the mode used to communicate ideas (written words only, sketches only, or a combination of written words and sketches). Four metrics are used to evaluate the data: quantity, quality, novelty, and variety. The data suggest that rotational viewing of sets of concepts described using sketches combined with words produces more ideas than having all concepts displayed in a "gallery view" form, but a gallery view results in more high quality concepts. These results suggest that a hybrid of methods should be used to maximize the quality and number of ideas. The study also shows that individuals gain a significant number of ideas from their teammates. Ideas, when shared, can foster new idea tracks, more complete layouts, and a diverse synthesis. Finally as teams develop more concepts, the quality of the concepts improves. This result is a consequence of the team-sharing environment and, in conjunction with the quantity of ideas, validates the effectiveness of group idea generation. This finding suggests a way to go beyond the observation that some forms of brainstorming can actually hurt productivity.

Toward a Better Understanding of Model Validation Metrics

Abstract: Model validation metrics have been developed to provide a quantitative measure that characterizes the agreement between predictions and observations. In engineering design, the metrics become useful for model selection when alternative models are being considered. Additionally, the predictive capability of a computational model needs to be assessed before it is used in engineering analysis and design. Due to the various sources of uncertainties in both computer simulations and physical experiments, model validation must be conducted based on stochastic characteristics. Currently there is no unified validation metric that is widely accepted. In this paper, we present a classification of validation metrics based on their key characteristics along with a discussion of the desired features. Focusing on stochastic validation with the consideration of uncertainty in both predictions and physical experiments, four main types of metrics, namely classical hypothesis testing, Bayes factor, frequentist’s metric, and area metric, are examined to provide a better understanding of the pros and cons of each. Using mathematical examples, a set of numerical studies are designed to answer various research questions and study how sensitive these metrics are with respect to the experimental data size, the uncertainty from measurement error, and the uncertainty in unknown model parameters. The insight gained from this work provides useful guidelines for choosing the appropriate validation metric in engineering applications. [DOI: 10.1115/1.4004223]

Multidisciplinary Design Optimization for Complex Engineered Systems: Report From a National Science Foundation Workshop

Abstract: Complex engineered systems are typically designed using a systems engineering framework that is showing its limitations. Multidisciplinary design optimization (MDO), which has evolved remarkably since its inception 25 years ago, offers alternatives to complement and enhance the systems engineering approach to help address the challenges inherent in the design of complex engineered systems. To gain insight into these challenges, a one-day workshop was organized that gathered 48 people from industry, academia, and government agencies. The goal was to examine MDO’s current and future role in designing complex engineered systems. This paper summarizes the views of five distinguished speakers on the “state of the research” and discussions from an industry panel comprised of representatives from Boeing, Caterpillar, Ford, NASA Glenn Research Center, and United Technologies Research Center on the “state of the practice.” Future research topics to advance MDO are also identified in five key areas: (1) modeling and the design space, (2) metrics, objectives, and requirements, (3) coupling in complex engineered systems, (4) dealing with uncertainty, and (5) people and workflow. Finally, five overarching themes are offered to advance MDO practice. First, MDO researchers need to engage disciplines outside of engineering and target opportunities outside of their traditional application areas. Second, MDO problem formulations must evolve to encompass a wider range of design criteria. Third, effective strategies are needed to put designers “back in the loop” during MDO. Fourth, the MDO community needs to do a better job of publicizing its successes to improve the “buy in” that is needed to advance MDO in academia, industry, and government agencies. Fifth, students and practitioners need to be better educated on systems design, optimization, and MDO methods and tools along with their benefits and drawbacks.

Modeling and Experiments of Buckling Modes and Deflection of Fixed-Guided Beams in Compliant Mechanisms

Abstract: This paper explores the deflection and buckling of fixed-guided beams used in compliant mechanisms. The paper's main contributions include the addition of an axial deflection model to existing beam bending models, the exploration of the deflection domain of a fixed-guided beam, and the demonstration that nonlinear finite element models typically incorrectly predict a beam's buckling mode unless unrealistic constraints are placed on the beam. It uses an analytical model for predicting the reaction forces, moments, and buckling modes of a fixed-guided beam undergoing large deflections. The model for the bending behavior of the beam is found using elliptic integrals. A model for the axial deflection of the buckling beam is also developed. These two models are combined to predict the performance of a beam undergoing large deflections including higher order buckling modes. The force versus displacement predictions of the model are compared to the experimental force versus deflection data of a bistable mechanism and a thermomechanical in-plane microactuator (TIM). The combined models show good agreement with the force versus deflection data for each device.

A Level Set-Based Topology Optimization Method for Maximizing Thermal Diffusivity in Problems Including Design-Dependent Effects

Abstract: This paper proposes an optimum design method, based on our level set-based topology optimization method, for maximizing thermal diffusivity in problems dealing with generic heat transfer boundaries that include design-dependent boundary conditions. First, a topology optimization method using a level set model incorporating a fictitious interface energy for regularizing the topology optimization is briefly discussed. Next, an optimization method for maximizing thermal diffusivity is formulated based on the concept of total potential energy. An optimization algorithm that uses the finite element method when solving the equilibrium equation and updating the level set function is then constructed. Finally, several numerical examples are provided to confirm the utility and validity of the proposed topology Optimization method.

Elliptical-Arc-Fillet Flexure Hinges: Toward a Generalized Model for Commonly Used Flexure Hinges

Abstract: Flexure hinges have been used to produce frictionless and backlashless transmissions in a variety of precision mechanisms Although there are many types of flexure hinges available, designers often chose a single type of flexure hinge (eg, circular flexure hinges) without considering others in the design of flexure-based mechanisms This is because the analytical equations are unique to each kind of flexure hinge This work offers a solution to this problem in the form of a generalized flexure hinge model We propose a new class of flexure hinges, namely, elliptical-arc-fillet flexure hinges, which brings elliptical arc, circular-arc-fillet, elliptical-fillet, elliptical, circular, circular-fillet, and right-circular flexure hinges together under one set of equations The closed-form equations for all the elements in the compliance and precision matrices of elliptical-arc-fillet flexure hinges have been derived The analytical results are within 10 percent error compared to the finite element results and within 8 percent error compared to the experimental results The equations for evaluating the strain energy and stress level for elliptical-arc-fillet flexure hinges are also provided This model can be used as a complementary model for the generalized model for conic flexure hinges

Time-Dependent Reliability Analysis for Function Generator Mechanisms

Abstract: A function generator mechanism links its motion output and motion input with a desired functional relationship. The probability of realizing such functional relationship is the kinematic reliability. The time-dependent kinematic reliability is desired because it provides the reliability over the time interval where the functional relationship is defined. But the methodologies of time-dependent reliability are currently lacking for function generator mechanisms. We propose a mean value first-passage method for time-dependent reliability analysis. With the assumption of normality for random dimension variables with small variances, the motion error becomes a nonstationary Gaussian process. We at first derive analytical equations for upcrossing and downcrossing rates and then develop a numerical procedure that integrates the two rates to obtain the kinematic reliability. A four-bar function generator is used as an example. The proposed method is accurate and efficient for normally distributed dimension variables with small variances.

Discovering Structure in Design Databases Through Functional and Surface Based Mapping

Abstract: 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 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. These results may provide a basis for automated discovery of cross domain analogy, among other implications for creating a computational design stimulation tool.Copyright © 2011 by ASME

Level of modularity and different levels of system granularity

Abstract: All system development projects involve analysis of the system architecture. However, it has been assumed t hus far that there is some correct system decomposition that can be used in the architectural analysis. The sensitivity of the results to the chosen level of decomposition has not been consider ed. We represent forty eight idealized system architecture s and a real complex system as a Design Structure Matrix at two different levels of decomposition. We analyze these architect ures for their degree of modularity. We find that the degree of modularity can vary for the same system when the system is represented at the two different levels of granular ity. For example, the printing system used in the case study is considered slightly integral at a higher level of d ecomposition and quite modular at a lower level of decomposition . We further find that even though the overall results c an be different depending on the level of decomposition, the direct ion of change toward more modular or more integral can be calculated the same regardless of the level of decomposition. Level of decomposition can distort the results of architectu ral analysis and care must be taken in defining the system decomposition for any analysis. OBJECTIVE Architectural decomposition is a key part of comple x system management. Architectural decomposition, division of a complex system into smaller subsystems, is a standa rd first step in most complex system analysis. The terms decomposition, system hierarchy, and level of granularity are used throughout the systems engineering literature, but what is lac king is the analysis of how the decomposition, or level of gran ularity, affects the results and thus the conclusions of the architectural analysis. In fact, there is no literature that show s empirical or theoretical work on how to properly decompose or define the level of granularity for architectural analysis, su ch as determination of level of system modularity. This is especially problematic in complex system development, as opposed to simple product development, since complex systems can have multiple possible levels of granularity. The term l evel of granularity in this paper is used to describe the “ grain size” i.e. the size and the detail of the system elements afte r system decomposition. To better illustrate the concept of granularity, Figure 1 shows a partial hierarchical decomposition of a vehicle system as well as three consecutive levels of granularity. In Figure 1, it is shown that the grai n size of the system elements decreases as the level of granulari ty increases. In other words, the subsystems elements at a lower level of granularity are more detailed individual smaller su bsystems; whereas at a higher level of granularity those same subsystems form a larger more abstract subsystem. The objectiv e of this paper is to explore level of granularity and specif ically if and how the level of modularity of a complex system is affected by the level of granularity chosen for the architectur al analysis. The specific research questions in this paper are a s follows: Research question 1: Is the level of modularity affected by the level of system granularity? Research question 2: Is a system at a lower level of granularity always either more integral or modular than the sam e system at a higher level of granularity?

Biologically Meaningful Keywords for Functional Terms of the Functional Basis

Abstract: Biology is recognized as an excellent source of analogies and stimuli for engineering design. Previous work focused on the systematic identification of relevant biological analogies by searching for instances of functional keywords in biological information in natural-language format. This past work revealed that engineering keywords could not always be used to identify the most relevant biological analogies as the vocabularies between biology and engineering are sufficiently distinct. Therefore, a retrieval algorithm was developed to identify potential biologically meaningful keywords that are more effective in searching biological text than corresponding engineering keywords. In our current work, we applied and refined the retrieval algorithm to translate functional terms of the functional basis into biologically meaningful keywords. The functional basis is widely accepted as a standardized representation of engineering product functionality. Therefore, our keywords could serve as a thesaurus for engineers to find biological analogies relevant to their design problems. We also describe specific semantic relationships that can be used to identify biologically meaningful keywords in excerpts describing biological phenomena. These semantic relations were applied as criteria to identify the most useful biologically meaningful keywords. Through a preliminary validation experiment, we observed that different translators were able to apply the criteria to identify biologically meaningful keywords with a high degree of agreement to those identified by the authors. In addition, we describe how fourth-year undergraduate mechanical engineering students used the biologically meaningful keywords to develop concepts for their design projects. DOI: 10.1115/1.4003249

Synthesis of Compliant Multistable Mechanisms Through Use of a Single Bistable Mechanism

Abstract: A compliant multistable mechanism is capable of steadily staying at multiple distinct positions without power input. Many applications including switches, valves, relays, positioners, and reconfigurable robots may benefit from multistability. In this paper, two new approaches for synthesizing compliant multistable mechanisms are proposed, which enable designers to achieve multistability through the use of a single bistable mechanism. The synthesis approaches are described and illustrated by several design examples. Compound use of both approaches is also discussed. The design potential of the synthesis approaches is demonstrated by the successful operation of several instantiations of designs that exhibit three, four, five, and nine stable equilibrium positions, respectively. The equations for determining the actuation force required to move a multistable mechanism are provided. The synthesis approaches enable us to design a compliant mechanism with a desired number of stable positions.

Multi-objective ease-off optimization of hypoid gears for their efficiency, noise, and durability performances

Abstract: Micro-geometry optimization has become an important phase of gear design that can remarkably enhance gear performance. For spiral bevel and hypoid gears, micro-geometry is typically represented by ease-off topography. The optimal ease-off shape can be defined as the outcome of a process where generally conflicting objective functions are simultaneously minimized (or maximized), in the presence of constraints. This matter naturally lends itself to be framed as a multi-objective optimization problem. This paper proposes a general algorithmic framework for ease-off multi-objective optimization, with special attention to computational efficiency. Its implementation is fully detailed. A simulation model for loaded tooth contact analysis is assumed to be available. The proposed method is tested on a face-hobbed hypoid gear set. Three objectives are defined: maximization of mechanical efficiency, minimization of loaded transmission error, minimization of maximum contact pressure. Bound constraints on the design variables are imposed, as well as a nonlinear constraint aimed at keeping the loaded contact pattern inside a predefined allowable contact region. The results show that the proposed method can obtain optimal ease-off topographies that significantly improve the basic design performances. It is also evident that the method is general enough to handle geometry optimization of any gear type.© 2011 ASME

A New Design of a Two-Stage Cycloidal Speed Reducer

Abstract: A new design of a two-stage cycloidal speed reducer is presented in this paper. A traditional two-stage cycloidal speed reducer is obtained by the simple combination of singlestage cycloidal speed reducers. A single-stage reducer engages two identical cycloid discs in order to balance dynamical loads and to obtain uniform load distribution. Consequently, the traditional two-stage reducer has four cycloid discs, in total. The newly designed two-stage cycloidal speed reducer, presented in this paper, has one cycloid disc for each stage, that is, two cycloid discs in total, which means that it is rather compact. Due to its specific concept, this reducer is characterized by good load distribution and dynamic balance, and this is described in the paper. Stress state analysis of cycloidal speed reducer elements was also realized, using the finite elements method (FEM), for the most critical cases of conjugate gear action (one, two, or three pairs of teeth in contact). The results showed that cycloid discs are rather uniformly loaded, justifying the design solution presented here. Experimental analysis of the stress state for cycloid discs was realized, using the strain gauges method. It is easy to conclude, based on the obtained results, that even for the most critical case (one pair of teeth in contact) stresses on cycloid discs are in the allowed limits, thus providing normal functioning of the reducer for its anticipated lifetime. [DOI: 10.1115/1.4004540]

Some Analytical Results on Transmission Errors in Narrow-Faced Spur and Helical Gears: Influence of Profile Modifications

Abstract: Some theoretical developments are presented, which lead to approximate analytical results on quasi-static transmission errors valid for low and high contact ratio spur and helical gears. Based on a multidegree-of-freedom gear model, a unique scalar equation for transmission error is established. The role of profile relief is analyzed by using Fourier series and it is shown that transmission error fluctuations depend on a very limited number of parameters representative of gear geometry and profile relief definition. An original direct solution to the optimum relief minimizing transmission error fluctuations is presented, which is believed to be helpful for designers. The analytical results compare well with the numerical results provided by a variety of models and it is demonstrated that some general laws of evolution for transmission error fluctuations versus profile modifications can be established for spur and helical gears.

A Generalized Complementary Intersection Method (GCIM) for System Reliability Analysis

Abstract: In many years, researchers desire to evaluate system reliability accurately and efficiently. This paper presents a generalized Complementary Intersection Method (CIM) for system reliability analysis for series, parallel, and mixed systems. The CIM provides an innovative way to evaluate system reliability by decomposing the probability of a high-order joint failure event into probabilities of complementary intersection events. However, its application has been limited to a series system only. In this paper, a generalized CIM framework is proposed for system reliability analysis with any system structure (or configuration) (e.g., series, parallel, and mixed). The CIM is generalized for both parallel and mixed system reliability. The System Structure Matrix (SS-Matrix) is proposed to characterize any system structure in a comprehensive manner. The Binary Decision Diagram (BDD) technique is employed to identify system’s mutually exclusive path sets, of which each path set is a series system. On consequence, system reliability with any system structure is decomposed into the probabilities of the mutually exclusive path sets, which can be evaluated using different reliability analysis methods. Three examples are used to demonstrate the uniqueness and effectiveness of the proposed methodology.

A Note on Flow Regimes and Churning Loss Modelling

Abstract: The purpose of this study is to investigate the various fluid flow regimes generated by a pinion running partly immersed in an oil bath and the corresponding churning power losses. In a series of papers, the authors have established several loss formulae whose validity depends on two different flow regimes characterized via a critical Reynolds number. Based on some new measurements for transient operating conditions, it has been found that the separation in two regimes may be not accurate enough for wide-faced gears and high temperatures. An extended formulation is therefore proposed which, apart from viscous forces, introduces the influence of centrifugal effects. The corresponding results agree well with the experimental measurements from a number of gears and operating conditions (speed, temperature). Finally, the link between churning and windage losses is examined and it is concluded that the physical mechanisms are different thus making it difficult to establish a general correlation between the two phenomena. In particular, it is shown that tooth geometry is of secondary importance on churning whereas, the air-lubricant circulation being different for spur and helical gears, it substantially impacts windage.Copyright © 2011 by ASME

Degree Distribution and Quality in Complex Engineered Systems

Abstract: Complex engineered systems tend to have architectures in which a small subset of components exhibits a disproportional number of linkages. Such components are known as hubs. This paper examines the degree distribution of systems to identify the presence of hubs and quantify the fraction of hub components. We examine how the presence and fraction of hubs relate to a system’s quality. We provide empirical evidence that the presence of hubs in a system’s architecture is associated with a low number of defects. Furthermore, we show that complex engineered systems may have an optimal fraction of hub components with respect to system quality. Our results suggest that architects and managers aiming to improve the quality of complex system designs must proactively identify and manage the use of hubs. Our paper provides a data-driven approach for identifying appropriate target levels of hub usage.

Wrench-Closure Workspace Generation for Cable Driven Parallel Manipulators Using a Hybrid Analytical-Numerical Approach

Abstract: In this paper, a technique to generate the wrench-closure workspace for general case completely restrained cable driven parallel mechanisms is proposed. Existing methods can be classified as either numerically or analytically based approaches. Numerical techniques exhaustively sample the task space, which can be inaccurate due to discretisation and is computationally expensive. In comparison, analytical formulations have higher accuracy, but often provides only qualitative workspace information. The proposed hybrid approach combines the high accuracy of the analytical approach and the algorithmic versatility of the numerical approach. Additionally, this is achieved with significantly lower computational costs compared to numerical methods. It is shown that the wrench-closure workspace can be reduced to a set of univariate polynomial inequalities with respect to a single variable of the end-effector motion. In this form, the workspace can then be efficiently determined and quantitatively evaluated. The proposed technique is described for a 3 degrees of freedom (3-DOF) and a 6-DOF cable driven parallel manipulator. A detailed example in workspace determination using the proposed approach and comparison against the conventional numerical approach is presented. © 2011 American Society of Mechanical Engineers.

A Fatigue Model for Spur Gear Contacts Operating Under Mixed Elastohydrodynamic Lubrication Conditions

Abstract: This paper presents a model to predict the crack formation fatigue lives of spur gear contacts operating under mixed lubrication conditions where surface roughnesses introduce intermittent metal-to-metal contacts and severe stress concentrations. The proposed model consists of several submodels including (i) a gear load distribution model to determine the normal tooth force distribution along the tooth profile, incorporating any profile modifications and manufacturing deviations, (ii) a mixed elastohydrodynamic lubrication model customized to handle transient contact conditions of gears, (iii) a stress formulation that assumes the plane strain condition to compute the transient elastic stress fields on and below the tooth surface induced by the mixed lubrication surface pressure and shear stress distributions, and (iv) a multi-axial fatigue model to predict the crack nucleation life distribution. The proposed spur gear fatigue model is used to simulate the contacts of gear pairs having different surface roughness amplitudes. The predictions are compared to the measured gear fatigue Stress-Life data for each surface condition to assess the model accuracy in predicting the crack nucleation fatigue lives as well as the location of the critical failure sites.© 2011 ASME

Some Recent Advances in the Integrated Layout Design of Multicomponent Systems

Abstract: We provide an introduction and state of the art overview of integrated layout design of multicomponent systems We review several packing optimization and overlap detection strategies, some tree-based methods, such as octrees and spheretrees, and a finite circle method (FCM) proposed to favor gradient-based optimization algorithms Integrated layout design techniques for simultaneous packing and structure topology optimization of multicomponent systems are reviewed; two typical approaches for system stiffness maximization are reviewed and compared in detail Design of multicomponent systems under inertia forces is presented using polynomial interpolation models; constraints to the centroid position, moment of inertia, and volume fraction are included Applications to piezoelectric multi-actuated microtools and integrated layout design of bridge systems are presented Finally, the effectiveness of the FCM, applications to 3D problems, and local optimum phenomena are discussed

An Experimental Investigation of the Efficiency of Planetary Gear Sets

Abstract: In this paper, results from an experimental study on power losses of planetary gear sets are presented. The experimental set-up includes a specialized test apparatus to operate a planetary gear set under tightly-controlled speed, load and oil temperature conditions, and instrumentation for an accurate measurement of power losses. The test matrix consisted of gear sets having 3 to 6 planets under loaded and unloaded conditions in order to separate load independent (spin) and load dependent (mechanical) power losses. The test matrix also included tests with planet gears having two levels of tooth surface roughness amplitudes as well as tests at varying oil inlet temperature. The results clearly indicate that spin power loss decreases with both reduction of number of planets and increase in oil temperature. Meanwhile, the mechanical power loss decreases with a decrease in oil temperature and reduction in gear surface roughnesses. Results also indicate that mechanical losses can be described by the power transmitted and lost by each planet branch.Copyright © 2011 by ASME and General Motors

An Integrative Methodology for Product and Supply Chain Design Decisions at the Product Design Stage

Abstract: Supplier selection is one of the key decisions in supply chain management. Companies need not only to make the "make" or "buy" decisions but also differentiate across potential suppliers in order to improve operational performance. Product design is an engineering based activity that realizes the customer requirements into functions of a new product. Many studies have pointed out that the integration of product and supply chain is a key factor for profitability and efficiency. However, most studies address supply chain performance after freezing the design of the product; only a few studies discuss when and how to incorporate supply chain decisions during product design. This paper presents a graph theory based optimization methodology to tackle this problem. The supplier selection issue is considered by evaluating its impact on both internal (e.g., ease of assembly) and external (e.g., transportation time) enterprise performances, which are aggregated as supply chain performance at the conceptual design stage. A case study in the bicycle industry demonstrates the advantages of this methodology. The presented mathematical programming formulation enables simultaneous optimization of both product design and supply chain design during the early design stages.

Kinematic Fundamentals of Planar Harmonic Drives

Abstract: This paper presents the kinematic model and offers a rigorous analysis and description of the kinematics of planar harmonic drives. In order to reflect the fundamental kinematic principle of harmonic drives, the flexspline of a harmonic drive is assumed to be a ring without a cup. A tooth on the flexspline is a rigid body, and the motion of the tooth is fully governed by the wave generator and the nominal transmission ratio of the harmonic drive. The proposed model depicts the flexspline tooth and the wave generator as a cam-follower mechanism, with the follower executing a combined translating and oscillating motion. With the rigid tooth motion obtained, the conjugate condition between the flexspline and the circular spline is determined, from which the conjugate tooth profile can be derived. In this paper, the motion is governed by geometry, and the flexibility of the flexspline only serves as a spring to maintain the contact between the cam and the follower. For any wave generator and any transmission ratio, the explicit expression of the conjugate condition is presented. For a given circular or flexspline tooth profile, the exact conjugate tooth profile can be obtained. The phenomenon of twice engagement is discussed for the first time.

Investigations on CFD Simulations for Predicting Windage Power Losses in Spur Gears

Abstract: In this paper, a computational fluid dynamics (CFD) code is applied to two- and three-dimensional simulations of windage power loss generated by spur gears rotating in air. Emphasis is placed on the various meshes associated with the finite volume method and on the choice of turbulence model. Comparing CFD predictions with the power losses measured on a specific test rig, it is shown that the fluid ejection in the radial direction must be included in order to reproduce the experimental evidence. The relative importance of the losses generated by the gear front and rear faces along with those due to the teeth is discussed. The volumetric flow rate expelled by the teeth is analyzed and the influence of flanges is highlighted.

Multi-Objective Robust Optimization Under Interval Uncertainty Using Online Approximation and Constraint Cuts

Abstract: Many engineering optimization problems are multi-objective, constrained and have uncertainty in their inputs. For such problems it is desirable to obtain solutions that are multi-objectively optimum and robust. A robust solution is one that as a result of input uncertainty has variations in its objective and constraint functions which are within an acceptable range. This paper presents a new approximation-assisted MORO (AA-MORO) technique with interval uncertainty. The technique is a significant improvement, in terms of computational effort, over previously reported MORO techniques. AA-MORO includes an upper-level problem that solves a multi-objective optimization problem whose feasible domain is iteratively restricted by constraint cuts determined by a lower-level optimization problem. AA-MORO also includes an online approximation wherein optimal solutions from the upper- and lower-level optimization problems are used to iteratively improve an approximation to the objective and constraint functions. Several examples are used to test the proposed technique. The test results show that the proposed AA-MORO reasonably approximates solutions obtained from previous MORO approaches while its computational effort, in terms of the number of function calls, is significantly reduced compared to the previous approaches.

Improved Screw–Nut Interface Model for High-Performance Ball Screw Drives

Abstract: Emerging applications of ball screw drives such as semiconductor inspection, fiber optic alignment, medical equipment, and miniature robotic actuators typically make use of ball screws that are compact, stiff, and precise. Existing models for the screw–nut interface stiffness of ball screw drives are however unable to accurately describe the dynamics of compact and stiff ball screws because they are derived based on the assumption that the portion of the screw within the nut is rigid. This paper proposes a new screw–nut interface stiffness model, which incorporates the elastic deformation of the screw within the nut using Timoshenko beam shape functions. The new model is shown, via simulation and experiments, to provide more accurate predictions of the natural frequencies of compact and stiff ball screw/nut assemblies compared to the existing models. It is therefore more suitable for use in the design simulation/evaluation of high-performance ball screw drives where compactness and rigidity are required.