736 research outputs found
A methodology for simulation-based, multiobjective gear design optimization
No full textDesign optimization of geared transmissions has become more of a necessity than ever before. Typically, conflicting design goals must be concurrently achieved. The difficulty of such a multiobjective design optimization problem is exacerbated by the fact that modern design practices rely on increasingly sophisticated, computationally-expensive simulation tools for tooth contact analysis. Their intrinsic nonlinearities add complexity to the problem, hampering gear designers’ efforts to obtain globally optimal solutions. Practical optimization problems of this class have often been solved by evolutionary algorithms, but their computational burden may well be inappropriate for CPU-intensive simulation models. The present work details an algorithmic framework inspired by deterministic multiobjective optimization methods, specially combined with a direct-search global optimization algorithm to obtain globally Pareto-optimal solutions. Nonlinear constraints are enforced through an exact penalty formulation. A comprehensive description of all theoretical and algorithmic details is provided, with the intention of enabling gear designers to implement or adapt the proposed methodology to their design optimization purposes. Two tests on a challenging gear design problem, namely ease-off topography optimization of a hypoid gear set for maximum efficiency and minimum contact stress, demonstrate that the proposed method can efficiently obtain solutions belonging to the global Pareto front
Revisiting Generation and Meshing Properties of Beveloid Gears
No full textThe teeth of ordinary spur and helical gears are generated by a (virtual) rack provided with planar generating surfaces. The resulting tooth surface shapes are a circle-involute cylinder in the case of spur gears, and a circle-involute helicoid for helical gears. Advantages associated with involute geometry are well known. Beveloid gears are often regarded as a generalization of involute cylindrical gears involving one additional degree-of-freedom, in that the midplane of their (virtual) generating rack is inclined with respect to the axis of the gear being generated. A peculiarity of their generation process is that the motion of the generating planar surface, seen from the fixed space, is a rectilinear translation (while the gear blank is rotated about a fixed axis); the component of such translation that is orthogonal to the generating plane is the one that ultimately dictates the shape of the generated, envelope surface. Starting from this basic fact, we set out to revisit this type of generation-by-envelope process and to profitably use it to explore peculiar design layouts, in particular for the case of motion transmission between skew axes (and intersecting axes as a special case). Analytical derivations demonstrate the possibility of involute helicoid profiles (beveloids) transmitting motion between skew axes through line contact and, perhaps more importantly, they lead to the derivation of designs featuring insensitivity of the transmission ratio to all misalignments within relatively large limits. The theoretical developments are confirmed by various numerical examples
Revisiting plane-generated gear tooth surfaces: a novel design perspective
No full textThe teeth of ordinary spur and helical gears are generatedby a (virtual) rack provided with planar generating surfaces. The resulting tooth surface shapes are a circle-involute cylinder in the case of spur gears, and a circle-involute helicoid for helical gears. Advantages associated with involute geometry are well known: in particular, the motion transmission function is insensitive to center distance variations, and contact lines (or points, when a corrective surface mismatch is applied) evolve along a fixed plane of action, thereby reducing vibrations and noise emission. As a result, involute gears are easier to manufacture and assemble than non-involute gears, and silent to operate. A peculiarity of their generation process is that the motion of the generating planar surface, seen from the fixed space, is a rectilinear translation (while the gear blank is rotated about a fixed axis):
the component of such translation that is orthogonal to the generating plane is the one that ultimately dictates the shape of thegenerated, envelope surface. Starting from this basic fact, we set out to investigate this type of generation-by-envelope process and to profitably use it to explore new potential design layouts. In particular, with some similarity to the basic principles underlying conical involute (or Beveloid) gears, but within a broader scope, we propose a generalization of these concepts to the case of involute surfaces for motion transmission between skew axes (and intersecting axes as a special case). Analytical derivations demonstrate the theoretical possibility of involute profiles transmitting motion between skew axes through line contact and, perhaps more importantly, they lead to apparently novel geometric designs featuring insensitivity of transmission ratio to all misalignments within relatively large limits. The theoretical developments are confirmed by various numerical examples
Identification of Motor Control Objectives in Human Locomotion via Multi-Objective Inverse Optimal Control
No full textPredictive simulations of human motion are a precious resource for a deeper understanding of the motor control policies encoded by the central nervous system. They also have profound implications for the design and control of assistive and rehabilitation devices, for ergonomics, as well as for surgical planning. However, the potential of state-of-the-art predictive approaches is not fully realized yet, making it difficult to draw convincing conclusions about the actual optimality principles underlying human walking. In the present study we propose a novel formulation of a bilevel, inverse optimal control strategy based on a full-body three-dimensional neuromusculoskeletal model. In the lower level, prediction of walking is formulated as a principled multi-objective optimal control problem based on a weighted Chebyshev metric, whereas the contributions of candidate control objectives are systematically and efficiently identified in the upper level. Our framework has proved to be effective in determining the contributions of the selected objectives and in reproducing salient features of human locomotion. Nonetheless, some deviations from the experimental kinematic and kinetic trajectories have emerged, suggesting directions for future research. The proposed framework can serve as an inverse optimal control platform for testing multiple optimality criteria, with the ultimate goal of learning the control objectives that best explain observed human motion
A computational framework to explore optimality in human movement
No full textPredictive model-based simulations of system dynamics are powerful tools to explore optimality criteria underlying human movement (e.g. walking). This field of research is raising interest from the biomechanics and robotics communities, as predictive approaches can provide new insights in many areas, such as in the design and control of robotic assistive devices
An ease-off based optimization of the loaded transmission error of hypoid gears
No full textLoaded transmission error (LTE) is one of the primary sources of gear noise and vibration.
While ease-off topography has been shown to be powerful in improving the contact
properties of a gear drive, its optimization to minimize LTEs has been an open problem
in the gear literature. Through the formulation of an appropriate nonlinear optimization
problem, this study proposes a novel methodology to systematically define optimal easeoff
topography to simultaneously minimize LTEs and contact pressures, while concurrently
confining the loaded contact pattern within a prescribed allowable region on the
tooth surface to avoid any edge- or corner-contact condition. Effectiveness of this optimization
is presented using a face-milled and a face-hobbed hypoid gear examples. These
example analyses reveal particularly promising results that feature both a drastic reduction
in LTE and an appreciable decrease in the maximum contact stress. Although the
method is employed here for hypoid gears, its intrinsically systematic formulation enables
straightforward applicability to any kind of gears. The methodology presented in
this work can be a useful aid for gear engineers to determine optimal ease-off topographies
without having to rely on time-consuming trial-and-error approaches or on a priori
subjective judgments
A Two-Stage Trajectory Optimization Strategy for Articulated Bodies with Unscheduled Contact Sequences
No full textIn this letter, we propose a two-stage strategy for optimal control problems of robotic mechanical systems that proves to be more robust, and yet more efficient, than straightforward solution strategies. Specifically, we focus on a simplified humanoid model, represented as a two-dimensional articulated serial chain of rigid bodies, in the tasks of getting up (sitting down) from (to) the supine and prone postures. Interactions with the environment are integral parts of these motions, and a priori unscheduled contact sequences are discovered by the solver itself, opportunistically making or breaking contacts with the ground through feet, knees, hips, elbows, and hands. The present investigation analyzes the effects on the computational performance of: 1) the explicit introduction of contact forces among the optimization variables, 2) the substitution of undesired contact forces with geometric constraints that prevent interpenetrations, and 3) the splitting of the planning problem into two consecutive phases of increasing complexity. To the best of our knowledge, these tests represent the only quantitative analysis of the performances achievable with different solution strategies for optimization-based, whole-body dynamic motion planning in the presence of contacts
On the Identification of Machine Settings for Gear Surface Topography Corrections
No full textIn this paper we set out to investigate the performances of some algorithms proposed in the gear literature for
identifying the machine-tool settings required to obtain predesigned gear tooth surface topographies, or needed to
compensate for flank form deviations of real teeth. For ease of comparison, the problem is formulated as a nonlinear
least squares problem, and the most widely employed algorithms are derived as special cases. The algorithms
included in the analysis are: (i) one-step methods, (ii) iterative methods, (iii) iterative methods with step control.
The performance index is devised in their ability of returning practical solutions in the presence of: (i) strong model
nonlinearities, (ii) ill-conditioning of the sensitivity matrix, (iii) demanding topographic shapes. Instrumental here
is an original classification of topographic modifications as either “simple” or “complex”, based on the SVD
analysis of the sensitivity matrix. Some selected numerical examples demonstrate that iterative techniques with step
control are the most convenient in terms of reliability and robustness of the obtained solutions. The generation
process considered here is face-milling of hypoid gears, although the methodology is general enough to cope with
any gear cutting/grinding method
Offset-free MPC explained: novelties, subtleties, and applications
No full textThis paper presents an updated and comprehensive description of offset-free MPC algorithms for nonlinear (and linear) discrete-time systems, with the intended objectives of clarifying the main concepts, showing new results, highlighting subtleties by means of challenging applications. First, the offset-free tracking problem for nonlinear systems is presented, putting a strong accent on the role of the disturbance model and observer, and then novel and stronger offset-free estimation results are presented. Next, recent advances in linear offset-free MPC are described, which show the equivalence of the velocity form algorithm (so far considered an alternative method) to a particular disturbance model and observer. Then, the concepts of offset-free estimation are exploited to design an offset-free economic MPC algorithm, which can asymptotically achieve the highest economic performance despite persistent model errors and disturbances. Extensive application results are presented to show the benefits of offset- free MPC algorithms over standard ones, and to clarify misconceptions and design errors that can prevent constraint satisfaction, closed-loop stability, and offset-free performance
Synthesis of hypoid gear surface topography by a nonlinear least squares approach
No full textThis paper outlines a systematic methodology for finding
the machine setting corrections required to obtain a predesigned
ease-off surface in spiral bevel and hypoid gear teeth. The problem
is given a nonlinear least squares formulation which, however,
is highly prone to numerical instabilities. The Levenberg–
Marquardt algorithm with a trust region strategy turned out to be
quite effective and robust to obtain feasible solutions. The proposed
method was tested on lengthwise crowning, profile crowning
and spiral angle correction. In all cases, the goal was
achieved with very high accuracy, in a few iterations and, remarkably,
with different sets of machine parameters
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