Raynald Guilbault

Genetic algorithms and finite element coupling for mechanical optimization

Optimization of mechanical components is an important aspect of the engineering process; a well designed system will lead to money saving during the production phase and better machine life. On the other hand, optimization actions will increase the engineering investment. Consequently, and since computer time is inexpensive, an efficient design strategy will tend to transfer the effort from the staff to the computers. This paper presents an efficient design tool made to carry out this task: a new optimization model based on genetic algorithms is developed to work with commercial finite element software. The objective is to automate optimization of static criteria (stresses, weight, strength, etc.) with finite element models. In the proposed model, the process acts on two geometric aspects of the shape to be optimized: it controls the position of the vertices defining the edges of the volume and, in order to minimize stresses concentrations, it can add and define fillet between surfaces. The model is validated from some benchmark tests. An industrial application is presented: the genetic algorithms-finite element model is employed to design the fillets at the crown-blade junctions of a hydroelectric turbine. The results show that the model converges to a very efficient solution without any engineer intervention.

Express Model for Load Sharing and Stress Analysis in Helical Gears

The performance of a gear set is strongly influenced by the manufacturing and assembly quality. Therefore, detailed analyses at the design stage, where the effects of expected assembly and manufacturing errors can be simulated, are crucial. At an early design stage, when contact conditions are addressed, the widely used finite element method (FEM) may still result in unwanted computing time. The paper presents an Express model developed to serve as a fast design tool offering fine simulation and a high precision level. The model establishes load sharing, fillet stresses and pressure distribution along the contacting surfaces of meshing helical gear teeth. The calculations combine the finite strip method with a pseudo-three-dimensional (3D) model of the tooth base solved with finite differences to calculate tooth bending deflexion and fillet stresses. The accuracy of the procedure is demonstrated through 3D FEM models. A contact cell discretization completes the model. This very fast and accurate approach gives the contact pressure distributions resulting from the roll-slide motion of mating teeth. An analysis of a helical gear set in two different assembly positions reveals the effects of edge contact, and exhibits the influence of tooth stiffness reduction near tooth corners.

Helical Gears, Effects of Tooth Deviations and Tooth Modifications on Load Sharing and Fillet Stresses

Based on a few specific cases, this paper presents a comparative investigation of the effect of helix slope and form deviation tolerances as specified by grades 5 and 7 of the ANSI/AGMA ISO 1328-1 Standard for Cylindrical Gears. In addition, the consequences of longitudinal flank crowning and radial tip relief modifications are investigated, as applied on a misaligned helical gear set. For all simulations, the express model (Guilbault et al., 2005, ASME J. Mech. Des., 127(6), pp. 1161-1172) is employed. The bending deflection and fillet stresses are obtained from a combination of finite strip and finite difference meshes. The rolling-sliding motion of mating gear teeth is modeled with a cell discretization of the contact area, which offers fast and accurate results. Similar contact conditions arise from a helix slope deviation or a misalignment of the gear set: the first contact point is driven to a theoretical contact line endpoint. Such a condition produces a localized, and clearly impaired, contact area subject to overloading. Consequently, flank crowning and tip relief corrections must be carefully regarded in the design process. The presented results highlight that, if improperly combined, profile modifications can amplify the overloading condition.

Review and Study of Genotypic Diversity Measures for Real-Coded Representations

The exploration/exploitation balance is a major concern in the control of evolutionary algorithms (EAs) performance. Exploration is associated with the distribution of individuals on a landscape, and can be estimated by a genotypic diversity measure (GDM). In contrast, exploitation is related to individual responses, which can be described with a phenotypic diversity measure. Many diversity measures have been proposed in the literature without a comprehensive study of their differences. This paper looks at surveys of GDMs published over the years for real-coded representations, and compares them based on a new benchmark, one that allows a better description of their behavior. The results demonstrate that none of the available GDMs is able to reflect the true diversity of all search processes. Nonetheless, the normalized pairwise diversity measurement proves to be the best genotypic diversity measurement for standard EAs, as it shows nondominated behavior with respect to the desired GDM requirements.

A Fast Correction for Elastic Quarter-Space Applied to 3D Modeling of Edge Contact Problems

Applying the Hertz theory to some non-Hertzian contact problems can produce acceptable results. Nevertheless, including the influence of free surfaces requires numerical methods, many of which are based on the Boussinesq-Cerruti solution. This paper presents a new approach, which is better capable of releasing quarter-space free surfaces from shear and normal internal stresses without engendering any increase in calculation times. The mirrored pressure for shear correction is multiplied by a correction factor (ψ), which accounts for the normal load. The expression ψ is derived from the Hetenyi correction process, and the resulting displacements show an enhanced correspondence with validation finite element method models; with an imposed fluctuating pressure, the maximum edge displacement error was -21.90% for a shear load correction (Poisson coefficient ν = 0.3), and introducing the ψ factor reduced the deviation to -9.55%, while for ν of 0.15, the maximum error was -11.30%, which was reduced to +0.60% with the ψ factor. This study introduces the factor ψ in a 3D elastic contact algorithm. The resulting calculation scheme is then able to simulate any point or line contact problems. Compared with coincident ends and sharp edge contact validation values, the model shows high conformity levels.

Review of phenotypic diversity formulations for diagnostic tool

Practitioners often rely on search results to learn about the performance of a particular optimizer as applied to a real-world problem. However, even the best fitness measure is often not precise enough to reveal the behavior of the optimizers added features or the nature of the interactions among its parameters. This makes customization of an efficient search method a rather difficult task. The aim of this paper is to propose a diagnostic tool to help determine the impact of parameter setting by monitoring the exploration/exploitation balance (EEB) of the search process, as this constitutes a key characteristic of any population-based optimizer. It is common practice to evaluate the EEB through a diversity measure. For any diagnostic tool developed to perform this function, it will be critical to be able to certify its reliability. To achieve this, the performance of the selected measure needs to be assessed, and the EEB framework must be able to accommodate any landscape structure. We show that to devise a diagnostic tool, the EEB must be viewed from an orthogonal perspective, which means that two diversity measures need to be involved: one for the exploration axis, and one for the exploitation axis. Exploration is best described by a genotypic diversity measure (GDM), while exploitation is better represented by a phenotypic convergence measure (PCM). Our paper includes a complete review of PCM formulations, and compares nearly all the published PCMs over a validation framework involving six test cases that offer controlled fitness distribution. This simple framework makes it possible to portray the underlying behavior of phenotypic formulations based on three established requirements: monotonicity in fitness varieties, twinning, and monotonicity in distance. We prove that these requirements are sufficient to identify phenotypic formulation weaknesses, and, from this conclusion, we propose a new PCM, which, once validated, is shown to comply with all the above-mentioned requirements. We then compare these phenotypic formulations over three specially designed fitness landscapes, and, finally, the new phenotypic formulation is combined with a genotypic formulation to form the foundation of the EEB diagnostic tool. The value of such a tool is substantiated through a comparison of the behaviors of various genetic operators and parameters.

Application of Time Descriptors to the Modified Hilbert Transform of Empirical Mode Decomposition for Early Detection of Gear Defects

Diagnosis and fault detection in mechanical systems during their time-varying non stationary operation is one of the most challenging tasks. The paper presents a method for the early detection of gearbox defects based on the empirical mode decomposition (EMD) algorithm and a proposed modified Hilbert transform. The EMD technique decomposes the measured signal into oscillatory functions called Intrinsic Mode Functions (IMF). A numerical model of damaged gears is used for generating a modulated vibratory signal with repetitive shocks. The application of time descriptors “Talaf” and “Thikat” to different IMF decomposition levels of the modified Hilbert envelope gives good results for early detection of defects in comparison with the IMF of the original time signal and its traditional Hilbert envelope or with the wavelet decomposition.

Numerical Analysis of ACSR Conductor–Clamp Systems Undergoing Wind-Induced Cyclic Loads

Submitted to wind-induced vibrations, overhead conductors are vulnerable to fatigue damage, especially at restraining fixtures such as the suspension clamp. This paper proposes an efficient finite-element modeling approach providing a full 3-D representation of both the conductor and suspension clamp. Validation based on experimental data shows the precision of the approach. An in-depth model response analysis also demonstrates its ability to describe inter-wire and conductor–clamp contact interactions. Finally, a study of conductor stress distributions reveals that in critical regions, conductor wires mostly sustain alternating bending loads.

Nonlinear Parameters for Monitoring Gear: Comparison Between Lempel-Ziv, Approximate Entropy, and Sample Entropy Complexity

Vibration analysis is the most used technique for defect monitoring failures of industrial gearboxes. Detection and diagnosis of gear defects are thus crucial to avoid catastrophic failures. It is therefore important to detect early fault symptoms. This paper introduces signal processing methods based on approximate entropy (ApEn), sample entropy (SampEn), and Lempel-Ziv Complexity (LZC) for detection of gears defects. These methods are based on statistical measurements exploring the regularity of vibratory signals. Applied to gear signals, the parameter selection of ApEn, SampEn, and LZC calculation is first numerically investigated, and appropriate parameters are suggested. Finally, an experimental study is presented to investigate the effectiveness of these indicators and a comparative study with traditional time domain indicators is presented. The results demonstrate that ApEn, SampEn, and LZC provide alternative features for signal processing. A new methodology is presented combining both Kurtosis and LZC for early detection of faults. The results show that this proposed method may be used as an effective tool for early detection of gear faults.

Tooth Influence on Flexural and Torsional Flexibility, and Model Tooth Number Prediction for Optimum Dynamic Simulation of Wide-Faced Spur Gears

Refined dynamic analyses of gear pairs, including precise tooth contact description, often lead to unreasonable simulation requirements. Therefore, numerous models employ simplifications, such as two-dimensional deflection of the engaged gear set, which is inappropriate for wide-faced wheels. Other models propose three-dimensional (3D) representation of one tooth on a complete hub. This approach introduces the torsional and flexural deflection of the gear body, but underestimates the corresponding stiffness. Since forthcoming improvements of gear analysis should offer efficient 3D dynamic simulation of wide-faced gear sets, this paper primarily quantifies the flexibility error levels implied with 3D one tooth full hub spur gear models. Subsequently, a procedure is developed to determine the number of teeth required for a 3D model so that it will include the torsional and flexural flexibility of the spur gear body, within acceptable error levels. This procedure offers an efficient approach to optimize the (precision)/(simulation time) ratio. The method deals with gears of any diametral pitch, and covers the common face width and tooth number ranges.