Papers by Jèrôme Bruyère
Mechanism and Machine Theory, 2015
Two original analytical formulations are presented which explicitly give the depths and extents o... more Two original analytical formulations are presented which explicitly give the depths and extents of symmetric profile modifications minimising the fluctuations of quasi-static transmission error in narrow-faced spur and helical gears. Numerous comparisons with quasi-static and dynamic simulation results are presented which prove that the proposed theory is sound. The proposed formulae can therefore help define adapted reliefs in terms of transmission error and dynamic tooth loading with minimum effort.
WORLD SCIENTIFIC eBooks, Apr 1, 2009
Tolerance verification permits to check the product conformity and to verify assumptions made by ... more Tolerance verification permits to check the product conformity and to verify assumptions made by the designer. For conformity assessment, the uncertainty associated with the values of the measurands must be known. In the ISO TS 17450 part 2, the notion of the uncertainty is generalized to the specification and the verification. The uncertainty is divided into correlation uncertainty, specification uncertainty and measurement uncertainty. Correlation uncertainty characterizes the fact that the intended functionality and the controlled characteristics may not be perfectly correlated. Therefore, we propose a new specified characteristics based on the statistical tolerancing approach which is directly in relationship with the design intent: the probability distribution of maximum range of the transmission error (the transmission error is the main source of vibratory and acoustic nuisances), and the evaluation of this characteristic based on 3D acquisition by Monte Carlo simulation and Tooth Contact Analysis. Moreover, the measurement uncertainty of the evaluation of this characteristic is estimated by Monte Carlo Simulation.
Analysis of the Dynamic Behaviour of Multi-Mesh Spur and Helical Gears - Application to the Definition of Optimum Profile Reliefs in Aeronautical Transmissions
Proceedings of the JSME International Conference on Motion and Power Transmissions, 2017
Set Based Robust Design of Systems – Application to Flange Coupling
Springer eBooks, 2011
A set-based approach to design of mechanical systems is presented in the following text. Set-base... more A set-based approach to design of mechanical systems is presented in the following text. Set-based technique allows keeping multiple alternatives alive during the design process while narrowing through the possibilities towards the most optimal solution. Using the Quantifier notion from QCSP (Quantified Constraint Satisfaction Problem), a formal expression for the problem has been developed. An algorithm using QCSP transformation through interval analysis has also been developed. In order to demonstrate the approach, an example of design of rigid flange coupling with a variable number of bolts and a choice of bolts from ISO M standard has been resolved and demonstrated.
Mechanism and Machine Theory, 2022
This study aims to implement multi-objective optimization of a gear unit in order to minimize the... more This study aims to implement multi-objective optimization of a gear unit in order to minimize the power loss and the vibrational excitation generated by the meshing, via a multi-scale approach that extends from gear contact to the complete transmission. All these indicators are closely linked to the macro and micro-geometry definition of the gear pair. The optimization is carried out using a genetic algorithm, namely the Non-Dominated Sorting Genetic Algorithm II (NSGA-II). The design variables chosen for the problem are the pressure angle and the helix angle, as macro-geometry characteristics of the gear, and/or the length and the amount of tooth profile modifications, as micro-geometry characteristics of the gear. Constraints are imposed in order to not exceed a maximum bending stress at the tooth root of the gear and to not fall below a minimum total contact ratio. From the results obtained, it is found that the multi-objective optimization with both micro and macro-geometry parameters simultaneously gives different results than those obtained with macro-geometry first and then micro-geometry parameters. In order to study the importance, or not, to take into account the complete gear unit, a comparison is made between the local power loss generated by gear tooth friction and the total power loss in the single stage gear unit in terms of design variables values.
Optimization of Profile Modifications With Regard to Dynamic Tooth Loads in Single and Double-Helical Planetary Gears With Flexible Ring-Gears
Journal of Mechanical Design, Nov 19, 2015
This paper is mostly aimed at analyzing optimum profile modifications (PMs) in planetary gears (P... more This paper is mostly aimed at analyzing optimum profile modifications (PMs) in planetary gears (PGTs) with regard to dynamic mesh forces. To this end, a dynamic model is presented based on 3D two-node gear elements connected to deformable ring-gears discretized into beam elements. Double-helical gears are simulated as two gear elements of opposite hands which are linked by shaft elements. Symmetric tip relief on external and internal gear meshes are introduced as time-varying normal deviations along the lines of contact and time-varying mesh stiffness functions are deduced from Wrinckler foundation models. The equations of motion are solved by coupling a Newmark time-step integration scheme and a contact algorithm to account for possible partial or total contact losses. Symmetric linear PMs for helical and double-helical PGTs are optimized by using a genetic algorithm with the objective of minimizing dynamic tooth loads over a speed range. Finally, the sensitivity of these optimum PMs to speed and load is analyzed.
Modelling of high power geared transmissions, introduction of a filling material
International Conference on Gears 2019, 2019
Parametric Study of a 3D trochoidal reducer model with involute profile
International Conference on Gears 2019, 2019
Optimization of Profile Modifications With Regard to Dynamic Tooth Loads in Planetary Gears With Flexible Ring-Gears
Volume 10: ASME 2015 Power Transmission and Gearing Conference; 23rd Reliability, Stress Analysis, and Failure Prevention Conference, 2015
This paper deals with the optimization of tooth profile modifications in planetary gears. A dynam... more This paper deals with the optimization of tooth profile modifications in planetary gears. A dynamic model is proposed based on 3D two-node gear elements connected to a deformable ring-gear discretized into beam elements. Symmetric tip relief on external and internal gear meshes are introduced as normal deviations along the lines of contact superimposed on a stiffness distribution aimed at simulating position- and time-varying mesh stiffness functions. The equations of motion are solved by the combination of a Newmark’s time-step integration scheme and a contact algorithm to account for possible partial or total contact losses. Symmetric linear profile modifications are then optimized by using a genetic algorithm with the objective of minimizing dynamic tooth loads over a speed range. Finally, the interest of the corresponding optimum profile modifications with regard to speed and torque variations is analyzed.
Statistical Tolerance Analysis of Gears by Tooth Contact Analysis
Models for Computer Aided Tolerancing in Design and Manufacturing
To analyze the influence of geometrical variations of parts on functional characteristics, a powe... more To analyze the influence of geometrical variations of parts on functional characteristics, a powerful way consist to simulate its geometrical behaviour. For gears, a specific method based on Tooth Contact Analysis is developed to evaluate influence of intrinsic and situation deviations of pinion and wheel on the assembly. Moreover, a statistical analysis allows to determine probability distribution of the functional characteristic - kinematic error for a list of random geometrical deviations
Definition of optimum profile and lead modifications in spur and helical gears using a genetic algorithm
A methodology is presented which relies on genetic algorithms (GA) in order to minimise the time-... more A methodology is presented which relies on genetic algorithms (GA) in order to minimise the time-variations of transmission error while including constraints on admissible contact and root stresses. It is demonstrated that the results from genetic algorithms compare favourably with those delivered by systematic sweeps over all the design variables for highly reduced computational times. Performances diagrams are derived for spur and helical gears leading to a number of practical conclusions in terms of designing optimum tooth shape modifications.
Analytical Investigations on the Mesh Stiffness Function of Solid Spur and Helical Gears
Journal of Mechanical Design, 2015
Approximate formulae are presented which give the time-varying mesh stiffness function for ideal ... more Approximate formulae are presented which give the time-varying mesh stiffness function for ideal solid spur and helical gears. The corresponding results compare very well with those obtained by using two-dimensional (2D) finite element (FE) models and specific benchmark software codes thus validating the proposed analytical approach. More deviations are reported on average mesh stiffness which, to a large extent, are due to the modeling of gear body deflections.
Simulation of the Dynamic Behavior of a Multi-stage Geared Systems with Tooth Shape Deviations and External Excitations
Applied Condition Monitoring, 2015
In this paper, a torsional dynamic model of multi-stage idler spur and helical gears is presented... more In this paper, a torsional dynamic model of multi-stage idler spur and helical gears is presented which combines time-varying internal and external excitations such as time-varying external torques. Each contact line in the various base planes is discretized in elemental cells which are all attributed a time-varying mesh stiffness element and an initial separation to account for tooth shape deviations from ideal involute flanks. The corresponding non-linear differential system is solved by combining a Newmark’s numerical scheme and a normal contact algorithm. A number of simulation results are presented on the influence of the combined effect of errors and shape deviations along with external excitation sources on dynamic tooth loads.
Multi-objective Optimization of Gear Tooth Profile Modifications
Lecture Notes in Mechanical Engineering, 2013
In a context of permanent technological progress to produce ever more reliable and efficient indu... more In a context of permanent technological progress to produce ever more reliable and efficient industrial products, modern gears are increasingly subject to strict requirements in terms of load capacity, performance, noise generation, etc. The definition of tooth modifications in order to improve performance criteria such as transmission error fluctuations, efficiency, wear resistance, etc. is a challenging problem for designers because these criteria often evolve in a contradictory manner. This paper deals with the multi-objective optimization of tooth profile modifications and its main purpose is to propose an approach to help design tooth corrections in order to simultaneously optimize several objective functions. An optimization technique based on a specific algorithm (NSGA-II) is presented and its effectiveness in terms of multi-criterion optimization in the sense of Pareto optimal is analyzed based on a number of case studies.
A torsional dynamic model of multi-stage geared systems submitted to internal and external excitations
International Gear Conference 2014: 26th–28th August 2014, Lyon, 2014
A simplified torsional model is presented which can be used to simulate the dynamic behaviour of ... more A simplified torsional model is presented which can be used to simulate the dynamic behaviour of multi-stage spur and helical gears. The time-varying mesh stiffness functions are estimated from the formulae of Weber & Banaschek and their relative phases are determined based on the gear geometry and relative positioning. A time-varying external torque can also be inserted at any node. The resulting differential system is solved by combining a Newmark’s numerical scheme and a normal contact algorithm. A number of simulation results are presented on the influence of the combined effect of errors and shape deviations and internal excitation sources on dynamic effort.
Robust Optimization of Gear Tooth Modifications Using a Genetic Algorithm
Condition Monitoring of Machinery in Non-Stationary Operations, 2012
ABSTRACT Most studies in gear design analysis and optimization do not account for the presence of... more ABSTRACT Most studies in gear design analysis and optimization do not account for the presence of uncertainties inherent to the manufacturing and assembly precisions. In this paper, the issue of robustness of gear modifications with regard to transmission error fluctuations is addressed. An approach based on numerical integration (Gauss Quadrature) is adopted and a statistical optimization based on a genetic algorithm is used to determine the robust areas for tooth modifications. Finally, the influences of the gear quality grade and the probability law are analysed.
A simplified multi-objective analysis of optimum profile modifications in spur and helical gears
Mechanism and Machine Theory, 2014
Parametric and robust design using the quantifier notion
2009 International Conference on Computers & Industrial Engineering, 2009
In this paper we present an approach for robust design of mechanical assemblies using the princip... more In this paper we present an approach for robust design of mechanical assemblies using the principles of parametric design and the notion of quantifiers from the approach ofQCSP (Quantified constraint satisfaction problem). The QCSP technique is an extension ofthe CSP (Constraint ...
Optimization of Gear Tolerances by Statistical Analysis and Genetic Algorithm
Advances in Integrated Design and Manufacturing in Mechanical Engineering II, 2007
The purpose of functional tolerancing process is to define the geometrical specifications(toleran... more The purpose of functional tolerancing process is to define the geometrical specifications(tolerances) of parts ensuring functional requirements. An important distinction in tolerance process is that engineers are more commonly faced with the problem of tolerance synthesis rather than tolerance analysis. In tolerance analysis the parts tolerances are all known and the resulting geometrical requirement respect is calculated. In tolerance synthesis,
Mechanism and Machine Theory, 2008
The purpose of functional tolerancing process is to define the geometrical specifications (tolera... more The purpose of functional tolerancing process is to define the geometrical specifications (tolerances) of parts ensuring functional requirements. An important distinction in tolerance process is that engineers are more commonly faced with the problem of tolerance synthesis rather than tolerance analysis. In tolerance analysis the parts tolerances are all known and the resulting geometrical requirement respect is calculated. In tolerance synthesis, on the other hand, the geometrical requirement is known from design requirements, whereas the magnitudes of the parts tolerances to meet these requirements are unknown. In this paper, we focus on the gear tolerances, and we propose an approach based statistical analysis for tolerance analysis and genetic algorithm for tolerance synthesis. Usually, statistical tolerance analysis uses a relationship between parts deviations and functional characteristics. In the case of tolerance analysis of gears, thus relationship is not available in analytic form, the determination of a functional characteristic (kinematic error,.. .) involves a numerical simulation. Therefore the Monte Carlo simulation, as the simplest and effectual method, is introduced into the frame. Moreover, to optimize the tolerance cost, genetic algorithm is improved. Indeed, this optimization problem is so complex that for traditional optimization algorithms it may be difficult or impossible to solve it because the objective function is not available in analytic form. For the evaluation of the fitness of each individual based on Monte Carlo simulation, the number of samples is the key of precision. By a large number of samples, the precision can be improved, but the computational cost will be increased. In order to reduce the computational cost of this optimization based on Monte Carlo simulation and genetic algorithms, the strategy is to adopt different precision of fitness; different numbers of samples during the optimization procedure are introduced into our algorithms.
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Papers by Jèrôme Bruyère