A Contribution to the Design of Robust Profile Modifications in Spur and Helical Gears by Combining Analytical Results and Numerical Simulations

2012 ◽  
Vol 134 (6) ◽  
Author(s):  
D. Ghribi ◽  
J. Bruyère ◽  
Ph. Velex ◽  
M. Octrue ◽  
M. Haddar
Keyword(s):  
Transmission Error ◽  
Computational Time ◽  
Design Parameters ◽  
Distribution Law ◽  
Helical Gears ◽  
Factorial Method ◽  
Transmission Errors ◽  
Analytical Results ◽  
Gradient Descent Algorithm ◽  
Definition Of

This paper addresses the definition of robust profile modifications in spur and helical gears. An original methodology is introduced which relies on closed-form analytical results on transmission errors combined with a gradient descent algorithm and a Gauss quadrature (GQ) based full factorial method. The results compare very well with those delivered by using classic Monte Carlo simulations with a considerable gain in computational time. The influence of the probability distribution law for the design parameters (depth and extent of modification) is analyzed along with the contribution of gear quality grade and load variation. Some optimum robust linear relief is presented which minimizes transmission error fluctuations over a broad range of loads even in the presence of significant geometrical tolerances.

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

2011 ◽  
Vol 133 (3) ◽  
Author(s):  
P. Velex ◽  
J. Bruyère ◽  
D. R. Houser
Keyword(s):  
Transmission Error ◽  
Direct Solution ◽  
Contact Ratio ◽  
Helical Gears ◽  
Transmission Errors ◽  
Versus Profile ◽  
Analytical Results ◽  
Gear Geometry ◽  
Theoretical Developments

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.

scholarly journals Computerized Design and Generation of Low-Noise Helical Gears with Modified Surface Topology

1995 ◽  
Vol 117 (2A) ◽  
pp. 254-261 ◽  
Author(s):  
F. L. Litvin ◽  
N. X. Chen ◽  
J. Lu ◽  
R. F. Handschuh
Keyword(s):  
Gear Tooth ◽  
Error Function ◽  
Transmission Error ◽  
Low Noise ◽  
Surface Topology ◽  
Helical Gears ◽  
Transmission Errors ◽  
Bearing Contact ◽  
Pinion Gear ◽  
Tooth Surfaces

An approach for the design and generation of low-noise helical gears with localized bearing contact is proposed. The approach is applied to double circular arc helical gears and modified involute helical gears. The reduction of noise and vibration is achieved by application of a predesigned parabolic function of transmission errors that is able to absorb a discontinuous linear function of transmission errors caused by misalignment. The localization of the bearing contact is achieved by the mismatch of pinion-gear tooth surfaces. Computerized simulation of meshing and contact of the designed gears demonstrated that the proposed approach will produce a pair of gears that has a parabolic transmission error function even when misalignment is present. Numerical examples for illustration of the developed approach are given.

scholarly journals Evaluation of Transient Response of Turbochargers and Turbines Using Database Method for the Nonlinear Forces of Journal Bearings

Lubricants ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 78 ◽  
Author(s):  
Chasalevris ◽  
Louis
Keyword(s):  
Transient Response ◽  
Standard Procedure ◽  
Computational Time ◽  
Design Parameters ◽  
Flexible Rotor ◽  
Turbine Generator ◽  
Rotating Systems ◽  
Approximation Formulas ◽  
Turbine Shaft ◽  
Definition Of

The paper extents the fluid film bearing database method to arbitrary fixed bearing profiles including floating ring bearings. The method is applied to evaluate rotordynamic response of an automotive turbocharger, modeled as rigid rotor, and of a turbine-generator shaft train for power generation modeled as flexible rotor through the transient transfer matrix method. The methodology claims to render drastically faster evaluation of transient response of rotating systems with nonlinear bearings regardless the complexity of the bearing models implemented. The computational time of transient response is similar to this when short bearing expressions are used. Turbocharger rotordynamic simulation considers the use of nonlinear bearing models as mandatory, and several case studies have to be performed for the definition of key design parameters of floating ring bearings. The bearing database method offers the tool for a severe total time reduction in rotordynamic calculations, with the possibility to implement advanced thermohydrodynamic bearing models to the rotordynamic algorithm as fast as short bearing approximation formulas. Furthermore, the rotordynamic design of large turbine shaft trains is still based on linear harmonic analysis which leads to conservative designs. The database method aims to include the transient response of nonlinear rotor models as a standard procedure in the rotordynamic design of large shaft trains, which nowadays is avoided due to high time cost and complexity.

A Study on the Correlation Between Dynamic Transmission Error and Dynamic Tooth Loads in Spur and Helical Gears

2016 ◽  
Vol 139 (1) ◽  
Author(s):  
N. Sainte-Marie ◽  
P. Velex ◽  
G. Roulois ◽  
J. Caillet
Keyword(s):  
Experimental Evidence ◽  
Three Dimensional ◽  
Transmission Error ◽  
System Behavior ◽  
Helical Gears ◽  
Transmission Errors ◽  
Linear Dependency ◽  
Lumped Parameter ◽  
Excitation Model ◽  
The Relationship

A three-dimensional (3D) dynamic gear model is presented which combines classic shaft, lumped parameter, and specific two-node gear elements. The mesh excitation model is based on transmission errors (TEs), and its mathematical grounding is briefly described. The validity of the proposed methodology is assessed for both spur and helical gears by comparison with experimental evidence. The model is then employed to analyze the relationship between dynamic transmission errors (DTE) and dynamic tooth loads (DF) or root stresses. It is shown that a linear dependency can be found as long as the system behavior is dominated by shaft torsion but that this linear relationship tends to disappear when bending cannot be neglected.

Guaranteed values – the basis of the analysis of the quality of individual products

2019 ◽  
pp. 20-33
Author(s):  
D. N. Kalacheva
Keyword(s):  
Frequency Distribution ◽  
Distribution Law ◽  
Basic Characteristics ◽  
Definition Of

Herein, the main features and rules of using guaranteed values when analyzing the quality of rocket - space equipment products are considered. The definition of the guaranteed value and the form of its presentation is given. It is indicated that guaranteed value is distributed and is characterized by the frequency distribution law. The main methods of representation and conversion of guaranteed values are statistical. Examples of determining the basic characteristics of guaranteed values are given.

scholarly journals Energy Minimization Scheme for Split Potential Systems Using Exponential Variational Integrators

2021 ◽  
Vol 2 (3) ◽  
pp. 431-441
Author(s):  
Odysseas Kosmas
Keyword(s):  
Numerical Solutions ◽  
Oscillatory Behavior ◽  
Lagrangian Function ◽  
Computational Time ◽  
Variational Integrators ◽  
Weighted Sum ◽  
Lagrange Equations ◽  
Exponential Functions ◽  
Intermediate Time ◽  
Definition Of

In previous works we developed a methodology of deriving variational integrators to provide numerical solutions of systems having oscillatory behavior. These schemes use exponential functions to approximate the intermediate configurations and velocities, which are then placed into the discrete Lagrangian function characterizing the physical system. We afterwards proved that, higher order schemes can be obtained through the corresponding discrete Euler–Lagrange equations and the definition of a weighted sum of “continuous intermediate Lagrangians” each of them evaluated at an intermediate time node. In the present article, we extend these methods so as to include Lagrangians of split potential systems, namely, to address cases when the potential function can be decomposed into several components. Rather than using many intermediate points for the complete Lagrangian, in this work we introduce different numbers of intermediate points, resulting within the context of various reliable quadrature rules, for the various potentials. Finally, we assess the accuracy, convergence and computational time of the proposed technique by testing and comparing them with well known standards.

scholarly journals CONCEPTUAL DESIGN FOR ASSEMBLY IN AEROSPACE INDUSTRY: SENSITIVITY ANALYSIS OF MATHEMATICAL FRAMEWORK AND DESIGN PARAMETERS

2021 ◽  
Vol 1 ◽  
pp. 731-740
Author(s):  
Giovanni Formentini ◽  
Claudio Favi ◽  
Claude Cuiller ◽  
Pierre-Eric Dereux ◽  
Francois Bouissiere ◽  
...  
Keyword(s):  
Sensitivity Analysis ◽  
Conceptual Design ◽  
Design Parameters ◽  
Design For Assembly ◽  
Mathematical Framework ◽  
Commercial Aircraft ◽  
System Architectures ◽  
Complex Engineering ◽  
Aircraft System ◽  
Definition Of

AbstractOne of the most challenging activity in the engineering design process is the definition of a framework (model and parameters) for the characterization of specific processes such as installation and assembly. Aircraft system architectures are complex structures used to understand relation among elements (modules) inside an aircraft and its evaluation is one of the first activity since the conceptual design. The assessment of aircraft architectures, from the assembly perspective, requires parameter identification as well as the definition of the overall analysis framework (i.e., mathematical models, equations).The paper aims at the analysis of a mathematical framework (structure, equations and parameters) developed to assess the fit for assembly performances of aircraft system architectures by the mean of sensitivity analysis (One-Factor-At-Time method). The sensitivity analysis was performed on a complex engineering framework, i.e. the Conceptual Design for Assembly (CDfA) methodology, which is characterized by level, domains and attributes (parameters). A commercial aircraft cabin system was used as a case study to understand the use of different mathematical operators as well as the way to cluster attributes.

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