Influence of Clearances and Thermal Effects on the Dynamic Behavior of Gear-Hydrodynamic Journal Bearing Systems

2013 ◽  
Vol 135 (6) ◽  
Author(s):  
R. Fargère ◽  
P. Velex
Keyword(s):  
Degrees Of Freedom ◽  
Integration Scheme ◽  
Time Step ◽  
Specific Element ◽  
Normal Contact ◽  
Contact Algorithm ◽  
Gear Teeth ◽  
Proposed Model ◽  
Elastic Couplings ◽  
Definition Of

A global model of mechanical transmissions is introduced which deals with most of the possible interactions between gears, shafts, and hydrodynamic journal bearings. A specific element for wide-faced gears with nonlinear time-varying mesh stiffness and tooth shape deviations is combined with shaft finite elements, whereas the bearing contributions are introduced based on the direct solution of Reynolds' equation. Because of the large bearing clearances, particular attention has been paid to the definition of the degrees-of-freedom and their datum. Solutions are derived by combining a time step integration scheme, a Newton–Raphson method, and a normal contact algorithm in such a way that the contact conditions in the bearings and on the gear teeth are simultaneously dealt with. A series of comparisons with the experimental results obtained on a test rig are given which prove that the proposed model is sound. Finally, a number of results are presented which show that parameters often discarded in global models such as the location of the oil inlet area, the oil temperature in the bearings, the clearance/elastic couplings interactions, etc. can be influential on static and dynamic tooth loading.

Simulations of Gear-Rolling Element Bearing Interactions in Geared Transmissions

2003 ◽  
Author(s):  
F. Lahmar ◽  
P. Velex
Keyword(s):  
Equations Of Motion ◽  
Rolling Element Bearing ◽  
Integration Scheme ◽  
Time Step ◽  
Normal Contact ◽  
Contact Algorithm ◽  
Rolling Element ◽  
Non Linear ◽  
External Forces ◽  
Gear Rolling

The modular model of geared systems presented in this paper makes it possible to simultaneously account for the contact conditions in gears and rolling element bearings. Gears are modeled as two rigid cylinders connected by distributed mesh stiffnesses while ball and roller bearings contribute to the equations of motion as time-varying, non-linear external forces. Solutions are obtained by combining a Newmark time-step integration scheme, a Newton-Raphson method for ball bearing non-linearity and a normal contact algorithm that deals with the contact problem between the teeth. It is found that the static gear-bearing couplings are generally more important than the dynamic couplings with a significant influence of the gear on the bearing response. Finally, it is shown that, in certain conditions, bearings can generate non-linear parametric excitations of the same orders of magnitude as those associated with the meshing of helical gears.

Simulations of the dynamic response of planetary gears in the presence of localised tooth faults

2019 ◽  
Vol 233 (21-22) ◽  
pp. 7212-7223 ◽  
Author(s):  
Q Thoret-Bauchet ◽  
P Velex ◽  
M Guingand ◽  
P Casanova
Keyword(s):  
Planetary Gear ◽  
Contact Forces ◽  
Vibration Monitoring ◽  
Integration Scheme ◽  
Ring Gear ◽  
State Equations ◽  
Time Step ◽  
Normal Contact ◽  
Planetary Gears ◽  
Contact Algorithm

This paper is aimed at analysing the influence of local tooth faults such as pitting on the dynamic behaviour of planetary gears. A model of one-stage planetary gear combining lumped parameters and Timoshenko beam elements is presented, which accounts for deformable shafts and ring gears. Local tooth fault are simulated by material removal from tooth flanks, which can be positioned on the sun-gear, the planets and the ring-gear. The corresponding state equations are solved by combining a Newmark time-step integration scheme combined with a unilateral normal contact algorithm, which verifies that all contact forces on gear teeth are compressive and that no contact can occur outside the contact areas. A number of results are presented, which show the influence of tooth fault positions, depths and extents on displacement and acceleration signals. The contribution of a deformable ring-gear is analysed and the possibility to detect such localised tooth faults from vibration monitoring is discussed.

Vibration analysis of multiple degrees of freedom mechanical system with dry friction

2012 ◽  
Vol 227 (7) ◽  
pp. 1505-1514 ◽  
Author(s):  
SD Yu ◽  
BC Wen
Keyword(s):  
Mechanical System ◽  
Dry Friction ◽  
Degrees Of Freedom ◽  
Simple Procedure ◽  
Mathematical Problem ◽  
Equations Of Motion ◽  
Inequality Constraints ◽  
Integration Scheme ◽  
Time Step ◽  
Multiple Degrees Of Freedom

This article presents a simple procedure for predicting time-domain vibrational behaviors of a multiple degrees of freedom mechanical system with dry friction. The system equations of motion are discretized by means of the implicit Bozzak–Newmark integration scheme. At each time step, the discontinuous frictional force problem involving both the equality and inequality constraints is successfully reduced to a quadratic mathematical problem or the linear complementary problem with the introduction of non-negative and complementary variable pairs (supremum velocities and slack forces). The so-obtained complementary equations in the complementary pairs can be solved efficiently using the Lemke algorithm. Results for several single degree of freedom and multiple degrees of freedom problems with one-dimensional frictional constraints and the classical Coulomb frictional model are obtained using the proposed procedure and compared with those obtained using other approaches. The proposed procedure is found to be accurate, efficient, and robust in solving non-smooth vibration problems of multiple degrees of freedom systems with dry friction. The proposed procedure can also be applied to systems with two-dimensional frictional constraints and more sophisticated frictional models.

Analytical Model for Rockfall Protection Galleries - a Blind Prediction of Test Results and Conclusion

2011 ◽  
Vol 82 ◽  
pp. 722-727 ◽  
Author(s):  
Kristian Schellenberg ◽  
Norimitsu Kishi ◽  
Hisashi Kon-No
Keyword(s):  
Degrees Of Freedom ◽  
Large Scale ◽  
Test Results ◽  
Blind Prediction ◽  
Proposed Model ◽  
Input Parameters ◽  
Scale Test ◽  
Definition Of ◽  
Protective Structures ◽  
Cushion Layer

A system of multiple degrees of freedom composed out of three masses and three springs has been presented in 2008 for analyzing rockfall impacts on protective structures covered by a cushion layer. The model has then been used for a blind prediction of a large-scale test carried out in Sapporo, Japan, in November 2009. The test results showed substantial deviations from the blind predictions, which led to a deeper evaluation of the model input parameters showing a significant influence of the modeling properties for the cushion layer on the overall results. The cushion properties include also assumptions for the loading geometry and the definition of the parameters can be challenging. This paper introduces the test setup and the selected parameters in the proposed model for the blind prediction. After comparison with the test results, adjustments in the input parameters in order to match the test results have been evaluated. Conclusions for the application of the model as well as for further model improvements are drawn.

Optimization of Profile Modifications With Regard to Dynamic Tooth Loads in Single and Double-Helical Planetary Gears With Flexible Ring-Gears

2015 ◽  
Vol 138 (2) ◽  
Author(s):  
M. Chapron ◽  
P. Velex ◽  
J. Bruyère ◽  
S. Becquerelle
Keyword(s):  
Equations Of Motion ◽  
Integration Scheme ◽  
Time Varying ◽  
Time Step ◽  
Planetary Gears ◽  
Contact Algorithm ◽  
Beam Elements ◽  
Internal Gear ◽  
Gear Meshes ◽  
Optimum Profile

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.

Static and Dynamic Tooth Loading in Spur and Helical Geared Systems: Experiments and Code Validation

2000 ◽  
Author(s):  
Sébastien Baud ◽  
Philippe Velex
Keyword(s):  
Linear Time ◽  
Primary Objective ◽  
Integration Scheme ◽  
Spur Gears ◽  
Mesh Stiffness ◽  
Response Curves ◽  
Time Step ◽  
Contact Conditions ◽  
Rotor Systems ◽  
Contact Algorithm

Abstract The primary objective of this study is to validate a specific finite element code aimed at simulated dynamic tooth loading in geared rotor systems. Experiments have been conducted on a high-precision single stage spur and helical gear reducer with flexible shafts mounted on hydrostatic or hydrodynamic bearings. The numerical model is based on classical elements (shaft, lumped stiffnesses, ...) and on an original gear element which accounts for non-linear time-varying mesh stiffness, gear errors and tooth shape modifications. External and parametric excitations are derived from the instantaneous contact conditions between the mating flanks by using an iterative contact algorithm inserted in a time-step integration scheme. In a first step, experimental and numerical results at low speeds are compared and it is demonstrated that the proposed tooth mesh interface model is valid. Comparisons are then extended to dynamic fillet stresses on both spur and helical gears between 50–6000 rpm on pinion shaft. Despite a localized problem in the case of spur gears with one particular bearing arrangement, the broad agreement between the experimental and numerical response curves proves that the model is representative of the dynamic behavior of geared systems.

Optimization of Profile Modifications With Regard to Dynamic Tooth Loads in Planetary Gears With Flexible Ring-Gears

2015 ◽  
Author(s):  
Matthieu Chapron ◽  
Philippe Velex ◽  
Jérôme Bruyère ◽  
Samuel Becquerelle
Keyword(s):  
Equations Of Motion ◽  
Integration Scheme ◽  
Mesh Stiffness ◽  
Time Step ◽  
Planetary Gears ◽  
Contact Algorithm ◽  
Beam Elements ◽  
Internal Gear ◽  
Gear Meshes ◽  
Optimum Profile

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.

Static and Dynamic Tooth Loading in Spur and Helical Geared Systems-Experiments and Model Validation

2002 ◽  
Vol 124 (2) ◽  
pp. 334-346 ◽  
Author(s):  
S. Baud ◽  
P. Velex
Keyword(s):  
Linear Time ◽  
Primary Objective ◽  
Integration Scheme ◽  
Spur Gears ◽  
Mesh Stiffness ◽  
Response Curves ◽  
Time Step ◽  
Contact Conditions ◽  
Rotor Systems ◽  
Contact Algorithm

The primary objective of this study is to validate a specific finite element code aimed at simulating dynamic tooth loading in geared rotor systems. Experiments have been conducted on a high-precision single stage spur and helical gear reducer with flexible shafts mounted on hydrostatic or hydrodynamic bearings. The numerical model is based on classical elements (shaft, lumped stiffnesses, …) and on a gear element which accounts for non-linear time-varying mesh stiffness, gear errors and tooth shape modifications. External and parametric excitations are derived from the instantaneous contact conditions between the mating flanks by using an iterative contact algorithm inserted in a time-step integration scheme. First, experimental and numerical results at low speeds are compared and confirmed that the proposed tooth mesh interface model is valid. Comparisons were then extended to dynamic fillet stresses on both spur and helical gears between 50–6000 rpm on pinion shaft. Despite a localized problem in the case of spur gears with one particular bearing arrangement, the broad agreement between the experimental and numerical response curves demonstrated that the model is representative of the dynamic behavior of geared systems.

Modeling and Detection of Localized Tooth Defects in Geared Systems

1999 ◽  
Author(s):  
M. El Badaoui ◽  
V. Cahouet ◽  
F. Guillet ◽  
J. Daniere ◽  
P. Velex
Keyword(s):  
Numerical Simulations ◽  
Gear Tooth ◽  
Equations Of Motion ◽  
Vibration Monitoring ◽  
Detection Methods ◽  
Implicit Time ◽  
Integration Scheme ◽  
Time Step ◽  
Normal Contact ◽  
Detection Techniques

Abstract The early detection of failures in geared systems is an important industrial problem which has still to be addressed from both an experimental and theoretical viewpoint. The proposed paper combines some extensive numerical simulations of a single stage geared unit with localized tooth faults and the use of several detection techniques whose performances are compared and critically assessed. A model aimed at simulating the contributions of local tooth defects such as spalling to the gear dynamic behavior is set up. The pinion and the gear of a pair are modeled as to two rigid cylinders with all six degrees of freedom connected by a series of springs which represent gear body and gear tooth compliances on the base plane. Classical shaft finite elements including torsional, flexural and axial displacements can be superimposed on the gear element together with some lumped stiffnesses, masses, inertias, ... which account for the load machines, bearings and couplings. Tooth defects are modeled by a distribution of normal deviations over a zone which can be located anywhere on the active tooth flanks. Among the numerous available signal processing techniques used in vibration monitoring, cepstrum analysis is sensitive, reliable and it can be adapted to a complex geared system with several meshes. From an analytical analysis of the equations of motion, two complementary detection techniques based upon the acceleration power cesptrum are proposed. The equations of motion and the contact problem between mating flanks are simultaneously solved by coupling an implicit time-step integration scheme and a unilateral normal contact algorithm. The results of the numerical simulations are used as a data base for the proposed detection techniques. The combined influence of the defect location, depth and extent is analyzed for two examples of spur and helical gears with various profile modifications and the effectiveness of the two complementary detection methods is discussed before some conclusions are drawn.

Numerical Solution of Vehicle-Bridge Coupling Vibration

2013 ◽  
Vol 859 ◽  
pp. 76-79
Author(s):  
Ze Peng Wen
Keyword(s):  
Numerical Solution ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Reliability And Validity ◽  
Element Model ◽  
Interaction Force ◽  
Integration Scheme ◽  
Coupled Vibration ◽  
Time Step ◽  
Coupling Vibration

The bridge simplified two-dimensional plane beam element model, Simplified to two degrees of freedom quarter vehicle model, The entire bridge system is divided into two subsystems vehicle and bridge, Using separate equations of motion of vehicles and bridges, Proposed bridge systems numerical solution of coupled vibration analysis, The law at the wheel in contact with the deck displacement compatibility conditions for a balanced relationship with the interaction force associated, At each time step using the Newmark-β integration scheme, Through this paper the numerical solution results do comparison with the literature, the results show that the proposed method is reliability and validity.

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