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.

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.

Efficient Loads Analyses of Shuttle-Payloads Using Dynamic Models With Linear Or Nonlinear Interfaces

1990 ◽  
Vol 112 (3) ◽  
pp. 366-373 ◽  
Author(s):  
P. D. Spanos ◽  
T. T. Cao ◽  
D. A. R. Nelson ◽  
D. A. Hamilton
Keyword(s):  
Dynamic Model ◽  
Dry Friction ◽  
Degrees Of Freedom ◽  
Dynamic Models ◽  
Space Shuttle ◽  
Equations Of Motion ◽  
Combined System ◽  
Time Step ◽  
Upper Stage ◽  
Loads Analysis

A technique is presented for conducting efficient loads analyses of Shuttle-payloads systems with linear or nonlinear attachment interfaces. The technique relies on representing the Space Shuttle and the payloads with physical and modal coordinates. Further, by invoking a standard algorithm of numerical integration of equations of motion, the kinematics of the interface degrees of freedom at a given time are determined without calculating the modes of the combined system involving the Space Shuttle and the payload. If the Shuttle-payloads interface coupling induces a linear dynamic model for the loads analysis, the equations of motion of the Shuttle and the payload are integrated separately step-by-step in time. If the dynamic model is nonlinear, the equations of motion of the Shuttle and the payload are again integrated separately. However, in the latter case an iterative procedure is used within a time step to converge to reliable values of the nonlinear terms of the equations of motion. The usefulness of the proposed technique is demonstrated by conducting a loads analysis for the Shuttle abort landing event with the Inertia Upper Stage (IUS) booster carrying a Tracking and Data Relay Satellite (TDRS) in the payload bay. This combined system has at its interface dry friction and hydraulic nonlinear dampers. For the analysis of this system, the discontinuous signum function used traditionally in modeling dry friction is replaced by an expeditious continuous approximation. Because of its efficiency and versatility, the new technique deserves serious consideration for becoming a standard tool for linear or nonlinear analysis of combined systems, in general, and of Shuttle-payloads systems, in particular.

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.

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.

On the Efficiency of Some Recently Developed Integration Algorithms for Offshore Problems

1983 ◽  
Vol 105 (1) ◽  
pp. 73-77 ◽  
Author(s):  
T. K. Datta ◽  
A. M. Sood
Keyword(s):  
Degrees Of Freedom ◽  
Large Time ◽  
Equations Of Motion ◽  
Iterative Solution ◽  
Response Analysis ◽  
Time Step ◽  
Beam Elements ◽  
Integration Schemes ◽  
Large Time Step ◽  
Integration Algorithms

The efficiency of some recently developed integration schemes, namely, Hilber’s ∝-method, collocation schemes and large time step integration schemes developed by Argyris, is evaluated by applying them to the response analysis of an idealized offshore tower. The tower is fixed at the base, having an additional mass at the top. For the analysis the tower has been modeled as an assemblage of 2-D beam elements. The dynamic degrees of freedom at each node are taken as those corresponding to the rotational and sway degrees of freedom. Using the normal mode theory the equations of motion have been decoupled except for the generalized loading vector which appear nonlinearly coupled, thus requiring iterative solution at every time step. The results of the study show that the large time step integration schemes developed by Argyris are more efficient than other integration methods considered here.

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.

Matrix Quadratic Models

1996 ◽  
Vol 210 (1) ◽  
pp. 31-43 ◽  
Author(s):  
R Whalley ◽  
D Mitchell ◽  
H Bartlett
Keyword(s):  
Mechanical System ◽  
Degrees Of Freedom ◽  
General Procedure ◽  
Dynamical Response ◽  
Multiple Degrees Of Freedom ◽  
System Models ◽  
Quadratic Models

Process mechanical system models are considered and the techniques for analysis are discussed. A method for the investigation of system models which possess multiple degrees of freedom is outlined. To illustrate this general procedure the dynamical response of a pulp blender-beater, with dual impellers and five degrees of freedom, for paper and board manufacturing is computed.

Hamiltonian formulation for mechanical systems with nonholonomic constraints

2014 ◽  
Vol 11 (03) ◽  
pp. 1450017
Author(s):  
G. F. Torres del Castillo ◽  
O. Sosa-Rodríguez
Keyword(s):  
Finite Number ◽  
Mechanical System ◽  
Infinite Number ◽  
Degrees Of Freedom ◽  
Hamiltonian Structure ◽  
Equations Of Motion ◽  
Hamiltonian Formulation ◽  
Mechanical Systems ◽  
Nonholonomic Constraints ◽  
Hamilton Equations

It is shown that for a mechanical system with a finite number of degrees of freedom, subject to nonholonomic constraints, there exists an infinite number of Hamiltonians and symplectic structures such that the equations of motion can be written as the Hamilton equations, with the original constraints incorporated in the Hamiltonian structure.

An Efficient Algorithm for Nonlinear Analysis of Vehicle/Track Interaction Problems

2016 ◽  
Vol 16 (08) ◽  
pp. 1550040 ◽  
Author(s):  
J. Sadeghi ◽  
A. Khajehdezfuly ◽  
M. Esmaeili ◽  
D. Poorveis
Keyword(s):  
Time Domain ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Computational Cost ◽  
Dynamic Interaction ◽  
Integration Scheme ◽  
Equilibrium Equations ◽  
Track System ◽  
Newton Raphson ◽  
Interaction Problem

In this paper, a new algorithm for solving the vehicle/track dynamic interaction problem is developed, aimed at reducing the computational cost. The algorithm called Advanced Solver Algorithm (ASA) uses the full Newton–Raphson incremental-iterative method in conjunction with the Newmark integration scheme to solve the equilibrium equations of the coupled vehicle/track system in time domain. Considering the track as a beam resting on a viscoelastic foundation and each vehicle as a wagon with ten degrees of freedom, the governing differential equations of motion of the vehicle/track system were derived. The wheel/rail contact was considered as a nonlinear Hertz spring and consequently the vehicle/track nonlinear dynamic interaction problem was solved. A comparison between the results of the ASA and those of the most advanced algorithm available was made to evaluate the efficiency of the ASA. It is confirmed that using the ASA can result in 40–70 % of reduction in computational cost.

scholarly journals An algorithm for deriving equations of motion of constrained mechanical system

1999 ◽  
Vol 21 (1) ◽  
pp. 36-44 ◽  
Author(s):  
Dinh Van Phong
Keyword(s):  
Differential Equation ◽  
Mechanical System ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Computer Processing

The article deals with the form of equations of motion of mechanical system with constraints. For holozoic systems the number of differential equation is equal to the degrees of freedom, without regard to the number of chosen coordinates. The possibilities of computer processing (symbolical and numerical) are shown. Two simple examples demonstrate the described technique.

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