scholarly journals Analysis of couple-stresses and piezo-viscous effects in a layered connecting-rod bearing

2018 ◽  
Vol 19 (6) ◽  
pp. 607
Author(s):  
Bouzid Laouadi ◽  
Mustapha Lahmar ◽  
Benyebka Bou-saïd ◽  
Hamid Boucherit ◽  
Ahcene Mouassa
Keyword(s):  
Dynamic Behavior ◽  
Reynolds Equation ◽  
Thickness Distribution ◽  
Continuum Theory ◽  
Algebraic Equations ◽  
Connecting Rod ◽  
Viscous Effects ◽  
Time Step ◽  
Compression Ignition Engine ◽  
Couple Stresses

In this work, the combined effects of couple-stresses and piezo-viscosity on the dynamic behavior of a compression ignition engine big-end connecting-rod bearing with elastic layer are investigated using the V. K. Stokes micro-continuum theory. It is assumed that the journal (crankpin) is rigid and the big-end bearing consists of a thin compressible elastic liner fixed in an infinitely stiff housing. The governing Reynolds' equation and the viscous dissipation term appearing on the RHS of energy equation are modified using the V. K. Stokes micro-continuum theory. The non-Newtonian effect is introduced by a new material constant η, which is responsible for couple-stress property, and the piezo-viscosity effect by the pressure–viscosity coefficient α appearing in the well-known Barus' law. In the proposed model, the nonlinear transient modified Reynolds equation is discretized by the finite difference method, and the resulting system of algebraic equations is solved by means of the subrelaxed successive substitutions method to obtain the fluid-film pressure field as well as the film thickness distribution. The crankpin center trajectories for a given load diagram are determined iteratively by solving the nonlinear equilibrium equations of the journal bearing system with the improved and damped Newton–Raphson method for each time step or crankshaft rotation angle. According to the obtained results, the effects of couple-stresses and piezo-viscosity on the nonlinear dynamic behavior of dynamically loaded bearings with either stiff or compliant liners are significant and cannot be overlooked.

Derivation of non-Newtonian squeeze-film Reynolds equation between convex surfaces and application to two different cylinders

2007 ◽  
Vol 221 (7) ◽  
pp. 813-821 ◽  
Author(s):  
J-R Lin
Keyword(s):  
Couple Stress ◽  
Reynolds Equation ◽  
Continuum Theory ◽  
Type Equation ◽  
Squeeze Film ◽  
Convex Surfaces ◽  
Couple Stresses ◽  
Load Carrying ◽  
Film Characteristics ◽  
Couple Stress Fluids

The derivation of non-Newtonian squeeze-film Reynolds-type equation between two convex surfaces and its application are of interest in the present study. Based upon the Stokes micro-continuum theory, the non-Newtonian squeeze-film Reynolds-type equation between two convex surfaces is derived to take into account the effects of couple stresses resulting from the lubricant blended with various additives. This non-Newtonian squeeze-film Reynolds-type equation is applicable to squeeze-film bearings lubricated with couple stress fluids when the general upper film shape and the lower film shape are specified. To guide the use of the equation, the squeeze-film mechanism between two different cylinders of infinite width with non-Newtonian couple stress fluids is illustrated. Comparing with the Newtonian-lubricant case, the presence of non-Newtonian couple stresses provides an increase in the load-carrying capacity, and therefore lengthens the approaching time. In addition, the effects of couple stresses on the squeeze film characteristics are more pronounced at lower squeeze-film height with larger couple stress parameters and larger radius ratios of cylinders. As the value of radius ratio approaches infinity, the present results agree closely with those of the previous studies by Hamrock [6] and by Lin et al. [19], respectively; it provides a support to the present study.

Comparison of Dynamic Behavior of Elastic Connecting-Rod Bearing in Both Petrol and Diesel Engines

1985 ◽  
Vol 107 (1) ◽  
pp. 87-91 ◽  
Author(s):  
Bernard Fantino ◽  
Jean Frene
Keyword(s):  
Diesel Engine ◽  
Film Thickness ◽  
Dynamic Behavior ◽  
Elastic Deformation ◽  
Flow Rate ◽  
Thickness Distribution ◽  
Connecting Rod ◽  
Significant Parameter ◽  
Minimum Film Thickness ◽  
Mechanical Factors

The method developed in an earlier work describing the dynamic behavior of an elastic connecting-rod bearing was used to compare the performance (minimum film thickness, torque and flow rate) of two different bearings which belong respectively to a petrol and a diesel engine. Results show that of all the mechanical factors considered (load, speed, viscosity . . . ), the most significant parameter is the load diagrams, which through the elastic deformation governs the film thickness distribution.

Bifurcation Analysis of Self-Acting Gas Journal Bearings

2001 ◽  
Vol 123 (4) ◽  
pp. 755-767 ◽  
Author(s):  
Cheng-Chi Wang ◽  
Cha’o-Ku`ang Chen
Keyword(s):  
Dynamic Behavior ◽  
Reynolds Equation ◽  
Rotational Velocity ◽  
Power Spectra ◽  
Journal Bearings ◽  
Operating Conditions ◽  
Finite Differences Method ◽  
Subharmonic Response ◽  
Rotor Center ◽  
Rotor Mass

This paper studies the bifurcation of a rigid rotor supported by a gas film bearing. A time-dependent mathematical model for gas journal bearings is presented. The finite differences method and the Successive Over Relation (S.O.R) method are employed to solve the Reynolds’ equation. The system state trajectory, Poincare´ maps, power spectra, and bifurcation diagrams are used to analyze the dynamic behavior of the rotor center in the horizontal and vertical directions under different operating conditions. The analysis shows how the existence of a complex dynamic behavior comprising periodic and subharmonic response of the rotor center. This paper shows how the dynamic behavior of this type of system varies with changes in rotor mass and rotational velocity. The results of this study contribute to a further understanding of the nonlinear dynamics of gas film rotor-bearing systems.

scholarly journals Studying Inertia Effects in Open Channel Flow Using Saint-Venant Equations

Water ◽  
2018 ◽  
Vol 10 (11) ◽  
pp. 1652
Author(s):  
Dong-Sin Shih ◽  
Gour-Tsyh Yeh
Keyword(s):  
Stokes Equations ◽  
Field Application ◽  
Benchmark Problems ◽  
Algebraic Equations ◽  
Step Size ◽  
Time Step ◽  
Cross Sectional ◽  
Inertia Effects ◽  
Time Step Size ◽  
Saint Venant Equations

One-dimensional (1D) Saint-Venant equations, which originated from the Navier–Stokes equations, are usually applied to express the transient stream flow. The governing equation is based on the mass continuity and momentum equivalence. Its momentum equation, partially comprising the inertia, pressure, gravity, and friction-induced momentum loss terms, can be expressed as kinematic wave (KIW), diffusion wave (DIW), and fully dynamic wave (DYW) flow. In this study, the method of characteristics (MOCs) is used for solving the diagonalized Saint-Venant equations. A computer model, CAMP1DF, including KIW, DIW, and DYW approximations, is developed. Benchmark problems from MacDonald et al. (1997) are examined to study the accuracy of the CAMP1DF model. The simulations revealed that CAMP1DF can simulate almost identical results that are valid for various fluvial conditions. The proposed scheme that not only allows a large time step size but also solves half of the simultaneous algebraic equations. Simulations of accuracy and efficiency are both improved. Based on the physical relevance, the simulations clearly showed that the DYW approximation has the best performance, whereas the KIW approximation results in the largest errors. Moreover, the field non-prismatic case of the Zhuoshui River in central Taiwan is studied. The simulations indicate that the DYW approach does not ensure achievement of a better simulation result than the other two approximations. The investigated cross-sectional geometries play an important role in stream routing. Because of the consideration of the acceleration terms, the simulated hydrograph of a DYW reveals more physical characteristics, particularly regarding the raising and recession of limbs. Note that the KIW does not require assignment of a downstream boundary condition, making it more convenient for field application.

A New Loss and Deviation Model for Axial Compressor Inlet Guide Vanes

2013 ◽  
Author(s):  
Milan Banjac ◽  
Milan V. Petrovic ◽  
Alexander Wiedermann
Keyword(s):  
Guide Vane ◽  
Thickness Distribution ◽  
Axial Compressor ◽  
Algebraic Model ◽  
Operating Conditions ◽  
Inlet Guide Vane ◽  
Viscous Effects ◽  
Through Flow ◽  
Trailing Vortices ◽  
Compressor Inlet

This paper describes a new universal algebraic model for the estimation of flow deflection and losses in axial compressor inlet guide vane devices. The model deals with nominal flow and far-off-design operating conditions in connection with large stagger angle adjustments. The first part of the model considers deflection and losses in 2D cascades, taking into account the main cascade geometry parameters and operating conditions, such as Mach number and stagger adjustment. The second part of the model deals with additional deviation and losses due to secondary flow caused by the endwall viscous effects and by the trailing vortices. The model is developed for NACA65 airfoils, NACA63-A4K6 airfoils and airfoils having an NACA65 thickness distribution on a circular-arc camber line. It is suitable for application in 1D or 2D through-flow calculations for design and analysis cases. The development of the method is based on systematic CFD flow calculations for various cascade geometries and operating parameters. The comparison of correlation results with experimental data for several test cases shows good agreement.

scholarly journals An Assessment of Quantitative Predictions of Deterministic Mixed Lubrication Solvers

2020 ◽  
Vol 143 (1) ◽  
Author(s):  
Yuechang Wang ◽  
Abdel Dorgham ◽  
Ying Liu ◽  
Chun Wang ◽  
Mark C. T. Wilson ◽  
...  
Keyword(s):  
Reynolds Equation ◽  
Thickness Distribution ◽  
Computation Time ◽  
Simulation Method ◽  
Coefficient Matrix ◽  
Mixed Lubrication ◽  
Contact Ratio ◽  
Lubricated Contacts ◽  
Discretization Schemes ◽  
Parametric Studies

Abstract The ability to simulate mixed lubrication problems has greatly improved, especially in concentrated lubricated contacts. A mixed lubrication simulation method was developed by utilizing the semi-system approach which has been proven to be highly useful for improving stability and robustness of mixed lubrication simulations. Then different variants of the model were developed by varying the discretization schemes used to treat the Couette flow terms in the Reynolds equation, varying the evaluation of density derivatives and varying the contribution of terms in the coefficient matrix. The resulting pressure distribution, film thickness distribution, lambda ratio, contact ratio, and the computation time were compared and found to be strongly influenced by the choice of solution scheme. This indicates that the output from mixed lubrication solvers can be readily used for qualitative and parametric studies, but care should be taken when making quantitative predictions.

The Methods to Study the Influence of the Clearance in the Case of Great Speeds and Small Speeds

2013 ◽  
Vol 837 ◽  
pp. 88-92
Author(s):  
Jan Cristian Grigore
Keyword(s):  
Dynamic Behavior ◽  
Reaction Force ◽  
Accurate Method ◽  
Angular Speed ◽  
Connecting Rod ◽  
Lagrange Equations ◽  
Joint Rotation ◽  
First Case ◽  
Multi Body ◽  
General Method

In kinematic couplings, clearances are inevitable for their operation. The size of these clearances but as a consequence of use, causes a malfunction of the mechanism to which it belongs. The law of motion of driveline changes, big clearances, non-technological system causes vibration, leading to discomfort, uncertainty, and thus reach its degradation. In the paper we shall make a few of geometric and mechanical type considerations about the clearances in the linkages, linkages planes with joint rotation links. Based on mathematical algorithm developed and applied crank mechanism, the model presented in [1], this paper scientifically developed mathematical model, proposing mathematical models to study the influence of the size of the clearance in general dynamic calculation mechanisms. Mechanism considered is crank connecting rod mechanism with clearance cinematic coupling between rod and crank rotation. The paper makes a study of the influence on the dynamic behavior of the crank rod mechanism at high speeds, but also general method algorithm is developed and accurate method to assess the dynamic behavior of multi-body mechanism. The first case is considered a constant angular speed motor and thus determine the elemental expressions that establish the mechanism position, velocity and acceleration expressions in the two directions heads elements. Finally we obtain the expression of the normal reaction force, as well as position expression that defines its angle. With reaction force can specify phase (contact, flight, impact) [1], the behavior of the journal. For the case of general method - the method multi-body - the exact method are established liaison relationships between the parameters , write matrices , inertia matrix. Use Lagrange equations, if non-holonomic constraints. Matrix differential equation of motion is written and it can be solved numerically using Runge-Kutta method of order four. Of the iterative method, we obtain the parameters used in calculating the reaction force expression that can be evaluated accurately in journal bearings behaviour. Any would be their source of appearance, they usually produce unwished effects during the mechanisms functioning.

A Modular Code for Real Time Dynamic Simulation of Gas Turbines in Simulink

2002 ◽  
Vol 128 (3) ◽  
pp. 506-517 ◽  
Author(s):  
S. M. Camporeale ◽  
B. Fortunato ◽  
M. Mastrovito
Keyword(s):  
Mathematical Model ◽  
Real Time ◽  
Gas Turbine ◽  
Dynamic Behavior ◽  
Gas Turbines ◽  
Simulation Software ◽  
Computational Time ◽  
High Fidelity ◽  
Time Step ◽  
The Mathematical Model

A high-fidelity real-time simulation code based on a lumped, nonlinear representation of gas turbine components is presented. The code is a general-purpose simulation software environment useful for setting up and testing control equipments. The mathematical model and the numerical procedure are specially developed in order to efficiently solve the set of algebraic and ordinary differential equations that describe the dynamic behavior of gas turbine engines. For high-fidelity purposes, the mathematical model takes into account the actual composition of the working gases and the variation of the specific heats with the temperature, including a stage-by-stage model of the air-cooled expansion. The paper presents the model and the adopted solver procedure. The code, developed in Matlab-Simulink using an object-oriented approach, is flexible and can be easily adapted to any kind of plant configuration. Simulation tests of the transients after load rejection have been carried out for a single-shaft heavy-duty gas turbine and a double-shaft aero-derivative industrial engine. Time plots of the main variables that describe the gas turbine dynamic behavior are shown and the results regarding the computational time per time step are discussed.

scholarly journals THE NUMERICAL TREATMENT OF NONLINEAR FRACTAL–FRACTIONAL 2D EMDEN–FOWLER EQUATION UTILIZING 2D CHELYSHKOV POLYNOMIALS

Fractals ◽  
2020 ◽  
Vol 28 (08) ◽  
pp. 2040042
Author(s):  
M. HOSSEININIA ◽  
M. H. HEYDARI ◽  
Z. AVAZZADEH
Keyword(s):  
Approximate Solution ◽  
Finite Difference ◽  
Test Problems ◽  
Operational Matrices ◽  
Algebraic Equations ◽  
Time Step ◽  
Discrete Method ◽  
Difference Formula ◽  
Fowler Equation ◽  
Chelyshkov Polynomials

This paper develops an effective semi-discrete method based on the 2D Chelyshkov polynomials (CPs) to provide an approximate solution of the fractal–fractional nonlinear Emden–Fowler equation. In this model, the fractal–fractional derivative in the concept of Atangana–Riemann–Liouville is considered. The proposed algorithm first discretizes the fractal–fractional differentiation by using the finite difference formula in the time direction. Then, it simplifies the original equation to the recurrent equations by expanding the unknown solution in terms of the 2D CPs and using the [Formula: see text]-weighted finite difference scheme. The differentiation operational matrices and the collocation method play an important role to obtaining a linear system of algebraic equations. Last, solving the obtained system provides an approximate solution in each time step. The validity of the formulated method is investigated through a sufficient number of test problems.

A Theoretical Series Solution for the Dynamics of Finite-Length Bearings and Squeeze-Film Dampers

2003 ◽  
Author(s):  
Jose´ Antunes ◽  
Miguel Moreira ◽  
Philippe Piteau
Keyword(s):  
Fourier Series ◽  
Galerkin Method ◽  
Finite Length ◽  
Reynolds Equation ◽  
Double Fourier Series ◽  
Squeeze Film ◽  
Algebraic Equations ◽  
Squeeze Film Dampers ◽  
Galerkin Solution ◽  
The Galerkin Method

In this paper we develop a non-linear dynamical solution for finite length bearings and squeeze-film dampers based on a Spectral-Galerkin method. In this approach the gap-averaged pressure is approximated, in the lubrication Reynolds equation, by a truncated double Fourier series. The Galerkin method, applied over the residuals so obtained, generate a set of simultaneous algebraic equations for the time-dependent coefficients of the double Fourier series for the pressure. In order to assert the validity of our 2D–Spectral-Galerkin solution we present some preliminary comparative numerical simulations, which display satisfactory results up to eccentricities of about 0.9 of the reduced fluid gap H/R. The so-called long and short-bearing dynamical solutions of the Reynolds equation, reformulated in Cartesian coordinates, are also presented and compared with the corresponding classic solutions found on literature.

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