Experimental and theoretical analyses of the contact-impact behavior of Babbitt ZChSnSb11-6

2017 ◽  
Vol 233 (7) ◽  
pp. 1267-1276 ◽  
Author(s):  
Yao Wang ◽  
Shujun Li ◽  
Dan Xiang ◽  
Wenjun Meng
Keyword(s):  
Contact Force ◽  
Numerical Solutions ◽  
Permanent Deformation ◽  
Absolute Error ◽  
Coefficient Of Restitution ◽  
Experimental Results ◽  
Impact Behavior ◽  
Impact Model ◽  
Oil Film ◽  
Contact Impact

Contact-impact between Babbitt and steel surfaces is an ubiquitous phenomenon during the operation of oil-film bearing. To study this phenomenon, a contact-impact method of Babbitt ZChSnSb11-6 was designed and the contact-impact test was performed. For the purpose of getting a more complete understanding of the contact-impact mechanical properties of Babbitt ZChSnSb11-6, the relationships of coefficient of restitution, permanent deformation, and drop height (i.e. the initial impact velocity) were analyzed; and, the constitutive behavior between the contact force and the contact deflection was studied. Then, based on the empirical formulation developed by Brake, an indentation contact-impact model during impact events was established, which theoretically explained the contact-impact behavior of Babbitt ZChSnSb11-6. Meanwhile, the experimental results were compared with the numerical solutions solved by using MATLAB. Results revealed the established model shows a good agreement with the experimental results. The mean absolute error of coefficient of restitution was less than 0.025, and the difference for the permanent deformation after impact was less than 1%. For the contact-impact tests with different size parameters, the length and the diameter of 20 steel rods were the two significant influencing factors on the permanent deformation and coefficient of restitution of Babbitt flat surface; and, the relationship of contact force and contact deflection appeared to display the similar trend. It was concluded that the established contact-impact model has the effectiveness and applicablility on describing its contact-impact behaviors, and which can provide theoretical and experimental supports for the prediction of contact deflection and contact force of the Babbitt ZChSnSb11-6 of oil-film bearing.

scholarly journals Analytical Study of Babbitt/steel Composite Structural Bars in Oblique Contact-impact with a Solid Flat Surface

2019 ◽  
Vol 10 (1) ◽  
pp. 213-228 ◽  
Author(s):  
Yao Wang ◽  
Zhuang Fu
Keyword(s):  
Angular Velocity ◽  
Contact Force ◽  
Flat Surface ◽  
Permanent Deformation ◽  
Coefficient Of Restitution ◽  
Contact Forces ◽  
Experimental Results ◽  
Impact Behavior ◽  
Contact Impact ◽  
Weak Material

Abstract. The oblique contact-impact characteristic of the composite structural bar composed of Babbitt alloy and low-carbon steel (ZChSbSb11-6 ∕ AISI 1020) with a solid flat surface (AISI 1045) was studied theoretically and experimentally. The dynamic equation of the composite structural bar with vibration response during the contact-impact was established using the momentum theorem and assumed mode method, and the instantaneous contact forces during different impact phases were analyzed based on modified Jackson–Green model. Four sets of experiments (i.e. different proportion of Babbitt, ξ={1/8,1/2,3/4,7/8}) for the initial angle, θ=45∘, and different initial velocities were performed; and, the rebound linear and angular velocity of the contact point of composite structural bar after impact was calculated and compared with experimental results. Besides, the coefficient of restitution, the relation of contact force and contact deflection, and the permanent deformation were also compared for the composite structural bars with different proportions in combination, ξ. Three critical angles are found to determine whether the composite bar slides or not, but are prominently different for the composite bars with different ξ. In comparing with the experimental results, the numerical solutions of rebound linear and angular velocity had yield encourage results and, all relative errors were small, indicating that the simulations are in good agreement with the experimental results. Also, the oblique contact-impact behavior involving the coefficient of restitution, the relation of contact force and contact deflection, and the permanent deformation was explained in detail. It can be concluded that as the proportion of Babbitt ξ increases, the composite structural bar presents a characteristic of ease of deflection. And the contact-impact behavior of structural entity is closely related to the inherent properties of the elasto-plastic material, especially for the weak material of composite structures. The more easily the impacting object is deformed, the small the contact force during the contact-impact, which also indicates the yield strength of weak material is a very significant parameter in the event of collision. Such work could give conducive insights to contact-impact problems of the key parts or structures composed of composite materials in mechanical system.

SIMULATION OF DYNAMIC EVENT OF IMPACT USING EXPLICIT 3D FEM MODEL AND VALIDATION BY EXPERIMENT AND CONTACT MODELS

2021 ◽  
Vol 6 (3) ◽  
Author(s):  
Akshay Mallikarjuna ◽  
Dan Marghitu ◽  
P.K. Raju
Keyword(s):  
Material Properties ◽  
Permanent Deformation ◽  
Oblique Impact ◽  
Coefficient Of Restitution ◽  
Impact Behavior ◽  
3D Fem ◽  
Dynamic Event ◽  
Contact Models ◽  
Explicit Dynamic ◽  
The Impact

— In this study, an optimized method to simulate the dynamic 3D event of the impact of a rod with a flat surface has been presented. Unlike the 2D FEM based contact models, in this study both the bodies undergoing the impact are considered elastic(deformable) and simulation is the dynamic event of the impact, instead of predefined 2D symmetric contact analysis. Prominent contact models and plasticity models to define material properties in ANSYS are reviewed. Experimentation results of normal and oblique impact of the rod for different rods provided the coefficient of restitution. Experimental results of permanent deformation on the base for different impact velocity is derived out of a prominent impact study. The simulation results are in co-relation with experiment and both indentation and flattening models on the coefficient of restitution (COR) and permanent deformation of the base and rod after the impact. Thus, the presented 3D Explicit Dynamic simulation of impact is validated to analyze the impact behavior of the 2 bodies without any predefined assumptions with respect to boundary conditions or material properties.

Analytical Study of the Oblique Impact of a Rod with a Flat Using an Elasto-Plastic Contact Model

2015 ◽  
Vol 801 ◽  
pp. 25-32
Author(s):  
Ozdes Cermik ◽  
Hamid Ghaednia ◽  
Dan B. Marghitu
Keyword(s):  
Impact Velocity ◽  
Contact Force ◽  
Analytical Study ◽  
Initial Conditions ◽  
Permanent Deformation ◽  
Oblique Impact ◽  
Coefficient Of Restitution ◽  
Contact Model ◽  
Impact Angles ◽  
The Impact

In the current study a flattening contact model, combined with a permanent deformation expression, has been analyzed for the oblique impact case. The model has been simulated for different initial conditions using MATLAB. The initial impact velocity used for the simulations ranges from 0.5 to 3 m/s. The results are compared theoretically for four different impact angles including 20, 45, 70, and 90 degrees. The contact force, the linear and the angular motion, the permanent deformation, and the coefficient of restitution have been analyzed. It is assumed that sliding occurs throughout the impact.

Predicting the Permanent Deformation After the Impact of a Rod With a Flat Surface

2014 ◽  
Vol 137 (1) ◽  
Author(s):  
Hamid Ghaednia ◽  
Dan B. Marghitu ◽  
Robert L. Jackson
Keyword(s):  
Flat Surface ◽  
Impact Force ◽  
Permanent Deformation ◽  
Element Model ◽  
Coefficient Of Restitution ◽  
Experimental Results ◽  
Normal Impact ◽  
Previous Contact ◽  
Contact Models ◽  
The Impact

In this study, a new expression for the permanent deformation after the impact of a rod with a flat surface is given. Both flat and the surface have been considered elastoplastic. The contact has been considered frictionless and has been divided into three phases, the elastic, the elastoplastic, and the unloading phase. For the normal impact force in the loading phase, we considered a nonlinear expression that satisfies the effect of deformation on both objects by using a finite element model. For the unloading phase, the contact force has been considered to follow the Hertz theory. The simulation and experimental results were conducted for different initial impact velocities of the rod. Permanent deformation after the impact and the motion of the rod has been measured accurately in the experiments. Based on the simulation and experimental results an expression for the permanent deformation has been developed. Finally, the model has been verified and compared with previous contact models in terms of the coefficient of restitution.

An improved compliant contact force model using a piecewise function for impact analysis in multibody dynamics

2020 ◽  
Vol 234 (2) ◽  
pp. 424-432
Author(s):  
Jie Yu ◽  
Jinkui Chu ◽  
Yang Li ◽  
Le Guan
Keyword(s):  
Contact Force ◽  
Impact Analysis ◽  
Numerical Solutions ◽  
Contact Process ◽  
Coefficient Of Restitution ◽  
Force Model ◽  
Actual Situation ◽  
Contact Force Model ◽  
Piecewise Function ◽  
Impact Problems

Contact-impact problems have attracted more and more attention in mechanical multibody systems. In the past period of time, a few compliant contact force models have been put forward. However, some compliant contact force models are only applicable to a specific range of coefficient of restitution impact problems. And, some compliant contact force models have large errors with the actual situation. In order to reduce the errors, an improved compliant contact force model is proposed in this paper, which is applicable to the whole range of coefficient of restitution impact problems. In this work, the permanent deformation is taken into account during the contact process. Meanwhile, the method of piecewise fitting is used to reduce the errors in numerical solutions. Therefore, the improved compliant contact force model uses a piecewise function for the whole range of coefficient of restitution. In order to illustrate the situation, six independent contact force models are numerically analyzed by using Matlab codes. The result shows that the improved compliant contact force model in this paper is applicable to both soft and hard impact and nearer to the actual situation.

scholarly journals A Pseudospectral Algorithm for Solving Multipantograph Delay Systems on a Semi-Infinite Interval Using Legendre Rational Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
E. H. Doha ◽  
D. Baleanu ◽  
A. H. Bhrawy ◽  
R. M. Hafez
Keyword(s):  
Numerical Solutions ◽  
Rational Functions ◽  
Absolute Error ◽  
Delay Systems ◽  
Infinite Interval ◽  
Algebraic Equations ◽  
Collocation Points ◽  
Nonlinear Algebraic Equations ◽  
Linear And Nonlinear ◽  
Pseudospectral Scheme

A new Legendre rational pseudospectral scheme is proposed and developed for solving numerically systems of linear and nonlinear multipantograph equations on a semi-infinite interval. A Legendre rational collocation method based on Legendre rational-Gauss quadrature points is utilized to reduce the solution of such systems to systems of linear and nonlinear algebraic equations. In addition, accurate approximations are achieved by selecting few Legendre rational-Gauss collocation points. The numerical results obtained by this method have been compared with various exact solutions in order to demonstrate the accuracy and efficiency of the proposed method. Indeed, for relatively limited nodes used, the absolute error in our numerical solutions is sufficiently small.

Modeling and Simulation of Clamp Band Dynamic Envelope in a LV/SC Separation System

2011 ◽  
Vol 141 ◽  
pp. 359-363 ◽  
Author(s):  
Jun Lan Li ◽  
Shao Ze Yan ◽  
Xue Feng Tan
Keyword(s):  
Friction Coefficient ◽  
Modeling And Simulation ◽  
Band System ◽  
Separation Process ◽  
Impact Behavior ◽  
Separation System ◽  
Lumped Mass ◽  
Lumped Mass Method ◽  
Simulation Results ◽  
Contact Impact

The clamp band system is a typical locked and separated device of the launch vehicle (LV) / the spacecraft (SC), and its release-separation process is one of the important factors that affect the LV/SC separation movement. A nonlinear spring-damper model was employed to describe the contact-impact behavior between the V-segment of the clamp band and the LV/SC interface, and lumped mass method was used to depict the clamp band. By using ADAMS, a dynamic model of the clamp band system was established. The simulation results show that the impulse of the explosive bolts and the stiffness of lateral-restraining springs have significant effects on the clamp band dynamic envelope. The shock of the satellite-vehicle separation is very vulnerable to the clamp band pretension and the friction coefficient between the V-segment and the LV/SC interface.

Numerical Simulation of Fractional Delay Differential Equations Using the Operational Matrix of Fractional Integration for Fractional-Order Taylor Basis

2021 ◽  
Vol 6 (1) ◽  
pp. 10
Author(s):  
İbrahim Avcı 
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Numerical Solutions ◽  
Fractional Integration ◽  
Operational Matrix ◽  
Absolute Error ◽  
Algebraic Equations ◽  
Fractional Delay ◽  
Delay Differential ◽  
Fractional Delay Differential Equations

In this paper, we consider numerical solutions for a general form of fractional delay differential equations (FDDEs) with fractional derivatives defined in the Caputo sense. A fractional integration operational matrix, created using a fractional Taylor basis, is applied to solve these FDDEs. The main characteristic of this approach is, by utilizing the operational matrix of fractional integration, to reduce the given differential equation to a set of algebraic equations with unknown coefficients. This equation system can be solved efficiently using a computer algorithm. A bound on the error for the best approximation and fractional integration are also given. Several examples are given to illustrate the validity and applicability of the technique. The efficiency of the presented method is revealed by comparing results with some existing solutions, the findings of some other approaches from the literature and by plotting absolute error figures.

scholarly journals RELIABLE ITERATIVE METHODS FOR SOLVING 1D, 2D AND 3D FISHER’S EQUATION

2021 ◽  
Vol 22 (1) ◽  
pp. 138-166
Author(s):  
Othman Mahdi Salih ◽  
Majeed AL-Jawary
Keyword(s):  
Iterative Methods ◽  
Numerical Solutions ◽  
Adomian Decomposition Method ◽  
Nonlinear Problems ◽  
Variational Iteration Method ◽  
Absolute Error ◽  
Fisher’S Equation ◽  
Adomian Decomposition ◽  
Fisher's Equation ◽  
2D And 3D

In the present paper, three reliable iterative methods are given and implemented to solve the 1D, 2D and 3D Fisher’s equation. Daftardar-Jafari method (DJM), Temimi-Ansari method (TAM) and Banach contraction method (BCM) are applied to get the exact and numerical solutions for Fisher's equations. The reliable iterative methods are characterized by many advantages, such as being free of derivatives, overcoming the difficulty arising when calculating the Adomian polynomial boundaries to deal with nonlinear terms in the Adomian decomposition method (ADM), does not request to calculate Lagrange multiplier as in the Variational iteration method (VIM) and there is no need to create a homotopy like in the Homotopy perturbation method (HPM), or any assumptions to deal with the nonlinear term. The obtained solutions are in recursive sequence forms which can be used to achieve the closed or approximate form of the solutions. Also, the fixed point theorem was presented to assess the convergence of the proposed methods. Several examples of 1D, 2D and 3D problems are solved either analytically or numerically, where the efficiency of the numerical solution has been verified by evaluating the absolute error and the maximum error remainder to show the accuracy and efficiency of the proposed methods. The results reveal that the proposed iterative methods are effective, reliable, time saver and applicable for solving the problems and can be proposed to solve other nonlinear problems. All the iterative process in this work implemented in MATHEMATICA®12. ABSTRAK: Kajian ini berkenaan tiga kaedah berulang boleh percaya diberikan dan dilaksanakan bagi menyelesaikan 1D, 2D dan 3D persamaan Fisher. Kaedah Daftardar-Jafari (DJM), kaedah Temimi-Ansari (TAM) dan kaedah pengecutan Banach (BCM) digunakan bagi mendapatkan penyelesaian numerik dan tepat bagi persamaan Fisher. Kaedah berulang boleh percaya di kategorikan dengan pelbagai faedah, seperti bebas daripada terbitan, mengatasi masalah-masalah yang timbul apabila sempadan polinomial bagi mengurus kata tak linear dalam kaedah penguraian Adomian (ADM), tidak memerlukan kiraan pekali Lagrange sebagai kaedah berulang Variasi (VIM) dan tidak perlu bagi membuat homotopi sebagaimana dalam kaedah gangguan Homotopi (HPM), atau mana-mana anggapan bagi mengurus kata tak linear. Penyelesaian yang didapati dalam bentuk urutan berulang di mana ianya boleh digunakan bagi mencapai penyelesaian tepat atau hampiran. Juga, teorem titik tetap dibentangkan bagi menaksir kaedah bentuk hampiran. Pelbagai contoh seperti masalah 1D, 2D dan 3D diselesaikan samada secara analitik atau numerik, di mana kecekapan penyelesaian numerik telah ditentu sahkan dengan menilai ralat mutlak dan baki ralat maksimum (MER) bagi menentukan ketepatan dan kecekapan kaedah yang dicadangkan. Dapatan kajian menunjukkan kaedah berulang yang dicadangkan adalah berkesan, boleh percaya, jimat masa dan boleh guna bagi menyelesaikan masalah dan boleh dicadangkan menyelesaikan masalah tak linear lain. Semua proses berulang dalam kerja ini menggunakan MATHEMATICA®12.

Theoretical and experimental studies of the oil film in lubricated point contact

1966 ◽  
Vol 291 (1427) ◽  
pp. 520-536 ◽  
Keyword(s):  
Surface Layer ◽  
Film Thickness ◽  
Strong Evidence ◽  
Experimental Studies ◽  
Point Contact ◽  
Elastohydrodynamic Lubrication ◽  
Experimental Results ◽  
Point Contacts ◽  
Previous Theory ◽  
Oil Film

A technique using Newton’s rings for mapping the oil film of lubricated point contacts is described. A theoretical value for the film thickness of such contacts in elastohydrodynamic lubrication is derived. The experimental results give the exit constriction predicted by previous theory but never shown in detail. The comparison of theoretical and experimental oil film thicknesses, which is satisfactorily accurate, gives strong evidence for a viscous surface layer some 1000Å thick. This film agrees with the known ‘lubricating power’ of the various oils tested.

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