Contact Finite Element Method Research Articles

Implementation of Fictitious Crack Model Using Contact Finite Element Method for the Crack Propagation in Concrete under Cyclic Load

The mixed freedom finite element method proposed for contact problems was extended to simulate the fracture mechanics of concrete using the fictitious crack model. Pairs of contact points were set along the potential developing path of the crack. The displacement of structure was chosen as the basic variable, and the nodal contact force in contact region under local coordinate system was selected as the iteration variable to confine the nonlinear iteration process in the potential contact surface which is more numerically efficient. The contact forces and the opening of the crack were obtained explicitly enabling the softening constitutive relation for the concrete to be introduced conveniently by the fictitious crack model. According to the states of the load and the crack, the constitutive relation of concrete under cyclic load is characterized by six contact states with each contact state denoting its own displacement-stress relation. In this paper, the basic idea of the mixed freedom finite element method as well as the constitutive relation of concrete under cyclic load is presented. A numerical method was proposed to simulate crack propagation process in concrete. The accuracy and capability of the proposed method were verified by a numerical example against experiment data.

Numerical Modeling of Soil-Pile Interface Behaviors of a Pipe Group Foundation under Complicated Load

A three-dimensional nonlinear contact finite element method was employed in this paper to simulate the soil-pile interface behaviors of a pile group under complicated load in the Jiyang dike. The displacement at the soil-pile interfaces was particularly calculated. The computational results show that interaction mainly occurred in the bottom of the cap, and interaction development was restrained with the help of friction effect between pipes and surrounding soil. Moreover, the most unfavorable load combination is vertical uplift force together with horizontal force. As a result, potential channels of seepage flow could be formed at the location where cracks develop. Seepage field would be changed and the probability for seepage failure is increasing.

Strength Calculation Analysis of Diesel Engine Linkage Based on Contact Finite Element Method and Experimental Study

Adopting the contact finite element method, with complex connecting rod group assembled body model of computation, the fatigue strength of the connecting rod of a certain type of diesel engine was verified. A transient stress analysis was conducted on the connecting rod. Compared with the connecting rod static stretching and compression test, the contact finite element method, which was used to analyze the strength of the connecting rod subassembly, was feasible. Based on the contact finite element method, the connecting rod transient stress analysis results showed that the maximum stress of the connecting rod did not occur under the highest pressure of the cylinder, and the dynamic stress value was greater than the static stress value.

Study on surface topography of 446M stainless steel as a bipolar plate on interfacial contact resistance of polymer electrolyte membrane fuel cell

The effect of the surface topography of 446M ferritic stainless steel as a bipolar plate for polymer electrolyte membrane fuel cell (PEMFC) is evaluated by interfacial contact resistance (ICR) measurement and finite element method (FEM) simulation. When the surface of stainless steel is in contact with the carbon paper under load, the surface roughness of stainless steel can affect the degree of deformation of the carbon fiber. Moreover, the higher deformation of carbon fiber under load in the rougher stainless steel could lead to larger real contact area between stainless steel and carbon fiber, and consequently the rough one has a lower ICR value than the fine one. The results suggest that the topography of stainless steel as a bipolar plate significantly affects the ICR. Furthermore, it was found that topography of bipolar plate is one of the key factors to decrease ICR.

Contact finite element method for dynamic meshing characteristics analysis of continuous engaged gear drives

The dynamic meshing characteristics of gear drives have been a major concern in the design of power transmission systems as they affect vibration, acoustic noise, durability and efficiency. Gaining a more comprehensive understanding of the dynamic meshing characteristics of continuous engaged gear drives is a key to the development of power transmission systems. In this paper, a dynamic contact finite element analysis method, considering the variation of the engaged teeth pairs, the loaded elastic and contact deformations, and the sliding friction, is presented for the dynamic meshing characteristics analysis of continuous and elastic engaged gear drives. Various kinds of continuous engaged gear models under low and high speed condition are simulated and compared using the presented method. The tooth profile modification was designed based on the simulation results. Moreover, the effects of the tooth profile modification, the sliding friction and the time-varying meshing stiffness upon the dynamic meshing characteristics of continuous engaged gear drives are discussed in detail. The results show that the method is not only effective in designing and evaluating the tooth profile modification, but also in studying the dynamic meshing characteristics of continuous engaged gear drives with realistic time-varying meshing stiffness and tooth sliding friction. The present method could provide an effective tool for vibration mechanism study and dynamic design of the continuous engaged gear drives considering more influence factors.

Multi-tooth contact behavior of helical gear applying modified meshing equation

In tooth contact analysis, the numerical process of searching for true contact lines or points is always a daunting task. The true contact lines for ideal helical gear transmission can be easily obtained through the helical gear meshing theory; however, in practice, this approach does not work well due to effect of tooth elasticity that shifts the contact lines from their ideal position. To address this problem, an approximate method to seek the true contact positions is proposed applying a modified meshing equation for a pair of helical gear with error free and no shaft deformation. First, the helical gear tooth deformation is calculated with the combination of contact mechanics and finite element method. Second, the deformed tooth flanks are fitted with Chebyshev polynomials. Third, the modified meshing equation is formulated by accounting for the influence of not only gear rigid body movement but also the gear deformation on the meshing process. Finally, the true contact points are determined by solving the correlated tooth flank equations, meshing equations, and force balance equations. The deformations of the gear and pinion teeth within the meshing plane are analyzed, and the contact load distributions along with the Von Mises stresses over a mesh cycle are examined. The study indicates that the proposed numerical method can yield true contact lines quickly while avoiding costly computational time in the traditional true contact line searching process that searches iteratively in the whole meshed tooth flank.

基于接触有限元方法的镜面面形仿真技术研究

To check if the mirror's surface satisfies the design requirement under the exterior loads,and to research the surface change rule under the bolt pretightening force and gravity in different direction,the mirror is analyzed using contact nonlinear finite element method.The surface displacement of mirror is processed using data processing algorithm based on Zernike polynomials in order to eliminate the rigid displacement.The surface parameter after eliminating the rigid displacement and distributed curve of the rigid displacement factor are gained.The result demonstrates the obvious rigid displacement appeared under the exterior loads and the piston term occupies the most aspect of the whole rigid displacement compared to the tilt term.The rigid displacement can be eliminated effectively using the surface processing algorithm based on integrated simulation method.The surface has the slight difference under the gravity in different direction.Compared to the bolt pretigtening force,the gravity has a small influence to the mirror surface.The mirror surface simulation under the bolt pretigtening force makes sense for designing and assembling the mirror and also shows engineering applicability of the surface simulation based on contact method.

Strength Calculation Analysis of Diesel Engine Linkage Based on Three-Dimensional Contact Finite Element Method

Adopting a three-dimensional contact finite element method, with complex connecting rod group assembled body model of computation, the fatigue strength of the connecting rod of a certain type of diesel engine was verified. A transient stress analysis was conducted on the connecting rod. Compared with the connecting rod static stretching and compression test, the three-dimensional contact finite element method, which was used to analyze the strength of the connecting rod subassembly, was feasible. Based on the three-dimensional contact finite element method, the connecting rod transient stress analysis results showed that the maximum stress of the connecting rod did not occur under the highest pressure of the cylinder, and the dynamic stress value was less than the static stress value.

Three-Dimensional Finite Element Simulation of Nonlinear Dynamic Rotor Systems of a Turbocharger

This paper presents the modeling procedure for a high-velocity rotor system (RS) combined with sliding bearings. The equations for motion of the RS parts were derived based on the model of a rotating elastic medium. Lubrication layers have been calculated with the use of the Reynolds equations. The discretization of the RS model has been carried out using three-dimensional contact finite element method and two-dimensional method of finite differences. The integration with respect to time is performed by an absolutely stable step-by-step method. The paper also compares and discusses computed and experimental amplitude-frequency characteristics of the self-oscillating turbocharger’s RS. The values of dynamic loads in parts, as well as reactions, clearances, and losses in bearings, computed based on the presented modeling procedure make the RS designing more accurate and reliable.

Non-linear dimensional variation analysis for sheet metal assemblies by contact modeling

The dimensional quality of product assembly is one of the most concerned issues in modern product design and manufacturing. During the assembly process, contact between rigid or non-rigid parts and/or fixtures is inevitable. The contact phenomenon of non-rigid parts, however, received little attention as compared with that of the rigid parts. We present in this paper the study of the contact problem of the non-rigid sheet metal assemblies. A systematic procedure of the non-linear dimensional variation analysis for the sheet metal assemblies is developed by using the contact finite element method and considering the friction force between the assembly surfaces. The proposed approach is validated in a case study of two sheet metal parts assembly via physical experiments. The simulation results agree well with the results obtained from physical experiments. This work provides a systematical and high-precision approach for dimensional variation analysis for non-rigid assemblies by contact modeling.

Modified pitch cone method in the hypoid gear design and tooth-cutting experiment

In order to improve the strength and endurance of hypoid gear,and extend the lifetime of hypoid gear,the modi- fied pitch cone method is firstly introduced.On the condition of the invariant mean working tooth depth,invariant outer diame- ter of gear and the gear addendum coefficient f_a≤0,the new pitch cone parameters are derived.The new pitch cone is coin- cident to face cone or out of the gear solid.The meshing be- havior,the tooth surface contact stress,the maximum tensile bending stress and the maximum compressive bending stress are researched by using tooth contact analysis (TCA),loaded tooth contact analysis (LTCA) and finite element method (FEM).The computer simulation results show that the tooth surface contact stress,the maximum tensile bending stress and the maximum compressive bending stress of the pinion to hy- poid gear pair designed by new method are markedly reduced. The results of the experiment show that the new type hypoid gear can be processed by the general cutter,and doesn't need other special tools.

The modified pitch cone design of the hypoid gear: Manufacture, stress analysis and experimental tests

Abstract In order to improve the strength and endurance of hypoid gear, and extend the lifetime of hypoid gear, the modified pitch cone method is firstly introduced. On the condition of the invariant mean working tooth depth, invariant outer diameter of gear and the gear addendum coefficient f a ⩽ 0, the new pitch cone parameters are derived. The new pitch cone is coincident to face cone or out of the gear solid. The meshing behavior, tooth surface contact stress, maximum tensile bending stress and maximum compressive bending stress are researched by using tooth contact analysis, loaded tooth contact analysis and finite element method. The computer simulation results show that the tooth surface contact stress, the maximum tensile bending stress and the maximum compressive bending stress of the pinion to hypoid gear pair designed by new method are markedly reduced. From the experiment, the new type hypoid gear pair can be processed by the general cutter, and the other special tool is unnecessary. In this paper, the approach of derivation for the pinion rough-machining machine tool settings designed by the modified pitch cone method is presented, and has been verified in the gear research center of Dong Feng Vehicle-bridge Co., Ltd.

Deformation overlap in the design of spur and helical gear pair

The elastic deflection of gear teeth is analyzed to investigate the deformation overlap. The deformation overlap, which is a numerically calculated quantity through displacement analysis at the initial contact, is defined as the piled region of a contact tooth pair due to the elastic deformation. The deformation overlap is suggested for an effective indicator to represent the whole deformation of a meshing gear pair. The elastic contact theory and finite element method are used to compute the contact force and teeth deflection. The contact problem is defined as a QP problem, and the contact forces between teeth are calculated from the transmitted torque. Then the deformation overlap is calculated with the contact forces as boundary conditions. For a spur gear pair, the calculated deformation overlap is used for the basis of the tooth tip relief, analysis of deformation characteristics for a profile shifted gear pair, and the selection of profile shift coefficient considering teeth deflection. Deformation overlap is extended to a three-dimensional problem, and implemented to a helical gear pair.

Finite element simulation of the dynamical behavior of a speed-increase gearbox

The simulation of dynamical behavior of a speed-increase gearbox was carried out using a finite element method. The profile error curves were determined by the gear precision and the time-variable stiffness curves of the meshing gears were acquired using a 3D contact finite element method. After the stiffness excitation and error excitation were determined and the dynamic model of the speed-increase gearbox was established, the normal frequencies of the whole gearbox and the vibration responses of the gearbox and transmission shafts were analysed.

Reliability analysis of flip chip packages using contact finite element method

The demand for electronic packages with lower profiles, lighter weights, and higher I/O densities are leading to a rapid expansion of the electronics industry, especially in portable electronic products. As a result, flip chip technology has become very popular in the electronic packaging industry. To enhance the long‐term reliability of flip chip technology, the space between the chip and substrate must be filled. This underfill improves reliability, which is influenced by coefficient of thermal expansion (CTE) mismatch between the chip and the substrate. However, it is difficult to fill the underfill space perfectly between the chip and the substrate because of the presence of impurities, voids and other defects in solder joining and underfilling during manufacturing. In addition, it is nearly impossible to achieve a perfect contact between the solder joints and the underfill. The purpose of this research is to investigate the impact of imperfect contact behavior and contact performance involving the solder joints and underfill on flip chip solder interconnects. Because of the above reliability issues, this study adopted the contact theory of the finite element and element death/birth methods to analyze the physical behavior of packaging structures under thermal cycling conditions. Simulation results indicated that the fatigue life of the flip chip packages would decrease due to two phenomena: One is imperfect bonding between solder ball and underfill, and the other is void size exceeding 334 μm2. Subsequently, this study effectively utilized a novel finite element method to simulate the real manufacturing processes of flip chip packaging.

Deformation overlap in the design of spur and helical gear pair

The elastic deflection of gear teeth is analyzed to investigate the deformation overlap. The deformation overlap, which is a numerically calculated quantity through displacement analysis at the initial contact, is defined as the piled region of a contact tooth pair due to the elastic deformation. The deformation overlap is suggested for an effective indicator to represent the whole deformation of a meshing gear pair. The elastic contact theory and finite element method are used to compute the contact force and teeth deflection. The contact problem is defined as a QP problem, and the contact forces between teeth are calculated from the transmitted torque. Then the deformation overlap is calculated with the contact forces as boundary conditions. For a spur gear pair, the calculated deformation overlap is used for the basis of the tooth tip relief, analysis of deformation characteristics for a profile shifted gear pair, and the selection of profile shift coefficient considering teeth deflection. Deformation overlap is extended to a three-dimensional problem, and implemented to a helical gear pair.

축대칭 변형체의 마찰 접촉문제에 관한 유한요소 해석

This paper is concerned with the numerical analysis of frictional contact problems in axisymmetric bodies using the rigid-plastic finite element method. A contact finite element method, based on a penalty function, are derived from variational formulations. The contact boundary condition between two deformable bodies is prescribed by the proposed algorithm. The program which can handle frictional contact problem is developed by using pre-existing rigid-plastic finite element code. Some examples used in this paper illustrate the effectiveness of the proposed formulations and algorithms. Efforts focus on the deformation patterns, contact force, and velocity gradient through the various simulations.

Computer simulation and stress analysis of helical gears with pinion circular arc teeth and gear involute teeth

The tooth contact analysis (TCA) technique and finite element method (FEM) have been applied to gear contact analysis and stress analysis. A mathematical model for helical gears with pinion circular arc teeth and gear involute teeth is assumed to be given by Litvin and Tsay. The geometry of the gears are described by the parameters of manufacturing. Simulation of the conditions of gear meshing, including the axes misalignment and center distance variation are performed. The locations of bearing contact and contact pattern of mating tooth surfaces are determined by the TCA. Results of the TCA provide the location and direction of applied loadings for the computer-aided FEM stress analysis. By applying the given mathematical model and the TCA techniques, a computer-aided stress analysis model for a new pair of gearing has been proposed. An automatic meshes generation (AMG) program has been developed for the FEM stress analysis. A three-dimensional stress analysis for this type of gearing has also been investigated and expressed by Von Mises stress contour distributions.

A Zooming Method for Dynamic Contact Stress Analysis by Finite Element Method

A dynamic zooming analysis method (ZAM) is presented, to calculate efficiently dynamic contact stresses and their distributions by the finite element method (FEM). The zooming region is determined by the same method as the static ZAM. However, displacements and velocities of nodal points in the region are iteratively computed by use of boundary values until their values approach the correct ones at a specific discrete time. this method is used to evaluate correctly the approximated initial values of the equation of motion. To verify this dynamic ZAM, we analyze the dynamic contact stresses of contact-impact problems under a condition starting from very roughly approximated initial values. The results calculated by this ZAM agree with those directly obtained by the elastodynamic contact FEM. The dynamic ZAM is efficient to analyze the dynamic contact problems and the dynamic stress concentrations by a small machine memory. Then, this method can be applied to the elastodynamic contact analysis of structures consisting of complicated configurations such as mating gears.