Investigation of contact stresses of a rotating cam by a digital photoelastic method

The maximum contact shear stresses (MCSS) and their locations of a rotating cam during rise and at a specific rotation speed were sought by a self-developed digital phototelastic system with added functions of syncronous trigger and continuous image taking. Also found were the MCSS of a camduring rise under static state. The difference between the dynamic and static states were compared and investigated.     

Use of weight functions and photoelastic experimental hybrid method to study the contact problem

The contact problem involving flat punches has been the subject of many investigations mainly due to the crucial role it plays in many engineering applications. The contact problem has however, been widely approached from a theoretical point of view and there is a lack of experimental verifications due to the limited number of laboratory techniques capable of supplying detailed information about contact parameters. In order to gain an understanding of such problems, this study uses an experimental approach to investigate the stresses arising from photoelastic models when compressed against each other using Riemann‐Hilbert's weight functions and photoelastic experimental hybrid method. The study shows that this approach is effective in determining the magnitudes of contact stresses as well as interior stresses which up to date have been scarcely investigated. It is further shown that high stresses exist when a photoelastic model with a sharp corner is pressed against straight surface of the bottom half space and by introducing fillet radii at the sharp corners, significant stress reductions of up to 62.66% is observed.     

A rapid method for stress separation in two dimensional photoelastic models

Obtaining the individual stress components at internal points in a two dimensional photoelastic model is time consuming and requires considerable expertise. A rapid method has been developed for calculating the stress distribution along an axis of symmetry. An example is given to show that the results are sufficiently accurate for engineerng design purposes.     

Photoelastic stress analysis of reinforced polycarbonate orthodontic brackets

A photoelastic investigation of the stresses in polycarbonate orthodontic brackets reinforced with stainless steel inserts is reported. Three inserts with different profiles are investigated. They are ranked with respect to the stresses generated at the interfaces of the metallic inserts and the polycarbonate material. Comparison of insert designs is quantified.     

Simulations of a stress and contact model in a chemical mechanical polishing process

A two-dimensional axisymmetric quasi-static contact finite element model for the chemical mechanical polishing process (CMP) was established. The von Mises stress on the wafer surface was investigated. The findings indicate that the profile of the von Mises stress correlated with that of the removal rate. The larger the elastic modulus of the pad or the smaller the elastic modulus of the carrier film, the larger is the maximum von Mises stress. The thicker the pad or the thinner the film, the smaller is the maximum von Mises stress. The larger the load exerted on the carrier, the greater is the maximum von Mises stress.     

A review of joint and muscle load simulation relevant to in-vitro stress analysis of the hip

Model analysis of the hip has become an important research technique in the assessment of implant performance in Total Hip Replacements (T.H.R.). In the literature to date, however, there is an absence of suitable criteria to aid in the selection of representative joint and muscle loading conditions relevant to such analyses. Consequently, the interpretation of information regarding the loading of the hip joint varies greatly between studies. The objective of this study, therefore, is to review the procedures used to establish these forces and to outline how they may be appliedto in-vitro modeltesting of the proximal femur and the pelvis. The muscles active at the hip joint are categorised with respect to their positions and primary actions. The magnitudes of the muscle and joint loads, as estimated by force determination studies employing in-vitro, in-vivo and mathematical modelling techniques, are reviewed. Applications illustrating the load simulations applied to the model analysis of an implanted Exeter femoral prosthesis and the in-vitro testing of cementless acetabular cups are also presented. While there is reliable information regarding the joint reaction between the femur and the acetabulum, it is difficult to represent accurately the muscular loading, due to the conflicting information presented in the literature. It is possible, however, to apply this information to load simulations in a limited manner in an attempt to predict trends in behaviour which are representative of the in-vivo situation.     

Photoelastic analysis of stress waves in building subjected to vertical impact under laboratory earthquake experiments

In an earthquake occurring directly under a city, the vertical impact induced from the source may cause a large amount of damage to a column and beam of the building. Model-based simulations are carried out with photoelastic material in order to examine the effect of a vertical impact on the building in the case of a near-field type earthquake. The dynamic photoelastic method combined with strain gages is utilized to conduct direct full field and real time observations of stress waves in a building due to vertical impact in laboratory earthquake experiments. The conditions under which vertical impact loading is applied to the model building in a controlled laboratory environment are derived from the data recorded for the 1995 Hanshin-Awaji earthquake in Japan. The experimental apparatus with which an impact of a longitudinal stress pulse is able to be applied to a model of a real building is shown. It is estimated from our earthquake simulations that large dynamic stress concentrations are produced in the beam–column joints of the building by the vertical impact arising from a seismic source located directly below a surface.     

Least squares asymptotic analysis of photoelastic data from stress concentration regions in plane problems

A complete separation of stresses throughout the entire stress concentration region near notches in plane, isotropic, linearly elastic plates is achieved using only conventional, easily obtained photoelastic (difference and directions of principal stresses) data. These data are analysed by a special least squares technique based on previously derived equations which describe the asymptotic character of the rapidly varying stress field near the root of the notch. The paper demonstrates the ability of the technique to predict stress concentrations as well as individual stresses accurately using only a small amount of data of typical experimental accuracy from arbitrary data points within the stress concentration zone.     

A single parameter to evaluate stress state in rail head for rolling contact fatigue analysis

Based on the Smith‐Watson‐Topper (SWT) method, a phenomenological approach for multiaxial fatigue analysis, the maximum SWT parameter is proposed as a single parameter to evaluate the stress state in the rail head for assessing the fatigue integrity of the structure. A numerical procedure to calculate the maximum SWT parameter from a finite element analysis is presented and applied in a case study, where the stress and strain fields due to wheel/rail rolling contact are obtained from a three‐dimensional finite element simulation with the steady‐state transport analysis technique. The capability of the SWT method to predict fatigue crack initiation in the rail head is confirmed in the case study. Analogous to von Mises stress for strength analysis, the maximum SWT parameter can be applied to evaluate the fatigue loading state not only in rail head due to rolling contact fatigue but also in a generic structure subjected to a cyclic loading.     

A contact analysis approach based on linear complementarity formulation using smoothed finite element methods

Based on the subdomain parametric variational principle (SPVP), a contact analysis approach is formulated in the incremental form for 2D solid mechanics problems discretized using only triangular elements. The present approach is implemented for the newly developed node-based smoothed finite element method (NS-FEM), the edge-based smoothed finite element method (ES-FEM) as well as standard FEM models. In the approach, the contact interface equations are discretized by contact point-pairs using a modified Coulomb frictional contact model. For strictly imposing the contact constraints, the global discretized system equations are transformed into a standard linear complementarity problem (LCP), which can be readily solved using the Lemke method. This approach can simulate different contact behaviors including bonding/debonding, contacting/departing, and sticking/slipping. An intensive numerical study is conducted to investigate the effects of various parameters and validate the proposed method. The numerical results have demonstrated the validity and efficiency of the present contact analysis approach as well as the good performance of the ES-FEM method, which provides solutions of about 10 times better accuracy and higher convergence rate than the FEM and NS-FEM methods. The results also indicate that the NS-FEM provides upper-bound solutions in energy norm, relative to the fact that FEM provides lower-bound solutions.     

On contact zone models for an electrically impermeable interface crack in a piezoelectric bimaterial

An electrically impermeable interface crack between two semi-infinite piezoelectric planes under remote mechanical tension-shear and electrical loading is studied. Assuming the stresses, strains and displacements are independent on the coordinate x ₂ the expressions for the elastic displacement and potential jumps as well as for the stresses and electrical displacement along the interface via a sectionally holomorphic vector function are found. Introducing an artificial contact zone at the right crack tip and assuming the materials possess the symmetry class 6 mm the problem is reduced for a wide range of bimaterial compounds to a combination of combined Dirichlet–Riemann and Hilbert boundary value problems which are solved analytically. From these solutions clear analytical expressions for characteristic mechanical and electrical parameters are derived. As particular cases of the above mentioned solution the classical (oscillating) and contact zone solutions are obtained. Further, a comparison with an associated solution for an electrically permeable crack has been performed. The fracture mechanical parameters for all models via the remote loads are found analytically and important relationships between these parameters are obtained. Due to these relationships an important algorithm of a numerical method applicable for the investigation of an interface crack in a finite sized piezoelectric bimaterial is suggested.     

A Direct analysis of elastic contact using super elements

Solutions to contact problems are important in mechanical as well as in civil engineering, and even for the most simple problems there is still a need for research results. In the present paper we suggest an alternative finite element procedure and by examples show the need for more knowledge related to the compliance of contact surfaces. The most simple solutions are named Hertz solutions from 1882, and we use some of these solutions for comparison with our finite element results. As a function of the total contact force we find the size of the contact area, the distribution of the contact pressure, and the contact compliance. In models of finite size the compliance depends on the flexibility of the total model, including the boundary condition of the model, and therefore disagreement with the locally based analytical models is expected and found. With computational contact mechanics we can solve more advanced contact problems and treat models that are closer to physical reality. The finite element method is widely used and solutions are obtained by incrementation and/or iteration for these non-linear problems with unknown boundary conditions. Still with these advanced tools the solution is difficult because of extreme sensitivity. Here we present a direct analysis of elastic contact without incrementation and iteration, and the procedure is based on a finite element super element technique. This means that the contacting bodies can be analyzed independently, and are only coupled through a direct analysis with low order super element stiffness matrices. The examples of the present paper are restricted to axisymmetric problems with isotropic, elastic materials and excluding friction. Direct extensions to cases of non-isotropy, including laminates, and to plane and general 3D models are possible.     

圆柱斜齿轮齿面接触动应力计算与分析研究

为了有效计算动态工况下斜齿圆柱齿轮副的齿面接触应力,建立了考虑时变啮合刚度激励和啮入冲击激励的滚动轴承支撑的斜齿圆柱齿轮副啮合型弯-扭-轴耦合六自由度振动模型,通过其计算了齿面啮合动载荷。提出了综合考虑轮齿动载荷、齿间载荷分配系数以及齿面赫兹接触的斜齿圆柱齿轮齿面接触动应力计算方法,同时也利用Abaqus有限元软件动力学模块分析了齿面接触动应力。分别计算了800 N·m、1 200 N·m、1 600 N·m三种负载扭矩下的齿面接触动应力变化过程,基于承载接触分析法的最大接触应力与AGMA标准计算值最大相差为11.6%,基于Abaqus有限元法的最大接触应力与AGMA标准计算值最大相差13.8%,而两种方法的齿面接触动应力变化曲线最大偏差11.3%,从而证实了本文提出的斜齿圆柱齿轮齿面接触动应力计算方法合理有效。     

A contact searching algorithm including bounding volume trees applied to finite sliding mortar formulations

This paper presents a new contact searching algorithm for large deformation mortar-based contact formulations. In this algorithm, a bounding volume hierarchy, defined in the context of a binary tree, is built for each contact surface based on the geometry of the surface. A global contact searching procedure based on these bounding volume trees is first performed to find all candidate contact element pairs, and then a local searching procedure is done to find all the mortar segments having contributions to the mortar integrals that define the contact formulation. The searching algorithm is shown to be very efficient and readily applicable to a variety of large sliding contact problems.     

Approximation of contact stress for a compressed and laterally one side restrained O-ring

This paper revisits the classical O-ring problem by using an experimental, finite element analysis and conventional theories. Especially, the elastic moduli, deformation shape, friction coefficient and extrusion behaviour were investigated in detail during the experiments. A computed tomography was used to detect the deformed shape of the O-ring. The used finite element method results were validated by comparing them with the experimental results. For an application to the present study, an actual case of a compressed and laterally one side restrained condition was analyzed experimentally and numerically. As a result of the finite element analysis, the friction coefficient affects the contact stress profile and magnitude considerably. Lindley’s formulae for a contact (compressive) force underestimated the measured force but it showed similar results to the finite element analysis results. Applicability of the Hertz theory to the contact stress field was discussed by comparing it with the finite element analysis results in the case of a compressed and laterally one side restrained condition. Consequently, it was found that the normalized results with respect to the peak stress and contact width followed the typical Hertzian profile. So an implementation of the appropriate factors to the Hertz equation can yield an approximate solution of the contact stresses.     

电连接器接触件应力场的数值分析与试验验证

利用ANSYS对某型号电连接器接触件应力场进行分析,以寻找应力变化规律.对接触件应力场分布特点、插孔形变、接触压力随温度升高的变化规律进行了仿真研究,并进行数据分析与接触压力的试验验证.结果表明:随着温度升高,插孔最大形变量增加,最大接触压力和接触压力区域都有所减少;尺寸较小的接触件插孔槽缝底部最大等效应力随温度升高增幅较大,交变载荷作用时易出现疲劳、破裂等,属产品失效薄弱点.通过分析得知最大等效应力值随温度上升而变化的趋势取决于温度软化效应和热应力增强作用的综合结果;仿真结果能较好地反映电连接器的工作应力状态,接触压力试验验证了有限元仿真方法的可行性.     

Highlights on some reflections on characteristic angle, light intensity and their correlation to wavelength in three dimensional photoelastic media

The minimum normalised light intensity I_n is introduced as a reliable characteristic parameter, in three dimensional photoelasticity, whose measurement is rather comfortable. Spectral, stress components, angle of divergence of the stress components, and material dependence of I_n is investigated. Limits of a cited method are pointed out. Some misunderstandings that took place in Ref. (1) are highlighted. The basic concepts of two methods in integrated photoelasticity are compared.     

A weight function technique for partially closed inclined edge cracks analysis

The Green Functions, giving the Crack Opening Displacement components of an inclined edge crack under general loading conditions, were obtained starting from the matrix-like structure of the Weight Functions developed for determining the Stress Intensity Factors. The mathematical formulation of the problem is presented and the computational efficiency of the method is demonstrated by solving and discussing the non linear problem of a partially closed inclined edge crack under bending. By means of an iterative procedure, the closed portion of the crack is determined and the effects of normal and friction contact forces on the Crack Opening Displacement components and on the Stress Intensity Factors are discussed. The efficiency and the accuracy of this approach are assessed by comparison with Finite Element solutions.     

BEM and FEM analysis of Signorini contact problems with friction

In this paper, we present a comparative study of the boundary element method (BEM) and the finite element method (FEM) for analysis of Signorini contact problems in elastostatics with Coulomb's friction law. Particularities of each method and comparison with the penalty method are discussed. Numerical examples are included to demonstrate the present formulations and to highlight its performance.     

A semi-analytical approach to three-dimensional normal contact problems with friction

 We present a semi-analytical approach for three-dimensional elastostatic normal contact problems with friction. The numerical approach to iteration on contact area and stick zone size is supported by an underlying analytical solution relating normal and tangential surface tractions to surface displacements in three coordinate directions. The governing equations are fully coupled. The analytical surface displacement solutions for a basic loading element have been derived elsewhere (Li and Berger 2001), and the total surface displacements are constructed as a superposition of deflections due to overlapping pyramid load segments. This approach requires no interpolation scheme for the field variables, which distinguishes it from other numerical techniques such as the FEM, BEM, and meshless methods. A background grid is defined only on the contact surfaces, and iteration approaches are used to determine a convergent configuration for contact domain and stick zone size. The approach is exercised on several normal contact problems, with and without friction, and the results compare favorably to existing analytical and numerical solutions. Received: 10 July 2002 / Accepted: 3 December 2002 The authors appreciate the support of the UC Department of Mechanical Engineering and the UC Office of the Vice President for Research, who jointly provided funds for this work.