Virtual Material Method Research Articles

Thermodynamic coupling performance analysis and simulation of aerated oil medium steel-BMC joint surface

In order to study the thermal coupling properties of aerated oil medium steel-basalt mineral composite (BMC) joint surface and establish an accurate and convenient simulation analysis method. The calculation method of the actual contact area ratio weight matrix of the aerated oil medium steel-BMC joint surface was studied. The virtual material theory model of the thermal coupling performance of the aerated oil medium steel-BMC joint surface was established by combining it with the virtual material theory. Based on the virtual material method, the thermodynamic coupling performance of the aerated oil medium steel-BMC joint surface was studied by finite element simulation, and compared with the experiment and numerical simulation methods of fractal theory. The results show that the temperature and strain changes of BMC specimen with virtual material method have a good coincidence with the experimental results, and the relative error is minimal. At the same time, the virtual material simulation model is simple, less computation and higher efficiency. It is proved that the method in this paper has better precision and convenience.

Effect of interfacial contact properties on the structural dynamics of PEMFC based on fractal theory and virtual material

The vibration from the road inevitably causes the microscopic dynamic contact of the contact interface inside the proton exchange membrane fuel cell (PEMFC), and the dynamic characteristics of the contact interface have an obvious influence on the dynamic behavior of the whole stack. In this paper, the normal and tangential contact between bipolar plate (BP) and membrane electrode assembly (MEA) is investigated by fractal theory, and the variation of contact stiffness with fractal dimension, characteristic length and loading force is studied comprehensively. Then, through the virtual material method, a dynamic model of the fuel cell stack reflecting the contact characteristics is established. It is found that the natural frequencies of the stacks considering the contact stiffness are lower than those not considering it. The larger the contact stiffness corresponding to the fractal dimension and characteristic length, the higher the natural frequency of the stack, and the effect of fractal parameters on the surface roughness is explored. Increasing the total clamping force can increase the stack global modal frequency, but it will decrease the cell local modal frequency.

Thermal Field Simulation and Analysis of Tulip Contact Based on Virtual Material Method

In order to analyze the temperature distribution of circuit breaker tulip contact, a thermal field simulation model for tulip contact is built combined with the electromagnetic-stress-thermal coupled finite element simulation and virtual material method which models the contact resistance characteristics of tulip contact. The temperature rise characteristic of tulip contacts under rated current conditions and short-circuit conditions is analyzed with the model. Results show that the virtual material method can describe the contraction resistance and additional resistance at the end of the contact finger simultaneously, so as to simulate the partial high temperature of the contact interface. Then, the influence of spring pressure and pressure uniformity on the thermal field of tulip contact is analyzed. Results show that the decrease of spring pressure and the imbalance of contact finger pressure may lead to an increase in the temperature rise of the tulip contact. The proposed method can be used as a reference for the design and the overheating analysis of tulip contact.

Equivalent characteristic model of a rough contact interface based on virtual material method

The characteristic of rough contact interface has a major influence on overall performance of machines. To facilitate the setting of contact interface characteristics during the performance analysis of the whole machine, an equivalent characteristic model of a rough contact interface based on virtual material method is established. The normal and tangential properties of the rough contact interface per unit area are first experimentally conducted. Furthermore, according to the Greenwood-Williamson (GW) model and stress wave propagation conditions of discrete elements, the relationship between normal and tangential contact characteristics is explored by assuming the rough contact interface per unit area as a thin virtual layer. Based on virtual material method, the equivalent characteristic model of a rough contact interface is established, including equivalent virtual elastic modulus, Poisson’s ratio, thickness, and density. Finally, taking two step-shaped steel plates connected by four bolts for example, a numerical simulation of structural characteristics under different preloads is carried out. Numerical analysis results are then compared with tested results to verify the validity of the equivalent virtual material model of rough contact interface, and a good agreement between them is obtained.

Fractal Dimension Fitting of Virtual Material and Experimental Verification

Virtual material is a dynamic model of mechanical contact surface, which is suitable for finite element simulation. This method can characterize the stiffness and damping of the contact surface well by using fractal geometry theory to describe the contour of the contact surface. Based on standard W-M function, we verify the accuracy of the fractal dimension calculated by wavelet transform, and then fit the fractal dimension of machined surfaces with different roughness. Using the fractal dimension, we calculate the virtual material parameters to establish the finite element model of the unit specimen. Finally, we carry out the experimental modal analysis to examine reproduce the virtual material method.

Semi-analytical modeling and analysis of nonlinear vibration of bolted thin plate based on virtual material method

Semi-analytical modeling and analysis of nonlinear vibration of bolted thin plate based on virtual material method

Investigation on dynamic performance of ultra-precision flycutting machine tool based on virtual material method

In the field of ultra-precision machining, the dynamic performance of ultra-precision equipment contributes a lot to the processing accuracy. In this paper, in order to study the dynamic performance of the flycutting machine tool, the virtual material method was adopted creatively to build a machine tool model. This method overcame the complexity of actual structure and obtained more accurate results than traditional methods. Subsequently, the finite element method was applied to analyze the dynamic performance of the virtual material model. Furthermore, the modal test for the flycutting machine tool was performed to verified the simulations by means of the one-point hitting and multi-point measurement. The simulation results indicate that the virtual material model has high comprehensive accuracy, of which the average error of natural frequency is 5.9% and errors are all less than 6% excepting the first order. Moreover, combined with the flycutting experiments, it can be found that the fifth order mode of machine tool contributes a lot to processing quality, which leads to the waviness of 53 mm on the machined surface directly because of the weak stiffness of beam-column joints. By increasing the stiffness of the key joints, the waviness can be eliminated, which greatly improves the surface quality of the workpiece.

An improved static stiffness analysis model for machine tools based on virtual material method

The static stiffness of machine tools can be used for the analysis of thermal deformation because of the uneven temperature field and can further be applied in the thermal error compensation. The prediction of static performance of machine tools is fundamental and essential during the design period. The purpose of this paper is to establish a precise static stiffness model for machine tools. Different from previous models, the proposed method in this paper, basing on the Fractal Geometry, takes both the elastoplastic deformation mechanism and friction into account. By analyzing the normal stiffness and tangential stiffness of joints, equivalent virtual material parameters are acquired for the finite element analysis calculation. An experimental set-up has been established to test X, Y and Z directional deformation of a vertical machine center with a magnitude of 200 kgf load applied to the node of the spindle along the respective direction. The results demonstrate that the proposed model can accurately simulate static characteristics of machine tools.

Dynamics modeling and experimental modal analysis of bolt loosening for lightning rod

Lightning rods are effective to prevent lightning damage in power systems. However, under the influence of severe weather conditions, they often face failure problems, mainly manifested as tilt and fracture caused by bolt loosening which can result in significant economic losses. Therefore, it is very meaningful to detect the loosening of the lightning rod. The vibration-based method is an effective method for bolt loosening detection and is suitable for use on large lightning rods. This paper built a finite element model of the lightning rod Flange-Bolt Structure Unit (FBSU) based on the virtual material method, designed an effective acquisition test of the vibration signal under different loosening conditions of the lightning rod FBSU. The experimental results showed that it was effective to establish the dynamic model of the lightning rod FBSU by using the virtual material method. According to the measured vibration signal, the frequency response function was obtained by TIME MDOF method, and the preliminary judgment of bolt loosening can be realized. This study lays the foundation for the precise positioning and the extent of loosening detection of lightning rod bolt loosening, and also provides a guideline for the vibration test design of large bolted structures similar to lightning rods.

Research on Dynamic Characteristics of Split TBM Cutterhead Based on Similarity Theory

Cutterhead with disc cutters is a key component of tunnel boring machine (TBM), and its dynamic characteristics greatly influences the cutting performance of the equipment rock disc cutters. This study investigated the dynamic characteristics of split TBM cutterhead under bolted connection based on the similarity theory. A simplified and scale similarity of split cutterhead was proposed. Based on a virtual material method, a simulation model was established and its dynamic characteristic was analyzed for each block of scaled cutterhead. Dynamic testing experiments of the center block, side block and scaled cutterhead were carried out to achieve the vibration mode and frequency. The results show that the errors of the center block and side block between theoretical natural frequencies and experimental ones are less than 7%, and the theoretical mode shapes are in agreement with the experiments. Besides, the errors between experiment and simulation of the scaled cutterhead are less than 15%, and the virtual material method is verified. The similarity theory and the virtual material method would be used to investigate the dynamic characteristics of split TBM cutterhead.

Comparison of equivalent model methods of joint surface based on modal analysis

The mechanical joint surface plays an important role in transmitting motion, load and energy during the normal operation of the mechanical system. Effective mechanical joint equivalent models are established to solve the practical problem of the dynamic model engineering. Equivalent models of joint surface in this study include spring damping method, virtual material method and Bond connection method. Firstly, the model is established by CATIA. Secondly, the physical properties of the model are assigned by ANSYS or Abaqus finite element simulation software. Then the modal analysis of the model carries out. By comparing the mode shapes and natural frequencies of the three methods, it is concluded that the mode shapes of the three methods are basically the same. Therefore, all three methods are reliable joint surface equivalent models. However, the natural frequency obtained by the virtual material method is significantly lower than the natural frequencies obtained by the other two methods. It is concluded by analysis that the natural frequency error obtained by the virtual material method is small, and the spring damping method and the finite element method have large errors.

Equivalent Method of Joint Interface Based on Persson Contact Theory: Virtual Material Method.

An accurate equivalent method of metal joint interface is of great significance to optimize the dynamic performance of the whole machine. Therefore, it is necessary to establish an accurate equivalent method of joint interface. The virtual material method is a precise equivalent method of joint interface. The traditional virtual material method is based on the M–B fractal contact theory. By modeling the contact mechanics of the joint interface, the physical properties of the virtual material are obtained separately, such as elastic modulus, Poisson’s ratio and density. In this paper, Persson contact theory is used to establish the interface contact mechanics model to find the physical properties of virtual materials. The virtual material methods constructed by two theories are respectively applied to the modal simulation to obtain the natural frequencies of the joint interface. By comparing the natural frequencies obtained by modal experiment and modal simulation, it is found that the natural frequencies obtained by the virtual material method based on Persson contact theory are closer to the results obtained by the modal experiment, and the error is within 5%. The error of the natural frequencies obtained by the virtual material method based on the M–B fractal contact theory is within 10%. Therefore, the Persson contact theory can establish a more accurate equivalent method of metal’s joint interface.

Modeling and analysis of an impact-acoustic method for bolt looseness identification

Abstract Bolted joints are fundamental building blocks and have been widely used to hold multiple structural components together, while their looseness may lead to costly disasters in industries. Compared to current bolt loosening detection methods that are often hampered due to the need for highly experienced personnel or an overly complex sensor-structure interaction, a new percussion-based method using analytical modeling and numerical simulation was proposed to reduce cost and avoid contact-type sensor installation, which is a great contribution. Analytically, the bolted joint was modeled equivalently as a laminated plate by using the virtual material method and the layer-wise theory, and its percussion-induced sound pressure level (SPL) can be obtained via the acoustic radiation mode approach. The corresponding numerical simulation was developed with the focus on the acoustic-structure coupling, and the acoustic boundary conditions were satisfied through a perfectly matched layer (PML). Compared to prior work, another contribution of this paper is that the proposed method further considers the critical effect of bolted interfacial roughness, which affects radiation sound signals significantly. Finally, acoustic tests were carried out, and the good agreement between results of modeling, simulation, and experiments demonstrate the effectiveness of the proposed method. As a rapid and non-invasive bolt looseness detection method, the investigations in this paper can provide guidance for the future development of bolt looseness detection methods.

Experimental Verification and Comparative Analysis of Equivalent Methods on Metal's Fixed Joint Interface.

In order to effectively improve the dynamic characteristics of the fixed metal joint interface, it is important to establish a correct equivalent model of the metal joint interface. In this paper, three equivalent methods for simulating the metal joint interface are analyzed, including the virtual material method, spring damping method, finite element method, and verification by modal experiment. First, according to the contact mechanics model of the constructed metal joint interface, the physical properties of the three-dimensional models of the fixed joint interface are assigned in the ANSYS software. Then, three methods are used for the modal analysis and compared with a modal experiment. The results show that the modal shapes of the three theoretical methods are consistent with those of the experimental modes. The first five natural frequencies obtained by the virtual material method are closest to the experimental natural frequencies, and the errors are within 10%. The errors of the other two methods are between 9% and 39%. Therefore, the virtual material method is a better equivalent method of the metal joint interface.

Contact Resistance Model and Thermal Stability Analysis of Bolt Structure

This paper introduces a contact resistance model of bolt structures based on virtual material method. The main idea of the model is to interpose a virtual layer between the overlapped bus bar and define properties including equivalent resistivity and equivalent modulus of elasticity to describe the dynamic characteristics of the distributed contact resistance. The determining method of these properties is introduced, and the validity of the model is demonstrated by comparing the calculated contact resistance with the measured results. The model is further applied to the coupled electromagnetic–stress–thermal finite-element calculation to analyze the thermal stability of the bolt structure. The temperature rise process inside the bolt structure is studied, and the strengthening effect of the electrodynamic force on the thermal field is revealed. Besides, the influences of contact loosening and oxidation are also researched with the method.

Non-uniform virtual material modeling on contact interface of assembly structure with bolted joints

Accurate modeling of contact interface in bolted joints is crucial in predicting the dynamic behavior for bolted assemblies under external load. This paper presents a contact pressure distribution based non-uniform virtual material method to describe the joint interface of assembly structure, which is connected by sparsely distributed multi-bolts. Firstly, the contact pressure distribution of bolted joints is obtained by the nonlinear static analysis in the finite element software ANSYS. The contact surface around bolt hole is divided into several sub-layers, and contact pressure in each sub-layer is thought to be evenly. Then, considering multi-asperity contact at the micro perspective, the relationship between contact pressure and interfacial virtual material parameters for each sub-layer is established by using the fractal contact theory. Finally, an experimental platform for the dynamic characteristics testing of a beam lap structure with double-bolted joint is constructed to validate the efficiency of proposed method. It is found that the theoretical results are in good agreement with experimental results by impact response in both time- and frequency-domain, and the relative errors of the first four natural frequencies are less than 1%. Furthermore, the presented model is used to examine the effect of rough contact surface on dynamic characteristics of bolted joint.

Virtual Material Method for Enabling a Single 2D-FEA Simulation of Electrical Machine Sets

When two or more electrical machines are electrically and mechanically interconnected, the implementation of a single two-dimensional finite element analysis (2D-FEA) of the whole system is complex or even impossible. This is mainly due to the feature of commercially available 2D-FEA software to use a domain depth equal for all the electrical machines drawn in the geometrical 2-D model. For any typology of rotating electrical machines, the proposed “ virtual material method ” easily consents to change the actual axial stack length to an arbitrary value, opening the way to describe all the machines in a single geometrical model. In the paper, the complete theory of this original approach is reported and validated on permanent magnet, induction, and field-wound synchronous machines. The cases of study with two and three interconnected machines are also presented and the results compared with the cosimulation technique of their separated bidimensional models. The perfect agreements observed in the comparisons definitely prove the feasibility of the proposed solution.

Modeling and Validation of Bolted Joints Based on Nonlinear Virtual Material Method

The bolted joint provides more than half of the stiffness and nearly all of the damping of the whole machine tool. It is necessary to study the dynamics mechanism and establish accurate model of joint surface. The paper proposes the model of nonlinear virtual material based on fractal theory and Hertz contact theory, the contact surface can be divided into several sections based on the pressure distribution, the elastic modulus and stress of each section can be calculated. An L-shaped specimen is designed to validate the accuracy of presented model. The maximum errors of natural frequencies between theoretical and experimental is 8.8%, suggesting that nonlinear virtual material method is appropriate for the bolted joint.

Interface contact pressure-based virtual gradient material model for the dynamic analysis of the bolted joint in machine tools

Bolted joints have significant influence on the dynamic characteristic of the machine tool assembly. This study proposes a new modeling method using virtual gradient material. On the basis of Hertz contact theory and fractal geometry theory, the relationship between contact stiffness and normal contact load is deduced. The contact pressure distribution at the interface is obtained through finite element contact analysis. An orthogonal material model is introduced to describe the properties of virtual material. The virtual material is divided into several layers, and the elastic modulus and shear modulus in each sub-layer are derived based on Hooke’s Law. Both experimental and theoretical results for a bolted lap structure are obtained. The experimental results are compared with theoretical ones in terms of qualitative comparison of similar mode shapes and quantitative comparison of corresponding natural frequencies. The comparison shows that the theoretical first three-order vibration mode shapes are in good line with the experimental ones. The relative errors of corresponding natural frequencies between the virtual gradient material model and the experiment are less than 9%, which are smaller than those between the traditional virtual uniform material model and the experiment. The proposed virtual gradient material method would be useful to accurately model the bolted joint in CNC machine tools.

Surface contact stress-based nonlinear virtual material method for dynamic analysis of bolted joint of machine tool

The components of machine tools are mainly fixed and connected by bolts. The performance of the assembly can be affected by the dynamic characteristics of the bolted joints. This paper presents a nonlinear virtual material method based on surface contact stress to describe the bolted joint for accurate dynamic performance analysis of the bolted assembly. Fractal geometry theory is used to describe the surface topography. The elastic modulus and shear modulus of one micro-contact are derived based on fractal contact theory. The equivalent elastic modulus, Poisson ratio, and density of the bolted joint can be obtained through the weighted mean method. In order to obtain the stress distribution, the contact surface is assumed flat in the macro-scale, and the uneven distribution of contact stress can be obtained by the finite element method (FEM). The contact surface can be divided into several sections, and the parameters of a virtual material layer can be determined based on the mean contact stress. Both theoretical and experimental results for a bolted joint are obtained for a box-shaped specimen under equal pre-tightening force and bending moment effect. The results show that the theoretical mode shapes are in good agreement with the experimental mode shapes. The relative errors between the theoretical and experimental natural frequencies are less than 4.41%, which indicates that the present nonlinear virtual material method is appropriate for the bolted joint in modeling CNC machine tools.