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This study aims to optimize the manufacturing process to improve the manufacturing quality, costs and delivering time with the help of multiscale multiphysics modelling and simulation. Multiscale multiphysics-based modelling and simulations are receiving more and more interest by research community and the industry particularly in the context of increasing demands for manufacturing high precision complex products and understanding the intrinsic complexity in associated manufacturing processes.

In this paper, some modelling and analysis techniques using multiscale multiphysics modelling are presented and discussed.

Furthermore, the possibility of adopting the multiscale multiphysics modelling and simulation to develop the virtual machining system is evaluated, and further supported with an industrial case study on abrasive flow machining (AFM) of integrally bladed rotors using the techniques and system developed.

With the development of multiscale multiphysics-based modelling and simulation, it will enable effective and efficient optimisation of manufacturing processes and further improvement of manufacturing quality, costs, delivery time and the overall competitiveness.

Optimized plating conditions, included proper designs of insulating shield (IS), auxiliary cathode (AC) and different patterns, contribute to the uniformity enhancement of copper deposition.

Plating experiments were implemented in vertical continuous plating (VCP) line for manufacturing in different conditions. Multiphysics coupling simulation was brought to investigate and predict the plating uniformity improvement of copper pattern. In addition, the numerical model was based on VCP to approach the practical application.

With disproportionate current distribution, different plating pattern design formed diverse copper thickness distribution (CTD). IS and AC improved plating uniformity of copper pattern because of current redistribution. Moreover, optimized plating condition for effectively depositing more uniformed plating copper layer in varied pattern designs were derived by simulation and verified by plating experiment.

The comparison between experiment and simulation revealed that multiphysics coupling is an efficient, reliable and of course environment-friendly tool to perform research on the uniformity of pattern plating in manufacturing.

The purpose of this paper is to provide a framework for the implementation of an adjoint sensitivity formulation for least‐squares partial differential equations constrained optimization problems exploiting a multiphysics finite elements package. The estimation of the diffusion coefficient in a Poisson‐type diffusion equation is used as an example.

The authors derive the adjoint formulation in a continuous setting allowing to attribute to the direct and adjoint states the role of different fields to be solved for. They are one‐way coupled through the mismatch between measured and direct states acting as a source term in the adjoint equation. Having solved for the direct and adjoint state, the sensitivity of the cost function with respect to the design variables can then be obtained by a suitable post‐processing procedure. This sensitivity can then be used to efficiently solve the least‐squares problem.

The authors derived the adjoint formulation in a continuous setting allowing the direct and adjoint states to be attributed the role of different fields to be solved. They are one‐way coupled through the mismatch between measured and direct states acting as a source term in the adjoint equation. It is found that, having solved for the direct and adjoint state, the sensitivity of the cost function with respect to the design variables can then be obtained by a suitable post‐processing procedure.

This paper implies that modern multiphysics finite elements packages provide a flexible and extendable software environment for the experimentation with different adjoint formulations. Such tools are therefore expected to become increasingly important in solving notoriously difficult partial differential equation (PDE)‐constrained least‐squares problems. The framework also provides the possibility of experimentation with different regularization techniques (total variation and multiscale techniques for instance) to handle the ill‐posedness of the problem.

In this paper the adjoint sensitivity computation is casted as a multiphysics problem allowing for a flexible and extendable implementation.

The purpose of this paper is to study the natural convection and radiation heat transfer inside Nonagon inclined cavity with variable heated source length, which contains a porous medium saturated with nanofluid in the presence of uniform heat generation or absorption under the effect of uniform magnetic field with variable direction. The shape factor of nano particles is taking account for the model of nanofluid.

This study is established in two-dimensional space. The 2D numerical study is effectuated with Comsol Multiphysics based on the on the finite element method. The 2D equation system is exposed on dimensionless form taking into account the boundary conditions.

Results obtained show that the convection heat transfer is ameliorated with the augmentation of heated source length. The convection heat transfer is enhanced by increasing Rayleigh, Darcy numbers and the heated source length; however, it is reduced by rising Hartmann number. The presence of radiation parameter lead to improve the convection heat transfer in the presence of both uniform heat generation/absorption. The average Nusselt number reaches a maximum for an inclination of cavity γ = 45° and a minimum for γ = 60°. Both the increase of the shape factor of nano particles and the solid fraction of nano particles improve the convection heat transfer.

Different studies have been realized to study the heat transfer inside cavity contains porous medium saturated with nanofluid under magnetic field effect. In this work, the Nonagon geometric of cavity studied has never been studied. In addition, the effect of radiation parameter with relation of the shape factor of nanoparticles in the presence of uniform heat generation/absorption on the heat transfer performance have never been investigated. Also, the effect of magnetic field direction with relation of the inclination cavity on heat transfer performance.

Multiphysics problems are solved either with monolithic or segregated approaches. For accomplishing contrary discretisation requirements of the physics, disparate meshes are essential. This paper is comparing experimental results of different interpolation methods for a segregated coupling with monolithic approaches, implemented using a global and a local nearest neighbour method. The results show the significant influence of discretisation for multiphysics simulation.

Applying disparate meshes to the monolithic as well as the segregated calculation of finite element problems and evaluating the related numerical error is content of the contribution. This is done by an experimental evaluation of a source and a material coupling applied to a multiphysics problem. After an introduction to the topic, the evaluated multiphysics model is described based on two bidirectional coupled problems and its finite element representation. Afterwards, the considered methods for approximating the coupling are introduced. Then, the evaluated methods are described and the experimental results are discussed. A summary concludes this work.

An experimental evaluation of the numerical errors for different multiphysics coupling methods using disparate meshes is presented based on a bidirectional electro-thermal simulation. Different methods approximating the coupling values are introduced and challenges of applying these methods are given. It is also shown, that the approximation of the coupling integrals is expensive. Arguments for applying the different methods to the monolithic and the segregated solution strategies are given and applied on the example. The significant influence of the mesh density within the coupled meshes is shown. Since the projection and the interpolation methods do influence the result, a careful decision is advised.

In this contribution, existing coupling methods are described, applied and compared on their application for coupling disparate meshes within a multiphysics simulation. Knowing their performance is relevant when deciding for a monolithic or a segregated calculation approach with respect to physics dependent contrary discretisation requirements. To the authors’ knowledge, it is the first time these methods are compared with a focus on an application in multiphysics simulations and experimental results are discussed.

Nowadays, the determination of the acoustic radiation of electric machines is of particular interest, because legal regulations restrict the maximum audible noise radiated by technical devices such as electrical machinery. The purpose of this paper is to analyze the electromagnetic excited structure‐borne sound and air‐borne noise of an AC servo drive.

This paper presents the required steps for the multiphysics acoustic simulation of electrical machines to evaluate its noise behaviour. This numerical approach starts with the electromagnetic force‐wave simulation. The computation by a structure dynamic model determines the deformation of the mechanical structure due to the force‐waves. The final step of the simulation approach consists of the computation of the acoustic radiation.

For the electromagnetic simulation analytical and numerical methods are combined to gain some acceleration of the entire multiphysics simulation approach. This combination offers additionally a detailed understanding of the noise generation mechanism in electrical machines.

Particular attention is paid to the structural‐dynamic model. Modelling of microstructures, such as the laminated iron core or insulated coils, is memory and computational expensive. A systematic material homogenisation technique, based on experimental‐ and numerical modal analyses, yields a higher accuracy at lower computational costs when compared to standard numerical approaches. The presented multiphysics simulation is validated by measurements. The methods are presented by means of a case study.

The purpose of this paper is to investigate the reliability of wire bonds with three varying ball bond diameters, which are ball bonded with three different sizes of gold wires in light-emitting diode (LED) package under high-temperature environment. In automotive applications, “lifted ball bond” issue is a potential critical point for LED device reliability, as the wire bonds are usually stressed under high operating temperature during their lifetime. Moreover, the reliability of wire bonds in recent LED production has fallen under scrutiny due to the practice of reducing wire diameters to cut down production costs.

Three gold wires with sizes of 2, 1.5 and 1 mm were ball bonded on the LED chip bond pad via thermosonic wire bonding method to produce three different ball bond diameters, that is, 140, 120 and 100 μm, respectively. The reliability of these wire bond samples was then studied by performing isothermal aging at 200°C for the time interval of 30, 100 and 500 hours. To validate hypotheses based on the experimental data, COMSOL Multiphysics simulation was also applied to study the thermal stress distribution of wire bond under an elevated temperature.

Experimental results show that the interfacial adhesion of wire bond degrades significantly after aging at 200°C for 500 hours, and the rate of interfacial degradation was found to be more rapid in the wire bond with smaller ball bond diameter. Experimental results also show that ball bonds randomly elongate along an axis and deforms into elliptical shapes after isothermal aging, and ball bonds with smaller diameters develop more obvious elongations. This observation has not been reported in any previous studies. Simulation results show that higher thermal stress is induced in the wire bond with the decrease of ball bond diameter.

The reliability study of this paper provides measurements and explanation on the effects of wire diameter downsizing in wire bonds for automotive application. This is applicable as a reliability reference for industries who intend to reduce their production costs. Other than that, the analysis method of thermal stresses using COMSOL Multiphysics simulations can be extended by other COMSOL Multiphysics users in the future.

To resolve “lifted ball bond” issue, optimization of the bond pad surface quality and the wire bond parameter has been studied and reported in many studies, but the influence of ball bond diameter on wire bond reliability is rarely focused. Moreover, the observation of ball bonds randomly elongate and deform more into elliptical shape, and ball bond with smaller diameter has the highest elongation after isothermal aging also still has not been reported in any previous studies.

The purpose of this paper is to optimize experimental parameters and gain further insights into the plating process in the fabrication of high-density interconnections of printed circuit boards (PCBs) by the rotating disc electrode (RDE) model. Via metallization by copper electrodeposition for interconnection of PCBs has become increasingly important. In this metallization technique, copper is directly filled into the vias using special additives. To investigate electrochemical reaction mechanisms of electrodeposition in aqueous solutions, using experiments on an RDE is common practice.

An electrochemical model is presented to describe the kinetics of copper electrodeposition on an RDE, which builds a bridge between the theoretical and experimental study for non-uniform copper electrodeposition in PCB manufacturing. Comsol Multiphysics, a multiphysics simulation platform, is invited to modeling flow field and potential distribution based on a two-dimensional (2D) axisymmetric physical modeling. The flow pattern in the electrolyte is determined by the 2D Navier–Stokes equations. Primary, secondary and tertiary current distributions are performed by the finite element method of multiphysics coupling.

The ion concentration gradient near the cathode and the thickness of the diffusion layer under different rotating velocities are achieved by the finite element method of multiphysics coupling. The calculated concentration and boundary layer thicknesses agree well with those from the theoretical Levich equation. The effect of fluid flow on the current distribution over the electrode surface is also investigated in this model. The results reveal the impact of flow parameters on the current density distribution and thickness of plating layer, which are most concerned in the production of PCBs.

By RDE electrochemical model, we build a bridge between the theoretical and experimental study for control of uniformity of plating layer by concentration boundary layer in PCB manufacturing. By means of a multiphysics coupling platform, we can accurately analyze and forecast the characteristic of the entire electrochemical system. These results reveal theoretical connections of current density distribution and plating thickness, with controlled parameters in the plating process to further help us comprehensively understand the mechanism of copper electrodeposition.

During thermal laser processes, heat transfer and fluid flow in the melt pool are primary driven by complex physical phenomena that take place at liquid/vapor interface. Hence, the choice and setting of front description methods must be done carefully. Therefore, the purpose of this paper is to investigate to what extent front description methods may bias physical representativeness of numerical models of laser powder bed fusion (LPBF) process at melt pool scale.

Two multiphysical LPBF models are confronted: a Level-Set (LS) front capturing model based on a C++ code and a front tracking model, developed with COMSOL Multiphysics® and based on Arbitrary Lagrangian–Eulerian (ALE) method. To do so, two minimal test cases of increasing complexity are defined. They are simplified to the largest degree, but they integrate multiphysics phenomena that are still relevant to LPBF process.

LS and ALE methods provide very similar descriptions of thermo-hydrodynamic phenomena that occur during LPBF, providing LS interface thickness is correctly calibrated and laser heat source is implemented with a modified continuum surface force formulation. With these calibrations, thermal predictions are identical. However, the velocity field in the LS model is systematically underestimated compared to the ALE approach, but the consequences on the predicted melt pool dimensions are minor.

This study fulfils the need for comprehensive methodology bases for modeling and calibrating multiphysical models of LPBF at melt pool scale. This paper also provides with reference data that may be used by any researcher willing to verify their own numerical method.

Based on the framework of Krylov subspace-based model order reduction (MOR), compact models of the piezoelectric energy harvester devices can be generated. However, the stability of reduced piezoelectric model often cannot be preserved. In previous research studies, “MOR after Schur,” “Schur after MOR” and “multiphysics structure preserving MOR” methods have proven successful in obtaining stable reduced piezoelectric energy harvester models. Though the stability preservation of “MOR after Schur” and “Schur after MOR” methods has already been mathematically proven, the “multiphysics structure preserving MOR” method was not. This paper aims to provide the missing mathematical proof of “multiphysics structure preserving MOR.”

Piezoelectric energy harvesters can be represented by system of differential-algebraic equations obtained by the finite element method. According to the block structure of its system matrices, “MOR after Schur” and “Schur after MOR” both perform Schur complement transformations either before or after the MOR process. For the “multiphysics structure preserving MOR” method, the original block structure of the system matrices is preserved during MOR. 

This contribution shows that, in comparison to “MOR after Schur” and “Schur after MOR” methods, “multiphysics structure preserving MOR” method performs the Schur complement transformation implicitly, and therefore, stabilizes the reduced piezoelectric model.

The stability preservation of the reduced piezoelectric energy harvester model obtained through “multiphysics structure preserving MOR” method is proven mathematically and further validated by numerical experiments on two different piezoelectric energy harvester devices.