A numerical framework for simulation of swirled adhesive application

A numerical framework for simulation of swirled adhesive application along arbitrary robot motions and substrate geometries is pre- sented. The momentum and continuity equa- tions are solved on a Cartesian octree grid using a finite volume discretization. A viscoelastic constitutive model is used to describe the com- plex rheology of the adhesive and is solved us- ing a previously presented Lagrangian-Eulerian method. The flow from the nozzle to the target surface is modelled using experimental data, and a projected injection model is used to add adhesive material in the simulation close to the surface. The two-phase flow of adhesive and air is then simulated. Numerical results are com- pared with experimental data and good agree- ment is found

A Backwards-Tracking Lagrangian-Eulerian Method for Viscoelastic Two-Fluid Flows

A new Lagrangian–Eulerian method for the simulation of viscoelastic free surface flow is proposed. The approach is developed from a method in which the constitutive equation for viscoelastic stress is solved at Lagrangian nodes, which are convected by the flow, and interpolated to the Eulerian grid with radial basis functions. In the new method, a backwards-tracking methodology is employed, allowing for fixed locations for the Lagrangian nodes to be chosen a priori. The proposed method is also extended to the simulation of viscoelastic free surface flow with the volume of fluid method. No unstructured interpolation or node redistribution is required with the new approach. Furthermore, the total amount of Lagrangian nodes is significantly reduced when compared to the original Lagrangian–Eulerian method. Consequently, the method is more computationally efficient and robust. No additional stabilization technique, such as both-sides diffusion or reformulation of the constitutive equation, is necessary. A validation is performed with the analytic solution for transient and steady planar Poiseuille flow, with excellent results. Furthermore, the proposed method agrees well with numerical data from the literature for the viscoelastic die swell flow of an Oldroyd-B model. The capabilities to simulate viscoelastic free surface flow are also demonstrated through the simulation of a jet buckling case

Computationally efficient viscoelastic flow simulation using a Lagrangian-Eulerian method and GPU-acceleration

A recently proposed Lagrangian-Eulerian method for viscoelastic flow simulation is extended to high performance calculations on the Graphics Processing Unit (GPU). The two most computationally intensive parts of the algorithm are implemented for GPU calculation, namely the integration of the viscoelastic constitutive equation at the Lagrangian nodes and the interpolation of the resulting stresses to the cell centers of the Eulerian grid. In the original CPU method, the constitutive equations are integrated with a second order backward differentiation formula, while with the proposed GPU method the implicit Euler method is used. To allow fair comparison, the latter is also implemented for the CPU. The methods are validated for two flows, a planar Poiseuille flow of an upper-convected Maxwell fluid and flow past a confined cylinder of a four-mode Phan Thien Tanner fluid, with identical results. The calculation times for the methods are compared for a range of grid resolutions and numbers of CPU threads, revealing a significant reduction of the calculation time for the proposed GPU method. As an example, the total simulation time is roughly halved compared to the original CPU method. The integration of the constitutive equation itself is reduced by a factor 50 to 250 and the unstructured stress interpolation by a factor 15 to 60, depending on the number of CPU threads used

A numerical multiscale method for fiber networks

Fiber network modeling can be used for studying mechanical properties of paper [1]. The individual fibers and the bonds in-between constitute a detailed representation of the material. However, detailed microscale fiber network models must be resolved with efficient numerical methods. In this work, a numerical multiscale method for discrete network models is proposed that is based on the localized orthogonal decomposition method [4]. The method is ideal for these network problems, because it reduces the maximum size of the problem, it is suitable for parallelization, and it can effectively solve fracture propagation. The problem analyzed in this work is the nodal displacement of a fiber network given an applied load. This problem is formulated as a linear system that is solved by using the aforementioned multiscale method. To solve the linear system, the multiscale method constructs a low-dimensional solution space with good approximation properties [5, 2]. The method is observed to work well for unstructured fiber networks, with optimal rates of convergence obtainable for highly localized configurations of the method

Numerical upscaling of discrete network models

In this paper a numerical multiscale method for discrete networks is presented. The method gives an accurate coarse scale representation of the full network by solving sub-network problems. The method is used to solve problems with highly varying connectivity or random network structure, showing optimal order convergence rates with respect to the mesh size of the coarse representation. Moreover, a network model for paper-based materials is presented. The numerical multiscale method is applied to solve problems governed by the presented network model

Network model for predicting structural properties of paper

Paper simulations that resolve the entire microscopic fiber structure are typically time-consuming and require extensive resources. Several such modeling approaches have been proposed to analyze different properties in paper. However, most use non-linear and time-dependent models resulting in high computational complexity. Resolving these computational issues would increase its usefulness in industrial applications. The model proposed in this work was developed in collaboration with companies in the papermaking industry within the Innovative Simulation of Paper (ISOP) project. A linear network model is used for efficiency, where 1-D beams represent the fibers. Similar models have been proposed in the past. However, in this work, the paper models are three-dimensional, a new dynamic bonding technique is used, and more extensive simulations are evaluated. The model is used to simulate tensile stiffness, tensile strength, and bending resistance. These simulated results are compared to experimental and theoretical counterparts and produce representable results for realistic parameters. Moreover, an off-the-shelf computer accessible to a paper developer can evaluate these models structural properties efficiently

Generating Optimized Trajectories for Robotic Spray Painting

In the manufacturing industry, spray painting is often an important part of the manufacturing process. Especially in the automotive industry, the perceived quality of the final product is closely linked to the exactness and smoothness of the painting process. For complex products or low batch size production, manual spray painting is often used. But in large scale production with a high degree of automation, the painting is usually performed by industrial robots. There is a need to improve and simplify the generation of robot trajectories used in industrial paint booths. A novel method for spray paint optimization is presented, which can be used to smooth out a generated initial trajectory and minimize paint thickness deviations from a target thickness. The smoothed out trajectory is found by solving, using an interior point solver, a continuous non-linear optimization problem. A two-dimensional reference function of the applied paint thickness is selected by fitting a spline function to experimental data. This applicator footprint profile is then projected to the geometry and used as a paint deposition model. After generating an initial trajectory, the position and duration of each trajectory segment are used as optimization variables. The primary goal of the optimization is to obtain a paint applicator trajectory, which would closely match a target paint thickness when executed. The algorithm has been shown to produce satisfactory results on both a simple 2-dimensional test example, and a non-trivial industrial case of painting a tractor fender. The resulting trajectory is also proven feasible to be executed by an industrial robot

An Immersed Boundary Based Dynamic Contact Angle Framework for Handling Complex Surfaces of Mixed Wettabilities

We propose a comprehensive immersed boundary-based dynamic contact angle framework capable of handling arbitrary surfaces of mixed wettabilities in three dimensions. We study a number of dynamic contact angle models and implement them as a boundary condition for the Continuum Surface Force method. Special care is taken to capture the contact angle hysteresis by using separate models for the advancing and receding contact lines. The framework is able to account for surfaces of varying wettability by making the contact angle dependent on the local boundary condition.We validate our framework using cases where glycerol droplets impact solid surfaces at low Weber numbers. We show how a truly dynamic contact angle model is needed for advancing contact lines and how a separate dynamic model is needed for receding contact lines. To test our framework for industrially relevant problems on a more complex surface, we simulate droplet impact on a printed circuit board. We show how the local surface properties control the final droplet deposition and that the framework is capable of handling adjacent surfaces of considerably different wettabilities