Numerical Simulation Techniques
There are many numerical methods used for simulation of engineering
problems, among which the finite difference method (FDM) and the
finite element method (FEM) are the most commonly used. As illustrated
in the figure below, the finite difference model gives a pointwise
approximation to a problem with an array of grid points subdividing
the geometry along each coordinate axis, while the finite element
model gives a piecewise approximation to a problem with an assemblage
of elements subdividing the geometry along the boundaries. The FDM
solves the governing equations by direct differentiation along each
coordinate axis thus it can run very fast. The FEM solves the governing
equations by discretization of the domain with elements of a selected
shape and assembling them into the entire system, thus it runs usually
slower than the FDM. The FDM is mostly used for solving fluid mechanics
and heat transfer problems often with stationary boundaries, but
it is impossible to use for solving problems with large strain/deformation.
The FEM is more advantageous to solve problems with large deformation
and can be used for nearly all kinds of engineering problems with
complex geometry and material combinations.
SORPAS® is developed based on the finite element method. All
numerical models and procedures have been developed and integrated
with the welding engineering expertise, which has been fully automated
inside the software. The graphical user interface of SORPAS®
is also tailormade for resistance welding. Users are not required
to have prior knowledge of the FEM. However, having some basic knowledge
of the FEM can help to better understand the simulations and obtain
more reliable simulation results. More details will be introduced
at the training course (usually 12 days). We hereby emphasize only
the two basic concepts that have essential influence in FEM simulations.
Mesh density
The mesh density or the size of elements has essential influence
on the accuracy of FEM calculations regarding distribution of variables
in the geometry. As a basic procedure of FEM, the problem domain
(geometry and materials) is divided into a number of elements (mesh).
This procedure is called the mesh generation. The FEM calculations
are mainly based on the values of variables on the nodal points.
The more nodal points or the more elements are divided, the more
accurate results can be obtained for the distribution of variables.
Increasing the total number of elements will increase the nodal
points, but also increase the number of calculations and the computation
time. It is more efficient to only increase the number of elements
in the areas with large changes (or gradients) of variables, leaving
fewer elements in the areas with small changes. The total number
of elements can thus still be kept in a reasonable number. This
is why the mesh density control is introduced to allow users to
determine where they need more elements (or higher mesh density).
In SORPAS® the mesh generation is fully automated according
to the user defined total number of elements and density control
points. The figure below shows the influence of the mesh density
in a spot welding simulation. It is noticed that the computation
time increases drastically with increasing number of elements but
the obtained nugget volume changes very little with more than 1000
elements. We have thus recommended that 1000 elements are normally
enough for an ordinary spot welding simulation.
Time step
In order to calculate the dynamic development of variables, the
process time is divided into small time steps during simulations.
The FEM calculations will be carried out incrementally at every
time step through the entire welding process. The time step has
significant influence on the accuracy of FEM simulations especially
for the dynamic variables rapidly changing with time. The smaller
the time step is, the more accurate results can be obtained regarding
the dynamically changing variables, but it will also increase the
number of calculations and thus the computation time. The figure
below shows the influence of the time step in a spot welding simulation.
It is noticed that the computation time decreases drastically with
increasing step size. There is no big influence to the nugget volume
when the time step size is below 0.5ms. To ensure the reliability
of results, we have recommended that a time step of 0.050.1ms should
be sufficient for most of the resistance welding applications.
Procedures for making simulations
Simulation with SORPAS® is a virtual resistance welding process
on a computer, where the whole process, from design to welding,
is done on the computer without using actual materials and welding
equipment. Users will see the results of welding graphically displayed
on the computer. In this way, the engineers can evaluate their design
of electrodes and weldability of new materials, and optimize process
parameter settings before actual welding tests. The procedure for
making simulations with SORPAS® includes three steps: 1) data
preparation, 2) running simulation and 3) evaluation of results.
The input data needed for simulation with SORPAS® are
summarized
below:
 Geometry and materials
 Define forms and select materials for electrodes
 Define geometry and select materials for workpieces
 Define thickness and select materials for coatings
 Machine settings
 Define connection of electrodes to the welding machine
 Set welding force
 Set welding current and time
 Simulation controls
 Define time step sizes and select numerical models
 Define automated optimization procedures
After all input data are prepared, the simulation can be started
simply by pressing a button; it will then run automatically. The
results will be saved through the progress of the simulation, which
can be graphically displayed for analysis after the simulation is
finished. With the automated optimization procedures, the optimal
weld current for achieving a desired size of weld nugget can be
obtained.
