JEC COMPOSITES MAGAZINE - Issue #135 - July/August 2020 - 60

TECHNOLOGY design

Fig. 3: Scheme of a genetic algorithm for optimization of fibre layups
Fig. 2: Stiffness and damping ratio of an exemplary CFRP
laminate as a function of fibre orientation [ADAM73, AVK14]

chine tool manufacturer Makino Milling Machine Co. Ltd. and the
Fraunhofer Institute for Production Technology IPT, Aachen, was
set up. The aim was to develop suited simulation and optimization
methods for designing structural components in machine tools
out of CFRP. For demonstration, the method is applied to a small
structural component - a boring tool similar to the one shown in
Figure 1 or [MASC19].

Optimization problem

60

Five characteristics have to be considered in the design process of
a structural component for a machine tool, which results in a multi-parameter optimization problem (MOP): 1) stiffness, 2) damping, 3) thermal expansion, 4) weight, and 5) costs.
For highly-accelerated structural components, for example, specific stiffness and damping are primarily optimized. Thus, the kinematic dynamics can be improved and the machining accuracy -
even in the case of excitation close to the natural frequency - can
be ensured. The design process for a boring tool is based on the
same target values: deformations due to cutting forces and its mass
for acceleration processes in rapid traverse or during tool change
should be reduced. When using CFRP, however, it should be noted
that the corresponding material properties within a unidirectional
(UD) laminate are inversely proportional to each other. Stiffness
decreases steadily for higher angles between load and fibre direction, whereas material damping increases between 0° and approximately 35° and decreases afterwards, see Figure 2. A compromise
for the optimal fibre orientation is therefore necessary.

ed with random mutation to avoid local optima, is able to find a
solution close to global optima requiring only a setup of the FEA
analysis and definition of the fitness function.
Next to a fitness function f, a constraint function g can be introduced that leads to a constraint optimization. In the presented
optimization, the algorithm aims to maximize the component
damping without exceeding a maximum allowed static displacement at the most deforming place of the bridge tool in the area of
a cartridge, see Figure 4. This demonstration shows the possibility
to optimize the fibre layup of a machine tool component with a
complex load case within hours using an automated method. The
result supplements the current optimization approaches that only
consider specific stiffness by itself or specific stiffness and thermal
expansion [KLIM15, KUSS17, KONO19].

Optimizing stiffness and damping

Simulation for machine tool applications

The inversely proportional behaviour of the laminate properties
leads to a complex optimization problem, especially if more than
one of the mentioned parameters is set as a target. For this type
of MOP, the use of a genetic algorithm (GA), which is a heuristic
optimization method, is very suitable [AYDI09, CHEN13]. The target parameters are combined in a fitness function and weighted by
their importance for the application. In a GA, a set of individuals,
called population, is tested and rated by their fitness value. The testing is carried out by a finite element analysis (FEA). The best rated
individuals are used and randomly combined in order to create a
new generation of individuals that is tested again, see Figure 3. This
robust, fully-automated optimization algorithm, which is extend-

With the capability to predict the damping of a CFRP component
including layup-specific material damping and part geometry, a
dynamic simulation can be implemented in Abaqus (Dassault
Systèmes). Two characteristics were discovered by simulating the
bridge tool itself. On the one hand, it was quantified how the static
and dynamic stiffness (reciprocal of compliance) of a CFRP machine structure can vary due to its layup without changing the part
geometry or wall thickness, see the black dots in Figure 5. On the
other hand, the automated optimization method showed that the
three relevant performance indicators of the bridge tool could be
improved compared to a lightweight aluminium version:
-	 Mass 						
- 23%

jec composites magazine / N°135 July - August 2020

Fig. 4: Part damping optimization using a genetic algorithm
under consideration of a maximum deformation of the CFRP tool
JEC COMPOSITES MAGAZINE - Issue #135 - July/August 2020

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