Zeitschrift Kunststofftechnik Journal of Plastics Technology

Transcription

Nicht zur Verwendung in Intranet- und Internet-Angeboten sowie elektronischen Verteilern.
www.kunststofftech.com
© 2014 Carl Hanser Verlag, München
Zeitschrift Kunststofftechnik
4Autor
Titel (gegebenenfalls gekürzt)
Journal of Plastics Technology
www.kunststofftech.com · www.plasticseng.com
archivierte, peer-rezensierte Internetzeitschrift
archival, peer-reviewed online Journal of the Scientific Alliance of Polymer Technology
handed in:
accepted:
07.04.2014
10.07.2014
Dipl.-Ing. Marc Schöneich1,2, Prof. Dr.-Ing. Markus Stommel2, Dr. Andrea Kratz3, Dipl.Mat. Valentin Zobel4, Prof. Dr. Gerik Scheuermann4, Dr. Ingrid Hotz5, Prof. Dr. Bernhard
Burgeth6
1
Chair of Polymer Materials, Saarland University
Chair of Plastics Technology, Technical University Dortmund
3
Department of Visualization and Data Analysis, Zuse Institute Berlin
4
Image and Signal Processing Group, Institute for Informatics, University of Leipzig
5
German Aerospace Center (DLR), Braunschweig
6
Department of Mathematics, Saarland University
2
Optimization strategy for the design of ribbed
plastic components
The engineer is supported for the design of ribbed plastic components by basic guidelines concerning
the shape and the position of the ribs. Thus, the experience and intuition of the individual engineer
plays an important role. For this reason, a component with an optimal rib structure cannot be
guaranteed. In this publication a new strategy is presented as assistance for the design of ribbed
plastic components. The guidance of the design of rib structures in injection molded plastic parts by
tensor visualization will result in an optimized rib structure which leads to stiffer parts when identical
material is used. FE-simulations as well as experimental tests validate the optimization potential of
tensor visualization for the design of ribbed plastic components.
Optimierungsstrategie zur Konstruktion
verrippter Kunststoffbauteile
Zur Gestaltung verrippter Kunststoffbauteile werden dem Konstrukteur neben grundlegenden
Gestaltungsrichtlinien kaum Hilfestellungen bei der Rippenpositionierung und -gestaltung gegeben.
Die Erfahrung und Intuition des Einzelnen spielen somit eine wichtige Rolle. Aus diesem Grund kann
für ein Bauteil eine optimale Rippenstruktur nicht unbedingt sichergestellt werden. In der vorliegenden
Veröffentlichung wird eine neue Strategie als Hilfestellung zur Konstruktion verrippter Kunststoffbauteile vorgestellt. Die Orientierung an Tensorvisualisierung zur Konstruktion von Rippenstrukturen
in Kunststoff-Spritzgussartikeln führt zu einem insgesamt steiferen Bauteil bei identischem Materialeinsatz als die intuitiv verrippte Referenzstruktur. Struktursimulationen sowie experimentelle Bauteiltests validieren in dem Beitrag das Optimierungspotential von Tensorvisualisierung zur Konstruktion
verrippter Kunststoffbauteile.
© Carl Hanser Verlag
Zeitschrift Kunststofftechnik / Journal of Plastics Technology 9 (2013) 4
Schöneich, Stommel et al.
Optimization of ribbed plastic components
Optimization strategy for the design of ribbed
plastic components
M. Schöneich, M. Stommel, A. Kratz, V. Zobel, G. Scheuermann, I. Hotz, B.
Burgeth
1
INTRODUCTION
Injection molded technical plastic parts are commonly supported by rib
structures to achieve a lightweight design while meeting the requirements of
strength and stiffness. In order to use the full potential of rib structures, their
design with respect to geometry, number of ribs and the position within the
component is the most crucial aspect. Existing design guidelines offer some
fundamental geometric advices towards the rib design [2-4]. However, the
positioning of the ribs within the component depends mostly on the experience
of the engineer. In the following, a method is presented to optimize the design
of rib structures by visualization methods. The stress tensors resulting from FEsimulations and therewith the load paths are visualized by tensor lines and
textures. Based on these, different rib structures are defined leading the
engineer towards a load-related rib structure. FE-simulations and experiments
are conducted to evaluate the method. Furthermore, the results are compared
to a reference part, which is ribbed according to the established guidelines to
highlight the benefits of the introduced method.
2
STATE OF THE ART
2.1
Ribbed Component Design
Several general guidelines exist to design ribbed plastic components [1-4]. For
instance, ribs are preferably located in tensile loaded areas of the part, oriented
in the direction of the applied load. However, perpendicular to the loading
direction the ribs result in a cross-sectional jump which leads to stress
concentrations. Therefore, the load path defined from the point of force
introduction to the fixation plays an important role for the design of rib
structures. Besides, there are a couple of further general rules for designing ribs
(see i.e. [2-3]), which are briefly summarized in the following:
The height of a rib should be chosen five to ten times the basic wall thickness of
the molded part to reach a sufficient stiffening effect. The upper height of a rib is
limited by an increasing tendency to buckling effects which often arise by tall rib
heights under compressive stressing. A further influence on the stiffness, other
than the height of a rib, is their number. The stiffness increases proportionally to
Journal of Plastics Technology 10 (2014) 4
161
the number of ribs. However, the material costs are equally increased so that
the number of ribs is to be optimized for a given load case.
Restrictions arising from processing aspects must also be considered for the
design of ribs in injection molded parts. Typical rib structures are shown in
figure 1. The maximum component stiffness is reached by a rib arrangement
which provides a continuous distribution of forces (figure 1, left side). However,
processing prescribes preferably an offset of the ribs (figure 1, right side).
Figure 1: Design conflict for rib structures [3]
The entire potential of ribbing in plastic components is often not sufficiently
utilized because of missing adequate design criteria considering the load path.
Hence, ribbed plastic components often feature oversized rib structures with a
high level of complexity.
2.2
Tensor Visualization: Basics and Possibilities
In this article a methodology to guide the process of designing ribs regarding
the mechanical loading in a technical plastic component is developed. The
concept is based on tensor information originating from Finite-Element (FE)
simulations.
The strains and stresses calculated by FE-simulations due to the applied
deformations and forces are stored in the form of tensors. In the 3D case, stress
and strain tensors are symmetrical 3x3 matrices.
The dimensioning of technical products is commonly based on the comparison
of a scalar, material specific strength quantity to a stress or strain value
calculated from the 3D-tensor data by e.g. the well-known von-Mises equation.
The prescribed procedure is well-established engineering practice. However, in
this way much of the tensor information cannot be used for the dimensioning.
Therefore, a new approach using different interpretation concepts of tensors is
introduced in order to use the full tensor information for dimensioning. In [5] and
162
[6] concepts for the visualization of tensor fields are presented. Based on these
concepts, a method for the design of rib structures based on visualized tensor
fields in plastic parts is introduced. In the following, the two main methods,
tensor lines and tensor fabric textures are described very briefly (for more
details see [5] and [6]):
1. Tensor Lines. Tensor lines represent a visualization method for tensors
similar to streamlines for vector fields. A tensor line is an integral curve, which is
tangent to one chosen eigenvector ﬁeld in each point [7, 8]. A three-dimensional
symmetrical tensor second order can be decomposed into its three eigenvalues
and three eigenvectors, whereby the eigenvectors form an orthonormal system.
A distinction is made between major, intermediate, and minor eigenvalue or
eigenvector. The representative lines of the major and minor eigenvector are of
particular interest for the stress tensor fields, because they can be interpreted
as the load path of tensile and compressive loads.
Figure 2: Tensor lines of the major (violet) und minor (green) eigenvector in a
cube of material under the demonstrated load case
An example to illustrate the tensor lines is shown in figure 2. Because of the
load case the cube is locally stressed either by tension or compression. The
description with tensor lines enables the direct distinction between the load path
of compression (green) and the load path of tensile stresses (violet). It should
be noted that tensor lines solely visualize the information of direction. By
163
analogy with streamlines the correct selection of these lines is seen as a great
challenge in research.
2. Tensor Fabric Textures. Tensor Fabric Textures describe texture-based
methods to visualize two-dimensional projections of the three-dimensional
stress ﬁeld. Thus, the three-dimensional tensor is projected on a twodimensional sectional plane [9]. The idea of this method is to generate a texture
that characterizes the eigenvector field and reflects the main characteristics of a
tensor field. For the identical load case of figure 2, figure 3 shows an example
for a two-dimensional tensor fabric texture. The position of the plane can be
varied in the present geometry.
Figure 3: Tensor textures in a plane of the cube from fig. 2
3
STRATEGY FOR THE DESIGN OF RIBBED PLASTIC
COMPONENTS
The above introduced visualization of tensor lines and textures generates
information on load paths in plastic molded parts. This information is used to
establish a methodology which supports the dimensioning and optimization of
rib structures. It is hypothesized that a rib structure, which follows the course of
tensor lines and structures, shows an optimized design regarding stiffness and
strength. A reference component with a ribbed structure in accordance with the
164
state of the art guidelines is designed. In a next step, new rib arrangements are
introduced based on the tensor visualization methods. A comparison of the
reference structure and the structures based on tensor visualization finally
evaluates the applied method.
3.1
Reference Part: Geometry and FE-Simulation
A brake lever used for bicycling is selected as the reference geometry. The
geometry of the brake lever is shown in figure 4. It contains a ribbed structure to
increase the component’s stiffness. The ribbed structure is placed in an area of
the component which is defined in the following as the design space (see figure
4). The handle of the lever is designed as a U-shaped profile analogous to
existing components. Furthermore, the developed brake lever shows an
intended asymmetry which guarantees multiaxial stress conditions under
service load.
Figure 4:
Developed reference geometry of a brake lever with the design
space for tensor line driven structural optimization
The loads and boundary conditions of the FE-simulation are presented in figure
5. Bolts are inserted into the brake lever which constitutes the holding of the
lever during testing. The service force is applied at the highlighted surface to
represent a braking action. The value of the load is derived from dynamometer
test results that showed for different operators an average service load of 200 N
[10]. The rib structures highlighted in the design space in figure 4 should be
designed according to this load case.
165
Figure 5: Representation of the load case in the simulation
The simulation results are presented in figure 6. The high-loaded areas in the
component are determined by evaluating the von-Mises stress criterion. The
focus of the following investigations lies on the reduction of the present
maximum von-Mises stress of approx. 69 MPa as well as the increase of the
component stiffness which is defined as the slope in the force vs. deflection
curve, by implementing a more appropriate rib structure.
Figure 6: Simulation results for the reference component with marked
maximum von-Mises stress (approx. 69 MPa)
166
3.2
Rib Structure Design by Tensor Visualization
3.2.1 Method for designing rib structures
This chapter presents a method to support the ribbing of a plastic part by tensor
visualization. It is the aim to optimize the brake lever’s stiffness without
increasing its volume. The principle idea of the design concept is that a
maximum component stiffness in ribbed structures will be achieved by
positioning the ribs in the direction of the load path in the component [3]. Both,
tensor lines and textures represent this load path in a part, so that ribs in a
plastic component should follow the course of the tensor lines and textures,
respectively.
In a first step, the design space is modeled as a full body to enable the
calculation as well as the representation of the load paths in the part by tensor
visualization. A fictitious material is therefore defined in the design space with a
very low stiffness to neglect its influence on the mechanical behavior of the
brake lever. In figure 7 (a) the results of the FE-simulations are presented.
Figure 7: Visualization of the stress in the brake lever after the FE-simulation
with a filled design space
(a) von-Mises stress on the component surface
(b) Tensor lines of the major (tension, violet) and minor
(compression, green) eigenvectors
(c) Tensor textures
167
3.2.2 Developed rib structures
Based on the tensor visualizations and therefore the tensile and compression
load paths (figure 7), three different rib structures are derived for a comparison
with the reference geometry. It has to be stated that there are usually several
possible rib patterns derivable from the tensor textures. The used lines of the
tensor texture and the corresponding rib structures are shown in figure 8. No
further design guidelines are considered to determine the optimization potential
of the tensor visualization with respect to ribbing. The only restrictions in
selecting the ribs are that the developed rib structures
a) possess a nearly equal total volume compared to the reference
geometry in figure 4.
b) are processable by injection molding without any further effort.
Figure 8: Selected tensor textures as well as the corresponding components
with a new rib design
168
4
OPTIMIZATION POTENTIAL OF THE TENSOR
VISUALIZATION
4.1
Validation by FE-Simulations
The FE-simulations are used to evaluate the derived rib structures. All used
simulation parameters are retained so that the stresses in figure 6 of the
reference geometry can be directly compared to the tensor texture driven rib
structures that are shown in figure 9.
Figure 9: Developed components and the corresponding simulation results;
maximum von-Mises stress: 69 MPa (reference), 50 MPa (1), 56
MPa (2), 54 MPa (3)
169
The optimized components show lower von-Mises stress maxima. The
maximum von-Mises stress is reduced by approx. 27 %. In addition, the
simulation results show an average decrease of 8 % in the deformation of the
reference components under the same load. Therefore, all reference
geometries show a higher stiffness.
4.2
Validation by Real Component Tests
4.2.1 Production of the component
Experiments on real components are carried out to confirm the simulation
results. These components are produced by rapid prototyping techniques. The
printed components are shown in figure 10. The reference geometry is also
produced to compare the stiffness of the tested brake levers. Because the
mechanical properties of the material used by the 3D print technique are not in
accordance with the material properties used in the FE-simulations, quantitative
statements are not possible. However, it is possible to make qualitatively
statements between the reference structure and the rib structures based on
tensor visualization.
Figure 10:
New brake lever geometries, 3D print technique
4.2.2 Experimental set-up and testing
Analogous to the FE-simulation, the break lever is fixed by bolts in the test
setup (figure 11). The force is applied by a metal stamp. The transverse speed
of the stamp is 2 mm/min to ensure a quasistatic loading. The analysis of the
stiffness is provided by measuring the force that is necessary for the deflection
of the metal stamp. The components are tested until failure.
170
Figure 11:
Test setup with fixed brake lever and stamp for the load
application
4.2.3 Experimental results
The experimental results are represented as a force-displacement diagram in
figure 12. All tensor line driven rib structures show a higher stiffness than the
reference structure. Up to a deflection of 3,5 mm these rib structures show an
increase of approx. 20 % in stiffness. It is remarkable that this is almost
independent from the rib structure which proves the robustness of the method.
It is most important to define a rib structure principally according to the tensor
texture. The different possible arrangements all result in comparable stiffness
values. The difference between the maximal force to reach failure of the tensor
driven rib structures and the reference geometry is approx. 25 %. The observed
increase in stiffness of simulation is qualitatively confirmed by the experimental
results (see figure 12).
171
Figure 12:
5
Experimental force-displacement curve; comparison of the
reference component with components after an implementation of
the optimization strategy
SUMMARY AND OUTLOOK
A method is developed that uses the information in stress tensors to support the
design of suitable rib structures of plastic parts. The presented results show that
rib structures based on tensor lines and textures can increase the total stiffness
of the component and decrease the local stress peaks in comparison to an
initial design based on common design guidelines. In figure 13 the maximum
von-Mises stresses of the developed components are summarized. With a
constant component weight compared to a reference design, it is shown that
optimized structures show a reduction of the maximum stress between 19 %
and 27 %.
172
Figure 13:
Maximum von-Mises stress of the developed components
compared to the reference component
It is a worthwhile observation that a considerable reduction of the material
stressing and increase in part stiffness can be achieved independently from the
specific rib structure of the component provided that the ribs are in accordance
to the tensor lines or textures. That means that the presented procedure is
relatively robust.
A further main advantage of the developed method is that no additional
optimization tools with additional demands on computing time are needed. The
tensor lines are based on the already available information in the stress tensor
and provide the basis for the selection of an optimized component ribbing.
Thus, a new method is provided to the engineer to accomplish a load-adequate
rib positioning and utilizing the lightweight potential of plastics in a more
effective manner.
173
Literature
[1]
Brinkmann, T.
Handbuch Produktentwicklung mit Kunststoffen
Carl Hanser Verlag, 2010
[2]
Erhard, G.
Designing with Plastics
[3]
Ehrenstein, G. W.
Mit Kunststoffen konstruieren
[4]
Shoemaker, J.
Moldflow Design Guide: A Resource for Plastics
Band 10, Carl Hanser Verlag, 2006
[5]
Kratz, A.;
Meyer, B.;
Hotz, I.
A Visual Approach to Analysis of Stress Tensor
Fields
[6]
Kratz, A.;
Auer, A.;
Stommel, M.;
Hotz, I.
Visualisation and Analysis of Second-Order
Tensors: Moving Beyond the Symmetric PositiveDefine Case. Computer Graphics Forum - State of
the Art Reports, 32(1):49-74, 2013
[7]
Weinstein, D.;
Kindlmann, G.;
Lundberg, E
Tensorlines: Advection-diffusion Based Propagation
Through Diffusion Tensor Fields
Jeremic, B.;
Scheuermann, G.;
Frey, J.;
Yang, Z.
Tensor Visualization in Computational
Geomechanics
Hotz, I.;
Feng, L.;
Hagen, H.;
Hamann, B.
Physically Based Methods for Tensor Field
Visualization
[8]
[9]
[10] Mathiowetz, V.;
Kashman, N.;
Volland, G.;
Weber, K.;
Scientific Visualization: Interactions, Features,
metaphors, Volume 2 of Dagstuhl Follow-Ups,
pp. 188-211, 2011
Proceedings of the IEEE Visualization conference,
IEEE Computer Society Press, pp. 249-253, 1999
International Journal for Numerical and Analytical
Methods in Geomechanics, 26:925-944, 2002
Proceedings of the IEEE Visualization conference,
IEEE Computer Society Press, pp. 123-130, 2004
Grip and Pinch Strength: Normative Data for Adults
American Occupational Therapy Program,
University of Wisconsin-Milwaukee, 1984
174
Keywords: Component optimization, rib structures, tensor visualization
Stichworte: Bauteiloptimierung, Rippenstrukturen, Tensorvisualisierung
Autor / author:
1,2
Dipl.-Ing. Marc Schöneich
2
Prof. Dr.-Ing. Markus Stommel
3
Dr. Andrea Kratz
4
Dipl.-Mat. Valentin Zobel
4
Prof. Dr. Gerik Scheuermann
5
Dr. Ingrid Hotz
6
Prof. Dr. Bernhard Burgeth
1
E-Mail: m.schoeneich @mx.unisaarland.de
Website: http://www.lpw.unisaarland.de
Tel.: +49 (0)681 302-6526
Fax: +49 (0)681 302-6530
Universität des Saarlandes
Lehrstuhl für Polymerwerkstoffe
Campus C6 3
66123 Saarbrücken
2
Technische Universität Dortmund
Lehrstuhl für Kunststoffverarbeitungstechnologie
Leonhard-Euler-Straße 5
D-44227 Dortmund
3
Zuse-Institut Berlin
Abteilung Visualisierung und Datenanalyse
Takustraße 7
14195 Berlin-Dahlem
4
Universität Leipzig
Institut für Informatik
Augustusplatz 10
04105 Leipzig
5
DLR Braunschweig
Lilienthalplatz 7
38108 Braunschweig
6
Universität des Saarlandes
Fachrichtung Mathematik
Campus E2 4
66123 Saarbrücken
Herausgeber / Editor:
Europa/Europe
Prof. Dr.-Ing. Dr. h.c. Gottfried W. Ehrenstein, verantwortlich
Lehrstuhl für Kunststofftechnik
Universität Erlangen-Nürnberg
Am Weichselgarten 9
D-91058 Erlangen
Deutschland
Phone: +49 (0)9131/85 - 29703
Fax.:
+49 (0)9131/85 - 29709
E-Mail-Adress: ehrenstein@lkt.uni-erlangen.de
Amerika/The Americas
Prof. Prof. hon. Dr. Tim A. Osswald,
responsible
Polymer Engineering Center,
Director
University of Wisconsin-Madison
1513 University Avenue
Madison, WI 53706
USA
Phone: +1/608 263 9538
Fax.:
+1/608 265 2316
E-Mail-Adresss:
osswald@engr.wisc.edu
Verlag/Publisher:
Carl-Hanser-Verlag
Kolbergerstraße 22
D-81679 München
Tel.: +49 (0)89 99830-613
Fax: +49 (0)89 99830-225
Redaktion / Editorial Office:
Dr.-Ing. Eva Bittmann
Christopher Fischer, M.Sc.
Beirat / Advisory Board:
38 Experten aus Forschung und
Industrie, gelistet unter
175

Zeitschrift Kunststofftechnik Journal of Plastics Technology

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