Revista de Ciencias Tecnológicas (RECIT). Volumen 3 (1): 10-22
Revista de Ciencias Tecnológicas (RECIT). Universidad Autónoma de Baja California ISSN 2594-1925
Volumen 7 (1): e335. Enero-Marzo, 2024. https://doi.org/10.37636/recit.v7n1e335
Case studies
Numerical assessment and characterization of automobile high-
voltage cable coverings
Evaluación numérica y caracterización de revestimientos de cables de alta tensión para
automóviles
José Antonio Martínez–González1, Iván Juárez–Sosa2, Víctor Hugo Mercado–Lemus3,
Hugo Arcos–Gutiérrez4, Isaías E. Garduño4
1POSGRADO CIATEQ A.C., Centro de Tecnología Avanzada, Circuito de la Industria Poniente Lote 11,
Manzana 3, No. 11, Col. Parque Industrial Ex Hacienda Doña Rosa, Lerma de Villada, 52004, Estado de México,
México
2CIATEQ A.C., Centro de Tecnología Avanzada, Av. Manantiales 23-A, Parque Industrial Bernardo Quintana, El
Marqués, Querétaro, 76246, México
3CONAHCYT–COMIMSA Corporación Mexicana de Investigación en Materiales, Eje 126 No. 225, San Luis
Potosí, 78395, San Luis Potosí, México
4CONAHCYT–CIATEQ A.C., Centro de Tecnología Avanzada, Eje 126 No. 225, San Luis Potosí, 78395, San
Luis Potosí, México
Corresponding author: Isaías Emmanuel Garduño Olvera, CONAHCYT-CIATEQ A.C., Centro de Tecnología
Avanzada, Eje 126 No. 225, San Luis Potosí, 78395, San Luis Potosí, México. isaias.garduno@ciateq.mx.
https://orcid.org/0000-0002-8944-7954
Received: December 6, 2024 Accepted: February 27, 2024 Published: March 18, 2024
Abstract. – In the automotive industry, arranging wire harnesses in assembly plants requires manual work. The stiffness of the high-voltage cable
implies that personnel applies sufficient force on the cable to achieve a proper installation. Sometimes, the applied force is not strong enough; thus,
the cable is not properly installed, or the personnel gets injured, raising ergonomic concerns that need attention. The challenges arise from the
intrinsic cable characteristics such as diameter, copper type, cable strand quantity, first-layer insulator, cable insulator glue, and protective covering.
The primary objective of this research is to examine how various factors, such as cable length and protective covering, impact the mechanical
properties that influence the assembly of high-voltage cables. The methodology proposed consisted of characterizing the mechanical properties of
the high-voltage cables in a cantilever beam test to measure deflection in response to an applied force. The measured properties were contrasted
through a Finite Element Analysis of the high-voltage cable. The results validated the initial hypothesis, revealing two key findings. Firstly, the
stiffness of cables varies with increasing length. Secondly, cables with tape exhibit greater stiffness than those with conduit and cables without
covering, as detailed in the results section. In conclusion, extending cables without attachment points is recommended until the interfaces and
environment permit. Furthermore, minimizing tape for cable protection while exploring alternative safeguards can enhance stiffness and facilitate
an ergonomic installation assembly under favorable conditions. This study contributes valuable insights for optimizing high-voltage cable installation
processes in assembly plants, addressing stiffness concerns through informed choices and design considerations.
Keywords: Materials characterization; Wire harnesses; High-voltage cables mechanical properties; Automotive industry; CAE Analysis; Coverings.
Resumen. – En la industria automovilística, la instalación de arneses y cables automotrices en las plantas de ensamble requiere mucho trabajo
manual. La rigidez del cable de alto voltaje implica que el personal aplique fuerza suficiente sobre el cable para lograr una instalación adecuada.
En ocasiones, la fuerza aplicada no es lo suficientemente fuerte; por lo tanto, el cable no está instalado correctamente o el personal resulta lesionado,
lo que genera preocupaciones ergonómicas que requieren atención. Los desafíos surgen de las características intrínsecas del cable, como el
diámetro, el tipo de cobre, la cantidad de hilos del cable, el aislante de la primera capa, el pegamento del aislante del cable y el revestimiento
protector. El objetivo principal de esta investigación es examinar cómo diversos factores, como la longitud del cable y el revestimiento protector,
impactan las propiedades mecánicas que influyen en el ensamblaje de cables de alto voltaje. La metodología propuesta consistió en caracterizar las
propiedades mecánicas de los cables de alta tensión en un ensayo de viga en voladizo para medir la deflexión en respuesta a una fuerza aplicada.
Las propiedades medidas se contrastaron mediante un análisis de elementos finitos del cable de alta tensión. Los resultados validaron la hipótesis
inicial y revelaron dos hallazgos clave. En primer lugar, la rigidez de los cables varía según aumenta su longitud. En segundo lugar, los cables con
cinta exhiben una mayor rigidez que aquellos con conductos y cables sin revestimiento, como se detalla en la sección de resultados. En conclusión,
se recomienda extender los cables sin puntos de conexión hasta que las interfaces y el entorno lo permitan. Además, minimizar la cinta para
protección de cables mientras se exploran salvaguardas alternativas puede mejorar la rigidez y facilitar un conjunto de instalación ergonómico en
condiciones favorables. Este estudio aporta información valiosa para optimizar los procesos de instalación de cables de alta tensión en plantas de
ensamblaje, abordando los problemas de rigidez a través de elecciones informadas y consideraciones de diseño.
Palabras clave: Caracterización de materiales; Arneses de cables; Propiedades mecánicas de cables de alta tensión; Industria automotriz; Análisis
CAE; Recubrimientos.
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1. Introduction
Currently, most of the main global automotive
enterprises tend to virtualize all the components
and systems of the vehicle in each vehicle
platform to evaluate them before each assembly
is built. This is a cost avoidance that all the
automotive brands want. It is important to
mention that not all automotive systems are well
represented in the virtual world due to the
complexity and the variety of all the components'
spectrum; for example, the automotive wiring
and cable coverings, usually the mechanical
information about those coverings are used
applying an average to get a rough
approximation. However, the mechanical
behavior of the wire harness is complicated by its
complex geometry and the number of materials
involved. As these are prestressed and loaded in
service, a complicated stress state condition
arises that combines the effects of tension,
torsion, bending, and shear along with multiple
non-linear phenomena such as cable-to-cable or
cable polymer motion (the relative motion
between cables), contact, friction, plasticity, and
large deformation.
One of the most failed assessments in the
assembly plant is the installation of high-voltage
cables. These cables face ergonomic problems
due to difficulties in the assembly vehicle line
cyclic processes, where mechanical stress is
being carried out above the established values [1-
3], affecting pre-productive and productive build
stages to the overall assembly plants [4]. Some
solutions to wiring and cables are being studied
to help with creative ideas to solve the main
difficulties presented in the assembly process.
One of them is manual installation, e.g., a
solution is the use of automation to achieve
hybridization of human-robot collaboration
(HCR), and this hybridization helps to alleviate
the installation effort [5, 6]. Furthermore,
implementing new technologies can significantly
increase the automation degree and product
quality by using intelligent manufacturing
technologies to overcome the challenges and
drawbacks of optimization solutions and the
current state of production [7]. The main factors
that generate harness installation difficulties are
listed below:
1. The human-manual process of
constructing an automotive harness, for example,
the distance between turns of tape, number of
turns, and tape speed [8-11].
2. The environment in the place where the
harness is installed on the vehicle, for example,
areas with low temperatures where greater
installation problems have been demonstrated,
causes damage to operators, their perception of
rigidity increases, and it is sometimes necessary
to install cable heaters to facilitate assembly [12].
3. Violation of double radii in the harness
design causes excessive effort in handling very
tight curves [13, 14].
4. Material and number of wires in the
wiring where the lower the number of wires, the
greater the resistance to being bent has been
tested [15].
5. Type of insulating material (first
coating). This refers to material selection due to
flexibility and temperature resistance [16].
6. Types of tapes for the protection of high
voltage cables made with materials that are more
rigid than others [17-20].
All the mentioned factors are agents that cause
overexertion in installing high-voltage cables, all
listed arbitrarily, without implying their level of
importance by their position. It can be said,
therefore, that the case of greatest ergonomic
criticality would be that high voltage cable that
combines all the above characteristics. This
research will focus on the selection of coverings
and the relationship between length and the
ergonomic performance of a high-voltage cable.
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After considering the information provided, it is
important to ask the following questions:
1. Could the selection with ergonomic
criteria of coverings for an automotive high-
voltage cable directly relate to deformation
resistance that could impact the performance in
the assembly plant installation?
2. Could the length of an automotive high-
voltage cable directly relate to the deformation
resistance that could impact the performance in
the assembly plant installation?
The research will focus on the selection of
coverings and their relation to the length of high-
voltage cables or any electrical harness. This
focus is motivated by the thorough examination
of other factors listed in installation issues in
previous studies [21-24]. The innovative aspect
of this research lies in addressing an area that has
not been extensively evaluated in the early design
stages of an engineering process: the selection of
coverings [25]. This gap exists due to insufficient
information on the mechanical characteristics of
automotive tapes. By conducting this evaluation,
the research aims to prevent the creation of
branches and covered wiring that, despite being
feasible in Computer-Aided Design (CAD)
software, are difficult to handle during
installation in assembly plants. Such difficulties
can lead to serious production problems,
including ergonomic issues for operators [27],
work accidents [28], and compromised product
quality, prompting companies to invest
significant resources in redesign efforts.
Some authors [29] did extensive research on the
dynamic stress and post-breakage behavior of a
prestressing strand and proposed a finite element
model that is generally useful to study the global
response of the strand, along with many localized
phenomena that have a strong influence on their
performance, but which are difficult to capture
either experimentally or through closed-form
analytical models [30, 31]. However,
investigations into certain behaviors, such as
cable breakage, require a relatively large or full-
scale model to adequately develop contact and
friction conditions [32]. Through a study of this
state-of-the-art, others describe the
manufacturing processes and analyze where the
manufacturing complexity of the component
originates. Another work that provides a process
to characterize the behavior of the wiring
harnesses was developed by Ehsan Taghipour et
al. [33-35], who explained the analysis and
computational modeling to evaluate electrical
wires, especially dynamic mechanical analyses
to investigate the viscoelastic properties of self-
adhering synthetic rubber, and to identify the
parameters of a viscoelastic model that be
accurate and represent the frequency dependent
on dynamic mechanics [36-38]. Therefore, the
intention and improvement of this research are to
provide predictions according to some scenarios
studied without being in a current application.
Consequently, this research aims to feed the
SIMSOLID finite element software database to
improve the accuracy of the mechanical analyses
and to predict the behavior of the cables in a
shorter time before the vehicle assembly process,
correcting and improving the components so that
they can be installed ergonomically, saving time
and without the associated cost.
This manuscript is organized as follows: Section
2 details the equations employed to calculate the
parameters to characterize the mechanical
properties of the high-voltage cables. Section 3
details the methodology and design of
experiments, including the geometry of the high-
voltage cable and the boundary conditions used.
Section 4 presents the characterization of the
properties of the high-voltage cables.
Additionally, it presents the results of the finite
element method of the high-voltage cable and
compares them to the experimental results.
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Finally, in Section 6, conclusions are
summarized.
2. Methods
The material under study does not exhibit a linear
response, implying that its behavior is best
described by a non-linear elastoplastic model,
which considers the material's ability to deform
under stress and its tendency to retain some
plastic deformation after removing it. Regarding
the material properties characterization of the
cable and its protective covering, it is necessary
to analyze the force-deflection data and convert
it into stress-strain data. This will allow for
calculating important parameters such as the
Elasticity Module, Poisson Ratio, and Yield
Stress for the linear region of the cable's
behavior. Calculating the non-linear region's
strength coefficient and strain hardening
exponent is also important to completely
understand the cable's mechanical properties.
The deflection cantilever beam equations show
the relationship between the force-deflection and
stress-strain curves [33].
The elasticity module E, which was only used for
the linear region, was calculated as follows:
Where:
Substituting I in equation 1:
Recognizing the non-linear behavior of an
elastoplastic material is crucial to
comprehending the two primary equations that
describe the strain-stress curve. The first region
is divided into the elastic and non-linear regions,
separated by the yield strength. By grasping the
concept of these regions, one can gain an in-
depth understanding of the behavior of an
elastoplastic material under various conditions.
According to the behavior of the cables and
coverings, Hollomon's proper equation used in
this manuscript to get the stress-strain charter
was defined by Power Law given by Ehsan
Taghipour et al. [33].
Total stress is defined by the stress at yield plus
the strain hardening behavior in the function of
strain, strength coefficient, and strain hardening
exponent values. Thus, starting with the elastic
region, the stress could be calculated with
equation (5), defining the lineal region in the
force-deflection plot.
Once it was calculated the stress and the elasticity
module for each point over the linear region, it is
also possible to calculate the strain in the elastic
region with equation (6):
At this point, the elastic region was determined,
so now it is possible to proceed with the non-
linear region, calculating the exponent strength
coefficient and strain hardening to get the non-
linear behavior. The first point to calculate n and
K that will be used in the elasticity module in the
non-linear region is to follow the procedure
extracted from Ehsan Taghipour et al [33].
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Where is the tangent elastic module at yield,
defined by the numeric derived from the last two
points of the elastic region, and the linear
estimation of all points of the elastic region
defines E.
Once the previous values were obtained, it is
necessary to calculate a first estimation of K.
The correct value of the exponent strength
coefficient and strain hardening is not yet found;
the initial. It is a small portion of the linear
ending and non-linear starting of the curve, and
it will probably not be the correct one. It is
needed to find the correct direction of the curve
where the unique value known is the final
maximum deflection.
Hence, it is indispensable to use the initial values
exponent strength coefficient and strain
hardening to find the correction of but now, in
the non-linear region .
Where is the estimation of the elasticity
module at the non-linear region, is the stress in
the small portion of the , and is the stress at
the yield point.
Finally, it is necessary to iterate the values
obtained from the previous calculations into the
Finite Element Method (FEM) to get an answer
and get the maximum virtual deflection. Thus, if
the result with the previous values is accepted
with an error of 0.005 between the virtual
deflection and the real deflection, it can be
considered the characterization finished for that
sample. The error is calculated with the
following equation.
3. Methodology
The methodology implemented in this research
is explained as follows:
1. Define the experimental conditions to bend
the cables and obtain values of force vs.
deflection using the cantilever beam test.
2. Perform force/deflection experiments for
each combination of lengths and protection
covering of the high-voltage cables.
3. Characterize the values from the force-
deflection test to incorporate them into the
equations, resulting in the stress-strain
evaluation. The latest brings experimental
support to understanding the behavior of the
cables in terms of the elasticity module, Poisson
ratio, strength, coefficient, and hardening
component.
4. Input the obtained values into the CAE
software (E, υ, n, and K) for the mechanical
analysis.
5. Iterate the values obtained from the CAE
analysis to achieve a maximum deflection
consistent with the physical model.
The methodological steps are summarized in
Figure 1.
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Figure 1. Summary of the methodology proposed.
3.1 Deflection test
When describing the deflection of a cantilever
beam, it refers to the bending or displacement
resulting from an external load applied to the
beam's free end. A cantilever beam is a structural
element fixed at one end but extending freely into
space, capable of carrying loads at its
unsupported end. The cantilever beam fixation
technique was necessary to accurately measure
the deflection force and generate a precise
bending curve that could approximate the
behavior of the cables in real-life installation
scenarios. The tensile test was performed using
the Instron tensile machine model 3400 Series of
1 kN, as highlighted in Figure 2. The procedure
carried out within the laboratory took place under
controlled conditions with a pressure of 1
atmosphere and a temperature of 23 °C. Two
samples were prepared with 100 mm, 200 mm,
and 300 mm dimensions.
Figure 2. High-voltage cable with tape covering deflection test at INSTRON Machine.
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During the cantilever beam deflection
experiment (see Figure 3), a high-voltage cable
was subjected to a rigorous test to determine its
strength and durability. The process involved
securing the cable with a tensile grip, leaving a
50 mm distance between the grip and the cable.
A steel cable with a mobile grip on one end
applied tension in a diagonal direction, causing
the high-voltage cable to deflect. The mobile grip
was centered directly over the fixed point, and it
contained a load cell model 2519-105 that was set
to move at a speed of 300 mm/min.
Figure 3. Diagram of the cantilever beam deflection experiment.
A high-voltage cable comprises a central core of
conducting material surrounded by an insulating
layer that protects the conductor from external
influences. The cable characteristics are
presented in Table 1. The insulating layer is
further enclosed by a shielding layer that
provides additional protection and prevents
electrical interference (see Figure 4). Together,
these three components make up the structure of
a high-voltage cable, which is essential for the
efficient and safe transmission of electrical
power over long distances.
Figure 4. High-voltage cable (a) front view and (b) right-side view.
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Table 1. High-voltage cable technical characteristics.
Conductor
Core
Screen
Cable
Constructio
n
Diameter
Wall
thickness
Diameter
Constructio
n
Wall
thickness
Diameter
N x Ømax.
[mm]
[mm]
[mm]
[mm]
N x N x
Ømax.
[mm]
[mm]
1600 x 0.21
10.5
0.71
12.2
24 x 9 x
0.21
0.88
15.2
The tape used to cover the cables is Coroplast
8375-X (see Figure 5b); these polyester cloth
tapes are designed for wire harness applications.
The heat-resistant PET-cloth tape is designed for
a solid and spiral taping of cable sets and wire
harnesses with abrasion-resistant and high tensile
strength properties. For the experiments, the tape
was manually added in a spiral conformation
with an overlap of approximately 50%. The
properties of the tape are presented in Table 2.
Figure 5. High-voltage cable and high-voltage cable with cover samples. (a) Cable, (b) Cable with conduit, and (c) Cable with
tape Coroplast 8375-X
Table 2. Dimensions and mechanical properties of tape Coroplast 8375-X for high voltage cables.
Carrier
Thickness
Widths
Length
Tensile Strength
Elongation at break
[mm]
[mm]
[m]
[N/cm]
%
PET-cloth
0.27
9, 15, 19 and 25
25
240
27
On the other hand, the Conduit is a protective
enclosure for high-voltage cables, providing
insulation and safeguarding the cables from
external environmental factors, mechanical
damage, and potential heat sources, as presented
in Figure 5c. In this case, the Conduit employed
is made of a high-heat impact modified
Polypropylene (MPP). For high-voltage cable
conduits that require resistance to high heat and
impact, Modified Polypropylene (MPP) is
commonly used. Modified Polypropylene is a
type of Polypropylene that has been enhanced
with additives or modifiers to improve its
performance characteristics. These modifications
may include reinforcements, flame retardants,
and impact modifiers, making it well-suited for
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applications where both high heat resistance and
impact strength are crucial. Some important
parameters are tensile strength greater than 27.5
MPa, elongation at break >50%, and 1.15 g/cm3
density.
The proposed experiment was developed using
high-voltage cables and mechanical protection
(Tape and Conduit). The experiments utilized
various combinations of cable length and
covering, listed in detail in Table 3 for easy
reference.
Table 3. High-voltage cable lengths and cable coverings tested.
Type
Length
[mm]
Cable without any
protection
100 mm of length,
75mm efficient length
200 mm of length,
140mm efficient
length
300 mm of length,
245mm efficient
length
Cable with Tape
Cable with Conduit
4. Results and discussions
4.1 Characterization of the properties of the
high-voltage cables: force/deflection
experiments
The experimentation process described
previously involved utilizing the prepared cables
and setup. The experiments was based on this
plan, aiming to study the force/deflection
behavior. The following section will provide a
detailed discussion of the results and outcomes of
the experimentation process. The behavior of
forces and deflection for covered and uncovered
100 mm cables is illustrated in Figure 6. The
deflection range for all tests is between 0 and 1.
The graph depicts the initial linear behavior,
followed by the non-linear start point at
approximately 0.1 mm, and ultimately, the non-
linear behavior until 1.0.
Figure 6. Experimental Force/Deflection responses for a
high-voltage cable length of 100 mm and various covers.
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The data plotted in Figure 7 illustrates the
relationship between the forces applied and the
deflection of two 200 mm cables, one with and
one without coverings. The deflection is the total
amount experienced during all tests, expressed
from 0 to 1 mm. The data distribution
demonstrates that the cables exhibit initial linear
behavior, followed by non-linear behavior
starting at approximately a deflection of 0.1 mm.
The non-linear behavior persists until the cable
reaches a deflection value of 0.8 mm. This
indicates that the cable has a soft behavior,
meaning that the force required to bend the cable
is not completely linear.
Figure 7. Experimental Force/Deflection responses for a high-voltage cable length of 200mm and various covers.
The results presented in Figure 8 depict the
relationship between the forces applied to 300
mm cables and their corresponding deflection
values, both with and without coverings. The
deflection values range from 0 to 1 mm and are
cumulative for all the tests performed. The graph
shows the cable's initial linear behavior and a
non-linear start-point at approximately 0.05 mm
deflection. Subsequently, the cable's behavior
becomes increasingly non-linear until it reaches
deflection values ranging from 0.1 mm to 0.9
mm, indicating softer behavior. The force
response required to bend the cable becomes
linear during this stage. The difference between
the cable curve before this stage and the
subsequent one is significant, emphasizing the
cable's changing behavior.
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Figure 8. Experimental Force/Deflection responses for a high-voltage cable length of 300 mm and various covers.
4.2 Computation of effective properties
through force-deflection values
The equations presented were utilized to analyze
the mechanical behavior of 100 mm cables. The
values of ε and σ were charted, and the acquired
data was used to provide the necessary curve
information to create a 3D model and fully
characterize the behavior of the cable. Figure 9
displays this behavior and serves as a visual aid
to better understand the cable's mechanical
properties. In this case, the comparison of cable,
tape, and Conduit as it is shown that the cable
with Conduit is deformed with less stress, the
cable without protection in second place, and
finally, the cable with tape has the stiffness
behavior; the deformation increases as the
reaction of the force applied to bend it.
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Figure 9. Stress-strain curves for high-voltage cables 100 mm in length.
Figure 10 depicts the behavior of the 200 mm
cables based on the equations presented earlier in
Section 2. The corresponding mechanical
behavior is obtained through the values of ε and
σ and presents the curve information to
characterize the cable. When it comes to these
200 mm cables, the behavior of the cable without
protection and the cable with tape had more
similarities when compared to the cable with
Conduit. This similarity is related to the relation
between the length and covering stiffness of the
cables. The comparison between cable, tape, and
Conduit results indicates that cable with Conduit
experiences less deformation under stress,
followed by cable without protection. The
stiffness behavior of the cable with tape is similar
to that of the unprotected cable. It was observed
that the degree of deformation increases with the
magnitude of the applied force used to bend the
cable.
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Figure 10. Stress-strain curves for high-voltage cables 200 mm in length.
Now, the attention goes to analyzing the behavior
of 300 mm cables. Thus, Figure 11 displays the
data generated by those equations, showing the
mechanical behavior of the cables. The data
collected from these cables could be used to
characterize them. Interestingly, the behavior of
the cables without protection, with tape, and in
Conduit showed similar patterns. The length of
the cables and the stiffness of their coverings may
be closely related, which could explain these
similarities. In this case, the comparison of cable,
tape, and Conduit as it is shown that the cable
with Conduit is deformed with much less stress,
followed by the cable without protection, and in
this experiment, cable sample (2) and tape
experiment (1) have almost the same behavior, it
is shown that the deformation against the force is
not the most important factor, in this case, the
length support to reduce the stiffness of the cable.
Figure 11. Stress-strain curves for high-voltage cables 300 mm in length.