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Modelo
matemático para el análisis del comportamiento térmico en el proceso de
soldadura de un acero estructural mediante un software con base en el métod=
o de
elementos finitos
Mathematical model for the analysis of the ther=
mal
behavior in the welding process of a structural steel using software based =
on
the finite element method
Artículo de Investigación Científica y
Tecnológica
Enviado: 13 /05/2022
Revisado: 22 /06/2022
Aceptado: 01/07/2022
Publicado:29/07/2022
DO=
I: https://doi.org/10.33262/concienciadigital.v5=
i3.1.2254
<=
o:p>
=
Cítese: <=
/o:p>
Villacís Ramón, M. E., & Yaulema Castaneda, =
J.
L. (2022). Modelo matemático para el análisis del comportamiento térmico =
en
el proceso de soldadura de un acero estructural mediante un software con =
base
en el método de elementos finitos. ConcienciaDigital, 5(3.1), 289-314. https:=
//doi.org/10.33262/concienciadigital.v5i3.1.2254
CONCIENCIA DIGITAL, e s una
revista multidisciplinar, trimestral, que se publicará en
soporte electrónico tiene como misión contribuir a
la formación de profesionales competentes con visión humaníst=
ica
y crítica que sean capaces de exponer sus resultados investigativos y
científicos en la misma medida que se promueva mediante su intervención
cambios positivos en la sociedad. https://concienciadigital.org
La revi=
sta
es editada por la Editorial Ciencia Digital (Editorial de prestigio
registrada en la Cámara Ecuatoriana de Libro con No de Afiliación 663) www.celibro.org.ec
Esta r=
evista
está protegida bajo una licencia Creative Commons Attribution Non Commerc=
ial No
Derivatives 4.0 International. Copia de la licencia: http://=
creativecommons.org/licenses/by-nc-nd/4.0/
Palabras claves: modelo matemático, GMAW,
simulación numérica, software CAE, método de elementos finitos, zona afec=
tada
térmicamente.
Resumen
Introducción: Un proceso de soldadura para unir dos piezas de
trabajo con la presencia de un arco eléctrico está ligado a un sistema
dinámico representado por la interacción de dos ecuaciones de gobierno. <=
/span> Objetivos: el objetivo general de esta investigación fue
desarrollar un modelo matemático para el análisis del comportamiento térm=
ico
en el proceso de soldadura por arco eléctrico GMAW de un acero estructura=
l. Metodología: haciéndose una
investigación del tipo propositiva descriptiva, con un alcance descriptiv=
o,
un enfoque cuantitativo, Por otro lado, se utilizó la metodología de la
simulación numérica con la técnica del Método de los Elementos Finitos (M=
EF)
y el instrumento principal que se manejó para procesar toda la información
recopilada fue un software CAE (Computer Aided Engineering). Resultados: se encontró las
soluciones aproximadas de la interacción de la ecuación diferencial parci=
al
(EDP) de conducción de calor y la ecuación de la fuente móvil de Goldak, =
con
el fin que se dio a conocer una propuesta que terminó con la parte analít=
ica,
descriptiva de la temperatura máxima del arco eléctrico, las curvas
isotérmicas y la Zona Afectada Térmicamente (ZAT) de una probeta virtual =
para
un tiempo determinado. Para la validación teórica del modelo propuesto se
utilizó otro software CAE. Concl=
usiones:
se concluye que el modelo matemático desarrollado es eficiente y váli=
do
ya que para un tiempo específico se obtuvieron los errores relativos de 2=
,43
% y 1,01 % al comparar las temperaturas máximas=
del
cordón y la longitud útil de la ZAT respectivamente.
Keywords: mathematical model, GMAW, numerical simulation, CAE software, fini=
te
element method, heat affected zone
Abstract
Introduction:
A welding process to join two pieces of work with the presence of an elec=
tric
arc is linked to a dynamical system represented by the interaction of two
governing equations. Objectives:=
The general objective of this research was to develop a mathematical model
for the analysis of thermal behavior in the GMAW electric arc welding pro=
cess
of a structural steel. Methodolo=
gy:
making an investigation of the descriptive propositional type, with a
descriptive scope, a quantitative approach, On the other hand, the
methodology of numerical simulation was used with the technique of the Fi=
nite
Element Method (MEF) and the main instrument that was handled to process =
all
the information collected was a CAE software (Computer Aided
Engineering)." Results: the approximate soluti=
ons of
the interaction of the partial differential equation (EDP) of heat conduc=
tion
and the Goldak mobile source equation were found, to present a proposal t=
hat
ended with the analytical, descriptive part of the maximum temperature of=
the
electric arc, the isothermal curves, and the Thermally Affected Zone (ZAT=
) of
a virtual specimen for a given time. For the theoretical validation of the
proposed model, another CAE software was used. Conclusions: it is concluded that the mathematical model
developed is efficient and valid since for a specific time the relative
errors of 2.43% and 1.01% were obtained when comparing the maximum
temperatures of the cord and the useful length of the ZAT, respectively.<=
o:p>
=
&n=
bsp;
&n=
bsp;
Introdu=
cción
En el Ecuador existen va=
rios
problemas en diferentes áreas de la construcción relacionados con el
comportamiento térmico representados por ecuaciones de gobierno, estas
ecuaciones mandatarias pueden ser desde unidimensionales hasta tridimension=
ales
ligadas a sistemas dinámicos donde sus soluciones y descripciones cuantitat=
iva,
cualitativa permiten analizar, medir, estimar y predecir el comportamiento =
del
evento en cuestión. Es entonces en este tipo de procesos donde hace
aparición la modelización numérica
y su respectiva simulación con el método de elementos finitos, que
permite definir una de las mejores aproximaciones de soluciones matemáticas=
que
surgen en la industria metalmecánica, por tal motivo varios países extranje=
ros
utilizan diversas herramientas
informáticas que incluyen este método para obtener una herramienta eficient=
e a
la hora de brindar soluciones para los diferentes problemas con condiciones
iniciales y de frontera. El presen=
te estudio
considera los parámetros del proceso de soldadura GMAW, las dimensiones de =
una
probeta virtual, así como el tipo de junta a tope, las propiedades físicas,
térmicas del material base (acero estructural ASTM A36) dependientes de la
temperatura, las condiciones iniciales y de contorno para resolver las
ecuaciones de gobierno que representan el fenómeno.
Proceso
de soldadura por arco eléctrico GMAW
Este
proceso de soldadura emplea un arco eléctrico entre un alambre que es
alimentado de manera continua y la pieza a soldar, este alambre es un elect=
rodo
continuo de metal de aporte. La Sociedad Americana de Soldadura de sus sigl=
as
en inglés AWS (American Welding Society)” identifica a este proceso =
como
GMAW que proviene del inglés “Gas Metal Arc Welding”.
Figura 1
Descripción del proceso de soldadura GMAW
Fuente: Dávalos (2017)
Zona afec=
tada
térmicamente ZAT: “Es aquella parte de metal en la fusión, que fue
modificada por el calor entre la zona fundida y el límite del metal de base”
(BFMéxico, 2017), ver figura 2. En la figura 3 se presenta la investigación
realizada por V. Tsegelsky en su manual titulado “The Electric Welder”, esta
obra está registrada en el libro de Horwitz (1997), donde se presenta un
diagrama que indica la temperatura donde empieza la ZAT (200 ͦ C aprox=
imadamente)
hasta llegar al punto de fusión o temperaturas mayores que se presentan en =
un
proceso de soldadura para un acero estructural ASTM A36. <=
/span>
Figura 2
Elementos de una unión soldada
Fuente: Pintado (2018, p.18)=
Figura 3
Diagrama de la ZAT de un acero con bajo contenido de carbono
Fuente: Horwitz (1997, p.515)
Material
base: acero de bajo carbono ASTM A36.- Los aceros
ASTM A36 son aceros estructurales de bajo contenido de carbono que cumplen =
los
requisitos de las normas ASTM A36/ A36M. Según Stamenkovic & Vasovic
(2009), “las propiedades térmicas del material ASTM A36 dependen de la
temperatura en la zona afectada por el calor (ZAT)” (p.2). A continuación, =
en
la tabla 1 se presentan las propiedades del material en función de la
temperatura.
Tabla 1
Variación de las propiedades térmicas del material
ASTM A36
Temperatura (°C)
Calor específico (J/Kg °=
C)
Conductividad (W/m°C)
Densidad (Kg/m3)
Coeficiente de expansión
térmica (10-5 /°C)
0
480
60
7850
1,15
100
500
50
7850
1,20
200
520
45
7800
1,30
400
650
38
7760
1,42
600
750
30
7600
1,45
800
1000
25
7500
1,45
1000
1200
26
7390
1,45
1200
1400
28
7300
1,45
1400
1600
37
7250
1,45
1550
1700
37
7180
1,45
Fuente: Stamenkovic & Vasovic (2009)
Ecuación
diferencial parcial de conducción de calor
En
un proceso de soldeo es necesario conocer el historial de la temperatura de=
una
placa tridimensional, haciéndolo un problema transitorio debido al ciclo de
enfriamiento-calentamiento. En el proceso de soldadura se generar transfere=
ncia
de calor por conducción en el momento que se crea el arco eléctrico, entre =
el
punto de contacto del electrodo con el material base, hasta los puntos
adyacentes de la zona de soldadura (Pintado, 2018). En la figura 4 se prese=
nta
el volumen diferencial para el análisis tridimensional de calor.
Figura 4
Volumen diferencial para el análisis tridimensiona=
l de
calor
Fuente: Holman (1999)
Elaborado por: Villacís
(2022)
Realizando
el balance de energía se tiene:
Donde
son las
energías que ingresan por conducción,
es el calor generado en el interior del =
elemento,
son las
energías que salen por conducción y
es la var=
iación
de la energía interna. Empleando la expansión de la serie de Taylor y
deducciones matemáticas la Ecuación 1 se transforma en la siguiente ecuació=
n:
Donde
la expresión 2 es una ecuación diferencial parcial no-lineal si las propied=
ades
del material
están en =
función
de la temperatura. En la Ecuación 2 el primer término representa la conducc=
ión
de calor, el segundo término
(x, y, z, t), es la fuente de generación de calor =
y el
último término representa la razón de cambio de energía interna (Hernández =
et
al., 2013). Si se considera que el
material base es un material isotrópico, se puede concluir que las
conductividades térmicas son las mismas:
. Adicionalmente se utiliza el operador diferencia=
l
Al reemplazar estas expresiones en la Ecuación 2 se
tiene:
Donde:
Ecuación
de la fuente móvil de Goldak
En el proceso de soldadura por arco eléctrico GM=
AW
se tiene una fuente de calor en movimiento, muy concentrada, que incide sob=
re
la junta, el calor en las placas se transfiere rápidamente por el mecanismo=
de
conducción y existe pérdidas de calor por convección, el cual además es
favorecido por la alta conductividad térmica que presenta el metal base al
llegar a la temperatura de fusión (Berrío et al., 2010). El modelo propuesto por Goldak consiste=
en
una fuente volumétrica conocida como doble elipsoide, en donde la distribuc=
ión
de flujo térmico es de tipo gaussiana a lo largo del eje longitudinal (Garc=
ía,
2019, p.257).
Figura 5
Fuente de calor de doble elipsoide
Fuente: Osmar (2016)
Es
así como la expresión matemática de la distribución de la densidad de energ=
ía
en el interior del cuadrante frontal es la siguiente:
Para los puntos que se encuentran en el cuadrante
posterior viene dado por:
Donde: =
A los coeficientes
y
también s=
e los
denomina fracciones de entrada de calor.
Ecuación del flujo de calor o densidad media de
potencia.
La distribución de energía que se produce en la fu=
sión
de los materiales presenta una ecuación que se deriva de la distribución
Gaussiana. Es así como Hitesh et al. (2013), relaciona la energía producida=
por
el arco eléctrico y el diámetro del electrodo como se observa en la Ecuació=
n 8.
Desglosando cada término se tiene:
Flujo de calor en la superficie <=
/i>
La
probeta tiene fronteras superficiales expuestas a una fuente de calor, esta
condición de borde menciona que el flujo de calor es constante en la superf=
icie
del cuerpo y se relaciona con el gradiente de temperatura; adicionalmente c=
on
esta situación, se puede colocar pérdidas constantes en la superficie (Lópe=
z &
Montenegro, 2008, p.35):
Donde:
Flujo de calor mediante la Ley de Newton
Esta ley asume que la pérdida de calor en las
superficies de la probeta virtual es proporcional a la diferencia entre las
temperaturas superficial Ts y ambiental T∞ o la temperatura del
alrededor, a través del coeficiente de transferencia de calor de convección=
(Hernánd=
ez et
al., 2013, p.1025). Por lo tanto:
La ecuación anterior también se puede formular de =
la
siguiente manera:
Donde: =
Metodología
Esta
investigación es del tipo propositiva-descriptiva; descriptiva porque se bu=
sca
la caracterización de un fenómeno y propositiva ya que este nivel de estudio
permite tomar la mezcla de las teorías existentes de las ecuaciones de gobi=
erno
que están relacionadas directamente al hecho particular o fáctico siendo es=
te
el comportamiento térmico del proceso de soldadura GMAW de un acero estructural; este estu=
dio no
se concluye solamente relacionando la teoría con el fenómeno sino se preten=
de
dar una solución de manera integral, consistente, profunda a modo de iniciativa a la cual=
se le
denomina propuesta (modelo matemático). Adicionalmente se tiene el apoyo de=
una
variable temática que es realizar una simulación con un software CAE con ba=
se
en el MEF. La investigación propositiva no tiene como requisito la
implementación de la solución, esta termina con la parte analítica y
descriptiva, cuya propuesta encontrada ya corre por cuenta de las empresas,
instituciones, fábricas, talleres, etc. evaluarla y en el mejor de los casos
implementarla. Adicionalmente se utilizó la metodología de la simulación
numérica con el Método de los Elementos Finitos.
Plan
de simulación. – La figura 6 presenta el plan de simulación numéric=
a.
Figura 6
Esquema del proceso de la
metodología para obtener una solución
Fuente: Goldak & Akhlaghi (2005)
Elaborado por: Villacís =
(2022)
Primera f=
ase.
- Existen algunos estudios que han desarrollado dive=
rsos
modelos desde estadísticos, analíticos, numéricos etc. para conocer el
comportamiento térmico de procesos de soldadura, los cuales sirvieron de ba=
se
para presentar los parámetros para la simulación de este estudio (ver tabla=
2):
Tabla 2
<=
span
style=3D'mso-bookmark:_Hlk81985521'>Par <=
span
style=3D'mso-bookmark:_Toc97969380'>á metros necesarios para la simulación del proceso GMAW
Parámetros
Nomenclatura
Valor (unidades)
Tensión de soldadura
V
19 V
Corriente de soldadura
I
180A
Eficiencia de soldadura
η =
0,8
Tiempo de soldadura promedio
tpr
65 seg =
Velocidad de soldadura constante
Vm
2,307 x 10-3 m/seg
Temperatura ambiente
Ta
20 ºC <=
span
style=3D'font-size:10.0pt;font-family:"Times New Roman",serif;mso-ansi-la=
nguage:
ES-EC'>
Posición de soldadura
-
Plana <=
span
style=3D'font-size:10.0pt;font-family:"Times New Roman",serif;mso-ansi-la=
nguage:
ES-EC'>
Diámetro del electrodo
D
1,2 x 10-3 m
Tipo de junta
-
A tope =
Ancho probeta virtual (simetría)
A
0,05 m =
Longitud de la probeta virtual
L
0,15 m =
Espesor de la probeta virtual
E
0,006 m
Ancho del cordón de soldadura
E
0,006 m
Longitud del cordón de soldadura
L2
0,15 m =
Espesor del cordón de soldadura
e
0,006 m
Fuente: =
Fosca (2007) y Pintado (2018)
Elaborado por: Villacís =
(2022)
Segunda F=
ase.
- Las dos ecuaciones de gobierno son la (Ecuación 5)=
y
la segunda (ecuaciones 6 y 7) es la expresión que define la fuente movil de
calor de Goldak. En la tabla 3 se presentan los valores necesarios calculad=
os
que se reemplazan en las ecuaciones 6 y 7, el conjunto ecuación-datos se
ingresan al software CAE con las dimensiones, coordenadas y posiciones
adecuadas de la probeta virtual.
Tabla 3
Par <=
span
style=3D'mso-bookmark:_Toc97969381'>á metros del Modelo de Goldak
Parámetros
Nomenclatura
Valor (unidades)
Parámetro adimensional
n
1,189 <=
span
style=3D'font-size:10.0pt;font-family:"Times New Roman",serif;mso-ansi-la=
nguage:
ES-EC'>
Longitud de la elipse frontal
af
1,482 x 10-3 m
Longitud de la elipse posterior
ar
3,518 x 10-3 m
Ancho de la fuente de calor
b
1,2 x 10-3 m
Profundidad de la fuente de calor
cc
4,802 x 10-3 m
Fracción de entrada de calor frontal
ff
0,593 <=
span
style=3D'font-size:10.0pt;font-family:"Times New Roman",serif;mso-ansi-la=
nguage:
ES-EC'>
Fracción de entrada de calor trasera
fr
1,407 <=
span
style=3D'font-size:10.0pt;font-family:"Times New Roman",serif;mso-ansi-la=
nguage:
ES-EC'>
Fuente Villacís (2022)
Tercera
fase. - Dentro de esta fase se realiza lo que básicamente =
es
la metodología de la simulación numérica con el Método de los Elementos Fin=
itos
MEF, con la aplicación y utilización de un software de ingeniería asistida =
por
computadora (Software CAE).
Metodología
de la simulación con un software CAE con base en el MEF
En
la figura 7 se presenta el diagrama de proceso de la aplicación al MEF.
Figura 7
Diagrama del proceso de aplicación al MEF<=
/span>
Fuente: Pérez & Romero (2017)<=
o:p>
Elaborado por: Villacís (2022)
Etapa de pre-procesamiento
Modelo geométrico de la probeta virtual. - =
La pieza =
de
trabajo se dibujó en el contorno gráfico del mismo software CAE siendo éste=
el
programa COMSOL como se aprecia en la figura 8. La unión es una junta a top=
e.
Figura 8
Representación en 3D del
conjunto junta a tope
Elaborado por: Villacís (2022)
Modelo
discreto: forma y tipo de la malla. - Se logro la convergencia de la solución en la malla
fina.
Figura 9
Refinamiento y selección d=
el
modelo discreto
Elaborado por: Villacís (2022)
Propiedad=
es
del material base. - Con la ayuda de los valores de la tabla 1 y su
respectiva conversión a grados Kelvin se presentan las siguientes funciones=
:
Tabla 4
Propiedades del material en función de la temperatura
Fuente: Villacís (2022)
Condiciones
iniciales. - Las condiciones iniciales se establecen en un tiem=
po
Fuente: Villacís (2022)
Condicion=
es
de contorno. - =
En la tabla 6 se presentan las condiciones de cont=
orno
o frontera.
Tabla 6
Condiciones de contorno para la simulación
Fuente: Villacís (2022)
En la figura 10 se muestran los respectivos domini=
os.
Figura 10
Probeta virtual con sus
dominios Ωn, en la herramienta computacional
Fuente: Villacís (2022)
Etapa
de procesamiento
Una
vez que el programa con el método MEF se ha ejecutado, es decir el “solver”
(solucionador del software CAE) ha generado la información necesaria, en un
archivo se muestra la solución de manera gráfica en diferentes tiempos (Ver=
figura
11).
Figura 11
Simulación computacional e=
n un
software CAE del proceso GMAW
Fuente: Villacís (2022)
Etapa
de Post-procesamiento
La
información que presenta el “Results” (Interfaz de resultados del software =
CAE)
se realiza la generación de reportes, tablas, figuras, etc. En la figura 11=
se
observa la “Probe Table 1” (Tabla
minuciosa de datos de salida de la simulación en la herramienta CAE ), dond=
e se
puede ver a detalle la variación de la temperatura con el tiempo, en este
caso la temperatura máxima es de 3012,6
ͦ K (2739,45 ℃) =
a la
que llega el arco de soldadura en las primeras chispas eléctricas en el
tiempo
, este fenómeno presentan todas las máquinas de
soldadura, para luego descender a una temperatura adecuada de soldeo con una
oscilación insignificantica de valores, hasta culminar el proceso de fusión=
.
Figura 12=
Variación=
de
la temperatura vs el tiempo
Fuente: Villacís (2022)
En la fig=
ura
12 se aprecian las curvas isotérmicas que representan el comportamiento tér=
mico
del fenómeno real, si se pone atención en particular a la curva más calient=
e en
forma de una elipse en el plano xz, se dice que esta isoterma representa la
proyección de la fuente de calor de Goldak y con la ayuda de la opción “Probe Table 1” de la herramienta C=
AE y para un tiempo
se tiene=
una
temperatura má xima de
.
Figura 13
Curvas isotérmicas del pro=
ceso
GMAW <=
span
style=3D'font-size:12.0pt;font-family:"Times New Roman",serif;mso-ansi-lang=
uage:
ES-EC'>
Fuente: <=
/span> Villacís
(2022)
De la mis=
ma
manera si se desea obtener otros valores de temperatura que no sea la má xima=
en el
cordó<=
/span>n
de soldadura sino en la afectació n té rmica en las proximidades de este se ti=
ene
las curvas isoté rmicas
que están representadas por la cantidad que el usuario programe en el softw=
are CAE,
los valores se obtienen de acuerdo con el color en la barra vertical al lado
derecho del panel de visualizació n, es así como en la figura 13 se puede=
contar
15 isotermas. Por otro lado, en la figura 14 se muestra la evolució n de=
la
temperatura versus el tiempo. A partir de los 10 segundos la temperatura
presenta una oscilació n con má ximos y mínimos no muy alejados. Calculando la temperatura
promedio a partir de este tiempo hasta culminar el proceso se tiene un valo=
r má ximo
promedio de
.
Figura 14=
Evolución de la temperatura en el proceso de solda=
dura
GMAW
Elaborado por: Villacís
(2022)
Resultados
Análisis y validación del modelo matemático
La validación del modelo matemático se realizó con=
un
segundo software CAE. Uno de los puntos más relevantes es enfatizar que los
valores obtenidos en las simulaciones numéricas tengan un error relativo mí=
nimo.
Figura 15
Simulación computacional e=
n un
software de validación
Elaborado por: Villacís
(2022)
En
la anterior figura se verifica que la temperatura máxima de fusión para un
tiempo t=3D30s es de 2316,00 T=
51;.
Cálculo
del error entre resultados simulados
Se
hace un análisis del error absoluto y error relativo comparando los resulta=
dos de
las temperaturas máximas en las dos simulaciones numéricas, en un tiempo
se tomó =
de la
“Probe Table 1”.
como la
relación entre el error absoluto y el valor de la temperatura máxima del
software de validación, ya que este programa es muy utilizado en el Ecuador=
por
su versatilidad, eficiencia (Pozo et al., 2011; Pintado, 2018; Hernández et
al., 2013).
Donde:
Entonces los errores
calculados son los siguientes:
Se
observa que el error relativo es tan solo un valor de 2,43 % y es razonable
pensar que un error absoluto de 56,25 ℃ es admisible en paridad con l=
as
elevadas temperaturas simuladas, es decir, esta estimación se la considera
intrascendente en comparación con las temperaturas extremas de fusión en los
aceros, en otras palabras, los 56,25 ℃ apenas es el 2,43 % de 2316
℃, por lo tanto, éste
muestra =
la
precisión de medición y se la puede considerar como aceptable.
Propuesta
Modelo
matemático propuesto. - Los recursos matemáticos utilizados en este modelo=
se presentan
en la figura 16. La variable dependiente es la temperatura que está en func=
ión
de las posiciones x, y, z y el tiempo, siendo un problema en estado
transitorio.
Figura 16=
Esquema d=
el
modelo matemático propuesto
Fuente: Villacís (2022)
Interpretación de la simulación del modelo =
matemátic=
o . - El ME=
F permite
obtener las soluciones aproximada sobre el dominio en el que gobierna el mo=
delo
matemático, en este caso, el modelo que describe el comportamiento térmico =
del
proceso GMAW. Estas soluciones aproximadas ayudan a reproducir virtualmente=
el
fenómeno de estudio a través de los contornos de las curvas isotérmicas que
afectan el material base en la ZAT (Zona Afectada Térmicamente). En una for=
ma
más sencilla el MEF consiste en convertir la probeta virtual en un número
finito de partes llamados elementos, estos elementos contienen una serie de
puntos interconectados entre si llamados nodos y todo este conjunto es lo q=
ue
llamamos malla y por medio del algoritmo de la herramienta CAE se construye=
un
espacio vectorial de dimensión finita asociado al espacio de los elementos
finitos, haciendo una combinación lineal en un espacio vectorial denominada
solución numérica. En la figura 17=
se
presenta las soluciones aproximadas del modelo matemático identificadas como
curvas isotérmicas para una sola pasada de la fuente de calor. En este caso=
el
número de niveles es 15, siendo el más caliente
y el punt=
o más
frio
Figura 17=
Soluciones aproximadas y dimensión de la ZAT del
modelo matemático
Fuente: <=
/span> Villacís
(2022)
Con
la ayuda de un software CAD (Diseño Asistido por Computadora) se mide de fo=
rma
aproximada a escala la longitud más útil de la ZAT, tomando como base para =
el
análisis la figura 17; entonces la ZAT empieza aproximadamente en la segunda
curva isotérmica en forma ascendente que corresponde a la solución aproxima=
da
de
Validación del
modelo <=
span
style=3D'font-size:12.0pt;line-height:115%;font-family:"Times New Roman",se=
rif;
mso-ansi-language:ES-EC'>matemático. - La valida=
ción
teórica cuantifica la incertidumbre de un modelo mediante la comparación de=
sus
predicciones con otra simulación numérica. En la figura 18 se observa el
comportamiento térmico del proceso GMAW en el software de validación. =
Figura 18
Curvas isotérmicas y dimensión de la ZAT en el
software de validación
Fuente: Villacís (2022)
Se utiliza dos isotermas lo más
cercanas en valor numérico para el cálculo de errores.
Tabla 8
Valores de la ZAT para el tiempo t =3D 30 s
Fuente: Villacís (2022)
Donde:
Entonces los errores calculados son los siguientes: =
28,90 -28,61
0,29
=
e r <=
span
style=3D'mso-bookmark:_Hlk81985521'>0 ,29 28,61
e r
El
error relativo de <=
/span>
es admis=
ible,
al menos si lo comparamos con la investigación realizada por Pozo et al. (2=
011),
donde nos dice que si la longitud de la ZAT es
se consi=
deran
las simulaciones aceptables, por lo tanto, el modelo matemático propuesto
muestra la confiabilidad de predecir los valores necesarios para entender el
comportamiento térmico en un proceso de soldadura por arco eléctrico GMAW. =
Conclusiones
·&nb=
sp;
Se desarrolló un modelo
matemático que permitió analizar el comportamiento térmico en el proceso de
soldadura del acero ASTM A36 mediante un software CAE con base en el Método=
de
los Elementos Finitos. Lo más importante de este desarrollo fue que se
diagnosticó y se planteó solo las variables, parámetros, condiciones inicia=
les
y de frontera más relevantes para hacer un modelo eficiente y lo más próxim=
o a
la realidad, por lo tanto, lo que más ayudo para generar este estudio fue u=
na
recolección exhaustiva de varios trabajos similares en otros países que se
apoyaron en la metodología de la simulación numérica con el MEF para abarat=
ar
costos de producción y errores de construcción.
·&nb=
sp;
Se diseñó y se propuso un
modelo matemático con la característica que se relacionaron dos ecuaciones =
de
gobierno, la primera siendo la ecuación diferencial parcial tridimensional =
no
lineal de conducción de calor y la segunda ecuación de la fuente móvil de
Goldak.
·&nb=
sp;
Con la simulación numéri=
ca,
en el panel de visualización del “Results” de la herramienta asistida
por computadora, se predijo un conjunto de curvas isotérmicas perteneciente=
s a
la Zona Afectada Térmicamente (ZAT); estas curvas muestran el historial de
temperaturas, es decir la distribución de estas con la variación del tiempo=
que
dura realizar el soldeo de una probeta virtual de ciertas características
físicas, es decir se conoció el comportamiento térmico requerido. Es así co=
mo
se obtuvo una temperatura de formación máxima del arco eléctrico de
en
un tiempo
y una temperatura máxima promedio de to=
do el
proceso a partir que se estabilizo el arco eléctrico de
. .
· &nb=
sp;
Se utilizó otro paquete =
CAE
muy manejado en el Ecuador, por su versatilidad, eficiencia entre otras
ventajas para la validación del modelo matemático donde lo más importante fue que se obtuvo un e=
rror
relativo de =
al comparar las temperaturas máximas del cordón de soldadura y un er=
ror de
al comparar la longitud útil de la ZAT e=
n un
tiempo t =3D 30 s, se puede decir =
que son
errores aceptables que dan por hecho que el modelo matemático es eficiente y
apropiado para este tipo de problemas térmicos que surgen constantemente en=
la
vida real en ingeniería, construcción, etc.
Referencias bibliográficas=
Berrío, M., Vanegas, N. A., & Serna, =
C.
P. (2010). Evaluación de las distorsiones de contracción lateral de uniones
soldadas a tope. Revista Colombiana de Materiales N.3, 25-41.
BFMéxico. (2017). Soldadura-Automatiza=
ción-Robótica.
BFMéxico https://www.bfmx.com/soldadura/zona-afectada-termicamente/
Dávalos, J. J. (2017). Análisis de la
distorsión de un elemento estructural soldado mediante el proceso GMAW .=
En
Instituto Tecnológico de Pachuca.
Fosca, C. (2007). Introducción a la Me=
talurgia
de la Soldadura.
García, G. V. (2019). Modelación
computacional de la soldadura de aceros avanzados alto-Mn austeníticos de
plasticidad inducida por maclaje (TWIP) mediante el proceso GTAW . (Tesis Doctoral).
Goldak, J. =
A.,
& Akhlaghi, M. (2005). Computational Welding Mechanics . <=
/span>Springer. https://link.springer.c=
om/book/10.1007/b101137
Hernández, I. A., Pérez, J. M., &
Aguilera, E. G. (2013). Determinación de Esfuerzos Residuales en una Estruc=
tura
Tipo I Producidos por Soldadura. Memorias del XIX Congreso Internacional
Anual de la SOMIM, 1022-1032. http://somim.org.mx/memorias/memorias2013/pdfs/=
A4/A4_222.pdf
Holman, J. P. (1999). Transferencia de
Calor.
Horwitz, H. (1997). Soldadura aplicaci=
ones
y práctica . Moscú.
Hitesh, D. =
V.,
Harimkar, S. P., Boetcher, S. K., & Dahotre, N. B. (2013). One-dimensio=
nal
multipulse laser machining of structural alumina: evolution of surface
topography. The International Journal of Advanced Manufacturing Technolo=
gy,
69-83. https://link.springer.com/article/10.1007=
%252Fs00170-012-4709-8
López, A. M., & Montenegro, S. B. (20=
08).
Estudio de distorsiones producidas en vigas tipo I fabricadas por soldad=
ura
a filete en el proceso GMAW.
Osmar, G. (2016). Determinación de
deformaciones y tensiones residuales en tuberías unidas por soldadura
utilizando simulación numérica para su aplicación en gasoducto. =
http://hdl.handle.net/2=
0.500.12404/6608
Pérez, J., & Romero, J. (2017). Si=
mulación
computacional de esfuerzo-deformación y transferencia de calor de un secado=
r cilíndrico
rotativo de la industria papelera.
Pintado, A. M. (2018). Determinación d=
el
efecto de la soldadura en el comportamiento mecánico en las estructuras
metálicas por medio del Método de Elementos Finitos. https://dspace.ups.edu.=
ec/handle/123456789/15163
Pozo, J. A., Acosta, P. E., Crespo, A. C.,
& Díaz, E. (2011). Análisis térmico de soldadura GTAW sobre placa de ac=
ero
AISI 316L empleando el Método de Elementos Finitos. Empresa de diseño y
servicios de ingeniería UEB Villa Clara, 256-264.
Stamenkovic,
D., & Vasovic, I. (2009). Finite Element Analysis of Residual Stress in
Butt Welding Two Similar Plates. Scientific Technical Review, LIX (1).
Villacís Ramón, M. E. (2022). Modelo m=
atemático
para el análisis del comportamiento térmico en el proceso de soldadura de u=
n acero
estructural mediante un software con base en el método de elementos finitos=
.
(Trabajo de Maestría). Escuela Superior Politécnica de Chimborazo,
Riobamba-Ecuador.
El artículo que se publica es de exclusiva
responsabilidad de los autores y no necesariamente reflejan el pensamiento =
de
la Revista Conciencia Digital. =
El artículo queda en propiedad de la revista y, por
tanto, su publicación parcial y/o total en otro medio tiene que ser autoriz=
ado
por el director de la Revista Conc=
iencia
Digital.
&nb=
sp;
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ooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiii
gAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKA
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ooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiii
gAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKA
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ooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiii
gAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKA
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ooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiii
gAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKA
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ooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiii
gAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKA
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ooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiii
gAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKA
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ooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiii
gAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKA
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ooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiii
gAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKA
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ooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiii
gAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKA
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ooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiii
gAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKA
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ooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiii
gAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKA
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gAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKA
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gAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKA
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gAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKA
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gAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKA
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gAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKA
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ooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiii
gAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKA
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ooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiii
gAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKA
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ooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiii
gAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKA
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gAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKA
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ooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiii
gAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKA
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ooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiii
gAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKA
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ooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiii
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ooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiii
gAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKA
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ooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiii
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ooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiii
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ooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiii
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ooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiii
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