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Determinación de dependencia estadística de la temperatura de trabajo de rodamientos rígidos en procesos industriales medi= ante ANOVA en RStudio

 

Determination of statistical dependence of the working temperature of rigid bearings in industrial processes using ANOVA in RStudio

 


= 1=

Luis Stalin López Telenchana=

 <= /span>

https://orcid.org/0000-0001-7548-0406

 

 <= /span>

Ingeniería Industrial, Facultad de Ingeniería, Universidad Nacional de Chimborazo, Riobamba, Ecuador.

luis.lopez@unach.edu.ec=

= 2=

Marco Vinicio Yanqui Avilés

 <= /span>

https:= //orcid.org/0009-0009-6808-1410

 

 <= /span>

Ingeniería Industrial, Facultad de Ingeniería, Universidad Nacional de Chimborazo, Riobamba, Ecuador.

marco.yanqui@unach.edu.ec=

= 3=

Ximena Alexandra Quintana López

 <= /span>

https:= //orcid.org/0000-0002-0177-1144

 

 <= /span>

Ingeni= ería en Tecnologías de la Información, Facultad de Ingeniería, Universidad Nacional de Chimborazo, Riobamba, Ecuador.

ximena.quintana@unach.edu.ec=

 

 

 

 

 

Artículo de Investigación Científica y Tecnológi= ca

Enviado: 05/01/2024

Revisado: 17/01/2024<= o:p>

Aceptado: 02/02/2024<= o:p>

Publicado:15/02/2024<= o:p>

DOI: https://doi= .org/10.33262/concienciadigital.v7i1.2904               

 

 

 

Cítese:

 

&= nbsp;

López Telenchana, L. S., Yanqui Avilés, M. V., & Quintana López, X. A. (202= 4). Determinación de dependencia estadística de la temperatura de trabajo de rodamientos rígidos en procesos industriales mediante ANOVA en RStudio. ConcienciaDigital, 7(1), 82-99. https://doi= .org/10.33262/concienciadigital.v7i1.2904

 

 

 

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<= span style=3D'text-decoration:none'> 

 

 

Esta revista está protegida ba= jo una licencia Creative Commons AttributionNonCommercialNoDerivatives 4.0 International. Copia de la licencia: http://creativec= ommons.org/licenses/by-nc-nd/4.0/<= /o:p>

 

Palabras claves:

Densidad, lubricante, rodamiento, temperatura, velocidad.

 

Resumen

Introdu= cción: Hoy en día la temperatura de trabajo se ha convertido en la variable más importante en la evaluación técnica del rendimiento general de un rodamiento rígido. Esto se debe principalmente a que varios factores críticos tienen una mayor o menor dependencia de la temperatura de trabajo, factores de funcionamiento como la viscosidad del lubricante, la capacidad de carga, la distribución de la carga y la pérdi= da de potencia que en distintas investigaciones se ha demostrado una proporcionalidad. Objetivo: En este artículo se determina la dependencia de la temperatura de trabajo de un rodamiento rígido de bolas= 618 en función de variables operativas como la densidad de película lubricant= e y velocidad de funcionamiento al que está expuesto este elemento dentro del= proceso industrial de trituración de minerales. Resultados: Se realizaron = 27 mediciones in situ de la temperatura de trabajo a velocidades operaciones entre 1200 y 3600 revoluciones por minuto y densidades de lubricantes ent= re 100 y 135 centistokes. Estos datos obtenidos fueron procesados mediante A= NOVA multifactorial para establecer la influencia de las variables antes expue= stas en relación con la temperatura de trabajo, como resultado se pudo estable= cer que la velocidad de funcionamiento influye de forma directa sobre la variación de temperatura de trabajo del rodamiento rígido de bolas en estudio, lo que implica que esta variable debe ser analizada cuando se reemplace o dimensione el rodamiento. Conclusiones: Se concluyó qu= e la temperatura de trabajo tiene una dependencia directa con la velocidad de funcionamiento del rodamiento en estudio y con el tipo de lubricante utilizado en el  mismo, además se= pudo determinar que el presente estudio aporta significativamente en la ejecuc= ión de tareas de mantenimiento, en la elaboración de planes de producción y e= n el análisis causa raíz de fallas en activos con elementos rotarios bajo contextos operacionales con distintas variables de funcionamiento a nivel industrial. Área de estudio general: Ingeniería. Área de estudio específica: Ingeniería Industrial.

 

 

Keywor= ds:

Density, lubricant, bearing, temperature, speed.=

&= nbsp;

Abstract

Introduction= : Nowadays the operating temperature has become the most important variable in the technical evaluation of the overall performance of a deep groove bearing. This is mainly since several critic= al factors have a greater or lesser dependence on the working temperature, operating factors such as lubricant viscosity, load carrying capacity, lo= ad distribution and power loss, which have been shown to be proportional in various investigations. Objective: In this article, the dependence= of the working temperature of a 618 deep groove ball bearing on operating variables such as lubricant film density and operating speed to which this element is exposed in the industrial process of mineral crushing is determined. Results: 27 in situ measurements of the working temper= ature were carried out at operating speeds between 1200 and 3600 revolutions per minute and lubricant densities between 100 and 135 centistokes. These data obtained were processed by means of multifactorial ANOVA to establish the influence of the above-mentioned variables in relation to the working temperature. As a result, it was established that the operating speed has= a direct influence on the variation of the working temperature of the deep groove ball bearing under study, which implies that this variable should = be analyzed when the bearing is replaced or sized. Conclusions: It was concluded that the working temperature has a direct dependence with the operating speed of the bearing under study and with the type of lubricant used in it, in addition it could be determined that the present study contributes significantly in the execution of maintenance tasks, in the elaboration of production plans and in the root cause analysis of failure= s in assets with rotating elements under operational contexts with different operating variables at industrial level.

 

 

 

 

Introducción

El análisis térmico de rodamientos es un tema que desde hace varios años se ha venido investigando, en donde estimar la temperatura de los componentes de = los rodamientos de bolas tiene gran connotación. Según Takabi & Khonsari (2= 013), "aplicando las leyes básicas de la transferencia de calor al conjunto = de rodamientos y utilizando el supuesto de masa concentrada, se puede estimar = la temperatura en estado estacionario de los componentes del rodamiento" = (p. 94).  Por lo antes mencionado, varios investigadores se han dedicado a desarrollar metodologías capaces de genera= r predicciones de la temperatura de trabajo del rodamiento.

En la actualidad los distintos procesos industriales se han convertido en el p= ilar fundamental del sector productivo, tienen como finalidad elaborar distintos productos, buscando siempre conseguir los más altos estándares de calidad y= que la empresa de esta, manera sea competitiva en el mercado y no desaparezca e= n el corto plazo. Para conseguir estos indicadores es necesario desarrollar seguimientos de orden técnicos de manera permanente, a las distintas variab= les propias del contexto operacional y que son emitidas por las máquinas que integran el proceso industrial intervenido, y que un cambio en ellas son un indicativo de posibles fallas, que de no ser tratadas a tiempo conllevarían= a llegar a un estado de avería al activo, con ello provocaría pérdidas a la organización, siendo mucho más rentable un seguimiento periódico frente a un paro imprevisto de una máquinas, equipo o instalación. 

Las máquinas rotativas son parte de todo proceso productivo, por lo que para conseguir mejoras en el proceso debemos realizar seguimientos a las variabl= es de dichas máquinas y descubrir la interrelación que existe en la aparición = de cada una de ellas. En las distintas máquinas rotativas los rodamientos son = los elementos mecánicos más comunes que podemos encontrar, por lo que los seguimientos de las variables en tiempo real requieren de mayor cuidado. "Pues permiten realizar evaluaciones técnicas apropiadas esto debido a= que las variables analógicas que emiten cuando los rodamientos están en funcionamiento dan una idea clara del estado en el que se encuentran. así c= omo el diagnóstico de los fallos que ocurren en sus componentes" (Estévez & Bernal, 2019, p. 86). Por lo que, lo anteriormente acotado se convier= ten en la fundamentación para el presente estudio.

Variables analógicas como la temperatura de trabajo pueden determinar fallos ocultos = en el funcionamiento óptimo de los rodamientos, tomando como prioridad a estos elementos debido a que si fallan pueden provocar paros imprevistos que sin = duda alguna merman los índices de producción y de mantenimiento deseados en cualquier organización, por lo que determinar el método adecuado para el análisis de la interrelación de las posibles causas que generan alteracione= s en la temperatura de trabajo es primordial, pues permite realizar acciones técnicas oportunas que garantizan la conservación de la función requerida de este elemento mecánico.  

Cabe recalcar que el análisis de la película lubricante se basó también en el análisis de ciclo de vida de la grasa lubricante, esto debido al impacto que tiene tanto en el orden ambiental como en la influencia en la operatividad = del rodamiento, es importante identificar ventajas y desventajas, así como dist= intas estrategias que permitan minimizar la posibilidad de eventuales riesgos. Se= gún Ji et al. (2023), "la temperatura máxima ocasionada por una película lubricante es uno de los indicadores clave para determinar si el equipo principal funciona normalmente" (p. 57). Por lo que es importante el análisis previo del proceso de lubricación para determinar la incidencia del mismo en el adecuado funcionamiento del rodamiento intervenido.<= /span>

El presente trabajo desarrolla una metodología capaz de analizar los datos emitidos por la temperatura como variable dependiente, mediante modelos estadísticos para observar la interacción que existe entre las variables independientes como las revoluciones por minuto de funcionamiento y la dens= idad de la grasa lubricante utilizada en el rodamiento, todo esto con el fin de = que la empresa donde se desarrolló el estudio cuente con procesos óptimos basad= os en la menor variabilidad. Por lo que utiliza el análisis de la varianza como herramienta estadística para poder tratar los datos obtenidos, un análisis = de variancia usando ANOVA se lleva a cabo, para determinar si algún factor controlable o alguna interacción entre factores tienen influencia significa= tiva en la variable de temperatura (López & Osorio, 2015).=

En el campo industrial se viene practicando y difundiendo la implementación de= la gestión del cambio en procesos industriales, la cual ha generado grandes ventajas competitivas. Según Oropesa & Martínez (2015), la gestión del cambio es el proceso formal para atender el cambio organizacional, que incl= uye un enfoque sistemático y de aplicación del conocimiento (p. 58). Por lo que= la presente investigación busca también generar dicha gestión, dado que un cam= bio organizacional genera sin duda alguna mayor rentabilidad a la organización,= sin importar la clase o el sector en el que se desarrolle, la sistematización y lógicamente la aplicación de conocimientos juegan un rol importe en la consecución de resultados en el sector industrial. En donde todo sistema de gestión debe ser progresivo y busca siempre la innovación.

El análisis experimental de la generación de calor en rodamientos es una metodología que en la actualidad demuestra grandes resultados en la evaluac= ión técnica de los nodos térmicos de un elemento rodante y su interacción con el medio. Según Gao et al. (2023), "los nodos térmicos alrededor de los rodamientos rígidos de bolas se establecen mediante el método de red de calor" (p. 34). Por lo antes acotado, se puede establecer que tanto la velocidad de trabajo como el lubricante utilizado en el rodamiento influyen directamente en los nodos térmicos de un rodamiento de bolas, por lo que es= tos pueden tener una connotación importante en la parte experimental. 

Otra variable indispensable en un rodamiento rígido es la altura de rugosidad, q= ue sin duda alguna influye significativamente en el adecuado funcionamiento. S= egún Zhu et al. (2020), "a medida que aumenta la altura de rugosidad de la superficie adimensional del rodamiento y el muñón o aumenta el grado de desalineación, aumentan la presión máxima de la película adimensional, la capacidad de carga adimensional y el momento de desalineación adimensional = del rodamiento" (p. 102).  Por lo = antes acotado se puede determinar que la lubricación tiene factores que influyen directamente en el comportamiento técnico adecuado de un elemento rodante.<= o:p>

En los elementos rodantes, la textura superficial juega un papel preponderante= al momento de evaluar la temperatura de trabajo en fricción. Según Song et al.= (2020), "la textura de la superficie es un método eficaz para resolver este problema, sobre todo la forma de textura convencional y el nuevo diseño de forma de textura superficial de cojinetes deslizantes radiales y de empuje&= quot; (p. 58).  Esta variable sin duda al= guna tiene gran connotación tanto en el diseño como en la evaluación en tiempo r= eal de los elementos deslizantes en forma radial como tangencial.

Las variables tomadas en cuenta en la presente investigación están en función d= el comportamiento dinámico de los rodamientos. Según Xiang et al. (2020), &q= uot;es de gran importancia estudiar el comportamiento dinámico de los cojinetes durante el arranque para optimizar el rendimiento de la tribología y mejora= r la vida útil " (p. 61). Por lo que es importante analizar además variables como la fricción al momento del arranque y el estado del lubricante después= de un turno de trabajo.

En la actualidad existen varios modelos estadísticos que buscan una evaluación integral de las condiciones de trabajo de un rodamiento, ya sea por la temperatura o por el aceite lubricante. Según Shan et al. (2023), "el método general para establecer el modelo de dependencia de análisis de lubricación de rodamientos de bolas y las características del flujo multifá= sico aceite-aire dentro del rodamiento de bolas se revela mediante ANOVA " = (p. 34).   Por lo antes señalado se puede evidenc= iar que los estudios generados toman en cuenta la característica geométrica del elemento que se introduce el microespacio en la cámara en el modelo de simulación y se desarrolla la complicada forma límite del rodamiento de bol= as.

Un tema relativamente nuevo en el estudio de procesos industriales es la gesti= ón térmica, misma que ha permitido tener una expectativa mayor de las influenc= ias de las variables que están alrededor de un adecuado funcionamiento de un eleme= nto rodante en un sistema de producción. Según Kim et al. (2023), " la ges= tión térmica adecuada del rodamiento es extremadamente importante, porque una temperatura alta más allá de su límite operativo puede degradar las propied= ades del material y del lubricante, provocando una falla inesperada" (p. 91= ). Es por ello por lo que esta investigación tiene como objetivo investigar las características térmicas de un rodamiento de bolas y su dependencia en func= ión de la velocidad de funcionamiento y la caracterización de diversos lubrican= tes.

Metodología

El presente estudio se realizó en una empresa de tratamiento de material minero ubicada en el cantón Ambato, de la provincia de Tungurahua, es una empresa = que realiza el proceso explotación,  tratamiento y transporte de material minero utilizado en distintos procesos a nivel industrial, siendo una de las principales empresas proveed= oras de materia prima de tipo pétreo en el país, por lo que el estudio realizado= fue de gran agrado para el personal técnico y administrativo de la organización, pues se pudo demostrar que con un seguimiento adecuado la empresa puede gen= erar una utilidad mayor y con ello garantizar los estándares de calidad que prom= ulga a sus clientes.

Como lo manifiesta Hernández & Diaz (2018), en su artículo ¨ EVALUACIÓN DE UN PROCESO INDUSTRIAL DE PRODUCCIÓN DE BIODIÉSEL MEDIANTE ANÁLISIS DE CICLO DE VIDA¨ es importante analizar el desempeño del proceso actual del sistema de producción, así como la propuesta que integra herramientas como el estudio = del Análisis del ciclo de vida y el ANOVA multifactorial que permiten una verda= dera integración del conocimiento a través de estudios técnicos y estadísticos. =

La película de lubricante juega un papel muy importante en la evaluación de la temperatura de trabajo de un rodamiento rígido. Según Rao et al. (2019), &q= uot;un método de cálculo adecuado podría superar la discontinuidad de la película = de aceite en el borde y describir la característica de la textura de la superf= icie en el anillo". Entonces, el modelado y la simulación son también técni= cas atractivas para mejorar el rendimiento de lubricación de rodamientos de bol= as y con conlleva a un mejor control de la temperatura de trabajo en un sistema rotativo, mismo que está presente en cualquier proceso industrial.

Las plantas productivas de la organización están distribuidas por líneas de producción, las mismas que tiene a cargo un líder por cada una de ellas qui= én es el encargado de supervisar los procesos y de realizar las intervenciones= de orden técnico en caso ser necesario, además de notificar y dar cumplimiento tanto al plan maestro de producción como al plan de mantenimiento preventivo que tiene la empresa, estos dos planes han sufrido cambios gracias al prese= nte estudio, pues se ha generado frecuencia óptimas de mantenimiento mediante un seguimiento apropiado de las variables propias del proceso productivo que no fueron tomadas en cuenta al momento del diseño de dicha documentación técni= ca.

En la planta de trituración, en la sección de pre triturado se emplean 12 máqu= inas trituradoras, máquinas semiautomáticas con sistemas mecánicos y neumáticos,= en función de las dimensiones del material pétreo las máquinas trituradoras funcionan a distintas velocidades, lo que provoca el comportamiento distint= o de las variables del proceso, las trituradoras tienen un conjunto de muelas capaces de mediante movimiento alternado disminuir el tamaño del material pétreo extraído de minas de orden natural, este conjunto está soportado en = ejes y para generar el movimiento emplea rodamientos con diámetros externos superiores a 19 centímetros, por lo que la falla de uno de estos elementos causaría un paro en la trituradora, y dependiendo el grado de afectación pu= ede ocasionar un lapso prolongado de improductividad de la planta.

Al analizar el proceso de triturado del material pétreo, se puede identificar = que se encuentran relacionadas directamente las variables viscosidad de la grasa lubricante y la velocidad de trabajo. Según Li et al. (2018), "se demu= estra experimentalmente que la adición de lubricante podría aumentar efectivament= e la eficiencia volumétrica en un 10,5% y el consumo de energía específico de un= SSC en un 43,3%" (p. 138). Es por ello que la primera que tiene como unida= d de medida los centistoke y la segunda las revoluciones por minuto, siendo técnicamente que estas dos variables independientes las que probablemente provoquen que la temperatura del rodamiento no sea estable, recalcando que = el rodamiento intervenido es de numeración 618, que por diseño tiene como lími= te de velocidad 9500 revoluciones por minuto, y que en el funcionamiento del compresor está muy por debajo de dicho límite, para la lubricación de emplea dos tipos de grasa, mismas que son las más apropiadas para el activo. =

Por lo tanto, se desconoce si la viscosidad de la grasa lubricante o la velocid= ad de funcionamiento provocan variaciones significativas en la temperatura de tra= bajo del elemento rodante, lo que ha ocasionado que se deteriore rápidamente, provocando paros imprevistos, que se traducen en pérdidas para la empresa, = no solo por el material pétreo no tratado, sino también otros problemas como la pérdida de confianza de los cliente por tardanza en las estregas de product= o, además que baja calidad en el producto pétreo final, debido a un mal funcionamiento del conjunto de muelas triturador.

 Por lo tanto, es necesario aplicar un di= seño experimental para identificar cuál de las dos variables genera que la temperatura de trabajo del rodamiento tenga distintos valores, siendo el análisis multifactorial la herramienta estadística ideal para el procesamie= nto de los datos obtenidos in situ, además que son dicho análisis se puede identificar de manera apropiada si las variables tratadas tiene influencia directa sobre la temperatura de trabajos del elemento intervenido en el presente estudio.

En la empresa minera. en el proceso de triturado, = se han generado paros imprevistos en la máquina trituradora, lo que provoca que todo el proceso se detenga, esto debido a que los rodamientos de dicho de d= icha máquina sufren un desgaste prematuro debido a distintas variables, propias = de proceso y que afectan de forma notoria en el funcionamiento habitual del ac= tivo mencionado, llegando incluso a estar en avería por varias ocasiones, por lo= que se realiza un seguimiento técnico a la temperatura de trabajo, a distintas velocidades de funcionamiento y con distintas densidades en las grasas lubricantes pues son las variables técnicas que se encuentran directamente relacionadas con el rodamiento y la temperatura que genera cuando trabaja b= ajo el contexto operacional establecido, cabe recalcar que las mediciones se realizaron in situ y en intervalos de tiempo iguales, para garantizar la medición, obteniendo los siguientes datos:

 

 

Tabla 1

Temperatura de trabajo del rodamiento rígido<= /o:p>

Velocidad de Funcionamiento (rpm)

  1200       = 1800       =       3600

 

Densidad de Grasa Lubricante utilizada

 

 

 

 

Grasa de Litio EP (100 cSt)

73

93

94

 

 

 

Temperatura

De

Trabajo

°C

80

89

98

76

91

101

Grasa de Aluminio AR-16 (120 cSt)

88

92

87

84

106

96

93

88

105

Grasa Asfáltica (135 cSt)

81

96

92

87

72

102

94

103

97

Nota: En esta tabla se muestra las mediciones que fueron tomadas in situ de forma técnica, en periodos iguales y bajo la repetitividad y reproducibilidad para garantizar la confiabilidad del estudio.

Planteamiento del objeti= vo

Determinar la dependencia de la velocidad de traba= jo del rodamiento rígido de bolas 18 en función de las variables densidad de g= rasa lubricante y velocidad de funcionamiento, considerando α =3D 0.05.

Hipótesis de Significanc= ia

H0=3D NO EXISTE UN PAR DISTINTO<= /p>

H1=3D AL MENOS UN PAR ES DISTINTO

α=3D 0,05

Hipótesis de Normalidad<= o:p>

H0=3D LOS RESIDUALES SIGUEN UNA DISTRIBUCIÓN NORMA= L

H1=3D LOS RESIDUALES NO SIGUEN UNA DISTRIBUCIÓN NO= RMAL

α=3D 0,05

 

Hipótesis de Homocedasticidad

H0=3D NO EXISTE DIFERENCIAS ENTRE LAS VARIANZAS

H1=3D EXISTE DIFERENCIAS ENTRE LAS VARIANZAS<= /o:p>

α=3D 0,05

Resultados

En la presente in= vestigación partimos del análisis de varianzas, para lo cual reordenamos los datos, de = tal manera que puedan ser tratados estadísticamente en el programa R Studio, pa= ra así demostrar que la metodología desarrollada puede ser repetida y reproducida en otro elemento, garantizando de esta manera que el presente estudio puede ser aplicado en distintos activos, en distintos elementos y en distintos procesos productivos.

Después, se transformó factor las variable= s y aplicamos ANOVA.

# TRANSFORMAS A FACTOR Y LUEGO APLICAR ANO= VA

Velocidad=3Dfactor (Velocidad)<= /span>

Densidad=3Dfactor (Densidad)

Posteriormente se creamos ¨aovdata¨ objeto= que contiene ANOVA DE DOS FACTORES para el análisis de las variables antes mencionadas.

aovdata=3Daov(Temperatura~Velocidad+Densid= ad+Velocidad*Densidad)

Obteniendo de esta manera los resultados siguientes:

summary(aovdata)

Figura 1

Transform= ación de factor las variables de estudio

=

=

Para la contrastación de hipótesis, analiz= amos la SIGNIFICANCIA:

La significancia del efecto VELOCIDAD=

Figura 2

Análisis de significancia de la variable Velocidad=

El valor p para VELOCIDAD es 0,00863 está = por debajo del umbral 0,05, por lo tanto, rechazo H0.

Significa que uno o más pares de esos resultados que se han obtenido en cuanto a VELOCIDAD son significativos. Po= r lo tanto, VELOCIDAD si es significativa.

La significancia del efecto DENSIDAD<= /o:p>

Figura 3

Análisis de la significancia del factor Densidad.<= o:p>

El valor p para DENSIDAD es 0,42101 está p= or encima del umbral 0,05, por lo tanto, acepto H0. Significa que DENSIDAD no = es significativa.

La significancia de la interacción VELOCID= AD vs. DENSIDAD

 <= /span>

 <= /span>

 <= /span>

 <= /span>

Figura 4

Análisis de la significancia de la interacción VELOCIDAD vs. DENSIDAD

El valor p para la interacción es 0,52342 = está por encima del umbral 0,05, por lo tanto, acepto H0. Significa que la interacción no es significativa.

Para comprobar la confiabilidad de los resultados, verificamos si cumple con los supuestos, empezando por la prueb= a de NORMALIDAD:

Al ser pocos datos, utilizamos la prueba de Shapiro,

Figura 5

Función normalidad de residuos

La significancia de la interacción VELOCID= AD vs. DENSIDAD

Figura 6

p - Valor de los residuales.

El valor p de los residuales es 0,5894 está por encima del umbral 0,05, por lo tanto, acepto H0.

Significa que los residuales seguirían una Distribución Normal.

Se verifica la Homocedasticidad mediante la prueba de Levene:

 <= /span>

Figura 7

Homocedasticidad TEMPERATURA vs. VELOCIDAD<= /i>=

La Homocedasticid= ad TEMPERATURA contra VELOCIDAD

Figura 8

p – Valor de TEMPERATURA vs. VELOCIDAD<= /span>

 

 

 

 

El valor p de TEMPERATURA contra VELOCIDAD= es 0,5964 está por encima del umbral 0,05, por lo tanto, acepto H0.=

Significa que existe homogeneidad de varia= nzas TEMPERATURA contra VELOCIDAD.

La Homocedasticidad TEMPERATURA contra DENSIDAD

Figura 9

p – Valor de TEMPERATURA vs. DENSIDAD

El valor p de TEMPERATURA contra DENSIDAD = es 0,8216 está por encima del umbral 0,05, por lo tanto, acepto H0.=

Significa que existe homogeneidad de varia= nzas TEMPERATURA contra DENSIDAD.

 

Discusión=

Para la discusión de la presente investiga= ción se desarrolló el gráfico de interacción

Para generar el gráfico utilizamos el códi= go:

#REALIZAMOS GRAFICO DE INTERACCION

interaction.plot(Velocidad,Densidad,Temper= atura,main=3D"Grafico de interacción")

Obteniendo el Gráfico de Interacción mostr= ado a continuación:

Figura 10

Gráfico de Interacción

De los resultados descritos en el punto anterior, podemos establecer que:

  • SOLO LA VELOC= IDAD influye en el cambio de temperatura de trabajo del rodamiento.
  • LA DENSIDAD no influye en el cambio de temperatura de trabajo del rodamiento.
  • LA INTERACCIÓN entre las dos variables no influye en el cambio de temperatura de trab= ajo del rodamiento.
  • Se pudo determinar que los residuales siguen una Distribución Normal.
  • Existe homogeneidad de varianzas TEMPERATURA contra VELOCIDAD.
  • Existe homogeneidad de varianzas TEMPERATURA contra DENSIDAD.
  • En el gráfico podemos establecer que las tres curvas tienen cierta semejanza gráfica, tienen la misma forma, gráficamente no hay interacción, es decir no hay significancia en la interacción, es decir la interacción no influye.
  • Compilando to= dos los resultados podemos establecer que es viable analizar la temperatur= a de trabajo en rodamientos rígidos de bolas utilizando Análisis de la vari= anza de dos factores.

Conclusiones<= /b>

·         Una vez analizado el método ANOVA para dos facto= res se puede concluir que es una herramienta que nos permite determinar de mane= ra fiable si un fenómeno o condición es el resultado de la influencia de una o= más variables, en este caso la dependencia de la temperatura de trabajo en func= ión de la velocidad del proceso industrial y del lubricante empleado.

·         Después de haber realizado el trabajo experiment= al se puede concluir que para el caso en estudio la velocidad es la variable independiente que influye en la temperatura de trabajo del rodamiento, esto basándonos en que los residuales son normales y que existe Homocedasticidad entre factores y respuesta, pudiendo lograr el objetivo de la presente investigación.

·         Se puede concluir que ANOVA puede ser aplicado p= ara establecer estadísticamente la dependencia de cualquier variable, en este c= aso de un proceso industrial, y que aporta significadamente en la potencializac= ión de un sistema productivo, al punto de ser una herramienta en la toma de decisiones como la compra de un lubricante o el control óptimo de la veloci= dad de una máquina.

·         Finalmente, con la utilización del Software R podemos concluir que incluso gráficamente se puede determinar la influencia= que tienen dos o más variables independientes sobre una variable dependiente, lo que sin duda clarifica el panorama de la dependencia de variables, sin impo= rtar el tipo de estas, haciendo que el presente estudio sea reproducible y replicable.

Conflicto de intereses

Los autores declaran que no existe conflicto de intereses en relación con el artículo presentado.

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El artículo que se publica es de exclusiva responsabilidad de los autores y no necesariamente reflejan el pensamiento de la Revista Concienc= ia Digital.

 


 

 

 

El artículo queda en propiedad d= e la revista y, por tanto, su publicación parcial y/o total en otro medio tiene = que ser autorizado por el director de la Revista Conciencia Digital.

 

 

 

 


 

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= ISSN: 2600-5859=

= Vol. 7 No. 1, pp. 82 –= 99, enero - marzo 2024

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www= .concienciadigital.org

 

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                                      Infinito                                  Página 82 | 99

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