Informe Final de torsión ensayo
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ensayo de torsión maqueta...
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TORSIÓN EN EN UNA BARRA CIRCULAR MACIZA DE ALUMINIO AL UMINIO
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“Sólo las situaciones difíciles hacen conocer al hombre sus ocultas capacidades.”
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IÓ S R O T
Bottach
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OI NI
INDICE L
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I.
INTRODUCCIÓN .......................................... ................................................................ ............................................ ........................................ .................. 3
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II.
OBJETIVOS: ............................................. ................................................................... ............................................ ............................................ ...................... 4
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III. MARCO TEÓRICO: .......................................... ................................................................. ............................................. .................................... .............. 5 M
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IV.
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DESARROLLO DEL TEMA ............................... ..................................................... ............................................ ................................. ........... 7
4.1
Materiales Empleados: ......................................... ............................................................... ............................................ ...................... 9
4.2
º Procedimiento de Construcción de la Máquina ............................................ ............................................ 11
V. CONCLUSIONES .......................................... ................................................................ ............................................ ...................................... ................ 15
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VI.
ANEXOS ........................................... .................................................................. ............................................. ............................................. .......................16
VII.
BIBLIOGRAFÍA ............................................ ................................................................... ............................................. .................................. ............19
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TORSIÓN EN UNA BARRA CIRCUL CIRCULAR AR MACIZA DE ALUMINIO AL UMINIO E
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INTRODUCCIÓN
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Cada vez que observamos un material en servicio, notaremos que está sujeto a fuerzas o cargas. En esas condiciones es indispensable conocer las características del material para diseñar el instrumento donde va a usarse de tal forma que los esfuerzos a los que va a estar sometido no sean excesivos y el material no se fracture.
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En nuestro ensayo consideraremos una barra sujeta rígidamente en un
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extremo y sometida en el otro a un par torsor aplicado en un plano perpendicular al eje. El ensayo de torsión es un mecanismo (en este caso de manera artesanal), en que se deforma una muestra aplicándole un par torsor. La deformación plástica que alcanzaremos con este tipo de ensayos es mucho mayor que en los de tracción o en los de compresión. Éste ensayo nos dará información directa del comportamiento a cortadura del material y la información de su comportamiento a tracción se puede
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II. OBJETIVOS: Objetivo General: Obtener el ángulo de torsión y el módulo de rigidez del material ensayado, el cual en nuestro M
caso es el Aluminio L
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Objetivos Específcos: A
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Analizar el comportamiento del Aluminio al ser sometido al esfuerzo cortante por torsión.
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º Conocer el funcionamiento y manejo de una máquina usada en ensayos de torsión, en nuestro caso será una máquina artesanal.
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Estudiar las características de la fractura por torsión en materiales dúctiles.
Determinar la relación entre momento torsor y deformación angular para el Aluminio.
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III. MARCO TEÓRICO: es la solicitación que se presenta cuando se aplica un momento sobre el eje longitudinal de un elemento constructivo o prisma mecánico, como pueden ser ejes o, en general, elementos donde una dimensión predomina sobre las otras dos, aunque es posible encontrarla encontrarla en situaciones diversas. Cambio permanente de forma o dimensión debido a una fuerza mecánica mayor que el límite elástico (proporcional) del material bajo presión, que no recupera su forma original al eliminar la fuerza deformante. La fuerza que excede el límite proporcional, hace que los átomos del enrejado cristalino se desplacen hasta el punto de no poder volver más a su posición original. Cambio temporal de forma producido por una fuerza mecánica
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dentro del límite elástico (proporcional) del material bajo presión, recuperándose la forma y M
dimensiones originales al eliminar la fuerza deformante. La fuerza, al estar por debajo del límite
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proporcional, hace que los átomos del enrejado cristalino se desplacen sólo en valores tales
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que, al disminuir aquélla, vuelvan a su posición original.
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Al aplicar las ecuaciones de la estática, en el
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empotramiento se producirá un momento torsor igual y de sentido contrario a T.
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El Diagrama de Momentos Torsores será: R
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La torsión en sí se refiere a un desplazamiento circular de una determinada sección transversal de un elemento cuando se aplica sobre éste un momento torsor o una fuerza que produce un momento torsor alrededor del eje. La torsión se puede medir observando la deformación que produce en un objeto un par determinado. Por ejemplo, se fija un objeto
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Los materiales empleados en ingeniería para elaborar elementos de máquinas rotatorias, como los cigüeñales y árboles motores, deben resistir las tensiones de torsión que les aplican las cargas que mueven. La deformación plástica alcanzable con este tipo de ensayos es mucho mayor que en los de tracción (estricción) o en los de compresión. Esfuerzo cortante y deformación angular: Si una probeta cilíndrica de longitud L es sometida a un torque T, el ángulo de torsión está dado por la siguiente ecuación: En donde G es el módulo de corte del material de la probeta e es el
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momento de inercia polar de la sección transversal de dicha probeta.
En donde G es el módulo de corte del material de la probeta es el momento de inercia NI
polar de la sección transversal de dicha probeta. L
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Sobre la base de la ecuación anterior, se ºpuede determinar experimentalmente el módulo de corte G del material constituyente de la probeta. R
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Si los esfuerzos cortantes no sobrepasan el límite de proporcionalidad, dicho esfuerzo se distribuye linealmente, es cero en el eje central de la probeta y tiene un valor máximo en la periferia. En esta figura se indica la distribución de esfuerzos cortantes, en una sección transversal cualquiera, de una
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IV. DESARROLLO DEL TEMA El ensayo de torsión consiste en aplicar un par torsor a una probeta por medio de un dispositivo de carga y medir el ángulo de torsión resultante en el extremo de la probeta. Este ensayo se realiza en el rango de comportamiento linealmente elástico del material. Los resultados del ensayo de torsión resultan útiles para el cálculo de elementos de máquina sometidos a torsión tales como ejes de transmisión, tornillos, resortes de torsión y cigüeñales. Las probetas utilizadas en el ensayo son de sección circular. El esfuerzo cortante producido en la sección transversal de la probeta (t) y el ángulo de torsión (q) están dados por las siguientes relaciones:
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Donde T: Momento torsor (N.m)
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C: Distancia desde el eje de la probeta hasta el borde de la sección transversal (m) c = D/2
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J: Momento polar de inercia de la sección transversal (m4)
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G: Módulo de rigidez (N/m2)
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Torsor = 164.64 N.m Long. = 0. 48m Ángulo de Torsión: 0.0873 rad. G = (164.64 N.m x 0.48) m / [(π/32) x 0.01274]x(0.0873) G = 354.44 GPa
4.2 Materiales Empleados: Base para la estructura del mecanismo. OI
Largo:95 cm Ancho:45 cm Espesor: 3 cm
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Consta de un eje circular giratorio mediante un rodaje, este material fue muy óptimo para usarlo como punto libre en la barra. T
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Bases de soporte para la chumacera y la prensa hidráulica.
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Polea de donde se extiende un cable de acero para poder R
aplicar las fuerzas. A L U C RI C A R R A B A N U N E N ÓI S R O T
Barra de aluminio sólido, con una longitud de 60 cm
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Usado para medir el ángulo de torsión de la barra.
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Nos indicó el valor del ángulo en el transportador 360º. D
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Usado para uniones de metal-madera o metal-metal.
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1) Lo primero en realizarse fue el medir la melanina para así obtener las proporciones indicadas para así poder ubicar simétricamente los parantes.
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2) Luego procedimos a perforar con el taladro la melamina D
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5) Proseguimos con la puesta del material y de la polea
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7) Finalmente ajustamos nuestra muestra con la prensa hidráulica, tomamos por última vez la nivelación y nuestra maquina está terminada. OI NI M U L A E D A ZI C A M R A L U RI
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VI. ANEXOS
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VII. BIBLIOGRAFÍA
BEER, Ferdinand P. y JOHNSTON, JOHNSTON, E. Russell. Mecánica Mecánica de de materiales. 2 ed. México: McGraw Hill, 1999. 742 p. ISBN 958-600-127-X
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