ISEN 281 - HW6

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Texas A&M University *

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281

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Mechanical Engineering

Date

Feb 20, 2024

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pdf

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Uploaded by DoctorRook5940

Problem #1 (5 points) (a) What is the difference between a pattern and a core in sand molding? Pattern: A pattern is a full-sized model or replica of the final object or casting you want to create. It is used to create the mold cavity into which the molten metal is poured. Patterns are typically made of wood, metal, or plastic and are designed to produce the external shape of the casting. Patterns come in various forms, including solid patterns (for solid castings) and split patterns (for complex shapes). Core: A core is a sand component used to create internal cavities or voids within the casting. Cores are used when you need hollow or intricate internal features in the casting, such as holes, passages, or recesses. Cores are typically made of sand mixed with binders to give them the required strength and shape. They are placed inside the mold to form the internal shape of the casting. (b) What does the ‘Continuity Law’ mean as it applies to the flow of molten metal in casting? It states that the mass of the material entering a system (such as the molten metal being poured into the mold) must be equal to the mass of the material leaving the system. This principle ensures that there are no gaps, voids, or discontinuities in the final casting, and it helps maintain the integrity of the part being cast. (c) What does heat of fusion mean in casting? Heat of fusion: Energy needed to melt a solid into a liquid. (d) In a sand-casting mold, the V/A ratio (volume to surface area ratio) of the riser should be (b) greater than the V/A ratio of the casting itself? Problem #2 (10 points) A disk 40 cm in diameter and 5 cm thick is to be cast of pure aluminum in an open-mold casting operation. The melting temperature of aluminum = 660 oC, and the pouring temperature will be 800 oC. Assume that the weight of aluminum heated will be 5% more than what is needed to fill the mold cavity, to account for the solidification shrinkage. (a) Compute the amount of heat (in Joules) that must be added to the metal to heat it to the pouring temperature, starting from a room temperature of 25 oC. The heat of fusion of aluminum = 389.3 J/g. Specific heat of aluminum is 0.9 J/goC in solid state and 0.8 J/goC in liquid state. Density is 2.7 g/cm3. 19064110.43 J (b) Also provide your answer for the heat needed in calories (or, more conveniently, in the number of burritos!). 4560888.198 calories = 6081.184264 burritos

Problem #3 (15 points) The downsprue leading into the runner of a certain mold has a length = 175 mm. The cross- sectional area at the base of the sprue is 400 mm2. The mold cavity has a volume = 0.001 m3. (a) Determine the flow velocity of the molten metal flowing through the base of the downsprue. V = 1.85297 m/s (b) Determine the volumetric flow rate. Q = AV = 741208 mm^3/s (c) Determine the time required to fill the mold cavity. T = V/Q = 1.35 s Problem #4 (15 points) The volumetric flow rate of liquid metal into the downsprue of a mold = 1 liter/s. The cross- sectional area near the top of the sprue = 800 mm2, and its length = 175 mm. (a) What area should be used at the base of the sprue to maintain constant flow rate, top and bottom, and avoid aspiration of the molten metal (i.e., separation of contact between molten metal and the mold walls)? Q = AV A = 540 mm^2 (b) Based on your answer in (a), calculate what should be the taper angle of the sprue. sin(400/175) = 0.75514 Problem #5 (10 points) In the casting of steel under certain mold conditions, the mold constant in Chvorinov’s rule is known to be 4.0 min/cm2, based on previous experience. The casting is a flat plate whose length = 30 cm, width = 10 cm, and thickness = 20 mm. (a) Determine how long it will take for the casting to solidify. T = Cm(V/A)^2 = 2.49 min (b) If the exponent value in Chvorinov’s rule is 1.9 instead of 2.0, what adjustment must be made in the units of the mold constant, and what would be the solidification time? Cm = [min/cm^(1.9)]; T = 2.382 min

Problem #6 (15 points) The total solidification times of three casting shapes are to be compared: (1) a sphere with diameter = 10 cm, (2) a cylinder with diameter and length both = 10 cm, and (3) a cube with each side = 10 cm. The same casting alloy is used in the three cases. (a) Determine the relative solidification times for each geometry. T = 9.72 min for all (b) Based on the results of part (a), which geometric element would make the best riser? They are all the same. (c) If the mold constant = 3.5 min/cm2 in Chvorinov’s rule, compute the total solidification time for each casting. 9.72 min Problem #7 (15 points) A cylindrical riser is to be used for a sand-casting mold. For a given cylinder volume, determine the diameter-to-length ratio that will maximize the time to solidify. V_riser = π * (D/2)^2 * L A_riser = 2 * π * (D/2)^2 + π * D * L T = Cm(V/A)^2 D/L = 1 Problem #8 (15 points) A riser in the shape of a sphere is to be designed for a sand casting mold. The casting is a rectangular plate, with length = 200 mm, width = 100mm, and thickness = 18 mm. If the total solidification time of the casting itself is known to be 3.5 min, determine the diameter of the riser so that it will take 25% longer for the riser to solidify. V = 350000 mm3 A = 50888 mm2 Cm = 0.06969 T = 4.375 min D = 47.54 mm Bonus Problem (if you get this right, we will add 2 points to your overall final grade) A cylindrical riser must be designed for a sand-casting mold. The casting itself is a steel part whose drawing is shown in the next page (all dimensions are in mm). Previous observations have indicated that the total solidification time for this casting is 2 minutes.

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(a) Determine the mold constant. (NOTE: Use SolidWorks to calculate the casting volume and surface area.) Volume = 446268.95 cubic millimeters and Surface area = 65105.69 square millimeters 120 sec = Cm*(6.85453068695)^2 Cm = 2.554 sec/mm^2 (b) The cylinder for the riser will have a diameter-to-height ratio = 2. Determine the dimensions of the riser so that its total solidification time is 3 minutes. 180 = 2.554(D/8)^2 D = 67.16078 mm and H = 33.58039 mm (c) What should be the minimum volumetric flow rate in the runner to ensure that the mold filling time is less than the solidification time? Q = V/T = 446268.95 mm^3 / 60s = 7437.82 mm^3/s