E29 Spring 2023 - HW4 - Forming processes

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1 University of California, Berkeley Department of Mechanical Engineering E 29: Manufacturing and Design Communication Spring 2023 Homework 4 Forming processes Due: Friday March 10, 11.59pm on Gradescope In all questions, please show your working or reasoning clearly. Responses showing only a final answer with no working or explanation will not receive full credit. Important note: uploads to Gradescope must be in image (e.g. .png) or .pdf format, and not .docx format (which is very cumbersome to download and grade). Also, we require that you use the Gradescope interface to identify the location of each part of your solutions in the file(s) you upload, so the reader does not have to scroll through a large document to find each of your answers. The instructions on how to do this are here . Total points: 40 1. Lego bricks [10 points] In this question we consider the design and manufacture of Lego bricks. The photographs below show some bricks that have suffered from certain defects during the injection molding process. (A) (B) (C) (D) http://bricksetforum.com/discussion/16396/marbled-lego-bricks-and-other-parts

2 1.1. Briefly name and describe the possible cause of any manufacturing defect(s) that you can identify in each photograph (A) to (D) above (some defect types may occur in more than one photo) [4 points]. An example of a drawing showing a typical Lego assembly is below: https://www.toysperiod.com/lego-set-reference/universal-building-set/basic/lego-507-1-basic-building-set/ 1.2. From a fit and tolerancing perspective, explain how Lego bricks work. What type of fit do you think exists between assembled Lego bricks? You do not need to give a specific numbered tolerance grade like “RC4”; we are looking for the general category of fit, like clearance, interference, transition, snap, shrink, or expansion. [3 points] 1.3. By considering fit and manufacturing issues, explain why the features on the underside of the bricks shown in photo B above are tubes rather than solid cylinders. [3 points] 2. Design for manufacture (DfM) by injection molding [6 points] In this question you will explore some key elements of a Solidworks tutorial on mold design for injection molding. Completing the whole tutorial would take longer than you are expected to take on this homework, so we have selected a few key steps to focus on below. You are welcome to work through the tutorial in detail if you have the time and interest. Steps: • Load Solidworks (you can use the CAD labs computers if needed; also, the whole class has had remote ME CAD computer enabled) • Click on the help icon (question mark in top right), then Tutorials, All SOLIDWORKS Tutorials, scroll down and click on Mold Design. • Advance to the page on “Opening the model”, and click on the link to open a 3D model of half of a telephone handset that could be injection-molded. • Save a local copy of the .sldpart file. • Skip over the “Inserting mounting bosses” section to the “Checking for Draft” section.

3 • To activate the Draft Analysis tool, click on the “Evaluate” ribbon above the view window, and then Draft Analysis (the tutorial says it is on the “mold tools toolbar” which has changed in this version of Solidworks). • Follow the instructions in the tutorial for checking for draft angles in the design (the tutorial tells you to set a draft angle criterion of 0.5 degrees: i.e., edges that have a draft angle less than 0.5 degrees will be flagged as needing draft). • After analysis parameters have been set in Step 4, you need to click the green tick in the Draft Analysis panel to run the analysis. • The 3D model will be colored with regions with positive, negative, and missing draft. Rotate the model so you can see some of each category of draft, and place a screenshot of this view in your responses [2 points] • Suppose that the minimum acceptable draft for the process is now increased to 1 degree. Update this criterion in the draft analysis panel, update the analysis, and capture a new screenshot clearly showing any new surfaces that require draft. Place this screenshot in your responses [2 points]. • Briefly describe which additional features require draft, when the required draft is increased to 1 degree [2 points] • If you advance to the “Adding Draft” tutorial section, you will see instructions for adding draft to the zero-draft region of the design around the edge of the casing. I have found that following the instructions here yields the error “could not construct draft”, so I recommend skipping over this section and noting the general principle that draft can automatically be added to features that need it. • Advance to “Applying Scaling”. Because the polymer contracts as it cools, the mold needs to be slightly larger than the intended final size of the component. Follow the instructions to scale up the dimensions by a factor of 1.05. (Step 2 says to select ‘Draft2’ under Solid Bodies(1) in the design tree. Assuming that you did not generate draft in the previous topic, ‘Draft2’ may not appear here; simply select whatever item appears under Solid Bodies(1) instead). 3. Sand casting [8 points] A sand mold has a downsprue of length = 15 cm. The cross-sectional area at the bottom of the sprue is 3.125 cm 2 . The sprue leads into a horizontal runner which feeds the mold cavity, whose volume is 1172 cm 3 . Determine: 3.1. the velocity of the molten metal flowing through the base of the downsprue, assuming that it is poured starting from a stationary state at the top of the downsprue, [4 points] 3.2. the volume rate of flow [2 points], and 3.3. the time required to fill the mold cavity, assuming continuity is preserved in the runner and gate system, and ignoring the time taken to fill runners and risers [2 points]. 4. Solidification in casting [6 points] A flat plate is to be cast in an open mold whose base has a square shape that is 200 mm × 200 mm. The mold is 40 mm deep. A total of 1,000,000 mm 3 of molten aluminum is poured into the mold. Volumetric solidification shrinkage is known to be 6.0%. The linear shrinkage due to thermal contraction after solidification is 1.3%. If the availability of molten metal in the mold allows the square shape of the cast plate to maintain its 200 mm × 200 mm dimensions until just after solidification is completed, determine the final dimensions of the plate. Show your calculations step-by-step.

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4 5. Solidification and Chvorinov’s rule [8 points] In a sand-casting process, the total solidification times of three potential riser shapes are to be compared: • a sphere with diameter 10 cm, • a cylinder with diameter and length both of 10 cm, and • a cube with side length 10 cm. Mold constant = 3.5 min/cm 2 in Chvorinov's rule. The same casting alloy is used in the three cases. 5.1. Determine the solidification time for each geometry. [6 points] 5.2. Based on the results of part 4.1 and any other practical considerations that you consider relevant (e.g. how the pattern interacts with the packed sand), which geometric element do you think would make the best riser? Explain your reasoning. [2 points] 6. Casting defects [2 points] Study the photo below of some sand-cast components: Name a processing defect visible in these castings and explain how it could be eliminated, either by modifying the casting process or via secondary processing.