University of California, Berkeley Department of Mechanical Engineering. E27 Introduction to Manufacturing and Tolerancing.

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1 University of California, Berkeley Department of Mechanical Engineering E27 Introduction to Manufacturing and Tolerancing Spring 2016 Take-home midterm assignment Issued March 10, Due Thursday March 17 at 11:59pm on bcourses You are welcome to access any resources you need when completing this assignment (including lecture notes, the Internet, reference texts, etc), and to ask the instructor and/or GSI if you need clarification of what is being asked. Please prepare your solutions individually although you are permitted to discuss the midterm with other students. Part 1: Lathe turning [21 points] Consider the component below which is to be fabricated from stainless steel: D B C A The component s design has rotational symmetry about its central axis. It is to be manufactured in a hybrid machine tool that is capable of both subtractive and additive processing. In subtractive mode, a cylindrical piece of stock material is turned down to form the shape of the component. In additive mode, stainless steel powder is fused to the rotating component with a laser. a. According to the machine manufacturer s specification sheet, a mass deposition rate of 2.2 lbs/hr is possible. Assuming the quoted value is for stainless steel with a density of 8000 kg/m 3, what volumetric material deposition rate is possible? [5 points] b. The manufacturer s specifications also state that in subtractive mode, the machine can deliver 25.5 horsepower. If stainless steel has a specific energy of 10 J/mm 3, what material removal rate is possible at maximum power? [5 points] 1

2 c. There are two options for manufacturing the component illustrated above. One is to start with stock material of diameter D and turn a portion of it down to have diameter B. The other option is to start with a cylinder of diameter B and add material to part of the cylinder to build up the flange with diameter D. If D = 200 mm, B = 50 mm, and A = 150 mm, below what value of C does it become quicker to deposit material additively than to manufacture this component completely subtractively? Explain your assumptions. [5 points] d. What consideration(s) other than processing time could be relevant in deciding whether to use additive or subtractive processing? [6 points] Part 2: Tolerancing [15 points] (a) A hole is specified with a diameter (in inches) of In the table below are several possible toleranced diameters for a shaft that is to be inserted into the hole. For each dimension, circle the description that most accurately describes the kind of fit that would be obtained [8 points]: Toleranced dimension Type of fit Clearance Transition Interference Clearance Transition Interference Clearance Transition Interference Clearance Transition Interference (b) Expansion fit. A cylindrical ABS component has an outside diameter of inches at room temperature and a steel collar into which it is to be mounted has an internal diameter of inches at room temperature. By how many Kelvin would the ABS component need to be cooled to be able to be placed inside the collar with a clearance of inches during fitting? Assume the thermal expansivity of ABS to be /K and that of steel to be /K. [7 points]. 2

3 Part 3: Stereolithography [64 points] In this question you will explore some factors that determine the rate at which components can be 3D-printed by projection stereolithography. In stereolithography an object is built up layer-by-layer, either with a scanning beam of light that solidifies a single spot of resin at a time, or with a projected pattern that creates an entire layer in one shot. Here we consider the latter, projection-based, approach. The first setup we will consider is illustrated in Figure 1. Here, the light pattern is projected down on to the surface of a resin bath. Material becomes crosslinked in a layer just below the surface of the bath, and the support platform moves down by the layer thickness after each layer is printed. Figure 1: First stereolithography configuration The apparatus is operated in a nitrogen atmosphere so there is no oxygen inhibition of the crosslinking process. The resin contains absorber molecules such that the illumination intensity falls exponentially with distance beneath the surface of the resin according to the Beer Lambert Law: e 3

4 In this model, is the illumination intensity at distance beneath the surface, is the intensity at the surface, and is the penetration depth which characterizes the resin s absorption properties. The projector used is a commercial video projector, of which only the blue channel is used. This channel uses a 455 nm-wavelength LED having a brightness of about 2000 lumens, which is equivalent to 40 W of optical power. The projector is a full-hd unit containing 1920 x 1080 pixels. It is focused on to a region of the resin surface that is 38.4 mm x 21.6 mm. The resin manufacturer reports that the curing dose,, of the resin is 3.5 J/cm 2 at 455 nm, and the penetration depth is equal to mm. a. What is the best lateral patterning resolution that could be achieved with the system in this configuration? [3 points] b. What is the illumination intensity at the surface of the resin? [5 points] c. Write an expression in terms of,, and for the exposure time,, required for each layer. A layer can be assumed to be sufficiently crosslinked when the bottom of the layer (i.e. the point in the layer furthest from the projector) has received a dose of. [10 points] d. Now assume that you wish to use this system to produce an object that is 100 mm tall. Plot the total time, T 1, needed to print the object as a function of the layer thickness,, used, for values of from 1 nm to 1 mm. Neglect any time required for moving the platform between layer exposure steps. [Hint: use logarithmic axes] [12 points] e. Comment on the trend you observe in your graph for part (d). What layer thickness would you want to use to minimize print time? What is the minimal print time achievable? [8 points] Now let s consider a modified setup as illustrated in Figure 2. Here, the illumination is projected upwards through an oxygen-permeable membrane into a shallower tray of resin. This time the apparatus is operated in air, so oxygen diffuses up through the membrane and inhibits crosslinking in a layer of thickness next to the membrane. This inhibited layer prevents the printed object from sticking to the membrane. The object is drawn up out of the resin tray as it is printed. 4

5 Figure 2: Second stereolithography configuration Assume that the resin and illumination parameters are the same as for the first apparatus. f. Write an expression in terms of,,, and for the exposure time,, required to solidify a layer of material. Again, assume that the lowest dose experienced by material within the layer is. You can assume that the presence of oxygen does not change the dependence of intensity on z. [4 points] g. Add a second line to your plot from part (d) to show the total time, T 2, needed to print a 100 mm-tall object with the system in Figure 2, as a function of the layer thickness,, used. Assume that = 5 µm. [6 points] h. Comment on any differences between T 1 and T 2 as functions of and recommend what you would do to maximize print speed. [6 points] i. Briefly summarize the relative pros and cons of the systems shown in Figures 1 and 2. [10 points] 5