Additive Manufacturing

ME 6180 – Additive Manufacturing

Summer 2018

Homework 4

Due date: July 6, Friday 5:00 pm in PILOT dropbox

1. Consider that you are using an extrusion based ABS printer. Calculate the required heater

power, total pressure drop in liquefier, and motor power for extrusion at steady state

condition for deposition speed of 0.5, 1, 1.5, 3, 5, 10, and 50 mm/s and plot them on three

separate graphs. Use the following data:

m = 2.16

 = 7.4 x 10-5 (kPa)-m s-1

 = 900 kg/m3

cp = 1500 J/kg-K

D1 = 1.8 mm

L1 = 10 mm

Some required data is missing that can be found from literature.

2. The generalized heat equation for laser melting is given by

𝜌𝑐 𝜕𝑇

𝜕𝑡 =

𝜕

𝜕𝑥 [𝑘𝑥

𝜕𝑇

𝜕𝑥 ] +

𝜕

𝜕𝑦 [𝑘𝑦

𝜕𝑇

𝜕𝑦 ] +

𝜕

𝜕𝑧 [𝑘𝑧

𝜕𝑇

𝜕𝑧 ] + 𝜌𝑐 (𝑉𝑥

𝜕𝑇

𝜕𝑦 + 𝑉𝑦

𝜕𝑇

𝜕𝑦 + 𝑉𝑧

𝜕𝑇

𝜕𝑧 ) + 𝑄

where

Reduce the above equation for steady-state thermal analysis of a system having a stationary heat

flux and no-heat generation. Then solve the following problem:

Consider a case where the surface of a metal plate is irradiated by a stationary laser so that the

steady-state temperature near the laser-irradiated region of the top surface is defined by an

exponential function given in the figure below. The remaining boundaries are maintained room

temperature (23oC). Consider kx = 50 W/m 2-K, ky = 60 W/m

2-K, and grid sizes x = 0.6 mm, y

= 0.5 mm.

1. Derive finite difference equations for all the interior nodes.

2. Develop a MATLAB code, and determine temperatures at all interior nodes.