2019美赛建模A题

2019MCM

Problem A:A Hot Youbot

Background:Thermal Analysis,using finite element techniques,is carried out as a steady-state or transient analysis.Conductive heat transfer is handled directly by finite element techniques; conduction occurs in a solid due to temperature differences.However,radiation heat transfer analysis may require additional particle-tracking or ray-tracing techniques to approximate the radiant energy arriving at a given surface.

The material is assumed to be a magnesium alloy and to have a thermal conductivity of52W/m?K. Material properties were taken from"Thermal Conductivity of Magnesium Alloys".Since the model is in inches you can use symunit to rewrite the value in inches.Now you need remove the units to obtain the value for the thermal properties.Unless overwritten,all of the side faces are set to have a natural convection coefficient of25W/m2?K representing heat transfer to an ambient air temperature of288.15K(25℃).Convert and calculate the convection coefficient to W/inch2?K to be consistent with the model dimensions.

Explore different material selections for the robotic https://www.sodocs.net/doc/1212828877.html,pute the change in max body temperature as a function of increasing thermal conductivity.Before begining calculate the expected run time from the previous run time.Run the models using a parfor loop to speed up the simulation by parallelizing the iterations across Parallel Computing Toolbox workers.If you do not have the Parallel Toolbox change parfor to for.

Problem:

Part I:Develop a mathematical model for the heat transfer among the gripper pivot.In the youBot,the gripper pivot sits underneath the electronics board and is exposed to the heat coming off the circut board.Here you will create the pde model,import the STL file of the gripper pivot, and plot it.Create and visualize a tetrahedral mesh of the component with a maximum value of 0.09inches.Measure the x,y and z dimensions of the mesh.

Part II:The bottom face is given a fixed temperature assuming that the rest of the robotic arm acts as a heat sink.The top face and inner hole is arbitrarily given a heat flux to represent the heat off the circuit board.Solve the model and calculate the max and bulk body temperatures and time how long the solve https://www.sodocs.net/doc/1212828877.html,pute the max temperature in K and rewrite that to℃and F,then plot the distribution of temperature of the gripper pivot in3D.

Part III:Develop a mathematical model for predicting the relationship between thermal conductivity and max temperature for this geometry and material.Assume the robotic arm shuts off at a max temperature of311K,find the associated allowable heat transfer coefficient for the alloy.Which materials are appropriate for being made into the the gripper pivot?

Part IV:Prepare a short(1to2pages)synopsis of your results suitable for publication as a short note in IEEE Communications Magazine.

Your submission should consist of:

●One-page Summary Sheet,

●Two-page synopsis,

●Your solution of no more than20pages,for a maximum of23pages with your summary

and synopsis.

●Note:Reference list and any appendices do not count toward the23-page limit and

should appear after your completed solution.

Reference:

Lee,Sanghyun,et al."Thermal Conductivity of Magnesium Alloys in the Temperature Range from-125℃to400℃."International Journal of Thermophysics34.12(2013):2343-2350. Appendix:

The structure of Gripper Pivot in youBot plotted by AutoCAD:

ProblemAData：youBot.stl