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HW5_solution - 16.881 HW#5 Design for Additivity Air Gap...

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16.881 HW#5 Design for Additivity Air Gap Problem ORIGIN := 1 Proposed Solution Objectives: Explore the effect of the choice of system response on the accuracy of an additive model of a system Reinforce material from earlier sessions Assignment The figure below depicts a side view of an electronic package. The ribbon leads are formed in a die into a leg shape (the industry uses a set of anthropomorphic terms as defined in Figure 1 ). The problem is that the yield strength of the leads varies by 10% about its nominal value of 200Mpa (assume the band is 3 s ). This tends to make the spring-back of the ribbon lead during the forming process inconsistent and hence the air gap is inconsistent. This is a problem as the air gap is filled with thermally conductive material. If the air gap is too small, the fill material will overflow from the bottom of the package and foul the contacts. If the air gap is too great, there will be insufficient area covered by conductive material. You have been given the task of making this process more robust to the variation in yield strength of the lead material and thereby reducing quality problems. See the next page for details. body depth air ga p thigh length knee radius shin le ngth foot leng th shin angle heel radius lead thickness thigh heig ht

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You have been told that you may vary the following parameters within the following ranges: Thickness of the lead material t = 0.1mm to 0.2mm Initial radius of the knee bend R i = 1mm to 2mm Initial knee angle Q o = 80 o to 120 o (see Fig. 2 below) Elastic modulus of the lead material E = 90GPa to 110GPa Shin length = 1mm - 4mm The other parameters of the problem are fixed : Air gap (desired) = 0.5 mm 0.2mm ( D o =0.2mm) Cost to rework a ribbon lead A o =\$0.50 Thigh length = 2mm Body depth = 2mm Thigh height = 5.3mm Foot length = 2 mm Shin angle is always equal to knee angle Heel radius is always equal to knee radius To simplify your analysis, you may wish to neglect the spring-back in the heel bend and focus on only the spring-back in the knee. You may assume that the springback of the knee bend is governed by the equation 3 R i = 4 R i Y � - 3 R i Y + 1 R f Ł Et ł Ł Et ł Estimate the quality loss in the system if each control factor is at the middle of its allowable range. Evaluate the significance of interaction between the control factors t and R i if variance in air gap is defined as the response of the system. Evaluate the significance of interaction between the control factors t and R i if percent conforming to air gap specification is defined as the response of the system. Evaluate the significance of interaction between the control factors t and R i if 20 log(mean air gap/variance in air gap) is defined as the response of the system.
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