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 springback 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 springback in the heel bend and
focus on only the springback 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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 Fall '03
 lDavidMiller
 Variance, Ri, air gap

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