| |
Robust Design Using Helical Spring Design
Equations
 The CTQ=Spring Rate, k is given below:
Table 2.1 Statistics of Spring
|
Parameter |
Description |
Distribution |
Mean |
Std. Dev. |
|
d |
Wire dia. |
Normal |
0.125 |
0.00104 |
|
D |
Coil dia. |
Normal |
2.0 |
0.028 |
|
G |
Modulus |
Normal |
1.5E6 |
0.346E6 |
|
N |
Active
Coils |
Deterministic |
10 |
0 |
In this table, the means are the controllable parameters
while the standard deviations are the noise parameters. Find the Robust Design
point for the desired spring rate, k, equal to 4.
Solution:
Random Variables:
Table 2.2 Definition of Random Variables in UNIPASS
|
Random
Variables |
Description |
Distribution |
Lower Bound |
Upper Bound |
|
X1 |
Range of Wire
dia. |
Uniform |
0.05 |
0.25 |
|
X2 |
Range of Coil
dia. 1 |
Uniform |
1 |
3 |
|
X3 |
Range of Coil
dia. 2 |
Uniform |
1 |
3 |
|
X4 |
Range of
Modulus |
Uniform |
10E6 |
2.0E6 |
|
Random
Variables |
Description |
Distribution |
Mean |
Stand.
Dev. |
|
X5 |
Wire dia., d |
Normal |
Range_d |
0.00104 |
|
X6 |
Coil dia., D1 |
Normal |
Range_D1 |
0.028 |
|
X7 |
Coil dia., D2 |
Normal |
Range_D2 |
0.028 |
|
X8 |
Modulus, G |
Normal |
Range_G |
0.346E6 |
Limit State Function:
The result is summarized as
***** ROBUST DESIGN *****
1st-order standard dev. of g(x)......=
2.0727449E-01
value of limit-state function.....g(x) = 1.22791E-08
Robust Point
|
Variable Name |
X-Space |
U-Space |
Directional
Cosine |
|
Wire dia., d |
1.38422E-01 |
-6.64796E-01 |
-0.01298 |
|
Coil dia., D1 |
1.50875E+00 |
1.56048E+00 |
0.00613 |
|
Coil dia., D2 |
2.91028E+00 |
2.17469E-01 |
0.00929 |
|
Modulus, G |
1.03478E+07 |
7.26377E-01 |
-0.01445 |
|
