Optimum Design
161
with
and
with
2_
Pmax -- Pmin
PmP,~ -
(3.46)
2
2
Sys = d-y Sno = ~7
(3.47)
The author [3.1] presents a sample problem which is duplicated here for a
fatigue condition.
A squared and ground spring is subjected to
Pmax = 88.2 lbs and emin = ¼ (88.2 lbs). These are substituted in Eq. (3.46)
yields
1
-- ~ Pmax 3
Pm Pmax + ~ Pmax 5
Pmax
1
-=
-2
2
~emax
(3.48)
6max - 0.5906 in, N = 1.15, Q = 2, andfa = 10 cps.
Table 3.1 is a sample of values found for a variety of materials. The computer solutions found need to be checked for validity.
1. The materials limits need examination.
(a) Are the answers in the range of the equations used for Sys
and Sno? ASTM 313 was not!
(b) Are the values exceeding the maximum stress values for
Sys and S,~o? Here dis substituted into Sys, and S,,o to verify
this. Also the maximum force is used in the stress equation
to check again for maximum stress.
(c) Check all function constraints for the criterion function
(the weight).
EXAMPLE 3.9. A two pound steel disk Fig. 3.4 is supported by a
round thin wall tube and requires bending and torsional frequencies of
greater than 200 Hz each. The minimum thickness for a spring dimension,
t, is greater than 0.0015 in, R is less than 2.1211 in so the round spring
can be attached and the spring length L is greater than 0.100 in. Since
the tube can have thin wall torsional and bending buckling, it must be
checked for both. A minimum weight spring is desired. The equations
are developed.
161
with
and
with
2_
Pmax -- Pmin
PmP,~ -
(3.46)
2
2
Sys = d-y Sno = ~7
(3.47)
The author [3.1] presents a sample problem which is duplicated here for a
fatigue condition.
A squared and ground spring is subjected to
Pmax = 88.2 lbs and emin = ¼ (88.2 lbs). These are substituted in Eq. (3.46)
yields
1
-- ~ Pmax 3
Pm Pmax + ~ Pmax 5
Pmax
1
-=
-2
2
~emax
(3.48)
6max - 0.5906 in, N = 1.15, Q = 2, andfa = 10 cps.
Table 3.1 is a sample of values found for a variety of materials. The computer solutions found need to be checked for validity.
1. The materials limits need examination.
(a) Are the answers in the range of the equations used for Sys
and Sno? ASTM 313 was not!
(b) Are the values exceeding the maximum stress values for
Sys and S,~o? Here dis substituted into Sys, and S,,o to verify
this. Also the maximum force is used in the stress equation
to check again for maximum stress.
(c) Check all function constraints for the criterion function
(the weight).
EXAMPLE 3.9. A two pound steel disk Fig. 3.4 is supported by a
round thin wall tube and requires bending and torsional frequencies of
greater than 200 Hz each. The minimum thickness for a spring dimension,
t, is greater than 0.0015 in, R is less than 2.1211 in so the round spring
can be attached and the spring length L is greater than 0.100 in. Since
the tube can have thin wall torsional and bending buckling, it must be
checked for both. A minimum weight spring is desired. The equations
are developed.