1. Integrated Analysis of Electronics Based on Random Vibration
and Thermal Cycling Constraints
Valeriy Khaldarov
Electronic Components Reliability Analysis
Mesa, AZ
vkbgoog@gmail.com
Abstract – There is a connection between the size of the
printed circuit board (PCB), its natural frequency and the
life of solder joints for a through-hole-mounted
component. An integrated software package, ASONIKA,
can quickly simulate electronics and chips subjected to
complex thermal and mechanical influences. Knowing
this general guideline allows for a combined thermal and
mechanical concept to move forward. Trade studies of
PCB size and appropriate parameters for vibration
isolators can produce a design that will satisfy the loads
experienced in random vibration and thermal cycling
environment. This saves time and money for the
electronic equipment designer and manufacturer.
I. INTRODUCTION
There must be a “Rule-of-Thumb” for designing electronic
equipment parameters based on vibration and thermal
environment influences the electronics must operate
under. By applying Miner’s cumulative damage ratio,
where
⋯ 1.0, (1)
and using ASONIKA-V subsystem, trade studies of PCB size
and vibration isolator parameters are easy to identify.
II. TRADE STUDY
We review an example described by Steinberg [1]. Figure 1
shows geometry of a polyimide glass PCB with a through-
hole-mounted hybrid component designed and used for
monitoring performance of a delivery truck combustion
engine located inside the engine compartment.
Figure 1: Dimensions (in inches) of the PCB and its
through-hole-mounted hybrid component
The electronics will be expected to go through and
withstand random vibrations from an environmental stress
screening (ESS), city, and highway driving. Power spectral
density values and their durations are shown in Figure
2(a).

2. Figure 2: Transient stresses experienced by the PCB and
its component due to random vibration and thermal
cycling.
In addition, the electronics will need to withstand thermal
stresses due to thermal cycling conditions experienced
during ESS, city, highway driving, and storage
environments. The expected temperature differences and
their respective number of thermal cycles are given in
Figure 2(b).
III. ASSUMPTIONS
We make the following assumptions with respect to
calculations:
A. There are equal number of failures in the lead wires
and solder joints from random vibration.
B. Solder joint height and PCB thickness are the same.
Since the differences of the coefficients of thermal
expansion of a through-hole component and the PCB
can produce overturning moments in the wires that
lead to shear tear-out in solder joints (see Figure 3), we
attribute PCB thickness as a variable parameter to
thermal cycling fatigue.
Figure 3: Solder shear tear out due to mismatch of
coefficients of thermal expansion for a through-hole
component and the PCB [1].
IV. RESULTS
Figure 4(a) shows a typical “Damage-Boundary” diagram,
where the x-axis represents PCB thickness, y-axis --
resonance frequency of the PCB,
Figure 4: Fatigue cycle ratio values with respect to
resonance frequencies of the PCB and thickness.

3. and the lines (referred to as Critical Frequency and Critical
PCB Thickness) -- separation of damage and no damage
regions.
We can see that only blue and purple regions can satisfy
the inequality condition specified in Equation (1).
Furthermore, in the context of Stress Margin Analysis [2]
only the blue region will satisfy six sigma design
robustness requirement.
Figure 4(b) and (c) show the response breakdown to each
influence with respect to either PCB thickness or natural
frequency. From Figure 4(b) we see that PCB thickness can
significantly change fatigue ratio values between 0.06 and
0.10 inches; while from Figure 4(c) we can infer that this
ratio will not change much at around 160 hertz for the
PCB. To achieve this natural frequency, we use ASONIKA-V
subsystem to identify appropriate parameters of vibration
isolators for the PCB.
Table 1 lists two types of vibration isolators taken from
ASONIKA database where the second type exceeds rigidity
values of the first by a factor of about 2.5.
Table 1: Rigidity values for
(a) type I and (b) type II
vibration isolators
Figure 5(a) and (b) show system response subjected to
highway driving conditions with natural frequency of
about 100 Hz for type I and 160 Hz for type II vibration
isolators along the x and y axes. Figure 5(c) shows that the
natural frequency of type II vibration isolators stays at
about 160 Hz when the electronics are subjected to city
driving conditions.
Figure 5: System response of (a) type I, (b) type II
vibration isolators subjected to highway driving
conditions, and (c) type II vibration isolators subjected to
city driving conditions.
We can use the following calculations [3] to double check
our results.
∗ ∗ ∗
9.8
where = 160 Hz, selected system natural frequency

4. = 6 in, width of the PCB
= 8 in, length of the PCB
= 0.075 in, PCB thickness
= 0.0578 lb/in
3
, density of the PCB
160 6 ∗ 8 ∗ 0.075 ∗ 0.0578
9.8
= 543.6 "/$%
Since 4 isolators will be used to support the system, the
required rigidity value of each isolator becomes
=
543.6
4
= 135.3 "/$%/$&' ()'*
Since this calculated rigidity value is less then ones shown
in Table 1(b) for x and y axes, we conclude that the
parameters listed for vibration isolators of the second type
are more appropriate for highway and driving conditions
given in Figure 2(a).
V. CONCLUSIONS
Calculating Miner’s cumulative damage ratio for an
electronic equipment operating under particular
environmental conditions allows easy access to vibration
isolator parameters in ASONIKA-V subsystem. Once the
relationship between PCB size and natural frequency is
known, the design has a robust concept. It is now ready for
detailed design by various experts.
REFERENCES
[1] D. S. Steinberg, Preventing Thermal Cycling
and Vibration Failures in Electronic
Equipment, John Wiley & Sons, 2001.
[2] N. Pascoe, Reliability Technology: Principles
and Practice of Failure Prevention in
Electronic Systems, John Wiley & Sons,
2011.
[3] LORD, "Aerospace and Defense Isolator
Catalog," [Online]. Available:
http://www.lord.com/products-and-
solutions/vibration-and-motion-
control/aerospace-and-defense. [Accessed 4
February 2016].
[4] A. Mangroli and K. Vasoya, "Optimizing
thermal and mechanical performance in
PCBs," Global SMT & Packaging, pp. 10-12,
December, 2007.