Shock & Vibration:

Case Study

For Northrop Grumman Information Systems

LX Course: 3rd Quarter 2011

The presentation material is a proprietary property of Luxea & Dunamis Inc.

Contact the company for appropriate distribution.

Luxea Inc. / Dunamis Tech Inc.

2 The presentation material is a proprietary property of Luxea & Dunamis Inc. Contact the company for appropriate distribution.

Rack on Isolators – Pulse Shock

Luxea Inc. / Dunamis Tech Inc.

3 The presentation material is a proprietary property of Luxea & Dunamis Inc. Contact the company for appropriate distribution.

Live meeting number:

1-877-740-2201

Pass code: 9702761

SCHEDULE

Week Topic/Case Study HW

1 Overview and Introduction

2 Review of Shock & Vibration for Electroincs I

3 Case I: Transportation random vibration

4 Case II: Rack on isolators – pulse shock

5 Case II: Rack on isolators – drop shock

6 Case II: Rack on isolators – random vibration

7 Case II: Rack on isolators – multi-DOF and nonlinear effect

8 Case III: Chassis/PCB – shock

9 Case III: Chassis/PCB – random vibration

10 Case IV: Transit Case Analysis – MIL-HDBK-304

11 Case V: Transit Case Analysis – Nonlinearity

12 Summary and Closing

CLASS NOTES & SOFTWARE

• LuxCalc Tools v1.2.3 is available for download from NG ESL server.

• Class notes will be posted on Fridays downloadable from Luxea.com site.

www.luxea.com/seminars

Create an account to access the files and blog access.

In the name field, start with “NG” before your name, e.g., name: NG Keith Yi

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HOMEWORK

• Homework description is included in the class notes.

• Answer is posted every Thursday pm.

• Discussions and comments are encouraged through Luxea HW blog

www.luxea.com/blog

Best comments/discussion/review will be selected bi-weekly for a prize.

Blog

Announcements

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Shock Environment Specifications

Shock types:

• Pulse shock

• Velocity shock (drop shock)

• Shock response spectrum

Pulse shock: MIL-E-5400, MIL-STD-810, MIL-T-5422

Velocity shock (drop shock)

• Drop shock (falling package),

• Hammer shock (sudden velocity to the specimen)

Shock response spectrum

• Shock specifications based on the structure’s expected response

to shock input as a function of frequency.

Pulse Shock

Pulse shocks do not represent the real environment.

Effective in revealing the weak area

½ sine pulse is the most common form.

Gin

p

p

pf2

1

p = 11 ms

fp = 45.5 Hz

SDOF Response to Half Sine Pulse

Response of a single DOF system to a half sine pulse input

Closed-form solution

c

m

k

Shock attenuation area

pulsen ff /

Am

plif

ication

A=

Go

ut/G

in

Shock isolator selection criteria depends on

fp

p

n

ff

Shock amplification area

m

kfn

2

1

fn/fp ~0.6

Half Sine and Saw-tooth Pulses

Comparison of responses to half sine pulse and the saw-tooth pulse

• 30g ½ sine vs. 40g saw-tooth pulse

• For the same Gin, the sine pulse causes higher response.

0

10

20

30

40

50

60

0 50 100 150 200 250

G r

esp

on

se

natural frequency (Hz)

Comparison of shock pulses

30 g sine

40g sawtooth

30 g input sine

40 g input saw-tooth

Pulse Response Comparison (SDOF)

0 1 2 3 4 5 6 7 8 9 10

Frequency ratio, f/fp

Am

pli

fica

tio

n, G

ou

t/G

in

Approximate max amplification

~1.8

~2.0

~1.4

~2.0

Exercise – SDOF Pulse Shock

11

Exposed to 11 ms, 20 g, ½ sine shock.

a. Calculate the pulse frequency

b. Determine the maximum acceleration transmitted to the chassis.

1f 2

f

P30 lbs Chassis

Chassis resonance was found to be 100 Hz at 5% damping.

Exercise - LuxCalc Tools Shock Input View

12

inlbk /71.30682)1002(386

30 2Spring constant for Chassis

Damping

K and m

Shock pulse data

Pulse shock

Observation time

13

Exercise – Acceleration View

Peak acceleration = 31.83 g

Frequency ratio, f/fp = 2.2

Amplification, Gout/Gin ~1.6

Gout ~ 32 g

0 1 2 3 4 5 6 7 8 9 10

Homework 4 – Two DOF Shock

14

1f 2

f

P

1 lb

30 lbs

PCB

Chassis

Exposed to 11 ms, 20 g, ½ sine shock.

Determine the maximum acceleration responses of the PCB and chassis.

PCB resonance at 200 Hz and Chassis resonance at 100 Hz at 5% damping

Test Case II – Equipment Rack Shock Isolation Analysis

• Problem Statement

A rack equipment is to be isolated from shock.

It is exposed to 40g 11 ms saw tooth pulse.

Limit the transmitted load to payload to 20 g.

Isolators

x

y

z

Rack frame

15

Isolators

Data and Assumptions

• Data and Assumptions

The payload weight = 774 lbs

The rack structure is significantly stiffer than isolators.

Modal damping coefficient = 0.15

• Analysis Task

Responses to the 40 g 11 ms saw-tooth pulse

IDC M16-540-08 isolators selected – is this adequate?

What if it’s exposed to 40 g 15-23 ms?

Show relevant displacement and acceleration plots.

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Isolator Specifications

17

IDC M16-540-08 isolators Max allowable isolator deflections:

Compression = -3.5 in Tension = 1.75 in Shear/Roll = 3.5 in

LuxCalc Analysis

18

40g, 11ms pulse

W = 774 lbs

K = 6680 lb/in

Saw tooth pulse

z

ζ = 15 %

500 ms, observation period

Responses – Displacement and Acceleration

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•Max allowable isolator deflections: Tension = 1.75 in

•Max acceleration at the rack equipment = 20 g

Max displacement = 1.173 in

Max 10.6 g

Longer Shock Pulse – 23 ms

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•What if shock is 40 g, 15-23 ms?

Max displacement = 2.36 in

Max 21.4 g

Isolator fails in both acceleration and

displacement (at 23 ms).

Graphic Solutions

21

• fp=21.7 Hz (23 ms saw-tooth pulse)

• fn = 9.19 Hz

• Frequency ratio, fn/fp = 0.42

• Amplification, Gout/Gin ~0.6

• Gout ~ 24 g

• Fp=45.5 Hz (11 ms saw-tooth pulse)

• fn = 9.19 Hz

• Frequency ratio, fn/fp = 0.20

• Amplification, Gout/Gin ~0.3

• Gout ~ 12 g

0 1 2 3 4 5 6 7 8 9 10

0.2

0.42

0.6

0.3

Hzm

Kfn 19.9

09.386/774

6680

2

1

Luxea Inc. / Dunamis Tech Inc.

22 The presentation material is a proprietary property of Luxea & Dunamis Inc. Contact the company for appropriate distribution.

Rack on Isolators – Drop Shock

Case Study II

Equipment Rack System

Shock and vibration analysis of an equipment rack system

mounted on coil isolators exposed to Drop Shock.

Shock pulse and drop shock per

MIL-STD-810F

Random vibration per MIL-STD-

810F

One and two DOF models,

various parameter effects

Use of LuxCalc Tools for quick

evaluations

This case study demonstrates the

influence of various parameters.

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