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, K

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 – pulse shock, K

6 Case II: Rack on isolators – multi-DOF and

7 Case II: Rack on isolators – drop shock

8 Case II: Rack on isolators – random vibration

9 Case III: Chassis/PCB – shock

10 Case III: Chassis/PCB –random vibration

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

12 Case V: Transit Case Analysis – Nonlinearity

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.

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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

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

Blog

Announcements

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Accessing Class Notes

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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

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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

IDC M16-540-18 isolators (four on top and four at the base)

Analysis Task - stiffness

How to represent the isolator K’s into the model K1.

What’s the effect of rack frame stiffness (qualitative assessment)?

How about the non-linear K?

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Isolator Modeling

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Springs in Parallel

K1 K2

21 KKKeq

Springs in series with fixed ends

21 KKKeq

K1

K2

m1

Springs in parallel – common deflection at each spring

Springs in series – common force at each spring

212121 KKKKFFF

FKKK

F

K

F

2121

21

11

Springs in Series

21

111

KKKeq

K1

K2

Isolator Specifications

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Shear/Roll

K = 470 lb/in

Bottom-out = -3.5 in

K = 1200 lb/in

Bottom-out = 1.75 in

K = 300 lb/in

Bottom-out = 3.5 in

Tension Compression

Estimate the expected deflection range.

Use different K for shock and vibration.

Check for g and max.

K in Vertical Direction

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• Isolators in tension and compression

• The slope is K.

• K’s are additive.

• The blue is used in previous analysis, and the red in current analysis.

• K in tension is more dominant (K variation in tension has more effect).

Compression (K=470 lb/in)

1.75 in

Tension (K=1200 lb/in)

1.75 in

Exercise – Build K Table for LuxCalc

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Roll & shear

Tension

Compression

Deflection (in)

Combined Force (lbs)

0.00 0

0.10 820

0.25 1540

0.88 5949

1.75 13280

Responses – Linear K from Last Week

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Max allowable isolator deflections: Tension = 1.75 in

Keq = 4 (470 + 1200) = 6680 lb/in

Max displacement = 1.173 in

Max 10.6 g

LuxCalc Input

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Load-deflection table

Nonlinear

selection

Add table rows.

Responses – Nonlinear K

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Max displacement:

1.116 vs. 1.174 in Max acceleration:

12.7 g vs. 10.6 g

Since the stiffness in tension is significantly larger, the acceleration response is expected to be

more influenced by the tension K. The maximum acceleration is increased from 10.6 g in constant

K case to 12.7 g using nonlinear K model. The corresponding maximum displacement is

decreased from 1.174 inch to 1.12 inch.

Summary

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Combination of K’s into model K1

Series or parallel (opposite of resistors)

Non-linear K effect

Better or worse than linear approximation?

Higher K higher fn higher g

Depends on K near maximum deflection

Response curve to 40 g saw-tooth

shock with 15% damping

A (g)

fn / fp

Increasing fn or p (or decreasing fp)

Homework 5

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Nonlinear effect for lateral shock

Linear assumption of K = 300 x 8 = 2400 lb/in

Nonlinear response comparison – build K table and run.

Roll & shear

40 g 11 ms saw-tooth shock

Luxea Inc. / Dunamis Tech Inc.

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

Rack on Isolators – & Multi DOF

Case Study II

Equipment Rack System

Shock and vibration analysis of an equipment rack system –

effect and 2 DOF case

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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