1 Dr. Peter Avitabile, Assistant Professor

Mechanical Engineering Department

Shock Isolation Assessment from Multiple Sensors

Shock Isolation of Equipmentusing

Acceleration/Displacement Sensors

2 Dr. Peter Avitabile, Assistant Professor

Mechanical Engineering Department

Shock Isolation Assessment from Multiple Sensors

Problem

Mechanical equipment is subjected to a variety of different loading that must be considered in the design process

DROP LOADS

MISC LOADS

OPERATING LOADS

TRANSPORTATION LOADS

3 Dr. Peter Avitabile, Assistant Professor

Mechanical Engineering Department

Shock Isolation Assessment from Multiple Sensors

Problem

•Electronic equipment is sensitive to shock loads

•Severe loadings are of concern

•Measurements of response are needed

•How can this be accomplished?

Shipboard equipment response due to shock

high speed video

showing shock response

4 Dr. Peter Avitabile, Assistant Professor

Mechanical Engineering Department

Shock Isolation Assessment from Multiple Sensors

Dynamic Response Considerations

•Measurements of both acceleration and displacement need to be obtained

•Various transducers are available for measurement of response

•Numerical evaluation of data required

Assessing Shock Response from Multiple Sensors

5 Dr. Peter Avitabile, Assistant Professor

Mechanical Engineering Department

Shock Isolation Assessment from Multiple Sensors

Measurement Considerations

•Response due to shock needs to be determined

•Measurements of displacement and acceleration using accelerometers and LVDTs are options for transducer selections

Assessing Shock Response from Multiple Sensors

6 Dr. Peter Avitabile, Assistant Professor

Mechanical Engineering Department

Shock Isolation Assessment from Multiple Sensors

Different Ways to Solve the Same Problem

TIME DOMAIN

FREQUENCYDOMAIN

LAPLACEDOMAIN

TRANSFORMATION TRANSFORMATION

PARAMETER ESTIMATIONSUBSET

* Time domain represents the physics of the system

* Frequency domain represents the system in terms of it's periodicities

* Laplace domain represents the system in terms of its poles and residues

Time Domain requires integration and differentiation numerically

7 Dr. Peter Avitabile, Assistant Professor

Mechanical Engineering Department

Shock Isolation Assessment from Multiple Sensors

Equivalent System Model Representation

The system can be modeled in an equivalent sense

m

k c

x(t) f(t)

f 1 x1

k 1x1 c1x1

m 1

Homogenous equation is

and assuming an exponential solution form gives

0kxxcxm

0ekcsms st2

FBD

8 Dr. Peter Avitabile, Assistant Professor

Mechanical Engineering Department

Shock Isolation Assessment from Multiple Sensors

Numerical Integration/Differentiation

The differential equation could also be processed in the time domain using numerical techniques

i1ii1i

1ii xx2

yyII

Displacement

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0 0.2 0.4 0.6 0.8 1

seconds

in/s/s

Accelerometer

LVDT

Velocity

-10

-8

-6

-4

-2

0

2

4

0 0.2 0.4 0.6 0.8 1

seconds

in/s Accelerometer

LVDT

Acceleration

-500

-400

-300

-200

-100

0

100

200

300

400

0 0.2 0.4 0.6 0.8 1

seconds

in/s/sAccelerometer

LVDT

9 Dr. Peter Avitabile, Assistant Professor

Mechanical Engineering Department

Shock Isolation Assessment from Multiple Sensors

Numerical Integration & Differentiation

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0 0.2 0.4 0.6 0.8 1

Numerical integration of acceleration data to obtain displacement data

Compare results to actual measured data

-2500

-2000

-1500

-1000

-500

0

500

1000

1500

2000

2500

0 0.2 0.4 0.6 0.8 1

Double DifferentiatedDisplacement

Measured Accleration

Numerical differentiation of displacement data to obtain accelerations and compare to measured data

10 Dr. Peter Avitabile, Assistant Professor

Mechanical Engineering Department

Shock Isolation Assessment from Multiple Sensors

Evaluation of Measurement Locations

•Strength of Materials (structural characteristics)

•Dynamics (mass, inertia properties)

•ME Lab (digital data acquisition)

•Numerical Methods (integration, differentiation)

•Math (ODE, Laplace, Fourier Series)

Need to know ………

11 Dr. Peter Avitabile, Assistant Professor

Mechanical Engineering Department

Shock Isolation Assessment from Multiple Sensors

Senior Project Results

Displacement vs. Time (Displacement Response)

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

8.3 8.5 8.7 8.9 9.1 9.3 9.5

Time (s)

Dis

plac

emen

t (in

)

Displacement Simulink

Acceleration vs. Time (Displacement Response)

-500

-400

-300

-200

-100

0

100

200

300

400

500

600

8.3 8.5 8.7 8.9 9.1 9.3 9.5

Time (s)

Acc

eler

atio

n (i

n/s^

2)

Acceleration Simulink

Displacement Acceleration

12 Dr. Peter Avitabile, Assistant Professor

Mechanical Engineering Department

Shock Isolation Assessment from Multiple Sensors

Skill Sets Needed

•Must have a firm understanding of underlying math related to problem

•Computer software helps provide solution to underlying mathematical formulation

•Upper level students are expected to have a firm understanding of basics to solve the problem

•Engineers utilizing tools to solve critical problems clearly must understand the basic underlying mathematical principles involved

Numerical methods used in problem evaluation

13 Dr. Peter Avitabile, Assistant Professor

Mechanical Engineering Department

Shock Isolation Assessment from Multiple Sensors

This project is partially supported by NSF Engineering Education Division Grant EEC-0314875

Multi-Semester Interwoven Project for Teaching Basic Core STEM Material Critical for Solving Dynamic Systems

Problems

Peter Avitabile, John White, Stephen Pennell

Acknowledgements

TIME

FREQUENCY

ACCELEROMETER

IMPACT HAMMER

FORCE GAGEHAMMER TIP

FOURIERTRANSFORM

LVDT

DISPLACEMENT

ACCELERATION

DIGITALANALOG TO

DIGITIAL DATA ACQUISITION

NUMERICAL PROCESSINGINTEGRATION / DIFFERENTIATION

i1ii1i

1ii xx2

yyII

QUANTIZATIONSAMPLINGALIASINGLEAKAGE

WINDOWS

DYNAMIC TESTINGPULLS ALL THE

PIECES TOGETHER !!!

TIME

FREQUENCY

X

Y

TRANSDUCERCALIBRATION

REGRESSION ANALYSIS

HAMMER TIP CHARACTERIZATION

FOURIER SERIES & FFT

m

k c

x(t) f(t)

SDOF DYNAMIC

MODEL APPROXIMATION

SYSTEM MODEL

100

10

1

n

0

-90

-180n

)t(fxkdt

dxc

dt

xdm 2

2

DIFFERENT PULSE SHAPES

)ps(

a

)ps(

a)s(h *

1

*1

1

1

FREE BODY DIAGRAM& EQUATION OF MOTION

LAPLACE & TRANSFER FUNCTION

tsinem

1)t(h dt

d

FIRST & SECOND ORDER SYSTEMS

SIGNAL CONDITIONER RISE & SETTLING TIME