pseudo velocity shock analysis velocity shock spectrum … · shock analysis using the pseudo...
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VelSSComparison 1
PSEUDO VELOCITY SHOCK ANALYSISVelocity Shock Spectrum and Analyses
Comparison
•Howard A. Gaberson, Ph.D., P.E.•Consultant
•234 Corsicana Drive•Oxnard, CA 93036-1300
•(805)485-5307•[email protected]
Mechanical Shock Test Techniques and Data Analysis
SAVIAC
VelSSComparison 2
SHOCK ANALYSIS USING THE PSEUDO VELOCITY SHOCK SPECTRUM
PART 3• Pseudo velocity is compared to relative velocity shock
spectra on 4CP and we find problems with relative velocity.
• Relative velocity has low frequency problem, and doesn't show the maximum acceleration.
• Review tests to determine which transient motion analyses method is the best indicator of damage potential.
• The best damage potential analysis is the damped PVSS on 4CP.
• Shaker Shock and Miscellaneous Issues
VelSSComparison 3
All kinds of shocks: package drops, collisions, transportation bumps, but face it; explosions are where its at
• Wait and see; I’ve got one.• Late 60’s; Prairie Flat
VelSSComparison 4
PRARIE FLAT ALBERTA
VelSSComparison 5
TNT PILE PHOTO
9 Aug 1968
VelSSComparison 6
Explosion I
VelSSComparison 7
Explosion II
VelSSComparison 8
This first set of slides tests relative velocity vs. PV as a spectrum ordinate
• Now we look at four shocks, and their integrals to velocity and displacement.
• Then I calculated their relative and pseudo velocity shock spectra and overlaid them.
• Relative velocity is about equal to pseudo velocity in the severe zone, but has no useful asymptotes or other meaning on 4CP.
• Peak relative velocity doesn't seem helpful.
VelSSComparison 9
Peak accel: 130
Velocity change and peak velocity are 120 ips
Max displacement 2.4 in
Reed’s time history
VelSSComparison 10
Very Low Frequency SDOF Relative Velocity
• Relative velocity sees peak shock (bogey) velocity.
• Pseudo Velocity sees peak shock (bogey) deflection.
VelSSComparison 11
2.4 inches
Vel change 120
130 g's
Rel Vel SS and PVSS for Reed
VelSSComparison 12
2.4 inches
130 gs
Blue rel vel does not hit asymptotesAgrees in center severe section
Reed SS’s, 5% Damping
VelSSComparison 13
HS54 Time History
VelSSComparison 14
130 g's
270 ips
I should have drawn 54 inch line.
Rel Vel SS and PVSS for HS54
VelSSComparison 15
Blue is rel vel, doesn’t hitaccel asymptote.Magenta is PV
HS54 SS’s, 5% Damping
VelSSComparison 16
900 g's
300 ips Vel change
8 inches
HW4 Time History
VelSSComparison 17
8 inches
300 ips
Blue is rel velMagenta is PVAt low frequencies, rel vel ismax velocity, PV is max z
Rel Vel SS and PVSS for HW4
VelSSComparison 18
900 g's
Low frequency SDOF see peak rel vel
PV shows peak spring deflection
HW4 SS’s, 5% Damping
VelSSComparison 19
Meaningless
HW4 SS’s, 10% Damping
VelSSComparison 20
Peak g: 0.35
Peak vel is 15, vel change is about 20 ips
Max z about 70 in.
El Centro EQ Time History
VelSSComparison 21
Rel Vel SS and PVSS for El Centro
VelSSComparison 22
Velocity change 20 ips
70"0.35 g
Peak velocity 15 ips
Rel Vel SS and PVSS for El Centro EQ
VelSSComparison 23
CONCLUSION: PVSS Gives More Useful Information than Relative Velocity SS
• PVSS has HF peak acceleration asymptote vice rel vel SS not.
• Both have about equal levels in plateau• PVSS has LF max deflection asymptote
vice rel vel SS not• Rel Vel SS has LF max velocity asymptote
vice PVSS not. Not that helpful.
VelSSComparison 24
The Magnitude of the Fourier Transform of a Shock is its Undamped Residual PVSS
VelSSComparison 25
Background
• Proved by many and Rubin in [Shock and Vibration Handbook, 2002, pp 23.24,23.25],
• Hopefully more clear here.• Undamped shock spectrum equation: (Set 1, Sli 24)
0
1 ( )sin ( )t
z y t dτ ω τ τω
= − −∫
VelSSComparison 26
Complex vector ideas
ie α
• is a complex vector at angle . ie α
α
( )
0
1 Im ( )t
i tz y e dω ττ τω
−⎡ ⎤= − ⎢ ⎥
⎣ ⎦∫
0
1 Im ( )t
i t iz e y e dω ωττ τω
−⎡ ⎤= − ⎢ ⎥
⎣ ⎦∫
The integral on the right is the FT. Call it Y.
( )
cos sin:
Im sin
i
i
e iso
e
α
α
α α
α
= +
=
0
1 ( )sin ( )t
z y t dτ ω τ τω
= − −∫
VelSSComparison 27
Continue vector ideas
1 Im i tz e Yω
ω⎡ ⎤= − ⎣ ⎦
iY Y e θ=
0
( ) −= ∫T
iY y e dωττ τ
Im i t iz e Y eω θω ⎡ ⎤= − ⎣ ⎦
Put this in here.
VelSSComparison 28
Combine the exponents and use the sine
( )Im i tz Y e ω θω +⎡ ⎤= − ⎣ ⎦
sin( )z Y tω ω θ= − +
( )maxz Yω =
z at every frequency is vibrating continuously at that frequency with the magnitude or value of Y. Y is the residual PV.
VelSSComparison 29
How do we calculate? Make it discrete.
ττ=ω ωτ−∫ de)(yz i
t
0
sf1nf2iN
1ns
e)n(yf1)f(Y
−π−
=∑=
A row times a column is a sum of the products. Actually used a row of N complex numbers or exponentials times a column of N accelerations times.
( )
21
1, 1:
s
s
i t ft
df
nt from n N
f
ω π
τ
=
=
−= =
VelSSComparison 30
Code crux
• for kk=1:nfreqs• Y(kk)=1/fs*abs(exp(-i*tpi*f(kk)*t)*yy);• end• loglog(f,Y);
sf1nf2iN
1ns
e)n(yf1)f(Y
−π−
=∑=
VelSSComparison 31
Example applied to 2000 g 0.4 ms half sine shock
• Fourier Transform Calculation In Matlab• Compare with Undamped PVSS
VelSSComparison 32
Plot Undamped PVSS and Fourier Transform of 2000g, 0.4 ms half sine
Fourier transform is residual undamped PVSS so it must lie under the overall undamped PVSS, which it does.
VelSSComparison 33
FT and DFT
sf1nf2iN
1ns
e)n(yf1)f(Y
−π−
=∑=
∑−=
=
π−
=1Nn
0n
Nkn2i
nk exN1X
Very similar; FT evaluates for a freq list, and divides by fs. Fewer values. Matlab’s DFT has N differently; confusing.
VelSSComparison 34
Matlab's DFT has 1/N in DSP position
21
0
1( 1) ( 1)i knN
N
k
x k X k eN
π−
=
+ = +∑
21
1 10
i knn NN
k nn
X x eπ−= −
+ +=
= ∑
This needs more explanation Matlab’s DFT has N differently; confusing.
VelSSComparison 35
HOW TO LOOK AT THE DFT
• Process involves these calculations.
• First Eq analyzes x’s into X’s which are complex sine wave amplitudes.
• Second Eq inverse transforms X's back to x's. Builds x’s from X’s. Amazing! But I have the 1/N in best place. Usually placed in the second Eq.
• This way, second Eq says add up for each n, content from each spiral at each frequency, k.
∑−=
=
π−
=1Nn
0n
Nkn2i
nk exN1X
∑−
=
π
=1N
0k
Nnk2i
kn eXx
VelSSComparison 36
TEST ANALYSIS METHODS ON EQUALLY SEVERE SHOCKS
• Develop several equally severe shocks; all able to just fail same equipment.
• Find analysis methods that show them all somewhat equally severe.
• Such an analysis is needed to describe shock severity.
• Needed to describe equipment hardness or fragility.
VelSSComparison 37
Equipment Fragility-Hardness
• The most severe shock equipment survives• Shock severity concept needed• Pseudo-velocity shock spectrum on four
coordinate paper: Recommended by Eubanks and Juskie, 1963 SVB
• Somewhat adopted by the seismic and nuclear defense community
• Chalmers and I advocated PVSS
VelSSComparison 38
Equipment Lowest Modal Frequency
• Postulate equipment can only accept energy and be damaged at its modal frequencies
• To damage equipment shock must have high PV at equipment modal frequencies.
• Shock isolation reduces the higher frequency, high PV severe range
• An item may be damaged by dropping on a concrete floor but survive a fall on a carpet because the carpet cushion reduced the severe high PV range to frequencies below the equipment's lowest frequency.
VelSSComparison 39
Equipment to test
• $50. Squirrel cage blower selected• Failure: blower can’t blow (pressure drop
through orifice)• Failure Equipment becomes hazardous• Purchased about 15
VelSSComparison 40
Develop equally severe shocks
• Test same equipment on progressively increasing different shock tests
• Drop tests: terminal peak, half sine, hard phenolic block
• Mil-s-901: Light weight, medium weight, heavy weight
• TP60, HS54, PB24, LW72, MW36, HW4
VelSSComparison 41
Abbreviations
• TP60, 60 inch drop to a terminal peak saw tooth• HS54, 54 inch drop on rubber pad to get half sine• PB24, 24 inch drop on hard phenolic block• LW72, 72 inch hammer drop to shelf bracket on light
weight shock machine• MW36, 36 in hammer drop on the medium weight shock
machine• HW4, 4th shot on the floating shock platform at Hunters
Point
VelSSComparison 42
Failures consisted of
• Spider members broken or deformed: belt flies off
• Motor knocked out of its supports: belt flies off or motor can’t turn
• Self tapping bolts deformed, loosened, pulled out
• Feet bolt holes deformed
VelSSComparison 43
f1
Test blower as originallyconfigured. Arrows point to thin spider members supportingbearings, and to sheet metalscrews. Notice sheet metal legs.
Weak sheet metalmotor mount beam.;
Blowers as purchased; trivial failure.
VelSSComparison 44
Original configuration, trivialfailure.
Trivial failure
VelSSComparison 45
Original bent sheet metalmotor support. Trivial failure.
Trivial failure, another view.
VelSSComparison 46
Motor mounted tobase plate.
Motor Mounted on Base Plate
VelSSComparison 47
f3a
Rubber pad forhalf sine test.
Drop table shockmachine.
Tagami’s China Lake MRC Shock
Machine
VelSSComparison 48
f3b
Mylar covered openingwith orifice to simulaterealistic delta p.
Manometer to checkfor adequate delta p
Terminal peaksawtooth programmer
Shock Machine with Terminal
Peak Programmer
VelSSComparison 49
f3c
Phenolic blocktaped to shockmachine anvil forshort duration halfsine test, pb24
Phenolic Block High Impact Set
Up
VelSSComparison 50
f4
Mounted todeck fixtureon light-weight shock mach.
Blower on Navy
Lightweight Shock
Machine
VelSSComparison 51
f4a5
Hammer
Blower on lightweightshock machine
Perspective View of Lightweight Shock Machine
VelSSComparison 52
f2
Mounted onmedium wgtshock machine.Extra plates added to increaseweight.
Blower Mounted on
Navy Medium Weight Shock
Machine
VelSSComparison 53
f5
Two blowers installedin FSP. One foundationstiff, and the other lessstiff
Two Blowers Mounted in FSP
VelSSComparison 54
f6
Spot weld fail
HS54 failure.Spot weld pulledout allowing beltto loosen.
HS54 Failures
VelSSComparison 55
f7
TP60 failure. Pulley side bearing supportspot weld failedallowing bearingsupport to deflectand loosen belt
TP60 Failures
VelSSComparison 56
f8
PB24 failure. Spidermember pulled outof housing, loosingbelt.
PB24 Failures
VelSSComparison 57
f9
MW 36 failure
Leg deformed
Leg pulled away from blower body. Sheet metalscrews gone.
Motor mount bentrubbing pulley
Bearing support bent
Accelerometer
MW36 Failures
VelSSComparison 58f10
Bent spider members
Deformed legs
Loosened self tappingscrews
MW36 failure
More MW36 Failures
VelSSComparison 59f11
MW36 damage. Motorbearing housing poppedout of end bracket
Accels
MW36 Failures Detail
VelSSComparison 60
f12
HW4 failure.
Sheet metal leg pulledaway from blower body
Bent spider members
Motor clamp bent andrubbing against pulley.Belt gone.
Loose self tappingscrews
HW4 Failures
VelSSComparison 61f13
Screw gone
BendingHW4 failure
VelSSComparison 62
f14
Non pulley end of motor supportbracket deformed. Motor bearingsupport popped out of bracket.
HW4 Motor Damage
VelSSComparison 63
f15
HW4 Failure. Bentmotor clamp. Motor
pivoted about clampand lost belt.
HW4 Motor Collar Bent
VelSSComparison 64
Failures consisted of
• Spider members broken or deformed: belt flies off
• Motor knocked out of its supports: belt flies off or motor can’t turn
• Self tapping bolts deformed, loosened, pulled out
• Feet bolt holes deformed
VelSSComparison 65
HS54 Time History
VelSSComparison 66
HW4 Time History
VelSSComparison 67
LW72 Time History
VelSSComparison 68
MW36 Time History
VelSSComparison 69
PB24 Time History
VelSSComparison 70
TP60 Time History
VelSSComparison 71
Here's all 6 shocks plotted to same scale. Only one of these did not fail the blower.
Time histories, same scale
VelSSComparison 72
HS54=r,HW4=g,LW72=bMW36=blk,PB24=m,TP60=c
5 of these 6 shock spectra failed the blower; which 5?
Composite Undamped SRS
VelSSComparison 73
HS54=r,HW4=g,LW72=bMW36=blk,PB24=m,TP60=c
5 of these 6 shock spectra failed the blower; which 5?
Composite 5% Damped SRS
VelSSComparison 74
HS54=r,HW4=g,LW72=bMW36=blk,PB24=m,TP60=c
Composite 10% Damped SRS
VelSSComparison 75
HS54=r,HW4=g,LW72=bMW36=blk,PB24=m,TP60=c
5 of these 6 shock spectra failed the blower; which 5?
Composite 20% Damped SRS
VelSSComparison 76
HS54=r,HW4=g,LW72=bMW36=blk,PB24=m,TP60=c
FT magnitude of a shock is it’s residual PVSS.5 of these 6 FT magnitudes failed the blower; which 5?
Composite FT Magnitudes
VelSSComparison 77
HS54=r,HW4=g,LW72=bMW36=blk, PB24=m,TP60=c
5 of these 6 shock spectra failed the blower; which 5?
Composite Undamped
PVSS on 4CP
VelSSComparison 78
HS54=r,HW4=g,LW72=bMW36=blk,PB24=m,TP60=c
5 of these 6 shock spectra failed the blower; which 5? (Any light?)
Composite 5% Damped PVSS
on 4CP
VelSSComparison 79
HS54=r,HW4=g,LW72=bMW36=blk,PB24=m,TP60=c
5 of these 6 shock spectra failed the blower; which 5?
Composite 10% Damped PVSS on 4CP
VelSSComparison 80
Here's all 6 shocks plotted to same scale. Only one of these did not fail the blower.
Time histories, same scale
VelSSComparison 81
HS54=r,HW$=g,LW72=bMW36=blk,PB24=m,TP60=c
5 of these 6 shock spectra failed the blower; which 5?
Composite 20% Damped PVSS on 4CP
VelSSComparison 82
Conclusions Presented evidence that:
• Damped Pseudo-velocity shock spectrum is the best severity indicator
• Peak g’s and time histories are useless• Shock spectrum calculation must become
widely available• Collect digitized time histories and make
available so others can test
VelSSComparison 83
This completes Velocity Shock Spectrum and Analyses Evaluations
Next is Shock Severity Estimation• Editing and Integration • Filtering Effects on the PVSS• Damping and Polarity• Fragility Concepts• Final Comments