influence of structural flexibility on the dynamic … · 2015-11-19 · paramsothy jayakumar, dave...

Paramsothy Jayakumar, Dave Mechergui, Ronald Renke

U.S.Army RDECOM TARDEC

INFLUENCE OF STRUCTURAL

FLEXIBILITY ON THE DYNAMIC

PRECISION OF A VEHICLE-MOUNTED

EQUIPMENT SYSTEM

UNCLASSIFIED: Distribution Statement A. Approved for public release. #26530

Report Documentation Page Form ApprovedOMB No. 0704-0188

Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering andmaintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information,including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, ArlingtonVA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if itdoes not display a currently valid OMB control number.

1. REPORT DATE 12 MAY 2015 2. REPORT TYPE

3. DATES COVERED 00-00-2015 to 00-00-2015

4. TITLE AND SUBTITLE INFLUENCE OF STRUCTURAL FLEXIBILITY ON THE DYNAMICPRECISION OF A VEHICLE-MOUNTED EQUIPMENT SYSTEM

5a. CONTRACT NUMBER

5b. GRANT NUMBER

5c. PROGRAM ELEMENT NUMBER

6. AUTHOR(S) 5d. PROJECT NUMBER

5e. TASK NUMBER

5f. WORK UNIT NUMBER

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) US Army RDECOM-TARDEC,6501 E. 11 Mile Road,Warren,MI,48397-5000

8. PERFORMING ORGANIZATIONREPORT NUMBER

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSOR/MONITOR’S ACRONYM(S)

11. SPONSOR/MONITOR’S REPORT NUMBER(S)

12. DISTRIBUTION/AVAILABILITY STATEMENT Approved for public release; distribution unlimited

13. SUPPLEMENTARY NOTES

14. ABSTRACT See Report

15. SUBJECT TERMS

16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT Same as

Report (SAR)

18. NUMBEROF PAGES

30

19a. NAME OFRESPONSIBLE PERSON

a. REPORT unclassified

b. ABSTRACT unclassified

c. THIS PAGE unclassified

Standard Form 298 (Rev. 8-98) Prescribed by ANSI Std Z39-18

SAE INTERNATIONAL

Outline

2

1. Problem Statement 3

2. Rigid Vehicle Model 4

3. Rigid Model Simulation Results 8

4. Component Mode Synthesis (CMS) 11

5. Craig-Bampton CMS Method 12

6. Craig-Chang CMS Method 13

7. Flexible Vehicle Model 14

8. CMS of Equipment 16

9. Equipment CMS Results 17

10. Frame CMS Results 20

11. Equipment Enclosure CMS Results 23

12. Influence of CMS Method on the Vehicle Dynamics 24

13. Influence of Flexibility on the Vehicle Dynamics 26

14. Conclusions 30

Page

UNCLASSIFIED

SAE INTERNATIONAL

Current project is to develop a precision equipment system

• Equipment system needs to be reliable for use from vehicle platform

• Equipment system is placed in enclosure attached to cargo bed

• For the equipment system to work properly, vibration should be minimized

• Vibration coming from the road through suspension is suppressed by

isolators

• Excessive vibration can cause the system to miss performance, and in

severe cases can cause mechanical failure

• Need to know vehicle motion accurately to design isolators

• Rigid and flexible vehicle models are developed and simulation results

compared

Problem Statement

3 UNCLASSIFIED

SAE INTERNATIONAL

• Adams/Car Model

Rigid Vehicle Model

4

Cargo bed

Frame

Body mounts

Bumper mounts

Equipment enclosure

UNCLASSIFIED

SAE INTERNATIONAL

• Suspension System

Rigid Vehicle Model

5

Double wishbone suspension

– Springs and dampers

– Bumpstops

– Tierod

– Drive shaft

Equipment enclosure

Equipment

Isolator mounts

UNCLASSIFIED

SAE INTERNATIONAL

• Pacejka 2002 tires

• Steering System

Rigid Vehicle Model

6

– Unloaded radius: 516 mm

– Tire width: 317 mm

– Vertical stiffness: 525 N/mm

– Vertical damping: 3.15 N-s/mm

Center link

Idler

Pitman arm

UNCLASSIFIED

SAE INTERNATIONAL 7

• Powertrain system

- Idle engine speed

- Max engine speed

- Max throttle

- Final drive ratio

Rigid Vehicle Model

Rear differentials Front differentials

Engine mounts Differential mounts

UNCLASSIFIED

SAE INTERNATIONAL

Rigid Model Simulation Results

8

• Time Histories, Accelerations

- Low random RMS road, vehicle speed is 31 mph

- High random RMS road, vehicle speed is 20 mph

UNCLASSIFIED

SAE INTERNATIONAL


9

• Acceleration Histograms

- Random road RMS 3.5" excites higher accelerations

UNCLASSIFIED

SAE INTERNATIONAL


10

Power Spectral Densities

- No low frequencies in response

UNCLASSIFIED

SAE INTERNATIONAL

Component Mode Synthesis

11

• Component mode synthesis (CMS) is a technique that allows to

analyze structure by dividing it into different substructures. The

substructures are analyzed separately, then assembled together

- This technique used for large and complex structures

- When FE components are built in different locations

• High modes in the modal analysis are truncated there is no loss in

resolution, the CMS technique will capture them with the static

deformation shapes

• CMS technique reduces significantly the model complexity,

computational time

UNCLASSIFIED

SAE INTERNATIONAL

Craig-Bampton Method

* R. R. Craig and M. C. C. Bampton, “Coupling of Substructures for Dynamic Analysis,” AIAA Journal, v. 6, pp. 1313-1319, 1968. 12

Fixed-Interface normal modes Constraint modes

Fundamental normal mode of fixed interface

u1 = 1

u2 = 0

u1 = 0

u2 = 1

Constraint modes of cantilever beam

Craig-Bampton Method *

(k-ω2m)ϕ = 0

Method is used when parts are connected

with joints

UNCLASSIFIED

SAE INTERNATIONAL

Craig-Chang Method

13

Free-Interface normal modes Attachment modes

Fundamental normal mode of free-interface

F = 1

Attachment modes of cantilever beam

Craig-Chang Method *

M = 1

* R. R. Craig and M. C. C. Bampton, “Coupling of Substructures for Dynamic Analysis,” AIAA Journal, v. 6, pp. 1313-1319, 1968.

Method is used when parts are connected with

- joints that are partially constrained

- Bushings that do not have high stiffness

UNCLASSIFIED

SAE INTERNATIONAL

Flexible Vehicle Model

14

Adams/car Flexible Model

34 attachment nodes

Flexible frame

UNCLASSIFIED

SAE INTERNATIONAL 15

16 attachment nodes

Equipment Enclosure

4 attachment nodes

Equipment

Flexible Vehicle Model

UNCLASSIFIED

SAE INTERNATIONAL

• Equipment was meshed and run for model analysis using different CMS

techniques, the analysis was done using Radioss software

• Cutoff frequency is 200 Hz

• There are 4 attachment nodes

CMS of Equipment

16

Bushings

UNCLASSIFIED

SAE INTERNATIONAL

Equipment CMS Results

17

Mode

Shape

Natural

Frequency (Hz)

1 39.6

2 89.2

3 135.7

4 170.4

5 204.0

6 232.9

7 334.9

8 504.4

9 676.2

10 717.9

. .

Highest 9,550


Mode

Shape

Natural

Frequency (Hz)

1 39.6

2 87.1

3 134.4

4 158.9

5 172.7

6 187.5

7 262.5

8 361.0

9 419.9

10 582.4

. .

Highest 9,655

- 24 static modes

- 8 normal modes - 24 static modes

- 12 normal modes

CMS Modes

- 32 orthonormalized modes

CMS Modes


Craig-Chang Method

UNCLASSIFIED

SAE INTERNATIONAL

Equipment Mode Shapes and Natural Frequencies

18

Mode Shape 1

ω1 = 39.6 Hz Mode Shape 2

ω2 = 89.2 Hz

Mode Shape 1

ω1 = 39.6 Hz

Mode Shape 2

ω2 = 89.7 Hz

Craig-Bampton Craig-Bampton

Craig-Chang Craig-Chang

UNCLASSIFIED


Mode Shape 3


ω4 = 170.4 Hz

Mode Shape 3

ω3 = 134.4 Hz

Mode Shape 4

ω4 = 158.9 Hz



Equipment Mode Shapes and Natural Frequencies

UNCLASSIFIED


Mode

Shape

Natural

Frequency (Hz)

1 19.8

2 22.5

3 28.1

4 32.5

5 46.7

6 61.1

7 63.5

8 66.7

9 70.4

10 71.8

. .

Highest 14,908

Mode

Shape

Natural

Frequency (Hz)

1 19.8

2 22.5

3 28.0

4 32.5

5 46.5

6 60.1

7 63.5

8 66.2

9 69.5

10 71.8

. .

Highest 15,507

- 204 static modes

- 53 normal modes - 204 static modes

- 72 normal modes

CMS Modes


CMS Modes


Frame CMS Results

Craig-Bampton Method Craig-Chang Method

UNCLASSIFIED


Frame Mode Shapes and Natural Frequencies

Mode Shape 1


ω2 = 22.5 Hz

Mode Shape 1

ω1 = 18.9 Hz

Mode Shape 2

ω2 = 22.5 Hz



UNCLASSIFIED


Frame Mode Shapes and Natural Frequencies

Mode Shape 3


ω95 = 382.0 Hz

Mode Shape 3


ω95 = 355.4 Hz



UNCLASSIFIED


Mode

Shape

Natural Frequency

(Hz)

1 14.9

2 21.7

3 28.8

4 31.5

5 37.0

6 43.8

7 44.6

8 49.2

9 49.5

10 50.2

. .

Highest 49,208 - 96 static modes

- 97 normal modes

CMS Modes


Equipment Enclosure CMS Results


UNCLASSIFIED

SAE INTERNATIONAL

Influence of CMS Method on the Model Dynamics

Random Road RMS 3.5"

24 UNCLASSIFIED

§ c: 0

i :;; -.; C)

<

§ c: 0

~ :;; -.; C) C)

<

7

6

5

4

3

2

-3

-4

-5

-6

-7 0

Frame Acceleration

---------.. -·-·· · · ·····

.................................

' ' ' ' ' ' .............................................. ' ' ' ' ' ' ' ' - . ... . .............. .... . ' '

---- ----:----·············1--··

5 10 15 nme(s)

7~--~--~--~--~~~~~~ 6

5

4

3

0

-1

-2

-3

-4

-5

-6

' ' ' . ' . .

I I t I

c: 0

~ ·-----------~~ :;; -.;

C) C)

<

§ c: 0 :g :;;

Frame Acceleration

7r----------------------r========~ 6 -- --- ----- --- ----- --- ----- - ------ --- ----- --- ----- --- ----- --- ----- - --Craig-Bampton

--Craig-Chang 5 --------------------------------------------------------------------------------------------------4 ................................................................................................. .

-3 .................... ................................ ................................ ............. .

-4 ----------------------·-----·-------------------------·-----·-------------------------·-----·-----

-5 ................................................................................................. .

-6 ................................................................................................. .

·i~5--------------------~3o

nme(s)

Cargo Bed Cradle Acceleration 7r----------------------r========~ 6 ----·······-··----·-- -·----·-·······-··----· -·-------···--- --Cralg-Bampton

5 --Craig-Chang

~ -1

< ·2

-3

-4

-5 ................................................................................................. .

-6 .................... ........ ................................ ................................ ..... .

-i~5---------------------~3o

nme(s)

SAE INTERNATIONAL

Influence of CMS Method on the Model Dynamics


25

Max Min

4.4 g -6.3 g

Max Min

4.5 g -6.4 g

Craig-Bampton

Craig-Chang

UNCLASSIFIED

7

6

5

4

3

§ c: 0

~ a; a; u u <

-3

-4

-5

-6

-7 0

. . . . . . --------·-·······-------------.--------------. . . . . . ···--·--·--···!·--·--·--·--···:··--·--·--·--·'-,.---1-~,-----"---'1 . . . . . . --------------·---------·-····'-··------------·-------· . . . . . . . . . . . . . ------------ ·------· ................ ··- ... - ----·

.. - - . ~ - -

. . . . - -- - ---- -- -- - -:- - - --- --- --- -- - i -- -- -- --- --- -- -:-- - -- - --- --- -- ~-- - -- - - - - ----:-------- --- ---. . . . . . . . . .......... ..... --------------· ------·-·······'-·-------------·---------. . . . . . . . . . . . .......... ..... --------------· ---------------.. ·--------- ----·---------. .

' ' ' ' ' - --- ---- ------.- -- --- ---- -----.------ ---- -----.------- ---- ---- , ------- --- ----.- ------- ---- --. . . . . . ' . . .

-.--.--. -- • • • ~- --.--.--.-- ••••• --.--.--.-- •• ·'· . --.--.--.-- •• J •• ·-. -----' . . ' . . . . ' ' ' '

5 10 15 Time (s)

20

Equipment Enclosure Acceleration 7 r----------------------r==========~ 6 ........................................................... --Craig-Bampton

5 ........................................................... ._-_ -_ c_r_a_,ig._-_C_h_a_n"'g-Jj

4

§

~ a; a; -1 u u < -2

-3

-4

-5

-6

-7 25 30

Time (s)

Equipment Acceleration

7r----------------------r==========~ 6 .......................................................... . --Craig-Bampton

5 ...................................... .............. ....... ._-_ -_ c::.cr...:ca"'ig,_--=c-'-h"'a.:..:n!'!.g_-'i

4 ....................................................................................... .

3

§ 2 c: 0

"" "' 0 a; ~ ·1 u < ·2

-3 -4 ......... ...... .. ..

-5 ................. ..

-6

·1'------------------------------------------~ 25 30

Time (s)


Influence of Flexibility on the Model Dynamics


UNCLASSIFIED

7

6

5

4

3

§ 2

c: 0

7il <; -.; u u <

·3

-4

·5

-6

·1 0 5

7

6

5

4

3 ....................

§ 2

c: 1 0

7il 0 <; -.; ·1 u u < ·2

-3

-4

·5

-6

·1 0 5

10

Frame Acceleration

15 Time (s)

Cargo Bed Acceleration

20

.....................

___ _._ __ __ ___ ___ __ _ _

__ ....._ ____ ________ _ _

··'-··············

--:------········· .. , ... ..... . ..... .

. ..,.. ............. .

25 3

§ c: 0

"" "' 1 ~1------i~~

10

.....................

.......................

------------- -----··:··----- ---- -- -r·---- -------

15 Time (s)

20

... ..,. ............. .

......................

25 0

u u <

Frame Acceleration 7,-----------------------~========~ 6 ...... .. ...... .. ...... .. ..... ........ .. ...... .. ...... .. ........... --Rigid Model

--Flexible Model 5

4 ................................................................................................. .

3 ······•· ·•····· · ······· · ········•·····•· ······· · ······ ·· ········•·····•· ·•····· · ······ ·· ······· · ··

· 3 ··································································································

-4 ...... .. ...... . .

·5 -6 ................................................................................................. .

-~L5---------------------~3o

Time (s)

Cargo Bed Acceleration 7 ,-----------------------~========~

6 .. ..... . .. ..... . .. ..... . .. ..... . ...... . .. ..... . .. ..... . .. ..... . .. --Rigid Model --Flexible Model

5 4 ...................................................................................... .

3

2 ......•.......•.......•...............•.......•.......•...............•.......•.......•...........

-3 ....... . ........ ....... . ....... . ....... . ........ ....... . ....... . ....... . ........ ....... . ........ . .

-4 -- -- --- --- -- --- --- -- --- - ------ --- -- --- --- -- --- --- -- --- --- -- --- - ------ --- -- --- --- -- --- --- -- --- ---

·5 ·6 ................................................................................................. .

-~L5----------------------=3o

Time (s)




- Flexible components were obtained using Craig-Bampton method

UNCLASSIFIED

7~---,-----::-----:: ----rc==~~==~ 6 -~ · ·· · ·· · ·· · ·· ~ - -· · ·· · ·· - ·- · --!- - ... ... ... .. .

5 4

3

--------------f-·-------------:-- -------------<:--JF ::.;:-:-::....:.:.:..::...=..:._'-'1 . . . . ................ ......... ............... ............... . . ' ' ' ' ' ' ' . ' ' ················ ·············-·············· ········

§ 2 -------r --<: 0

~ Qj 4i 0 0 c( -2

§ <: 0

"' "' Qj 4i 0 0 c(

. . . ' . -3

_____________ .. _______________ . ______________ .._ ______________ . ______________ .. ____________ _ . . . ' ' . . . ' . . . ' -4 -········----~---········----: .............. .:. ...................... -------~ -------------

' ' ' ' ' ' -5 -·- .... ·-. ·-. ~- ........ ·-. ·-. :· ........ ·-. ·- -~· ........ ·-. ·- ~--. -· .... ·- ... ~ -· ........ ·-. . . . ' .

-6 --.--.------. ~-. --.--.------. ; .. --.--.------ -~-. --.--.------ ~--. --.. ----..... --.-- .... ----

-7 0

7 6

5 4

3

2

-3

-4

-5 -6

-7 0

' ' ' ' ' '

5 10 15 Time (s)

20


. . ' '

..................

..................

------·-··---.,--------·-··---,--------·-··-··,·····----------,---------- ... ,. ............ . . . ' ' . . . . . . ' ' ••••••••••••• .I ••••••••••••••••••••••••••••••• • ••••••••••••••• J ............................ . . . . . . . ' ' . . ' '

5 10 15 Time (s)

20 25 30

Equipment Enclosure Acceleration

7 ~--------------------~========~ 6 ··· ··· ··-··-·· ·· -· -·-··· ·--·· · .. ·· ··--·-·--·· ·· -·· -·-·--·· --Rigid Model

5 --Flexible Model

4 ··-----------·-···--·--·-···-··-··--··-·-··--·····-----------·····-----------·-· ··--·--·-·

3 ··--··-·-···· ·····- -·--·-···-·····--··-·-··-······-----------·····--··-·-·········--·--·-·

§ 2 <: 0

"' "' Qj 4i 0 0 c( -2 ......................................................................................... .

-3 ·------··-··-··-·------·--··-··-----------··-··-·---------·--··-·-------·-·--··-·---------

-4 ·------··-··-··-·------·--··-··--------··-··-··-·------··-··-··-·------··-··-··-·------·--

-5

-6 ·------------·--·------------·--·------------·--·------------·--·------------·--·---------

-7 L-------------------------------------------~ 25 30

Time (s)

Equipment Acceleration 7

6 --Rigid Model

5 --Flexible Model

4

3

§ <: 0

~ Qj 4i -1 0 0 c(

-3

-4

-5

-6

-7 25 30

Time (s)




Max Min

3.0 g

Max Min

2.8 g -1.9 g

Rigid acceleration

Max Min

Max Min

3.3 g -1.4 g

Rigid acceleration

Flex acceleration

3.4 g -2.2 g

Flex acceleration

-2.0 g

UNCLASSIFIED

7r-----,-----,-----,-----Tr==~~~~ 6

5

4

3

_____ _ _._ _____ _ _

-3 --------------->--------------··r··------------··r··-------------·r··------------... ............... ; ................. i················i················:··············· :: ::::::::::::::::::: - ::::::c::::::::::::r -----··::r::::::::::··· "7oL-----~~----~~----~~----~~-----.~-----730

Frame Acceleration 7,------------------------r========~ 6 .................................................................. . --- Rigid Model

- - Flexible Model 5 ··················· ............................................................................. .

4

3

§ c .!!

·3 .. ..... .. ..... .. ..... .. ..... .. ..... .. ..... .. ..... .. ..... .. ..... .. ..... .. ..... .. ..... . .

-4

-5 ··································································································

-6

-~~5------------------------------------------~30'

Time (s)

Cargo Bed Acceleration 7 ,------------------------r========~ 6 .................................................................... --- Rigid Model

--Flexible Model 5 .... ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ..... .

4 .. .. ....... . ...... .. ...... . ....... . ....... . ...... .. ....... . ....... . ....... . ...... .. ...... .. ..... .

3

§ c 0

~ ., ~ ·1

~ -2

-3

-4 ................................................................................................. .

-5 .... ................ ................ ................ ................ ................ ............. .

-6 ...... . ...... .. .. .... .. ...... .. ....... . ...... .. .. .... .. ...... .. ....... . ...... ..

-~-~5------------------------------------------~30

Time(s)




Flex acceleration

Max Min

4.5 g -6.6 g

Max Min

3.6 g -4.2 g

Rigid acceleration

Flex acceleration

Max Min

3.6 g -2.3 g

Max Min

3.4 g -1.4 g

Rigid acceleration

UNCLASSIFIED

7

6

5

4

3

§ 2

c: 1 0

~ 0 Q; ~ -1 .:( -2

-3

-4

-5 -6

-7 0 5 10 15

Time (s) 20

···········+·············;·············+············

25 30

............ ·:· .............. :· ............. ·:·· ...... ...... '----1-.:..:.:..:.:.:.;::. __ ---'1

· · · ·· · · ·· · ··j· · i · · · ·· · · ·· · ·-~- - -· · · · · · · :: : :t : · ,· · · ·· · · ·· ·

c: 0

~ Q;

Equipment Enclosure Acceleration

7,---------------------~==========~ 6 ..................................... ...................... --Rigid Model

5 ··························································· - - Flexible Model

4 ......................................................................................... .

~ -1 0

< -2

-3

-4 ......... .. .............. .. .............. ... .......... ... .. .............. .. ... ........... .

-5

6 ............... . - - ......................... ---- -- - - · ················ ······ --------

-7 25 30

Time (s)


7,---------------------~==========~ 6 ............................ ................ ............... --Rigid Model

5 ··························································· - - Flex ible Model

4

-4

-5

-6 ···············

-7 25 30

Time (s)

SAE INTERNATIONAL

Conclusions

30

• Developed a vehicle model that carries a precision equipment, the latter

can be reliably used. In order to function properly, its vibration is

minimized; the vibration coming through the suspension is suppressed

by isolator mounts.

• Integrated flexible components (frame, equipment enclosure, and

equipment) into the vehicle rigid model using CMS.

• Equipment system vibration was not affected by the type of CMS

method.

• Equipment acceleration increased by 50 % when the model is flexible,

for rough roads (3.5" rms).

UNCLASSIFIED

influence of structural flexibility on the dynamic … · 2015-11-19 · paramsothy jayakumar, dave...

Documents