influence of structural flexibility on the dynamic … · 2015-11-19 · paramsothy jayakumar, dave...
TRANSCRIPT
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
Rigid Model Simulation Results
9
• Acceleration Histograms
- Random road RMS 3.5" excites higher accelerations
UNCLASSIFIED
SAE INTERNATIONAL
Rigid Model Simulation Results
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
Craig-Bampton Method
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
- 32 orthonormalized 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
SAE INTERNATIONAL 19
Mode Shape 3
ω3 = 135.7 Hz Mode Shape 4
ω4 = 170.4 Hz
Mode Shape 3
ω3 = 134.4 Hz
Mode Shape 4
ω4 = 158.9 Hz
Craig-Bampton Craig-Bampton
Craig-Chang Craig-Chang
Equipment Mode Shapes and Natural Frequencies
UNCLASSIFIED
SAE INTERNATIONAL 20
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
- 257 orthonormalized modes
CMS Modes
- 276 orthonormalized modes
Frame CMS Results
Craig-Bampton Method Craig-Chang Method
UNCLASSIFIED
SAE INTERNATIONAL 21
Frame Mode Shapes and Natural Frequencies
Mode Shape 1
ω1 = 19.8 Hz Mode Shape 2
ω2 = 22.5 Hz
Mode Shape 1
ω1 = 18.9 Hz
Mode Shape 2
ω2 = 22.5 Hz
Craig-Chang Craig-Chang
Craig-Bampton Craig-Bampton
UNCLASSIFIED
SAE INTERNATIONAL 22
Frame Mode Shapes and Natural Frequencies
Mode Shape 3
ω3 = 28.1 Hz Mode Shape 95
ω95 = 382.0 Hz
Mode Shape 3
ω3 = 28.0 Hz Mode Shape 95
ω95 = 355.4 Hz
Craig-Chang Craig-Chang
Craig-Bampton Craig-Bampton
UNCLASSIFIED
SAE INTERNATIONAL 23
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
- 179 orthonormalized modes
Equipment Enclosure CMS Results
Craig-Bampton Method
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
Random Road RMS 3.5"
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)
SAE INTERNATIONAL 26
Influence of Flexibility on the Model Dynamics
Random Road RMS 1.0"
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)
SAE INTERNATIONAL 27
Influence of Flexibility on the Model Dynamics
Random Road RMS 1.0"
- 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
Equipment Acceleration
. . ' '
..................
..................
------·-··---.,--------·-··---,--------·-··-··,·····----------,---------- ... ,. ............ . . . ' ' . . . . . . ' ' ••••••••••••• .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)
SAE INTERNATIONAL 28
Influence of Flexibility on the Model Dynamics
Random Road RMS 3.5"
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)
SAE INTERNATIONAL 29
Influence of Flexibility on the Model Dynamics
Random Road RMS 3.5"
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)
Equipment Acceleration
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