Nonlinear interactions between a cable with no axial...
Transcript of Nonlinear interactions between a cable with no axial...
� Incremental method + co –rotationnal FE formulation + contact penalty-barrier method
lamcos.insa-lyon.frLaMCoS, Université de Lyon, CNRS, INSA-Lyon UMR5259, 18-20 rue des Sciences - F69621 Villeurbanne Cedex
Research steps Drag force and Efficiency analysis
Technological and Scientific contexts
� Drag force: threshold load to move the cable into the casing
� Efficiency: ratio between In/Out forces
� Experimental design influence analysis � Drag and Efficiency per unit length
Nonlinear interactions between a cable with no axial preload and its casing. Application to automotive gearshift command systems
N. LEVECQUE 1,2, Dr. L. MANIN1, Dr. T. NOURI BARANGER1, Pr. R. DUFOUR1
1LaMCoS INSA-Lyon, 2 RENAULT S.A
Dynamic and Vibration transmission analysis
Curvilinear casing geometry and contact points prediction
casing casing casing casing stopstopstopstop
casing stopcasing stopcasing stopcasing stop
rubber rubber rubber rubber guideguideguideguide
available available available available spacespacespacespace
car floorcar floorcar floorcar floor
Gearshift Gearshift Gearshift Gearshift boxboxboxbox
gearboxgearboxgearboxgearbox
rubber passrubber passrubber passrubber pass----throughthroughthroughthrough
cable
casing
leverleverleverlever
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 2 4 6 8 10
Curvature (m-1)
Effi
cien
cy F_o
ut/F
_in
pushpull
0
2
4
6
8
10
12
14
0 2 4 6 8 10curvature (m-1)
Dra
g fo
rce
per
unit
leng
th (
N/m
)
pushpull
Driving comfort requires to reduce:
- Drag friction force during gear shifting,
- Gearbox vibration transmission to the gearshift lever
- cable-casing vibro-impacting noise
Main scientific challenges
- cable-casing spatially curved geometry simulation,
- non-linearities: cable-casing contact, large displacement,
- vibrations and dynamic instabilities, parametric excitations
5 2 2 6 2 70,559 0,006. 39,11. 0,001. 2,38.10 . 520,4. 3,1.10 . 0,06. . 6,6.10 . . 0,019. .push F C T F C T F C F T C T− − −− − −− − −− − −= + − + − − − − + += + − + − − − − + += + − + − − − − + += + − + − − − − + +ρρρρ
2 -4 24,41-1251,6. - 0,038. 327950. 5,4.10 . -7,4. .pushDrag C T C T C T= + +2 -4 23,957 -336,8. - 0,087. 221783. 10,1.10 . - 8,09. .pullDrag C T C T C T= + += + += + += + +
5 2 2 6 2 70,693 0,003. 27,03. 0,002. 1,03.10 . 3083,6. 11,3.10 0,02. . 44,5.10 . . 0,079. .pull F C T F C T F C F T C Tρρρρ − − −− − −− − −− − −= + − + − − − − + += + − + − − − − + += + − + − − − − + += + − + − − − − + +
Cable and casing mechanical properties (E,
EI, ρρρρ), geometry characteristics
Boundary conditions and surrounding components
(start, end, intermediate, points)
Non linear FE Computation, large displacements, co-
rotational formulation, cable-casing contact problem
solved with penalty method
Elementary Drag force and
efficiency experimental
identification
Drag force and efficiency calculation on real
car gearshift mechanism
Dynamic
Ananysis
• Modes and frequencies computation
around static equilibrium position
• Forced response to:
• Cable axial excitation
• Casing transverse excitation
• Vibration instabilities prediction
Spatially curved cable-casing path,
contact points and forces
Drag force and efficiency
models integration
Experimental validation
kEkEk
k EE k
E
kE
kE
u
v
wU
x
y
z
θθθ
=
kO
kO
kk OO k
OkO
kO
u
v
wU
x
y
z
θθθ
=
18 50 100 150 200
[Hz]
0.001
0.01
0.1
[g/(m/s²)]1. 002:
2. 002:
3. 002:
4. 002:
12
34
18 50 100 150 200
[Hz]
0.001
0.01
0.1
[g/(m/s²)]1. 002:
2. 002:
3. 002:
4. 002:
1
23
4
k = 0
( )( )
int
int
k ktc c C C C
k ktG G G G G
K U F R U
K U F R U
= −
= −
,
,
k kC G
C extC G extG
P P
F F F F= =
( ),k kcont C GF F U U=
C extC cont
G extG cont
F F F
F F F
= += −
1
1
k k kC C C
k k kG G G
P P U
P P U
+
+
= += +
1
1
finale kC C
finale kG G
P P
P P
+
+
==
k = N-1
k < N-1
k = k+1
Newton iterativeconvergence loop
Incrementalloop
N2vN1
wuwu
v
θy
••
θx
θz
θyθx
θz
casingcvjeu
gv
cableδ
Planar-S casing path
FE modeling, cable-casing contact interaction
¼ circle casing path
Car configuration testCable axial excitation3-axes accelerometers
Input axial acceleration on cable
0
10
20
30
40
50
60
70
10 50 90 130 170 210Hz
Acc
el m
/s²
rms
Computation algorithm
•
••
•• •
iC
1iG +
1iG −
1iC +
1iC −
iG
nr
droitenr
gauchenr
•M
•
••
•• •
iC
1iG +
1iG −
1iC +
1iC −
iG
nr
droitenr
gauchenr
•M
Oi (xOi, yOi, zOi)
Ni+1 (xi+1, yi+1, zi+1)
Ni (xi, yi, zi)
Ni-1 (xi-1, yi-1, zi-1)
Ri
.n ig jeu C M n= −uuuur r
.
. 0
. 0n n
cont n n n na g
cont n n
F t e g si g
F t e si g
= + < = ≥
sin /
/ sin
.
.
r r
r rca g cable cont
cable ca g cont
F F n
F F n
= − =
Electricjack
Load anddisplacement
sensors
Powderbrake
FinFou
tFin
Fout
Fin
Fout
85°C
150 N40°C6.25 m-1
100 N0°C5 m-1
50 N-30°C∞
Force FTemperature TCurvature C
85°C
150 N40°C6.25 m-1
100 N0°C5 m-1
50 N-30°C∞
Force FTemperature TCurvature C
85°C
150 N40°C6.25 m-1
100 N0°C5 m-1
50 N-30°C∞
Force FTemperature TCurvature C
γγγγin
NEU
1NOU −
NOU
E
O
E
O Initial state
Final state
1OU
2OU3OU
1EU
OU
EU
D1 =0.378 m
D2 =0.278 m
D1 =0.378 m
D2 =0.278 m
O
E
UE
0 0.1 0.2 0.3 0.4 0.5
-2
0
2
x 10-4
curvilinear abscissa (m)
cabl
e-ca
sing
neu
tral
fibe
r di
stan
ce (
m)
0 0.1 0.2 0.3 0.4 0.5
0
0.02
0.04
0.06
0.08
cont
act f
orce
s m
odul
us (
N)
0 0.1 0.2 0.3 0.40
0.05
0.1
0.15
0.2
0.25
0.3
x (m)
y (
m)
computed cable-casing geometry
casingcable
_
_1
( ).i Nb z
lin i zone ii
Drag Drag R L=
=
= ∑
1 1out in out totalglobal
in in in
F F F F
F F Fη − ∆= = − = −
1
_1
n
total zone ii
F F−
=
∆ = ∆∑
_ _ _.zone i lin i zone iF F L∆ = ∆
__ 1 lin i
lin ii
F
Fη
∆= −
( )1__ −=∆ iliniilin FF η
(N/m)(N/m)
N3
N1 N2
Nn-2
Nn-1 Nn
Zone 1
E
Zone 2
Zone n-2
Zone n-1
R
3F
n-1F
n-2F
2FFin
Fout
� Drag force an efficiency computation from cable-casin g path decomposition andexperimentally identified model
(Fin,C1) ηlin_1 _1zoneF∆ 2 _1in zoneF F F= − ∆ ….
�Time response around static equilibrium position� cable axial harmonic excitation � casing transverse excitation
�Time integration to predict dynamic response�Experimentation-Validation on
� basic casing curved geometry� car cable-casing geometry
Computed cable-casingspatially curved geometry
Kcable-casing , Mcable-casing
Newmark schemeTime response computation
u(t)P(t)=P0 + u(t)
F(t)=F1sin(ωt)Or
γ(t)=γ1sin(ωt)
0 1 2 3 4 5
x 10-4
-0.03
-0.025
-0.02
-0.015
-0.01
-0.005
0
Cable-Casing neutral fiber distance (m)
Con
tact
For
ce (
N)
tn -0.001 N, en 10 N/mtn -0.001 N, en100 N/mtn -0.001 N, en 50 N/mtn -1e-4 N, en 10 N/mtn -1e-4 N, en 50 N/mtn -1e-5 N, en 10 N/mtn -0.00316 N, en 100 N/mtn -0.00316 N, en 50 N/mtn -0.005 N, en 100 N/m