ANÁLISE DINÂMICA DE TRANSMISSÕES POR CORRENTE …

LISBOA | 18 JUNHO 2014

ANÁLISE DINÂMICA DE TRANSMISSÕES POR CORRENTE

UTILIZANDO UMA ABORDAGEM MULTICORPO

CÂNDIDA PEREIRA MALÇA

ISEC/INSTITUTO POLITÉCNICO DE COIMBRA

[email protected]


TRANSMISSÕES MECÂNICAS

TRANSMISSÕES POR CORRENTE

FORMULAÇÃO MULTICORPO

ANÁLISE DINÂMICA



CONTRIBUIÇÕES


TRANSMISSÕES MECÂNICAS

CATERPILLAR D9H



AUDI V6



WARTSILA ENGINE



Zoom1

Zoom2


Pitch

Inner Link

Outer Link

Pin

Zoom1:

Bushing

Roller

Clearance Pin/Bushing

Clearance Bushing/Roller



Pitch

ηsr

ηi

θi

·

Rs

ξsr

ξi

θi

θs

α

X

Y

ri

r

rcr

r

scr

r

Pitch

ηsr

ηi

θi

·θi

·

Rs

ξsr

ξi

θi

θs

α

X

Y

ri

rri

r

rcr

rrcr

r

scr

rscr

r


Zoom 2:


DINÂMICA DE SISTEMAS DE CORPOS MÚLTIPLOS

Body 1Body 1

Revolute joint

Body 2

Body i

Body 3

Multi-revolute jointwith clearance

Actuator

Spherical joint

Spring/DamperApplied forces

Flexible body Translational joint

Contact bodies

Body n

Gravitationalacceleration field

Spring

Body j

Lubricated joint

Ground body

Applied Torque

Revolute jointwith clearance

Body K


MECANISMO BIELA - MANIVELA


Clearance

1η

1ξ

4η

3η2η2ξ

3ξ

4ξX

Y

1

2

3

4

Clearance

1η

1ξ

4η

3η2η2ξ

3ξ

4ξX

Y

1

2

3

4


Pankoke et al, 1998 Silva et al, 1997

MODELAÇÃO DO MOVIMENTO HUMANO



III

XII

5

V

VI

X

VII

II IV

IX

XII

VIII

XI

XIV

1

8

2

4

7

11

9

3

6

12

10

13

I

Body no. 50% Human Male

Li [m]

50% Human Male

Mass [Kg] *

I 0.260 14.2

II 0.250 24.9

III 0.230 4.24

IV 0.320 1.99

V 0.260 1.84

VI 0.320 1.99

VII 0.260 1.84

VIII 0.410 9.84

IX 0.385 4.81

X 0.410 9.84

XI 0.385 4.81

XII 0.160 1.06

XIII 0.053 1.62**

XIV 0.053 1.62 **

L3-5 (a) 0.375 -

L6-7 (a) 0.188 -

L1-2 (b) 0.199 -

L1-3 (b) 0.155 -

MODELO

BIOMECÂNICO

MASSAS E DIMENSÕES DOS

CORPOS RÍGIDOS

Source: Silva et al. (1997)




−−−−−−−−====

ΦΦγ

g

λ

q

0Φ

ΦM

q

q

2

T

2 βα &

&&

CLEARANCE REVOLUTE JOINTS

PERFECT KINEMATIC JOINTS


Read input data

Is t >tend ?

ttt ∆++++====

Yes

No

STOP

START

Evaluate

gGeneralized forces,

Φq

Jacobian matrix,

MSystem mass matrix,

γΦConstraint functions, ,

0qq ====

t

0==== tt

==== &&0

qqt

Solve linear equations ofmotion for andq&& λ

T =

q

q

M Φ q g

Φ 0 λ γ

&&

Form the auxiliary vector

TTT][qy && ====

tq&&

Integrate the auxiliary vector

∆y ====

++++ tt

TTT][q q&




X

Y

ηηηηi

ξξξξi

(i)

Oi

(j)

ηηηηj

ξξξξjOj

PiPj

Qj

Qi

rP

is

rP

js

re

rP

irrP

jrrir

rjr

δr

rn

rt

1. ECCENTRICITY VECTOR

P P

j i= −e r r

2. ECCENTRICITY

Te = e e

3. PENETRATION (C - CLEARANCE)

δ e c= −

4. NORMAL AND TANGENT VECTORS

e=n eT

y xn n = − t

5 . CONTACT FORCE

( ) ( )*

234 ( )

0.49∆R + 0.1 E1 1

∆R −

= + −

f n

&

&144424443

n

n r

lc

K

δδ

δ

( )1

t f d n T Tc c f v

−= −f v



1

26

7

4

53

a*

b*

c* c

b

a

d* dcc

bc*

cc*

bc

oc

RIGHT SIDELEFT SIDE

TOOTH CENTER LINE



IF AND

THERE IS CONTACT WITH THE SEATING CURVE

1 12 2θ θ θ− ≤ ≤

o e o( ) 0e t r

R Rδ = − − >eIF

THERE IS NO CONTACT AT

ALL

( ) 0e t rR Rδ = − − ≤e

��

��

��

��

��

��

��

2Rr

θe

Rt

cc*cc ηηηηst

θo

oc

ξξξξst

��

δr

e

crsr

er

ocsr

Qt

Qr



Strand A

Strand B

(K)

Strand C

(i)(j)

Pi

Strand A

Strand B

(K)

Strand C

(i)(j)

Pi



( )1a 1b

1a 1b1

× ϕ ≥ ϕ=

+ × ϕ < ϕstrand

n Pitch ifL

n Pitch if

1a 1b

_ _

1a 1b

1

2

+ ϕ ≥ ϕ=

+ ϕ < ϕPins in strand

n ifN

n if

i jP - P = ×n Pitchpd

=

n integerPitch

X

(n+1)×Pitch

Y

n×Pitch

rj

riP- rj

φ1a φ1b

Pj*(position1b)

r

Pi

Rj

(i)(j)

r

r

riPr

Pj*(position1a)

X

(n+1)×Pitch

Y

n×Pitch

rj

riP- rj

φ1a φ1b

Pj*(position1b)

r

PiPi

Rj

(i)(j)

r

r

riPr

Pj*(position1a)



δ1a

δ1b

Pk (position1b)

X

αj

n×αj

(n+1)×αj

(j)

ψ

Pj

Strand BStrand A

Y

δ1a

δ1b

Pk (position1a)

rj

rrjP

r

ujP

r

rjk

r

sk

rsP

r

δ1a

δ1b

Pk (position1b)

X

αj

n×αj

(n+1)×αj

(j)

ψ

Pj

Strand BStrand A

Y

δ1a

δ1b

Pk (position1a)

rj

rrjP

r

ujP

r

rjk

r

sk

rsP

r

j

n integer ψ

= α

T

p k

2

j

cosR

ψ =s s

( ) ( )

( ) ( )

( ) ( )

( ) ( )

( ) ( )

( ) ( )

( ) ( )

/ 4

3 / 4

2 5 / 4

2

2

arccos cos if cos αnd sin

arcsin sin if


arcsin sin if

arcsin sin if cos αnd sin

arccos cos if


arcsin sin

ψ = ψ ψ ≥ 0 ψ ≥ 0

ψ = ψ ψ < π

ψ = ψ ψ < 0 ψ ≥ 0

ψ = π − ψ ψ > π

ψ = π − ψ ψ ≤ 0 ψ < 0

ψ = π − ψ ψ > π

ψ = π − ψ ψ > 0 ψ < 0

ψ = π + ( ) ( )7 / 4ifψ ψ > π

x y y xp k p k

2

j

sinR

ψ =s s - s s

k

k j j=s r - rP

P j j=s r - r



Rc

ββ

ββ β

(K)

Strand C

Pi

X

Y

c

ψ

r

Pm (position 1a)

Pm (position 1b)

(i)

rc

r

uk

Pn (position 1a)

Pn (position 1b)

rm

r

rn

r

Rc

ββ

ββ β

(K)

Strand C

PiPi

X

Y

c

ψ

r

Pm (position 1a)

Pm (position 1b)

(i)

rc

r

uk

Pn (position 1a)

Pn (position 1b)

rm

r

rn

r

( ) ( )

( ) ( )

T2

c m c m

T2

c n c n

c

c

R

R

=

=

r - r r - r

r - r r - r

sec =

Ln integer

Pitch

sec m n= r r-L

arcL n Pitch= ×arc c

L R= ψ ×

PRÉ-TENSION


ANÁLISE DINÂMICA

WITHOUT PRETENSION WITH A PRETENSION OF 25 N


ANÁLISE DINÂMICA


CONTRIBUIÇÕES

COMPORTAMENTO CINEMÁTICO E DINÂMICOGEOMETRIAMATERIAISDESGASTE

…

CONCEPÇÃO E OTIMIZAÇÃO DE MECANISMOS (E OUTRO TIPO DE SISTEMAS)

FOLGASATRITO

DISSIPAÇÃO DE ENERGIALUBRIFICAÇÃO

VIDA ÚTIL…




CÂNDIDA PEREIRA MALÇA

ISEC/INSTITUTO POLITÉCNICO DE COIMBRA

[email protected]

ANÁLISE DINÂMICA DE TRANSMISSÕES POR CORRENTE …

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