MODELING, VERIFICATION, OPTIMAL DESIGN OF NONLINEAR VALVE SPRING

8/12/2019 MODELING, VERIFICATION, OPTIMAL DESIGN OF NONLINEAR VALVE SPRING

1/130

MODELING, VERIFICATION, OPTIMAL

DESIGN OF NONLINEAR VALVE SPRING

A T

F G S

U MC

I P F

R D

M S

YUCHENG SU

D. YUYI LIN, T S

DECEMBER 2009


2/130

T , G S,

MODELING, VERIFICATION, OPTIMAL

DESIGN OF NONLINEAR VALVE SPRING

YUCHENG SU

,

, , .

DR. YUYI LIN

DR. ROGER FALES

DR. JAMES NOBLE


3/130

ACEDEE

T ,

Y L, P. D, P.E.,

;

T ,R F, P.D, J N, P.D,

F

T , F H,

;

T ,

.

T L S,

T J, A, I

F

A J H,


4/130

ABAC

T

. T , , , . I

,

. T ,

. M

. I ,

, ,

. T

,

.

N .

I ,

. D ,

,

. F F T (FFT)

.

T

,

ABAQUSMATLAB . R

, F D

M (FDM), .

N

.


5/130

TABLE OF CONTENTSACEDEE ....................................................... .........................................................

ABAC ............................................................................................. ............................................

ABE ................................................... ............................................................ ...............

E ............................................................ ............................................................ ..

ECAE ................................................................................................. ...........................

C 1 DC ....................................................................................................... 1

1.1 B M .............................................................................. 1

1.2 A ............................................................................. 2

C 2 DAC EA AD EACE ........................................................ 5

2.1 I G P ........................................................... 5

2.2 D E .............................................................................................. 7

2.2.1 E ...................................................... 7

2.2.2 E E ................................................... 9

2.2.3 A E ...................................................... 11

2.2.3.1 C A ...................................................................... 11

2.2.3.2 A....................................................................... 112.2.3.3 C D................................................................... 13

2.2.3.4 D................................................................. 15

2.2.3.5 A, D, C D............ 16

2.2.4 , , C.......................................... 17

2.3 ....................................................................................... 21

2.3.1 D ................................................................... 21

2.3.1.1 E D ................................................. 22

2.3.1.2 D ................................................. 24

2.3.1.3 C D ............................................. 26

2.3.2 ...................................................................................... 28

2.3.3 E ....................................................................... 28

2.4 E D ............................................................ 29

2.4.1 F F T (FFT) ................................................................ 29

2.4.2 N F ............................................................................... 32

2.4.3 S D R R ................................................. 33

C 3 EEEA E AD DEC .............................................. 35

3.1 ....................................................................................... 35


6/130

3.2 .......................................................................................................... 35

3.3 E A ................................................................................ 35

3.4 .................................................................................................. 36

3.5 C ......................................................................................... 40

C 4 A ...................................................... ...................................................... 42

4.1 .................................................................................................... 42

4.2 D, ............................................................. 44

4.2.1 D...................................................................................... 44

4.2.2 F F ............................................................................ 46

4.3 E ...................................................................... 56

C 5 A ............................................................ ............................................ 59

5.1 .................................................................................................................. 59

5.2 A ........................................................................................................ 59

5.3 D ................................................................................................ 60

5.4 AAB .............................................................. 61

5.4.1 A........................................................................... 63

5.4.2 C D (C )........................................... 66

5.4.3 D..................................................................... 68

5.4.4 A, D, C D........................ 71

5.5 ABAAAB .................................................. 75

5.5.1 ................................................ 75

5.5.2 A........................................................................... 76

5.5.3 C D ....................................................................... 77

5.5.4 ............................................................................................ 78

C 6 CC AD E ............................................................ .... 80

6.1 ......................................................................................................... 80

6.2 ................................................................................ 81

EEECE ................................................ ........................................................... .......................... 82

AED .................................................................................... ..................................................... 84

1. C ( )....................................................... 84

1.(A) ..................................................................................... 84

1.(B) C C D............. 95

1.(C) C .......................................................................... 95

1.(D) A....................................................................... 96

1.(E) E D .............................................................. 97


7/130

1.() C .......................................................... 97

1.() ............................................................... 97

1.() .............................................................................. 98

1.() C ............................................................................ 98

1.() D ........................................................ 98

2. C (ABAAAB ) ............................................. 100

2.(A) ............................................................................................ 100

2.(B) ..................................................................... 106

2.(C) ............................................................................ 106

2.(D) C .......................................................................... 106

3. E D ........................................................................................ 108

3.1 I D ......................................................................... 108

3.2 T F F 1368, 2165, 2372 () ............................. 1093.2.1 N I 1368 ..................................................... 109

3.2.2 O I 1368 .................................................. 109

3.2.3 N I 2165 ..................................................... 110

3.2.4 O I 2165 .................................................. 110

3.2.5 2372................................................. 111

3.2.6 O I 2372 .................................................. 111

4. E E..................................................................... 112

4.1 E ............................................................................. 1124.2 D C D ..................................................... 112

4.3 C ............................................... 113

4.4 E .............................................................. 113

4.5 E C A ............................................................... 113

4.6 DAA A........................................................................... 115

4.7 B................................................................................................. 116

4.8 .................................................................................... 116

4.9 E C .................................................................................. 116

5. ........................................................................................................ 117


8/130

ABE

T 3.1 N ......................... 40T 3.2 T .................................................. 41

T 4.1 T ................... 42

T 4.2 T ..................................................... 56

T 4.3 T ................................................................. 56

T 5.1 T .................................................. 75

T 5.2 C

..................................................................................................................... 79


9/130

E

F.1.1 T [F, 2007] ......................................... 3

F.1.2 T [F, 2007] ........................................... 4F.2.1 T .................................... 6

F.2.2 F .................................................. 8

F.2.3 H [C, 1961] ........................................ 12

F.2.4 A ...................................................... 14

F.2.5 I [C, 1961] ........................................................ 18

F.2.6 C ..................................................................................................... 20

F.2.7 C .............................................................................................. 20

F.2.8 T ................................................... 20

F.2.9 T ........................................................................ 22

F.2.10 T ............................................................................ 23

F.2.11 T ............................................................................ 25

F.2.12 T CN ............................................................. 26

F.2.13 T ................................... 29

F.3.1 T ...................................................... 36

F.3.2 T .............................................................. 37

F.3.3 T .................................................... 37

F.3.4 D F M [K, 1989] ....................................................... 38

F.3.5 S [B, 2008] ........................................... 39

F.4.1 T

............................................................ 43

F.4.2 T ................................................................................................. 44

F.4.3 T , 1368 ............ 45

F.4.4 T 8, 21, 34 2372 .......................... 45

F.4.5 T 5 ............................................................... 46

F.4.6 A 1368 ............................ 49F.4.7 A 1368 .................................................... 49

F.4.8 T 1368 ......................... 50

F.4.9 T 1368 ..................... 50

F.4.10 A 2165 ....................................................... 51

F.4.11 A 2165 ................................................... 51

F.4.12 T 2165 ........................ 52

F.4.13 T 2165 ................... 52

F.4.14 A 2372 ....................................................... 53F.4.15 A 2372 ................................................... 53


10/130

F.4.16 T 2372 ........................ 54

F.4.17 T 2372 ................... 54

F.4.18 T ....................................................... 55

F.4.19 T 1368

................................................................................................................... 55

F.4.20 T ............................................................. 57

F.4.21 T ................................... 57

F.4.22 T .............................................................. 58

F.4.23 T ......................................................... 58

F.5.1 T .......................................................... 63

F.5.2 T .............................. 65

F.5.3 T (

) ...................................................................................................................... 65F.5.4 T .......................... 67

F.5.5 T (

) ...................................................................................................................... 68

F.5.6 T ...................... 70

F.5.7 T (

) .................................................................................................................... 70

F.5.8 T ............................. 73

F.5.9 T .......................... 73F.5.10 T .............................. 74

F.5.11 T

( ) ............................................................................................................ 74

F.5.12 F ............................ 76

F.5.13 T ABAQUSMATLAB

(O ) .................................................. 77


(O ) .................................................. 78

A 3.1.1 S ................................................................. 108

A 3.1.2 S .............................................................. 108

A 3.2.1 F 1368 ................................... 109

A 3.2.2 F 1368 ............................... 109

A 3.2.3 F 2165 ................................... 110

A 3.2.4 F 2165 ............................... 110

A 3.2.5 F 2372 ............................... 111

A 3.2.6 F 2372 ............................... 111

A 4.3 P S T ................................................................... 113


11/130


12/130

ECAE

: spring force, a function of time and displacement: spring rate, a function of time and displacment: the displacemnt of spring for one end when the other end is ixed:coil radius of helical springs,a function of helix length,s:coil diameter of helical springs,a funciton of helix length,s: wire diameter of helical springs:pitch angle: variable pitch angle: variable wire diameter

: variable coil diameter: coil turns: shear modulus: polar moment of inertia of wire cross section:Youngs Modulus: area moment of inertia:area moment of inertia with respect to x axis:area moment of inertia with respect to y axis

: the arc length along the spring helix:time: mass moment of inertia:mass per unit length: density of spring materialtotal helix length: the clashed mass of wire segment

:curvature of the helix,a function of time and location,s,t

:torsion: rotation of wire in radians: the torsional strain energy: the irst bending strain energy: the second bending strain energy: the rotary kinetic energy: the radial kinetic energy

: the translatonal kinetic energy

:the damping force per unit length of the wire per unit of velocity: wave speed along the helix


13/130

: the instant acceleration: the same as x: the mass of wire segment to be deformed: curvature change

:torsion chagne:rotation change: the coeficient of restitution:the viscous damping coeficient determined by the measurement : the coeficients of Fourier Series:fundamental frequency 2

: number of harmonics

: period of cyclic motion


14/130

1

C 1

1.1 B

T 300

, H [1678] :

(1.1)T . I

. J. H.

M [1890] . H L ,

. E

C

. L [1944]

J.H. M . H,

L . W [1935]

. T

T [1951, 1956] W [W, 1935].

T [1963] TB ,

. D

, A G [1958]

. A

.

W [1963] 50 ,

1930 1950.

T . I

,

, .

T

. F.1.1 1.2

. U,

5000 RPM. T,

4800 RPM ( C 5).


15/130

2

A L [1989],

. A ,

. W [1963]

,

. P F [1983]

. T

[L, 1987]

H P . T L

20 ,

, .

1.2 A U H P

,

, .

F ,

.

T, . C O

, . M

, .

C T ,

. I

,

. I

,

. I ,

,

. T

,

.

C T . F

. F

F T .

S ,

,

.


16/130

3

C F

. E

. T ,

. T

C T.

C F . T

MATLAB

C T. T MATLAB

, ABAQUS. T,

,

, ,

, .

C S , ,

.

A C S

. E

ABAQUSMATLAB .

F.1.1 T [F, 2007]


17/130

4

F.1.2 T [F, 2007]


18/130

5

C 2 D E

2.1 A . F

, . I

, . A

. D, ,

,

( ) ( ). T

. T,

, ,

. T

F.2.1. I ,

. T

. I

.T

. T

. T

,

. A

,

. T

[L, 1989].

I F.2.1,

, , . T ,

, . T ,

[G, 1988; K, 2006]. I ,

.

G

. T

, FS


19/130

,

, L

T

A

, , 0

F.2.1 T

6

[L, 1988]. B

K

, , , ,

, cos, sin , , ,

, , ,0 . L [1988

. I

.

:

(2.1)

(2.2)

(2.3)

,


20/130

7

2.2 D ES

. W [1963]

. T . A, P

F [1984] ,

. F ,

. T

.

2.2.1 E T ,

N 2

L A 1707.

(2.4)A . F

, [L,

1927; J, 1972; P F, 1984]. I W [1963],

,

. F

F.2.2.

T

4 (2.5)T :

8 (2.6)I ,

1. I 2. A 3. D 4.

D


21/130

8

T, :

(2.7)

S

T

4 2 (2.8)W, .

F.2.2 F

T . F

, , ,

, . I ,

. T

[W, 1963]. A , E (2.8)

. T

. I ,


22/130

9

, ,

. I , ,

P F [1984].

2.2.2 E E T

, H . P

. I ,

, , . O

, , ,

. D ,

. A ,

[L,

1987]. L . T

. I ,

. B

. I

, , ,

. T

12 , (2.9) , ,0 (2.10)

12

,

(2.11)

A , . I ,

. W ,

. I . S . T . T


23/130

10

12 , (2.12)

12 ,

(2.13)

12 , (2.14)A , T . T T . B , ,

,

4

A ,

,

4

(2.15)

W, .

E. (2.15)

. A 15 . F ,

. I ,

. A W [1963].

4 14 4 0.615 T ,

. E. (2.8) , .

I , E. (2.15)

E. (2.8), . T

SECTION.2.2.3.3.

I , . F ,


24/130

11

E. (2.15), E. (2.16)

. T

L P [1987].

4 4 (2.16)

2.2.3 A ET ,

, ,

.

2.2.3.1 C AE. (2.8) W [1963]

. F , . I

E. (2.8), E. (2.15) .

2.2.3.2 AA ,

E. (2.8) (2.15). I , E. (2.16)

, J. A , . W

.

M .

T . I

, F 2.3,

. A ,

.

T,

, ,

[C, 1961].


25/130

12

F.2.3 H [C, 1961]

S

12 (2.17)W A , K and x,

8 and 8A E. (2.17) :

4 (2.18)F F.2.3,

,

,

I =

4 4 16 16 8 2

W, is mass of wire segmentT


26/130

13

(2.19)T E. (2.19) F.4.1. W ,

3 2 (2.20)A F.4.1. S E.

(2.20) ,

2 I (2.16)

4 2 4 (2.21)

2.2.3.3 C DA [N, 2007],

, . T

F O . T

S S. T, F O

. F G P ,

18,000 ,

. I

. T ,

. T

F.5.4

and /2 (2.22)I E. (2.21) ,

. T

. T M I . T


27/130

14

. T . T

:

: A

: A

F.2.4 A

T O

. T

. B P A T,

:

F

64 32

S E. (2.21), :


28/130

15

8 /

B,

,

2 (2.23)

T

4 2 s 2 (2.24)F ,

; , E. (2.16)

. A

, E. (2.8)

E. (2.16). T ,

. F , 95

. A , E. (2.8)

.

in eq. 2.8 2/

in eq. 2.16

4

/

2

/

2.2.3.4 DL [1993]

. I ,

. T

, . I

O ,


29/130

16

, ,

. T ;

, . T

F.5.6

(2.25)T E. (2.24) E. (2.25)

:

(2.26) ,

, , , 0,0,0,I ,

, , , 0,0,0,E. (2.26) ,

, , . F

, .

2.2.3.5 A, D, C DE. (2.26) , ,

. A

,

. I O , . F

, ,

, (2.26) . C

:, , , 0,0,0,A , :

, , , 0,0,0,A , :

, , , 0,0,0,

L O , E. (2.26)


30/130

17

.

2.2.4 , , CD ,

. T [W, 1963]

cos sin (2.27)E. (2.27) . I

, ,

. A , E. (2.8)

[W, 1963]. A

, E. (2.27)

. F , L

[1987]. H H , .

cos sin 12 (2.28)T .

H, F , F

D M F E M . I

S , MATLAB F D

M CN M.

I , . F ,

(

). T

. F

, . W , . B ,

, . T

F 2.5.


31/130

18

F.2.5 I [C, 1961]

T . I 1,

,

. W 2, .

T 2 3 . W

2 3, . I ,

1 2 2 3 , ,

W, M , . H E. (2.28)

cos sin (2.29)F ,

, F.2.7, . B,

, , ,

. I , , . T . I ,

, ,

. I ,

. T ( SECTION.2.4.2).

T S ( F3.3). C

F.2.6 F.2.7. T

[R, 2004]. T

F.2.8. T A, B. T A


32/130

19

. T A V, B V; W A

B, [G, 1988]

1

1 I

= 1,

12 12 2 2

A , . T

B , A . T

S E. (2.29),

cos sin (2.30)

W , (2.30) ,

, . E. (2.30)

.


33/130

20

F.2.6 C

F.2.7 C

F.2.8 T


34/130

21

2.3 2.3.1 D

B ,

. H,

,

. H

FD, FEM,

.

T

, . T

. F

s , . T ,

,

. B,

: . T ,

. T

:

F D:

B D:

C D:

12 12 W : F.2.9

T, P D E ,

,


35/130

. A

CN

E M F 0 > F > CN > G

1 > B

F

()

(

2.3.1.1 E U

F. , F D

F

S

22

[C, J P N

. I , R [1984]

,

D M.

>

>

>

>

, CN F D

E. (2.26). H,

1/2) [T, 1995].

D

.9. T . F

M,

.2.9 T

( F.2.10)

, 1947],

F

. T .

E. (2.26),


36/130

23

, 2, , , ,2 , 2, , W,

2 / 4 2

F.2.10 T

I

. F F.2.10

,; , . H, ,

. E ,

, , , , , (2.31)W,

1 2 1 2 1 2


37/130

24

2 2

1 2

1 2

ys, 0 fsand , gs = 0

y0, t 0 at s 0 and y, t htat s H,

,

,

[T, 1993]

1 (2.32)

2.3.1.2 D T

. T

,

,,, . I , . S

( F.2.11) E. (2.26),

,,, ,, ,,,


38/130

25

F.2.11 T

E ,

y, ky, , , , (2.33)

W,

1 2

1 2

2


y0, t 0 at s 0 and y, t htat s


39/130

26

2.3.1.3 C D T CN

( F.2.12). I ,

,,, ,, ,,, ,,,

F.2.12 T CN

T

, , , ,. I y, , , , , , , W

1 2

12

1 212

2 4 12


40/130

27


y0, t 0 at s 0 and y, t htat s I ,

,

, , , (2.34) , , , , T t

1 10 1 0 00 0 0 0

1 0 1

,,,,

A

U ,

(2.35)

W,

,

,,,,

and

1 10 1 0 00

0

0 0

1

0 1

B , . W

, .A . I

, . I ,

, ,

. D ,


41/130

28

CN F D M

. W

. E

,

;

, E. (2.20)

,W is space index in the grid is space step

I MATLAB,

. T ,

. F CN , 2.5

, 5

, E. (2.27).

2.3.2 T F S, , PDE.

S . I ,

F D M. B

, ys, t fsgt, ODE, (), (). N . F, F

, F [K,

2006]

ys, t e a coswt bsin wt sin nl s

H,

. H, .

2.3.3 E S FEM ,

FEA . W FEA (ABAQUS)

. T

. I . O . W ,


42/130

29

. B

,

[S, 2003].

1.

2. 3.

I O ,

, ABAQUSMATLAB .

2.4 E D

2.4.1 ()

S,

. A ,

. T

,

. I , ,

[N, 2007]

F , F F T (FFT)

. T

. I O ,

. I ,

F.2.13. T

FFT , .

F.2.13 T


43/130

30

T

[T, 1993]

A F F T (FFT)

D F T (DFT); FFT

. I , FFT

. I ,

.

T [T, 1993]

sin (2.36)

: the valve lift curve

: the coeficients of Fourier Series

:fundamental frequency 2 : number of harmonics: periodic motion of periodF , aand b

2 //

2 // (2.37)

. A ,

|C| a b

tan

ba

I ,


44/130

31

. F .

E. (2.36) [K, 2006]

cos

sin

sin

I [W, 1963]

sin sin2 sin W

12 1

2

~: the amplitudes of these harmonics ~:phaseA .

B, .

S

12

12 E. (2.36),

2 12 12

A N ,

1

|| (2.38)


45/130

32

H E. (2.38) F.4.8,

. T . A ,

1

F.4.8

[W, 1963]. T

. I O , E. (2.26), (2.30), (2.34) (2.38)

SQP .

2.4.2

T G G

1602. H,

J R 'A, L E, D B,

JL L. T ,

H 1887. A ,

.

I ,

, ,

. T

, . I

,

. T ,

, .

W ,

.O ,

. A

. I ,

. B ,

(R F.4.19

SECTION.3.2.2). T

[G G, 1602]


46/130

33

2 (2.39)A

[L, 1987; L G. M, 1988]:

2 , 1 , 2 , (2.40)I [SMI, 2002]

2 2 2 2 (2.41) = 1

2.4.3 D

T

. V

. [C, 1961; W, 1963; P, 1990; K, 1991; N,

2007]

D , . F,

, . T

,

. T

.

T

. A,

.

C . S , ,


47/130

34

. T

,

. I ,

.

V , , . H,

.


48/130

35

C 3 E D

3.1 V

S (C 4). T

. I

. T

. T

. T

S

, . I ,

. T

. O

,

. .

3.2 T , WDAQ (A 5),

W . T

,

. E

.

T EXCEL . MATLAB

EXCEL

WDAQ.

3.3 E AT (1987 GM & I

1.5L), AC

, . A

, , . T F.3.1.


49/130

36

F.3.1 T

M

. T

40 . T

(A 4.3). T :

GM&ISUZU E (A 4.1)

D C D M (A 4.2) O P O S P G C (A 4.9) O T P (A 4.8) VB (A 4.7) M O CT P S T (A 4.3) KISTLER F T (A 4.4) KISTLER C A (A 4.5) DATAQ (A 4.6)

3.4 A

, F.3.2. A


50/130


51/130

38

,

. T

.

W ,

F.3.4. T

. T . T

F.3.5. I

MOSFET JFET . T

[K, 1989]

11 1

(3.1)

: transducer capacitance:cable capacitance: rangefeedback capacitor: time constant resistor

: insulation resistance of input circuit

:charge generated by the transducerinput charge: output voltage

F.3.4 D F M [K, 1989]


52/130

39

F.3.5 S [B, 2008]

B , E. (3.1)

,

(3.2)

F A 4.5, S C A,

.T ,F 6000N . T

[B, 2008].

5000 10 6000 (3.3)

8 ? (3.4)

T , 10 ? (3.5)

C (3.3) (3.5), .

(3.6): output voltage


53/130

40

:range capacitor: the gain of charge ampliier:the ratio of the full voltage in the acquisiton and the standard full voltage :the maximal charge in standard full voltage

:the maximal force in standard full voltageS A 4.4 4.6, E. (3.7)

103.68Newton (3.7)E A 3.2.

M . O

. T .

T DATAQ A 14400 H. N D

E. (3.8). D 1368

632 , 2165 399. T

T.3.1.

Data points sample rate 60 mincamshaft speedrpm (3.8)

T 3.1 N

C S() D P

1368 632

2165 399

3.5 C T 4 ,

(A 3.1.1 3.1.2). T

T 3.2. T 1368 2165

A 3.2.1 3.2.4. T 2372 L

[2006] A 3.2.5 3.2.6. T

(A 4.2) 3450 . D

(A 4.8). T

r 1 w 1 r 2 w 2


54/130

41

w 2 w 1 r1r2

w1 ,

r1 ,

w2

, r2 T 3.2 T

G C S() S I D

1 1368 N

2 1368 O

3 2165 N

4 2165 O


55/130

42

C 4

4.1 T

, E. (2.35),

H P

.

A (A 1) MATLAB,

5 (INTEL C S

T1350, DRAM= 1GB, CPU= 1.86 GH).

O

, 1368, 2165 2372 . T 4.1

. F.4.1

, . I

,

. H,

y, t ht spring installed lengthcam proileF.4.2 . A . I ,

. I (

SECTION.2.2.1). F4.1 4.2

T 4.1.

T 4.1 T

T V

D( ) 0.0255

( ) 0.004

O F H 0.0485()

P H(

)

0.0399()

P H(

)

0.0386

S 0.024


56/130

43

D

( )

M D

7860

S M 77.9G

C () 1368, 2165, 2372

D (1368) 60.7462(N./)

D (2165) 30.3731(N./)

D (2372) 70.8705(N./)

T 0.000015()

S (N) 0.01()

F.4.1 T


57/130

44

F.4.2 T

4.2 D, 4.2.1 DT . F.4.3 = 0 = 0.0704 () 1368 . F.4.4

8, 21, 34. T

( SECTION.2.3.1.3,

). F.4.5 F.4.4,

, ( E. (2.19) (2.20). T

,

. T

O (C 5) 5

. T

. F , E V

(C 4). I ,

[L, 1987, 1989 2006].


58/130

45

F.4.3 T , 1368

F.4.4 T 8, 21, 34 2372


59/130

46

F.4.5 T 5

4.2.2 R

. R

. R ,

. T ,

13

. A 15

.

F ,

: 1368, 2165 2372 . T

. N ,

,

. T F.4.6, 4.7, 4.10,

4.11, 4.14 4.15. I


60/130

47

, .

I , . H

E. (2.23.2) (2.27).

I , SECTION.2.4,

FFT . T ,

FFT ( SECTION.2.4.1). T F.2.13. T

F.4.8, 4.9, 4.12, 4.13, 4.16 4.17. T

. A

1368 , 2165

2372 . A ,

. T

[W, 1963;

P, 1983; L, 1993; R, 2004; S, 2004]. I F.4.8 4.9, 19

,

the fundamental natural frequency 136860 min 19433.2HertzF, .

F.4.19 1368 . T . B

,

. I 19

[T, 1993]. A ,

19

.

T

. I F.4.12 4.13, 12

,

the fundamental natural frequency 216560 min 12 433HertzI F.4.16 4.17, 11

,


61/130

48

the fundamental natural frequency 237260 min 11 434.86Hertz

T 433 434 (H). I ,

, F.4.18. T

T 4.2. B , ,

E. (2.39 2.41), . T

,

.

the fundamental natural frequency 2 2 423.29Hertzthe fundamental natural frequency 12 423.21Hertzthe fundamental natural frequency 2 422.02Hertz

where 79 10,7860 ,0.004,0.0255,and 0.42, other parameters: Table 4.1I , (

) ( )

. T

. T 4.3 . I

O ,

(SQP).


62/130

49

F.4.6 A 1368

F.4.7 A 1368


63/130

50

F.4.8 T 1368

F.4.9 T 1368


64/130

51

F.4.10 A 2165

F.4.11 A 2165


65/130

52

F.4.12 T 2165

F.4.13 T 2165


66/130

53

F.4.14 A 2372

F.4.15 A 2372


67/130

54

F.4.16 T 2372

F.4.17 T 2372


68/130

55

F.4.18 T

F.4.19 T 1368


69/130

56

T 4.2 T

C () E N N F (H)

1367 19 432.88

1443 18 432.9

1528 17 432.93

1624 16 433.06

1732 15 433

1856 14 433.06

1998 13 432.9

2165 12 433

2362 11 433.03

2598 10 433

2887 9 433.05

T 4.3 T

G C

S()

I

D

A

(P S)

1 1368 N 4983.67

2 1368 O 7133.64

3 2165 N 4807.59

4 2165 O 6079.23

5 2372 N 6924.64

6 2372 O 8340.4

4.3 E

I , FEA ABAQUS,

. F.4.20 ,

. F.4.21 150 N

. T

9.4 10Pa. T , F.4.22, 4.23. F.4.22 3.31 10Pa . A W [1963], . F.4.23

5.01 10Pa , .D .


70/130

57

F.4.20 T

F.4.21 T


71/130

58

F.4.22 T

F.4.23 T


72/130

59

C 5

5.1 A

. A

. S

: , ,

. T

. T , ,

,

. T

ABAQUS SECTION.5.5.

5.2 AF ,

(SQP) . F , (QP)

BFGS H

L. T QP

(SQP). T

, .

W [V, 1984; A, 2001;

V, 2002]

1. S =0, , , , , . L QP . S

0 1

L


73/130

60

, L ,

T .

2. A

, . H, , 3. U , , 2 , , , .

4. C 1 and 2.

I .

5. C ,

.6. S , , , .L . U = + 1 2.

T

. I

. M

.

5.3 DF , MATLAB

. I MATLAB,

SQP, QN,

. T

. T ,,

. T ,,

N

. T

,. A , QP

. O

MATLAB.

T FFT MATLAB ( ), C. I ,

a

b (

SECTION.2.4). P :


74/130

61

C a b S .

5.4 AABI , F F T

. I . F

, E. (2.38),

, .T ; , . I , 5

F F T. T

.

5 , 5 ( ) is 0,1,2 N 1T

1 5,1

1 , , (5.1)

is space step, is time step, is total samples, is the harmonic number, is time index in the grid, is space index in the grid.S E. (2.34) E. (5.1),

1 ,

. (5.2)


75/130

62

T , , , , , ,

,

,

,

,

,

,

,

,

,

,

,

8 ( ),T E. (5.2) :

total sample time stepis 0.000015 sec, camshaft speedis 2372 rpm, time of one cycleis 0.02529511 sec.T

0.025295110.000015 1686.A ,

, , , , , , , , , , ,

the power spectral amplitude on the excited harmonic number

120230 (5.3) 0.03850.0387. (5.4)I ,

. I , . I ,

(A 4.1) . F

.

1. V P A2. V C D (C S)3. V W D4. V P A, V C D, V W D

I C, (E. 5.2) (E. 5.3 5.4)


76/130

63

. F

, . T

F.5.1.

F.5.1 T

5.4.1 AA . O

( ) ,

. I ,

,

0 , 0 , 0 , 0.004

0 , 0 , 0 , 0.0255

, , , 8 ( ).

F SQP,


77/130

64

0.2187, 0.1716, 0.0585, 0.00009.T

. B (5.3) (5.4),

, , , , E. (2.20). 0. 4 0 0. 2 0.3 0. 1 0.1 0. 1 0.1A ,

0.268699 , 0.145742, 0.079511, 0.000198, F.5.2 . T

159.11 (N). I

182.63(N), . F.5.3

. I ,

. T

11 6911. I 6924,

. H .

A [W, 1963; F, 2007],

. I ABAQUSMATLAB ,

SECTION.5.5.1. I ,

. I

SECTION.5.6.


78/130

65

F.5.2 T

F.5.3 T (

)


79/130

66

5.4.2 C D (C )C

. T

, . C

. E

.A H S

D [SMI, 2002], .

S V G R N

I ,

,

0.2187,

0.1716,

0.0585,

0.00009,

0 , 0 , 0, and 0.004.T E. (2.22),

, , , , 8F SQP,

0 , 0 , 0 , 0.0255.B (5.3) (5.4), :

0.0003 0.00020.004 0.0050.006 0.0040.022 0.029A , :

0.000198, 0.004731, 0.004397, and 0.02345.


80/130

67

F.5.4 . F ,

. M 195.52(N)

. F.5.5

. T 13

3378. T 11 6924. T

51.22 .

F.5.4 T


81/130

68

F.5.5 T (

)

5.4.3 DB, . T

, . T

.

T F G R S D

I ,

,

0.2187, 0.1716, 0.0585, 0.00009, 0 , 0 , 0, and 0.0255.

T E. (2.25),


82/130

69

, , ,

8

F SQP,

0 , 0 , 0 , 0.004B (5.3) (5.4),

.

0.0001 0.0003

0.004 0.008

0.004 0.0020.0035 0.0048A ,

0.000111, 0.005998, 0.001993 ,and 0.0046.F.5.6 . T

0.004 . T .

F , 166.78(N)

. F.5.7 . T

13

2752.11. I

6924. T

60.25 .


83/130

70

F.5.6 T

F.5.7 T (

)


84/130

71

5.4.4 A, D, C DT, . B

,

. T , ,

. T

. I

.

S V G R

D , ,

E. 2.20, 2.22 2.25,

, , , , , , , , , , , , 8F SQP, ,

0.2187, 0.1716, 0.0585, 0.00009, 0 , 0 , 0 , 0.004, 0 , 0 , 0, and 0.0255.B (5.3) (5.4), :

0. 4 0

0. 2 0.3 0. 1 0.1 0. 1 0.10.0001 0.00030.004 0.0080.004 0.0020.0035 0.0048

0.0003

0.0002

0.004 0.0050.006 0.004


85/130

72

0.022 0.029A , :

0.279762, 0.149103 , 0.091418 , 0.001535

0.000072 , 0.000363 , 0.002625 , 0.004683 0.000231 , 0.001972 , 0.003628 ,and 0.028783.F.5.8 F.5.2.

F.5.9

F.5.4. F.5.10 . A

[W, 1963; S, 2004]],

, .

T

. I ,

[W, 1963]. T

129.16(N) , . I

F.5.9 5.10. F.5.11

, 2159.9 13

. A .

T 68.8 . I ,

, 10 . L

[, , , , , , , , , , , 10%, :

[, , , , , , , , , , , = [0.2518, 0.1640, 0.1006, 0.0017, 0.0001, 0.0004, 0.0029, 0.0052, 0.0002, 0.002,

0.0040, 0.0317]

T 3129.61.

I , :

[, , , , , , , , , , , = [0.3077, 0.1342, 0.0823, 0.0014, 0.0001, 0.0003, 0.0024, 0.0042, 0.0003, 0.0018

0.0033, 0.0259]

T 4944.26. T . H,


86/130

73

10 ,

30 . A ,

.

F.5.8 T

F.5.9 T


87/130

74

F.5.10 T

F.5.11 T

( )


88/130

75

F ,

, . F ,

, , . T

, . T

, ,

. T

,

2372 rpm60 secmin 13 th 514 Hertz.T 5.1 .

T 5.1 T

W

()

M. S

S F

(N)

T

T

()

O 0.0415 182.63 6924.64 11

V. P 0.0415 134.11 6911.68 11

V. C. D 0.0415 195.52 3378 13

V. W D 0.056 166.78 2752.11 13

V. P, W, C D 0.0738 129.16 2159.9 13

5.5 ABAAAB 5.5.1

T

. T

SECTION.5.4.1 5.4.4

ABAQUSMATLAB . T MATLAB

SECTION.5.4,

ABAQUS. T

F.5.12. T , ,


89/130

76

. A

. T

SECTION.5.4.

F , ,

.

F.5.12 F

5.5.2 AT SECTION.5.4.1

433 (H) ABAQUSMATLAB . T

F.5.13 436 H.I

. A

. T

,

. V

, ,

( SECTION.2.4.4).


90/130

77


(O )

5.5.3 C DT SECTION.5.4.2 MATLABABAQUS

. T F.5.14

510 H F.5.5. I ,

,

. T

.

I ,

. H . W

13

[SMI, 2002]. T

engine speed red line2 rpm 160 minsec 1 3th fundamental natural frequency.

T 433 (H),

4006 (). T


91/130

78

514(H),

4726 (). I 700 ()

.


(O )

5.5.4 A ABAQUSMATLAB

SECTION.5.4, ,

. A , , ,

. T ABAQUSMATLAB

,

. A

FEA . C ,

FFT

. T

T 5.2.


92/130

79

T 5.2 C

O

D

O P N

(H)

P

V P

A 0.268699 0.145742 0.079511 0.000198433 O

P

436 ABAQUSMATLAB

P

V C

D

0.000198 0.004731

0.004397

0.02345

514 O

P

510 ABAQUSMATLAB

P

V. W D R SEC.5.4.3 514 O

P

X ABAQUSMATLAB

PROGRAM

C R SEC.5.4.4 514 O

P

X ABAQUSMATLABPROGRAM


93/130

80

C 6 C

6.1

1. T . T

, ,

.

2. F D .B CN

, . W

, ,

. F

MATLAB, CN

. I , .

W ,

.

3. F , F F T (FFT) . B

,

. I O ,

. T

68.8 .

S , ,

52 . T , GMISUZU 1987 , 433 H.

4. T ,

, . I

13

( )

2200, 512 H.


94/130

81

5. ABAQUSMATLAB , F D

.

6.2 1. D

, ABAQUSMATLAB

O . I ACIS

3D M 3D . F

, . I ,

3D ACIS

ABAQUS. T

, .

2. T F F T. F

[L, 2009],

. I

, .

3. A , , ,

. I

,

,

.


95/130

82

A, C. J. J. G, J. N., P C C H S,

ASME, 1958A, J S., I O D, MGH, 2001

B, R H., M S, S, A, CRC P, 2008

B, A H, 2007

C , N P., S D A, MGH, 1961

C, J P N, A

, P.

C. P. S, 1947

F, A, , V J P U D S D

A V T, M M T P, 2007

G, D T., P D, P H, 1988

J, W., , N L, S ,

P 30

AIAA/ASME/ASCE/AHS/ASC S, S

D M C, 1989

KISTLER, KISTLER PI, 1989

K, E, A E M, W, 2006

K, T, , A S J B V T, SAE, 1991

L, L L, Y, S A O CS D N

S W, ASME, 1994

L, Y H, D, D M E V

H S V P, CCAMMS, 2006

L, Y, , O D R S H S, ASME,

1993

L, Y J, S, D M S V P,

S I T S, 1999

L, Y P, A P., G D E H S WS S E V, ASME, 1987

L, Y P, T D D H S

, ASME, 1989

L, H. K, D., EFFECTS OF END COILS ON THE NATURAL FREQUENCY

OF AUTOMOTIVE ENGINE VALVE SPRINGS, I J A

T, 2009

L, A. E. H., A , D P,

1944M, I G., V W P, C U P, 1988


96/130

83

M, J.H., T

, M. M, 1890

N, M J, L , T &

E, 2007

P, F, H F S: M, C, E,

A I A & A, 2007

P, R.S., D A V S W CF D,

ASME, 1990

P, A. P. F, F., A E A I

D R HS CF S P 1:

E I, ASME, 1983

P, A. P. F, F., A E A I

D R HS CF S P 2: A C,L/D D M, ASME, 1983

R, J. N., A I T T F E M, MGH, 1984

R, H A., C D H, MGH, 2004

S, T, , E P A D S H

S, JSME, 1986

S, M., , FEM S, JSSR, 2003

SMI, H S D, 2002

T, J. W., N P D E: F D M,A M, 1995

T, W., T, P. G., T N P, O, 1883

T, W T., T V A, P H, 1993

T, S, T E, MGH B C, I., 1951

T, S, S M, D. N C, I., 1956

T, S, T E S, MG H, 1963

V, G N., N O T F E D

A, MGH, 1984

V, P., A O MATLAB P,

WI, 2002

W, A. M., H C T , J. A. M., 1935

W, A. M., M S, C O, P P CO, 1963

W, H F., A

, D, 1995

W, R, C V, D E, MGH, 1974


97/130

84

A

1. C ( )1.(A)

%

%

%1:

%2: 15%

%3:

%4:

%5:

%6:

%7:

;

;

('T C F D M\');

G = 779; %

= 7.863;%

= 0.004; %

= 0.01275; %

D = 2*; %

J = 2.6211; %

= 0.3; %

= D/; %

= 0.0386; %

= 0.024; %

= 1 /; %

L = 0.42; % = 2400; %

= (1+)*G*J; % G J E I

= *(*.2/4*L); %

= 8; %

= *L/; %

= /(2*D*L)*(G/2/); %

= ((G*.2)/(*(8*.2+.2))); %

F = 10; %


98/130

85

= *((5*/180)/(6*/180)/).2;%

= *.4*G/(8*D.2); % 1 L

= (4* 1)/(4* 4) + 0.615/; %

1 = /(*D*5); %

%

('T : %9.4()\',D);

('T : %9.4()\', );

('T : %9.4()\',);

('T : %9.4()\',);

('T : %6.2(/3)\',);

('T : %9.4()\',);('T : %9.4(N/)\',1);

('T : %9.4(/)\',);

('T : %6.2(/)\',);

('T : %7.2()\',);

('T : %7.2()\', );

= 0.01; %

= 0::L; %

= (); %

= 0.000027; %

= /60; %/ / 60 = /

= 0::(1/*4); %

1 = 0::(1/); % '

= (); %

= */; %

('T :

%6.4 \',);

(


99/130

86

%

%

= [0.2187 0.1716 0.0585 0.00009]; %

= (L,); %

%

= 0.15;

= [0 0 0:0.00001:*];% 10%

= ((),);

(1,:) = (1).*.3+(2).*.2+(3).* +(4); %

(,0) = ()

= (1,:); % (:,1) = 0; % = 0

(:,) = (1,) ;

(2,:) = (1,:); % (,0) = ()

%

= 3*(1).*.2+2*(2).*+(3);

= 1; = 1;

%

(' ....\');

(


100/130

87

L = ();

= ()/L;

;

= (,);

(1,:) = *;

= (1,,);

= [ 0 0 0 ];

= (1:()3);

(:,) = (1,) (:);

(2,:) = (1,:); % (,0) = ()

1 = ;

= 1;

1;

% ,

% ,

01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17

18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36

37 38 39 40 41

(


101/130

88

07 = (//).2.*2.*(07 2*(+1,8) + (,8)) ((+1,9) 2*(+1,8) +

(+1,7)) (08 2*07 + 06) + /*(/).2*(07 (,8)) +

2*(/).2*F*08/L;

08 = (//).2.*2.*(08 2*(+1,9) + (,9)) ((+1,10) 2*(+1,9) +

(+1,8)) (09 2*08 + 07) + /*(/).2*(08 (,9)) +

2*(/).2*F*09/L;

09 = (//).2.*2.*(09 2*(+1,10) + (,10)) ((+1,11) 2*(+1,10)

+ (+1,9)) (10 2*09 + 08) + /*(/).2*(09 (,10)) +

2*(/).2*F*10/L;

10 = (//).2.*2.*(10 2*(+1,11) + (,11)) ((+1,12) 2*(+1,11)

+ (+1,10)) (11 2*10 + 09) + /*(/).2*(10 (,11)) +

2*(/).2*F*11/L;

11 = (//).2.*2.*(11 2*(+1,12) + (,12)) ((+1,13) 2*(+1,12)+ (+1,11))(12 2*11 + 10) + /*(/).2*(11 (,12)) +

2*(/).2*F*12/L;

12 = (//).2.*2.*(12 2*(+1,13) + (,13)) ((+1,14) 2*(+1,13)

+ (+1,12)) (13 2*12 + 11) + /*(/).2*(12 (,13)) +

2*(/).2*F*13/L;

13 = (//).2.*2.*(13 2*(+1,14) + (,14)) ((+1,15) 2*(+1,14)

+ (+1,13)) (14 2*13 + 12) + /*(/).2*(13 (,14)) +

2*(/).2*F*14/L;14 = (//).2.*2.*(14 2*(+1,15) + (,15)) ((+1,16) 2*(+1,15)

+ (+1,14))(15 2*14 + 13) + /*(/).2*(14 (,15)) +

2*(/).2*F*15/L;

15 = (//).2.*2.*(15 2*(+1,16) + (,16)) ((+1,17) 2*(+1,16)

+ (+1,15)) (16 2*15 + 14) + /*(/).2*(15 (,16)) +

2*(/).2*F*16/L;

16 = (//).2.*2.*(16 2*(+1,17) + (,17)) ((+1,18) 2*(+1,17)

+ (+1,16)) (17 2*16 + 15) + /*(/).2*(16 (,17)) +

2*(/).2*F*17/L;

17 = (//).2.*2.*(17 2*(+1,18) + (,18)) ((+1,19) 2*(+1,18)

+ (+1,17)) (18 2*17 + 16) + /*(/).2*(17 (,18)) +

2*(/).2*F*18/L;

18 = (//).2.*2.*(18 2*(+1,19) + (,19)) ((+1,20) 2*(+1,19)

+ (+1,18))(19 2*18 + 17) + /*(/).2*(18 (,19)) +

2*(/).2*F*19/L;

19 = (//).2.*2.*(19 2*(+1,20) + (,20)) ((+1,21) 2*(+1,20)

+ (+1,19))(20 2*19 + 18) + /*(/).2*(19 (,20)) +


102/130

89

2*(/).2*F*20/L;

20 = (//).2.*2.*(20 2*(+1,21) + (,21)) ((+1,22) 2*(+1,21)

+ (+1,20))(21 2*20 + 19) + /*(/).2*(20 (,21)) +

2*(/).2*F*21/L;

21 = (//).2.*2.*(21 2*(+1,22) + (,22)) ((+1,23) 2*(+1,22)

+ (+1,21))(22 2*21 + 20) + /*(/).2*(21 (,22)) +

2*(/).2*F*22/L;

22 = (//).2.*2.*(22 2*(+1,23) + (,23)) ((+1,24) 2*(+1,23)

+ (+1,22))(23 2*22 + 21) + /*(/).2*(22 (,23)) +

2*(/).2*F*23/L;

23 = (//).2.*2.*(23 2*(+1,24) + (,24)) ((+1,25) 2*(+1,24)

+ (+1,23))(24 2*23 + 22) + /*(/).2*(23 (,24)) +

2*(/).2*F*24/L;24 = (//).2.*2.*(24 2*(+1,25) + (,25)) ((+1,26) 2*(+1,25)

+ (+1,24))(25 2*24 + 23) + /*(/).2*(24 (,25)) +

2*(/).2*F*25/L;

25 = (//).2.*2.*(25 2*(+1,26) + (,26)) ((+1,27) 2*(+1,26)

+ (+1,25))(26 2*25 + 24) + /*(/).2*(25 (,26)) +

2*(/).2*F*26/L;

26 = (//).2.*2.*(26 2*(+1,27) + (,27)) ((+1,28) 2*(+1,27)

+ (+1,26)) (27 2*26 + 25) + /*(/).2*(26 (,27)) +2*(/).2*F*27/L;

27 = (//).2.*2.*(27 2*(+1,28) + (,28)) ((+1,29) 2*(+1,28)

+ (+1,27)) (28 2*27 + 26) + /*(/).2*(27 (,28)) +

2*(/).2*F*28/L;

28 = (//).2.*2.*(28 2*(+1,29) + (,29)) ((+1,30) 2*(+1,29)

+ (+1,28)) (29 2*28 + 27) + /*(/).2*(28 (,29)) +

2*(/).2*F*29/L;

29 = (//).2.*2.*(29 2*(+1,30) + (,30)) ((+1,31) 2*(+1,30)

+ (+1,29)) (30 2*29 + 28) + /*(/).2*(29 (,30)) +

2*(/).2*F*30/L;

30 = (//).2.*2.*(30 2*(+1,31) + (,31)) ((+1,32) 2*(+1,31)

+ (+1,30)) (31 2*30 + 29) + /*(/).2*(30 (,31)) +

2*(/).2*F*31/L;

31 = (//).2.*2.*(31 2*(+1,32) + (,32)) ((+1,33) 2*(+1,32)

+ (+1,31)) (32 2*31 + 30) + /*(/).2*(31 (,32)) +

2*(/).2*F*32/L;

32 = (//).2.*2.*(32 2*(+1,33) + (,33)) ((+1,34) 2*(+1,33)


103/130

90

+ (+1,32)) (33 2*32 + 31) + /*(/).2*(32 (,33)) +

2*(/).2*F*33/L;

33 = (//).2.*2.*(33 2*(+1,34) + (,34)) ((+1,35) 2*(+1,34)

+ (+1,33)) (34 2*33 + 32) + /*(/).2*(33 (,34)) +

2*(/).2*F*34/L;

34 = (//).2.*2.*(34 2*(+1,35) + (,35)) ((+1,36) 2*(+1,35)

+ (+1,34)) (35 2*34 + 33) + /*(/).2*(34 (,35)) +

2*(/).2*F*35/L;

35 = (//).2.*2.*(35 2*(+1,36) + (,36)) ((+1,37) 2*(+1,36)

+ (+1,35)) (36 2*35 + 34) + /*(/).2*(35 (,36)) +

2*(/).2*F*36/L;

36 = (//).2.*2.*(36 2*(+1,37) + (,37)) ((+1,38) 2*(+1,37)

+ (+1,36)) (37 2*36 + 35) + /*(/).2*(36 (,37)) +2*(/).2*F*37/L;

37 = (//).2.*2.*(37 2*(+1,38) + (,38)) ((+1,39) 2*(+1,38)

+ (+1,37)) (38 2*37 + 36) + /*(/).2*(37 (,38)) +

2*(/).2*F*38/L;

38 = (//).2.*2.*(38 2*(+1,39) + (,39)) ((+1,40) 2*(+1,39)

+ (+1,38)) (39 2*38 + 37) + /*(/).2*(38 (,39)) +

2*(/).2*F*39/L;

39 = (//).2.*2.*(39 2*(+1,40) + (,40)) ((+1,41) 2*(+1,40)+ (+1,39)) (40 2*39 + 38) + /*(/).2*(39 (,40)) +

2*(/).2*F*40/L;

40 = (//).2.*2.*(40 2*(+1,41) + (,41)) ((+1,42) 2*(+1,41)

+ (+1,40)) (41 2*40 + 39) + /*(/).2*(40 (,41)) +

2*(/).2*F*41/L;

41 = (//).2.*2.*(41 2*(+1,42) + (,42)) ((+1,) 2*(+1,42)

+ (+1,41)) ((+2,) 2*41 + 40) + /*(/).2*(41 (,42)) +

2*(/).2*F;

=

(01,02,03,04,05,06,07,08,09,10,11,12,13,14,15,16,17,18,19,

20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40

,41);

(+2,2) = ((.01));

(+2,3) = ((.02));

(+2,4) = ((.03));

(+2,5) = ((.04));

(+2,6) = ((.05));


104/130

91

(+2,7) = ((.06));

(+2,8) = ((.07));

(+2,9) = ((.08));

(+2,10) = ((.09));

(+2,11) = ((.10));

(+2,12) = ((.11));

(+2,13) = ((.12));

(+2,14) = ((.13));

(+2,15) = ((.14));

(+2,16) = ((.15));

(+2,17) = ((.16));

(+2,18) = ((.17));

(+2,19) = ((.18));(+2,20) = ((.19));

(+2,21) = ((.20));

(+2,22) = ((.21));

(+2,23) = ((.22));

(+2,24) = ((.23));

(+2,25) = ((.24));

(+2,26) = ((.25));

(+2,27) = ((.26));(+2,28) = ((.27));

(+2,29) = ((.28));

(+2,30) = ((.29));

(+2,31) = ((.30));

(+2,32) = ((.31));

(+2,33) = ((.32));

(+2,34) = ((.33));

(+2,35) = ((.34));

(+2,36) = ((.35));

(+2,37) = ((.36));

(+2,38) = ((.37));

(+2,39) = ((.38));

(+2,40) = ((.39));

(+2,41) = ((.40));

(+2,42) = ((.41));

1(+2,:) = (+2,:) + ((1).*.3+(2).*.2+(3).*+(4)

.*)*(1(+2)/(L ));


105/130

92

= + 1;

;

('F ....\');

%

(,1,L,,);

= 6; %

= 1;

= 0; %

(


106/130

93

2 = 0;

3 = 0;

4 = 0;

= 0; %

F = 0; %T S F W' F = GJ/*()*()

EI/*()*() M*/

(


107/130

94

[,] = ((8:20));

('T %7.2 \',8+1);

('T %7.2\',);

('T %7.2()\',/2/L);

%

(3,2,1);

(,1(:,8),,1(:,21),,1(:,34));

([0.055 0.085 0 0.05]);

(' 8',' 21',' 34');

('()');('()');

(3,2,2);

(,,,1(3,:),,1(1525,:));

(' ',' 0 ',' 0.0152 ',2);

(' ()');

('()');

(' CTCS');

(3,2,3);(,F2,'.',1,,':');

([0.0575 0.075 50 200]);

(' ',' ');

('T()');

('S S F(N)');

(3,2,4);

((1:20));

('N H');

('P H');

('P ');

(3,2,5);

(,);

(' ()');

(' ()');

('P 0');

(3,2,6);

(,);


108/130

95

([0.055 0.085 0.06 0.08]);

('()');

(' ');

(' ');

1.(B)C C D%

= (L,)

= 0:0.001:L;

= ();

1 = 0(1).*.3+(2).*.2+(3).* +(4);

= (1);2 = 1;

= 1;

= ();

(


109/130

96

2045 2215 2388 2557 2731 2909 3078 3247 3413 3578....

3734 3899 4069 4238 4399 4560 4716 4860 4996 5114....

5229 5326 5411 5478 5533 5576 5601 5610 5605 5584....

5546 5483 5394 5284 5124 4983 4788 4577 4344 4103....

3849 3586 3336 3095 2858 2621 2397 2189 1986 1795....

1618 1457 1309 1169 1042 923 818 720 635 559....

492 432 381 339 301 267 242 216 195 178....

161 149 132 119 106 94 81 68 56 39 26 13 5]/1000000;

= 2**.*/*180;

= ();

= 0;

= 1;

= 1;%

( (1,))

= + 1;

;(>1)

() = (() (1,1))/((1,) (1,1))*((2,) (2,1)) + (2,1);

;

= 1;

= + 1;

;

1.(D) A% ( )

(,1,L,,)

('C ....\');

=1;

= 1; %

= 2;%

= 0.01389; %

= 0:0.001:L;


110/130


111/130

98

% = [1 2 3 4]; %

% = [1 2 3 4]; %

%0 = [ ];

0 = [0.2187 0.1716 0.0585 0.00009 0 0 0 0.004 0 0 0 0.0255];

%

0 = [0.2817 0.1716 0.0585 0.00009 0 0 0 0.004 0 0 0 0.0255]; %[]

= [0.4 0.2 0.1 0.1 0.0002 0.007 0.003 0.0035 0.0003 0.004 0.006 0.022];

%

= [0 0.3 0.1 0.1 0.0002 0.007 0.003 0.0048 0.0002 0.005 0.004 0.029]; %

%

= ('LS','');

% , [, ] = (@,0,[],[],[],[],,,@,);

%

[ ] = ();

1.() %

%[1 2 3 4 1 2 3 4 1 2 3 4]

= ()%

= ' ';

1.() C %

%[1 2 3 4 1 2 3 4 1 2 3 4]

[ ] = ()

= 0.42; %

= [' ' 210;

' ' + 120;];

= [];

1.() D;

;

%


112/130

99

0 = [0.2187 0.1716 0.0585 0.00009];

%

= [ 0 0 0.0386/0.42 0];

%

% 1

1 = [0.268699 0.145742 0.079511 0.000198];

% 4

4 = [0.279762 0.149103 0.091418 0.001535];

% >

= 0;

1 = 0;

= 50;

= 0.0386/;

= 1;

= 0.00001;

2 = 0;

2 = 0;

= 1; ( = 0.0001)

= ((1).*(2.3 1.3) + (2).*(2.2 1.2) + (3).*(2 1));

2 = 2 + ;

;

2(+1) = 2 ;

SL()= 2(+1) 1;

12() = (1 + 2(+1))/2;

1 = 2(+1);

= 1;

= + 1;

;

G = 779; %

= 7.863; %

%


113/130

100

0 = [0 0 0 0.004];

D0 = [0 0 0 0.0255];

%

% 2

2 = [0.000111 0.005998 0.001993 0.0046];

% 3

D3 = [0.000198 0.004731 0.004397 0.02345];

% 4

4 = [0.279762 0.149103 0.091418 0.001535];

4 = [0.000072 0.000363 0.002625 0.004683];D4 = [0.000231 0.001972 0.003628 0.028783];

% >

= 0;

% >

D = D0;

%

= ((G.*((1).*12.3 + (2).*12.2 + (3).*12 +(4)).2)./(.*(2.*((D(1).*12.3 + D(2).*12.2 + D(3).*12 +

D(4)).2)+((1).*12.3 + (2).*12.2 + (3).*12 + (4).2))))./SL;

(12,,'.');

(' ()');

('F D ');

('F D')

2. C (ABAAAB )2.(A) F = (, , , )

;

%

= [0.2187 0.1716 0.0585 0.00009];

% ( )

D = [ ];

= 0.004;%


114/130

101

= 0.0386;%

= 0.024;%

L = 0.42;%

= 0:0.0001:10*2*;

(1:()) = 0;

(1:()) = 0;

(1) = (D(1).*0.3 + D(2).*0.2 + D(3).*0 + D(4))/2;

= 1;

= 1;

= 0.002;

= ;

= 1;

(1) = (1);(1) = 0;

(1) = 0;

(1) = 1;

= 2;

%

%

= ((1)))

= 2;

() = DD/2*((1));

() = DD/2*((1));

() = (1).*.3 + (2).*.2 + (3).* + (4);

= + ;

= + 1;

= ;

(1) = 1;


115/130

102

(1) = (2);

;

= + 1;

;

= 1;

;

;

= ;

= ;

= ;

;

= ();

% IGES

= ('1.','');

%

= ('1.','');

1

= (); (), ,

(,(1:80));

(,'\');

();

= 1;

%

= ('2.','');

1

= ();

(), ,

(,(1:80));

(,'\');

();

= 4;


116/130

103

= ('.','');

= 1;

= 1;

% DE

(


117/130

104

= + 2;

;

= 1;

%

= [(,'S') (,'G') (,'D') (,'P')];

(,[ (72()) (1,'T')]);

();

= ('.','');

= ('1.', '');

1

= (); (), ,

(,);

(,'\');

();

%

= ; = 1;

= ();

(


118/130

105

();

(,['.[N].CP(=''CP'', ='

2(/2) ')' '\']);

= ('3.', '');

1

= ();

(), ,

(,);

(,'\');

();

();

('T : %8.7 %8.7 %8.7 %8.7\',, , , );

% A

('T F E A ABAQUS \');

[,] = ('ABAQUS GUI=.');

('T F E A ABAQUS ...\');

% ABAQUS

= 1;

= 9;

V = 0;

F = 0;

= ('.', '');


119/130

106

();

%

('T %6.2\',F);

('T %7.5\',V);

2.(B) %

;

;

0 = [0.2187 0.1716 0.0585 0.00009];

%

= [0.4 0.2 0.1 0.1];%

= [0 0.3 0.1 0.1];

%

= ;

.D = '';

% ,

('V S O\');

('T YC S\');(' U M C\');

('06.20.2009\');

('R \');

[ ] = (@1,0,[],[],[],[],,,@1,);

%

[ ] = 1();

(' : %16.15 %16.15 %16.15\',(1),(2),(3),(4));

(' : %6.4\', );

2.(C) %

%

= 1()

%

= ((1),(2),(3),(4));

2.(D) C


120/130

107

%

[ ] = 1()

= 0;

= [];

= [];


121/130

108

3. E D3.1 D

A 3.1.1 S

A 3.1.2 S


122/130

109

3.2 1368, 2165, 2372 ()

3.2.1 1368

A 3.2.1 F 1368

3.2.2 1368

A 3.2.2 F 1368


123/130


124/130

111

3.2.5 2372

A 3.2.5 F 2372

3.2.6 O I 2372

A 3.2.6 F 2372


125/130

112

4. E E4.1 E

YEAR: 1987

DISPLACEMENT: 90inch 1.5 HP@RPM: 70@5400

TORQUE F.L@RPM: 87@3400

C R: 9.6:1

B: 77

S: 79

C: 25.93225.96

0.050.1 CV S: F L: 48.50

V C L: [email protected]

4.2 D C D


126/130

113

4.3 C RPM : 2.599999 D S A +/ 0.05% 5 LCD

A 4.3 P S T

4.4 E M: 9031A

4.5 E C AM: 5004


127/130

114

A 4.5 T A

T A:


128/130

115

4.6 DAA AM: DI158UP

A 4.6 DATAQ A

D:


129/130

116

4.7 BM: G

T:

VB, HYT PLUS, 59, B56(5L590) X 1 VB, HYT PLUS, 63, B60(5L630) X 1

4.8 T:

M R: 2.1 X1 M R: 3.2 X1 M R: 5.5 X1 M R: 6 X1

A 4.8 T

4.9 E CM: 1361A(X)

F:

W T :195 240 C: 30F/ S 30 A 1 5


130/130

5. WINDAQ V. 2.49 MATLAB R2007

FEA , ABAQUS

CATIA V5R17 3D ABAQUS V. 6.8.1 F E M

F

D M

Documents

MODELING, VERIFICATION, OPTIMAL DESIGN OF NONLINEAR VALVE SPRING