00 8 ( CAD / CAE )
00 8
00 8 3
i,,,.,, CATIA V5.6,..,,.
ABSTRACT This thesis investigates the theoretical calculation method of initial clamping force required for bolted structure hen the external force acts on the bolted structure. Applied force to bolted structure as calculated ith theoretical method and analytical one by settling a basic model. The results ere compared, and then researched the influence of changes in design parameter upon bolted structure. As a theoretical approaching method, settled a basic model ith general design formulas and calculated initial clamping force required against external force and force applying to bolt and member due to the increase of external force. As an analytical approaching method, calculated force applying to bolt and member due to the increase of external force by using CATIA V5.6 to a basic model. Then compared the results came from analytical method ith ones from theoretical method. There as a discrepancy beteen the results by theoretical method and the ones came from analytical method hich member as bended from analytical process. Therefore, for the design of bolted structure, shall consider that stiffness calculated in theoretical can be changed because of the bending of member hen external force is applied to bolted structure. And additional studies based on experimental method are needed. ii
------------------------------------------------------------------------ ABSTRACT ------------------------------------------------------------------- ----------------------------------------------------------------------------- ----------------------------------------------------------------------- ------------------------------------------------------------------------- ------------------------------------------------------------------- 1 1.1 ------------------------------------------------------------- 1 1. ------------------------------------------------------------- 3.1 ------------------------------------------ 3. ---------------------------------------------------- 10.3 ------------------------------------------------------------- 11.4 ---------------------------------------------------------- 1.5 Stiffness parameter & Initial Clamping Force --------------------- 1.6 Tightening torque ------------------------------------------------------ 1.7 ------------- 7 iii
3 3.1 --------------------------------------------------------------- 8 3. -------------------------------------------------------- 8 3.3 ----------------------------------------------------- 9 3.4 ------------------------------------------------------------ 9 3.5 ------------------------------------------------ 30 4 4.1 Aspect Ratio ------------------------------------------- 31 4.,, ------------------------ 31 4.3 ------------------------------------------------ 3 5 5.1 ---------- 33 5. -------- 34 6 --------------------------------------------------------------- 36 ----------------------------------------------------------------- 38 iv
Figure.1 Figure.1. Figure.1.3 Figure.1.4 Figure..1 Figure.. Figure..3 Figure.7.1 Figure.7. Figure 3.1 Figure 3. Figure 3.4 Figure 3.5.1 Figure 3.5. Figure 3.5.3 Figure 3.5.4 Figure 3.5.5 Basic model of bolted joint Bolted joint and spring schematic Bolted & joint load curves Joint Diagram Basic model of bolt Basic model of nut Basic model of Plate Resultant bolt load versus external force for each method Resultant members load versus external force for each method Modeling Mesh generation Boundary condition Comparison of resultant bolt load by method A, analysis Comparison of resultant members load by method A. analysis Comparison of resultant bolt load by method B. analysis Comparison of resultant members load by method B. analysis Comparison of resultant bolt load by method C. analysis v
Figure 3.5.6 Figure 3.5.7 Figure 3.5.8 Figure 3.5.9 Figure 3.5.10 Figure 4.1.1 Figure 4.1. Figure 4..1 Figure 4.. Figure 4.3.1 Figure 4.3. Comparison of resultant members load by method C. analysis Comparison of resultant bolt load by method D. analysis Comparison of resultant members load by method D. analysis Comparison of resultant bolt load by method E. analysis Comparison of resultant members load by method E. analysis Variation of Resultant bolt load ith aspect ratio Variation of Resultant members load ith aspect ratio Variation of Resultant bolt load ith material Variation of Resultant members load ith material Variation of Resultant bolt load ith effective area Variation of Resultant members load ith effective area vi
Table..1 Table.. Table..3 Table.3 Table.4 Table.5.1 Table.5. Table.6 Table.7.1 Table.7. Table 3.4 Table 3.5.1 Table 3.5. Table 3.5.3 Table 3.5.4 Table 3.5.5 Table 4.1.1 Dimension of bolt Dimension of nut Dimension of Plate Calculation of bolt stiffness Calculation of joint stiffness for each method Calculation of stiffness parameter for each method Calculation of preload for each method Calculation of tightening torque for each method Resultant bolt load for each method by increasing external force Resultant members load for each method by increasing external force Applied force Comparison of resultant bolt and members load by method A, analysis Comparison of resultant bolt and members load by method B, analysis Comparison of resultant bolt and members load by method C, analysis Comparison of resultant bolt and members load by method D, analysis Comparison of resultant bolt and members load by method E, analysis Variation of resultant bolt load ith aspect ratio vii
Table 4.1. Table 4..1 Table 4.. Table 4.3.1 Table 4.3. Variation of resultant members load ith aspect ratio Variation of resultant bolt load ith material Variation of resultant members load ith material Variation of resultant bolt load ith effective area Variation of resultant members load ith effective area viii
δ : A : L : Grip length P : p : P : b P : j : δ b : δ j F i : F b : F j : K b : K j : E : ix
C : A N : d N : d : α : cone dz : cone D : j X : Y : µ : ρ : µ : T : T : T t : d i : d o : x
1 1.1,..,., ( = ),, stiffness parameter..,, stiffness parameter, relaxation effects, fatigue.. Shigley (1977) 1
, Edards (1991), VDI 30 (1988),,,..,. Sneddon (1946), Greenood (1964), Nelson (196), Lardner (1965), Fernlund (1961), Gould and Mikic(197) Tang, Deng(1988). Osman (1976) 1.5 hollo cylinder. Shigley, mitchell (1983) Shigley, Mischke (1989) 30 45. Rotscher (197) cone angle. Lehnhoff Mckay (199),. iteration,, nadal point. 30
cone angle... relaxation, embedding 5% ~ 15%, Fisher Struik (1987) 5%.,. 1.,,,,..1 3
.. ( small spring ), ( large spring ). ( small spring ), ( large spring ). ( Fig.1.1).,,..,. k b, k j ( Fig.1.)., Fig.1.3. Fi (preload),. Fi Joint Diagram. (Fig.1.4) 4
Tightening the bolts compresses the joint spring Tension in bolts makes them acts like stretched springs Figure.1.1 k b k j Figure.1. 5
,..1.1 PL = AE. A= Stiffness constant L= Grip length ( ) δ - (.1.1 ) P AE k = = - (.1. ) δ L ( External load) P 'e' P = F k e - (.1.3 ) b i + P = F k e - (.1.4 ) j i b δ = - (.1.5 ) b δ = - (.1.6 ) j P k P k j j b b j. ( Fig.1.5 ) 6
F b (tension) ( compression) F j δ b(extension) δ j ( contraction) Figure.1.3 bolt & joint load curves F b (tension) ( compression) F i F j extension Figure.1.4 Joint Diagram 7
F b (tension) ( compression) F j F i + k b e P=increase in Fb & decrase in Fj F i k b e e ( = ) Figure.1.5 F b smaller _ Fb P smaller _ kb same P k b k j k j Figure.1.6 8
k P b j = - (.1.7 ) k b P P k j b Pb = Since P P j kb + k b + P j = - (.1.8 ) P = ( total external load applied) P = b P = j F = b F j = Joint Diagram.1.9. F kb = Fi + P = Fi CP - (.1.9) k + k b + b j.1.10. F j = F k e - (.1.10 ) i j kb = Fi 1 kb + k j P 9
= F i ( 1 C)P C (Stiffness parameter ) 1. C. ( Fig.1.6 ) (external force) ' 0 ',...1.10 F = 0 j F j = F ( 1 C)P - (.1.10 ) i ( Initial Clamping force ) F i..1.11. F i = ( 1 C )P - (.1.11 ).,. M11.5P. aspect ratio. 10
3. 50KN. Fig., Fig..1, Fig.., Fig..3, Table..1, Table.., Table..3..3 fillet,,.. Shigley (1977),. /.3.1. PL = AE δ - (.3.1 ).3.. A = 11
P = L = Grip length E= Young's modulus k b EA L Eπd = N = N - (.3. ) 4L A = N d N =. ( Table.3 ).4. 1 ~ 8 ( Fig.4.1) Bickford (1990).. 1
Figure.4.1 Lines of equal compressive stress in joint.4.1 Shigley (1977) - Hollo cylinder model < Method A > shigley hollo cylinder., 3 hollo cylinder. A A * ( d ) = π d * 3d N 4 = equ d N equ k j π = 4 A ( 9d d ) = πd N N E πd N E = L L equ = - (.4.1 ) shigley.4.1 N 13
. ( Table.4.).4. Mischke (1989) - Truncated cone model < Method B > Hollo cylinder. Mischke.( Fig.4.). d dz α d z L z tanα + d Figure.4. Truncated cone model d = α = cone 14
dz = cone p = d = L = Grip length cone.4..1. Pdz d = AE δ - (.4..1 ) A.4... A = π ( r o r i d = π z tanα+ = ) d d + d d z tanα + z tanα + d π - (.4..) d Pdz = d + d d πe z tanα + z tanα + δ - (.4..3) d 15
.4..3 L/. P δ = πe L / 0 dz d + d d z tanα + z tanα+ d P = ln πed tanα ( t tanα + d d )( d + d ) ( t tanα + d + d )( d d ) - (.4..4 ) P k = δ = ln πed tanα ( t tanα + d d )( d + d ) ( t tanα + d + d )( d d ) - (.4..5).4..5..4..6. 1 k 1 1 + k k = ( k = ) 1 1 k k k m = - (.4..6 ).4..7 16
Mischke fixed angle =30. k m P = = δ ln πed tanα ( t tanα+ d d )( d + d ) ( t tanα+ d + d )( d d ) ο Mische α = 30 - (.4..7).4..7. ( Table.4 ).4.3 VDI ( Verein Deutscher Ingenieure 1988) 30 < Method C > VDI 30 d ).( Fig.4.3) ( b A equ = π ( D d ) ( ) 4 j d - (.4.3.1 ) D j A equ π = 4 D j d ( ) L L d + 1 d + d 5 100 ( d < D 3d, L d ) j 8 - (.4.3. ) A equ π L = d + d ( D j 3 d, L < 8d ) 4 10 > - (.4.3.3 ) 17
d = d = 1.5d b D j = d D j,.4.3.1,. grip length 8 D j 3 d.4.3....4.3.3. Grip length 8 D j 3 d. ( D 3 d, L < d ) >, j 8.4.3.3 ( Table 4. ) 18
3d d deq ( D > 3 d, L < d ) j 8 Dj d deq ( d < D 3d, L d ) j 8 Dj deq L ( d D j ) Figure.4.3 Equivalent joint area for stiffness (VDI 30) 19
.4.4 Edards (1991 ) Conical shape model < Method D > Edards VDI, Conical Shape. A equ [ 1] π ( d d ) + d ( D d ) ( + 1) π = h j X 4 8 - (.4.4. ) Ld X = d Dj d + L D 3 j..4.4 ( Table 4. ).4.5 Juvinall & Marshek (1991) < Method E> Juvinall Marshek Conical effective Area Effective stress Area. standard 60. A equ = d N + 0.68d N L + 0.065L - (.4.5 ) L = Grip length 0
d N =.4.5 ( Table 4. ).5 Stiffness parameter & Initial Clamping Force,.1.5.1. F i = ( 1 C )P C k k + k b = P 50KN b j = - (.5.1 ) C (stiffness parameter ). 50KN.. ( Table.5.1 ) 50KN. ( Table.5. ).6 Tightening torque 1
.....6.1. (Fig.5.1) X Y. (Helical angle)β, X, Y XY.6.1.1.6.1.. X cos β X Y sin β X sin β p Y cos β β Y π d Figure.6.1
F n Y cos β + X sin β = - (.6.1.1 ) F t = X cos β Y sin β - (.6.1. ).6.1.3. F = 0 ; F t µ Fn = 0 - (.6.1.3 ) µ 0.1. ρ µ tan ρ = X.6.1.4. X tan ρcos β + sin β tan ρ + tan β = Y = Y cos β tan ρsin β 1 tan ρtan β = tan ( β + ρ ) Y - (.6.1.4 ) T 3
.6.1.5. d 1 = X = Yd tan ( β + ρ) T - (.6.1.5 ).6.1.6. F n Y µ = µ ' Y cosα = - (.6.1.6 ) µ µ ' = = tan ρ' cosα.6.1.7. d 1 µ T = X = Yd tan( β + ρ' ) µ ' = tan ρ' cosα = - (.6.1.7 ).6. Y,.6..1. 4
T - (.6..1 ) = rdfn F N Y. p.6... T = p rda µ - (.6.. ).6..3. ( πr ) T = µ p rd - (.6..3 ) = πµ p r r i o r dr = πµ p 3 3 3 ( r r ) o i p = Y A Y = π r o r i ( ).6..4. 5
1 T = µ Yd = µ Y 3 1 = µ Y 3 3 ( ro ri ) ( r r ) o 3 i 3 3 ( do di ) ( d d ) o i d 3 3 3 ( d o di ) ( d d ) = - (.6..4 ) o i µ : T : r : i r o : d : i d : o d :.6.3..6.3. T T + = - (.6.3 ) t T 6
T = 1 Y ' µ [ d tan ( β + ρ ) + ] T t : Yd T : T :. ( Table.6 ).7, 50KN,., 0 ~ 50KN 10KN,..1.7.1.7.. Table.7.1, Table.7., Fig.7.1, Fig.7. F = F CP - (.7.1 ) b i + F = F ( 1 C)P - (.7. ) j i 7
3 3.1,,., 3.., slotting. Boolean operation.,,, Assembly.,, Coincidence Constraint.,,, Surface Contact Constraint. ( Fig 3.1 ) 3. OCTREE TETRAHEDRON Method. OCTREE TETRAHEDRON Method solid modeling part. 589, 44. 8
Contact Connection mesh. Contact Connection mesh mesh. 455. ( Fig 3. ) 3.3,, steel 1.1 material.,, steel 1.1 Aluminium. Table 3.3. Table 3.3 defining material 3.4, Surface slider. Surface slider supports 9
.,. ( Fig 3.4 ) 3.5 Force Method A,B,C,D,E bolt tightening, 50KN 0 50KN 10KN (Table 3.5) 4.. 30
. Aspect Ratio,,,. method A, Aspect Ratio,,, d. 4.1 Aspect Ratio Aspect Ratio..,, Aspect Ratio.0 ~ 3.0 0.. 0 ~ 50KN 10 KN. Table 4.1.1, Table 4.1., Fig 4.1.1, Fig 4.1. 4.., 31
,,. 3..,. ( Table 4..1, Table 4.., Fig 4..1, Fig 4.. )..,,..,,. 3... 1d,1.5d,d,3d,4d. ( Table 4.3.1, Table4.3., fig 4.3.1, fig4.3.) d. 3
., 5.,.. 5.1, Method A,B,C,D,E,., 0 ~ 50KN 10KN. 33
,,.. 3 method A.,,. 5. aspect ratio,.0.,.4,.6,.8, 3.0 Aspect Ratio,. Aspect Ratio.0. Aspect Ratio. Aspect Ratio. Aspect Ratio 0. 60N.,,,,, 40KN, 34
40KN.,.. 50KN.. 1d 1.5d. 1d 50KN preload. 35
6,,.,,.,,.,. Aspect Ratio,,,. Aspect Ratio,,,,.,,, 36
.,,.,, aspect ratio,,,. 37
1. Shigley, Joseph E., Mechanical Engineering Design, Mc-Gra Hill, 1977.. Edards, Kenneth S. Jr. and Mckee, Robert B., Fundamentals of Mechanical Component Design, McGra-Hill, Inc., 1991 3. Verein Deutscher Ingenieure, VDI 30, Systematic Calculation of High duty bolted Joints, VDI Society for Product Development, Design and marketing, Committee for bolted Joints, Dusseldorf, 1988 4. Juvinall, Robert C., and Marshek, Kurt M., Fundamentals of Machanical Component Design, John Wiley & Sons, Inc., 1991. 5. Bickford, Jogn H., An Introduction to the Design and Behavior of bolted Joints, d ed. Marcel Dekker, Inc, Ne York, 1990 6. Kulak, Geoffrey L., Fisher, John W., Struik, John H.A., Guide to Design Criteria for Bolted and Riveted Joints, Second Edition, John Wiley & Sons, 1987. 7. Gould,H.H., and Mikic,B.B., Areas of contact and pressure distribution in bolted joints.asme Journal of engineering for Industry,. Vol.94, no.3, pp864-870. 197 8. Lehnhoff,Terry.F., Ko,Kang II-Ko, Mckay Matthe L., Member stiffness and contact pressure distribution of bolted joints. Private Communication. 199 38
9. Wileman,J., and Choudhury,M., Green,I., Computation of member stiffness of bolted connections, Transactions of ASME,vol.113, Dec 1991, pp 43 437 10. Tand,J.,and Deng,Z., Better Stress and Stiffness estimates for bolted joints, Machanical design,1988 11. Young Gon Kim., A Parametric Study of Bolt Nut Joints by the Method of Finite Element Contact Analysis,Korea Advanced Institute of Science and Technology, 1989 1. CATIA Training Finite Element Analysis., DASSAULT SYSTEMS,1998 39
40 Table...1 Dimension of Bolt
Table... Dimension of Nut Table..3 Dimension of Plate 41
Figure.1 Basic model of Bolted joint Figure..1 Basic model of bolt 4
Figure.. Basic model of Nut Figure..3 Basic model of Plate 43
Calculation of bolt stiffness Equation : bolt stiffness k b EA = L N = Eπd 4L N TABLE.3 : Calculation of bolt stiffness 44
Calculation of joint stiffness Equation : joint stiffness Method A : k j = A equ L E πd = L N E Method B : k j P = = δ ln πed tanα ( t tanα + d d )( d + d ) ( t tanα + d + d )( d d ) ο Mische α = 30 Method C : k j = A equ L E A equ π L = d + d ( D j > 3 d, L < 8d ) 4 10 Method D : k A L E π 4 [ 1] equ j = Aequ = ( d dh ) + d ( D j d ) ( X + 1) π 8 Method E : k j = A equ L E A equ = d N +.68d N L + 0 0.065L TABLE.4 Calculation of joint stiffness for each method 45
Calculation of stiffness parameter Equation : stiffness parameter kb C = k + k b j TABLE.5.1 Calculation of stiffness parameter for each method Calculation of preload Equation: preload F i = ( 1 C )P P = 50KN TABLE.5. Calculation of preload for each method 46
Calculation of tightening torque Equation : Tightening torque T = 1 Y ' µ [ d tan ( β + ρ ) + ] Yd TABLE.6 Calculation of Tightening torque for each method 47
Equation : Resultant bolt load : F = F CP b i + TABLE.7.1 Resultant bolt load for each method by increasing external force ( : N) Figure.7.1 Resultant bolt load versus external force for each method 48
Calculation of resultant members load for each method by increasing external force Equation : Resultant members load : F = F ( 1 C)P j i TABLE.7. Resultant members load for each method by increasing external force ( : N) Figure.7. resultant members load versus external force for each method 49
Figure 3.1 Modeling Figure 3. Mesh Generation 50
Table 3.4 Applied Force Figure 3.4 Boundary Condition 51
Table 3.5.1 Comparison of resultant bolt and members load by Method A,analysis ( : N) Figure 3.5.1 comparison of resultant bolt load by method A, analysis Figure 3.5. comparison of resultant Members load by method A, analysis 5
Table 3.5. Comparison of resultant bolt and members load by Method B,analysis ( : N) Figure 3.5.3 comparison of resultant bolt load by method B, analysis Figure 3.5.4 comparison of resultant Members load by method B, analysis 53
Table 3.5.3 Comparison of resultant bolt and members load by Method C,analysis ( : N) Figure 3.5.5 comparison of Resultant bolt load by method C, analysis Figure 3.5.6 comparison of Resultant members load by method C, analysis 54
Table 3.5.4 Comparison of resultant bolt and members load by Method D,analysis ( : N) Figure 3.5.7 comparison of Resultant bolt load by method D, analysis Figure 3.5.8 comparison of resultant members load by method D, analysis 55
Table 3.5.5 comparison of resultant bolt and members load by Method E, analysis ( : N) Figure 3.5.9 comparison of Resultant bolt load by method E, analysis Figure 3.5.10 comparison of resultant members load by method E,analysis 56
Table 4.1.1 Variation of resultant bolt load ith aspect ratio ( : N) Figure 4.1.1 Variation of Resultant bolt load ith aspect ratio 57
Table 4.1. variation of resultant members load ith aspect ratio ( : N) Figure 4.1. variation of resultant members load ith aspect ratio 58
Table 4..1 variation of resultant bolt load ith material Figure 4..1 variation of resultant bolt load ith material 59
Table 4.. variation of members load ith material Figure 4.. variation of resultant members load ith material 60
Table 4.3.1 variation of resultant bolt load ith effective area Figure 4.3.1 variation of resultant members load ith effective area 61
Table 4.3. variation of resultant members load ith effective area Figure 4.3. variation of resultant members load ith effective area 6
,..,,.,,,. 00 8 63