くさびモデルに基づくタッピンねじ締結プロセスに関する研究 び

Wedge Model for Controlling Torque in Tapping Screw Fastening
47
Atsushi Yoshioka
,
1.
,
(
.
)
,
Fig.1(b)
.
.
(d)
,
,
.
Fig.1
.
.
(a)
,
,
,
,
,2
3
.
1
,
.
,
,
(c)
3
,
,
,
,
.
.
.
,
,
.
(a)
(b)
(c)
Thrust Force Fth
Tapping
Screw
Near
Plate
,
,
.Tightening
,
.
Driving
Torque TD
Driver
Bit
,
,
Tapping
2.Tapping
2.1
Fig.3
.
Tapping
Tightening
Tap Plate
,
Z
R
,
,R
90[deg]
θ
(d)
.
2α
Tapping
2α
.
β
p
,
,
.
Tapping
Fig.1 Technological requirements and research focus
of tapping screw fastening
(a)
,
.
.
,
,
,
Fig.2
.
,
,
.
.
,
,
.
Fig.2
Nominal diameter of screw d1
,
Length of actual
(
),
(
)
Rotation speed
.
tapered screw y
R
θ
tap plate t
Z
θ
Diameter of
Tap plate
Z
Cross-Section
Thickness of
Tightening
Driving torque
[N mm]
Pre
Tightening
Lead angle β
Tapered screw
Length of
Rotation speed
[rpm]
Driving torque
Thread angle 2α
swaging part ytap
(
),
Pre Tightening
Tightening
Tapping
Screw thread
Cylindrical screw
,
Tapping
β
screw end d4
R
Tap hole diameter Dh
Fig.3 Definition of geometrical parameters of tapping screw
2.2
Angle of rotation [rad]
,
Fig.4
,
.
Engaging
Tapping
Pre Tightening
Tightening
Fig.2 Driving torque under controlled rotation speed
in tapping screw fastening cycle
Fig.2
.Tapping
(a)
,Tightening
,
,
.
,Tightening
(1)
.
(Fig.4(a)).
(Fig.4(b)).
β
.
(b)
,Tapping
2α
,
(b)
,(a)
.
1
A=
,
1
1
+
+1
tan 2 α ' tan 2 β
,
.
,
(1)
FR
.
Fig.3 R
,Fig.4(b)
.
3.1.2
Tapping
,
,
.
Thread angle 2α
Lead angle β
(2)(3)
.
,
Axial Force
FR
α
(b) Wedge for
.
,
Fφ
p
(a) Wedge for
tapping process
Tapping
Fig.5
tightening process
FR ' = 2 K M
.Fig.5(a)
,(b)
FR’
Z
µ F NU
Fφ
α
FR
β
β
F NL
FR
Upper surface
r Depth of wedge
r
3.1.3
FR
,
∆b/∆φ
.
∆r/∆φ
Y
∆r/∆φ
a.
Cylindrical
screw
(c) Tapping process model
,
,
R
FNL
θ
,
yeng
FR
.
(b)
,
d
Dh
(6)
d d1 − d 4 p
Dh
=
φ+
2
2 y 2π
2
d − Dh d1 − d 4 p
=
φ
r=
2
2 y 2π
.
,
.
(c) ,
,
,
(6)
.
,
,
.
,
,
,
.
,
,
d4/2
d/2
d1/2
Dh/2
-yeng
Fig.6 Geometrical modeling
.
for tapered screw top
(5)
(6)
γ
.
(7)
(7)
∆r/∆φ
p
.
b.
Fφ
(1)
∆r/∆φ (7)
∆r d1 − d 4 p
=
=γ
2 y 2π
∆φ
,
3.
3.1 Tapping
3.1.1
Fig.5(a)
,
θ
FR
FR
Aµ
Fφ =
Aµ 
sin β 

 sin α '+
tan α ' 

tan α ' = tan α cos β
d/2
r
,
Tapered
screw
y-yeng
0
.
φ
(5)
FR’ (a)
,
FR
Y=0
.
Fig.6
Fig.6
FR ’
.Tapping
R
φ
,
.
Fig.5 Extension of wedge based model
FNU
,µ
.
b
∆φ
,(4)
Z
,
FR’
.
θ
Angle of rota tion [ra d]
.
ρ
⊿φ
Lower surface
,
Fφ
,
(4)
b Width of wedge
KG Geometrical
coefficient
KM Yield stress
Driving Torque TD
R
(a)
KM,
.
b,
FR’
Fφ
µ F NL
,ν
.
Ta pping
torque [N mm]
Driving
b
Z’
F NU
α
r
Screw thread
(4)
FR’
α
Slip-Line field method
FR=KG KM b r
R
,b
r,
(b) Simplicity wedge model
θ
(4)
.KM
.
(4)
,(c)
.
Decomposition
of force
R
.
Aµ 

(1 + α '−ν + ρ ) sin α '+

tan α ' 

r ⋅b
cos α '−(cos ρ + sin ρ ) sin ν
r
,ρ
(a) Geometrical model
β
FR’
β
Fig.4 Two wedge models for tapping screw fastening
2.3
Fig.4
(3)
R
R
.
(1)
(2)
(8)
∆b/∆φ
∆b
d/2
,(5)
(8)
.
D 
1  d1 − d 4 p

∆b =
φ + h ∆φ
cos β  2 y 2π
2 
b
(8)
φ
,
b
d5
φ
d5
∆b
=
=η
∆φ 2 cos β
,(9)
.
η
.
(9)
d5
(8)
φS
b
(9)
(10)
3
.
.
.
d + Dh
d5 = 1
2
,
β
2.6[mm]
(10)
2α
.
Tap-tite
,
Table 1
.
Table 1 Specification of tapping screw
c.
(7)
(9)
∆r ∆b (4)
,Tapping
r b
.
,KG
d1/2
.
(4)
µA
∫∫ sin β K G K M γη∆φ∆φ
d µA
TD = 1
K G K M γηφ 2
2 sin β
TD = 2
Screw
Type
S-tite
B-tite
Fit-tite
,(1)
d1
2
end d 4 [mm]
Pitch
p [mm]
Lead angle
β [deg]
1.8
1.8
1.8
0.45
0.907
0.45
3.1
6.3
3.1
Diameter of screw
245[N/mm2]
,
t
.
8
8
8
1.8
1.6
1.8
,
KM
Dh
2.1, 2.2, 2.3, 2.4, 2.5[mm]
1.2, 2.0, 2.5, 3.2[mm]
4.2
.
,
.
,
(12)
(11)
.
.
Table 2
Table 2
,
,
.
Process
Thrust force [N]
(15)
(16)
φ
.
φ=0),
.
Table 2 Screw driving condition in experiment
 d µA

log TD = 2 log φ + log 1
K G K M γη 
 2 sin β

(11)
,
,
φ
,
.
φS
(
60
60
30
(11)
1 + α '−ν + ρ
KG =
cosα '−(cos ρ + sin ρ )sinν
,(11)
Thread angle Length of screw Length of tapered
2α [deg]
L [mm]
screw y [mm]
Rotation Speed [rpm]
Fig.7
Tapping
Pre Thightening
Thightening
52
400
52
300
52
50
5.
(Fig.7
(11)
)
.
φ
φS
.
TSmax
φS
Swaging
Dh
.
.
t
.
5.1
α
Fig.9(a)
Fig.7 Rotation angle φ
Fig.9(a)
d − Dh
φS = 1
2γ
(16)
φS
φS
.
4.
Tapping
,
.
Driving torque [N mm]
.
φS
,(7)
)
.
Fig.8
2.6[mm]
0.2
.
γ
,
,(4)
2.3[mm]
((11)
d1
,
.
3.2
(11)
3
,(7)
,
.
Dh
(11)
Dh
4.1
①
②
③
γ
φS
.
S-tite Dh2.3 t1.2
600
B-tite Dh2.3 t1.2
500
400
300
200
100
0
0
3
.
.
400
Experiment Theory
300
200
100
0
S-tite
30
,Fig.9(a)
p
B-tite
Screw type
φS
.Fig.10
2
)
Fig.10
2α
(
S-tite
B-tite
Fit-tite
150
10
20
Angle of rotation [rad]
φS
Table 1
) 3.2
(
Fig.10
,(11)
.
100
.
2
,
,
.
(7),(9)
50
,
0
.
0
Fit-tite
(a)
(b)
Fig.9 Influence of screw geometry on driving torque
,
250
200
Fit-tite Dh2.3 t1.2
Driving torque
,
Driving torque [N mm]
(16)
p
(b)
.
2.3[mm],
1.2[mm]
,Fig.8
.Fig.9(b)
,
Swage angle
φ=φS
N mm]
φ=0
β
.
2
4
6
Angle of rotation [rad]
8
10
,
,
Fig.8 Example of simulation
results based on eq.(11)
.
,
,
.
(11)
S-tite t1.2
S-tite t2.5
S-tite
1000
.Fig.10
Fit-tite
,S-tite
,
B-tite
1.5
.
S-tite
Fit-tite
B-tite
1000
1.2
Driving torque [N mm]
,
(
)
(
B-tite
S-tite
Fit-tite
)
(
)
(
)
100
10
1
Driving torque [N mm]
S-tite t2.0
S-tite t3.2
100
1
2
4
Angle of rotation [rad]
10
B-tite t1.2
B-tite t2.5
B-tite
1000
2
4
Angle of rotation [rad]
6
8
Driving Torque [N mm]
1
10
Fig.10 Influence of screw geometry on driving torque (log-log scale)
5.2
1.2[mm]
Dh
Fig.11
Fig.12
Dh
φS
.
,
.
10
)
10
2
4
Angle of Rotaiton [rad]
.
,
Dh
,
Fig.12
Dh
)
Dh
.
,
(1)
,
.
B-tite
.
,
2.4, 2.5[mm]
,5.1
,
,
,
.
,
(2)
.
,
φ
.
S-tite
(
S-tite Dh2.2
S-tite Dh2.4
2
(3)
,
①
β
,
②
10
2
4
6
Angle of rotation [rad]
8
B-tite Dh2.1
B-tite Dh2.3
B-tite Dh2.5
β
.
φ
α
φ
③
1
,
.
Dh
t
10
Dh
Fig.11 Influence of drilled hole diameter on driving torque
in case of S-tite (log-log scale)
1000
.
S-tite Dh2.1
S-tite Dh2.3
S-tite Dh2.5
)
100
1
10
(Tapping
.
,
,
1000
8
6.
,
.
,
S-tite
6
Fig.14 Influence of thickness of tap plate on driving torque
in case of B-tite (log-log scale)
Dh
.
(
100
1
2
Fig.11
B-tite t2.0
B-tite t3.2
1
Dh
.
,
Driving torque [N mm]
8
Fig.13 Influence of thickness of tap plate on driving torque
in case of S-tite (log-log scale)
1
Driving torque [N mm]
6
B-tite Dh2.2
B-tite Dh2.4
B-tite
(
,
(2)
(4)
Dh
.
2
.
,
)
100
Tapping
,
,
,
10
,
.
,
1
1
2
4
Angle of rotation [rad]
6
8
10
,
,
.
Fig.12 Influence of drilled hole diameter on driving torque
in case of B-tite (log-log scale)
5.3
2.3[mm]
Fig.13
t
Fig.14
.
(1)
φS
t
.
.
t
2
,
.
,
.
t
t
,
, 2007
(2) Martin Wagner, G. Seliger, Modeling of Geometry Independent Endeffectors for Flexible Disassembly Tools,
Proceedings of 3rd Int. Seminar on Life Cycle Engineering,
Zurich, (1996)
(3)
,
,
,
(1981)