〔 PRODUCT DATA 〕 STRENGTH OF INLAY SECTION OF POSITIONING LOCKING BLOCKS WEDGE AND CUTTING AMOUNT
〔 PRODUCT DATA 〕 METHODS FOR COMPUTING ONE–STEP CORE PIN DIMENSIONS
■ One Step Core Pins: Computing the Gradient θ of the Shaped Section
■ Strength of Positioning Locking Block Inlay Sections
ℓ
Considering the force acting on the inlay section to be cantilever as shown in the figure on the left Bending Moment Section Modulus Mmax. = F∙H Z = A∙ L 2 6 Allowable Stress σ b = Mmax. Z = F∙H Z F = σ b ∙Z H = σ b ∙A∙ L 2 6 × H {maximum stress}
For A ＝ A 1
F
F
H
ℓ
ℓ
F
L
F
A
Step 1A
Step 1B/1E
Step 1C
Step 1D
A–V 2 L –D + A
D–V 2 L
A–V 2 L
A–V 2 ( L –C)
Gradient θ computation
θ= tan –1
θ= tan –1
θ= tan –1
θ= tan –1
① Inlay height H The below table shows that the longer the H, the lower the maximum stress a locking block can endure.
σ b = 1200–1800kgf/cm
A = 25mm L = 10mm H = 4mm, then F =
V = D–2 L tan θ
V = A–2 L tan θ
V = A–(2 L –D + A) tan θ
V = A–2 ( L –C) tan θ
V dimension computation
2 {11760–17640N/cm 2 }
(When the material is hard steel) Assuming that σ b = 1200kgf/cm 2 {11760N/cm 2 }
F { Maximum stress }
H
Strength coefficient
E For the shaft diameter designation 0.01mm increments type, calculate using P for D. Calculation of tan –1 (arc tangent) is simple using a function calculator. • How to derive the tan –1 ( arc tangent ) value from “ Conversion table of trigonometric functions ” ■ To find tan –1 ( x ) , please refer to the Conversion table of trigonometric function on D P.1215 . When the x of tan –1 (x) is less than or equal to 1 When the x of tan –1 (x) is greater than or equal to 1
kgf { N }
4 5 6 7 8 9
1250 {12258} 1000 {9800} 833 {8163} 714 {6997} 625 {6125} 556 {5449} 500 {4900}
100
1200 × 2.5 × 1 2 6 × 0.4
= 3000 2.4
= 1250kgf {12250N}
80 67 57 50 44 40
Assuming stress concentrating factor α = 2.5 { α = 2.5 when inlay corner area R is close to 0} F = 1250 2.5 = 500kgf {4900N}
① Locate the tan θ column from among the trigonometric functions listed on the top section of the Conversion table, then proceed down the column until you find the relevant value. ② The angle for θ on the left–hand column for that relevant value will be almost equal to the calculated value for tan –1 .
① Locate the tan θ column from among the trigonometric functions listed on the bottom section of the Conversion table, then proceed down the column until you find the relevant value. ② The angle for θ on the right–hand column for that relevant value will be almost equal to the calculated value for tan –1 .
10
② Inlay length L In the above case, maximum stress F 1 when L is lengthened from 10mm to 12mm is: F 1 = 1200 × 2.5 × 1.2 2 6 × 0.4 = 4320 2.4 = 1800kgf {17640N} L = 10 c 12 F 1 F = 1800 1250 = 1.44 The calculation indicates that the strength of the inlay section is 1.44 times greater.
③ Inlay corner area R The larger the corner area R, the smaller the α (stress concentrating factor). Therefore, the maximum stress which the locking block can endure increases.
(Example) tan –1 (1.4281) ≒ 55°00’
(Example) tan –1 (0.0875) ≒ 5°00’
R
tan –1 (0.0850) = 4°50’–5°00’
tan –1 (1.4315) = 55°00’–55°10’
θ (theta)
When deg (angle) = 0°00’–11°50’
.5640 .5664 .5688 .5712 .5736 .5760 .5783 .5807 .5831 .5854
.8250 .8241 .8225 .8208 .8192 .8175 .8158 .8141 .8124 .8107 sin θ
.6380 .6873 .6916 .6959 .7002 .7046 .7089 .7133 .7177 .7221 cot θ
1.4641 1.4550 1.4460 1.4370 1.4281 1.4193 1.4106 1.4019 1.3934 1.3848 tan θ
20 30 40 50 10 20 30 40 50
40 30 20 10 50 40 30 20
sin θ .0000
cos θ 1.0000
tan θ .0000
cot θ
deg (angle°)
Large R ←→ Small R 1 ≦ α ≦ 3
∞ 90°00’
0°00’
・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・
・ ・ ・ 30 20 10 50 40 30
55°00’
35°00’
30 40 50 10 20 30
.0785 .0814 .0843 .0872 .0901 .0929 .0958
.9969 .9967 .9964 .9962 .9959 .9957 .9954
.0787 .0816 .0846 .0875 .0904 .0934 .0963
12.706 12.251 11.826 11.430 11.059 10.712 10.885
■ Relationship Be tween Wedge and Cutting Amount
Sinking quantity of the wedge when cut 0.1mm to inclined plane with an angle of A°
Sinking quantity of the wedge when cut 0.1mm in perpendicular direction with an angle of A°
85°00’
5°00’
54°10’
cos θ
deg (angle°) θ (theta)
When deg (angle) = 54° 10’–66° 00’
(Reference Data) Method for Computing Dimensions During Tip Shape Selection ( ※ V is the dimension prior to tip shape processing. ) C (Chamfering) G (Cone cutting) T (Tapering) R (Rounding) B (Spherical processing)
0.1
A
B
A
B
A
B
A
B
A
C
A
C
A
C
A
C
0° 30´
11.460 5.730
7° 8° 9°
0.820 0.720 0.640 0.580 0.520 0.480 0.440 0.410 0.390
16° 17° 18° 19° 20° 21° 22° 23° 24°
0.360 0.340 0.320 0.310 0.290 0.280 0.270 0.260 0.250
25° 26° 27° 28° 29° 30° 35° 40° 45°
0.240 0.230 0.220 0.210 0.210 0.200 0.170 0.160 0.140
0° 30´
11.460 5.730
7° 8° 9°
0.810 0.710 0.630 0.570 0.510 0.470 0.430 0.400 0.370
16° 17° 18° 19° 20° 21° 22° 23° 24°
0.350 0.330 0.310 0.290 0.270 0.260 0.250 0.240 0.220
25° 26° 27° 28° 29° 30° 35° 40° 45°
0.210 0.200 0.200 0.190 0.180 0.170 0.140 0.120 0.100
x 1
x 1
x 1
S
G
1°
1°
1° 30´
3.820 2.870 2.290 1.910 1.430 1.150 0.960
1° 30´
3.820 2.860 2.290 1.910 1.430 1.140 0.950
2°
10° 11° 12° 13° 14° 15°
2°
10° 11° 12° 13° 14° 15°
2° 30´
2° 30´
3° 4° 5° 6°
3° 4° 5° 6°
Cutting amount to inclined plane when the sinking quantity of the wedge is 1.0mm with an angle of A°
Cutting amount in perpendicular direction when the sinking quantity of the wedge is 1.0mm with an angle of A°
G = Standard:
SR = automatically determined.
S = Standard:
0.1mm increments
0.1mm increments
SR ± 0.1 E The spherical shape of the tip is not a perfect sphere.
K = 1° increments
Q = 0.1mm increments
Precision/Extra precision: 0.05mm increments
Precision/Extra precision: 0.05mm increments
20 ＜ K ≦ 60 and θ= K
L ∙tan θ – A 2 (1–sin θ )∙tan θ –cos θ
0.2 ≦ Q ≦ V/2 x 1 = Q(1–sin θ ) x 2 = Q {1–(1–sin θ )tan θ }
V 2
0.5 ≦ G ＜ θ＜ 45°
SR =
V 2(tanK–tan θ ) Processing limit value α for L : α = V 2tanK
0.1 ≦ S ＜ V 2tanK K = 1° increments 10 ≦ K ≦ 45 and θ＜ K
x 1 =
E
x 1 = SR(1–sin θ )
x 2 = G(1–tan θ ) Processing limit value α for L : α = G
Processing limit value α for L : α = Q
Processing limit value α for L : α = V 2
A
D
A
D
A
D
A
D
A
E
A
E
A
E
A
E
x 2 = S(tanK–tan θ )
0° 30´
0.009 0.017 0.026 0.035 0.044 0.052 0.080 0.087 0.105
7° 8° 9°
0.122 0.139 0.156 0.174 0.191 0.208 0.225 0.242 0.259
16° 17° 18° 19° 20° 21° 22° 23° 24°
0.276 0.292 0.309 0.326 0.341 0.358 0.375 0.391 0.407
25° 26° 27° 28° 29° 30° 35° 40° 45°
0.423 0.438 0.454 0.469 0.485 0.500 0.574 0.643 0.707
0° 30´
0.009 0.017 0.026 0.035 0.044 0.052 0.070 0.087 0.105
7° 8° 9°
0.123 0.140 0.158 0.176 0.194 0.212 0.231 0.249 0.268
16° 17° 18° 19° 20° 21° 22° 23° 24°
0.287 0.306 0.325 0.344 0.364 0.384 0.404 0.424 0.445
25° 26° 27° 28° 29° 30° 35° 40° 45°
0.466 0.488 0.510 0.532 0.554 0.577 0.700 0.839 1.000
1°
1°
θ= 0° c SR = x 1 θ＞ 0° c SR ＞ x 1
θ= 0° c Q = x 1 = x 2 θ＞ 0° c Q ＞ x 1 ＞ x 2
1° 30´
1° 30´
θ= 0° c G = x 2 θ> 0° c G ＞ x 2
Processing limit value α for L : α = S
2°
10° 11° 12° 13° 14° 15°
2°
10° 11° 12° 13° 14° 15°
2° 30´
2° 30´
3° 4° 5° 6°
3° 4° 5° 6°
1193
1194
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