〔 TECHNICAL DATA 〕 CALCULATION OF CUBIC VOLUME / WEIGHT / PHYSICAL CHARACTERISTICS OF MATERIALS QUANTITY SYMBOLS / UNIT SYMBOLS / CHEMICAL SYMBOLS AND ELEMENT SYMBOLS
〔 TECHNICAL DATA 〕 GENERAL DIMENSIONAL TOLERANCE EXCERPT FROM JIS B 0405 (1991) / JIS B 0419 (1991)
■ How to Calculate the Volume Solid Volume V Truncated cylinder
1. General dimensional tolerance of cutting JIS B 0405 (1991)
Solid
Volume V
Solid
Volume V
Solid
Volume V
Spherical segment
Spherical belt
Ellipsoidal ring
Unit: mm
Length dimensional tolerance (excluding chamfered parts)
π 4
b
V =
d 2 h
2 3
V =
πr 2 h
Tolerance degree
Standard dimension
a 2 + b 2 2
πh 6
π 2 4
V =
V =
(3a 2 + 3b 2 + h 2 )
d 2
h 1 + h 2 2
= π 4
= 2.0944r 2 h
d 2
0.5 (1) to 3 incl.
Over 3 to 6 incl.
Over 6 to 30 incl.
Over 30 to 120 incl.
Over 120 to 400 incl.
Over 400 to 1000 incl.
Over 1000 to 2000 incl.
Over 2000 to 4000 incl.
d
a
Explana- tion
a
Symbol
When circumference makes a curve equal to the circular arc, V = πℓ 12 (2D 2 + d 2 ) When its periphery makes a curve equal to a parabolic line, V = 0.209ℓ (2D 2 Dd + 1/4d 2 )
Barrel
Torus
Crossing cylinders
h 3
h 6
Pyramid
V = 2π 2 Rr 2
V = arn A = Area of base A =
Tolerance
R
= 19.739Rr 2 = π 2 4 Dd 2 = 2.4674Dd 2
± 0.05
± 0.05
± 0.1 ± 0.2 ± 0.5
± 0.15
± 0.2 ± 0.5 ± 1.2 ± 2.5
± 0.3 ± 0.8
± 0.5 ± 1.2
f
Fine
-
d 2 (ℓ + ℓ ,
π 4
d 3
V =
)
–
r = Radius of inscribed circle a = Length of a side of a regular polygon n = Number of sides ofa regular polygon
± 0.1 ± 0.2
± 0.1 ± 0.3 ± 0.5
± 0.3 ± 0.8 ± 1.5
± 2 ± 4 ± 8
m Medium
ℓ
D
± 2 ± 4
± 3 ± 6
c v
Coarse
ℓ
a
± 1
Very coarse
-
Circular cone
Spherical crown
Hollow cylinder (tube)
πh 2 3
V =
Note (1) : Tolerance for standard dimensions of less than 0.5mm shall be specified individually.
π 4
(3r–h)
■ How to Calculate the Weight Weight W [g] = Volume [cm 3 ] × Specific gravity
V =
h (D 2 –d 2 )
π 3 r 2 h = 1.0472r 2 h
V =
t
d
= πh 6
= πth (D–t) = πth (d + t)
(3a 2 + h 2 )
3. Tolerance of angle dimension
2. L ength dimensional tolerance in chamfered parts (corner roundness or chamfer dimension)
a
[Example] Material: Soft steel
r
D
a is the radius.
D = φ 16 L = 50mm then the weight is: W = D 2 × L × Specific gravity
π 4
Sphere
Truncated pyramid
Ellipsoid
4 3
V =
Unit: mm
πabc
h 3
V =
(A + a + Aa)
= π 4
4 3
× 1.6 2 × 5 × 7.85
V =
πr 3 = 4.1888r
Tolerance degree
Standard dimension
Tolerance degree
Length of shorter side of target angle
In case of a spheroid (b = c) V = πab 2
A, a = Surface area of both ends
= π 6
(Unit: mm)
≒ 79 [g]
d 3 = 0.5236d 3 3
0.5 (2) to 3 incl.
a c
Over 3 to 6 incl.
Over 6
d
4 3
Expla- nation
Over 10 to 50 incl.
Over 50 to 120 incl.
Over 120 to 400 incl.
Over 400
Explana- tion
Symbol
Symbol
10 or less
D
■ Physical Characteristics of Metals
Tolerance
Tolerance
■ How to Calculate Dimensional Changes due to Thermal Expansion When the temperature of a pin whose φ D = 2 and L = 100mm raises by 100°C, its dimensional change amount δ is: δ = Thermal expansion coefficient x Overall length x Temperature change = 10.8 × 10 –6 × 100mm × 100°C =0.108 [mm] [Example] Material: SKD61
■ How to Calculate Distortion from Young's Modulus E [Example] The distortion λ obtained when a load of P = 1000kgf is applied to a φ 10 × L60 pin (Material: SKD61)
f
Fine
Thermal expansion coefficient [×10 -6 /°C]
Density [g/cm 3 ]
Young's modulus E [kgf/mm 2 ]
f
Fine
± 0.2
± 0.5
± 1
Materials
± 1°
± 30 ′ ± 20 ′ ± 10 ′ ± 5 ′
m Medium c Coarse
m Medium c Coarse
Soft steel
7.85
21000 20500 21000 21000 22300 56000 54000
11.7 12.5 11.7 10.8 10.1
± 1°30 ′ ± 1°
± 30 ′ ± 15 ′ ± 10 ′
NAK80 SKD11 SKD61 SKH51
7.8
± 0.4
± 1
± 2
7.85 7.75
PL A λ
Very coarse ± 3°
± 2°
± 1°
± 30 ′ ± 20 ′
v
Very coarse
v
E =
Pkgf
Note (2) : Tolerance for standard dimensions of less than 0.5mm shall be specified individually.
1000 × 60 78.5 × 21000
8.2
PL AE =
λ=
Carbide V30 Carbide V40
14.1 13.9
6.0 6.0
≒ 0.036mm Cross sectional area A = π 4 D 2 ≒ 78.5
100
Cast iron SUS304 SUS440C
7.3 8.0
7500—10500
9.2—11.8
［ 20 ℃］
19700 20400 11700 10300 13000
17.3 10.2 17.6 20.8 17.1 23.6 23.6
4. General tolerance of perpendicularity JIS B 0419 (1991)
φ 10
Unit: mm
7.78
0.108
Oxygen free copper C1020 8.9
Nominal length on shorter side
［ 120 ℃］
6/4 Brass C2801
8.4 8.3 2.7 2.8 4.5
Over 100
Over 300
Over 1000 to 3000 incl.
Beryllium steel C1720
Tolerance degree
100 or less
Aluminum A1100 Duralumin A7075
6900 7200
to 300 incl.
to 1000 incl.
Perpendicularity tolerance
Titanium
10600
8.4
H K
0.2 0.4 0.6
0.3 0.6
0.4 0.8 1.5
0.5
1kgf/mm 2 = 9.80665 × 10 6 Pa
■ Greek Symbols
1 2
L
Uppercase Lowercase Pronunciation
General Usage
Uppercase Lowercase Pronunciation
General Usage
1
α β γ δ ε ζ η θ ι κ λ μ
ν ξ ο π ρ σ τ υ χ ψ ω
Α Β Γ Δ Ε Ζ Η Θ Ι Κ Λ Μ
Ν Ξ Ο Π Ρ Σ Τ Υ Χ Ψ Ω
alpha
nu
Oscillation frequency
Angle, coefficient Angle, coefficient
beta
xi
Variable
gamma
Angle, weight per unit area, relation (uppercase)
omicron
Number π (3.14159 … ), angle, symbol of volume (uppercase)
delta
Fine change, density, displacement
pi
5. General tolerance of straightness and flatness JIS B 0419 (1991)
epsilon
Small quantity, strain
rho
Radius, density
Unit: mm
zeta
Variable Variable
sigma
Stress, standard deviation, summation (uppercase)
eta
tau
Time constant, time, torque
Nominal length
theta
Angle, temperature, time
upsilon
Φ φ,
iota
phi kai psi
Angle, function, diameter
Over 10 to 30 incl.
Over 30 100 or less
Over 100 to 300 incl.
Over 300 to 1000 incl.
Over 1000 to 3000 incl.
kappa
Radius of gyration
Tolerance degree
10 or less
lambda
Wavelength, eigenvalue
Angle, relation
Coefficient of friction 10 -6 (micro)
Angular velocity = 2πf, Ohm = Unit of electric resistance (uppercase) Note: Unless particularly specified (uppercase), lowercase letters are the norm
mu
omega
Straightness and flatness tolerance
H K
0.02 0.05
0.05
0.1 0.2 0.4
0.2 0.4 0.8
0.3 0.6 1.2
0.4 0.8 1.6
■ Names and Symbols of Elements
Atomic Number
Element Name
Symbol
Atomic Number
Element Name
Symbol
Atomic Number
Element Name
Symbol
0.1 0.2
29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58
Copper
Cu Zn Ga Ge As Se Br Kr Rb
59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88
Praseodymium
Pr
89 90 91 92 93 94 95 96 97 98 99
Actinium Thorium Protactinium
Ac Th Pa
Atomic Number
Element Name
Symbol
Zinc
Neodymium Promethium Samarium Europium Gadolinium
Nd Pm Sm
L
0.1
Gallium
1 2 3 4 5 6 7 8 9
Hydrogen
H
Uranium
U
Germanium
Helium Lithium
He
Neptunium Plutonium Americium
Np Pu
Arsenic
Eu Gd Tb Dy Ho
Li
Selenium Bromine
Beryllium
Be
Am Cm
Terbium
Boron
B C N O
6. General tolerance of symmetry
Curium
Krypton
Dysprosium
Carbon Nitrogen Oxygen Fluorine
Unit: mm
Berkelium Californium
Bk Cf Es
Rubidium Strontium
Holmium Erbium Thulium Ytterbium Lutetium Hafnium Tantalum Tungsten Rhenium Osmium Iridium Platinum
Sr
Er
Nominal length
Yttrium
Y
Tm
Einsteinium Fermium
F
Zirconium
Zr
Yb Lu Hf Ta
100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 116 117 118
Fm Md No
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
Neon
Ne Na Mg
Over 100 to 300 incl.
Over 300 to 1000 incl.
Over 1000 to 3000 incl.
Niobium
Nb Mo Tc Ru Rh Pd Ag Cd
Mendelevium
Sodium
Tolerance degree
100 or less
Molybdenum Technetium Ruthenium
Nobelium
Magnesium Aluminum
Lawrencium Rutherfordium
Lr Rf
Al Si
W
Silicon
Symmetry tolerance
Rhodium Palladium
Re Os
Dubnium
Db Sg Bh Hs Mt Ds Rg Cn Nh
Phosphorous
P S
H K
0.5
Seaborgium
Sulfur
Silver
Ir
Bohrium Hassium
Chlorine
Cl Ar
0.6
0.8 1.5
1 2
Cadmium
Pt
Argon
Indium
In
Gold
Au Hg
Meitnerium
Potassium
K
L
0.6
1
Tin
Sn Sb Te
Mercury Thallium
Darmstadtium Roentgenium Copernicium
Calcium
Ca Sc
Antimony Tellurium
Tl
Scandium Titanium Vanadium Chromium Manganese
Lead
Pb
Ti
Iodine Xenon
I
Bismuth Polonium Astatine
Bi
Nihonium Flerovium
V
Xe Cs Ba La Ce
Po At Rn
Fl
Cr
Cesium Barium
Livermorium Tennessine Oganesson
Lv Ts Og
Mn
Radon
Iron
Fe Co
Lanthanum
Francium
Fr
Cobalt Nickel
1213
1214
Cerium
Radium
Ra
Ni
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