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Physics: 2. r oeri 49
Moments of area and Polar section m od uli1'
Shape of the Bending and Buckling Torsion
cross-section Polar section
Area mo ment of Axial section mo dulu s l/Vn
inertia I modulus W
44 ^ ji-d4 ji-d 3 p 16
/=
W=
64 32
jt-(P4-d4) i-(D 4 - d 4 ) p 16 • D
W=
/=
32 D
64
1=0.05 • D 4 - 0.083 d • D 3 W = 0 . 1 • D 3 - 0.17 d • D 2 W p = 0.2 • D3 - 0.34 d • D 2
1= 0.003 • ( D + d ) 4 W= 0.012 • ( D + d ) 3 dW 0 2p 3
•
/= 0.003 • ( D + d ) 4 W = 0.012 • (D + d ) 3 W n = 0.024 • ( D + d ) 3
also applies for m ore keys x z 1 2 h3 Wp = 0.208 • h 3
x -c:
x 6 W p = 0.188 • s 3
= 0.123 • d 3
V2-/73
W p = 17 • w 2 • h
W z = 12 Values for rj
see table below
M 5-V3-S4 5 s 3 = 5-V3-d3
48 ~ 128
x\ 1 x y 144 W x =
W X ~tD 5 • V3 • d 4 W yv = 5 s 3 - 5 - d 3
24-V 3 64
/x~/y" 256
4 I -X -c 3 2
j
7 x = w1-2h W x =w 6• h
/7-W2
/7-W 3
Wy = 6
w
x-1 4 \-x B • H 3 -w-h3 B • H 3 - w • h 3
•4—
7x = 12 W x = 6 H t-(H + h)-(B + w )
w
m B m H- B3-h-w 3 W y = H • B 3 - h • w3 % =
/ y = 12 B
6
1 ) 2nd mo me nts of inertia and axial section mo duli for profiles see pages 146 to 151.
Aux iliary v alue i] for polar s ec tion m odu li of rec tangular c ros s -s ec tions
h/w 1 1.5 8 10
0.313
0 208 0.231 0.246 0.267 0 282 0.299 0.307 0.333
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50 Physics: 2.6 Strength of Materials
Comparison of various cross -sectional shapes
Cross-section Linear Slec tion n moduli o r s tatic m o m e n t s f or t y p e •of loadin g
mass (tensity
Ben d i n g Bucld i n g T o ns i o n
Shape Standard nn' V VYy In nin U"P
designation k g / m f a c t o r 11 c m 3 f a c t o r 11 c m 3 factor1' c m 3 f a c t o r 11 c m 3 f a c t o r 11
y, round bar
x-r + j -* EN 10060- 61.7 1.00 98 1.00 98 1.00 491 1.00 196 1.00
100
V
- t - square bar
EN 10059- 78.5 1.27 167 1.70 167 1.70 833 1.70 208 1.06
i 100
J
pipe 16.8 0.27 55 0.56 55 0.56 313 0.64 110 0.56
EN 10220-
114.3x6.3
/ hollow 18.3 0.30 67.8 0.69 67.8 0.69 339 0.69 110 0.56
structural
<v section
i EN 10210-2
+ - I - X
100 x 100 x6. 3
+/ hollow
structural
section
X-- i -X 16.1 0.26 59 0.60 38.6 0.39 116 0.24 77 0.39
E1N2 01x06201x0-62. 3
t X flat bar 39.3 0.64 83 0.85 41.7 0.43 104 0.21 - -
EN 10058-
-h 100 x 50
X- i
i
c= T-section
EN 10055- 16.4 0.27 24.6 0.25 17.7 0.18 88.3 0.18 - -
X— T100
r)V U-Channel 10.6 0.17 41.2 0.42 8.5 0.08 29.3 0.06 -
section
x- EN 1026-
Jr U100
J/ I-beam section
c
DIN 1025- 8.3 0.13 34.2 0.35 4.9 0.05 12.2 0.02 -
x — - - X 167 0.34 -
1100
c)r P
)t
cz I-beam section
X —" p x
DIN 1025- 20.4 0.33 89.9 0.92 33.5 0.34
1=
IPB100
J
1 1 Factor referenced to rou nd bar EN 10060-100 (cross-section in first row of table)
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Physics: 2. eric 51
Effects of changes in temp erature
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52 Physics: 2.7 Th erm od yn am ics
Heat for Melting, Vaporizing, Combustion
H e at o f f u s i o n , H e at o f v a p o r i z a t io n
Heat of vaporization Heat energy is necessary to transform substances from Heat of fus ion
quantity of heat Q a solid state to a liquid state or from a liquid state to a
gaseous state. This is know n as the heat of fusion or heat Q = q • m
of vaporization.
Q heat of fusion r ospf eecviafipc ohraetaiton Heat of v aporiz ation
heat of evaporation m mass
Q = r- m
q specific heat of fusion
For specific heat of
Example: fusion and heat of
evaporation see
Coppe r, m = 6.5 kg; qr = kJ ; Q = ? pages 116 and 117.
213 —
kg
Q = q m = 2 1 3 — • 6.5 kg = 1384.5 k J * 1.4 MJ
kg
Heat flux
T he heat flux <Z> continually occurs within a substance H e at flu x w i th
thermal conduction
with movement from higher to lower temperatures.
T he heat transmission coefficient k also com pensates,
along with the thermal con ductivity of a part, for th e heat
transmission resistance on the surfaces of the part.
<P heat flux Af, A# temperature difference H ea t fl u x w i t h
s com ponent thickness heat transmission
A thermal conductivity A area of the compone nt
k heat transmission
coefficient
/*2< t\ Exam ple: (p = k - A • At
Heat protection glass, k = 1.9 W2 ; 4 = 2.8 m 2 ;
Af = 32°C; <Z> = ? m °C
• For thermal conductivi-
ty values A see
<Z> W •2.8 m 2 • 32°C = 170 W pages 116 and 117.
1m.92 • °C For heat transmission
<P = k - A • At = coefficients k see
below.
Heat of com bustion
T he net c alorific v alue H n e t (H ) of a substance refers H e at o f c o m b u s t i o n o f
to the heat quantity released during the complete solid and liquid sub-
co m b u sti o n o f 1 kg or 1 m 3 of that substance.
stances
Q heat of combustion Q =H -m
^net' H net calorific value ne t
m mass of solid and liquid fuels
V volume of fuel gas H e at o f c o m b u s t i o n o f
Example: gases
Natural gas, V = 3.8 m 3 ; H ne t=3 bM J Q = ? Q=H, net V
m-
MJ
Q = Hnet l/= 35 —^ • 3.8 m 3 = 133 M J
m3
Net calorific valu e Hne t (H) for fuels Heat trans mis s ion c oeffic ients k
for construction materials and parts
Solid Qnet Liquid Qnet Gaseous Qnet Construction s W
fuels M J / k g f u el s M J / k g f u el s M J /m 3 elements mm
*k m 2 • °C
wood 15-17 alcohol 27 hydrog en 10 outer door, steel 50
biomass (dry) 14 -18 benzene 40 natural gas 34 -36 sash windo w 12 5.8
brow n coal 16-2 0 gasoline 43 acetylene brick wa ll 365 1.3
coke diesel 41 -43 propane 57 intermediate floor 1 25 1.1
pit coal 30 fuel oil 40 -43 butane 93 heat insulating board 80 3.2
30-34 1 23 0.39
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P hy sic s: 2. e r i c i y 53
Quantities and Units, Ohm's Law, Resistance
Electrical quantities and units
Quantity Unit
Name
Symbol Name Symbol
electrical voltage E volt V
ampere A
electric current I ohm Q
Siemens S
electrical resistance R watt W
electrical conductance G Electric current
electrical power P
Ohm's Law
© E voltage in V
/ electric current in A
R resistance in Q
Example:
R = 88 Q; E = 230 V; / = ?
1 = RE- = 2^8380— Q V = 2.6A For circuit symbols see
page 351.
Electrical resistance and c ond uctance
Resistance
\ R resistance in Q
G conductance in S
ce
Example:
'<Q>/J 0 0.5 1 1.5 2 S 2.5 R = 20 Q; G = ?
conductance 0 - G = — = —-— = 0.05 S
R 20 Q
Electrical resistivity, electrical con duc tivity, condu ctor resistance
g electrical resistivity in Q • m m 2 / m Electrical resistivity
y electrical cond uctivity in m/(Q • m m 2 )
1
R resistance in Q Y
A wire cross section in m m 2
Conductor resistance
/ wire length in m g-l
Example: R=
Copper wire, / = 100 m ; Change in resistance
A = 1.5 m m 2 ; g = 0.0179 ° m m ; R = ? AR = a • /?2o • Af
m
Resistance at
0.0179 • 100m temperature t
R = 1.19 a RT = R 2Q + A R
VA ' _ 1.5 mm m 2
R t = R 20 .( 1 +cc-At)
For electrical res istivities, see pages 116 and 117.
Resistance and Temp erature
Material Tk value a in 1/K AR change in resistance in Q
aluminum 0.0040 R2o resistance at 20°C in Q
lead 0.0039 Rt resistance at the temp erature t in Q
gold 0.0037 a temp erature coefficient (7"k value) in 1/K
copper 0.0039 At temperature difference in K
silver 0.0038 Example:
tungsten 0.0044 Resistance of Cu; R 20 = 150 Q; t = 75°C; Rx = ?
tin 0.0045 a =0.0039 1/K; A t = 75°C - 20°C = 55°C = 55 K
zinc 0.0042 Rx = R 20 • (1 + a • At)
graphite -0.0013
constantan ± 0.00001 = 150 Q • (1 + 0.0039 1/K • 55 K) = 182.2 n
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54 Physics: 2.8 Electricity
Current density, Resistor circ uits
Current density in wires
| ^ allowable current density J current density in A/ m m 2 Current dens ity
j-L
conductor (cross-sectional) area A I electric current in A
Voltage drop in wires A conductor cross section in m m 2 A
Example: Voltage drop
- A = 2.5 m m 2 ; / = 4 A ; J = ? Eri = 2 • / • in/?e,i
j _ l _ 4 A = 1.6 A Voltage at load
A 2.5 m m 2 mm'
EC = E-EC
I R ine Ed voltage drop in wire in V
Total resistance
E ^ E d /2 E voltage at terminal in V
Ez /?=/? + R 2 +
E c voltage across load in V
E d /2 Total voltage
I electric current in A £ = Ei + £o +
Aline resistance for feed or
Total current
return line in Q /=/ i = / =
' I R ine Voltage drops
fl
Series resistor circuit ff 2
R total resistance, equivalent resistance in Q Total resistance
I total current in A
E total voltage in V Total voltage
R-\, R2 individual resistances in Q
/•i, / 2 partial current in A E = Ei = E? =.
R 1 E-i, E 2 voltage drop across Ry & R2 in V Total current
Example: / = /-, + / 2 +
/? = 10 Q; R2 = 20 Q; E =12 V;/7 = ?; / = ?; Partial currents
Ei= ?; E 2 = ?
/1 _r 2
R =Ry R2= 10Q + 2 0 Q = 30 il /2
R-
/? 30 Q
= -/ = 10n-0.4A = 4 V
E 2 = / ? 2 ./ = 20Q 0.4A = 8 V
Parallel resistor circuit
ft total resistance, equivalent resistance in Q
/ total current in A
E total voltage in V
ff-i, R2 individual resistances in Q
/•I, / 2 partial current in A
E 1f E2 voltage drop across & R2 in V
Example:
fl, = 15 Q2 ;= R ?2 = 30 Q; E = 12 V; R = ?; I = ?;
= ?;/
/?i 1 5 Q - 3 0 Q
-1011
/?,+/? 2 15 Q + 3 0 Q
' -I-SS-™ 12V = 0.4 A
Ro 30 n
1 ) Use this formula if there are only tw o parallel
resistors in the circuit.
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Physics: 2.8 Electricity
Types of current
Direct current (DC; sym bol - ), DC voltage
Direct current flows in one direction only and main- Electric current
tains a constant level of current. The voltage is also constant
constant.
/ electric current in A
E voltage in V Voltage
t time in s
constant
A l t e r n a t i n g c u r r e n t (A C ); s y m b o l A C v o l t a g e
Cycle duration and Frequency
While the voltage is continuously changing in a sinu- Cycle duration
soidal pattern, the free electrons are also continuou s-
ly alternating their direction of flow. 7=1
f frequency in 1/s, Hz f
T period in s Frequency
o) angular frequency in 1/s '•f
/ electric current in A Angular frequency
E voltage in V
t time in s
Example: 0) = 2 • n • f
Frequency 50 Hz; T = ?
2 • 71
T = — = 0.02 s
50 1 (0 =
s T
1 Hertz = 1 Hz = 1/s =
1 period per second
Maximu m value and effective value of current and voltage
im a x ma xim um value of the electric current in A Maximu m value of the
4ft effective v alue of the electric current in A electric current
^max ma xim um value of the voltage in V
^eff effective value o f the voltag e in V (voltage Jmax = / 2 ' 4 ff
that produces the same power as an identical Maximu m value of the
voltage
DC voltage across an ohmic resistor),
electric current in A
voltage in V
time in s
Example: •max = {2E(eff
Eeff = 2 3 0 V ; E m a x = ?
f m a x = / 2 • 230 V = 325 V
Three-phase current Three-phase current is created from three Maximu m value of the
120° 120° 120° AC voltages each offset by 120°. voltage
Y L I \ L2 /13 E voltage in V •max = 1 (2-E,eff
X / 7 T period in s
L1 phase 1
Uj L2 phase 2
T (360°) L3 phase 3
£eff effective voltage between phase wire and
neutral wire = 230 V
Eeff effective voltage between two phase wires
= 400 V
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56 Physics: 2.8 Electricity
Electric al Wo rk and Pow er, Transformers
El ec t r ic al w or k
fF W electrical work in kW • h Electrical work
100 00H H P electrical power in W
t time (power-on time) in h W = P • t
A> Example: 1 kW • h = 3.6 MJ
Hot plate, P= 1.8 k W ;f = 3 h ; = 3 6000 00 W - s
I I C^D CZJ CD W = ? in kW • h and MJ
No i 1
W = P -t = 1.8 kW • 3 h = 5.4 kW • h = 19.44 MJ
J
Electrical pow er w ith direct current and alternating or three-phase cu rrent w ith non -reactive l o ad1)
Direct or alternating current P electrical power in W Power w ith direct
E voltage (phase-to-phase voltage) in V or alternating current
/ / electric current in A
R resistance in Q P= E • I
1st example:
P = I2-R
R Light bulb, E = 6 V; / = 5 A; P = ?; R = ? p=
P = E • / = 6 V • 5 A = 3 0 W R
Three-phase current
/? = -/ = 5— A = 1 . 2 f t P o w er w it h
three-phase current
CsI mi 2nd example:
P = / 3 - E-I
ff Ry Annealing furnace, three-phase current,
L E = 400 V; P = 12 kW; / = ?
I R P 12000 W
I ' I = 73 E = 17.3 A
R 73 400 V
1 ) i.e. only with heating devices (ohm ic resistors)
E le c tr ic a l p o w e r w i t h a l t er n a t i n g a n d t h r ee -p h a s e c u r r e n t w i t h r e ac t i v e l o ad c o m p o n e n t l 2 )
Alternating current P electrical power output in W Electric power output
E voltag e (phase-to-phase voltage) in V wi th alternating current
I I electric current in A
cos<p powe r factor P= E • I • cos(p
Three-phase c urrent Example: Electric power outpu t
Three-phase motor, E = 400 V; / = 2 A; wi th three-phase current
CNI cos^? = 0.85 ; P = ?
P=F3-E-I-cos p
P = fi • E • I • co s^ = / 3 • 400 V • 2 A • 0.85
= 1178 W « 1.2 kW
2) i.e. in electric motors and generators
Transformers
Input Output /V 1f N2 number of turns /-i, I 2 current level in A Voltages
side side E2 voltages in V E2 N2
(primary coil) (secondary
coil) Example:
/i
h /V, = 2875; N 2 = 100; E, =230 V; /, = 0.25 A; E 2 = ?; I2 = ?
A/i
A/, ErA /2 =230V.100 Electric cu rrent
Ey
2 N, 2875
j _/1/Vl_0.25A.2875_7OA /1_/v2
2 N2 100
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Table of Contents 57
3 Technical drawing
3.1 Basic geom etric cons tructions 58
Lines and angles 59
Tangents, Circular arcs, Polygo ns 60
Inscribed circles, Ellipses, Spirals 61
Cycloids, Involute curves, Parabolas
temperature 3.2 Graphs 62
Cartesian coordinate system 63
Graph types
64
3 .3 D r a w i n g e l em e n t s 65
Fonts 66
Preferred num bers, Radii, Scales 67
Drawing layout
Line type s
3.4 Representation
VPireowjesction methods 7691
Sectional views 73
Hatching 75
3.5 Entering dim ension s
Dimensioning rules 76
t A 1 Diameters, Radii, Spheres, Chamfers, Inclines, 78
Tapers, Arc dim en sion s 80
} 17 // / / Tolerance specifications
20 Types of dimen sioning 81
Simplified presentation in drawings 83
3.6 Machine elemen ts 84
Gear types 85
Roller bearings 86
Seals 87
Retaining rings, Springs
3.7 Work piece elemen ts 88
89
Bosses, Wo rkpiece edges 90
Thread runouts, Thread undercuts 91
Threads, Screw joints
Center holes, Knurls, Undercuts
Flare-V 3.8 Welding and Soldering 93
groove Graphical sym bols 95
Dimensioning examples
weld ))))))))))
3.9 Surfaces 97
Hardness specifications in drawings 98
Form deviations, Roughness 99
Surface testing , Surface indica tions
102
h-tolerance zone h-tolerance zone 3.10 ISO Tolerances an d Fits 106
Fundamentals 1 10
zero line es=0 Basic hole and basic shaft sys tem s 110
\E l = 0 \ General tolerances 1 11
Roller bearing fits 112
.c2 <c32(0 Fit recom me ndations
Geom etric tolerancing 59/431
E.E -3 p EE .5
E
hole shaft
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58 Technical dra win g: 3.1 Basic geo me tric cons tructions
4 Line segments. Perpendiculars and Ang les
A2 Parallels t o a line
Given: Line segme nt AB and point P on the desired parallel line g'
1. Arc with radius r about A results in intersecting point C.
2. Arc with radius r abo ut P.
3. Arc with radius r about C results in intersecting point D.
4. Connecting line segment PD is parallel line g' to AB.
Constructing a vertical line at point P
Given: Straight line g and point P
1. Arc 1 about P with any radius r results in intersecting point A .
2. Arc 2 with same radius r about point A results in intersecting point B.
3. Arc 3 with equal radius r about B.
4. Construct a line from A to B and extend it (to intersecting po int C).
5. Construct a line from point C to point P to obtain the vertical at P.
Bisecting an angle
Given: Angle
1. Any arc 1 about S yields intersecting points A and B.
2. Arc 2 with radius r about A; AB.
3. Arc 3 wit h equal radius r about B results in intersecting point C.
4. The line joinin g intersecting point C with S is the desired
bisected angle.
Dividing a line
Given: Line AB shou ld be divided into 5 equal parts.
1. C onstruct a ray from A at any desired an gle.
2. Mark 5 equal lengths with a compass on the ray from A.
3. Construct a line from point 5' to B.
4. Construct parallels to 5' B throu gh the other division p oints 1'-4 '.
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T e c h n i c a l d r a w i n g : 3 .1 B a si c g e o m e t r i c c o n s t r u c t i o n s
Tangents, Circular arcs. Polygons
Tangent thro ugh poin t P on a circle
Given: Circle and p oint P
1. Construct line segment MP and extend it.
2. Arc about P gives intersecting points A and B.
3. AanrcdsDa.bout A and B wi th the same radius yield intersecting points C
4. The line passing throu gh C and D is perpendicular to PM.
T an g e n t f ro m a p o i n t P to a circle
Given: Circle and point P
1. Bisect MP. A is the m idp oin t.
2. Arc about A with radius r = AM yields intersecting point P. T is the
tangent point.
3. Connect T an d P.
4. MT is perpendicular to PT.
R o u n d i n g a n a n g l e (ar c t an g e n t t o t w o s t r a i g h t l in e s )
Given: Angle ASB and radius r
1. Construct parallels to AS and BS of distance r. Their intersection M is
the desired center o f the circular arc of radius r.
2. The intej^ection of the perpendiculars from M to the line segments
AS and BS are the transition points C and D for the arc.
C o n n e c t in g t w o c i rc l es b y a r cs 61/431
Given: Circle 1 and circle 2; radii R\ and R0
1. Circle about Mt with radius R\ + r \.
2. Circle about M 2 with radius R\ + r2 intersects with 1 to yield
intersecting point A.
3. Connecting Mt and M 2 with A yields contact points B and C
for the inside radius R {.
4. Circle about Mt with radius R0 - r v
5. Circle about M 2 with radius R0 - r2 comb ined w ith step 4 results
in the intersecting point D.
6. D connected to M-] and M 2 and extended gives the contact points E
an d F for the outside radius R0.
C ir c u m s c r i b ed r eg u l a r p o l y g o n (e.g. pentagon)
Given: Circle of diameter d
1. Divide AB into 5 equal parts (page 58).
2. An arc centered at A wit h radius r= AB yields po ints C and D.
3. Construct lines from C and D to 1, 3, etc. (all odd numb ers).
The intersecting points on the circle yield the desired vertices of the
pentagon.
Fo r polygons with an even num ber of angles C and D are conn ected
to 2, 4, 6 etc. (all even numbers).
C ir c u m s c r i b ed h e x a g o n , d o d e c a g o n
Given: Circle of diame ter d
1. Arc centered at A with radius r= y
2. Arc with radius r about B and A.
3. Construct line segments connecting the intersecting points to yield
the hexagon.
For a dodecagon find intermediate points
including intersections at C and D.
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60 T e c h n i c a l d r a w i n g : 3 .1 B a sic g e o m e t r i c c o n s t r u c t i o n s
Inscribed and circumscribed circles fo rtriangles, Circle center point, Ellipse, Spiral
Circle inscribed in a triangle
Given: Triangle A, B, C
1. Bisect angle a.
2. Bisect angle ft (intersecting at point M).
3. Inscribed circle about M.
Circle circums cribing a triang le
Given: Triangle A, B, C
1. Construct the perpendicular bisector of line segment AB.
2. Construct a perpendicular bisector on line segment BC (intersecting
at point M).
3. Circumscribed circle about M.
Finding th e center of a circle
G iv e n : Circle
1. C hoose any straight line a that intersects the circle at A and B.
3 2. Straight line b (approx imately perpendicular to straight line a) inter-
sects circle at C and D.
3. Construct perpendicular bisectors on line segments AB and CD.
4. Intersecting p oint of the perpendicu lar bisectors is the center M of
the circle.
C o n s t r u c t i n g a n e l l ip s e f ro m t w o c i rc l es
Given: Axes AB and CD
1. Two circles about M with diameters AB and CD.
2. Construct several rays through M which intersect both circles
(E, F).
3. Construct parallels to the two principle axes AB and CD thro ugh E
and F. Intersecting points are p oints on th e ellipse.
Constructing an ellipse in a parallelogram
Given: Parallelogram with axes AB and CD
1. A semi-circle with radius r= MC about A yields point E.
2. Subdividing A M (or BM) into halves, qua rtersjind eighths yields
points 1, 2 and 3. Construct parallels to axis CD throu gh these points.
3. Dividing EA in halves, quarters and eighths y ields points 1, 2 and 3
on the axis AE. Parallels to axis CD throu gh those points give inter-
secting points F on the circular arc.
4. Construct parallels to AE throu gh intersection points F to the semi-cir-
cle axis, from there construc t parallels to axis AB.
5. Parallel intersection points of match ing num bers are points on the ellipse.
Spiral (approximate construction using a compass)
na| -j- Given: Rise a
1. C onstruct square ABCD wi th a/4.
2. A quarter circle of radius AD centered at A yields E.
K 3. A quarter circle of radius BE centered at B yields F.
4. A quarter circle of radius CF centered at C yields G.
5. A quarter circle of radius DG centered at D yields H.
6. A quarter circle of radius AH c entered at A yields I (etc).
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T e c h n i c a l d r a w i n g : 3 .1 B a sic g e o m e t r i c c o n s t r u c t i o n s
Cycloid, Involute, Parabola, Hyperbola, Helix
auxiliary intersection point of Cycloid
circle 5 auxiliary circle 5 with
parallel line 5 Given: Rolling circle of radius r
^ l ^ U 5.
1. Subdivide the pitch circle into any numb er of equal sized parts, e.g. 12.
rolling base line extend ed 2. Divide the base line (= exten t of the p itch circle = n • d) into equal parts,
circle C-n-d horizontal
center line in this case 12.
3. Vertical lines from segm ent p oints 1-12 on the base line to the ex-
tended vertical center line of the rolling circle yield the midpoints
M-|-M 12.
4. Construct auxiliary circles about the midpoints M -| -M 1 2 with radius r.
5. The intersecting points of these aux iliary circles with the parallels
through the points on the rolling circle having the same numbers give
the points of the cycloid.
4- nv 12 Involute
s/\ 1 Given: Circle
1 \ /11 1. Sub divide the circle into any desired num ber of equal sized parts,
•\ e.g. 12.
7 \ / : -""mo
2. Construct tangents to the circle at each section.
8 3. Mark off the length of the develop ed circumference on each tangen t
from its contact point.
4. The curve through the endpoints forms the involute.
92 Parabola
/p 2 \ Given: Orthogonal parabola axes and parabola point P
r 1. Parallel g to vertical axis thro ugh point P gives P'.
2. Divide distance OP' on the horizontal axis into any desired number of
parts (e.g. 5) and construct parallels to the vertical axis.
3. Subdivide distance PP' into the same number of segments and connect
to origin at 0.
4. Intersecting points of the lines wit h the matching nu mb er yield points
on the parabola.
Hyperbola
Given: Orthogonal asymptotes throu gh M and point P on the hyperbola.
1. Construct lines g-i and g 2 parallel to the asymptotes through point P on
the hyperbola.
2. Construct any desired number of rays from M.
9i 3. Cpaornasllterul ctto litnheesatshyromupgtohteths.e intersections of the rays with g-| and g 2
4. Intersecting points of the parallel lines (P-|, P 2(...) are points on the
hyperbola.
p,
Heliocoid al line (Helix)
Given: Circle of diam eter d and pitch P
1. Divide semicircle into equal sections, e.g. 6.
2. Divide the pitch P into twice the num ber of equal segm ents, e.g. 12.
3. Extend the same nu mb er of horizontal and vertical lines to intersec-
tion. The intersecting points yield points on the heliocoidal line.
10/|p109 8 7 6 5 4 3 2 1 of
pitch P 2
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62 Technical dra win g: 3. ra
Cartesian coo rdinate system din 46i (1973-03)
P 1 (xo4,y2) Coordinate axes
• abscissa (horizontal axis; x-axis)
P2(x-2.y-1) • ordinate (vertical axis; y-axis)
units 200 characteristic Values to be plo tted
N/mm 2 curve
•• pnoesgiatitvivee: :frfroomm ththee oorrigiginintotowwaarrddss ththee rliegfht,t,oorrduopwn
150
Mark ing the p os itiv e ax is direc tion w i t h
-0.4 -0.3 -0.2 - 0 . l 7 0 0.1 0.2 0.3 0.4 • arrow heads on the axes, or
-50 • arrows parallel to the axes
200 cur ve Formula symbols are entered in italics on the
N/mm 2 • abscissa below the arrow point
• ordinate to the left next to the arrow p oint
150 or in front of the arrows parallel to the axes.
| 100 Scales are normally linear, but sometimes they are di-
vided logarithmically.
o
50 Magnitu des of values. They are placed next to the scale
ticks. All negative values have a minus sign.
Value units are placed between the two last positive
num bers o n the abscissa and ordinate or after the for-
mula symbol.
Grid marks simplify plotting of the values.
Lines (curves) connect the values that have been plotted
on the graph.
Line width s. Lines are drawn in the following propor-
tion:
G r id l in e s : a xes : cu rve s = 1 : 2 : 4 .
Graph sections are constructed if values are not to be
plotted in each direction from the origin. The origin m ay
also be hidden.
\ g r i c I lines
/
0.1 0.2 0.3 0.4 % 0.5
Example (spring characteristic curve):
The following disk spring values are known:
Spring displace- 0 0.3 0.6 1.0 1.3
ment s in m m
Spring force F 0 600 1000 1300 1400
in N
What is the spring force F with a spring displace-
ment of s = 0.9 m m?
Solution:
The values are plotted on a graph and the po ints are
connected by a curve. A vertical line at s = 0.9 mm
intersects the curve at point A .
0 0.2 0.4 0.6 0.8 1.0 1.2 mm 1.4 With the help of a horizontal line throu gh A , a spring
force of F » 1250 N is read from the ordinate.
spring displacement s •
Graphs are used to represent value-based relationships between changing variables. 64/431
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Techn ical dra win g: 3.2 Grap hs 63
Polar coordinate systems, Area graphs
Cartesian coordinate system (continued) cf. DIN 461 (1973-03)
1600 N \ \ G r ap h s w i t h m u l t i p l e c u r v es
N/mm 2 v Whe n me asured values are highly scattered, a different special
_ Re i symbol is used for each curve, e.g: O, X, •
1200
1000 N Marking the curves
800 • wh en the same type of line is used, by using the names or
600 A
400 formula symb ols of the variables or by using different colors
200 1 for the curves
• by different types of lines
0
100 200 300 400 °C 600
temperature •
P o la r c o o r d i n a t e s y s t e m cf. DIN 461 (1973-03)
Polar coordinate systems have a 360° division.
Origin (pole). Intersection of horizontal and vertical axis.
Angle layout. The angle 0° is assigned to the horizontal axis to
the right of the origin.
Angle position. Positive angles are plotted counter-clockwise.
Radius. The radius corresponds to the magnitude of the value to
be plotted. Concentric circles may be drawn about the origin to
simplify plotting of the values.
Example:
Using a measuring machine, the roundness of a turned bush-
ing is checked to see if it lies wit hin the required tolerance.
The out-of-roundness found w as probably caused by clamp-
ing the bushing forcefully in the chuck.
Area graphs Bar graphs
In bar graphs the quantities to be represented are drawn as hori-
E ** zontal or vertical columns of equal width.
a .§
Pie ch arts
2005 2006 2007 2008 Percent values are normally represented by pie charts. In these
the circumference of a circular area corresponds to 100%
(= 360°).
Central angle. The percentage xt o be plotted determines the cor-
responding central angle:
360° • x %
a = 100%
Example:
What is the central angle for the percentage of lead in the
alloy CuPb15Sn8?
S o l u t i o n : a _ 360° 15% = 54°
~ 100o/o
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64 Technical draw ing: 3.3 Elem ents of draw ing
Fonts
Lettering, fonts cf. DIN EN ISO 3098-0 (1998-04) and DIN EN ISO 3098-2 (2000-11)
The lettering of technical d rawing s can be done using type style A (close-spaced) or type style B. Both styles may be
drawn vertical (V) or slanted by 15° to the right (I = italics). To ensure goo d legibility, the distance b etween the char-
acters should be two line widths. The distance may be reduced to one line width if certain characters are together,
e.g. LA, TV, Tr.
Font st yle B, V (vertical)
JHttt
F o n t s t y l e B , I (i t a l i c )
Dimensions cf. DIN EN ISO 3098-0 (1998-04)
a m e a £>i with diacritic1' characters
£>2 wi th ou t diacritic cha racters
F < ; n i n Q f f BTT MH6 b3 wit h upper case letters and
Ml
Hk R h~ Ecrifure * numbers
1 ) diacritic = used to further dif-
ferentiate, especially for letters
Character height h or height of upper 1 8 2.5 3.5 10 14 2 0
case letters (nom inal size) in m m
R atio of dimens ion t o c har ac ter h eight cf. DIN EN ISO 3098-3 (1998-04)
Type style a b. b2 bs C2 C3 d e f
A 25 h 2 1 h 1 7 h 10 .
> > >> >^B
14 1 4 *
19 . 15 . 13 . 0 6 h
10 10 10 10
Greek alphabet cf. DIN EN ISO 3098-3 (2000-11)
A a alpha Z£ zeta AX lambda n JI Pi <t> cp phi
Bp beta eta MH mu pP rho chi
r y gamma H ri theta nu sigma XX psi
A6 delta iota NV o tau omega
E e epsilon e ft kappa xi upsilon Q to
iI ZI TX
K K omicron YV
Oo
Roman numerals
I =1 n= m =3 IV = 4 V =5 VI = 6 vn = 7 vm = 8 IX = 9
X = 10 XX =20 XXX = 30 XL = 40 L = 50 LX = 60 LXX = 70 LXXX = 80 XC = 90
C = 100 CC = 200 CCC = 300 CD = 400 D = 500 DC = 600 DCC == 700 DCCC = 800 CM = 900
M = 1000 M M = 2000
Examples: MDCLXXXVE 1687 MCMXCIX = 1999 M M V m = 2008
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Technical drawing: 3. e e n t s drawing 65
Preferred numbers, Radii, Scales
P re fe rr ed n u m b e r s a n d s e r ie s o f p r ef er r ed n u m b e r s 1' cf. DIN 323-1 (1974-08)
R5 R 10 R 20 R 40 R5 R 10 R 20 R 40
4.00
1.00 1 00 1.00 1.00 4.00 4.00 4.00
5.00
1.06 6.30 4.25
8.00
1 12 1 12 4.50 4.50
10.00
1 18 4.75
1.25 1.25 1.25 5.00 5.00
1.32
5.30
1.40 1.40
1.50 5.60 5.60
6.00
1 60 1 60 1 60 1.60 6.30 6.30 6.30
1.70
6.70
1.80 1.80 7.10 7.10
1.90 7.50
2.00 2.00 2.00 8.00 8 00
2.12 8.50
2.24 2.24 9.00 9.00
2.36 9.50
2.50 2.50 2.50 2.50 10.00 10.00 10.00
2.65 Series Multiplier
2 80 2 80 R5 q5 = /TO - 1.6
3.00
3.15 3.15 3.15 R 10 Q10 = 10 o * 1 .2 5
/T
3.35 20
R 20
920 = /To «* 1.12
3.55 3.55
q 4 0 =4 0 /To « 1 . 0 6
3.75 R 40
Radii cf. DIN 250 (2002-04)
0.2 0.3 0.4 0.5 0.6 0.8
1 1.2 1.6 2 2.5 3 4 5 6 8
10 12 16 18 20 22 25 28 32 36 40 45 50 56 63 70 80 90
100 110 125 140 160 180 200 Values show n in bold font in the table are preferred values.
cf. DIN ISO 5455(1979-12)
Scale factors 21
Actual size Reduc tion fac tors Enlargement factors
1:1 1:2 1 : 20 1 : 200 1 : 2000 2:1 5:1 10: 1
1:5 1 : 50 1 : 500 1 : 5000 20: 1 50 : 1
1 : 10 1 : 100 1 :1000 1 : 10000
1 ) Preferred num bers, e.g. for length dim ens ions and radii. Their usage prevents arbitrary gradu ations. In the series
of preferred num bers (base series R 5 to R 40), each number of the series is obtained by multiplying the previous
num ber by a constant m ultiplier for that series. Series 5 (R 5) is preferred over R 10, R 10 over R 20 and R 20 over
R 40. The numbers of each series can be multiplied by 10, 100, 1000, etc. or divided by 10, 100, 1000, etc.
2 ) For special applications the given enlargement and reduction factors can be expan ded by mult iplyin g by who le
multiples of 10.
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66 Technical draw ing: 3.3 Eleme nts of draw ing
Drawing layout
Paper sizes (ISO) AO AI cf. DIN EN ISO 5457 (1999-07) and DIN EN ISO 216 (2002-03)
841 x1189 594 x 841 A2 A3 A4 A5 A6
Format 420 x 594 2 97 x 4 20 2 1 0 x2 9 7 1 4 8 x 2 1 0 1 0 5 x 1 4 8
Format
dimensions1' in mm
dDirmaweninsgioanrseain mm 821 x115 9 57 4x 81 1 400 x 564 277 x 390 180 x27 7 - -
1 ) The height: wid th aspect ratio of the drawing papers are 1 : f2 (= 1 : 1.414).
F o l d in g f o r D I N A 4 f o r m a t cf. DIN 824(1981-03)
'2CoccEO>I5°<oOo H3T—oCJ: A3 297x420 1st fold: Fold right side (190 mm wide)
toward the back.
o
2nd fold: Fold the remainder of the sheet
\J CM 190 so that the edge of the 1 st fold is
title block 20 mm from the left edge of the
20 paper.
2nd fold ^ 4th fold A2 42 0x 594 1st fold: Fold the left side (210 m m wide)
towards the right.
title block
2nd fold: Fold a triangle of 297 mm height
by 105 mm width towards the
left.
3rd fold: Fold the right side (192 m m w ide)
towards the back.
4th fold: Fold the folded packet of 297 mm
height toward the back.
Title block cf. DIN EN ISO 7200 (2004-05), Replacement for DIN 6771-1
The width of the title block is 180 mm. The sizes of the individual data fields (field widths and heights) are no longer
stipulated, in contrast to the previous standard. The table at the bottom of this page has examples of possible field sizes.
Example of a title block:
Resp. dept. Technical reference Cre at e d b y Approved by
AB 131 11 Susan Miller 12 Kristin Brown 13 John Davis 14 15
Type of document Document status
9 10
John Smith Co.1 Assembly drawing released
Title, additional title A225-03300-012 4
2
Changes Release date L. Sheet
Circular saw s h a f t / 3
A 5 78
complete with bearing
2008-01-^5 de 1/3
Drawing specific ca llouts, such as scale, projection sym bol, tolerances and surface sp ecifications sh ould be indicated
on the drawing outside of the title block.
D a ta f i el d s i n t h e t i t l e b l o c k
Field Max. no. of Field nam e Field size (mm )
no. characters wid th height
rieio name r eq u i r ed optional
1 not specified 69 27
2 Owner of the draw ing 25 yes - 60 18
3 Title (drawing name) 25 yes - 60 1 o
Additional title
4 16 - yes 51
5 Drawing number 2 7
6 Change sym bol (drawing version) 10 yes -
Issue date of the draw ing - yes 25
7 4
8 Language identifier (de = German) 4 yes - 10
Page number and numb er of pages 9
- yes
- yes 60 Q
51
9 Type of document 30 yes - 26
10 Document status 20 - 43
11 Responsible department 10 - yes
12 Technical reference 20 - yes 44
yes 43
13 Drawing originator 20 yes 24
-
14 Auth orizing person 20 yes
yes
15 Classification/key word s not specified -
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T e ch n ic a l d r a w i n g : 3. e e n t s d r a w i n g 67
Line types
L i n es i n m e c h a n ic a l e n g i n e e r in g d r a w i n g s cf. DIN ISO 128-24 (1999-12)
E xamples of app lication
No. Nam e, representation
01.1 Solid line, thin • dim ensio n and extension lines • origin circles and dim ens ion line
• leader and reference lines termin ators
•• hroaotct hoifngthread • dsuiargfaocneasl crosses to mark plane
• position direction of layers • framing details
• projection and grid lines
(e.g. lamination) • deflection lines on rough and
• outline of hinged section
• short center lines machined parts
• imaginary intersections from • marking for repeated details (e.g.
penetrations root diame ter of tooth ed gear)
Free-hand line, thin 1) • preferably hand-drawn representing border of partial or broken views
and sections, provided that the border is not a line of symmetry or a
center line
Break line, thin 1) • preferably automated drawing representing border of partial or bro-
X 'V ken views and sections, provided tha t the border is not a line of sym -
metry or a center line
01.2 Solid line, thick • visible edges and outlines • main representations in graphs,
• crests of threads edges and flowc harts
• limit of the usable thread length
• cross-section arrow lines • system lines (steel construction)
• surface structures • mo ld parting lines in view s
(e.g. knurls)
02.1 Dashed line, thin • hidden edges • hidden contours
02.2 Dashed line, thick
• identifies allowab le areas for surface treatme nt (e.g. heat treatmen t)
04.1 Dot-dash line • center lines • partial circle in gears
(long dash), thin • lines of sym metry • hole circle
04.2 Dot-dash line • marking areas of (delimited) • marking section planes
(long dash), thick required surface treatment
(e.g. heat treatment)
05.1 Two-dot dash-dot line • outlines of adjacent parts • contours of finished parts within
(long dash), thin
• final position of mov able parts rough parts
• centroidal axes • fram ing special areas or fields
• contours of the shape • projected tolerance zone
• portions in front of the cutting plane
• outlines of alternative designs
1 ) Free-hand and break line types sho uld not be used togethe r in the same d rawin g.
Lengths of line elements cf. DIN EN ISO 128 20 (2002 12)
Line element Line type no. Length Line element Line type no. Length
long dashes 04.1 and 05.1 24 d gaps 02.1,02.2, 04.1, 3 • d
short dashes 02.1 and 02.2 12 • d 04.2 and 05.1
Example: Line typ e 04.2
points 04.1, 04.2 a nd < 0 . 5 -d 2W 3 -d^ IJL40.5 -d 3.d
05.1 m- ff | ^
m
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68 T e c h n i c a l d r a w i n g : 3 .3 E l e m e n t s o f d r a w i n g
Line types
Line thicknesses and line groups cf. DIN ISO 128-24(1999-12)
L in e w i d th s . No rmally tw o line types are used in drawings. They are in a ratio of 1:2 .
Line groups. The line groups are ordered in a ratio of 1: (« 1: 1.4).
Selection. Line thicknesses and line groups are selected correspon ding to the type an d size of drawing , as we ll as to
the drawing scale and the requirements of m icrofilming and/or method of reproduction.
As s oc iated line thic k nes s es (dimens ion in m m) for
Line group Thick lines Thin lines Dimension and tolerance
c allouts , graphic al s y m bols
0.25 0.25 0.13 0.18
0.35 0.35 0.18 0.25
0.5 0.5 0.25 0.35
0.7 0.7 0.35 0.5
0.5 0.7
1.4 1.4 0.7
1.4
E x a m p l e s o f l i n es i n t ec h n i c a l d r a w i n g s cf. DIN ISO 128-24(1999-12)
end position of the dimension line (01.1)
moving part (05.1)
line of symmetry identification of
(04.1) section plane (04.2)
dimension line
visible contours
01.1)
extension 01.2) A-A
line (01.1)
crests of threads
hatching 01.2)
line (01.1)
visible
center line contour (01.2)
(04.1)
root of
root of threads (01.1),
thread (01.1)
border
lines (01.1)
imaginary of an adjacent part line of symmetry (04.
(05.1) border line (01.1)
intersections
(01.1)
surface structure short center line (01.1) hidden
(knurl) edge (02.1)
01.2) frame of
detail (01.1)
fully
— v ^ h ar de ne d
hole circle
(04.1)
visible contou rs S hidden designation
(01.2) co nto ur (02.1) of (heat) treatment (04.2)
edge in front of section plane (05.1)
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Technical draw ing: 3.4 Represe ntations in draw ings 69
General princ iples of p resentation. Projection methods
G e n e ra l p r i n c i p l es o f p r e s e n t a t i o n cf. DIN ISO 128-30 (2002-05) and DIN ISO 5456-2 (1998-04)
Se le c ti o n o f th e fr o n t v i e w . The view that is selected for the front view is the one which provides the most informa-
tion regarding shape and dimensions.
Other views. If other views are necessary for clear representation or for complete dimensioning of a workpiece, the
following should be observed:
• The selection of the views sh ould be limited to those most necessary.
• Add itional views should contain as few hidden edges and contours as possible.
Position of other views . The position of other views is dependent upon the method of projection. For drawings based
on the first- and the third-angle projection methods (page 70) the symbol for the projection method must be given in
the title block.
A x o n o m e t r i c r e p r e s e n t a t i o n 11 cf. DIN ISO 5456-3(1998-04)
Isometric projection Diametric projection
circle as an X : Y :Z = 1 :1:1 circle as an X : Y : Z = 0 , 5 :1 : 1
ellipse circle as an ellipse ellipse ellipse as a circle
Approx imate construction of the ellipse: Construction of ellipses:
1. Construct a rhomb us tang ential to the hole. Bisect the 1. Construct an auxiliary circle with radius r= d/2.
sides of the rhombus to yield the intersecting points
2. Subdivide height d into any desired number of equal
M 1 # M 2 and N. segments and construct grids (1to 3).
2. Draw conne cting lines from M-i to 1 a n d fro m M 2 to 2
3. Subdivide the diameter of the auxiliary circle into the
to yield the intersecting points 3 and 4. same number of grids.
3. Construct circular arcs with radius R about 1 and 2 4. Transfer the segment lengths a, b etc. from the aux-
and with radius r about 3 and 4. iliary circle to the rhombus.
Cavalier projection Cabinet projection auxiliary circle
circle as an X : Y : Z = 1 : 1 : 1 circle as an X :Y :Z = 0.5:1:1
ellipse ellipse ellipse as a circle
ellipse as
a circle
Ellipse construction identical to that on page 60 (ellipse Ellipse construction identical to that of the diametric pro-
construction in a parallelogram). jection (above).
1 1 Axo nom etric representations: simp le, graphical representations. 71/431
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T e c h n i c a l d r a w i n g : 3 .4 R e p r e s e n t a t io n s i n d r a w i n g s
Projection methods cf. DIN ISO 128-30 (2002-05)
and DIN ISO 5456-2 (1998-04)
Arrow projection method
At Marking the direction of observation:
• with arrow lines and upper case letters
Marking the views:
A • i1 • with upper case letters
Loc ations of the v iews :
• any location with respect to front view
Layout of upper case letters:
_ r • above the views
• vertical in reading direction
• above or to the right of the arrow
lines
First-angle projection Locations with respect to front view F:
RS 1 top view below F
LS view from right of F
1_
the left side left of F
LS RS view from
above F
• the right side left or right
bottom view of F
rear view
Symbol
Third-angle p rojectio n 11
Locations with respect to front view F:
top view above F
LS view from left of F
the left side
RS view from right of F
the right side
LS RS
bottom view below F
rear view left or right
of F
1 Symbol ©
S y m b o l s f or p r o j ec t i o n m e t h o d s
S y m b o l2' for Sy m bol for firs t-angle pro jec tion
first-angle projection third-angle projection I
Application in h font height in m m (page 64)
H = 2h
Germany and most English speaking countries, d = 0.1h
European countries e.g. USA/Canada
1 ) Second -angle projection is not provided.
2 ) The symb ol for projection me thod is included in the draw ing layo ut (page 66).
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Partial views Technical draw ing: 3.4 Representations in draw ings cf. DIN ISO 128-30
and -34 (2002-05)
Views
Application. P artial view s are used to avo id unfavorable
projections or shortened representations.
Position. The partial view is sho wn in the direction of the
arrow or rotated. The angle of rotation must be given.
Boundary. This is identified w ith a break line.
Application. It is sufficient to represent just a portion of
the whole workpiece, for example if space is limited.
Marking. With two short parallel solid lines through the
line of sym metry on the outside of the view.
Application. If the represe ntation is clear, a partial view is
sufficient instead of a full view.
Representation. The partial view (third-angle projection)
is connected with the m ain view by a thin dot-das h line.
Adjacent parts
housing Application. Adjacent parts are drawn if it aids in under-
standing the drawing.
Simplified penetrations Representation. This is done with thin two -dot dash-dot
lines. Sectioned adjacent parts are not hatched.
-Sl
Application. If the drawing remains clearly understanda-
[-a ble, rounded penetrating lines may be replaced by
straight lines.
*FP5zzz3J ) J Representation. Rounded penetrating lines are drawn
T9l with thick solid lines for grooves in shafts and penetrat-
n_r ing holes whose diameters significantly differ.
Implied penetrating lines of imaginary intersections and
rounded edges are drawn with thin solid lines at the
location at which the (circumferential) edge would have
been wi th a sharp edged transition. The thin solid lines
do not contact the outline.
B r o k en v i e w s rir^ Alopnpgliwcaotrikopni.e cTeos snaeveed stpoabcee roenplyretsheentiemdp.ortant areas of
i Representation. The boundary of the remaining parts is
shown by free-hand lines or break lines. The parts must
-LO be drawn close to each other.
f
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72 Technical dra win g: 3.4 Represen tations in draw ings
Views cf. DIN ISO 128-30
and -34 (2002-05)
Repeating geom etrical elemen ts
t01O Application. For geometric elements which repeat regu-
larly, the individual element only needs to be drawn
once.
12 r Rdreapwrens, entation. For geometric elements which are not
r— /
• the positions of symmetrical geometric elements are
show n with thin dot-dash lines.
• asymm etrical geometric elements of the area in which
they are found are drawn with thin solid lines.
The number of repeated elements must be given in the
dimensioning.
Parts at a larger scale (details)
Z (10:1) Abeppclliecaartliyonre. pPreasrteianlteadremasayofbea dwroarwknpieactea wlahrigcehr csacnalen.ot
Representation. The partial area is framed with a thin
solid line or encircled and m arked wit h a capital letter.
The partial area is represented in an enlarged detail vie w
and is identified with the same capital letter. The en-
larged scale is additionally given.
Minimal inclines Ampidpslicwahtiiochn. cManinniomt abl einschlionwens colneasrlloyp, edso, ncootnehsavoer tpoyrbae-
~L fX I drawn in the corresponding projection.
\f Representation. The edge representing the projection of
the smaller dim ension is draw n with a thick solid line.
Moving parts
Application. Depicting alternative positions and limits of
move ment of parts in assembly drawings.
Representation. Parts in alternate pos itions and lim its of
movement are drawn with tw o-dot dash-dot lines.
Surface structures
Representation. Structures such as knurls and emboss-
ing are represented with thick solid lines. Partial repre-
sentation of the structure is preferable.
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Section types Technical draw ing: 3.4 Represen tations in drawin gs
view Sectional views cf. DIN ISO 128-40,
-44 and -50 (2002-05)
full section Section. The interior of a workpiece can be shown with
a section. The front part of the workpiece, which hides
V////
the view to the interior, is perceived to be cut out.
/////. / In a section it is possible to represent:
• the cutting plane and additional workpiece outlines
lying behind the cutting plane or
• only the cutting plane.
half section partial section Full section. The full section shows the conceptualized
workpiece sectioned in a plane.
Definitions Iu
Half section. In a symmetrical workpiece one half is
section 1/ represented as a view, the other half as a section.
line
// Partial section. A partial section shows only part of the
workpiece in section.
Cutting plane. The cutting plane is the imaginary plane
with which the workpiece is sectioned. Complicated
workpieces can also be represented in two or more cut-
ting planes.
Cross-section area. It is formed by the theoretical sec-
tioning of the workpiece. The cross-section area is
marked w ith hatch lines (see below and page 75).
Section line. It marks the position of the cutting plane;
for two or more cutting planes it marks the cutting path.
The section line is draw n w ith a thick dot-dash line.
For two or more cutting planes the path of the section
line is emphasized on the ends of the correspond ing
plane using short thick solid lines.
Marking t he section line. It is done w ith the sam e up per
case letters. Arrows drawn with thick solid lines indicate
the direction for viewing the cutting plane.
Marking the section. The sectional view is marked with
the same upper case reference letters as the section
lines.
Hatching of sections
Hatching. The hatching is draw n wit h parallel solid lines,
preferably at an angle of 45° to the centerline or to the
main outlines. The hatching is interrupted for lettering.
Hatching is used for
• individu al parts - all hatch lines for cross-section areas
should be in the same direction and at the same spa-
cing.
• parts adjacent to each other - hatch lines for the dif-
ferent parts sho uld be in different directions or at dif-
ferent spacing.
• large cross-section areas - h atching preferably only
near boundaries or edges.
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74 T e c h n i c a l d r a w i n g : 3 .4 R e p r e s e n t a t i o n s in d r a w i n g s
Sectional views cf. DIN ISO 128-40,
-44 and -50 (2002-05)
Special sections
// // / Profile sections. They may be
• drawn rotated in a view (revolved section).
The contou r lines of the section are represented wit h
thin solid lines and are drawn within the interior of the
part.
• taken out of a view (removed section).
The section m ust be connected with the view by a thin
dot-dash line.
Sections with intersecting planes. If tw o planes inter-
sect, one cutting plane may be rotated in the projection
plane.
Details of ro tated parts. Uniformly arranged details out-
side of the cross-section area, e.g. holes, may be rotated
in the cutting plane.
Outlines and edges. Contours and edges lying behind
the cutting plane are only dra wn if they add clarity to the
drawing.
P ar t s t h a t a re n o t s e c t i o n e d
Not sectioned in the lengthwise direction:
• parts that are not lx>llow, e.g. screws, bolts, pins,
shafts
• areas of an individu al part wh ich shou ld protrude from
the base body, e.g. ribs.
Notes on drawing
circumferential Tool edges
edges • Circum ferential edges. Edges exposed by sectioning
/ must be represented.
• Hidden edges. In sections the hidden edges are not
V//// / / / w i
represented.
edge on the • Edges on the center line. If an edge falls on a center-
„w line by sectioning, it is represented.
Y Half-s ec tions in s y mm etric al wo rk piec es
/ /'.J .J
Section halves of sym metrica l workpieces are preferably
A drawn in relation to the center line,
//////. • below, wi th horizontal center lines
Vl • to the right, for vertical center lines.
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Technical draw ing: 3.4 Representations in draw ings
Hatching, Systems for entering dimensions
Hatching cf. DIN ISO 128-50 (2002-05)
Section areas are generally marked with basic hatching without consideration of the material.
Parts who se m aterial should be emphasized can be identified u sing specific section lining.
Basic hatching (without considering the material)
Gases Liquids
fo o o o 6~o~o 61
loooooooo; water
[ooooooooj oil
Natural materials Metals Plastics jIl—-—ooo———ooo———oo o———o r|
Ferrous Non-ferrous grease
metals metals
wooc {.A ^yZTf/Ty//1 thermoset plastics
alloyed steel light alloys
_y ////// //A
WA
glass heavy metals
ceramic cast iron elastomers, rubber
Systems for entering dimensions cf. DIN 406-10 (1992-12)
012 d9 The dimensionin g and tolerancing of workpieces can be
based on
• function,
• manufacturing or
• testing.
Several systems of dim ensioning may be used within a
single drawing.
ml j m Dimensioning based on function
012 H8 Cdihmaerancstioenrisstiisc. d Soneelecatcioconr,deinngtryto adnedsitgonlerreaqnuciirnegmeonf tsth. e
55 ±0.01 Dimensioning based on fabrication
Characteristic. Dimensions which are necessary for
20 ±0.01 fabrication are calculated from functional dimensions.
mi HH m Dimensioning based on testing
i Characteristic. Dimensions and tolerances are entered
012 H8 +0.04 i in the drawing according to the planned testing.
47 -0.01
+0.01
14 -0.02^
m Im m i
-0.01 j i
23 -0.02 i
012 H8
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Technical draw ing: 3.5 Entering dim en sion s
Dimensioning drawings
D i m e n s i o n l i n es , d i m e n s i o n l i n e t e r m i n a t o r s , e x t e n s i o n l i n es , d i m e n s i o n n u m b e r s cf. DIN 406-11 (1992-12)
Dimension lines
extension line dimension number ^ dimen sion line Design. Dimension lines are drawn as thin solid lines.
Entry. Dim ension lines are used for:
dimension line terminator • length dimensions parallel to the length to be dimen-
65
sioned
20 • angle and arc dimensions as a circular arc about the
i center of the angle or arc.
Ln • extended to the outside using extension lines
• entered within the workpiece
\ • draw n to the edges of the part body.
Spacing. Dimension lines should have a minimum dis-
tance of
• 10 m m from the edge of bodies and
• 7 mm between each other.
Dimension line terminator Dimension arrowheads. Generally arrowheads are
used to delimit the boundaries of dimension lines.
d • arrowhead length: 10 x dimension line width
• angle of lateral side: 15°
5 xd Dots. Used if space is limited .
• diameter: 5 x dimension line width
Extension lines
15 35 Design. Extension lines are drawn perpendicular to the
length to be dimensioned with thin solid lines.
010 012
Special features
± • Symmetrical elements. Centerlines may be used as
16 extension lines within symm etrical elements.
• Breaks in extension lines may be used e.g. for enter-
50 extension line passing
D i m e n s io n n u m b e r s through part ing dimensions.
• Within a view the extension lines may be drawn to
35 o 11
20 spatially separate elements of the same or similar
shape.
I • Extension lines may not be extended f r o m o n e v i e w t o
another view.
2.5 2 2.5
Entry. Dimension numbers are entered
[ L(10) 6 \ • in standard lettering acc ording to DIN EN ISO 3098
• with a min imu m font size of 3.5 m m
• above the dimension line
• so that they are legible from below and from th e right
• for multip le parallel dimens ion lines - separated from
each other.
Lim ited space. If there is limited space, the dime nsion -
ing numbers may be entered
• on a leader line
• over the extension of the dimen sion line.
40
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Technical draw ing: 3.5 Entering d ime nsio ns
Dimensioning drawings
Dimens ionin g rules, leader and reference lines, angle d imens ions , cf. DIN 406-11 (1992-12) and
square and wid th across flats DIN ISO 128-22 (1999-11)
Dimensioning rules
{oo Entering dimensions
— • hEaavceh didimenetnicsaiol ndiims eonnsliyonesntebruet ddoifnfecree.nItf tswhoapeelse,mtehnetys
must be dimensioned separately.
7,5
• If multiple views are drawn, the dimensions sho uld be
12 -J ^ entered where the shape of the workpiece is best
50 recognized.
70 t = 5 • Symm etrical workpieces. The position of the center
(15) 10 15 7 8 15 line is not dimensioned.
C h a i n e d d i m e n s i o n s . Series of chained dimen sions
shou ld be avoided. If chained dim ension s are required
for reasons related to manufacturing, one dimension of
the chain must be in parentheses.
Flat workpieces. For flat workpieces that are only drawn
in one view, the thickness dimension may be entered
wit h the reference letter t
• in the view or
• near the view.
Leader and reference lines Leader lines. Leader lines are drawn as thin solid lines.
leader line They end
• with an arrowhead, if they point to solid body edges
Angular dimensions
or holes.
• wit h a dot, if they p oint to a surface.
• wit ho ut m arking, if they point to other lines.
Reference lines. Reference lines are drawn in the read-
ing direction with thin solid lines. They may be connec-
ted to leader lines.
Extension lines. The extension lines point toward the
vertex of the angle.
Dimension numbers. Normally these are entered tan-
gentially to the dimensioning line so that their lower
edge points to the vertex of the angle if they are above
tthheeyhaorreizboenltoawl cite.nter line and with their upper edge if
Square, wid th acros s flats WAF17 Square
WAF17
S y m b o l . For square shaped elements the symbol is set
in front of the dimensioning number. The size of the
symbol corresponds to the size of the small letters.
Dimensioning. Square shapes should preferably be
dimensioned in the view in which their shape is recog-
nizable. Only the length of one side of the square shou ld
be entered.
Wid th acros s flats
S y m b o l . For widths across flats the upper case letters
WAF are placed in front of the dimensioning number, if
the width between flats cannot be dimensioned .
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78 Technical drawing: 3. E n t r i n
Dimensioning drawings cf. DIN 406-11 (1992-12)
Diameters, radii, spheres, chamfers, inc lines, tapers, arc dim ension s
Diameter, radius, sphere
vO Diameter
nO LO Sy m b o l . For all diameters the sym bol 0 is placed befo-
troe tthhee dhiemigehntsoiofnthneudmimbeern. sItisonoivnegranlluhmebigehr.t correspo nds
a Limited space. In the case of limited space the dimen-
sion references the workpiec e feature from the outside.
Radius
Symbol. For radii the lower case letter r is placed before
the dimensioning number.
Dimension lines. Dimension lines should be drawn
• from the center of the radius or
• from the direction of the m idpoint.
Sphere
Sy mbol. For spherical shape workpiece features the
capital letter S is placed before the diameter or radius
symbol.
Chamfers, countersinks
2x45 o 3 45° chamfers and countersinks of 90° can be simply
dimensioned by indicating the angle and the chamfer
0.6x45° width. Both drawn and undrawn chamfers may be
dimensioned using an extension line.
Other chamfer angles. For chamfers with an angle de-
viating from 45° the
• angle and the chamfer width or
• the angle and the chamfer diameter
are to be entered.
Inclines, tapers Incline
Symbol. The symbol C^ is entered before the dimen-
t ^ 30% sion numbers.
Orientation of the sym bol. The sym bol is oriented so that
_ 1:10 its incline m atches the incline of the workpiece . Preferably
the symbol is connected to the inclined surface with a
Arc dimensions 32 reference line or a leader line.
r\3 Taper
Sy m b o l . The sym bol O is entered before the dimen-
sion numbers on a reference line.
O r i en t a t io n o f t h e s y m b o l . The orientation of the s ymb ol
must match the direction of the workpiece taper. The
reference line of the symbol is connected to the outline
of the taper with a leader line.
Sy m b o l . The sym bol ^ is entered before the dime n-
sion numbers. For manual drawing the arc may be
labeled with a similar sym bol over the dimen sion num-
ber.
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Technical draw ing: 3.5 Entering dim ens ions 79
Dimensioning drawings
Slots, threads, p atterns cf. DIN 406-11 (1992-12) and DIN ISO 6410-1 (1993-12)
Slots
10P9 10N9
Csji h(J + k4\ Slot depth. The slot depth is measured
=1> • from the slot side for closed slots
• from the opposing side for open slots.
n-
S i m p l i f ie d d i m e n s i o n i n g . For slots represented only in
Cv 1 the top view, the slot depth is dimensioned
• with the letter h o r
032h9 • in com bination with the slot width.
closed slot open slot open slot W i t h slots for retaining rings the slot depth m ay also be
entered in combination with the slot width .
/? = 5+0.2 10N9x5+0.2
Limit deviations for tolerance classes JS9, N9, P9 and
/I >n \ ^ H11: page 109
Qs . > tQil ii 36 0.3 Slot dimensions
• for wedge s see page 239
>oH s. • for fitted keys see page 240
• for retaining rings see page 269
36+0.3
1.3 H13x021h11 1.1 H13x023 H11
f//
A/
- U JL
—U-
Threads
'1 V/ Code designation. Code designators are used for stand-
ard threads.
17 vt /////,
Left hand threads. Left hand threads are marked with
// / / / / / . LH. If both left hand an d right hand threads are found on
a workpiece, the right hand threads get the addition RH.
20
Multiple screw threads. For multiple screw threads the
pitch and the spacing are entered behind the nominal
diameter.
Length specifications. These give the usable thread
length. The depth of the basic hole (page 211) is norma l-
ly not dimensioned.
Chamfers. Chamfers on threads are only dimensioned if
their diameters do not correspond to the thread core or
the thread outside diameter.
Radial and linear patterns
20 x 16 (= 320)
Identical design elements. The following data is given
for spacing of identical design elements having the
same distance or angle between them
• the number of elements
• the distance between the elements
• the overall length or overall angle (in parentheses).
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80 Technical drawing: 3. E n t r i n
Dimensioning drawings
Tolerance specifications cf. DIN 406-12 (1992-12), DIN ISO 2768-1 (1991-06) and DIN ISO 2768-2 (1991-04)
Toleranc e s pec ific ations us ing dev iations
c+d CC+MD C+D Entry. The deviations are entered
LTl
+0.15 • after the nominal size
35-0.10 CD1
20 ±0J • if there are two deviations, the upper deviation is
LTl show n above the lower deviation
40 -0.1/-0.3
+0° 30' • for equally large upper and lower deviations by a
30°+0° 15' ± mark before the number value, which is only entered
once
• for angle dimensioning with units specified.
+ 0° 0' 45'
30°+0° 0' 30'
Tolerance specifications using tolerance classes
Entry. Tolerance classes are entered for
• single nominal sizes: after the nominal size
• parts shown inserted: the tolerance class of the interior
dimension (hole) is before or over the tolerance class
of the outer dimension (shaft).
Tolerance sp ecifications for specific areas
7777777 rz*n- 1 1 cd ' ' Area of application. The area to which the tolerance
Cs 1 CD applies is bounded by a thin solid line.
i C— +1 - -
rIs Q CQD
/// L 11 8
Cy /
Tolerance specifications using general tolerances
checked by: scale: drawn by: date: Application. General tolerances are used for
1:1 company : sheet no.: • linear and angular dimensions
• form and position.
ISO 2768 10 They apply to dimensions without individual tolerance
entry.
m
Drawing entry. The note for general tolerances (page
/ DIN 509 - E 0.8x0.3 110) can be located:
2x45( • near the individual part drawing s
LTl • for title blocks according to DIN 6771 (retracted):
mS NO 16 Ra 3.2
in the title block.
\ LcTnl- bolts
CSsi 10 SPb 20 Entries. Given are:
5x 45° • the sheet num ber of the standard
40 ISO 2768-m • the tolerance class for linear and angular dimensions
53 • the tolerance class for form and positiona l tolerances,
as needed.
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Dimensions T e c h n i c a l d r a w i n g : 3 .5 E n t e r i n g d i m e n s i o n s
Types of dimensioning Dimensioning in drawings
positional
dimensions cf. DIN 406-10 a nd -11 (1992-12)
basic basic dimension Basic Dimensions. The basic dimensions of a workpiece
dimensions are the
• total length
• total width
• total height.
Shape dimensions. Shape dimen sions establish, e.g. the
• dimensions of slots
• dimensions of shoulders.
shape Positional dimensions. These are used to specify the
dimensions location of
• holes
• slots
• elongated holes, etc.
Spec ial dimens ions Rough dimensions
F u n c ti o n . Rough dimensions might be used to give
/ information about, for example, the dimensions of cast
or forged w orkpieces before machining.
Labeling. Rough dimensions are put in brackets.
/ rough dimension Auxiliary dimensions
Function. Auxiliary dimensions give additional in-
30 t = 2 formation. They are not necessary to geometrically defi-
[35] 20 ne the workpiece.
Labeling. Auxiliary dimens ions are
25 •z: • put in parentheses
(42-0.1100% • e ntered wit ho ut tolerances.
W////////A
Dimensions not drawn to scale
Labeling. Dimensions not drawn to scale might be used
for drawing changes, for exam ple, and they are marked
by underlining.
Prohibited are underlined dimensions in computer aided
(CAD) drawings.
Control dimensions
Function. It should be noted that these dimensions are
especially checked by the purchaser. If necessary a 100%
check will be performed.
Labeling. Control dimensions are set in frames with
rounded ends.
Theoretic ally prec is e dimens ions
Function. These dimens ions give the geome trically ideal
(theoretically precise) position of the shape of a design
feature.
Labeling. The dimensions are placed in a frame withou t
tolerance specifications and correspond with geometric
tolerancing.
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82 Technical drawing: 3. E n t r i n
Types o fdimensioning
Parallel dimensioning , running dimension ing, coordinate dimension ing 1* cf. DIN 406-11 (1992-12)
Stack dimensioning
Dimension lines. Several dim ens ion lines are entered
together for
• stacked linear dimensions
• concentric angular dimensions.
t = 12
R u n n in g d i m e n s i o n i n g
Origin. The dimensions are entered outwards from the
origin in each of the three pos sible directions. The orig in
is indicated by a small circle.
Dimension lines. The following applies for the entries:
• As a rule only one dimension line is used for each
direction.
• If there is limited space two or more dim ens ion lines
may be used. The dimension lines may also be shown
broken.
Dimensions
• must be provided w ith a minus sign if they are entered
from the origin in the opposite direction.
• may also be entered in the reading direction.
C o o r d i n at e d i m e n s i o n i n g
Item X Y d Cartesian coordinates (page 63)
1 50 50 040
2 180 190 030 Coordinate values. These are
3 220 115 075 • entered in tables or
4 325 50 -
• entered near the coordinate points.
X = 18 0- f Point of origin. The point of origin
Y = 190 1 X = 220 • is entered with a sm all circle
030 i Y = 115 • can lie at any location of the draw ing.
X = 50 i 075
Dimensions. These must be provided wit h a minus sign
_l_ Y = 50 X = 325 if they are entered from the origin in the oppo site direc-
04 0 t = 1 2 ' Y = 5 0 tion to the positive direction.
X
Item r V d Polar coordinates (page 63)
1* ' 140 0° 030 Coordinate values. The coordinate values are entered in
2 140 30° 030 tables.
3 I 100 60° 030
4 140 90° 030
1 ) Parallel dimensioning, running dim ensioning and coordinate dimens ioning m ay be com bined with each other. 84/431
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Te ch n i ca l d ra w i n g : 3 .5 En te ri n g d i m e n si o n s 83
Simp lified presentation in drawings
Simplified representation of holes cf. DIN 6780 (2000-10)
Hole bas e, line widt hs for s implified repres entation Hole base
Tifhneecsehsaspaeryo.f the hole base is given by a symbol
Full scale represen- Full scale repre- Simplified repre- The symbol U for ex amp le means a flat hole
tation, full scale sentation, simpli- sentation, simpli- base (cylindrical end bore).
dimensioning fied dimensioning fied dimensioning
010 01Ox14U 01Ox14U
z:
010x1411 01Ox14U 01Ox14U Line width s
m For holes depicted in simplified form, the posi-
tions of holes should be drawn as:
Stepped holes, countersinks and chamfers, internal threads
• simply the intersecting axes in the top view
• the position of the holes in thick solid lines in
parallel axis representation.
011. ^ 011x6.5U 011x6.5U Stepped holes
06.6 06.6 For holes with tw o or m ore steps the dimens ions
are written under each other. Here the largest
A1 011x6.5U diameter is written on the first line.
011x6.51) 06.6
06 6 v
012.4x90° 012.4x90° Counters ink s and c hamfers
For countersinks and hole chamfers the largest
06 6 06 6 countersink diameter and the countersink angle
/X are given.
/
'A Ya Internal th reads
M1Qx15/20 The thread length and the hole depth are sepa-
M10x15/20 V rated by a slash. Holes without depth specifica-
tion are drilled through.
/
A
01OH7 012x90° 012x90° Hole 0 10H7
M10-LH 01OH7 Through hole
01OH7 Chamfer 1 x 45c
2
M10-LHx12 £
M10-LHx12 Left hand thread M10
Thread length 12 mm
4L Drilled through core hole
08x0.3 08x0.3 Cylindrical countersink 0 8
08x90° 08x90° Bore depth 0.3 mm
04.3 T h r o u g h h o le 0 4 .3 w i th
04.3 cone shaped counterbore 90°
Countersink diameter 0 8
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T e ch n ic a l d r a w i n g : 3 . a c e n ts
84
Representation of gears Gear types cf. DIN ISO 2203 (1976-06)
Worm gear
Spur gear Bev el gear
EZZ
External helical gear Internal spur gear
zzzz
left-
-hand
Z
righf-
y hand
Rack and Pinion Bevel gear set (shaft angle 90°)
c € L___r
W o r m a n d w o r m g ea r Sprockets Positive drive belts
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T e ch n ic a l d r a w i n g : 3 . a c e n ts
Roller b earings
Representation of roller bearings cf. DIN ISO 8826-1 (1990-12) and DIN ISO 8826-2 (1995-10)
Representation Elements of a detailed s im plified repres entation
simplified graphical explanation element explanation, application
Froollregr ebneearrailngpuisrproesperse-a Long, straight line; for representing
sented as square or rec- the axis of the roller bearing elements for
tangular with a free-stand- bearings that cannot be adjusted.
ing upright cross.
Long, curved line; for representing the axis
of the roller bearing elements for bearings
that can be adjusted (self-aligning bearing).
If necessary, the roller o Short straight line; used to represent the
bearing can be repre- position and number of rows of roller
sented by its outline bearing elements.
and a free-standing
upright cross. Circle; for the represe ntation of roller bear-
ing elements (balls, roller, needle rollers)
which are drawn perpendicular to their axis.
Ex amples of detailed s im plified repres entation of roller bearings
Representation of s ingle-row roller bearings Repres entation of dou ble row roller b earings
sdi me tpal.ii.lf.ei.edd. graph• i-ca•l designation d e t a i l e d graphical designation
simplified
Radial-deep Radial-deep
groove ball
±Z2l bearings, ++ groove ball
cylindrical roller bearings,
bearings cylindrical roller
bearings
Radial spherical m Spherical roller
bearing, radial-
a roller bearing
(barrel-shaped spherical
bearing)
roller bearing
Angular-contact Angular-contact
ball bearing, ball bearings
tapered roller
bearing
// / Needle bearing, Hh Needle bearing,
needle roller needle roller
m assembly assembly
Axial-deep grooved Axial-deep grooved
ball bearing, ball bearing,
axial-roller bearing dual action
Axial-spherical Axial-deep grooved
roller bearing ball bearing with
spherical seating,
dual action
H f- Comb ined ball bearings Repres entation p erpendic ular to th e rolling element ax is
FR Combined Roller bearing with
radial-needle aronlyledr eeslieremdentytpe of
bearing with shape (balls,
angular-contact rollers, needles)
ball bearing
Combined
axial-ball bearing
with radial needle
bearing
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86 T e ch n ic a l d r a w i n g : 3 . a c e n ts
Representation of seals and roller bearings
S i m p l i f i e d r e p r e s en t a t i o n o f s e al s cf. DIN ISO 9222-1 (1990-12) and DIN ISO 9222-2 (1991-03)
Representation Elements of a detailed s implified repres entation
simplified graphic al explanation element explanation, application
Long line parallel to the sealing surface;
For general purposes a for the fixed (static) sealing element.
X seal is represented by a Long diagonal line; for the dynamic seal-
square or rectangle and a ing element; e.g. the sealing lip. The
separate diagonal cross- sealing direction can be given by an
mark. The sealing direc- arrow.
tion can be given by an
arrow. Short diagonal line; for dust lip seal,
scraper rings.
fX= If necessary, the seals can Short lines pointing to the m iddle of the
sym bol; for the static parts of U -rings
be represented by the out- und V-rings, packing.
line and a free-standing di-
agonal cross-mark. Short lines, which point to the middle of
the sym bol; for the sealing lips of U-
rings und V-rings, packing.
u T and U; for non-contact seals.
Ex amples of detailed s implified repres entation of s eals
Shaft s eals and pis ton rod s eals Profile gaskets, packing sets, labyrinth seals
designation for
detailed graphical rotation linear detailed graphical detailed graphical
simplified motion simplified simplified
Shaft seal Rod seal >-
without dust without
lip seal stripper
X »Shaft seal
with dust lip
seal
Rod seal
with stripper
Rod seal,
dual
action
X )Shaft seal,
dual action
Ex amples of s im plified repres entation of s eals and roller bearings
Deep grooved roller bearings and Dual row deep groov ed roller bearings Packing set2*
radial shaft seal with dust lip seal11 and radial shaft seal2'
m M » >
1 ) Top half: simp lified representation; botto m half: graphical representation. 88/431
2 ) Top half: detailed simplified representation; botto m half: graphical representation.
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T e ch n ic a l d r a w i n g : 3. a c e n ts
Representation of retaining rings. Slots for retaining rings,
Springs, Splines and serrations
R e p r es e n t a ti o n o f r e t a i n i n g r i n g s a n d s l o t s fo r r e t ai n i n g r i n g s
Representation Assembly dimension Deviations
Retaining ¥ t n\ _ _ _ froerfedrei mnceen spiloannien g 1 ' Dupepveiartdioenvsiaftoior nd:20: (zero)
rings for <i _ lower deviation: negative
shafts a= roller bearing
(page 269) width + retaining Deviations for a :
H13 i ring width upper deviation: positive
mim lower deviation : 0 (zero)
Retaining reference plane Deviations for d2.
rings for for dimensioning1' upper deviation: positive
holes lower deviation : 0 (zero)
(page 269)
Deviations for a:
upper deviation: positive
lower deviation : 0 (zero)
1 ) For functional reasons the reference plane for the dime nsioning of slots is the locating face of the part to be secured.
Representation of springs cf. DIN ISO 2162-1 (1994-08)
Name Representation Symbol Name Representation Symbol
view section view section
Cylindrical Cylindrical
helical com- helical ten-
pression sion spring
spring (round
wire)
Cylindrical Cylindrical
helical ten- helical com-
sion spring pression
spring (square
wire)
Disk spring Disk spring cf. DIN ISO 6413(1990-03)
(simple) assembly Joint
(disks layered
Disk s pring as- in alternating J~L
sembly (disks directions)
layered in the Sb
same direction) Hub IP*2
Representation of splines and serrations
Shaft
Splines or
spline hubs
with straight
flanks.
Symbol: J T
Toothed shafts
oh ru bt osowt hi tehd — i _n
involute
splines or s\\\\l
serrations.
Splines ISO 14-6 x 26 f7 x 30: Spline profile with straight flanks according to ISO 14, number of
Symbol: splines N = 6, inner diameter d= 26f7, outer diameter D= 30 (page 241)
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T ec hn ica l d ra w in g : 3. o r e n ts
88
Bosses on turned parts, Workp iece corners and edges
Bosses on turn ed parts cf. DIN 6785(1991-11)
Boss Vw o r kPiec e Boss Largest diameter of the finished part in mm
dimensions dimen- up to 3 over 3 over 5 over 8 over 12 over 18 over 26 over 40
boss sions
to 5 to 8 to 12 to 18 to 26 to 40 to 60
/r
Example r- 00.5 max 0.3 0.5 0.8 1.0 1.5 2.0 2.5 3.5
in mm
0.3
Drawing j 1> 00.5x0,3 'max 0 . 2 0.3 0.5 0 . 6 0.9 1 2 2.0 3.0
entry in mm
Workpiece corners and edges cf. DIN ISO 13715 (2000-12), replacement for DIN 6784
Edge or Work piec e edge/c orner lies in referenc e to t he ideal geom etric al form
corner
inside out side in area
outer material removal burr sharp edged
edge a. a fa
l£ <0• \ 13
inner material removal transition sharp edged
edge -0.05;-0.02;+0.02;+0.05
ft, ' E a a
LL
ur ]/ OJ I |
Dim. a ( m m ) \m '
I
-0.1 ;-0.3;-0 .5;-1.0;-2.5 +0.1;+0.3;+0.5;+1.0;+2.5
S y m b o l for Symbol Meaning for Burr and material removal direction
labeling workpiece element outer edge inner edge
outer edge inner edge
edges/corners
field for entering Burr allowed, Transition allowed, Specification Material
dimension allowed removal
material removal material removal not for Burr
not allowed allowed
Removal required, Removal required, Example +1
L
burr not transition not
allowed allowed
Burr or transition Material removal or Meaning
allowed transition allowed r
1 ) only allowed with a dimension callout
Labeling of w ork piec e c orners and edges
Collec tiv e indic ations Examples
^0.5 t0.3 Outside edge without burr.
The allowable material removal
Collective indications apply to all edges for which an -tU is between 0 and 0.3 mm.
edge condition is not given.
Edges for w hic h the c ollec tiv e indic ation does not J=+0.3 Outside edge with allowable
apply m ust be marked in the drawing. burr of 0 to 0.3 mm
The exceptions are placed after the collective indication XL (burr direction specified).
in parentheses or indicated by the base symbol.
-0.1 Inside edge with allowable
Collective indications which are L05 material removal between 0.1
only valid for ou tside or inside and 0.5 mm (material removal
edges are given by the corre- XKT direction not specified).
sponding symbols.
[±0.02 Inside edge with allowable
material removal between 0 and
IKT 0.02 mm or allowable transition
up to 0.02 mm (sharp edged).
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T ech nic al d ra w in g : 3. o r e nts
Thread runouts, Thread u ndercuts
T h r e ad r u n o u t s f o r m e t r i c IS O t h r e ad s cf. DIN 76-1 (2004-06)
External thread Pitch ISO Thread run out2' Pitch ISO Thread run out2'
1) standard 1) standard
J— t max. ai 1.3 *1 max. ei
P thread 0.5 1.5 P thread 3.75
r- 0.6 max. 1.8 max. 4.5 6.2
0.2 d 0.75 0.6 2.1 1.25 d 3.2 5.25 7.3
0.25 0.9 0.75 1.5 3.8 6 8.3
0.3 — 0.9 1.75 M8 4.3 9.3
0.35 1.05 2 M10 5
Ml M12
M16
M1.6
0.4 M2 1 1.2 2.3 2.5 M20 6.3 7.5 11.2
3
0.45 M2.5 1.1 1.35 2.6 3.5 M24 7.5 9 13.1
4
0.5 M3 1.25 1.5 2.8 M30 9 10.5 15.2
4.5
0.6 1.5 1.8 3.4 5 M36 10 12 16.8
5.5
Internal thread 0.7 M4 1.75 2.1 3.8 6 M42 11 13.5 18.4
0.75 20.8
0.8 M5 1.9 2.25 4 M48 12.5 15 22.4
1 M6 24
2 2.4 4.2 M56 14 16.5
2.5 3 5.1 M64 15 18
1 ) For fine threads the dimen sion of the thread run out is chosen acco rding to the
pitch P.
2 ) As a rule; applies if no other entries are given.
If a shorter thread runout is necessary, this applies:
x2 « 0.5 • x-|," 32 *0 .6 7- 3- ,; e2 « 0.625 • e^
If a longer thread runout is necessary, this applies:
a3 « 1.3 • ay, e3 *> 1.6 •
S c r e w t h r e a d u n d e r c u t s fo r m e t r i c IS O th r e a d s cf. DIN 76-1 (2004-06)
External thread Pitch ISO External threads Internal threads
form A and form B 1) standard Form A 2' Form B 3) Form C2' Form D3'
p thread d 9^ 92 01 92 01 92 01 92
0.2
0.25 d r h1Q3 min. max. min. max. H13 min. max. min. max.
0.3
0.35 M1 0.1 d- 0.3 0.45 0.7 0.25 0.5 d + 0.1 0.8 1.2 0.5 0.9
0.12 of-0.4 0.55 0.9 0.25 0.6 d + 0.1 1 1.4 0.6 1
- 0.16 d- 0.5 0.6 1.05 0.3 0.75 d+0.1 1.2 1.6 0.75 1.25
0.16 d- 0.6 0.7 1.2 0.4 0.9 d+ 0.2 1.4 1.9 0.9 1.4
M1.6
30° min 0.4 M2 0.2 d- 0.7 0.8 1.4 0.5 1 d +0 .2 1.6 2.2 1 1.6
0.45 M2.5 0.2 d- 0.7 1 1.6 0.5 1.1 d+ 0. 2 1.8 2.4 1.1 1.7
0.5 M3 0.2 d- 0.8 1.1 1.75 0.5 1.25 d+ 0. 3 2 2.7 1.25 2
0.6 0.4 d- 1 1.2 2.1 0.6 1.5 d +0 .3 2.4 3.3 1.5 2.4
0.7 M4 0.4 d -1 .1 1.5 2.45 0.8 1.75 d + 0.3 2.8 3.8 1.75 2.75
0.75 - 0.4 d- 1.2 1.6 2.6 0.9 1.9 d + 0.3 3 4 1.9 2.9
0.8 M5
0.4 d - 1 . 3 1.7 2.8 0.9 2 d+0.3 3.2 4.2 2 3
Internal thread 1 M6 0.6 d-1.6 2.1 3.5 1.1 2.5 d+ 0.5 4 5.2 2.5 3.7
form C and form D 1.25 M8 0.6 d - 2 2.7 4.4 1.5 3.2 d+ 0.5 5 6.7 3.2 4.9
0.8 d - 2 . 3 3.2 5.2 1.8 3.8 d+ 0. 5 6 7.8 3.8 5.6
Lx — 1.5 M10 1 d - 2.6 3.9 6.1 2.1 4.3 d+ 0.5 7 9.1 4.3 6.4
1.75 M12 1 d - 3 4 .5 7 2.5 5 d+0.5 8 10.3 5 7.3
x / / / V / /,
2 M16
2.5 M20 1.2 d-3.6 5.6 8.7 3.2 6.3 d+ 0. 5 10 13 6.3 9.3
3 M24 1.6 d - 4.4 6.7 10.5 3.7 7.5 d+0.5 12 15.2 7.5 10.7
3.5 M30 1.6 d - 5 7.7 12 4.7 9 d +0 .5 14 17.7 9 12.7
4 M36 2 d - 5.7 9 14 5 10 d+0.5 16 20 10 14
4.5 M42 2 d - 6.4 10.5 16 5.5 11 d + 0.5 18 23 11 16
5 M48 2.5 6-1 11.5 17.5 6.5 12.5 d + 0.5 20 26 12.5 18.5
5.5 M56 3.2 d- 7.7 12.5 19 7.5 14 d + 0.5 22 28 14 20
6 M64 3.2 d -8 .3 14 21 8 15 d+0.5 24 30 15 21
DIN 76-C: Screw thread undercut shape C
30° min. 1 ) For fine thread screws the dim ens ion of the thread und ercut is chosen according
to the pitch P.
2 ) as a rule; always applies if no other entries are m ade
3 ) Only in cases whe re a shorter thread unde rcut is required.
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90 T ech nic al d ra w in g : 3. o r e nts
Representation of threads and screw joints
Representation of threads cf. D IN ISO 6410-1 (1993-12)
V T V V/s Internal thread
e^ accord, to DIN 76-1. Thread runout is normally not shown.
-f+4- •/ / £/ /
v b //
£•1
Bolt thread Bolts in internal thread
2
Thread undercut Pipe threads and pipe screw joints
graphical symbolic
DIN76-D
DIN76-A Hexagonal bolt and nut
R e p r es e n t a ti o n o f s c r ew j o i n t s simplified
detailed
bolt head hight h 2 « 0.8 • t/
e *2-d
hh23 wn uatshheeri gthhti ckn e ss s ^ 0.87 • e
e diagon al betwee n corners
s w idth across flats Screw joint
d thread nominal 0 with stud
Screw joint with Screw joint with Screw joint with
cap screw hexagonal screw countersunk head screw
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T ec hn ic al d ra w in g : 3. o r e nts
Center holes. Knurls
Center holes cf. DIN 332-1 (1986-04)
form R form A Nominal sizes
, Form d, 1 1.25 1.6 2 2.5 3.15 4 5 6.3 8
d2 2 1 2 2.65 3.35 4.25 5.3 6.7 8.5 10 6 13.2 17
CM 1.9 2.3 2.9 3.7 4.6 5.8 7.4 9.2 11.4 14.7
"ta
11 14 18 22
a 1.9 2.3 2.9 3.7 4.6 5.9 7.4 9.2 11.5 14.8
11 14 18 22
'min 2.2 2.7 3.4 4.3 5.4 6.8 8.6 10.8 12.9 16.4
3.5 4.5 5.5 6.6 8.3 10 12.7 15.6 2 25
0.3 0.4 0.5 0 . 6 0 . 8 0.9 1 2 1.6 1.4 1.6
3.15 6.3 10 12.5 16 18 22.4
^mir 1.9 2.3 2.9 3.7 4.6 5.9 7.4 9.2 11.5 14.8
3.5 4.5 5.5 6.6 8.3 10 12.7 15.6 2 25
0.4 0.6 0.7 0.9 0.9 1 1 1.7 1.7 2.3
4.5 5.3 6.3 7.5 11.2 14 18 22.4 2 8
7.1 8.5 10 12.5 16 2 25 31.5
Form curved bearing surface, without protective countersink
straight bearing surface, without protective countersink
Drawing callout for center holes straight bearing surface, conical protective countersink
straight bearing surface, truncated conical protective counter
sink
cf. DIN ISO 6411 (1997-11)
requireAd coennttehrehfoinleis ihsed part A coennttehre hfoinleis hi seda lpl oawrte d A centeor nhothlee mfinaiyshneodt pbaertpresent
ISO 6411 - A 4 / 8 . 5 K ' S O 6411 - A 4 / 8 . 5
ISO 6411 - A 4 / 8 . 5
/
< ISO 6411 - A4/8.5: center ho le ISO 6411: a center hole is required on the finished part.
Form and dimensions of the center hole according to DIN 332: form A; d-\ = 4 m m ; d2 = 8.5 mm.
Knurls cf. DIN 82 (1973-01)
Letter Representation Name Point Initial
symbol shape diameter d2
Knurls with
RAA axially parallel do = d^ - 0.5 • t
grooves
dy n o m i n a l d i a m e t e r RBR Right-hand d2 = d<l- 0.5 • t
d2 initial diam eter -3 0( knurl
t spacing
Standard spacing values RBL i i Left-hand knurl do = di - 0.5 • t
f: 0.5; 0.6; 0.8; 1.0; 1.2; 1.6 m m RGE Left-hand/right- raised do = di - 0.67 • t
RGV d? = d-i- 0.33 • t
Drawing entry (example): hand knurls recessed
DIN 82-RGE 0.8
RKE Axial and cir- raised d o = d^ - 0.67 • t
cumferential
RKV knurl recessed d2 = dy- 0.33 • t
DI N 82-RGE 0. 8: Left-hand/right-hand knurls, raised points, t = 0.8 m m 93/431
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92 T ec hn ic al d ra w in g : 3. o r e n ts
Undercuts
U n d e r c u t s 1} cf. DIN 509 (2006-12)
fo rm E form F form G form H
for cylindrical surface to for shoulders and cylindrical for sma ll transitio n for planar and cylindrical surfaces
surfaces to be further machined
be further machined (for low loading) to be further machined
z z
Zv Z2 = machining allowances
Undercut DIN 509 - E 0.8 x 0.3: form E, radius r= 0.8 mm, undercut depth f, = 0.3 mm
Undercut dimensions and countersink dimensions
Form r2) :i 0.1 h t2 f 9 Correlation tc> diameter d- \3) Minimum dir nensi on a f:or coijnter-
for workptieces with sink on tl"le opp>osingI piece;4)
Series Series + 0.1 + 0.05 + 0.2 normal increased Undercut Fo rm
loading fatigue strength r x f-| FG
1200 0 E 0- H
> 0 1.6-03 - 0.2x0.1 0.2
- R0.2 0.1 0.1 1 (0.9) -
R0.4 - 0.2 0.1 2 (1.1) > 0 3 - 0 18 - 0.4x0.2 0.3 0 - -
0.6x0.2
- R0.6 0.2 0.1 2 (1.4) > 0 1 0 -0 18 - 0.6x0.3 0.5 0.15 - -
0.8 x 0.3
- R0.6 0.3 0.2 2.5 (2.1) > 0 1 8 - 0 80 - 1.0x0.2 0.4 0 - -
1.0x0.4
R0.8 - 0.3 0.2 2.5 (2.3) > 0 1 8 - 0 80 - 1.2x0.2 0.6 0.05 - -
1.2 x0.4
E R1 0.2 0.1 2.5 (1.8) - > 0 1 8 - 0 50 1.6x0 .3 0.9 0.45 - -
and - R1 0.4 0.3 4 (3.2) 2.5 x 0.4
> 0 80 - 4.0x 0.5 0.7 0 - -
F 0.4x0.2
0.8 x 0.3
R1.2 - 0.2 0.1 2.5 (2) - > 0 1 8 - 0 50 1.2x0.3 1.1 0.6 - -
R1.2 0.4 0.3 4 (3.4) > 0 80 - 0.9 0.1 - -
R1.6 - 0.3 0.2 4 (3.1) - > 0 5 0 -0 80 1 .4 0 .6 - -
R2.5 - 0.4 0.3 5 (4.8) - > 0 8 0 - 0 125 2.2 1.0 - -
R4 - 0.5 0.3 7 (6.4) - > 0 125 3.6 2.1 - -
G R0.4 - 0.2 0.2 (0.9) (1.1) > 0 3 - 0 18 - 0- - -
H R0.8 - 0.3 0.05 (2.0) (1.1) > 0 1 8 - 0 80 - - - - 0.35
R1.2 - 0.3 0.05 (2.4) (1.5)
- > 0 1 8 - 0 50 - - - 0.65
1 ) All forms of undercut apply to both shafts and holes. 4 ) Countersink dimension a o n
2 ) Undercuts w ith Series 1 radii are preferred. opposing piece
3 ) The correlation to the diame ter area does not apply w ith curved shoulders and
°o l
thin wa lled parts. For workpiec es wi th differing diameters it may be advisable
to design all undercuts for all diameters in the same form and size. I
CN
- H
D r a w i n g e n tr y for u n d e rc u ts
Normally undercuts are represented in drawings as a simplified entry with the designator. However they can also be
completely drawn and dimensioned.
Example: Shaft with undercut DIN 509 - F1.2 x 0.2 Example: Hole with undercut- DIN 509- E1.2 x 0.2
simplified entry s i m p l i f i ed e n t r y
m DIN 509-E 1.2x0.2
DIN 509-F 1.2x0.2
/ 0.1+0.05 2.5+0.2
complete entry complete entry
X
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T e c h n i c a l d r a w i n g : 3 .8 W e l d i n g a n d s o l d e r i n g 93
Symbols for Welding and Soldering
P o s it io n i n g o f s y m b o l s f o r w e l d i n g a n d s o l d er in g i n d r a w i n g s cf. DIN EN 22553 (1997-03)
Bas ic term s
Reference line. This consists of the solid reference line
and the dashed reference line. The dashed reference line
solid reference line bruenloswpiat.raTlhleel dtaoshtheed rseofelirdenrceefelrineencies olminietteadndforabsoymvemoer-
trical welds.
arrow line x we ld sym bol I tail
joint Arrow line. It connects the solid reference line with
(e.g. butt joint) the joint.
Tail. Additional entries can be given here as needed for:
• metho d, process • working position
• evaluation group • additional material
Joint. O rientation of the parts to be joine d to each other.
Weld information
symbolic S y m b o l . The symbol identifies the form of the weld. It is
pnreecfeesrsaabrlyy opnlatcheed dnaosrhmeadl rtoefethreenscoelidlinree.ference line, or if
VP*
Arrangement of the weld sym bol
7a3 17" a
position of the position of the weld
>a4 weld symbol (weld surface)
solid reference line "arrow side"
dashed reference line "other side"
"other / "arrow side" I7I 'other side' For welds represented in section or view, the position of
side" arrow line the sym bol must agree with the weld cross section.
/// V arrow line
"arrow side' Arrow side. The arrow side is that side of the joint to
which the arrow line refers.
Other side. The other side of the joint that is opposite th e
arrow side.
Supplemental and auxiliary symbols cf. DIN EN 22553 (1997-03)
r Weld all around Weld surface hollow (concave)
/ Field weld (weld is made on We ld surface flat (planar)
the construction site)
, <^23 Weld surface curved (convex)
jf Entry of the weld ing
process in the tail JO Weld surface notch free
Representation in drawing s (basic symbols) Weld type/ cf. DIN EN 22553(1997-03)
symbol
Weld type/ Representation Representation
symbol symbolic
graphical symbolic graphical
iiiiiiiiiiiii I V groove SL
weld
Butt /— £r
weld
I £R
II
jTT r 95/431
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94 Technical draw ing: 3.8 W eldin g and so ldering
Symbols for Welding and Soldering
Representation in drawings (basic symbols) cf. DIN EN 22553 (1997-03)
Weld type/ graphical Representation Weld type/ graphical Representation
symbol symbolic symbol symbolic
Flare-V j/ J/
gwr oeol vde f*- L
Bevel
groove weld
V
Plug
we ld in g Si- I f
TV T\
Frontal Y-butt X. X
flush weld weld
3
Steep- \L [77 A L HY-weld YI
flanked weld
V r b
\i
£ JA w
Build-up t ar U-groove
weld weld
MI ImI 1f
r>r\ V
====
Fold weld J-groove
- weld
2
Weld all —1— aB
around Spot weld
O
Fillet weld Line w eld
aB 5BM03SB
Field weld aBjs^ Surface we ld Vssss/A II
with 3 mm
r~i
seam alb,
thickness
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Technical draw ing: 3.8 W eldin g and soldering 95
Symbols for Welding and Soldering
Composite symbols for sym metrical w eld s 1) (examples) cf. DIN EN 22553 (1997-03)
Weld type Symbol Representation Weld type Symbol Representation
D(ouble)- D(ouble)- K
V-weld HY-weld
(X-weld)
D(ouble)- K D(ouble)-
bevel weld U-weld
1 ) The symbols are loca- graphical symbolic
ted symm etrical to the
D(ouble)- reference line.
Y-weld Example:
App lication examp les for auxiliary sym bols cf. DIN EN 22553 (1997-03)
Weld type Symbol Representation Weld type Symbol Representation
2m
Flat V Flat V cf. DIN EN 22553 (1997-03)
V-weld reworked Meaning of the symbolic
V-weld V
dimension entry
Convex Flat Butt weld, penetrating,
double V-weld with we ld seam thickness s = 4 m m
V-weld flat backing
run
Y-weld Hollow fillet
with weld, weld
transfer
backing run unnotched
Dimensioning examples
Weld type Representation and dimensioning
graphical symbolic
l-weld s4
(penetra-
ting) (7 7 K
l-weld s3 Butt weld, non-penetrating,
t(rnaot inn-gp)e n e - weld seam thickness s = 3 m m ,
\/ / /.
running over the entire
workpiece
Flare-V -S2_JL Flare-V groove weld,
groove not completely melted down,
weld 31 weld seam thickness s= 2 m m
V-weld w 111/IS0 5817-C / V-weld (penetrating weld)
(penetrating - V - < ( ISO 69A-7-PA/ with backing run, fabricated by
manual arc welding (code 111
wbaecldk)inwg irthun EN 499-E 42 0 RR12 accord, to DIN EN ISO 4063),
required evaluation group C
L
accord, to ISO 5817; flat w eld-
-Zl ing po sition PA accord, to ISO
6947; electrode E 42 0 RR 12
accord, to DIN EN 499
1 ) Sup plem entary requireme nts can be entered in a tail at the end of a reference line. 97/431
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96 Technical draw ing: 3.8 W elding and so ldering
Symbols for Welding and Soldering,
Representation of adhesive, folded and pressed joints
Dimensioning examples (continued)
Weld type R e p r es e n t a t io n a n d d i m e n s i o n i n g Meaning of the symbolic
dimension entry
graphical symbolic
J3jv ji K . Fillet weld,
/J we ld leg thickness a = 3 m m
£ (height of the isosceles trian-
gle)
Fillet weld
(contin- Fillet weld,
uous) weld leg thickness z = 4 m m
(side length of the isosceles
/ triangle)
Fillet weld ^30 I ^30 a5| \ 2x 20(10) Fillet weld (interrupted),
(inter-
rupted) ')))))] mmi / w2 eslidnglleegwtheilcdksneeascs h aw =it5hm m;
/ = 20 mm length;
20 20 weld spacing e = 10 m m,
\ end distance v = 30 m m
(10)
Double >)))))) ))))))) ))))))' a4|\ 3x30(10) Double fillet w eld
fillet weld / a A - ^ j x 30 (10) (interrupted, symmetrical),
(inter- >))))); )))))). mr. we ld leg thickness a = 4 m m ;
rupted) single weld length / = 30 m m,
30 10 30 10 30 weld spacing e = 10 m m ,
without end distance
Double 25 20 30 20 25 z5 k 2 X 2 0 " 7(30) Double fillet w eld
fillet weld ' z5 ^ 3 x 2 0 / -(30) (interrupted, staggered),
(inter- I)))) i)))): weld leg thickness z= 5 mm;
rupted, single weld length / = 20 m m,
staggered) ')))). ))))). »))). weld spacing e = 30 m m ,
end distance v=25 m m
20 30 20 30 20
S y m b o l i c r e p r e s e n t a t io n o f a d h e s i v e, f o l d e d a n d cf. DIN EN ISO 15785 (2002-12)
pressed joints (examples)
Type of Weld type/ Meaning/ Type of Weld type/ Meaning/
joint symbol drawing entry joint symbol
draw i ng entry
20 Folded Folded 7 1
seam seam — u
5x20= NO
Surface e>
seam1) 7
Adhesive 6x7<? 1
bonded-
seams 7
05
Slant z : Pressed
seam1)
Pressed seam
seam 5 x 4 H
ZS
-4
1 ) The adhesive media is not shown for adhesive seams.
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Technical dra win g: 3.9 Surfaces 97
Heat treated parts - Hardness sp ecifications
Presentation and indication of heat treated parts on d rawings cf. DIN 6773 (2001-04)
Heat treatm ent s pec ific ations
Term(s) for Measurable parameters of the m aterial con dition Pos s ible addition s
material condition
Examples: hardness HRC rockwell hardness Measuring points. Entering and dimen-
quenched and value HV vickers hardness sioning in the drawing with symbol
tempered HB brinell hardness
Heat treatment diagram. Simplified, usu-
hardened hardness Eht case hardening thickness ally reduced scale representation of the
nitriding depth part near the title block.
hardened and inden- Nht effective hardening de pth
tempered M i n i m u m t e n s i le s t r en g t h o r m i c ro -
tation Rht structure. If it is possible to test a part
annealed treated in the same batch.
HTA carburizing depth
nitrided WL nitride white layer thickness
All entries are made with plus tolerances.
Identify ing areas of the s urfac e to undergo loc aliz ed h eat treatm ent
yV // ' // // /) // \ \ Ahereaat tmreuastet db.e yv /, / ,/ ,/ ,/ ,\ • Ahereaat tmreaaytebde. \Z////y\ Intermediate area may
not be heat
treated.
Heat treatm ent s pec ific ations in drawings (ex amples )
Method Heat treatmen t of the entire part Heat treatment
localized
same requirements different requirements
•— rTo + 5
Quenching TT rp^ T| part temp hearerdde6n0ed+ a3nHdReCntire
and temper- J3K ' r
ing, 75 + 10
60
Hardening,
Hardening
and
tempering 3q5u0en+c5h0edHBan2d.5t/e1m87p.e5red 5ha8r+de4nHeRdCan©d 4te0m+pe5rHedRC
Nitriding, 1_
Case
hardening case-hardened and
tempered 700 + 100 HV 10
nitrided case-hardened and tempered Eht = 1.2 + 0.5
>90 0 HV 10 © 6 0 + 4 HRC Eht = 0.5 + 0.3
Nht = 0.3+ 0.1 (D <52 HRC
Surfaced surface hardened surface hardened
hardening and entire part tempered and tempered
© 5 4 + 6 HR C © «= 35 HRC 6 1 + 4 HRC Rht 600 = 0.8 + 0.8
surface hardened © <3 0 HRC
620 + 120 HV 50
Rht 500 = 0.8 + 0.8
Hardening depths and tolerances in mm
Case-hardening depth Eht 0.05+0.03 0.1+0.1 0.3+0.2 0.5+0.3 0.8+0.4 1.2+0.5 1.6+0.6
Nitriding dep th Nht 0.05+0.02 0.1+0.05 0.15+0.02 0.2+0.1 0.25+0.1 0.3+0.1 0.35+0.15
Induction hardening depth Rht 0 . 4 + 0. 4 0.8+0.8 1.3+1.1
0 . 2 + 0. 2 0.6+0.6 1.0+1.0 1.6+1.3
Laser/electr. beam hardening depth Rht 0.2+0.1 0.4+0.2 0.6+0.3 0.8+0.4 1.0+0.5 1.3+0.6 1.6+0.8
Control lim it hardnes s es at the s pec ified hardening d epths
Case-hardening depth Eht 550 HV 1
Nitriding depth Nht core hardness + 50 HV 0.5
Effective hardening depth Rht 0.8 • min imu m surface hardness, calculated in HV
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98 Technical dra win g: 3.9 Surfaces
Form deviations and roughness param eters
Form deviations cf. DIN 4760 (1982-06)
Form deviation s are deviations of the actual surface (surfaces ascertainable by m easurem ent) from the
geometrically ideal surface, whose standard shape is defined by the drawing.
Degrees of form deviation (Profile sec- Examples Possible causes
tion repres. with vertical exaggeration)
1st degree: form deviation deviation in Deflection of the workpiece or the mach ine during fabrica-
2nd degree: w aviness straightness, tion of the part, malfunction or wear in the guides of the
machine tool.
z i roundness
Vibrations of the machine, runout or shape deviation of a
waves milling machine during fabrication of the part.
3rd degree: roughness grooves Geometry of the cutting tool, feed or depth of cut of the
tool du ring fabrication of the part
4th degree: roughness scoring, Sequence of chip formation (e.g. tearing chip), surface
scales, deformation due to blasting during fabrication of the part.
5th and 6th degree: roughness
Cannot be represented bumps Crystallization cycles, matrix changes due to welding or hot
as a simple profile section working, changes due to chemical effects, e.g. corrosion,
matrix etching.
structure,
lattice structure
S u rf ac e t e x t u r e p r o f il es a n d p a r am e t e r s cf. DIN EN ISO 4287 (1998-10) and DIN EN ISO 4288 (1998-04)
Surface profile Parameters Exp lanations
Primary profile (act. profile , P profile) Total heig ht of The primary profile represents the foundation for calculat-
the profile Pt ing the parameters of the primary profile and forms the
Waviness profile (W-profile) basis for the waviness and roughness profiles.
in Total height of
the profile Wt The total height of the profile Pt is the sum of the height of
Roughness profile (R-profile) the highest profile peak Z p and the depth of the lowe st pro-
Total height of file trough 2V within the evaluation length / n .
the profile R t
The waviness profile is obtained by low-pass filtering, i.e. by
Rp, Rv suppressing the short wav elength com ponents of the profile.
Highest peak The to tal h eight of the profile Wt is the sum of the height of
of the profile the highest profile peak Zp and the depth of the low est pro-
file trough Zvwithin the evaluation length /n.
The roughness profile is obtained by high-pass filtering, i.e. by
suppressing the long wavelength components of the profile.
The total height of the profile Rt is the sum of the height of
the highest profile peak Z p and the depth of the lowe st pro-
file trough Zvwithin the evaluation length /n.
Height of the h ighest profile peak Zp, d e p th o f th e l o we s t
profile trough Zv with in the single evaluation length /r.
The highest peak of the profile Rz is the sum of the height
of the highest profile peak Zp and the depth of the lowest
profile trough Zv within the single evaluation length /r.
0 RD m r i•n %o/ 100 Arithmetic T h e a r i th m e ti c m e a n o f th e p r o fil e o r d i n a te s Ra is the
mean of the arithmetic mean of all ordinate values Z x) within the sin-
Z(x) height of the profile at any posi- profile ordina- gle evaluation length /r.
tion x; ordinate value tes fla1)
The material ratio of the profile expressed as a percentage,
/ n evaluation length Material ratio Rmr, is the ratio of the sum of the contributing material
/r single evaluation length of the profile lengths at a specified section height to the total evaluation
Rmr length /n.
Center line The center line (x-axis) x is the line corresponding to the
(x-axis) x long wavelength profile component which is suppressed
by profile filtering.
1) For parameters defined ove r a single eva luation length, the arithmetic mean of 5 single
evalua tion lengths to DIN EN ISO 4288 is used for determ ining the parameters.
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