Machine design basics B (cở sở thiết kế chi tiết máy)

Giúp tra cứu các tiêu chuẩn, kích thước hình học cho các bộ phận, chi tiết máy trong thiết kế và gia công cơ khí. Các qui chuẩn, tiêu chuẩn theo ISO hoặc DIN. Rất quan trọng đặc biệt trong quá trình làm việc tại các nhà máy có ứng dụng việc bảo dưỡng, sửa chữa, chế tạo mới các vật tư, phụ tùng cơ khí..

Kon-41.2010 Machine design basics B (4 cr)

Machine elements

Strength calculation 1

Symbols and units 1

Stresses 1

Failure theories 2

Static load 3

Fatigue loads 3

Stress concentration factors 4

Reversed stress (mean stress zero) 5

Smith diagrams (non-alloy structural steels) 7

Engineering materials 8

Steels 8

Cast irons 10

Aluminium 11

Copper alloys 11

Physical properties of steels and cast irons 12

Physical properties of materials 13

Bolted joint 14

1 Stresses of a bolt during tightening 14

2 Torque required to tighten the bolt 15

Welded connections 17

Stresses in fillet weld 17

Simple calculation method 17

Parallel keys 18

Interference fits 19

Spring design 20

1 Helical extension and compression springs 20

2 Belleville springs 21

3 Rubber springs 22

Gears 23

Helical gears (external gears) 24

Forces on gear teeth 25

Mechanical power transmission 26

Narrow V-belt drives (SFS 3527) 27

Datum lengths of narrow V-belts and datum diameters of pulleys 28

Rolling bearings 30

Equivalent dynamic bearing load (constant) 32

Lubrication and lubricant classification 33

1 Lubrication mechanisms 33

2 Oil classification 34

Design of pressure vessels 36

1 Pressure equipment directive 36

2 Nominal design stress 36

3 Cylindrical and spherical shells 36

4 Dished ends 38

Strength calculation

Symbols and units

N

N kgm2

Nm

kg r/min, r/s

ReH upper yield strength

ReL lower yield strength

Stress concentration factors

Bending

Torsion

Fig 3. Stress concentration factor for a shaft shoulder

The maximum stress (bending)

Fig 4. Surface quality factor k1

1 0,9 0,8 0,7 0,6 0,5

300 400 500 600 700 800 900 1000 1100 1200 1300 1400

Surface roughness R = 0,3 a

0,6

3,2 6,3

25

0,8 1,6

0,6

10 20 30 40 50 60 70 80 90 100 110 120

d (mm)

k2

Fig 5. Size factor k2

Reversed stress (mean stress zero)

Bending or tensile-compression load (mean stress σm = 0)

nim

wσ

σft

2 1

K

k k

Torsion load (mean stress τm = 0)

nim

wτ

τfv

2 1

K

k k

In other cases the safety factor is calculated using Smith diagram

Table 1. Physical properties of structural steels

(N/mm2)

τvsτvw 170 135

205

175

240

215

Notched specimen Shape Stress concentration factor Kf

* Stress concentration factor depends on corner radius and material

Fig 6 Preliminary design values for stress concentration factors

Smith diagrams (non-alloy structural steels)

Raaka-ainekäsikirja 1 Muokatut teräkset 3 uudistettu painos Metalliteollisuuden Kustannus

E295 S235

195

-195

300 400 500 N/mm 2

-175

135

300 N/mm 2

S235

-215 -135

• P steels for pressure purposes

• L steels for pipelines

• E engineering steel

̇ followed by a number being the specified minimum yield strength (N/mm2), e.g S235, E295

̇ for steel casting the name shall be preceded by the letter G

̇ additional symbols for impact strength etc, e.g S355J2

Tensile strength 2)

Impact strength

SFS-EN

10025

SFS 200

v 2004 ReH (N/mm 2 ) Rm (N/mm 2 ) KV (J) / t (°C) v 1991 v 1986 S235JR

Classification by impact strength

2 Steels designated according to chemical composition

(Examples in tables 2…4)

Non-alloy steels

• letter C and the carbon content % multiplied by 100

high speed steels) where the content, by weight, of every alloying element is < 5 %

• carbon content % multiplied by 100

• chemical symbols indicating the alloy elements (in decreasing order)

• numbers indicating the values of contents of alloy elements

Alloy steels (except high speed steels)

• letter X

• carbon content % multiplied by 100

• chemical symbols indicating the alloy elements (in decreasing order)

• numbers indicating the values of contents of alloy elements

Table 2. Quenched and tempered steels (SFS-EN 10083)

̇ heat treatment including hardening and annealing in relative high temperature (500…700 °C)

̇ shafts, couplings, gears, bolts and nuts

Table 3. Case hardening steels

̇ higher carbon content in thin surface layer

̇ high wear resistance and fatigue strength and bending strength

̇ gears and shafts

Table 4 Stainless steels

SFS-EN Yield strength Tensile strength Modulus of elasticity

̇ ductile at low temperatures

̇ pipes, vessels, valves, machinery in process industry, containers and tanks

̇ low cost, good for casting and easy machining, absorption of vibration

̇ machine beds, valves, pipes, cylinders and lining, brake drums and disks

Table 6. Spheroidal graphite cast irons (ductile irons)

̇ high strength compared to grey cast iron, heat treating possible

̇ gears, bodies and frames, power transmission, combustion engine and paper machine components

Table 7. Austempered Ductile Irons (ADI)

EN 1564

Yield strength

(N/mm2)

Tensile strength(N/mm2)

Elongation(%)

Hardness (HB) 800-8 500 800 8 260 320

1000-5 700 1000 5 300 360

1200-2 850 1200 2 340 440

Aluminium

̇ low weight

̇ corrosion resistant

̇ good heat and electricity conductivity

̇ special alloys with high strength

Table 8. Aluminium profile alloys

Alloy Yield strength

(N/mm2)

Tensile strength(N/mm2)

Elongation

A5 (%)

Hardness(HB)

Modulus of elasticity E ≈ 70 000 N/mm2

Copper alloys

̇ journal bearings are most important applications

Table 9. Common copper alloys

Alloy

Products

Yield strength (N/mm2)

Tensile strength (N/mm2)

Elongation

A5 (%)

Hardness (HB)

Tin bronze

Gears and worm wheels, sliding surfaces, journal bearings

GS-CuPb10Sn10

Lead tin bronze

Heavily loaded journal bearings (edge contact) 80 180 7 65 GS-CuAl10Fe3

Aluminium bronze

Crane wheels, bushings, gears, journal bearings 180 500 13 115

Physical properties of steels and cast irons

(GN/m 2 )

Poisson's ratio

ν

Density ρ

(kg/m 3 )

Linear sion coefficient

expan-α (1/K)

Thermal conductivity

λ (W/(m K))

Specific heat capacity c

(kJ/(kg K))

Structural steels

Quenched and tempered steels

Case hardening steels

52…63 42…59 42…59

15 13,5

0,50 0,50 0,50 0,44 0,44 Grey cast irons

0,26 0,26 0,26 0,26 0,26

1) 52,5 50,0 48,5 47,5 45,5

0,46 0,46 0,46 0,46 0,46 Spheroidal graphite cast irons

2) 36,2 36,2 36,2 35,2 32,5 31,1 31,1 31,1

0,515 0,515 0,515 0,515 0,515 0,515 0,515 0,515 ADI - Austempered ductile

22,1 21,8 21,5 21,2 1) t = 100 °C

Physical properties of materials

(GN/m 2 )

Poisson's ratio

ν

Density ρ

(kg/m 3 )

Linear sion coeffi- cient α (1/K)

expan-Thermal conductivity

λ (W/(m K))

Specific heat capacity c

0,30 0,30 0,30 0,33 0,2 0,3

7800

7800 7100 7300

11,9⋅10 -6 11⋅10 -6 17⋅10 -6 10,3⋅10 -6 10…13⋅10 -6

35

15 31 53

0,450 0,450 0,46 0,54 Diamond (natural)2)

800

2000

30

50 30,7

55

102

0,510 0,510 0,752 0,670 0,710 0,543 0,205 Graphite3)

68

0,30 0,32 0,36 0,32 0,36 0,41 0,45 0,16

(135…151) ⋅ 10-6

0,6⋅10 -6

178 0,25 0,22…0,48 0,36…0,98 0,24 1,25

0,710 1,670

- 1,13…1,30 1,050 0,800 1) Values are representative Exact values vary with composition and processing

2) Materials are anisotropic Values vary with crystallographic orientation

3) Typical properties of bearing quality materials Ceramics are hot pressed or equivalent sintered These erties are representative and depend on detailed composition and processing

Bolted joint

1 Stresses of a bolt during tightening

A flange joint is a typical bolted joint (fig 1-1)

Fig. 1-1 Flange joint

When the bolt is tightened, a tensile stress and torsional stress is developed in the bolt For ISO metric threads (thread angle 60°) the friction torque in threads is /1/

2 2

1

d

P F

d M

π

where FM is the preload (from tightening)

d2 the pitch diameter (table 1-1)

µG the friction coefficient in threads

S

M 2 v

d

P d

F d W

M

π

µπ

where d3 is the root diameter of the thread If the bolt has a reduced diameter (< dS), use the

minimum diameter dT The tensile stress in the cross-section due to the preload force is

2 S

M S

The effective stress should not be more than 90 % of the yield stress (0,9Rp0,2 or 0,9ReL) The maximum tensile stress during tightening is /1, 3/

2

2

G S

2

2 , 0 S

)155

,1(231

9,0

=

d

P d

d R

πµ

The friction coefficient in threads depends on the material, surface treatment and lubrication (table 1-2) For bolts M6 M16 σS ≈ 0,7ReL, when the friction coefficient in threads is µG = 0,15 The maximum axial force (in assembled state) is

d/mm

Pitch

P/mm

Pitch diameter

d2/mm

Root diameter

d3/mm

Tensile stress area

Table 1-2 Friction coefficient µG in threads /4/

Untreated Phosphated Phosphated black Zinc electroplated Cadmium electropl

0,20 0,35 0,28 0,40 0,26 0,37 0,14 0,20 0,10 0,19

0,16 0,23 0,16 0,33 0,24 0,27 0,14 0,19 0,10 0,17

0,13 0,19 0,13 0,19 0,14 0,21 0,10 0,17 0,13 0,19

Table 1-3. Property classes (strength grades) of bolts

Rm / N/mm 2 (nominal) 500 600 800 1000 1200

ReL or Rp0,2 / N/mm2 (nominal) 300 480 640 900 1080

Rm tensile strength, ReL or Rp0,2 yield strength

2 Torque required to tighten the bolt

The total torque required to tighten the bolt is a sum of the friction torque in threads and

torque between the head or nut and the surface (fig 2-1) The friction torque MK between the nut and the surface is

M km K 2

1

where µK is the friction coefficient between the nut (or head) and the surface

Dkm = (dK+DK)/2 the mean diameter (location of friction force)

dK the outside diameter of the nut (or head) ≈ width across flats s (wrench opening)

DK the diameter of the hole

The friction coefficient between the nut (or head) and the surface is µK ≈ 0,08 0,22 ing on the material, surface treatment and lubrication The friction coefficient of stainless steels (between the nut (or head) and the surface or in threads) can be even 0,5

depend-The total torque required to tighten the bolt is

=

πµ

F M

Fig 2-1 Bolt tightening using wrench

The preload FM depends on friction coefficients and torque With hand tools only bolts M10 (10.9) and M12 (8.8) are tightened properly (preload of small bolts is usually too high and preload of big bolts is too small) /1/

References

1 Verho A Ruuviliitokset ja liikeruuvit Julkaisussa: Airila M et al Koneenosien suunnittelu, 2 painos

Porvoo: WSOY 1997 S 161 243 ISBN 951-0-20172-3

2 Decker K-H Maschinenelemente Gestaltung und Berechnung 12 Auflage München: Carl Hanser Verlag 1995 677 s ISBN 3-446-17966-6

3 VDI Richtlinie 2230 Blatt 1 Systematische Berechnung hochbeanspruchter Schraubenverbindungen

Düsseldorf: VDI-Verlag 1986 (Systematic calculation of high duty bolted joints)

4 Haberhauer H & Bodenstein F Maschinenelemente Gestaltung, Berechnung, Anwendung 10 Auflage

Berlin: Springer-Verlag 1996 626 s ISBN 3-540-60619-X

Welded connections

Stresses in fillet weld

The stresses of the fillet weld are calculated for the minimum cross section A = al (a is the throat thickness (height of the cross section area) and l is the length of the weld) The mini-

mum cross section area is located at 45° to the legs The stresses of the area are divided into three components (fig 1)

a

Simple calculation method

In the simple calculation method the equation for the stress of the weld σw is regardless of the direction of the load

The calculation method is valid when 3 mm ≤ a ≤ 15 mm (SFS 2373) The length of the weld has also limitations

Mechanical properties of structural steels are in the table 1

Steel Thickness t / mm ReL / N/mm2 σsall / N/mm2 σwsall / N/mm2 Factor β

S 235 (Fe 37) .16

17 40 41

Parallel keys

The torque that can be transmitted (the bearing action between the side of the key and the hub material) (fig 1)

where pn is the compressive stress of the hub

l is the length of the key

t2 the depth of the keyway in the hub

d the diameter of the shaft

The torque that can be transmitted (the bearing action between the side of the key and the

shaft material)

where pa is the compressive stress of the hub and t1 the depth of the keyway in the shaft

The compressive stress po is:

◊ the steel 150 N/mm2

◊ grey cast iron 90 N/mm2

◊ spheroidal graphite cast iron 110 N/mm2

The load factor is in the table 2

a

Fig 1. Parallel key (SFS 2636)

Table 1. Dimensions of keys (SFS 2636) Key length is in the standard

One-way load, heavy shocks

Reverse load, light shocks

Reverse load, heavy shocks

Fig 1 An interference fit and stresses in interference fits

Nominal

> ≤ Devia-tions

tions

tions

tions

tions 3

Devia-+0,010 0

+0,020 +0,014

+0,024 +0,018

+0,012 0

+0,027 +0,019

+0,031 +0,023

+0,015 0

+0,032 +0,023

+0,037 +0,028

+0,060 +0,047

0 +0,035 +0,054

+0,041

+0,061 +0,048

+0,068 +0,055

30 40 +0,025 +0,059

+0,064 +0,048

+0,076 +0,060

+0,084 +0,068

0 +0,043 +0,070

+0,054

+0,086 +0,070

+0,097 +0,081

50 65 +0,030

+0,072 +0,053

+0,085 +0,066

+0,106 +0,087

+0,121 +0,102

0 +0,078 +0,059

+0,094 +0,075

+0,121 +0,102

+0,139 +0,120

80 100 +0,035

+0,093 +0,071

+0,113 +0,091

+0,146 +0,124

+0,168 +0,146

0 +0,101 +0,079

+0,126 +0,104

+0,166 +0,144

+0,194 +0,172

+0,117 +0,092

+0,147 +0,122

+0,195 +0,170

+0,227 +0,202

+0,040 0

+0,125 +0,100

+0,159 +0,134

+0,215 +0,190

+0,253 +0,228

+0,133 +0,108

+0,171 +0,146

+0,235 +0,210

+0,277 +0,252

+0,151 +0,122

+0,195 +0,166

+0,265 +0,236

+0,313 +0,284

Table 1. Interference fits (sizes mm)

Spring design

1 Helical extension and compression springs

Common forms of helical springs are in fig 1 For springs with end treatments the total

num-ber of coils nt is bigger than the number of active coils n Other forms are possible such as

conical helical compression springs If the place for a spring is small it is possible to put eral helical springs within each other

sev-Fig 1 Helical compression springs (a) and extension spring (b)

The force of a helical spring is

where G is the shear modulus of elasticity

d the wire diameter

D the mean coil diameter

n the number of active coils

where k is the stress concentration factor The stress concentration factor kw for the dynamic

load (the Wahl factor) is as a function of the spring index C = D/d in fig 2

The stress concentration factor for the static load is

C

k

2

11

C C

C

44

14

Fig 3. Forms of Belleville springs, the top and bottom of springs in group 3 are

cham-fered Belleville springs have three dimension classes A, B and C (DIN 2093)

The force-deflection relationship is nonlinear The allowed deflection f ≤ 0,75h0

Fig 4. Deflection of Belleville spring

3 Rubber springs

The modulus of elasticity E and G (in shear) for rubber depends on the durometer hardness

number (e.g IRHD) Dynamically loaded rubber springs have higher stiffness than statically loaded A cylindrical rubber spring is frequently used as a compression spring (fig 5)

Fig 5 Cylindrical rubber spring with compression loading

Fig 6. Simple rubber shear spring Fig 7 Cylindrical rubber spring

(torsion loading)