Machine Component’s Design II

Machine Component’s Design II

J. Jafari Fesharaki

J. Jafari Fesharaki

JJafari.f@gmail.com

1- Standard components (Screw, Chain, Belt, …)

2- Components need manual calculation (Shaft, Welded joints, Spring,…) 3- Components need computer analysis (wing, Gear box Skin, …)

2 2

Spur Gear Helical Gear Helical Gear Bevel Gear Worm Gear 2- Chain

3- Belt

4- Brake & Clutch

5- Contact Bearing

5- Contact Bearing

دز ه ر ! نا" # $%

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*+ '( نازرا ,

& '( ! +-, نازرا +-, . ز

& '( ! +-, نازرا +-, . ز

4 4

Machine Component’s Design II Machine Component’s Design II

Spur Gear

Helical Gear Bevel Gear Worm Gear

6 6

Pitch circle: a theoretical circle upon which all calculations are usually based

“ d”: Pitch circle diameter

Circular pitch: “P” is the distance, measured on the pitch circle, from a point on one Circular pitch: “P” is the distance, measured on the pitch circle, from a point on one tooth to a corresponding point on an adjacent tooth.

“N” : Number of Teeth

Module: “m” is the ratio of the pitch diameter to the number of teeth. The module is the index of tooth size in SI

P = π d/N

m= d/N P=π.m

8 8

Addendum: “a” is the radial distance between the top land and the pitch circle a= m

a= m

Dedendum: “b” is the radial distance from the bottom land to the pitch circle

Clearance: “c” is the amount by which the dedendum in a given gear exceeds the addendum of its mating gear

Next Choice: 1.125, 1.375, 1.75, 2.25, 2.75, 3.5, 4.5, 5.5, 7, 9, 11, 14, 18, 22, 28, 36, 45

Modules selection:

Preferred: 1, 1.25, 1.5, 2, 2.5, 3, 4, 5, 6, 8, 10, 12, 16, 20, 25, 32, 40, 50 For upper Power

10 10

Note:

For Contact two gears, their modules must be Equal.

Pinion: is the smaller of two mating gears.

r

_A

.n

₂

= r

_B

.n

₁

12 12

Φ = Pressure Angle

14 14

Φ = 20 °

Undesirable force Undesirable force

2- Grinding the top face Decrease the contact ratio 3- tall tooth Weak tooth

4- Increase number of teeth Growth every circle

16 16

Φ = Pressure Angle

k = 1 for full-depth teeth, 0.8 for stub teeth

The largest gear with a specified pinion that is interference-free is G P

P G

G

N N n n

m = / = /

 + ^{2 ). sin} φ 

1

( m

_G

The largest gear with a specified pinion that is interference-free is

20 20

2. Design for pitting resistance (contact stress)

22 22

2- AGMA Design (Design for contact stress):

24 24

v : velocity (m/s) d : Pitch diameter of pinion (mm) n : speed (rpm) W ^t : Transmitted load (N) P : Power (hp)

26 26

K

_v

: Dynamic factor, K

_v

=1.1~1.4

v : velocity (m/s) Q: quality number

Q: quality number

for most commercial quality gear : 3---7 for precision quality : 8---12

Ks : Size factor, Standard size factors for gear teeth have not yet been established for cases where there is a detrimental size effect

Ks = 1

28 28

K^m = Load-Distribution Factor

mm 25

F

025

.

 0

≤ F −

mm 25

F

025

. 10 0

 3



≤

<

×

× +

−

≤

−

= F ⁻

d F

K^m = Load-Distribution Factor

30 30

K^m = Load-Distribution Factor

Condition A B C

Open gearing 0.247 6.57 e-04 -1.19 e-07

Commercial, enclosed units 0.127 6.22 e-04 -1.44 e-07 Precision, enclosed units 0.0675 5.04 e-04 -1.44 e-07 Precision, enclosed units 0.0675 5.04 e-04 -1.44 e-07 Extra precision enclosed gear units 0.0036 4.02 e-04 -1.27 e-07

32 32

m F

m 5

3 π ^{≤ ≤} π

34 34

S = 1 S

_F

= 1

K

_T

= 1 for T < 250 °C

36 36

38 38

W ^t : Transmitted load (N) , (Defined before) K^o : Over Load Factor , (Defined before) K_v : Dynamic factor , (Defined before) Ks : Size factor , (Defined before) K^m : Load-Distribution Factor , (Defined before) d = d_P : Pitch diameter of pinion (mm) , (Defined before) F : Net face width (mm) , (Defined before) C_f : Surface condition factor

C_f : Surface condition factor

-- Standard surface conditions for gear teeth have not yet been established.

I : Geometry factor of pitting resistance

m_G = Gear ratio (never less than 1)

n n

N N

m = / = /

Φ_t = Pressure Angle = 20°

m_N = Load-sharing ratio = 1 (for spur gear )

40

G P

P G

G

N N n n

m = / = /

40

Z_N = Stress cycle factor for pitting resistance

42 42

C_H = Hardness-ratio factor H = Brinell hardness of gear H_BG = Brinell hardness of gear H_BP = Brinell hardness of pinion

S = Safety factor—pitting

S

_H

= 1

S_H = Safety factor—pitting

KT : Temperature Factor , (Defined before) K^R : Reliability Factor , (Defined before)

44 44

7$ ،9ا< ر= >?ا '= @. ه+ار(

W^t , K_v , K_m , m ,F 7$ ،9ا< ر= >?ا '=

ط 7 Pinion

ا Gear .

لو س9

?D( و # ه+ار( - ) راE د ?D( ز Fه F =

&? راGHF ار 4πm (

W , K_v , K_m , m ,F

&? راGHF ار 4πm (

رد +>% لو F < 3πm

Machine Component’s Design II Machine Component’s Design II

Helical Gear

The initial contact of spur-gear teeth is a line extending all the way across the face of the tooth. The initial contact of helical- of the tooth. The initial contact of helical- gear teeth is a point that extends into a line

The smooth transfer of load from one tooth to another that gives helical gears the ability to transmit heavy loads at high speeds.

2

Ф_n = Normal pressure angle , Ф=20°

Ф_t = Transverse pressure angle Ψ = Helix angle

cos ) ( tan

tan

^{1 n}

ψ φ

_t

=

⁻

φ

48

,

_x ^t

n t

m m

m = m =

ψ ψ ^{, tan}

cos

^x

t

m

m = =

Next Choice: 1.125, 1.375, 1.75, 2.25, 2.75, 3.5, 4.5, 5.5, 7, 9, 11, 14, 18, 22, 28, 36, 45

Modules selection:

Preferred: 1, 1.25, 1.5, 2, 2.5, 3, 4, 5, 6, 8, 10, 12, 16, 20, 25, 32, 40, 50 For upper Power

Parallel shafts The helix angle is the same on each gear, 22, 28, 36, 45

50 4

other reasons, it may be desirable to use double helical gears. A double helical gear (herringbone) is equivalent to two helical gears double helical gear (herringbone) is equivalent to two helical gears of opposite hand, mounted side by side on the same shaft.

52 6

Φ = Pressure Angle

k = 1 for full-depth teeth, 0.8 for stub teeth

The largest gear with a specified pinion that is interference-free is G P

P G

G

N N n n

m = / = /

 + ² m

_G

^{). sin} φ

_t



1 (

The largest gear with a specified pinion that is interference-free is

°

°

=

=

≥ 2 π ^m

_x

⇒ ψ

_min

21 . 8 , ψ

_max

33 . 7 F

1 )

t

t

F m

m 5 . . .

.

3 π ≤ ≤ π

=

=

≥ 2 π ^m

_x

⇒ ψ

_min

21 . 8 , ψ

_max

33 . 7 F

2 )

ψ

min

ψ <

ψ ψ >

ا ا

ﺩﻮﺷ ﯽﻤﻧ ﺭﺍﺮﻗﺮﺑ ﺰﮔﺮﻫ ﻝﻭﺍ ﻁﺮﺷ ﺩﻮﺷ ﺭﺍﺮﻗ ﺮﺑ ﻡﻭﺩ ﻁﺮﺷ ﻭ .

ﺩﻮﺷ ﯽﻣ ﺭﺍﺮﻗﺮﺑ ﺎﻤﺘﺣ ﻝﻭﺍ ﻁﺮﺷ ﺩﻮﺷ ﺭﺍﺮﻗ ﺮﺑ ﻡﻭﺩ ﻁﺮﺷ ﻭ

.

ψ > ψ

_max

ψ ψ

ψ < <

ﺩﻮﺷ ﯽﻣ ﺭﺍﺮﻗﺮﺑ ﺎﻤﺘﺣ ﻝﻭﺍ ﻁﺮﺷ ﺩﻮﺷ ﺭﺍﺮﻗ ﺮﺑ ﻡﻭﺩ ﻁﺮﺷ ﻭ

ا

.

ﺖﺴﻴﻧ ﺺﺨﺸﻣ ﻝﻭﺍ ﻁﺮﺷ ﯼﺭﺍﺮﻗﺮﺑ ،ﺩﻮﺷ ﺭﺍﺮﻗ ﺮﺑ ﻡﻭﺩ ﻁﺮﺷ ﻭ .

t

J

s v

o

K K F m

K

= W

σ F m

_t

J

R T

N f

t

all

K K

Y S

= S σ

Gear bending endurance strength equation:

2- AGMA Design (Design for contact stress):

2 /



1

 K C

Gear contact stress equation:

10

2 / 1

F  





 



= 

I C d

K K K K W

C

^f

P m s

v o t P

σ

C

R T H

H N C all

C

S K K

C Z

= S σ

,

Gear contact endurance strength equation:

56

σ =

t

J

s v

o

K K F m

K

= W σ

R T

N f

t

all

K K

Y S

= S σ

Gear bending endurance strength equation:

v : velocity (m/s) d : Pitch diameter of pinion (mm)

n : speed (rpm)

P

t

N

m d = .

n : speed (rpm) W ^t : Transmitted load (N) P : Power (hp)

58 12

K

_v

: Dynamic factor, K

_v

=1.1~1.4

v : velocity (m/s) Q: quality number

Q: quality number

for most commercial quality gear : 3---7 for precision quality : 8---12

Ks : Size factor, Standard size factors for gear teeth have not yet been established for cases where there is a detrimental size effect

Ks = 1

60 14

K^m = Load-Distribution Factor

mm 25

F

025

.

 0

≤ F −

mm 25

F

025

. 10 0

 3



≤

<

×

× +

−

≤

−

= F ⁻

d F

K^m = Load-Distribution Factor

62 16

K^m = Load-Distribution Factor

Condition A B C

Open gearing 0.247 6.57 e-04 -1.19 e-07

Commercial, enclosed units 0.127 6.22 e-04 -1.44 e-07 Precision, enclosed units 0.0675 5.04 e-04 -1.44 e-07 Precision, enclosed units 0.0675 5.04 e-04 -1.44 e-07 Extra precision enclosed gear units 0.0036 4.02 e-04 -1.27 e-07

64 18

module

Transverse

t : m

F : Net face width

t

t

F m

m 5 . . .

.

3 π ≤ ≤ π

F : Net face width

J : Geometry factor for bending strength

66 20

68 22

S = 1 S

_F

= 1

K

_T

= 1 for T < 250 °C

K

F  

 



= 

I d

K K K K W

C

^f

P m s

v o t P

σ

C

R T H

H N C all

C

S K K

C Z

= S σ

,

Gear contact endurance strength equation:

70 24

W ^t : Transmitted load (N) , (Defined before) K^o : Over Load Factor , (Defined before) K_v : Dynamic factor , (Defined before) Ks : Size factor , (Defined before) K^m : Load-Distribution Factor , (Defined before) d = d_P : Pitch diameter of pinion (mm) , (Defined before) F : Net face width (mm) , (Defined before) C_f : Surface condition factor

C_f : Surface condition factor

-- Standard surface conditions for gear teeth have not yet been established.

C_f =1

72 26

I : Geometry factor of pitting resistance

m_G = Gear ratio (never less than 1)

n n

N N

m

_G

= N

_G

/ N

_P

= n

_P

/ n

_G

m = / = /

tan ) (

tan

¹

φ

ⁿ

φ =

⁻

I : Geometry factor of pitting resistance

Z

m

_N

m

^{n n}

95

. 0

cos φ π ×

= ×

t g

p t

g g

t p

p

a r r a r r r

r

Z = ( + )

²

− ( . cos φ )

²

+ ( + )

²

− ( . cos φ )

²

− ( + ). sin φ

28

r

_P : Pitch radius of pinion (mm)

r

_g : Pitch radius of gear (mm)

a

: addendum (for Ф_n=20 , a=m_n)

A B C

IF A>C A=C IF B>C B=C

74

Z_N = Stress cycle factor for pitting resistance

76 30

C_H = Hardness-ratio factor H = Brinell hardness of gear H_BG = Brinell hardness of gear H_BP = Brinell hardness of pinion

S = Safety factor—pitting

S

_H

= 1

S_H = Safety factor—pitting

KT : Temperature Factor , (Defined before) K^R : Reliability Factor , (Defined before)

78 32

345 ،#1ا8 ر 9 :;ا 9<

=> هار ?- W^t , K_v , K_m , I , m ,F واز ند- دز 345 ،#1ا8 ر 9 :;ا 9<

طB 3&

Pinion /&ا Gear

.

لو( س(1

;E و F(4 G 2هار %&' ) را(H دB ;E ز Iه F =

J ;- # 2راKLI ار 4πm (

ن واز ند- دز

/+ز و ر ترNB? لوا

4πm_t J ;- # 2راKLI ار

(

رد :NB- لو(

F < 3πm

YES

Machine Component’s Design II

Bevel Gears

Hypoid gears Hypoid gears Spiroid gears

Straight bevel gear Spiral bevel gear

2

Straight bevel gear Spiral bevel gear

Hypoid gears

82

84 4

1000

60 × V

v : velocity (m/s) d_av: Average diameter (mm) d_av=d - F.cos Γ

d : Outer pitch diameter (mm) F : Face Width (mm) n : speed (rpm) W^t : Transmitted load (N) P : Power (hp) Φ : Pressure angle

6

Φ : Pressure angle

γ φ

γ φ

sin . tan .

cos .

tan .

t a

t r

W W

W W

=

=

86

J m F K K

K K W

x s v

1000

o

σ =

J m F K

_x

R T

L f

t

all

K K

K S

= S σ

Gear bending endurance strength equation:

2- AGMA Design (Design for contact stress):

2 /



1

 C

Gear contact stress equation:

2 / 1

1000  





 



= 

I Fd C C

K K K W

C

_P ^t _{o v m s} ^xc

σ

C

1000 60 ×

=

V W = V d = m

_et

. N

v : velocity (m/s) n : speed (rpm) d : Outer diameter (mm) P : Power (hp) W^t : Transmitted load (N) m_et : Outer module

1000

60 × V

88 8

v

_et : Outer velocity (m/s) Q_v: quality number

for most commercial quality gear : 3---7 for precision quality : 8---12

10

F : Net face width

module Outer

: m

et

m ₌

90

92 12

S

_F

= 1

94 14

W^t : Transmitted load (N) , (Defined before) K : Over Load Factor , (Defined before)

96 16

98 18

100 20

S = Safety factor—pitting

S

_H

= 1

S_H = Safety factor—pitting

K^T : Temperature Factor , (Defined before) K^R : Reliability Factor , (Defined before)

ط را

Machine Component’s Design II Machine Component’s Design II

Worm Gears

118 16

120 18

لو س b لو N_G لو س

اور 1,2,3,4

N_G لو

b

لو

a 5,6,7,8 اور

لوا ط اور

9,10,11

ندرو! "

را#

F_e زا %د&ا

'()ا ل* +(, -./01