HES3350 Machine Design, Assignment 2: Gear Specification with Consideration of Bending Fatigue and...

7/30/2019 HES3350 Machine Design, Assignment 2: Gear Specification with Consideration of Bending Fatigue and Surface Du

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SWINBURNE UNIVERSITY OF TECHNOLOGY (SARAWAK CAMPUS)

FACULTY OF ENGINEERING AND INDUSTRIAL SCIENCE

HES3350 Machine DesignSemester 1, 2012

Assignment 2: Gear Specification with Consideration of Bending Fatigue and Surface

Durability

By

Group 9

Stephen, P. Y. Bong (4209168)

Kueh Min Hui (4209974)

Mohd Azmudin Bin Isa @ Danial (4209028)

Jimmy Huong How Lee (4209761)

Lecturer: Dr. Soon Kok Heng

Due Date: 4 pm, 27th

April 2012 (Thursday)


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Assignment 2 Group 9

HES3350 Machine Design, Semester 1, 2012 Page 2 of21

1. OBJECTIVEThe principal objective of this assignment is to select appropriate spur gears for a two-stage

compound reverted gear train from the gear catalog provided. Apart from that, the computations of

the maximum module, the face width, and the material used for the gears with the consideration of

bending fatigue and surface durability are also the purposes of this assignment as well.

2. INTRODUCTIONWith the operating parameters provided such as the amount of power to be delivered, the number of

teeth for Gear 1, 2, 3 and 4, the input speed, the maximum gearbox height, the clearance and wall

thickness, and the pressure angle; we are required to determine the maximum module and select

appropriate spur gears for the two-stage compound reverted gear train from the gear catalog given

based on the prerequisite stated which is the safety factor should not exceed 2.2. In addition, the

determination of the face width and the material used, and the identification of the most critical gear

are incorporated in this report as well. The spur gears are selected from the gear catalog with the

consideration of bending fatigue and surface durability.

Since the assignment by all means, cannot be tantamount to a real life design project as most of the

selection of operating parameters such as the dynamic factor and the surface factor for the

computations of bending stresses and endurance limit respectively are based on experimental data

or charts provided and appropriate assumptions for instance the surfaces in contact (bore and shaft)

are frictionless and thus there has no power losses through the transmission. By neglecting the

power losses due to friction and surface roughness as a result of various manufacturing

methodology and heat treatment processes, we only centralize our design based on the bending

fatigue and surface durability in the selection of spur gears.

3. MAIN CONTENT3.1 Parameters and Schematic Diagram for the Two-stage Compound Reverted Gear

Train in the Gearbox

The schematic diagram of the gearbox is shown in Fig. 1 below:

Fig. 1: Schematic of the gearbox


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The operating parameters given are tabulated in Table 1 below:

Power to be delivered, 9 kWN1 &N3 42 Teeth

N2 &N4 86 Teeth

Input speed, 1 2300 rpm

Maximum Gearbox Height,H 600 mmClearance and Wall Thickness 20 mm

Pressure angle for spur gear, 20Expected life for 40 hr./week, 50 week/year operation 3.25 years

Table 1: Operating parameters

where the Maximum Gearbox Height,His given by the following equation:

ThicknessWallClearance2

22

412 +++++= m

dddH

where m is the module and d1 = mN1, d2 = mN2 and d4 = mN4.

3.2 Calculations and Selection of Maximum Module and Face WidthBased on the operating parameters given, the module of the gear train can be determined by using

the relation of gears diameters and maximum height of gearbox:


412 +++++= m

dddH

SinceN2 =N4, therefore, d2 = d4 and the equation above can be expressed as:


3

2


21

21

2

++++=

+++++=

mdd

H

mdd

dH

Substituting d1 = mN1 and d2 = mN2 into equation above yields:

22

3

2

Thickness)Wall(Clearance

21++

+=NN

Hm

Since the KHK Gear Catalog does not have spur gears with 86 teeth, therefore, spur gears with 85

teeth has been selected in the analysis. Given that N1 = 42 Teeth,N2 = 85 Teeth,H= 600 mm and

Clearance + Wall Thickness = 20 mm, hence the module can be computed as follows:

Toothmm3.8538=

++

=

++

+=

22

Teeth)85(3

2

Teeth42

mm20mm600

22

3

2

)ThicknessWallClearance(

21 NN

Hm


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Based on the computations of module above, the module employed for the two-stage compound

reverted gear train must not exceed m = 3.85388 mm/Tooth. In addition, according to KHK Gear

Catalog, spur gears with module of 2 have the closest number of teeth (N= 85 Teeth) to the number

of teeth for gears 2 and 4 given in this assignment. As a result, steel spur gears with 85 Teeth and

module 2 has been chosen in the analysis of gear tooth strength and surface durability.

According to KHK Gear Catalog, Steel Spur Gears with 42 and 85 Teeth with module of 2 haveface widths of 20 mm (See KHK Gear Catalog in Appendix):

mm20Toothmm20

Teeth42146)pp.Catalog,Gear(KHK

31=

=

== b

m

NN

mm20Toothmm20

Teeth85156)pp.Catalog,Gear(KHK

42=

=

== b

m

NN

Therefore, b1 = b2 = b3 = b4 = 20 mm.


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3.3 Analysis of Gear Tooth Strength3.3.1 Bending Fatigue Analysis by Using Steel Spur Gear with Module 2For m = 2 mm/Tooth,

( )( )( )( )

( )( )

( )( ) mm170Teeth58Toothmm2

mm84Teeth42Toothmm2

mm170Teeth58Toothmm2mm84Teeth42Toothmm2

44

33

22

11

===

===

===

===

mNd

mNd

mNdmNd

The gear ratio for a pair of spur gears (pinion and gear) is given by:

p

g

g

p

d

d=

where

g = Angular velocity of gearp = Angular velocity of piniondg = Diameter of gear

dp = Diameter of pinion

By using the relation of gear ratio above, the angular velocity of gear 2 can be obtained:

rpm1136.47=

=

== mm170

mm48rpm2300

2

112

1

2

2

1

d

d

d

d

Since gear 2 and gear 3 are located on the same shaft, therefore,

rpm1136.47== 23

The speed ratio for double-reduction gear train is given by:

rpm561.55=

=

==

8585

4242rpm2300

42

3114

31

42

4

1

NN

NN

NN

NN


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Stage 1 (Gear 1 & Gear 2)

Pitch Line Velocity,60000

dV=

sm10.12=

===

===1Stage

222

11

1

sm12.0160000

rpm)7mm)(1136.4170(

60000:2Gear

sm12.0160000

rpm)mm)(230084(

60000:1GearV

dV

d

V

Tangential Forces, Ft= /V

N889.33=

===

===

1Stage,

1Stage2

1Stage1

N33.889sm10.12W9000:2Gear

N33.889sm10.12W9000:1Gear

t

t

tF

VWF

VWF

Gear Tooth Bending Stress, movt KKK

bJm

F=

From Figure 14-6 (Budynas, R. G. & Nisbett, J. K., pp. 753), the Geometry Factor for spur

gears of 42 Teeth and 85 Teeth areJ1, 30.2725 andJ2,40.295.


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minft1992.13===m.30430

ft1

min1

s60

s

m12.10sm12.101StageV

Velocity (Dynamic) Factor,78

78 VKv

+= (Highest precision, shaved and ground)

1.2539=+

=+

==78

13.199278

78

78 1StageVKK vv

From TABLE 15.1 (Juvinall, R. C. & Marshek, K. M., pp. 615), the Overload Correction

Factor, Ko = 1 (Uniform source of machinery and power)

From TABLE 15.2 (Juvinall, R. C. & Marshek, K. M., pp. 616), the Mounting Factor,

Km = 1.3 (Accurate mounting, small bearing clearance, minimum deflection)

MPa132.99=== )3.1)(1)(2539.1(Tooth)mm)(2mm)(0.272520(

N33.889

11

1Stage,

1 mov

tKKK

mJb

F

MPa122.85=== )3.1)(1)(2539.1(Tooth)mm(2mm)(0.295)20(

N33.889

22

1Stage,

2 mov

tKKK

mJb

F


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dV=

sm4.8895=

===

===2Stage

444

33

3

sm9985.460000

rpm)mm)(561.55170(

60000:4Gear

sm9985.460000

rpm)7mm)(1136.484(

60000:3GearV

dV

d

V


N1800.54=

===

===

2Stage,

2Stage4

2Stage3

N54.1800sm4.9985W9000:4Gear

N54.1800sm4.9985W9000:3Gear

t

t

tF

VWF

VWF


bJm

F=




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minft983.96===m.30430

ft1

min1

s60

s



78 VKv


1.1844=+

=+

==78

96.98378

78

78 1StageVKK vv





MPa269.19=== )3.1)(1)(2539.1(Tooth)mm)(2mm)(0.272520(

N54.1800

33

2Stage,

3 mov

tKKK

mJb

F

MPa248.73=== )3.1)(1)(2539.1(Tooth)mm(2mm)(0.295)20(

N54.1800

44

2Stage,

4 mov

tKKK

mJb

F

By comparing the four bending stresses above, the maximum bending stress is max = 3 = 269.19

MPa.


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The gear in the gear train which is subjected to the highest tooth bending stresses is the one which

has the largest possibility to fail in advance. Based on the stresses computed above, max = 269.19MPa and therefore the critical gear is Gear 3.

Refined Analysis of Gear-Tooth Bending Strength Endurance Limit

msKKKCCCSS trSGLnn =

whereun SS 5.0=

Since the Steel Spur Gears are made of S45C Steel with a maximum Brineel Hardness of 194 HB,

therefore, the tensile strength, Su, can be determined by using the relation:

Su = Kh(HB) = (3.45)(194) MPa = 669.3 MPa (Kh = 3.45 in SI Units)

( ) MPa65.334MPa3.6695.05.0 === un SS

Load Factor, CL = 1 (Bending loads)

)5(1

in.Teeth7.12

mm25.4

in.1mm170

Teeth58

in.Teeth7.12

mm25.4in.1mm84

Teeth42

in.Teeth7.12

mm25.4

in.1mm170

Teeth58

in.Teeth7.12

mm25.4

in.1mm84

Teeth42

4

44

3

33

2

22

1

11

>=

=

==

=

==

=

==

=

==

PC

D

NP

D

NP

D

NP

D

NP

G

From TABLE 15.3 (Juvinall, R. C. & Marshek, K. M., pp. 615), the Reliability Correction

Factor, Kr= 1 (50% Reliability)

Temperature Factor, Kt= 1 (Assumed the temperature lower than 160 F)

Mean Stress Factor, Kms = 1 (Gear 3 is idler)


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From FIGURE 8.13 (Juvinall, R. C. & Marshek, K. M., pp. 301), the Surface Factor,

CS= 0.76 (Machined or cold-drawn)

Therefore, the endurance limit is computed as follows:

MPa254.334=

=

=

1)76)(1)(1)(MPa)(1)(0.(334.65

msKKKCCCSS trSGLnn

Safety Factor, 0.9448===MPa19.269

MPa334.254SF

max

nS

Since the safety factor obtained above is less than 2.2 in which the pre-requisites is not

satisfied. Therefore, Steel Spur Gear with module of 2 cannot be employed in the double-reduction gear train. As a result, Steel Spur Gear with module of 3 has been selected for the

application.


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3.3.2 Bending Fatigue Analysis by Using Steel Spur Gear with Module 3 (N2 =N4 = 90)For m = 3 mm/Tooth,

( )( )

( )( )

( )( )

( )( ) mm270Teeth09Toothmm3

mm126Teeth42Toothmm3



44

33

22

11

===

===

===

===

mNd

mNd

mNd

mNd

The gear ratio for a pair of spur gears (pinion and gear) is given by:

p

g

g

p

d

d=

where

g = Angular velocity of gearp = Angular velocity of piniondg = Diameter of gear

dp = Diameter of pinion

By using the relation of gear ratio above, the angular velocity of gear 2 can be obtained:

rpm1073.33=

=

==

mm270

mm261rpm2300

2

112

1

2

2

1

d

d

d

d

Since gear 2 and gear 3 are located on the same shaft, therefore,

rpm1073.33== 23

The speed ratio for double-reduction gear train is given by:

rpm500.89=

=

==

0909

4242rpm2300

42

3114

31

42

4

1

NN

NN

NN

NN


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dV=

sm15.17=

===

===1Stage

222

11

1

sm17.1560000

rpm)3mm)(1073.3270(

60000:2Gear

sm17.1560000

rpm)mm)(2300126(

60000:1GearV

dV

d

V


N593.28=

===

===

1Stage,

1Stage2

1Stage1

N28.593sm15.17W9000:2Gear

N28.593sm15.17W9000:1Geart

t

tF

VWF

VWF


bJm

F=




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minft2991.13===m.30430

ft1

min1

s60

s



78 VKv


1.3043=+

=+

==78

13.199278

78

78 1StageVKK vv





MPa41.02=== )3.1)(1)(3043.1(Tooth)mm)(3mm)(0.272530(

N93.285

11

1Stage,

1 mov

tKKK

mJb

F

MPa37.57=== )3.1)(1)(3043.1(Tooth)mm)(3mm)(0.297530(

N93.285

22

1Stage,

2 mov

tKKK

mJb

F


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dV=

sm7.079=

===

===2Stage

444

33

3

sm079.760000

rpm)mm)(500.89270(

60000:4Gear

sm079.760000

rpm)3mm)(1073.3126(

60000:3GearV

dV

d

V


N1271.37=

===

===

2Stage,

2Stage4

2Stage3

N37.1271sm7.079W9000:4Gear

N37.1271sm7.079W9000:3Geart

t

tF

VWF

VWF


bJm

F=




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minft23.23===m.30430

ft1

min1

s60

s



78 VKv


1.0304=+

=+

==78

23.2378

78

78 2StageVKK vv





MPa69.44=== )3.1)(1)(0304.1(Tooth)mm)(3mm)(0.272530(

N37.1271

33

2Stage,

3 mov

tKKK

mJb

F

MPa63.61=== )3.1)(1)(0304.1(Tooth)mm(3mm)(0.295)30(

N34.1271

44

2Stage,

4 mov

tKKK

mJb

F

By comparing the four bending stresses above, the maximum bending stress is max = 3 = 69.44

MPa.


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The gear in the gear train which is subjected to the highest tooth bending stresses is the one which

has the largest possibility to fail in advance. Based on the stresses computed above, max = 269.19MPa and therefore the critical gear is Gear 3.

Refined Analysis of Gear-Tooth Bending Strength Endurance Limit

msKKKCCCSS trSGLnn =

whereun SS 5.0=

Since the Steel Spur Gears are made of S45C Steel with a maximum Brineel Hardness of 194 HB,

therefore, the tensile strength, Su, can be determined by using the relation:

Su = Kh(HB) = (3.45)(228) MPa = 786.6 MPa (Kh = 3.45 in SI Units)

( ) MPa3.393MPa86.675.05.0 === un SS

Load Factor, CL = 1 (Bending loads)

)5(1

in.Teeth4667.8

mm25.4

in.1mm270

Teeth58

in.Teeth4667.8

mm25.4in.1126mm

Teeth42

in.Teeth4667.8

mm25.4

in.1mm270

Teeth09

in.Teeth4667.8

mm25.4

in.1mm126

Teeth42

4

44

3

33

2

22

1

11

>=

=

==

=

==

=

==

=

==

PC

D

NP

D

NP

D

NP

D

NP

G

From TABLE 15.3 (Juvinall, R. C. & Marshek, K. M., pp. 615), the Reliability Correction

Factor, Kr= 1 (50% Reliability)

Temperature Factor, Kt= 1 (Assumed the temperature lower than 160 F)

Mean Stress Factor, Kms = 1 (Gear 3 is idler)


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From FIGURE 8.13 (Juvinall, R. C. & Marshek, K. M., pp. 301), the Surface Factor,

CS= 0.74 (Machined or cold-drawn)

Therefore, the endurance limit is computed as follows:

MPa291.042=

=

=

1)74)(1)(1)(MPa)(1)(0.(393.3

msKKKCCCSS trSGLnn

Safety Factor, 4.19===MPa9.446

MPa042.291SF

max

nS

Since the safety factor is equal 4.19 (SF > 2.2), therefore, the pre-requisite is attained and Steel Spur

Gears with module 3 and face width of 30 mm has been selected from the KHK Gear Catalog forthe double-reduction gear train.


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3.4 Analysis of Surface Durability of Tooth SurfaceThe critical gear (Gear 3) has been selected for the analysis of surface durability as it is subjected to

maximum bending stress.

Surface Fatigue Stress,mov

p

t

p

g

g

p

p

gp

t

HKKK

Ibd

FC

E

v

E

vb

ddF

=

+

+

=22

11cos

sin

2

sin

2

564.0

Gear 3: Ft3 = 1271.37 N, b = 30 mm = 0.03 m, dp = d3 = 126 mm = 0.126,R = dg/dp = 270/126 =

2.14. From previous calculations, Kv = 1.0304, Ko = 1 and Km = 1.3.

From TABLE 15.4b (Juvinall, R. C. & Marshek, K. M., pp. 621), the Surface Factor, the Values of

Elastic Coefficient Cp for Spur Gears is Cp = 191 ( )Pa10191MPa 3= .

Geometry Factor, 1024.0114.2

14.2

2

20cos20sin

12

cossin=

+

=

+=R

RI

Surface Fatigue Stress, MPa123.8===m)(0.1024)m)(0.126(0.03

(1)(1.3)N)(1.0304)37.1271(mov

p

t

HKKK

IbdF

Surface Fatigue Strength, SH= SfeCLiCR

The angular velocity of gear 3, 3 = 1073.33 rpm and given that the expected life for 40 hr/week,and 50 week/year operation is 3.25 years. Therefore, the Surface Fatigue Life (Cycle) is given by:

Cycle102.4hr1

min60years25.3

year

week50

week

hr40

min

rev1073.33LifeFatigueSurface

8=


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From FIGURE 15.27 (Juvinall, R. C. & Marshek, K. M., pp. 624), the Life Factor, CLi = 0.83 for a

surface fatigue life of 4.2(108) Cycle.

From TABLE 15.6 (Juvinall, R. C. & Marshek, K. M., pp. 625), the Reliability Factor, CR = 1.25

for a reliability of 50%.

From TABLE 15.5 (Juvinall, R. C. & Marshek, K. M., pp. 624), the relation for the computation of

the Surface Hardness, Sfe, is Sfe = 2.8(Bhn) 64 MPa.


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Since the maximum Brineel Hardness of the Steel Spur Gear is 228 HB or 228 Bhn, therefore, the

surface hardness can be determined by using the relation above:

Sfe = 2.8(228 Bhn) 64 MPa = 574.4 MPa

Thus, the Surface Fatigue Strength SHcan be computed as follows:

SH= (574.4 MPa)(0.83)(1.25) = 595.94 MPa

Checking of Safety Factor for Surface Durability:

4.8===MPa123.9

MPa94.595SFFactor,Safety

H

HS

Since the Safety Factor SF = 4.8 (> 2.2), therefore, the selection and utilization of Steel Spur Gear

with module of 3 from the KHK Gear Catalog will not results in any operating failure. As a verdict,

based on the analysis of bending fatigue and surface durability of gear tooth strength above and asin previous section, it is ascertain that the Steel Spur Gear with Module 3 from the KHK Gear

Manufacturer can be employed in the compound-reverted gear train. 2 models have been selected

from the KHK Gear Catalog due to the same size of pinions and gears.

Gear 1 & Gear 3 (Pinion):

42TeethofNumber3ModuleGearSpurS45C:Steel

423SS=

Gear 2 & Gear 4 (Gear):

90TeethofNumber3ModuleGearSpurS45C:Steel

903SS=

The material used for the spur gears is Steel S45C with Brineel Hardness of 228 HB or 228 Bhn.

HES3350 Machine Design, Assignment 2: Gear Specification with Consideration of Bending Fatigue and...

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