Spur Gear - Chulapioneer.netserv.chula.ac.th/~rchanat/2183351_ME Design/CRW02_Spur... · Spur Gear....

Spur Gear

2103320 Des Mach Elem Mech. Eng. Department

Chulalongkorn University

Introduction

Gear • Transmit power, rotation

• Change torque, rotational speed

• Change direction of rotation

Friction Gear

Less slip

Small gear “Pinion”

(usually driving)

Large gear “Gear”

+ +

Slip

Gear tooth nomenclature (1)

+ +

Pitch circle

Pitch cylinder

Pitch surface

+

Center distance

Same

transmission

The pitch circle is a theoretical circle

upon which all calculations are usually

based; its diameter is the pitch diameter.

Depend on the types of gears

Center distance

+ +


• Circular pitch (CP) = π D/z • Diametral pitch (DP) = z/D (inch.) • Module (m) = D/z (mm)

D = pitch dia. z = number of teeth

• m = 25.4/DP • CP×DP = p

Module and tooth size

Module sizes shown are converted inch sizes

โมดูลเลือก โมดูลเลือก

อันดับสอง อันดับสอง

0.1 0.15 1.5 1.75

0.2 0.25 2 2.25

0.3 0.35 2.5 2.75

0.4 0.45 3 3.5

0.5 0.55 4 4.5

0.6 0.7 5 5.5

0.8 0.75 6 7

1 0.9 8 9

1.25 10 11

โมดูลนิยม โมดูลนิยม

Standard module Pressure angle Diametral Pitch

For inch Size gears

Module

For metric Size gears 14.5° 20°

1st choice 1st choice 2nd choice 2nd choice


Pressure angle (deg.)

14.5 (FD) 20 (FD) 20 (Stub)

Addendum a m m 0.8m

Dedendum b 1.157m 1.25m m

FD: Full depth

Stub: Tooth is shorter than FD

Tooth height a+b

Working depth a1+a2

Top diameter (Addendum dia.)

Do = D+2a

Root diameter (Dedendum dia.)

Dr = D-2b

Clearance b-a

Involute Curve

Gear profile is designed to be involute curve. With this design the velocity ratio of a

gear pair is constant all the time.

Base cylinder is the circle used to construct an involute curve (not a dedendum circle

and cannot be located with the naked eye

Base cylinder

Involute curve

Construction of

an involute curve Involute curve

Pressure angle (1)

φ = Pressure angle (14.5°, 20°, 25°)

φcospb rr =

• Line of action (pressure line)

line that tangent with the base

circles and pass the pitch point

• During meshing, transmitted

force acts along the line of action

φ

Line of action (Pressure line) is perpendicular to

Contact surface at contact point

Line tangent with the

pitch circle

φ

φ

Pitch circle

Pressure angle (2)

φ

Line of action (Pressure line) is perpendicular to

Contact surface at contact point

Driving

Driven

Base circle

Line tangent with the

pitch circle

φ

φ

Pitch circle

Velocity ratio

ω1(rad/s) n1(rpm)

D1 z1

ω2(rad/s) n2(rpm)

D2 z2

1

2

1

2

2

1

2

1

zz

DD

nnm ====

ωω

ω

+

+

Gear ratio & Center distance (1)

Example Center distance 240 mm

module 3 mm

Velocity ratio 5:1

Pressure angle 20°

1

2

1

2

2

1

2

1

zz

DD

nnm ====

ωω

ω

1

2

1

2

15

zz

DDm ===ω

Gear dia : Pinion dia

5:1

Divide the center distance into 5+1 = 6 parts

Each part = 240/6 = 40 mm

R=200

R=40

240

40

Rpinion = 40, Dia. = 80

z = D/m = 80/3 = 26.6 No. of pinion teeth choose 27 teeth

No. of gear teeth zgear = 5 × zpinion = 5 × 27 = 135

Dia. Pitch D = m×z 81 405

Center distance = (Dpinion+Dgear)/2 243

Dia. Addendum = D+2a = D+2m 87 411

Dia. Base = D×cos(PA) = D×cos(20°) 76.115 380.58

Addendum = m 3

Dedendum = 1.25m 3.75

Tooth depth = a+b 6.75

Tooth thickness = πD/2z = πm/2 4.712

pinion gear

(240)


z = D/m = 80/3 = 26.6 choose 26 teeth

Dia. Pitch D = m×z 78 402

Center distance = (Dpinion+Dgear)/2 240

Dia. Addendum = D+2a = D+2m 84 408

Dia. Base = D×cos(PA) = D×cos(20°) 73.30 377.76

Addendum = m 3

Dedendum = 1.25m 3.75

Tooth depth = a+b 6.75

Tooth thickness = πD/2z = πm/2 4.712

pinion gear

134 Velocity ratio = 134/26 = 5.15


No. of pinion teeth

No. of gear teeth

Gear train

Pin Pout

Increase gear ratio Change direction of rotation

No. of teeth of gear G2 dose not affect

to the ratio

z1 z2

z3

z5

z4

z6

ωi

ωo

mω = ωi/ωo

mω = (z2/z1) (z4/z3) (z6/z5)

Planetary gear train

Epicyclic gear train, Planetary gear train

• Sun gear

• Planet carrier

• Ring gear

Each part can be set to be input,

output or fixed

Various gear ratio

can be obtained

All parts rotate around the center point

Sun gear

Planet carrier


Epicyclic gear train, Planetary gear train

Zs = 60

Zp = 20

ZR = 100

Fixed member

Input

(rpm)

Planet (rpm)

Output (rpm)

Ratio (ωi/ωo)

Ring fix Carrier

9 36

Sun

24 0.375

Sun fix Carrier

9 36

Ring 14.4

0.625

Carrier fix

sun 9

27 Ring 5.4

1.667


http://www.diseno-art.com/encyclopedia/terms/automatic_transmission.html

Gear manufacture

Methods of machining

Form milling : used mostly for large gears. A

milling cutter that has the shape of the tooth

space is used.

Shaping : frequently used for internal gears.

Cutter used reciprocates on a vertical spindle.

Hobbing : similar process to milling except

that both the workpiece and the cutter rotate

in a coordinated manner.

Casting : used most often to make blanks for

gears which will have cut teeth. Possible to

use to make toothed gears with little or no

machining

Milling cutter Hobbing

Shaping

VDO

Gear quality (1)

Quality in gearing is the precision of the individual gear teeth and the precision with

which two gears rotate in relation to one another.

• Runout

• Tooth-to-tooth spacing

• Profile

Schematic diagram of a typical

gear rolling fixture Chart of gear-tooth errors of a typical gear

when run with a specific gear in a rolling

fixture.

Gear quality (2)

• Gear quality is specified by AGMA as quality numbers.

• Quality numbers range from 5 to 15 with increasing precision (AGMA)

• Besides AGMA standard, there are also other standards (JIS, DIN, ISO-similar to DIN)

Selected values for total composite tolerance Table of Gear Precision Grade

Gear quality (3)

Recommended AGMA quality numbers

Pitch line speed:

Velocity at the pitch circle v

pitch circle

Materials

Steel:

• medium-carbon steel is usually used

• Due to low surface endurance capacity, heat treatment (Flame hardening, Induction

hardening, Carburizing, Nitriding) is required

• Surface finishing (grinding) is probably done after heat treatment to obtain high

precision gear

Cast iron:

Cheap, ASTM grade 20, 30, 40, 50, 60 are normally used

surface fatigue strength is higher than bending fatigue strength

Quieter than steel due to the damping property of cast iron

Ductile or nodular cast-iron is probably used to increase strength of gear

Gear force analysis (1)

Pinion

Gear

Base circle Pitch circle

Pressure line

φ

Pinion

Pressure line

φ

F

Fb

Fr

Gear

Pressure line φ

F

Fb

Fr

FBD

Neglect sliding friction in FBD

Gear force analysis (2)

φcosFFb =

φsinFFr =

rFrFT bb ⋅=⋅=

Pinion

Pressure line

φ

F

Fb

Fr

Gear

Pressure line φ

F

Fb

Fr

FBD

( ) ( ) ωωω ⋅⋅=⋅⋅== rFrFTP bb

From FBD

Transmitted torque can be calculated from

Transmitted power can be calculated from

rb = base radius

r = pitch radius

Gear tooth strength

Photoelasic pattern of stresses in a spur gear tooth

Max. stress

position

Contact point Tooth root

Failure Pitting

Crack

Design

principle

Contact stress

Hertzian stress

Bending stress

Lewis equation

Gear tooth bending stress (1)

Fb

L

t

b

Lewis equation

Assumptions

1. Gear tooth is considered as a cantilever beam

2. All transmitted force acts at the tooth tip of a tooth

pair

3. Fr is neglected

4. Sliding friction is neglected

23

6)12/()2/(

btLF

bttLF

IMc bb ===σ

LbtFb 6

2σ=


For constant bending stress

22 const.)(6

ttFbL

b

=

=

σ

The relation between L and t is parabola.

Tooth tip area has more material than parabola,

hence the failure will occur at the tooth root (BED)

From triangle relation

LbtFb 6

2σ=

Lt

tx 2/2/

=x

tL4

2

=

Hence bypppxbFb σσ =

=

32

p : circular pitch

y : Lewis form factor

Y : Lewis form factor

P : Diametral pitch

m : module

PbYFb

σ=

bYmFb σ=

bYPFb=σ

bYmFb=σ

No Teeth Load Near Tip of Teeth Load at Near Middle of Teeth

14 1/2 deg 20 deg FD 20 deg Stub 25 deg 14 1/2 deg 20 deg FD Y y Y y Y y Y y Y y Y y

10 0,176 0,056 0,201 0,064 0,261 0,083 0,238 0,076 11 0,192 0,061 0,226 0,072 0,289 0,092 0,259 0,082 12 0,21 0,067 0,245 0,078 0,311 0,099 0,277 0,088 0,355 0,113 0,415 0,132 13 0,223 0,071 0,264 0,084 0,324 0,103 0,293 0,093 0,377 0,12 0,443 0,141 14 0,236 0,075 0,276 0,088 0,339 0,108 0,307 0,098 0,399 0,127 0,468 0,149 15 0,245 0,078 0,289 0,092 0,349 0,111 0,32 0,102 0,415 0,132 0,49 0,156 16 0,255 0,081 0,295 0,094 0,36 0,115 0,332 0,106 0,43 0,137 0,503 0,16 17 0,264 0,084 0,302 0,096 0,368 0,117 0,342 0,109 0,446 0,142 0,512 0,163 18 0,27 0,086 0,308 0,098 0,377 0,12 0,352 0,112 0,459 0,146 0,522 0,166 19 0,277 0,088 0,314 0,1 0,386 0,123 0,361 0,115 0,471 0,15 0,534 0,17 20 0,283 0,09 0,32 0,102 0,393 0,125 0,369 0,117 0,481 0,153 0,544 0,173 21 0,289 0,092 0,326 0,104 0,399 0,127 0,377 0,12 0,49 0,156 0,553 0,176 22 0,292 0,093 0,33 0,105 0,404 0,129 0,384 0,122 0,496 0,158 0,559 0,178 23 0,296 0,094 0,333 0,106 0,408 0,13 0,390 0,124 0,502 0,16 0,565 0,18 24 0,302 0,096 0,337 0,107 0,411 0,131 0,396 0,126 0,509 0,162 0,572 0,182 25 0,305 0,097 0,34 0,108 0,416 0,132 0,402 0,128 0,515 0,164 0,58 0,185 26 0,308 0,098 0,344 0,109 0,421 0,134 0,407 0,13 0,522 0,166 0,584 0,186 27 0,311 0,099 0,348 0,111 0,426 0,136 0,412 0,131 0,528 0,168 0,588 0,187 28 0,314 0,1 0,352 0,112 0,43 0,137 0,417 0,133 0,534 0,17 0,592 0,188 29 0,316 0,101 0,355 0,113 0,434 0,138 0,421 0,134 0,537 0,171 0,599 0,191 30 0,318 0,101 0,358 0,114 0,437 0,139 0,425 0,135 0,54 0,172 0,606 0,193 31 0,32 0,101 0,361 0,115 0,44 0,14 0,429 0,137 0,554 0,176 0,611 0,194 32 0,322 0,101 0,364 0,116 0,443 0,141 0,433 0,138 0,547 0,174 0,617 0,196 33 0,324 0,103 0,367 0,117 0,445 0,142 0,436 0,139 0,55 0,175 0,623 0,198 34 0,326 0,104 0,371 0,118 0,447 0,142 0,44 0,14 0,553 0,176 0,628 0,2 35 0,327 0,104 0,373 0,119 0,449 0,143 0,443 0,141 0,556 0,177 0,633 0,201 36 0,329 0,105 0,377 0,12 0,451 0,144 0,446 0,142 0,559 0,178 0,639 0,203 37 0,33 0,105 0,38 0,121 0,454 0,145 0,449 0,143 0,563 0,179 0,645 0,205 38 0,333 0,106 0,384 0,122 0,455 0,145 0,452 0,144 0,565 0,18 0,65 0,207 39 0,335 0,107 0,386 0,123 0,457 0,145 0,454 0,145 0,568 0,181 0,655 0,208 40 0,336 0,107 0,389 0,124 0,459 0,146 0,457 0,145 0,57 0,181 0,659 0,21 43 0,339 0,108 0,397 0,126 0,467 0,149 0,464 0,148 0,574 0,183 0,668 0,213 45 0,34 0,108 0,399 0,127 0,468 0,149 0,468 0,149 0,579 0,184 0,678 0,216 50 0,346 0,11 0,408 0,13 0,474 0,151 0,477 0,152 0,588 0,187 0,694 0,221 55 0,352 0,112 0,415 0,132 0,48 0,153 0,484 0,154 0,596 0,19 0,704 0,224 60 0,355 0,113 0,421 0,134 0,484 0,154 0,491 0,156 0,603 0,192 0,713 0,227 65 0,358 0,114 0,425 0,135 0,488 0,155 0,496 0,158 0,607 0,193 0,721 0,23 70 0,36 0,115 0,429 0,137 0,493 0,157 0,501 0,159 0,61 0,194 0,728 0,232 75 0,361 0,115 0,433 0,138 0,496 0,158 0,506 0,161 0,613 0,195 0,735 0,234 80 0,363 0,116 0,436 0,139 0,499 0,159 0,509 0,162 0,615 0,196 0,739 0,235 90 0,366 0,117 0,442 0,141 0,503 0,16 0,516 0,164 0,619 0,197 0,747 0,238 100 0,368 0,117 0,446 0,142 0,506 0,161 0,521 0,166 0,622 0,198 0,755 0,24 150 0,375 0,119 0,458 0,146 0,518 0,165 0,537 0,171 0,635 0,202 0,778 0,248 200 0,378 0,12 0,463 0,147 0,524 0,167 0,545 0,173 0,64 0,204 0,787 0,251 300 0,38 0,122 0,471 0,15 0,534 0,17 0,554 0,176 0,65 0,207 0,801 0,255

Rack 0,39 0,124 0,484 0,154 0,55 0,175 0,566 0,18 0,66 0,21 0,823 0,262

Lewis Form Factor

Y, y

Load near tip of teeth

• Total transmitted force

acts at the tooth tip

(actually at this point

double teeth meshing

occurs, hence the force

acting on a tooth pair is

reduced)

• Safer design

Load near middle of teeth

• Total transmitted force

acts at the position near

the middle of teeth (single

tooth meshing occurs)

• Close to the actual

condition


Lewis form factor, Y or y 1. Y and y increase when no. of teeth is increased

2. More Y or y, gear tooth can withstand more Fb

3. Pinion has lower no. of gear teeth than gear. Pinion can

withstand low load than gear.

4. Calculation is done at pinion bY

PFb=σ

bYmFb=σ

The effect of Fr 1. Compressive stress at B side increase, but tensile stress at

D side decrease.

2. Most material can withstand compressive force more than

tensile force. Fatigue will occur at tensile side.

3. The presence of Fr will increase strength of gear tooth,

since it help to reduce the stress in tensile side

AGMA Stress Equation (bending)

American Gear Manufacturers Association (AGMA) proposed the method to design gear

based on the Lewis equation (bending stress consideration)

bYmFb=σ

Lewis Equation AGMA Equation (bending)

vBmsOJ

tt KKKKK

mFYWs =

Y JYYJ : Geometry factor is Y that include the effect of root fillet stress-concentration factor

KO : Overload factor

Ks : Size factor

Km : Load-distribution factor

KB : Rim thickness factor

Kv : Dynamic factor

K >= 1.0 (Always)

σ

bFts

tWb F

Geometry factor (YJ)

Bending strength geometry factor YJ for full depth teeth spur gears

vBmsOJ

tt KKKKK

mFYWs =

20° pressure angle 25° pressure angle

Overload factor (KO)

Suggested overload factors, KO

Driven Machine

Power source Uniform Light shock

Moderate

shock

Heavy

shock

Uniform 1.00 1.25 1.50 1.75

Light shock 1.20 1.40 1.75 2.25

Moderate shock 1.30 1.70 2.00 2.75

Power sources Uniform: Electric motor, Constant-

speed gas turbine

Light shock: Water turbine, variable-

speed drive

Moderate shock: Multicylinder engine

Driven machine Uniform: Continuous-duty generator

Light shock: Fans and low speed centrifugal pump, variable-duty

generators, uniform loaded conveyors

Moderate shock: High-speed centrifugal pumps, reciprocating pumps

and compressors, heavy duty conveyors, machine tool drives

Heavy shock: Rock crushers, punch press drivers

vBmsOJ

tt KKKKK

mFYWs =

Size factor (Ks)

Suggested size factors, Ks

Diametral pitch, Pd Metric module, m Size factor, Ks

>=5 <=5 1.00

4 6 1.05

3 8 1.15

2 12 1.25

1.25 20 1.40

vBmsOJ

tt KKKKK

mFYWs =

Load dist. factor (Km)

Used to reflect nonuniform distribution of load across the line of contact.

If load is uniformly distributed Km = 1.0

Causes of nonuniform distribution

1. Gear tooth error

2. Misalignment, Eccentricity

3. Deformation of gear, shaft, bearing,

housing

4. Clearance between shaft, gear, bearing,

housing

5. Deformation from the temperature

6. Gear tooth modification (crowning, end

relief)

The method to reduce Km (min = 1.0)

1. Use high quality gear (high quality

number)

2. Narrow face widths

3. Locate gear at the center between two

bearings

4. Short shaft spans between bearing

5. Large shaft diameters (high stiffness)

6. Rigid stiff housings

7. High precision, small clearance on all

drive components

vBmsOJ

tt KKKKK

mFYWs =


Load distribution factor (Km) can be

calculated by

( )emapmpfmcm CCCCCK ++= 0.1

Cmc = 1 for uncrowned teeth

Cmc = 0.8 for crowned teeth

Cmc = lead correction factor

Cpm = pinion proportion modifier

Cpm = 1 S1/S < 0.175

Cpm = 1.1 S1/S ≥ 0.175

Cpf = pinion proportion factor

025.010

−=d

FCpf

Fd

FCpf 0125.00375.010

+−=

in 1 ≤F

in 17 1 ≤< F

d, dp = pinion diameter

vBmsOJ

tt KKKKK

mFYWs =


Load distribution factor (Km) can be

calculated by

( )emapmpfmcm CCCCCK ++= 0.1

Cma = mesh alignment factor

Ce = mesh alignment correction factor

Ce = 0.8 for gearing adjusted at assembly, compatibility is improved by lapping

Ce = 1 for all other conditions

2CFBFACma ++=

Condition A B C

Open gearing 0.247 0.0167 -0.765(10-4)

Commercial, enclosed units 0.127 0.0158 -0.093(10-4)

Precision, enclosed units 0.0675 0.0128 -0.926(10-4)

Extraprecision enclosed gear

units

0.00360 0.0102 -0.822(10-4)

* Face width F in Inches

vBmsOJ

tt KKKKK

mFYWs =

Rim thickness factor (KB) vBmsOJ

tt KKKKK

mFYWs =

Used when the rim thickness is not sufficient to provide full support for the tooth root.

Bb m

K 242.2ln6.1=

1=bK mB ≥ 1.2

mB < 1.2

t

RB h

tm =

Dynamic factor (Kv) vBmsOJ

tt KKKKK

mFYWs =

To compensate the effect of vibration, dynamic unbalance that will increase load that

the gear tooth must withstand especially at high velocity.

B

tv A

vCAK

+=

)0.1(5650 BA −+=667.0)12(25.0 vQB −=

m/sin for 200

ft/minin for 1

t

t

vC

vC

=

=

Qv = Gear quality number

vt = Pitch line velocity

Maximum recommended pitch line velocity:

2

2

max,)]3([

CQAv v

t−+

=

Selection of material (bending stress)

vBmsOJ

tt KKKKK

mFYWs =

R

Natat KSF

Yss⋅

=′<

AGMA Equation (bending)

(Load that the gear must withstand)

Adjusted Allowable Bending

Stress Numbers

(Depend on the material property)

sat : Allowable bending stress

YN : Bending strength stress cycle number

KR : Reliability factor

SF : factor of safety (design decision)


Reliability KR

0.90, one failure in 10 0.85


0.999, one failure in 1000 1.25

0.9999, one failure in 10000 1.50


• To compensate any uncertainty in analysis,

material property, or error in manufacturing

• Most of factors are included in AGMA

equation, hence the recommended SF is

around 1.00-1.50

Allowable bending stress, Sat

Allowable bending stress number for

through-hardened steels

Allowable bending stress number for

nitriding steel gears

Bending strength stress cycle number, Yn

LnqN 60= N : expected number of cycles of loading

L : design life in hours

n : rotational speed of the gear (rpm)

q : number of load applications per revolution

Bending strength stress cycle number, Yn

Application Design life (h)

Domestic appliances 1,000-2,000

Aircraft engines 1,000-4,000

Automotive 1,500-5,000

Agricultural equipment 3,000-6,000

Elevators, industrial fan, multipurpose gearing 8,000-15,000

Motors, industrial blowers, general industrial machines 20,000-30,000

Pumps and compressors 40,000-60,000

Critical equipment in continuous 24-h operation 100,000-200,000

Gear tooth contact stress (1)

r1

r2

Driving Driven

r1

r2

W

W

+

+

+

+

r1

r2

W

W

F

• The contact of gear teeth can be modeled as the contact of two cylinders

• r is radius of involute curve at the contact point (not the radius of pitch cylinder)

• Radius r is changed along the meshing position

• W is force in the direction of pressure line and

• Stress at contact point can be calculated by Hertzian stress equation

Base circle

rWrWT tb ⋅=⋅= tWW =φcos

Gear tooth contact stress (1)

+

+

rp

rG

W

W

F

2/1

2221

21

21

])1()1([)/1/1(

−+−

+=

EEFrrW

ννπσ

Hertzian stress can be calculated from

( ) 2sin2 φGdr =

( ) 2sin1 φPdr =

φcostWW =

Define Cp (Elastic coefficient) 2/1

2221

21 ])1()1([

1

−+−

=EE

Cp ννπ

2/111

sincos2

+=

GP

tp ddF

WCφφ

σ

2/11

sincos2

+=

G

G

P

tp m

mFd

WCφφ

σ

2/1

=

IFdWC

P

tpσ

12sincos

+=

G

G

mmI φφ

PGPGG ddZZm ==

Define I (Geometry factor)

Basic equation related closely

with AGMA for contact stress

AGMA Stress Equation (contact)

2/1

=

IFdWC

P

tpσ

Hertzian stress AGMA Equation (Contact)

2/1

= vmsO

P

tpc KKKK

IFdWCs

KO : Overload factor

Ks : Size factor

Km : Load-distribution factor

Kv : Dynamic factor

Can be found as same as

the bending stress cal. 12

sincos+

=G

G

mmI φφ

2/1

2221

21 ])1()1([

1

−+−

=EE

Cp ννπ

โดย

dP : Pitch diameter (pinion)

F : Face width

Elastic coefficient, Cp

2/1

= vmsO

P

tpc KKKK

IFdWCs

2/1

2221

21 ])1()1([

1

−+−

=EE

Cp ννπ1 - Pinion

2- Gear

Subscript:

Geometry factor, I 2/1

= vmsO

P

tpc KKKK

IFdWCs

12sincos

+=

G

G

mmI φφ PGPGG ddZZm ==

Selection of material (Contact stress)

R

HNacac KSF

CZss⋅

=′<

AGMA Equation (contact)

(Load that the gear must withstand)

Adjusted Allowable Contact

Stress Numbers

(Depend on the material property)

sac : Allowable contact stress

ZN : Pitting resistance stress cycle number factor

CH : Hardness ratio factor




Reliability KR



0.999, one failure in 1000 1.25

0.9999, one failure in 10000 1.50


2/1

= vmsO

P

tpc KKKK

IFdWCs

As same as

bending case

• To compensate any uncertainty in analysis,

material property, or error in manufacturing

• Most of factors are included in AGMA

equation, hence the recommended SF is

around 1.00-1.50

Allowable contact stress, Sac

Repeatedly Applied Contact

Strength Sc at 107 Cycles and

0.99 Reliability for Steel Gears

ANSI/AGMA 2001-D04.

Contact-fatigue strength Sc at 107 cycles

and 0.99 reliability for through-hardened

steel gears.

ANSI/AGMA 2001-D04 and 2101-D04.

Pitting resistance stress cycle number factor, ZN

LnqN 60= N : expected number of cycles of loading

L : design life in hours

n : rotational speed of the gear (rpm)

q : number of load applications per revolution

As same as bending case

Hardness ratio factor, CH

• Pinion is smaller and rotate faster

than gear

• If the surface of pinion is harder than

gear, the capacity of pitting

resistance is increase

• HBP : Brinell hardness of pinion

• HBG : Brinell hardness of gear

• CH is used for gear only (does not

use for pinion calculation)

• If the hardness of pinion and gear

are equal, CH = 1

Design Guidelines

1. Gear ratio should be less than 1:6 (Too much gear ratio will bring about interference

problem and large gear will cause the weight and size problem).

2. If gear ratio more than 1:6 is required, multi-stages gear reduction should be used.

3. Recommended face width is around 8m < F < 16m (commonly use 12m).

4. Very large face width will bring about the alignment and load distribution problem.

5. At the same center distance, the gear pair with small teeth + more no. of teeth is

quieter than the gear pair with large teeth + less no. of teeth.

6. Small no. of teeth make the compact gear pair, but the interference must be checked.

Design Guidelines

Data for all curves:

mG = 4, NP = 24

KO = 1.0, Class 1 service

20° full-depth teeth

Example

A gear pair is to be designed to transmit 15 kW of power to a large meat grinder in a

commercial meat processing plant. The pinion is attached to the shaft of an electric motor

rotating at 575 rpm. The gear must operate at 270-280 rpm. The gear unit will be enclosed

and of commercial quality. Commercially hobbed (quality number 5), 20°, full depth, involute gears are to be used in the metric module system. The maximum center distance is to be 200

mm. Specify the design of the gears. [Ex.9-6 Machine Elements in Mechanical Design. Robert L. Mott]

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