Chapter 10 Design of gears

Key points: ⑴ Failures, materials and design criteria;

⑵ Force analysis;

⑶ The factors affecting the gear strength;

⑷ The procedure of gearing design.

Difficulties: ⑴ Strength calculation for spur gearing;

⑵ Force analysis for helical gearing.

§10-1 Introduction

1. Advantages and disadvantages of gears

⑴High efficiency

⑵High reliability

⑶High service life

⑷ i=c

⑸ Take small room

⑹ Can transmit a large range of power and speed (ten thousand

KW，150m/s)

⑺ Special machine tools are needed

⑻ High precision is required

⑼ Cost is high

2. Types of gears

⑴ Classify by the relative position of gear shafts

① Gear pair with parallel axes;

1

② Gear pair with intersecting axes; ③ Gear pair with nonparallel and nonintersecting axes that can be

called skew axes.

⑵ Classify by tooth elements relation to the gear shaft

① Spur gears; ② Helical gears; ③ Herringbone gears.

⑶ Classification by work conditions

① Encased gearing; ② Open gearing; ③ Semi-open gearing

⑷ Classification by tooth profiles

① Involute gear;② Cycloi gear; ③ Circular tooth gear.

⑸ Classification by the shapes of gear

① Cylindrical gear; ② Bevel gear; ③ Worm gear.

⑹ Classification by the case hardness of gear tooth

① Soft tooth surface (case hardness≤350HBS);

② Hard tooth surface (case hardness >350HBS).

§10-2 Gear failures and design criteria

1. gear failures1) BreakageOverload breakageFatigue breakage

2) Pitting (1) Three features

Begins at pitch line, develops on flank and operates in grease.3) GluingGluing is a kind of lubrication failure.

4) Abrasive wearOpen and semi-open gearing.

5) Ridging

2

Driving gear: notchDriven gear: Crown

2. Design criteria

Design Criteria Main failuresEnclosed gearing αF≤[σF] σH≤[σH] Pitting breakage

Open or semi-open σF ≤0.7[σF]

Wearing breakage

§10-3 Gear materials

1. Requirements: Gear teeth core: Sufficient toughnessGear teeth surface: Sufficient hardness

2. Materials most in use Typical materials include forged steel, cast steel, cast iron, plain

carbon steel, alloy steel and non-metal. 1 Forged steel

High strength and low costThe forged steel most in use is medium carbon steel or alloy steel,

low carbon steel or alloy steel.Medium carbon steel: quenching and temperingLow carbon steel: case-hardening, carburizing, and nitriding

2 Cast steel for big size gearsGood wear resistance, good strengthNormalizing, annealing, quenching and tempering

3 Cast iron such as gray cast iron and nodular ironGood wear resistance, gluing resistance, pitting resistance, lower

noise, but low tensile strengthIt is easy to cast and to machine.It can be used in gears with smooth operation, low speed, light-duty,

low precision. 4 Non-metal

Good corrosion resistance, good wear resistance, low weight, low friction, quite operation, but low hardness, low contact strength, low bending strength.

Pinion can be made from non-metal Gear can be made from metal

3. Choice of gear materials

⑴ HBS1 – HBS2 = 30 ～ 50

3

⑵ Small size: bar steel

Medium size: forged steelLarge size: cast steel or cast iron

⑶ Most of steels: case-hardening

Low-carbon steel or low-carbon alloy steel: carburizingQuenched and tempered steel or Nitrided steel: Nitriding

⑷ Normalizing: steady load or light impact

Quenching and tempering: Medium impact

⑸ Alloy steel: high speed, heavy-duty, impact

§10.4 Design of spur gears

1. Forces acting on gear teeth

2. Calculated load

Calculated load

Where: ——Load factor

K K K K KA v

1 Application factor K A Table 10-2

2 Dynamic factor KV

Caused by the deformation of the gear teeth and the base pitch error

4

Improvement——Modifying the tooth face profile

3 Load partition factor K

Caused by the load partition between teeth.

4 Load distribution factor K

Caused by the deformation of the shafts and the pinion body.

Improvement——Crowning the gear teeth. 鼓形修齿法

3. Contact fatigue strength of spur gear teeth

⑴ Hertz formula

Where ——contact length,

——coefficient of contact ratio,

Set Z

E E

E

1

1 112

1

22

2

——Elastic coefficient,

5

Gear ratio

Transmission ratio

set

——Zone factor, see Fig. 10.

checking formula

Set

design formula

4. Bending fatigue strength of spur gear teeth

Strength equation

For spur gears, 30° tangent method

h K mh , S K ms

— module, mm

6

Fn

γ

S

h

YFa——Tooth form factor

YFais independent of module. It depends on the tooth form, the shape

and size of the fillet at the root of the tooth, and the point of application of the force on the tooth.

1. tooth form , , , ( fillet )

2. pt e, pt a　　　　　　　　3. z, x

Strength concentration factor——YSa

　check calculation

——coefficient of contact ratio, ,when

Set db

d

1

, d mz1 1

Check calculation

Design calculation

——face width factor

4. Notes

Design Check

Enclosed drive

Soft surface

Hard surface

Exposed drive

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Soft surface: Normalizing, quenching and temperingHard surface: Quenching, case-hardening, cementation, nitrizing, carbonitrizing

⑵ Contact strength calculation

⑶ Bending strength calculation

In design calculation

⑷ Because KV、K、K depend on the size of gears，so we can select a trial

Kt, then calculate . If is not closed to Kt

, or can be corrected.

d dK

Ktt

1 1 3

m mK

Kn ntt

3

§10.5 Allowable stresses and design parameters

1. Allowable stresses

⑴ Safety factor

——Table 10.5

⑵ Life factor

Expected number of load cycles

Where ——rotational speed of the gear, rpm

8

——number of load applications at one tooth profile per

revolution

——design life, h

⑶ Endurance limit Fig. 10.14 Fig 10.15

Three lines: ME——high qualityMQ——medium qualityML——low quality

Generally, the value between MQ and MQ is suitable. Pulsation cycle loadingSymmetrical cycle loading or open gear drive 0.7

Interpolation method 2. Design parameters

⑴ Pressure angle

⑵ Number of pinion z1

Z↑ ε↑ operate smoothly. Enclosed gear drive:

Open gear drive:

⑶ Face width factor Table10-7

3. Precision/ quality classes of gearsFig 10.22 Select of gear precision.

Example: The meshing gears (see figure)

have same module, same number of teeth, same face width, same material and same heat-treatment.

Find out which gear has worst bending fatigue strength, which gear has worst contact fatigue strength.

bending fatigue strength from

best to worst: 2,2’ → 1 →3,3’

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driving

driven

1

2’2

3’3

contact fatigue strength from best to worst: 1 → 2,3,3’

§10.6 Design of helical gears

1. Forces acting on gear teeth

⑴ Three component forces:

Tangential force

Radial force

Axial force

⑵ composite force

Normal force

⑶ Direction of forces:

Ft—— in opposite direction of turn round for driving gear;in same direction of turn round for driven gear.

Fr——Point to gear’s own center Fa—— Left or Right-hand rule for driving gear

When driving gear is L-up (or R-up) , we hold up it by four fingers of our left hand (or right hand), the hold direction is in the same direction of driving turn round motion, then the thumb direction is axial force’s direction of driving gear.2. Contact fatigue strength of helical gears

Lb

b

cos；

Transverse contact ratio

nt

b

cos

;

10

3. Bending fatigue strength of helical gears

， ，

——Normal module, that is standard module

Transverse module

Helix angle factor ,

Overlap contact ratio

Tooth form factor table10-5。

11

Equivalent number of teeth

Strength concentration factor

§10.7 Design of straight bevel gears

1. Design parameters

⑴ Gear ratio

⑵ Cone distance

Rd d d

u

1

2

2

2

1 2

2 2 21

d

d

d

d

R b

Rm m

R1

1

2

2

051 05

..

⑶ Face width factor:

R 0 25 0 35. ~ . ; Generally, R 1

3

⑷ Mean reference diameter

d dm R 1 05.

⑸ Mean module

m mm R 1 05.

Module of large end is standard module.

⑹ Equivalent reference radius

rd

vm

2 cos

⑺ Equivalent number of teeth

12

⑻ Equivalent gear ratio

uz

z

z

zuv

v

v

2

1

2

1

1

2

2cos

cos

2. Forces acting on gear teeth

⑴ Three component forces:

Tangential force

Radial force F F F tg Fr t a1 1 1 2 cos cos

Axial force F F F tg Fa t r1 1 1 2 sin sin

⑵ One composite force:

Normal force

⑶ Force direction:

Ft——In opposite direction of turn round for driving gear. In same direction of turn round for driven gear.Fr——Point to gear’s own center.Fa——Form Small end to large end.

3. Contact fatigue strength

vvd

sin

2

13

set

Equ.（10.19）

Equ.（10.20）

4. Bending fatigue strength

Ft

mFa Sa

t Fa Sa

RF

KF

bmY Y

KF Y Y

bm

1 05. Equ. （10-23）

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Ft Fa Sa

R R

t Fa Sa

R R

Fa Sa

R R m

Fa Sa

R R

Fa Sa

R R

F

KF Y Y

Rm

KF Y Yd

u m

KY Y

d u m

T

d

KT Y Y

d u m

KTY Y

z u m

1 0 52

1 1 0 5

2

1 1 0 5

2 4

1 1 0 5

4

1 1 0 5

1 2

12

1

1

1

12 2 2

1

12 2 3 2

. .

. .

.

=

m

KT

z u

Y Y

R R

Fa Sa

F

4

1 1 053

1

12 2 2 .

Equ.（10.23）

§10.8 Gear blank design

1. Gear shafts1) When for spur and helical gear

2) When for bevel gear

2. Gear with solid hub

3. Gears with thinned web

4. Spoked gears

§10.9 Efficiency and lubrication in gear sets

1. Efficiencty of gear set

2. Lubrication

⑴Bath lubrication

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⑵Splash lubrication

⑶Atomized lubrication

When , the oil infection nozzle may be on either side of meshing in or side of meshing out; when , the oil infection nozzle must be on the side of meshing out in order to cool the meshing gear teeth simultaneously.

SURFACE ENGINEERING L T P C

OBJECTIVES: To impart knowledge on surface engineering and surface modification methods that will come in handy to solve the industrial problems. This will also serve as a precursor for future

UNIT I ELEMENTS OF SOLID MECHANICS 9 The geometry of stress and strain, elastic deformation, plastic and elasto-plastic

deformation – limit analysis – Airy’ s function – field equation for stress intensity factor.

UNIT I STATIONARY CRACK UNDER STATIC LOADING Two dimensional elastic fields – Analytical solutions yielding near a crack front –

Irwin’s approximation - plastic zone size – Dugdaale model – determination of J integral and its relation to crack opening displacement.

UNIT I ENERGY BALANCE AND CRACK GROWTH Griffith analysis – stable and unstable crack growth –Dynamic energy balance –

crack arrest mechanism –K1c test methods - R curves - determination of collapse load. UNIT IV FATIGUE CRACK GROWTH CURVE 9

Empircal relation describing crack growth law – life calculations for a given load amplitude –efects of changing the load spectrum - rain flow method– external factors afecting the K1c values.- leak before break analysis.

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UNIT V ENGINEERING MATERIALS 10Introduction – Advanced alloys – Super alloys, Titanium alloys, Magnesium alloys,

Aluminum alloys, and Nickel based alloys – Ceramics – Polymers – Biomaterials – Applications – Bio Tribology Nano Tribology.

1. G.W.Stachowiak & A.W .Batchelor , “Enginering Tribology”, Buterworth-Heineman, UK,

2. Rabinowicz.E, “Friction and Wear of materials”, John Wiley &Sons ,UK,1953. Haling, J. (Editor) – “Principles of Tribology “, Macmilian – 1984.4. Wiliams J.A. “Enginering Tribology”, Oxford Univ. Pres, 194.5. S.K.Basu, S.N.Sengupta & B.B.Ahuja ,”Fundamentals of Tribology”, Prentice –

Hal of India Pvt6. Fontana G., “Corosion Enginering”, McGraw Hil, 1985

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