Chapter 2 Gear Drive-2

8/10/2019 Chapter 2 Gear Drive-2

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Driving gear

Driven gear

Driving gear

1. Force Analysis

2.4 Loading, and Stress on Spur Gear

Fn1

Fn2

Fn1

Ft1

Fr1

c

b

aFn1

Fr1

T1

C

Ft1

Considering

pitch point

Given a pair of standard spur gear with standard center

distance. Assuming Force is exerted on the middle point of

tooth width, ignoring friction force.


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Fn1

Ft1

Fr1

1. Magnitude of force components

2000 20001 2

t1 t2

1 2

T TF F

d d

For the driving gear,

decomposing Fn on pitch point C:

Tangential force

Radial forcer1 t1

tanF F

Normal force t1n

cos

F

F

Torque 3 11

1

9.55 10 N mP

Tn

20001

1

cos

T

d

r2F

Only a normal force Fn acting on the tooth face,

with an invariable direction, always along the

acting line.

Driving

gear


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2. Direction of force components

Tangential forceF

t

Radius Force Fr

Along the tangential line, pointing to

Pointing to the gear center along the center line

Ft1Ft2

Fr1

Fr2

For driving gear: Opposite to the rotational speed

Driving

gear

Driven

gear

For driven gear: Coincident with the rotational speed


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Example

n2

n1

Fr1

Ft1Ft2

n1

n2

Fr2

Ft2

Ft11

2Fr2

Fr1

Front View Side View


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2. Load Calculation Nominal loadt1

n

cos

FF

nc nF KF

K: Load coefficient, K>1

Actual loadLoad coefficient

KAOverload coefficientConsidering the types of engine

and driven machine. Vibration, impact

KKAKVKKb

Power

source

Driven machine

uniform Slight shock Moderate shock Heavy shock

Uniform 1.0 1.25 1.5 1.75

Light

shock 1.1 1.35 1.6 1.85

Moderate

shock1.25 1.5 1.75 2

KA, Table 2-7

Electric motor

or constant-speed gas turbine

Water turbine

or variable-speed driveMulti-cylinder engine

Constant

generator

Fans, conveyor and

pump

Machine tool,

textile machineryRock crusher


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Dynamic load coefficient Kv

Considering the tolerance of gear in mesh,

such as tolerance of tooth profile and deformation of tooth profile

resulting from manufacturing tolerance, et al

Additional loading

Spur gear KV 1.05 ~1.4

Helical gearKV 1.02 ~ 1.2

Precision Kv

Linear speed of pitch circle Kv


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Load-distribution coefficient among teeth K

Loading-distribution coefficient among teeth for bending: KFLoading-distribution coefficient among teeth for contact: KH

For the continuous gear driving, the contact ratio is above 1. The

actual loading on the teeth in mesh is not uniform because of the error

of manufacturing and the different stiffnesswhile engaged.

Gear drive conditions:

1. Material of teeth is steel, or grey iron ;

2. The basic teeth profile meets the requirements of GB/T 1356-2001;

3. Spur gear or helical gear with a helical angle not above 30

.

Table 2-8 Loading distribution coefficient KH and KF


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Table 2-8 Loading distribution coefficient KH and KF

KAFt/b 100N/mm


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Load-distribution coefficient from tooth alignment Kb

1. Inaccurate gear teeth profile

2. Misalignment of shafts carrying gears

3. Elastic deformations of the gear, shafts, bearings, housings, and supportstructures

4. Clearances between the shafts and the gears, the shaft and bearings, or

the bearing and housing

5. Thermal distortion during operation

6. Crowning or end relief of gear teeth

If the intensity of loading on all parts of all teeth in contact at any given

time were uniform, the value of Kb

would be 1.00. But the following

reasons cause misalignment of the teeth on the pinion w.r.t. those on thegear.

Loading-distribution coefficient from tooth alignment for bending: KFb

Loading-distribution coefficient from tooth alignment for contact: KHb


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Considering the arrangement and deformation of shaft seated by a gear

Loading concentration

Bending deflexion of shaft

1. A deflexion of the gear axis, and an unbalanced

loading acting on the teeth.

3. If the shaft can be regarded as a

cantilever, the unbalanced loading will be

more significant.

2. Gear is not at the middle of shaft, and a larger

bending load acts on the teeth near bearings.
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Stress distribution for torque

Stress distribution for moment

CombinedStress distributionInputting

torque

Shearing deformation of shaft

A larger torque load acts on the teeth

root closer to the inputting component.

Combined deformation

If the gear is located closer to theinputting component, the unbalanced

loading can be more serious.

If the gear is located farther fromthe inputting components, the

unbalanced loading can be less

serious.
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So, if the position of gear is not straddling at the middle of two bearings, it

is necessary to locate the gear far from the inputting end.

vFF v

Example

Which design is better?

The right design is better.


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Table 2-9 Loading distribution coefficient from tooth alignment KH

symmetricalasymm

etrical

Cantile

ver

Formula

Precision grade, under

hardening & tempering

Not examiningwhen assembling

Examining whenassembling


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Table 2-9 Loading distribution coefficient from tooth alignment KH

Precision grade,

under hard surface processing

Not examining

when assembling

Examining when

assembling


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Fig. 2-9 Loading distribution coefficient from tooth alignment KHand KF

Unbalanced loading ->K

Teeth width band working depth h:

1. If band HB, K;

2. Drum-like gear tooth, K.


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3. Stress Analysis of Gear Drive

For gear drive, a normal force acts on the tooth surface. There are two kinds

of stress:

1. Contact stress on tooth surface HFluctuating stress;

Relating to loading, deformation of

contact area and material properties

Unidirectional working condition:

Fluctuating stress or reverse and repeated stress

Bidirectional working condition:

Reverse and repeated stress

Fig. 2-11 Bending stress at the root of tooth

2. Bending stress at the root of tooth F


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(1) Tooth breakage

Bending fatigue

Overload

1. Failure type of gear drive

2-5 Failure Type and Design Principles of Gear Drive

Fatigue breakage is one of the most

important failure types for closed gear drive

Measures to avoid tooth breakage:module;

Fillet radius;

Surface quality;

Material ductility;

Positive-modified gear drive .

1. Crack initiation. Plastic deformation occurs in areas of

stress concentration or discontinuities, such as notches or

inclusions, leading to microscopic cracks.

2. Crack propagation. A smooth crack grows perpendicular

to the maximum tensile stress.3. Fracture. When the crack grows large enough, it causes

sudden fracture.

Sudden fracture for a short time, poor static strength of tooth

(2) F i i i


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(2) Fatigue pitting

Forming process of pitting:

Variable contact force

Fatigue cracks either at or below the surface

Lubrication into cracks

A piece of surface material to break out

Macropitting is categorized as nonprogressive, progressive.

The nonprogressive type consists of pits less than 1 mm diam. in localized areas.

These pits distribute load more evenly by removing high points on the surface. Then

pitting stops after a certain period of service .

Progressive macropitting consists of pits larger than 1 mm diameter that cover a

significant portion of the tooth surface.

A pit with sharp edges

Hardness;

Surface quality;

Equivalent curvature radius;

Viscosity of lubrication.

Measures to relieve fatigue pitting:

(3) S ffi
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(3) Scuffing

Under Heavy duty and high speed

Metal contact, adhesive;

A relative sliding on tooth surfaces;

Oil film breaks because of great friction;

Hard to form oil film

Phenomenon

Scratches form along the sliding direction

Measures to relieve scuffing:

Metal on soft surface is torn along the sliding direction.

Hot Scuffing

The surface oil film is punctured

and adhesion occurs.

Cool Scuffing

Forming process of scuffing

Under Heavy duty and low speed

Hardness;

Surface quality;

Pitch diameter;

Module and whole depth.

(4) W
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(4) Wear

It is one of the most important failure

types for open gear drive.

Measures to relieve wear

Lubrication;Sealing condition;

Gear tooth surface wear involves removal or

displacement of material due to mechanical,

chemical or electrical action.

The three major types of wear are adhesion,

abrasion and polishing.

(5) Pl ti d f ti
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(5) Plastic deformation

Phenomenon

Concave on the pitch circle of driving gear;

Convex on driven gear.

If soft surface,

Metal will flow along the friction direction

Loading and friction is significant

forming process of plastic deformation

Measures to relieve plastic deformation

Hardness;

Viscosity of lubrication;
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2. Design principles of gear drive

Fatigue pitting1. Closed gear drive, soft surface

For the two major failure types: Fatigue breakage and fatigue pitting

While in service

gears should havereliable root strength under bending

fatigue stress andsurface strength under contact fatigue stress

First design the main geometries of gear by HHP ;Then check by FFP.

Fatigue breakage2. Closed gear drive, hard surface

First design the main geometries of gear by FFP;

Then check by HHP.

3. Open gear drive

Only by the principles of bending fatigue strength,

without contact fatigue strength check.

Increasing the module by 10% for the negative influence of wear.


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Transmission Types Failure types Design PrinciplesSmall, or medium

power

Soft surface pitting

Fatigue root breakage

Contact fatigue strength

Bending fatigue strength

Hard surface Fatigue root breakage

pitting



Great power orheavy duty

High speed pittingFatigue root breakage

Hot scuffing

Contact fatigue strengthBending fatigue strength

Strength on hot scuffing

Low speed pitting

Fatigue root breakage

Cool scuffing

Plastic deformation



Strength on cool scuffing

Static strength

Table 2-10 Design principles of closed gear drive

2 6 M i l d H T f G D i


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2-6 Materials and Heat Treatments for Gear Drive

1. Requirements on materials

(1)hard surface, to resist wear, pitting and deformation,

(2)High ductility of gear hub, to resist bending fatigue breakage;

(3)Low price, and commercially available.

2. Common materialsSteelis the best material to manufacturing a gear.

Proper heat treatment is needed to improve the

materials performance.

Metallic

material

#45Medium carbon

alloy steel

Low carbon

alloy steel

Most commonly used

Cast

iron

35SiMn, 40MnB, 40Cr, et al

20Cr, 20CrMnTi, et al

ZG310-570, ZG340-640, et al

HT350, QT600-3, et al

Non-

metallic

material

Plastic, textolite, et al

Forged

steel

Criteria of material choice

Working condition, Load

pattern, Economical efficiency,

Manufacturing method, et al

Cast

steel


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3. Heat treatment

Hardening

& tempering

Normalizing

Casehardening

Carburizing

Nitriding

Softsurface

Hard

surface

It is applicable for medium carbon steel or medium carbon

alloy steel, such as 45, 40Cr, 35SiMn et al. After H&T process, the

tooth surface is soft, with a good property for finishing cutting.

It can be used to reduce internal stress, refine grain, improvemechanical properties and machinability. Normalizing medium

carbon steel can be used under a light duty working condition.

Normalizing cast steel is available for a gear with large diameter.

It is applicable for medium carbon steel or medium carbon

alloy steel, such as 45, 40Cr. To produce a high hardness in the

surface layer of gear teeth. To provide surface hardness values

from 50-64 HRC.

It is applicable for low carbon steel or low carbon alloy steel,

such as 20, 20Cr. Carburizing produces surface hardness in the

range of 55-64 HRC. It results in some of the highest strengths in

common use for gear.

Nitriding produces a very hard but very thin case. Nitriding

should be avoided when overloading or shock can be experienced,

because the case is not sufficiently strong or well supported toresist such load. It is applicable for 38CrMoAl.


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2. Case hardening, caburizing and nitriding can produce very hard surfaces,

which can improve the load capacity of gear drive, but require grinding process.

So it is often applicable for the compact structure.

1. Hardening & tempering and normalizing can produce a soft surface, HB 350,

which is valid for common gear drive.

Attentionif teeth of the gear and the pinion are both soft surface, the pinion

hardness should be 20~40HB higher than the gear. That is because the contact

cyclic number of the pinions teeth root is much greater than the gears.

4. Features of heat treatments

Table 2-11 Gear Material and heat treatment


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Table 2-11 Gear Material and heat treatment

N.Normalizing;

H.T.Hardening &

Tempering;

T.H.Through Hardening;

C.H.Case Hardening;

CA.Carburizing;

NI.Nitriding.

BUltimate strength

sYield strength

-1Bending fatigue

strength

Mate

rialHT HB B

(Mpa)s(Mpa)

-1(Mpa)

N.

H.T.

N.H.T.

T.H.

C.H.

H.T.

H.T.

T.H.

C.H.

CA.

NI.

CA.

Mechanical Properties


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Homework-7

Question A closed spur gear drive for speed reduction;

Speed ratio i=3;

pair of mating spur gear, m=2.5;

z1=32, n1=970r/min;

Transmission power P=10kW;

Try to calculate the tangential force Ft and the radialforce F

r

on the pinion and gear.

Chapter 2 Gear Drive-2

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Transcript of Chapter 2 Gear Drive-2