Design of Spur and Helical Gears

7/25/2019 Design of Spur and Helical Gears

1/10

Design of Spur and Helical Gears

ObjectivesTo be able to analyze, select, and design spur and helical geafor strength and life based on service conditions

Modes of Failure

Spur and Helical Gear FailureTooth bending and breakage

Bending stress on tooth root fromthe transmission of forces

Repeated bending loads causesfatigue failure of teeth

Shock overloading frommajortorsional shock in drive system,usually caused by nature of powersource, failure in the machinesystemor external loads.

Breakage can cause catastrophic

failure of drive systems

Spur and Helical Gear FailureSurface Failure

Pitting of tooth surfacesSurface fatigue failure due to manyrepetitions of high contact stresses

Abrasion and Scoring

Causes decreased drivetrainefficiency, noise, and increased stressconcentration on gear teeth. Severe

surface failures can eventually causeseizure of the drive systemorbreakage of teeth.

Spur and Helical Gear FailureIn both cases, we are interested in the tooth load, which is

the tangential force on the teeth (radial load is neglected inboth modes of failure)

This can be computed fromthe following equations

Torque:

Power:

Power:

T= Torque

H= Power

V= Pitch line velocity

Force can be affected by the gear train contact ratio


2/10

Lewis Bending Equation

Lewis Bending EquationEquation introduced to estimate the bending stress in gearteeth

Basis for most gear designs today

Derived by treating the tooth as a simple cantilever and withtooth contact occurring at the tip

Lewis Bending Equation

= Tangential Load (lbs)

= Diametral Pitch

= Face Width

= Lewis FormFactor

Lewis Bending EquationValues of Lewis FormFactor Y for aNormalPressure Angle of 20,Full Depth Teeth,and a

Diametral Pitch of Unityin the Plane of Rotation

Dynamic EffectsAt high speed, increased load is present due to impacts at

initial contact

=Dynamic Factor

English: Metric:

Dynamic EffectsEnglish: Metric: Type:

Cast iron, cast profi

Cut or milled profil

Hobbed or s ape

S ave or groun p


3/10

Stress ConcentrationStress concentrations are not taken into account by Lewis,and are not approximated by our previous methods

Method fromMitchiner and Mabie:

rf= fillet radius

b = dedendum

d = pitch diameter

Surface Durability

Surface DurabilityFor pitting due to contact stresses, equation is derived fromthe Hertz Theory.

Surface compressive stress (HertzianStress)

Elastic Coefficient

Gear and pinion radii near the pitchline (where wear occurs)

AGMA Methodology

AGMA MethodologyAmerican Gear Manufacturers Association

Developed one of the current state of the art in gearstandardization which includes an analysis methodology

(other common standards are ISO, JIS, DIN)

Two fundamental equations: bending stress and pittingresistance

AGMA MethodologyPreviously discussed:

AGMA Stress Equations:

Bending Stress: Surface Stress:



4/10

AGMA MethodologyBending Stress: Contact Stress:


AGMA Methodology

AGMA Strength Equations:

Bending Strength: Contact Strength:

Fully Corrected Bending Strength:

=

Fully Corrected Contact Strength:

=

AGMA Methodology:Strength Equations

Strength EquationsGear Bending Strength ( )

Example for Steels: (Table 14-3: Repeatedly Applied BendingStrength at 107Cycles and 0.99 Reliability for Steel Gears)

Table 14-4 for Iron and Bronze

Strength EquationsGear Bending Strength ( )

Example for through hardened steels


5/10

Strength EquationsGear Contact Strength ( )

Example for Steels: (Table 14-6: Repeatedly Applied ContactStrength at 107Cycles and 0.99 Reliability for Steel Gears)

Table 14-7 for Iron and Bronze

Strength EquationsGear Contact Strength ( )

Example for through hardened steel gears

Strength EquationsStrength Modifying Factors

For BendingLoading Factor

Stress Cycle Factor

Temperature Factor

Reliability

For ContactLoading Factor

Stress Cycle Factor

Temperature Factor

Reliability

Hardness Ratio Factor for Pitting Resistance

Strength Modifying Factors:Loading

AGMA Strengths are based on unidirectional loading

For reversed bending (eg. Idler gears):

Use 70% of Stvalues

Strength Modifying Factors:

Stress Cycle Factors (YNand ZN)

AGMA Strengths are based on 107load cycles (YN= ZN= 1)

For other load cycles use YNand ZNfromfiguresMating gears may have different stress cycles


Stress Cycle Factors (YNand ZN)

AGMA Strengths are based on 107load cycles (YN= ZN= 1

For other load cycles use YNand ZNfromfiguresMating gears may have different stress cycles


6/10


Hardness Ratio Factors (CHand ZW)

Pinion teeth are generally subject to more cycles than gearteeth

Hardness ratio factor is used to adjust the surface strength of

gears to have uniform surface strengths for both pinions andgears. (CHis applied only for gears)


Hardness Ratio Factors (CHand ZW)

Strength Modifying Factors:Hardness Ratio Factors (CHand ZW)

For surface hardened pinions above 48 Rockwell C scale(Rockwell C48) run with through-hardened gears (180-400Brinell), work hardening occurs

CH is a function of pinion surface finish and gear hardness

Strength Modifying Factors:Hardness Ratio Factors (CHand ZW)


Reliability Factors (KRand YZ)

AGMA Strengths are based on 0.99 reliability

For reliabilities in between above values, use the followingequations which accounts for the nonlinearity:


Temperature Factors (KTand Y )

KTand Y =1 for operating temperatures up to 250F

(120C)Recommended to maintain oil lubricants below these

temperatures

Higher temperatures should have factors greater than 1


7/10

AGMA Methodology:Stress Equations

AGMA MethodologyPreviously discussed:

AGMA Stress Equations:





Stress Equations:Stress Modifying Factors includes:

OverloadDynamic Factors

Size

Geometry (pitch and face width)

Distribution of load across teeth

RimSupport

Lewis FormFactor and Root Fillet Stress Concentration

Stress Modifying Factors:

Geometry Factors I and J (ZIand YJ)

Bending Strength Geometry Factor J (YJ)

Same purpose with the Lewis FormFactor with more detailIncludes stress concentration factor and load sharing ratio


8/10





For gears with a75 tooth mate

Stress Modifying Factors:Geometry Factors I and J (ZIand YJ)

Stress Modifying Factors:Geometry Factors I and J (ZIand YJ)

Surface Strength Modifying Factor I (ZI)

Pitting resistance geometry factor

mN= Load sharing ratio (1 for spur gears)pN= normal base pitchpn= normal circular pitchZ = length of line of action in transverse plarP, rG= pitch radiirbP

, rbG

= base circle radii


Elastic Coefficient Cp(ZE)


Dynamic Factor KvAccounts for inaccuracies in the manufacture and meshing o

gears teethErrors in tooth spacing, profile, and runout

Vibration

Dynamic unbalance of rotating members

Wear and permanent deformation of teeth

Shaft misalignment

Friction


9/10


Dynamic Factor Kv


Overload Factor KoApplication specific and are usually based on field experienc

Stress Modifying Factors:Surface Condition Factor Cf (ZR)

Affected by

surface finishing process

Residual stresses

Plastic effects

Values not yet established

Stress Modifying Factors:Size Factor Ks

Accounts for nonuniformity of material properties due tosize

If Ksfromformula is less than 1, use Ks=1


Load Distribution Factor Km(KH)

Accounts for nonuniform distribution of load across the line

of contactApplicable to:

Net face width to pinion pitch diameter ratio

Gear elements mounted between bearings

Face widths up to 40in

Contact across the full width of the narrowest member



If


10/10





Stress Modifying Factors:Rim Thickness Factor KB Safety Factors

SFfor bending failure and SHfor pitting failure

When comparing SFwith SHin identifying threats to loss of

function, use 2 as exponent of SHfor linear or helical contacand 3 for crowned teeth (spherical contact)

This normalizes the SHdue to the nonlinearity of stress withload

Design of Spur and Helical Gears

Documents

Transcript of Design of Spur and Helical Gears