Date post: | 26-Feb-2018 |
Category: |
Documents |
Upload: | gino-jardinico |
View: | 243 times |
Download: | 2 times |
of 10
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
7/25/2019 Design of Spur and Helical Gears
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
7/25/2019 Design of Spur and Helical Gears
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:
Bending Stress: Surface Stress:
7/25/2019 Design of Spur and Helical Gears
4/10
AGMA MethodologyBending Stress: Contact Stress:
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
7/25/2019 Design of Spur and Helical Gears
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
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
7/25/2019 Design of Spur and Helical Gears
6/10
Strength Modifying Factors:
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)
Strength Modifying Factors:
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)
Strength Modifying Factors:
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:
Strength Modifying Factors:
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
7/25/2019 Design of Spur and Helical Gears
7/10
AGMA Methodology:Stress Equations
AGMA MethodologyPreviously discussed:
AGMA Stress Equations:
Bending Stress: Surface Stress:
Bending Stress: Surface Stress:
AGMA MethodologyBending Stress: Contact Stress:
AGMA MethodologyBending Stress: Contact Stress:
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
7/25/2019 Design of Spur and Helical Gears
8/10
Stress Modifying Factors:
Geometry Factors I and J (ZIand YJ)
Stress Modifying Factors:
Geometry Factors I and J (ZIand YJ)
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
Stress Modifying Factors:
Elastic Coefficient Cp(ZE)
Stress Modifying Factors:
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
7/25/2019 Design of Spur and Helical Gears
9/10
Stress Modifying Factors:
Dynamic Factor Kv
Stress Modifying Factors:
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
Stress Modifying Factors:
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
Stress Modifying Factors:
Load Distribution Factor Km(KH)
If
7/25/2019 Design of Spur and Helical Gears
10/10
Stress Modifying Factors:
Load Distribution Factor Km(KH)
Stress Modifying Factors:
Load Distribution Factor Km(KH)
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