Gear Tooth: Gear Tooth: Introduction Introduction Gear is a typical component studied in machine Gear is a typical component studied in machine design design In analyzing the stresses in gears one uses In analyzing the stresses in gears one uses stress/strain and failure theories stress/strain and failure theories The stresses were measured using a polariscope The stresses were measured using a polariscope Objective: Objective: minimize stress at the root of a gear minimize stress at the root of a gear tooth by introducing a stress relief hole tooth by introducing a stress relief hole Parameters: location (r, Parameters: location (r, θ) θ) and size of hole and size of hole Analytical model: I-DEAS Master Series Analytical model: I-DEAS Master Series – Solid Model, FEA, Optimization, .stl file Experimental analysis to validate analytical model – Stereolithography model, Polariscope
Gear Tooth: IntroductionGear is a typical component studied in
machine designIn analyzing the stresses in gears one uses
stress/strain and failure theoriesThe stresses were measured using
a polariscopeObjective: minimize stress at the root of a gear tooth
by introducing a stress relief holeParameters: location (r, ) and
size of holeAnalytical model: I-DEAS Master Series Solid Model,
FEA, Optimization, .stl fileExperimental analysis to validate
analytical modelStereolithography model, Polariscope
Gear Tooth: Two Gears Meshing
Gear Tooth: Two Gears Meshing
Gear Tooth: Solid Model CreationInvolute and gear created in
I-DEASSimplifications: no fillets, one toothPitch Diameter = 360
mmNumber of teeth = 30Pressure angle = 20oAddendum = 12 mmDedendum
= 15 mmGear thickness = 5 mmCircular tooth thickness = 18.85 mm
Gear Tooth: FEAResults: original model Band of high max
principal stressMax tensile stress Area of concernCrack
propagationFatigue failure begins at a crackLoadMaxTensile
Stress
Gear Tooth: FEAMeshTriangular shell elementsWith and without
holePartitionsFree locals mesh control
Boundary conditionsCantilever beam approx.Load: along 20o
pressure line
Gear Tooth: OptimizationObjective: Minimize stressDesign
Variables:Hole diameter Angular locationRadial
locationConstraintsDisplacement restraintsAlgorithm:
Fletcher-Reeves optimization algorithmGradient based, improved
steepest descent methodXq = Xq-1 + a*Sq Initial search direction is
the steepest decent: -F(Xq)Sq = -F(Xq)+qSq-1q = | F (Xq) |2 / | F
(Xq-1) |2
Gear Tooth: Optimized Hole Location=29or = 4 mmdiameter =2
mm
Gear Tooth: Stereolithography Model CreationStereolithography
machine SLA-250Laser cured one layer at a timeThickness: 0.006 inch
(103 layers)Material: SL5170Ultraviolet oven for 45 minModels
created in 15 hoursWith and without hole
Gear Tooth: Experimental SetupExperimental study to verify FEAA
flange with holes for mounting was added to the models to hold the
parts in place in the polariscopeCompression force was
appliedBracket was used to distribute the forceCircular polariscope
dark field was usedUsed to analyze stress in 2D models
Gear Tooth: Circular Polariscope
Gear Tooth: Isochromatic FringesExtinction of light of a
particular wave lengths (colored light)Determines the magnitude of
the stress differencen = hc/*(1- 2)n: fringe orderhc/: constants1-
2: stress difference
black yellow red | blue yellow red | green yellow red | green
yellow red | g y r | ...
Gear Tooth: Comparison of Fringes With and Without Hole
Gear Tooth: Concluding RemarksStresses were analyzed and
measured for a gearStresses decreased by 15%.Deflection increase of
2.3% has no major effect on the kinematics and functionality of
gear.Hole was introduced close to the corner of maximum tensile
stress at an angle of 29 degrees from vertical. Photoelasticity
results verified the analysis
