Microsoft PowerPoint - Curtis

8/2/2019 Microsoft PowerPoint - Curtis

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The Influence of a Taper on theThe Influence of a Taper on the

Stress Concentration Factor of aStress Concentration Factor of aShoulder Filleted ShaftShoulder Filleted Shaft

Curtis A. Schmidt

University of Tulsa


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Rolivich, Tipton, Sorem,.Multiaxial stressconcentrations in filleted shafts, Jornal ofMechanical Design, 2001

Rolivich, Tipton, Sorem,.Udated stressconcentration factors for filleted shafts in bendingand tension, Journal of Mechanical Design, 1996

TensionTension TorsionTorsionBendingBending

Stress Concentration Factor Graphs:Stress Concentration Factor Graphs:Stress Concentration Factor Equations:Stress Concentration Factor Equations:Maximum Stress Location Chart:Maximum Stress Location Chart:Maximum Stress Location Equations:Maximum Stress Location Equations:


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Stress Relief

Taking away material has been found to lower the StressConcentration factor

Shioya, 1963 shows this for semicircular notches in a semiinfinite plate as seen below (from Petersons SCFs, Pilkey)

This phenomena can be taken advantage in standard

filleted shafts by adding a taper

Notches

get closer


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DtD d

r

Geometry of a tapered-filleted shaft

Geometry range to be tested is similar to that offilleted shafts

d = 1d = 1

0.0020.002


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ANSYS Element Type:

Tension

Plane 82 Element=.3, E = 30x 106

x = 1000psi

ANSYS Element Type:

Bending

Plane 83 Element=.3, E= 30x 106

xMAX= 1000psi

ANSYS Element Type:

Torsion

Plane 83 Element=.3, E= 30x 106

= 1000psi

xxxMAX

xMAX


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The geometry was divided up

into regionsSmall element sizes could be

used when looking at the stress

case in the radius and larger

ones could be used elsewhere

The transition from small to

large was done by establishing a

gradient across the regions.

Divisions set

at Small

Element Size

(SE)

Area 1 divisions

set at GRAD times

Small Element

Size (SE

)

Area 2 divisions set

at GRAD3 times

Small Element Size

(SE

)

Divisions set at GRAD2 times

Small Element Size (SE)

Divisions set at GRAD4 times

Small Element Size (SE)

Element size transition

1

2Small

element sizes

Larger

element sizes


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Figure 12 - Percent change in tensile stress concentration factor vs. element size for different

r/d ratios

-20.00%

-15.00%

-10.00%

-5.00%

0.00%

5.00%

10.00%

15.00%

20.00%

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014

Smallest element size (in)

PercentChangef

romn

extlargerelementsi

ze

0.46

0.32

0.1

0.02

To Determine the smallest element size (SE) and transition gradient (GRAD)

simulations were run to show convergence

As the small element size approached a value of 0.003 convergence was

illustrated in the stress concentration factor

This was also shown over a range of r/d ratios

Though 0.003 was a sufficient element size for convergence of the stress

concentration factor it had to be reduced to provide enough resolution along the

arc (at least 1o increments) for all cases of r/d. Reducing the small element size

made it necessary to adjust the GRAD constant as well so the amount of nodes

would not saturate the computers being used.

Figure 10 - Tensile Stress concentration factor vs. r/d for different element sizes

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

r/d ratios

Tensilestressconcentrationfactors

0.025

0.011764706

0.005882353

0.003921569

0.002941176

r/d < .002, SE = 1/1200, GRAD = 3.85r/d < .002, SE = 1/1200, GRAD = 3.85r/d > .002, SE = 1/600, GRAD = 2.50r/d > .002, SE = 1/600, GRAD = 2.50

For all cases where SE along the radius does not provide atFor all cases where SE along the radius does not provide at

least 1 degree resolution, 1 degree resolution will beleast 1 degree resolution, 1 degree resolution will be

assignedassigned


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The resulting mesh and

model can be seen

below for a samplecase

~ 1/600~ 1/4~ 1/8~ 1/60

SCALE


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r/d D/d Eq. 1 Eq. 1 MAXAVERAGE -0.92% -1.34% -0.59% -0.37% -4.26% -0.27% -0.57% -0.04%

MAX 0.59% 6.18% 0.92% 0.72% 11.66% 0.59% 9.88% 2.33%

MIN -5.85% -7.14% -5.67% -1.59% -20.38% -2.26% -10.35% -1.80%

Tensile Loading

Bending

Loading

Torsional

Loading

Standard

Geometry

To check the accuracy of the models, data was generated for 46 standard filleted

shaft geometries under all three loading conditions.

The stress concentration factors for1, eq and MAX were found to be very similar

to published data

However the location of the maximum stress differed significantly from previous

work

The mesh size in the radius most likely explains this discrepancy.

From: From: Updated Stress ConcentrationUpdated Stress Concentration

Factors from Filleted shaftsFactors from Filleted shafts, Journal, Journalof Mechanical Design, Sep 96. Oneof Mechanical Design, Sep 96. One

can see that there are approximatelycan see that there are approximately

26 division along the radius26 division along the radius

compared to the >90 criteria of thecompared to the >90 criteria of the

current modelcurrent model


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0.00

0.50

1.00

1.50

2.00

2.50

1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 1.5

Dt/d

Kq

Reduction in Kq = 0.03%Reduction in Kq = 0.32%Reduction in Kq = 1.92%Reduction in Kq = 3.86%Reduction in Kq = 6.83%Reduction in Kq = 11.45%Reduction in Kq = 14.66%Reduction in Kq = 24.60%Reduction in Kq = 31.44%

D/d = 1.5D/d = 1.5

r/d = .05r/d = .05

=75=75oo

0.00

0.50

1.00

1.50

2.00

2.50

1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 1.5

Dt/d

Kq


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0

1

2

3

4

5

0 10 20 30 40 50 60 70 80

Theta (degrees)

Kq

0

1

2

3

4

5

0 10 20 30 40 50 60 70 80

Theta (degrees)

Kq

D/d = 3.0D/d = 3.0

r/d = .01r/d = .01

Dt/d = 1.2Dt/d = 1.2

Reduction in Kq = 0%INCREASE in Kq = 2.4%INCREASE in Kq = 2.6%Reduction in Kq = 0%Reduction in Kq = 6.1%Reduction in Kq = 15.3%


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1

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 1.5

Dt/d

Kq

Theta = 75Theta = 60

Theta = 45

Theta = 30

Theta = 15

Nominal

radius intersection

D/d = 1.5

r/d = .05

Kq,nom=2.43

Illustration of the effects of a changing transition diameter for

different values of theta for a single standard fillet geometry

DtD d

r

DtD d

r

DtD d

r


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0

5

10

15

20

25

1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 1.5

Dt/d

Theta

Theta = 75

Theta = 60

Theta = 45

Theta = 30

Theta = 15

D/d = 1.5

r/d = .05

Thetanom=20

Illustration of the effects on the maximum stress location for achanging transition diameter for different values of theta for asingle standard fillet geometry

DtD d

r

DtD d

r

DtD d

r


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2

2.5

3

3.5

4

4.5

5

5.5

1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3

Dt/d

Kq

Theta = 60

Theta = 75

Theta = 45


Nominal

radius intersection

D/d = 3

r/d = .01

Kq,nom=5.04

Illustration of the effects of a changing transition diameter for

different values of theta for a single standard fillet geometry

DtD d

r

DtD d

r

DtD d

r


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2

2.5

3

3.5

4

4.5

5

5.5

0 10 20 30 40 50 60 70 80

Theta (degrees)

Kq

Dt/d = 1.02

Dt/d = 1.025

Dt/d = 1.1

Dt/d = 1.2

Dt/d = 1.3

Dt/d = 1.5

Dt/d = 2

Dt/d = 2.8

Nominal

D/d = 3

r/d = .01

Kq,nom=5.04

Illustration of the effects of a changing taper angle for

different values of Dt for a single standard fillet geometry

DtD d

r

DtD d

r

DtD d

r


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0

5

10

15

20

25

30

35

1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3

Dt/d

Theta

Theta = 60

Theta = 75

Theta = 45

Theta = 30

Theta = 15

D/d = 3

r/d = .01

Thetanom=31

Illustration of the effects on the maximum stress location of achanging taper angle for different values ofDt for a singlestandard fillet geometry

DtD d

r

DtD d

r

DtD d

r


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0

2

4

6

8

10

12

0 0.05 0.1 0.15 0.2 0.25 0.3 0.Dt/d

Kq

Theta = 0


Theta = 45

Theta = 60

Theta = 75

Special case of tangency between the fillet and the taper

yields the highest reduction in stress concentration factor

D/d = 2

DtD d

r

DtD d

r

DtD d

r


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!!Develop a set of equations similar to ones for filleted shaftsDevelop a set of equations similar to ones for filleted shafts

!!Predict the location of the maximum stress over entirePredict the location of the maximum stress over entire

range of geometryrange of geometry!!Predict the change in maximum stress compared to thePredict the change in maximum stress compared to the

standard filleted geometrystandard filleted geometry

!!Develop a program that can interpolate current resultsDevelop a program that can interpolate current results

!!Program will linearly interpolated between the data pointsProgram will linearly interpolated between the data points(4,000 per loading scenario 12,000 total) to minimize the(4,000 per loading scenario 12,000 total) to minimize the

inherent error that may develop by fitting a curve throughinherent error that may develop by fitting a curve through

datadata

!!Will show the corresponding geometry on the screen toWill show the corresponding geometry on the screen toaid designer in visualizing the effects of the differentaid designer in visualizing the effects of the different

variablesvariables


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Microsoft PowerPoint - Curtis