shafts calculation

7/23/2019 Shafts calculation

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Estimating Stress Concentration

The stress analysis process for fatigue is highly

dependent on stress concentrations. Stress

concentrations for shoulders and keyways are

dependent on size specications that are not known

the rst time through the process. Fortunately, since

these elements are usually of standard proportions, it ispossible to estimate the stress-concentration factors

for initial design of the shaft. These stress

concentrations will be ne-tuned in successie

iterations, once the details are known. The following table, Table 7-1, summarizes some

typical stress-concentration factors for the rstiteration in the design of a shaft.


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!

Table 7-1 First Iteration Estimates forStress-Concentration Factors K

t

and Kts

.

"n cases where the shoulder at the bearing is found

to be critical, the designer should plan to select a

bearing with generous llet radius, or considerproiding for a larger llet radius on the shaft by

relieing it into the base of the shoulder as shown in

Fig. 73.


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#

Figure 7-3 Techniues for reducing stress concentration at ashoulder su!!orting a bearing "ith a shar! radius.

Example 7-2

$a) Large radius undercut

into the shoulder. $b) Large radius relief groove into the back ofthe shoulder. (c) Large radius relief groove into the small diameter


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Defection Considerations

%e&ection analysis at een a single point of interestre'uires complete geometry information for the

entire shaft. For this reason, it is desirable to design

the dimensions at critical locations to handle the

stresses, and ll in reasonable estimates for all otherdimensions, before performing a de&ection analysis.

%e&ection of the shaft, both linear and angular,

should be checked at gears and bearings

(s a rough guideline, typical ranges for ma)imumslopes and transerse de&ections of the shaft

centerline are gien in Table 7#.

*


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Table 7-# T$!ical %a&imum 'anges for Slo!es andTrans(erse )e*ections

+


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( de&ection analysis is straightforward, but it is

lengthy and tedious to carry out manually,

particularly for multiple points of interest.onse'uently, practically all shaft de&ection analysis

will be ealuated with the assistance of software.

Special-purpose software solutions for #-% shaft

analysis

are aailable, but somewhat e)pensie if only

used occasionally.

Software re'uiring ery little training is readily

aailable for planar beam analysis, and can be

downloaded from the internet.


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/nce de&ections at arious points hae been

determined, if any alue is larger than the allowable

de&ection at that point, since I is proportional to d4, a

new diameter can be found from

0hereyallis the allowable deection at that station and

nd is the design factor. imilarly, if any slope is largerthan the allowable slope all, a new diameter can be

found from

0here $slopeall is the allowable slope. (s a result of

these calculations, determine the largest dnew!dold ratio,

then multiply all diameters by this ratio.


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2


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3


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14


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11


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1!


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1#


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1*


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1+


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Surface Factor +a

0here utis the minimum tensile strength and a

and b found in Table -!

1

b

a ut

aSk =


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Si,e Factor +b

For a)ial loading there is no size e5ect, so

"b#$.%

olution & on bord

1

(4)


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Homework

6roblem -#, te)tbook page *41

12


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13


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!4


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!1


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!!


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!#


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!*


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!+


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!


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!


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!2


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!3


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#4


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#1


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#!


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##


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#*


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#+


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#


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#


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#2


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#3


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*4


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*1


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*!


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*#


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**


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*+


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*

7imits and ts of the shafts

please refer to mech !11

course


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shafts calculation

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