The spool shown above is connected to a system that allows a

The spool shown above is connected to a system that allows a 360lb load to be pulled and placed at a higher location. The wall thickness of the shaft is 7.5mm. Calculate the bending moment of the spool due to the load, as well as the torque applied by the rope. Finally conduct fatigue analysis of the spool. For any missing information, assume a suitable value. Please state all assumptions and display steps clearly.

Solution

solution:

1)here torque acting on the spool is

T=F*R=1601.359*((20/2)+(101.6/2)+(19.05/2))=1601.359*70.325=112615.57 Nmm

2)for bending moment diagram

taking mpment about A support of spool

w1=load of spool=.5278 N/mm

w2=load =7.88 N/mm

Ma=0

Rb*330-1601.359*179.9-17.7551*9.81=0

Rb=873.51 N

Ra=902.02 N

here moment at bearing A=0,B=330mm,E=78.3 mm,C=179.9 mm,F=48.5 mm from B

Ma=0

Me=66777.89 Nmm

Mc=45245.09 Nmm

Mf=43127.52 Nmm

Mb=0

4)for fatigue analysis of finite life

with material steel,Sut=540 MPa,Syt=400 MPa,Se=200 MPa

here for finite life analysis we have both bending and torsional stresses acting on shaft

Sb=32Mmax/pi*Do^3(1-k^4)

t=16Tmax/pi*Do^3(1-k^4)

K=Di/Do=86.6/101.6=.8523

Do=101.6 mm

we get

Sb=1.373 MPa

t=1.1578 MPa

resultant mean and amplitude stress is

Sm=Sa=1.2152 MPa

here by goodman criteria

Sxf=SUt.Sm/(Sut-Sa)=1.2179 MPa

4)life is given by

log(Sxf)-LOg(se)/(6-logN)=log(.9Sut)-log(se)/(6-3)

so we get

N=1.72*10^23 cycle for given diameter of spool and material with considering load is uniformly distrubuted over spool both external and self weight.