I am trying to evaluate forces exerted on an axle The axle i

I am trying to evaluate forces exerted on an axle.

The axle is driven by engine(chain drive) and a sprocket with d=10\"

(The loose side of the chain is assumed to be zero tension and the tight side of the chain is entirely horizontal)

There is also an 8\" diameter disk rotor brake. (the position of the caliper is important due to the frictional force to stop the axle)

The axle accelerates from 0-35MPH in 50ft, runs at constant speed, and decelerates to stop in 50ft.

Please help me to understand both forces of the chain drive and disk brake on the axle of this vehicle.

Solution

solution:

1) firstly axle is non rotating element and it is only subjected bending moment and bending stress and not to torsional stress as in case of shaft

2) bending moment acting on axle due to chain drive is

T1=tension in tight side

T2=tnsion in slack side

resultant tension=Fr=T1-T2

as it is in horizontal plane hence,bending moment in horizontal planeas

Mbh=Fr*l1

l1=lenght from bearing support of sprocket

3) brake caliper bending moment

Fbr=braking force

l2=lenght fromsupport of brake disc

as it is in vertical plane,moment in vertical plane is

Mbv=Fbr*l2

4)resultant bending moment

M=(Mbh^2+Mbv^2)^.5

5)bending stress is

Sb=32*M/(pi*d^3)

if factor safety

Nf=1

Sall=Sb

and we can get diameter of axle

5) but if it is rotating element mean shaft then it is subjected to torsional moment too,we have to considder it too

6)torque on shaft due to sprocket

t1=(T1-T2)*ds/2=(Fr*5\'\')

torque on brake disc

t2=Fbr*db/2=4*Fbr

resultant torque

Tr=t1-t2

7)as bending moment and torque both are acting hence resultant torque is

Te=((kb*M)^2+(kt*Tr)^2)^.5

kb=1.5 and kt=1.5 constant for sudden load

8) here diameter of shaft by ASME code is

shear stress allowable=16*Te/(pi*d^3)

9)shear stress allowable=.3*Syt or .18Sut whichever minimum,if keyway provided then give reduction by 25%

10) by putting this value in equation we can get diameter of shaft of vehicle

11) this much data is neccesarry for design of shaft or first bending portion is sufficient for axle