Math Is Fun Forum

ninjaman

Member

Registered: 2013-10-15

Posts: 61

mechanical engineering,

hello

I have a question

a hollow steel shaft with a diameter ratio of 0.75 and a length of 4m is required to transmit 1Mw at 120rpm. the maximum shear stress is not to exceed 7 Mpa and the overall angle of twist is not to exceed 1.75degree. assume the modulus of rigidity for steel is 80Gpa.

a) determine the necessary outside diameter of the shaft so that both of the above limitations are satisfied

b) determine the actual maximum shear stress and the actual angle of twist.

first I tried finding the torque(T) using P(power) = Tw(w being 2piN( N is rotational speed in rps)) I think w is omega

I rearranged the formula to get T = P/w

so, 1000,000 / 2pi 2                   the second 2 is from 120(rpm) / 60(rps) to get seconds

= 79577.47

then, as I have degrees and would require radians I converted that

1.75 * pi / 180 = 0.0305 radians

so using a formula to find J ( the symbol for second moment of area)

the formula is J = T * L / G (theta sign), so

79577.47 * 4 / 80x10^9 * 0.0305 = 130454.87x10^-9 = J

which im not sure about. I have to find the outside diameter using D^4-d^4,  D is outside diameter and d is inside diameter.

J = pi * (D^4 - d^4) / 32, this is the formula using diameter to find J, I have J and so would try to rearrange

I tried this,

D^4 - d^4 = pi * J / 32

any help would be great, I only know that diameter ratio is 0.75, the inside diameter is three quarters

If I did, d^4 = pi * J / 32, then d^4 answer would be three quarters of the D^4 answer. so if I took that and cut it into thirds that is what I would add to d^4 to get D^4???

any help would be great

thanks
simon
:):)