Solving Steel Axle Connection Problem

[raymanmusic]

Homework Statement

Two axels of steel are connected with gears. Both axels have the same diameter (d) and length (1000mm). Diameter of gear B is 150 mm and diameter of gear C is 450 mm. Gear D is stationary. A torque of 100 Nm is applied to gear A.Maximum allowed shearstress in the axels are 60 Mpa. Shear modulus of the steel the axels are made of is G = 8*10^4 Mpaa) Calculate the necessary axel diameter (d) and the angle of twist (in degrees) that gear A will move.

b) Calculate the necessary axel diameter when the angle of twist in axel CD is 0,25 degrees. Both axels have the same diameter.https://dl.dropboxusercontent.com/u/11241083/problem_axle.png

Homework Equations

https://dl.dropboxusercontent.com/u/11241083/formulas_axle.png [/B]

The Attempt at a Solution

https://dl.dropboxusercontent.com/u/11241083/answer_axle.png [/B]

 

[Asim Riaz]

a)I used the formula τ = G*α*J to calculate the angle of twist (α).τ = 100 NmG = 8*10^4 MpaJ = (π/32)*d^4100 = (8*10^4)*α*[(π/32)*d^4]d^4 = 0,0000031250*αd = sqrt[sqrt[0,0000031250*α]]d = 0,091 mα = 57,3°b)Using the same formula as above, but now with the given angle of twist (0,25°):0,0000031250*α = 0,000000078125 d = sqrt[sqrt[0,000000078125]]d = 0,071 m