Question
Full working is appreciated, thanks
The segment of torsion bar shown in Figure 1 is machined from AISI4130 annealed steel. The centre section of the bar is fine turned with a diameter of D=30 mm and with a drilled transverse hole of d=3 mm diameter. The mounting sections of the bar are D=50 mm and the shoulder fillet radius is r=1.5 mm. After manufacture, a sample of torsion bars is to be fatigue tested, and you are required to provide estimates of this for validation purposes. Calculate the maximum allowable fully reversed torque, Tn, permissible if the torsion bar must have a life in excess of 106 load reversals Calculate the maximum allowable fully reversed torque, T3, permissible if the torsion bar is only required to last for 103 load reversals. In normal service, the torque condition in the bar fluctuates between values in a generally random manner, but with some observable trends as indicated in Table 1. Machine usage patterns (e.g. operating loads) cause the torque to be a proportion of the T3 value that you determined in part (b). Estimate the life of the torsion bar in normal service.
Explanation / Answer
the equation of torque is
T = F x r x sinA
where F is force,r is perpendicular distance and A is the angle made
the torque is maximum when A = 90o that is
T_max = F x r
the torque is minimum when A = 0o that is
T_min = 0
the frequency is
f1 = 1/5 Hz,
f2 = 1/10 Hz
and f3 = 1/8 Hz
the velocity of the waves is
v1 = 2pi x r x f1
where r = 1.5 mm = 1.5 x 10^-3 m
v2 = 2pi x r x f2
and v3 = 2pi x r x f3
