Mechanical Engineering Answers

The shaft shown in the figure is machined from AISI 1040 CD steel. The shaft rotates at 1600 rpm and is supported in rolling bearings at A and B. The applied forces are F1 = 2500 lbf and F2 = 1000 lbf. Determine the minimum fatigue factor of safety based on achieving infinite life. If infinite life is not predicted, estimate the number of cycles to failure. Also, check for yielding.

A stepped shaft, as shown in figure made from BS080M50 cold drawn steel is subjected to a completely reversed torque T. Based on infinite life, 90% reliability and a factor of safety of 2.1, find the maximum allowable safe torque T, that can be applied, if d = 8 mm.

The figure shows the free-body diagram of a connecting-link portion having stress concentration at three sections. The dimensions are r = 0.25 in, d = 0.40 in, h = 0.50 in, w1 = 3.50 in, and w2 = 3.0 in. The forces F fluctuate between a tension of 5 kip and a compression of 16 kip. Neglect column action and find the least factor of safety if the material is cold-drawn AISI 1018 steel.

The cold-drawn AISI 1040 steel bar shown in the figure is subjected to a completely reversed axial load fluctuating between 28 kN in compression to 28 kN in tension. Estimate the fatigue factor of safety based on achieving infinite life and the yielding factor of safety. If infinite life is not predicted, estimate the number of cycles to failure.

A completely reversed axial load of 20 kN is applied to a machine finished plate (BS 080M50, HR) as shown in the figure. Determine the size b of the plate for indefinite cycle of operation based on Goodman equation. Consider b = 10d = 10t. Choose safety factor of 1.5 and reliability of 99%.

The welded cantilever is subjected to a cyclic torsional load of Tmax = 2 kN-m and Tmin = 1 kN-m. The material is AISI 1018 CD. Calculate: Fatigue safety factor according to Gerber criterion. Consider 90% reliability and stress concentration at end of parallel fillet weld.

A thick walled cylinder is subjected to a fluctuating internal pressure of 0 to 100 MPa. The outer and inner diameters of the cylinder are 250 mm and 150 mm, respectively. The material is Ferritic-pearlitic steel with Sut = 800 MPa and Sy = 600 MPa. The fracture toughness of the material is 50 MPa√m. The ultrasonic detector detects a nick of 0.2 mm (as shown in the following figure). Estimate the No. of cycles life remaining of this cylinder.

A machine part is loaded as shown in the following figure. The moment, M varies from -10 kN-m to +20 kN-m and the force, F varies from 0 to 10 kN. The material is AISI 1040 annealed steel. Consider, machined surface, 100° Celsius temperature operation, 95% reliability. Determine the minimum factor of safety for this part based on Soderberg equation. Given that, d = 50 mm and thickness of the part t = 20 mm.

3.2.1 Write the state-space form of equation using the state assignments

X = [Vx iL]^t , y = Vx.

3.2.2 Write the state-space form of equation (7) using the state assignments

X = [Vx V×]^t , y = Vx

3.2.3 Show that the transfer function of the circuit in Figure 4, could be written :

G2(s) = Vx/Vu = 1/ (LCs² + CRs +1)

3.2.4 Show that the transfer function G2(s) could also be written as :

G3(s) = w²n/(s² + 2 ζwns + w²n) where the natural frequency is given as wn = 1/√LC .

What is the expression for the damping factor ζ.

•Derive the transfer function G1(s) = X(s)/U(s) for the first-order system given by the dynamic equation: dx/dt + kx = u(t).

•Obtain and sketch the impulse response for the given first-order system, when

(i) k >0

(ii) k=0

(iii) k<0