Consider the crankshaft from an inline four-cylinder engine with respective pistons and connecting rods. The size of the engine components, cylinder 4 pressure profile, and phase diagram are in accordance with the information given in MP1. The figure shows output torque coming out of the crankshaft on the right side of the engine.  The crankshaft can be considered, for simplicity, as a simply supported beam with the supports and dimensions as shown in Figure 1.

Figure 1: Crankshaft, connecting rods, and pistons for inline four-cylinder engine (all dimensions in mm).

a)   Based on a static-analysis FBD, determine and plot as a function of crank angle the y component, the  z  component,  and  the  vector  sum  of  the  force  transmitted  by  the  connecting  rod  to  the  crank  for cylinders 3 & 4. Note that these forces are all transverse to the axis of the crankshaft.

b)   Determine the crank angles for cylinders 3 and 4 for which the total transverse force acting on the crankshaft is maximum. Note that the crank angle is considered to be at zero degrees for the position of the pistons shown in Figure 1.

c)   Calculate and plot the shear and bending moment diagrams as a function of x for cylinders 3 and

4 at the crank angles corresponding to maximum transverse shear force. At these crank angles, what is the magnitude of torque applied to the crank shaft? Plot the torque in the crank shaft as a function of x at these crank angles. This is called a torsion diagram.

d)   Determine the crank angles for cylinders 3 and 4 that correspond to maximum torque about the axis of the crankshaft. At these angles, plot the torque in the crank shaft as a function of x and the shear and bending moment diagrams.

e)     Identify  the  axial  location  (the  x  coordinate  value)  on  the  crank  shaft  in  terms  of  maximum bending moment and calculate the maximum bending stress at this section. The crank shaft has a diameter of 39 mm.  Note that while the force delivered by the connecting rod to the crank imposes a torque about the axis of the crank shaft, there is no torsion in the crank shaft at the section where the crank connects to the connecting rod.

f)   The critical section is identified as the section of the crankshaft that experiences the maximum equivalent stress during the engine cycle. Equivalent stress for a stress element which experiences one

normal stress and one shear stress  component is given by the formula

eq  =

2  +32

(1)