Problem Graphic

A two-cylinder piston engine is idling at 1000 rpm when the throttle is opened. How will the asymmetric shape of the crankshaft and the forces exerted on it affect the motion of the crankshaft?

What is known:

• The crankshaft is composed of nine identical segments of steel rod as shown.
• At the instant the throttle is opened, the crankshaft is in the horizontal plane and is rotating at 104 rad/s.
• Piston 1, which is firing, exerts a force F₁ perpendicular to the horizontal plane.
• Piston 2, which is compressing fuel for the next cycle, exerts a resisting force F₂ in the same direction as F₁.

At the instant the throttle is opened, what is the angular acceleration, α_z, of the crankshaft? What are the dynamic reaction forces A_X and A_Y from the bearing at point A?

• Use the equations of rotational motion in 3-D to develop three scalar equations summing the moments about a coordinate system fixed at O.
• Solve the three equations simultaneously for the three unknowns: α_z, A_X, A_Y.
• Assume each section of the crankshaft is a slender rod.