
DYNAMICS  CASE STUDY



Introduction

Problem Graphic


A twocylinder 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 F_{1} perpendicular to the horizontal plane.
 Piston 2, which is compressing fuel for the next cycle, exerts a resisting force F_{2} in the same direction as F_{1}.




Problem Diagram






Questions



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?






Approach



 Use the equations of rotational motion in 3D 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.




