The essential moving elements of a reciprocating engine are the piston, the crank, and the connecting rod. Vibrations in reciprocating engines arise due to (1) periodic variations of the gas pressure in the cylinder and (2) inertia forces associated with the moving parts [9.19]. We shall now analyze a reciprocating engine and find the unbalanced forces caused by these factors.

9.6.1 Unbalanced Forces Due to Fluctuations in Gas Pressure Figure 9.14(a) is a schematic diagram of a cylinder of a reciprocating engine. The engine is driven by the expanding gas in the cylinder. The expanding gas exerts on the piston a pressure force F, which is transmitted to the crankshaft through the connecting rod. The reaction to the force F can be resolved into two components: one of magnitude acting along the connecting rod, and the other of magnitude acting in a horizontal direction. The force induces a torque which tends to rotate the crankshaft. (In Fig. 9.14(b), acts about an axis perpendicular to the plane of the paper and passes through point Q.) Mt (9.52) = a F cos f b r cos u Mt

F/cos f Mt, F tan f, F/cos f, h r F P F tan f (a) (b) (c) P F tan f u F tan f cos f f F cos f F cos f F Q Q F F F F tan f

FIGURE 9.14 Forces in a reciprocating engine.