Allan T. Kirkpatrick - Internal Combustion Engines

Figure 1.11Cylinder volume vs. crank angle for ( Equations 1.33and 1.36).

The instantaneous piston velocity can be found by replacing with and differentiating Equation ( 1.32) with respect to time giving

(1.37)

Equation ( 1.37) can be nondimensionalized by the mean piston speed , resulting in

(1.38)

Using the Matlab® program Velocity.mlisted in the Appendix, the nondimensional velocity is plotted versus crank angle from top dead center (tdc) to bottom dead center (bdc) in Figure 1.12for a value of . The piston velocity is zero at tdc and bdc. Due to the geometry of the slider crank mechanism, the velocity profile is nonsymmetric. For this example, the maximum nondimensional velocity = 1.65 occurs at = 72 after tdc.

Figure 1.12Nondimensional velocity vs. crank angle for ( Equation 1.38).

If we neglect terms of , and use the trigonometric identity , the piston velocity can be approximated as

(1.39)

The acceleration is found by differentiating Equation ( 1.39) with respect to time

(1.40)

Note that the velocity and acceleration terms have two components, one varying with the same frequency as the crankshaft, known as the primary term, and the other varying at twice the crankshaft frequency , known as the secondary term. In the limit of an infinitely long connecting rod, i.e., , the motion reduces to a simple harmonic at a frequency .

The reciprocating motion of the connecting rod and piston creates accelerations and thus inertial forces and moments that need to be considered in the choice of an engine configuration. In multicylinder engines, the cylinder arrangement and firing order are chosen to minimize the primary and secondary forces and moments. Complete cancellation is possible for the following four‐stroke engines: in‐line 6‐ and 8‐cylinder engines; horizontally opposed 8‐ and 12‐cylinder engines, and 12‐ and 16‐cylinder V engines (Taylor 1985).

The performance characteristics of three different diesel engines are compared in Table 1.1. The engines are a four‐cylinder 1.9 L automobile engine, a six‐cylinder 5.9 L truck engine, and a six‐cylinder 7.2 L military engine. Comparison of the data in the table indicates that the performance characteristics of piston engines are remarkably similar when scaled to be size independent. As Table 1.1illustrates, the mean piston speed is about 12 m/s, the bmep is about 15 bar, the power/volume is about 40 kW/L, and the power/mass about 0.5 kW/kg for the three engines.

Table 1.1Performance Comparison of Three Different Four‐Stroke Turbocharged Diesel Engines

	1.9 L	5.9 L	7.2 L
Parameter	Automobile	Truck	Military
# Cylinders	4	6	6
Bore (mm)	82	102	110
Stroke (mm)	90	120	127
Displacement per cylinder (L)		0.983	1.20
Power (kW)	110	242	222
Mass (kg)	200	522	647
Engine speed (rpm)	4000	3200	2400
Mean piston speed (m/s)	12.05	12.78	10.16
Bmep (bar)	17.3	15.4	15.4
Power/Volume (kW/L)	57.9	41.0	30.8
Mass/Volume (kg/L)	105	88	90
Power/Mass (kW/kg)	0.55	0.46	0.35

There is good reason for this; all engines in a given era tend to be made from similar materials. The small differences noted could be attributed to different service criteria for which the engine was designed. Advances in engine technology have allowed manufacturers to continue to increase the power/mass. The iron in engine blocks and cylinder heads has been replaced by aluminum, which has half the weight of iron, and intake manifolds are now made of composite materials. With turbocharging, engines for vehicles have also become smaller, with four‐ and six‐cylinder engines replacing six‐ and eight‐cylinder engines, respectively.