Hypocycloidal Engine

 

A conventional four-stroke spark-ignition reciprocating engine employs a simple cranking mechanism with a crank pin that revolves in a circle, causing the pistons to undergo a periodic motion consisting of four "strokes" of equal lengths. These four strokes are

 

Intake: A mixture of air and fuel is drawn into the cylinder as the piston moves from top center to bottom center.

Compression: The mixture is compressed as the piston moves back from bottom center to top center.

Expansion: A spark near top center causes the mixture to combust, raising the pressure and temperature. The resulting gas expands as the piston moves from top to bottom center.

Exhaust: The products of combustion are expelled from the cylinder as the piston returns from bottom to top center, at which point it begins the cycle again.

 

The basic cranking mechanism and the corresponding pressure/volume diagram illustrating the four-stroke spark-ignition engine are shown in the figure below:

 

 

The simplicity of the conventional cranking has many beneficial effects, such as ease of construction, durability, low mechanical complexity, and so on. However, one disadvantage of the conventional mechanism is that the compression ratio of the cycle, i.e., the ratio of the volumes of the fuel-air mixture at the beginning and end of the compression stroke, is necessarily equal to the expansion ratio, i.e., the ratio of volumes of the fuel-air mixture at the beginning and end of the expansion stroke. This is a disadvantage because the compression ratio of a spark-ignition engine with modern fuels can usually not be greater than about 9:1, and typically must be even less to avoid "knock", which is the spontaneous detonation of the mixture rather than the intended controlled burning initiated by the spark. Knock is very destructive to an engine, and must be avoided.

 

Unfortunately, this implies (with the conventional cranking mechanism) that the expansion ratio is also limited to about 9:1. At high power this is typically somewhat wasteful, because after the gas has expanded through a ratio of 9:1 it is still at a significantly elevated pressure and capable of doing more useful work, but since the piston has reached bottom center we have no choice but to open the valves and allow the gas to "blow down", after which the remaining products of combustion are exhausted by the exhaust stroke.

 

Typically (at high power) the gas inside the cylinder at the time when the exhaust valves are opened is more than 1.9 times the atmospheric pressure, so we get "choked" sonic flow at the valves, which creates extremely high sound levels. This is why automobile engines are equipped with mufflers on the exhaust. If the muffler of an internal combustion engine is removed and the engine is run at high power, it is incredibly loud. This noise is an indication of the energy that is being wasted.

 

Another disadvantage of the conventional cranking mechanism is due to the fact that extremely high forces are applied to the piston during the "power stroke" (i.e., the expansion stroke), when the high-pressure products of combustion force the piston downward, and during this motion the link rod between the piston and the crankpin is deflected sideways because the crankpin moves horizontally as well as vertically (as it moves around in a simple circle). At the mid point of the expansion cycle the link rod is at its maximum angle relative to the axis of the cylinder, which results in extremely high side loads and friction between the piston and the cylinder.

 

Both of these disadvantages of the conventional cranking mechanism can be alleviated by adopting a somewhat more complex cranking mechanism, so that the path of the crankpin is hypocycloidal instead of circular. A schematic of the hypocycloidal cranking mechanism is shown below.

 

 

The outer green circle represents a fixed gear with teeth on the internal circumference, and this engages the external teeth of a gear wheel of 2/3 the diameter represented by the next smaller green circle. The center of this inner gear is connected to the crankshaft, and follows the path indicated by the red circle. The actual crankpin is offset from the center of the internal gear by 1/3 of the length of the primary crank link. The hypocycloidal path of the crankpin is indicated by the blue curve in the figure above.

 

Since the path of the crankpin has three-way symmetry, it is possible to locate cylinders along three radial axes, as indicated by the red radial lines in the figure. The wrist pins and link rods connecting them to the crankpin are shown in purple. Notice that the absolute rotation of the internal gear is in the opposite direction and at 1/2 the speed as the main crankshaft. The thermodynamic cycle of the hypocycloidal engine is illustrated in the PV diagram below:

 

 

The improved efficiency of the engine is due largely to the elongated expansion stroke, which is made possible without increasing the compression ratio beyond the "knock" limit by means of the hypocycloidal cranking mechanism. (Of course, similar cycles can be produced by offsetting the usual valve timing, but this results in greatly increased pumping losses, which offset the cycle gains.)

 

If your browser is Internet Explorer, you can see an animated view of the kinematics of the hypocycloidal engine.

 

To maximize the benefits of the hypocycloidal design, it would be possible to mount the external (outer) gear in a collar that enabled it's orientation to be adjusted slightly. This would allow for variations in the in-cylinder compression and expansion ratios, and could be used in conjunction with external turbo-charging to optimize the cycle over a wide range of power outputs. Throughout this range the full expansion of the products of combustion would provide high thermodynamic efficiency by not "throwing away" gas that is still at fairly high pressure. In addition, this arrangement provides reduced exhaust noise levels which would allow operation with less pressure drop across a muffler.

 

In addition, notice that the power (expansion) stroke, during which the greatest force is applied to the piston and link rod, occurs when the crankpin is on the "inner" loop of the hypocycloidal path, so that the deflection of the link rod is less than for a conventional cranking mechanism, resulting in reduced side loads, friction, and losses on the piston and cylinder walls.

 

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