Kramer graph

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A Kramer graph is a specific multiple-line 2D geometric symbolic representation of the characteristics of intake, scavenging and exhaust components in a two-stroke cycle engine.

Contents

They are typically used to visualize the opening time versus area and/ or lift of the following components:

Description

These representations are used to describe corresponding changes in crankshaft angle and port-area.

A Kramer graph plots the relation of the open area of various ports with respect to the angle of the crankshaft in a two-stroke engine. So that upon completion of the cycle (one revolution of 360°) there has been no net change in state of the system; i.e. the device returns to the starting position and area which is zero.

They do not show the specific configuration of ports like in a port-map, which enables it to illustrate a more useful visualization of port area distribution,

This could be useful because different types of port configurations could have the same opening time and area.

Application

In these graphs the X-axis represents the crankshaft angle (θ) in degrees, and the Y-axis represents the open area in any square unit of measurement such as mm². To discern the different types of ports each type is given a designated color.

For example, (commonly used):

Many engineers and engine tuners prefer to use the version of a polar graph of this concept to compare different engines to one another. These are commonly called "Kramer cams", referring to a four-stroke camshaft.

Origin

Kramer graphs are named after Dutch engineer Hans Kramer, who is considered to have been the first to use this type of graph in a publication on the effect of port shape and area on two-stroke cycle engine performance.

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Two-stroke engine Internal combustion engine type

A two-strokeengine is a type of internal combustion engine that completes a power cycle with two strokes of the piston during only one crankshaft revolution. This is in contrast to a four-stroke engine, which requires four strokes of the piston to complete a power cycle during two crankshaft revolutions. In a two-stroke engine, the end of the combustion stroke and the beginning of the compression stroke happen simultaneously, with the intake and exhaust functions occurring at the same time.

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  2. Compression: This stroke begins at B.D.C, or just at the end of the suction stroke, and ends at T.D.C. In this stroke the piston compresses the air-fuel mixture in preparation for ignition during the power stroke (below). Both the intake and exhaust valves are closed during this stage.
  3. Combustion: Also known as power or ignition. This is the start of the second revolution of the four stroke cycle. At this point the crankshaft has completed a full 360 degree revolution. While the piston is at T.D.C. the compressed air-fuel mixture is ignited by a spark plug or by heat generated by high compression, forcefully returning the piston to B.D.C. This stroke produces mechanical work from the engine to turn the crankshaft.
  4. Exhaust: Also known as outlet. During the exhaust stroke, the piston, once again, returns from B.D.C. to T.D.C. while the exhaust valve is open. This action expels the spent air-fuel mixture through the exhaust valve.

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