Short Answer:

A crank effort diagram is a graphical representation that shows how the effort or torque on the crankshaft varies with the crank angle during one complete cycle of an engine. It helps to understand how the turning moment or crank effort changes due to the varying gas pressure on the piston and the movement of the connecting rod.

This diagram is useful for analyzing the power output and smoothness of the engine. It helps engineers to design flywheels and balance engine parts so that torque fluctuations are reduced, and the crankshaft runs more smoothly during operation.

Detailed Explanation :

Crank Effort Diagram

A crank effort diagram is a graph that represents the variation of crank effort or torque acting on the crankshaft throughout one complete working cycle of an engine. The term crank effort refers to the tangential force acting on the crank pin, which produces the turning moment (or torque) on the crankshaft.

This diagram gives a clear idea about how the torque changes as the crank rotates through different angles. The torque does not remain constant during a cycle because the gas pressure inside the engine cylinder changes continuously. Hence, the crank effort diagram helps in studying how the torque fluctuates during various strokes such as suction, compression, power, and exhaust strokes.

The horizontal axis of the diagram represents the crank angle, while the vertical axis represents the crank effort (or torque). The area enclosed by the diagram indicates the work done per cycle by the engine.

Concept of Crank Effort

When an engine operates, the gas pressure in the cylinder acts on the piston, creating a force on the connecting rod. This force is transmitted to the crank pin, which produces a tangential component of force that turns the crankshaft. This tangential component is called the crank effort or tangential effort.

The crank effort changes with the crank angle because:

The gas pressure inside the cylinder varies during each stroke.
The position of the connecting rod and crank keeps changing.
The inertia of the moving parts also affects the effort on the crank.

Mathematically,

where,

F_t = Tangential force on the crank pin
r = Radius of the crank

This torque or crank effort is what actually rotates the crankshaft and delivers power to the engine output shaft.

Construction of Crank Effort Diagram

To construct the crank effort diagram, the following steps are followed:

Plotting the Crank Angle (X-axis):
The horizontal axis represents the crank angle, showing one complete cycle of the engine (two revolutions for a four-stroke engine).
Plotting the Crank Effort (Y-axis):
The vertical axis represents the turning moment or crank effort at each crank angle.
Determining Forces:
The gas pressure on the piston is converted into a tangential force on the crank pin through the connecting rod. The effective crank effort is calculated at various crank angles considering both gas pressure and inertia effects.
Drawing the Curve:
The calculated crank effort values are plotted against corresponding crank angles and connected by a smooth curve. The resulting curve is known as the crank effort diagram.

The shape of this diagram depends on the type of engine and the variations in cylinder pressure during the cycle.

Features of Crank Effort Diagram

The diagram shows positive torque when the crank effort acts in the direction of rotation.
It shows negative torque when the crank effort acts opposite to the direction of rotation (such as during the compression or exhaust strokes).
The mean crank effort or mean torque line divides the diagram into equal positive and negative energy areas.
The area under the curve represents the total work done in one cycle.

The difference between the maximum and minimum energy levels represents the fluctuation of energy, which is used to design the engine flywheel.

Crank Effort During Engine Strokes

Suction Stroke:
The pressure inside the cylinder is slightly below atmospheric pressure, so the crank effort is small and slightly negative.
Compression Stroke:
The piston compresses the mixture, doing work on the gas. Hence, the crank effort is negative because energy is consumed.
Power Stroke:
The high-pressure gases push the piston down, generating a large positive crank effort. This is the main stroke that produces useful work.
Exhaust Stroke:
The exhaust gases are expelled, requiring some energy from the flywheel, so the crank effort becomes negative again.

Thus, the crank effort diagram for a four-stroke engine shows one large positive loop (power stroke) and smaller negative loops (other strokes).

Importance of Crank Effort Diagram

The crank effort diagram plays a vital role in engine design and analysis. Some important applications include:

Design of Flywheel:
It helps to determine the fluctuation of energy during one cycle, which is necessary to calculate the required size and mass of the flywheel for smooth rotation.
Study of Engine Smoothness:
By analyzing the torque variations, engineers can identify when the torque is high or low and ensure uniform speed of the crankshaft.
Performance Evaluation:
The diagram helps in studying how effectively the engine converts gas pressure into useful work on the crankshaft.
Balancing of Engines:
It assists in designing multi-cylinder engines where torque from different cylinders is combined to reduce overall fluctuation.
Design of Shafts and Couplings:
It provides information about the maximum and mean torque, helping in the design of engine components to handle varying loads.

Example

In a single-cylinder four-stroke engine, the crank effort diagram shows a large positive torque during the power stroke and small negative torque during the other three strokes. When multiple cylinders are used (like in a four-cylinder engine), the combined crank effort diagram becomes smoother, as the power strokes of different cylinders overlap. This results in more uniform torque and less vibration.

Conclusion

The crank effort diagram is an essential tool for understanding how torque or effort on the crankshaft varies during an engine cycle. It shows both positive and negative efforts that help engineers analyze energy fluctuations, design efficient flywheels, and ensure smooth engine operation. By studying this diagram, the performance, balance, and uniformity of engine rotation can be improved, leading to better overall efficiency and durability of the mechanical system.