Short Answer:

A crank effort diagram is a graphical representation that shows how the turning effort or torque acting on the crankshaft varies with the crank angle during one complete revolution of the crank. It helps to understand the fluctuation of torque in an engine cycle.

In simple terms, the crank effort diagram displays the variation of the effort (force × leverage) applied on the crank by the piston throughout the engine operation. This diagram is useful in designing the flywheel and maintaining uniform speed of the engine.

Detailed Explanation :

Crank Effort Diagram

A crank effort diagram is a very important graphical tool used in the study of internal combustion engines and reciprocating machinery. It shows how the turning effort or torque on the crankshaft changes with the crank angle during a complete revolution. The turning effort at any instant is the tangential component of the force acting on the crank multiplied by the crank radius.

In an engine, the pressure inside the cylinder varies continuously during different strokes — suction, compression, power, and exhaust. Due to these variations, the torque produced by the piston on the crankshaft also changes at every crank position. The crank effort diagram helps in visualizing these torque changes and analyzing how much work is done in each part of the cycle.

Mathematically,
Turning Moment (T) = Force (F) × Crank Radius (r)

Where the force (F) is the tangential component of the thrust transmitted by the connecting rod to the crank pin. The crank effort diagram plots this torque (turning moment) on the vertical axis and the corresponding crank angle on the horizontal axis.

Construction of Crank Effort Diagram

To draw the crank effort diagram, several steps are followed:

1. Determine Gas Pressure on Piston:
   From the indicator diagram of the engine, the gas pressure acting on the piston at different crank positions is obtained.
2. Calculate Force on Connecting Rod:
   The gas pressure multiplied by the piston area gives the force acting on the piston.
3. Find Tangential Component:
   The force on the connecting rod can be resolved into two components — tangential (Ft) and radial (Fr). Only the tangential component produces torque.

Mathematically,
Ft = F × sin(θ + φ)
where θ is the crank angle and φ is the angle between the connecting rod and the line of stroke.

1. Calculate Turning Moment:
   The turning moment or torque at any crank position is given by,
   T = Ft × r,
   where r is the crank radius.
2. Plot the Diagram:
   The torque (T) is plotted on the y-axis, and the crank angle (θ) on the x-axis. The resulting curve shows how the turning moment varies through the complete cycle.

Shape of the Crank Effort Diagram

The shape of the crank effort diagram depends on the type of engine and the variation of gas pressure inside the cylinder. For a single-cylinder four-stroke engine:

• The turning moment is zero at the beginning of the suction stroke.
• It becomes negative during compression because work is done on the gas.
• During the power stroke, it becomes highly positive due to combustion.
• Finally, it becomes negative again during the exhaust stroke.

Thus, the curve consists of alternate positive and negative loops, representing variations of torque. The area under the curve represents the work done during one revolution of the crankshaft.

Uses of Crank Effort Diagram

1. Flywheel Design:
   The crank effort diagram helps to determine the fluctuation of energy during a cycle. The flywheel is designed based on these energy variations to maintain uniform rotation.
2. Determining Mean Turning Moment:
   The average torque developed during one revolution, called the mean turning moment, can be calculated from the diagram.
3. Studying Torque Fluctuation:
   It helps in understanding how torque varies during the engine cycle and assists in improving smoothness of operation.
4. Balancing of Engines:
   For multi-cylinder engines, crank effort diagrams of individual cylinders can be combined to study total torque and balance the engine effectively.
5. Efficiency Analysis:
   The area of the diagram gives the total work done, which helps in analyzing engine performance and efficiency.

Difference between Indicator Diagram and Crank Effort Diagram

Though both diagrams are graphical tools, they represent different quantities:

• The Indicator Diagram shows variation of gas pressure with piston stroke.
• The Crank Effort Diagram shows variation of turning effort (torque) with crank angle.

While the indicator diagram is used to find the work done inside the cylinder, the crank effort diagram is used to analyze the mechanical output and design the flywheel.

Importance of Crank Effort Diagram

The crank effort diagram is vital in mechanical design because:

• It provides the basis for the calculation of flywheel size and moment of inertia.
• It helps in determining energy storage and release during various strokes.
• It identifies uneven torque distribution and assists in achieving smoother operation.
• It is useful in engine testing and performance evaluation.

In high-speed engines, where torque variation is large, this diagram becomes essential for predicting speed fluctuation and ensuring safe operation of the crankshaft and connected parts.

Conclusion

The crank effort diagram is a graphical method used to study how the torque on the crankshaft varies with the crank angle during the working cycle of an engine. It provides valuable information for analyzing energy fluctuations, designing flywheels, and maintaining uniform engine speed. By converting pressure forces into tangential efforts on the crank, the diagram links cylinder performance with mechanical output, making it an essential tool in mechanical engineering and engine analysis.