MBD Simulation on a Piston Assembly
Project Title: MBD simulation on the piston assembly
Objective:
1. Draw all part in piston crank assembly.
2. MAke assembly of piston crank mechanism.
3. Study the MBD of piston crank mechanism.
4. Plot linear displacement of the piston at various wrist pin offsets.
Theory:
A slider-crank linkage is a four-link mechanism with three revolute joints and one prismatic, or sliding, joint.[1] The rotation of the crank drives the linear movement the slider, or the expansion of gases against a sliding piston in a cylinder can drive the rotation of the crank.
There are two types of slider-cranks: in-line and offset.
- In-line: An in-line slider-crank has its slider positioned so the line of travel of the hinged joint of the slider passes through the base joint of the crank. This creates asymmetric slider movement back and forth as the crank rotates.
- Offset: If the line of travel of the hinged joint of the slider does not pass through the base pivot of the crank, the slider movement is not symmetric. It moves faster in one direction than the other. This is called a quick-return mechanism.
There are also two methods to design each type: graphical and analytical.
Kinematics of the in-line slider-crank
The displacement of the end of the connecting rod is approximately proportional to the cosine of the angle of rotation of the crank when it is measured from the top dead centre (TDC). So the reciprocating motion created by a steadily rotating crank and connecting rod is approximately simple harmonic motion:
where x is the distance of the end of the connecting rod from the crank axle, l is the length of the connecting rod, r is the length of the crank, and α is the angle of the crank measured from top dead centre (TDC). Technically, the reciprocating motion of the connecting rod departs from sinusoidal motion due to the changing angle of the connecting rod during the cycle, the correct motion, given by the Piston motion equations is:
As long as the connecting rod is much longer than the crank {\displaystyle l>>r}{\displaystyle l>>r} the difference is negligible. This difference becomes significant in high-speed engines, which may need balance shafts to reduce the vibration due to this "secondary imbalance".
The mechanical advantage of a crank, the ratio between the force on the connecting rod and the torque on the shaft, varies throughout the crank's cycle. The relationship between the two is approximate:
where {\displaystyle \tau \,}\tau \, is the torque and F is the force on the connecting rod. But in reality, the torque is maximum at a crank angle of less than α = 90° from TDC for a given force on the piston. One way to calculate this angle is to find out when the Connecting rod small end (piston) speed becomes the fastest in the downward direction given a steady crank rotational velocity. Piston speed x' is expressed as:
For example, for rod length 6" and crank radius 2", numerically solving the above equation finds the velocity minima (maximum downward speed) to be at a crank angle of 73.17615° after TDC. Then, using the triangle sine law, it is found that the crank to connecting rod angle is 88.21738° and the connecting rod angle is 18.60647° from vertical (see Piston motion equations#Example).
When the crank is driven by the connecting rod, a problem arises when the crank is at the top dead centre (0°) or bottom dead centre (180°). At these points in the crank's cycle, a force on the connecting rod causes no torque on the crank. Therefore, if the crank is stationary and happens to be at one of these two points, it cannot be started moving by the connecting rod. For this reason, in steam locomotives, whose wheels are driven by cranks, the connecting rods are attached to the wheels at points separated by some angle, so that regardless of the position of the wheels when the engine starts, at least one connecting rod will be able to exert torque to start the train.
Problem Statement:
Model all the parts and then assemble them in SolidWorks. The motion analysis is going to be carried out in three different conditions,
| Sl.No |
Wrist Pin Offset ` |
Crank Speed (Rpm) |
| 1 | "0" mm | 2000 |
| 2 | 10 mm Positive | 2000 |
| 3 | 10 mm Negative | 2000 |
Wrist Pin Offset - The position of the wrist pin is going to be varied as followed. But the center of the axis of the piston head and the crank are coincident to each other (i.e) They are on the same plane in all the three cases.
"0" mm Offset - Run a simulation as seen in the video.
10 mm Positive Offset - If the crank rotation is in the Clockwise direction.
10 mm Negative Offset - If the crank rotation is in the Clockwise direction.
Obtain the Linear displacement of the Piston Head in all the three cases. Then export the graphs into Excel. Then Superimpose all the three graphs into a single graph.
Solution:
Parts
1. Piston
The piston is a cylindrical block that moves up and down inside the internal combustion engine. the main function of the piston is to convert the heat energy produced inside the engine to convert it into linear motion of the piston movement inside the engine.
during the combustion of the fuel high amount of heat and pressure is built up inside the cylinder nowhere else to escape this rising pressure it pushes the piston downwards which in turn pushes the connecting rod and it rotates the crankshaft.
the end result as rotation energy at the end of the flywheel
2. Crank
The crankshaft is a moving part of the internal combustion engine (ICE). It's main function is to transform the linear motion of the piston into rotational motion. The pistons are connected to the crankshaft through the connecting rods. The crankshaft is mounted within the engine block.
3. Connecting rod
A connecting rod is an engine component that transfers motion from the piston to the crankshaft and functions as a lever arm. Connecting rods are commonly made from cast aluminum alloy and are designed to withstand dynamic stresses from combustion and piston movement.
4. wrist pin
In internal combustion engines, the gudgeon pin (UK, wrist pin or piston pin US) connects the piston to the connecting rod, and provides a bearing for the connecting rod to pivot upon as the piston moves.
5. Endcap
Assembly:
Motion Study:
1. Motor
RPM is 2000
Rotation in a clockwise direction
2. Contacts
Contact between the end cap and crank
Contact between the crank and connecting rod
Contact between piston and wrist pin
Contact between connecting rod and wrist pin
3. Gravity
Gravity direction in the negative y-direction
Results:
Case 1
No wrist offset
There is no offset between the wrist pin and crank
the linear displacement of the piston
The highest point of a wave is called the peak, and the lowest point is called the trough.
The distance between the peak and the trough is called the wave height.
A wave is often described by its amplitude instead of its wave height. The amplitude is half of the wave height.
The time period between one peak and the next is called the period of a wave.
Case 2
Positive 10 mm
There is a positive 10 mm offset between the wrist pin and crank
Case 3
Negative 10 mm
There is a negative 10 mm offset between the wrist pin and crank
Combined
All three plots are superimposed on a single graph
Conclusion
- The displacement v/s time graph obtained is a smooth sinusoidal curve since the frames per second.
- In offset conditions, the load on the wrist pin is more than that in a 0 offset condition. This is because the crank has to rotate a larger angle to bring the piston downwards than when compared with 0 offset condition.