MBD Simulation on a Piston Assembly

AIM:

Motion Analysis of piston Kinematics.

OBJECTIVES OF THE PROJECT:

The motion analysis has to be carried out in three different conditions: -

INTRODUCTION:

The Internal combustion engine is those that burn their fuel which is mixture of air and petrol from carburettor inside the cylinder or compress air only on the cylinder and injects diesel from injector nozzle.

These IC engines convert the chemical energy stored in their fuel into heat energy during the power stroke of piston. The energy produced from burning of fuel is used for motion of piston, the working of a four-stroke engine is based on simple slider crank mechanism.

The crank mechanism comprised of components like crank shaft, connecting rod and piston which changes the sudden displacement to a smooth rotary output which is the input to many devices such as pumps generators and compressors.

Kinematic Modelling of Piston Motion

Piston is one of the main parts in the engine and its purpose is to transfer force from expanding gas in the cylinder to the crankshaft via a connecting rod.

Piston Instantaneous Position

The instantaneous piston position is formulated using the vector loop method from the figure 1 and 2 depicted.

`x = (l + r) - s` ...(1)

where s – position from crank centre to piston pin centre

l –connecting rod length

r – crank radius

x – instantaneous piston position from piston pin to TDC

As it is depicted in figure 1, we can draw the schematic diagram of crank mechanism components relationship.

As in figure2 depicted above it is possible to formulate between the variables of crank mechanism.

`s = l cos phi + r cos theta` ...(2)

`lsin phi = rsin theta` ...(3)

From equation 3 we can rearrange in angle phi form

`sin⁡ϕ=(r sin⁡θ)/l`... (4)

Let `r/l=λ`

`sin⁡ϕ=λ sin⁡θ`...(5)

`therefore cos⁡ϕ=√(1-sin^2⁡ϕ )` or `cos⁡ϕ=√(1-λ^2 sin^2⁡θ )`...(6)

Equation can be factorized and as the powers of lambda (l ) becomes higher and higher it approaches to null as a result:

`cos⁡ϕ=1-((λ^2 sin^2⁡θ)/2)` ...(7)

To formulate the piston instantaneous displacement in the crank mechanism we can calculate based on figure 1 as follows:

`s = l cos phi - r cos theta` ...(8)

To be suitable in manipulating it is better to express the equation in easily estimated variable such that angle phi is very difficult to estimate so it is better to express the equation in terms of an angle theta which is the crank angle. Therefore, Substitute equation (8) in equation (2) provides:

`x = (l + r) - (l cosphi + r costheta )`..(9)

Collect like terms to gather and gives

`x = l(1- cosphi) + r(1- costheta )` ....(10)

Substitute equation (7) in to equation (10)

`x = l((λ^2 sin^2⁡θ)/2) + r(1- costheta )`,

This is the instantaneous position of piston from piston pin centre to TDC in crank mechanism. Where `lamda`– the ratio of crank radius to connecting rod length.

Piston Pin Position: -

The displacement of the piston with respect to crank angle can be derived from simple trigonometry. The piston pin position is the position from crank centre to the piston pin centre and can be formulated from cosine rule of the trigonometry in fig.2

`l^2=r^2+s^2-2rs cos⁡θ`

From the above polynomial equation degree two we can drive the piston position as follows:

`s=r cos⁡θ±√(l^2+r^2 sin^2⁡θ )`

BODY OF THE CONTENT:

PARTS: -

• Connecting rod

1^st create the sketch as per the given dimension

Extrude the sketch and then create another sketch at the front end of the connecting rod, inner circle will be cut extruded and the outer one will be extruded.

Apply the fillets at the edges of connecting rod the final result is shown below:

• End cap

As this is going to get attached with the connecting rod, creating the sketch based on the front end of the connecting rod, and extruding it.

Now creating another sketch like we have done in the case of connecting rod, the inner circle will be extruded cut and the outer circle will be extruded.

At the end providing the fillets to the edges and the result is shown below:

• Wrist Pin

Its really simple to create just create two concentric circles extrude it and provide the champers at the two ends.

• Crank

Creating the sketch as per the given dimension and extruding it.

Creating the circles at the faces of the extrude as shown below and extruding it.

From the right plane cutting the edge from upward as well as downward side.

Mirroring the whole body from the extruded circle as shown below,

The final results are shown below:

• Piston Head

Creating the sketch as per the dimensions and revolving it about the given line as shown,

Now creating the slots for the piston rings using the revolve cut and then as we need 3 slots using the linear pattern tool for the operation to create slots.

Now creating the hole for inserting the wrist pin here we have to give out the three conditions as per the objective, all the three cases are been shown below,

NO-OFFSET POSITIVE-OFFEST NEGEATIVE-OFFSET

(Note – these are being saved as three different parts)

Now creating the shape of the piston sketching in the right plane and performing extruded cut.

Next creating the extruded boss for inserting the wrist pin and mirroring it to the other side as well

Providing fillets at the end, the final result is shown below:

ASSMEBLY: -

Creating the assembly with some of the fundamental mates.

The crank should be rotate about its axis mating it in such a way that it rotates in a single plane, then joining the connecting rod and the end cap together by aligning its axis and mating the faces, mating the end of the connecting rod with the face of the Crank with a offset of 1 mm, Now aligning the wrist pin into the piston head and mating both of their right planes, similarly mating the axis of wrist pin and other end of the connecting rod and coinciding the right planes of both to make it centred, lastly as the piston head has to be moving it in a vertical direction only, therefore mating the right plane of the piston head with the right plane of the assembly.

The result obtain is shown below: -

Note: Same procedure has to be followed for other two cases as well

Now performing simple motion analysis as discussed in the video by providing the contacts,motor as well as the gravity factor, setting the fps to 10,000 as the speed is really high to get accurate results, we need to provide that much of fps.

CONCLUSION:

The linear displacements of piston head for all the three cases are shown below: -

from the above graph it can be seen that the maximum and the minimum displacements are almost the same means the results are accurate but the is changes in the intial positions of the starting the graph may be due to the change is the phase of at the starting points.

All the files are being given below in the link:

https://drive.google.com/drive/folders/1CTckgUUxf3uNNbr8sAdzi0Ah_pfohHDQ?usp=sharing