MBD Simulation on a Piston Assembly

Aim:- Study of Variation of Piston Linear Displacement with change in eccentricity

Theory:-

Crank Shaft is a famous mechanism which is used for converting rotary motion into translation motion or vise versa.They find their major application in automotive industry inside IC Engines.

In Ic Engines when the charge(fuel +air) undergoes combustion it generate a translation motion of the piston which is converted into rotary motion and used by the vehicle.

This Piston Assembly is kinematically a slider crank mechanism.

It is also called as the first inversion of slider crank mechanism.(Inversion of Mechanism means fixing various link one after another)

 Piston Assembly

Slider Crank

All names are similar to the assembly .The piston in the assembly is analogus to the slider.

Simulation showing the motion of entire assembly

The Assembly consists of 

1. Crank

2. Connecting Rod

3. Piston Head

4. Gudgeon Pin

Crank 

Crank is the part that is attached to the shaft which drived the wheel of a vehicle.It has only one degree of freedom i.e rotation about one axis.The axis is the turning joint betwen link 1 and link 2 i.e. origin and crank,

Connecting Rod

It Connect the piston/Slider with the crank.It has a roatational degree of freedom at specific distance from origin also called as the crank length.

Piston

It is the part of the assembly which performs translation motion about about only one axis.

Gudgeon Pin

It gives turning joint between the piston and connecting rod

Kinematic Study of Slider Crank Mechanism

The figure is the Configuration diagram of a slider crank mechanism

a=Crank

b=Connecting Rod

e:- Eccentricity (distance between the slider path and fixed link)

Here

`x0=0 , y0=0`

`x1=a*cos(theta)`

`y1=a*sin(theta)`

`x2=x1+b*cos(beta)`

`y2=y1-b*cos(beta)`

Beta can be calculated by

`beta=sin^-1((a*sin(theta)-e)/b)`

Matlab was used to calculate analytical results

The 3 cases of study is as follows

1. no eccentricity

2.10 mm positive eccentricity

3.10 mm negative eccentricity

Case 1. No Eccentricity

Simulation of piston Having no Eccentricity

Using Solidworks

 

Using Matlab

Both the above video are the same one represent the actual body but the latter represents the configuration diagram.The Slider Crank is simulated using Matlab the code is attached below.

Linear displacement of the piston (Solidworks)

Linear Displacement of piston (Matlab)

As it is observed same answered has been optained using anlytical method and simulation

Case2. 10 mm Positive Eccentricity

 Using Solidworks

 

Using Matlab

Graph represetating Linear Displacement(Solidworks)

Graph representating Linear Displacement (Matlab)

Case 3. 10 mm Negative Eccentricity

Using Solidworks

 Using MATLAB

 

Graph showing the linear displacement of slider crank.

Using Solidworks

Using Matlab

The graph consisting all three positions simulated in Solidworks.

Effect of eccentricity on linear displacement of the piston assembly

It is observed that the graph obtained by the simulation are cosine graph.

Analytically the value of e(eccentrcity) effects the value of beta angle.

`beta=sin^-1((a*sin(theta)-e)/b)`

`x2=x1+b*cos(beta)`

Thus by adding e to to the equation results in phase lag .Therefore a positive eccentricity or shift to left as seen in the above graph causes the output wave to lag behind the no eccentricity wave 

On the other hand by adding negative e or shifting toward right causes a phase lead .The resultant will have an led than the standard wave as seen in the graph

Matlab Code used to calculate anlytically

clc       %clears the command window
clear all %clears the workspace
close all %closes all figures
%inputs
n=2;      %no of rotation of crank
fp=360;   %no of frames
a=50;     %crank length
b=212.50; %connecting rod length
e=-10     %eccentricity
theta=linspace(0,n*360,fp); %Crank angle

x0=0;    %Origin
y0=0;

ct=1;
for i=1:length(theta)
    Theta=theta(i);
    %Calcuclating Beta
    sbeta=(a*sind(Theta)-e)/b;
    beta=asind(sbeta);                
    %Calcuating x1y1
    x1=a*cosd(Theta);
    y1=a*sind(Theta);
%     Calculating x2y2
     x2=(x1+b*cosd(beta));
     y2=(y1-b*sind(beta));
     
    %storing value of displacement is variable d
     d(i)=x2+40;
     
%      Plottig results
     plot([x0 x1],[y0 y1],'b','LineWidth',3);
     hold on
     cle(a)  %plotting a circle to show the path of crank
     plot([x1 x2],[y1 y2],'k','LineWidth',3);
     hold off
    rectangle('Position',[x2-10 y2-10 20 20],'FaceColor','r');
     yline(e,'-.k');
     yline(0,'-.k');
     axis ([-50 300 -250 250]);
     
     % Getting the current figure
      M(ct)=getframe(gcf);
    
     %incrementing the counter
     ct=ct+1;

    
end

%Makes a Movie
movie(M);

%Creating a video object
videof=VideoWriter('slider_kinematics10neg.avi','Uncompressed AVI');
%Opening the created object

open(videof);
%Writting the created movie inside the video object
writeVideo(videof,M);
close(videof)
function m = cle(r)

th=0:5:360;
x=r*cosd(th);
y=r*sind(th);

plot(x,y,'.k');
end

Conclusion

Thus by adding eccentricity we add a phase shift to the output displacment.