To study the mean effective pressure inside an engine on various components and varying the values with the variation in engine speeds and thus plotting the results in comparison

OBJECTIVE: To study the mean effective pressure inside an engine on various components and varying the values with the variation in engine speeds and thus plotting the results in comparison.

LITERATURE:

Since , pressure in the cylinder keeps on changing w.r.t the position of the piston. Thus , for the purpose of calculation , we must consider some pressure .

Hence , Mean effective pressure is the constant pressure acting on the piston during the working stroke to do the same work as done by actual varying pressure produced during cycle.

Mean effective pressure is a tool used to represent the capacity of a reciprocating engines to do work. Mean effective pressure is independent of engines displacement.

It\'s basically an average value of pressure acting on a piston during different portions of an engine cycle, So engines with higher mean effective pressure will be powerful and efficient.

This is the derivation for Mean Effective Pressure

MATLAB CODE:

This fragment of code is the input values for the mean effective pressre.

engine_speed = linspace(0,6000,10); %engine speed rpm
b = 82.5; % bore (mm)
s = 82; % stroke (mm)
cylinder_count = 4; % # cylinders
p_intake=50; % intake manifold pressure (kPa)
dia_bearing = 54; % main bearing diameter (mm)
len_bearing = 21.6; % main bearing length (mm)
n_iv = 2; % # intake valves/cyl
n_ev = 2; % # exhaust valves/cyl
dia_iv = 36.5; % intake valve diameter (mm);
dia_ev= 31.5; % exhaust valve diameter (mm);

val_lift = 12; % valve lift (mm)
dyna_visc = 100.e-3 ; % dynamic viscosity (Pa s)
atm_pa= 101; %atmospheric pressure (kPa)

speed_piston_mean = 2.* engine_speed * s/60; % mean piston speed (mm/s)
disp_engine = cylinder_count*b^2*s*(pi/4);  % Engine displacement
num_bearing = cylinder_count+1; %# main crankshaft bearings
total_valve = (n_iv + n_ev)*cylinder_count; % # valves (total)

We have assumed the engine to have two valves per cylinder and to be a 4 cylinder inline cylinder engine.

These Code fragments are the various parts in which the code is divided. Essemtially the various parts on which the effective pressure is calculated.

This fragment is for the pressure on the crankshaft

% components for frictional mean effective pressure 
% crankshaft

p_cb=crank_bearing*num_bearing*engine_speed.^(0.6)*dia_bearing^3*len_bearing/disp_engine; % Bearing pressure
p_cs = crank_seals*dia_bearing/disp_engine; % pressure due to the crank seals
p_crank=p_cb + p_cs; % Total pressure  

This code depicts the calculation for the piston mean effective pressure

% piston assembly

p_pb=piston_bearing*num_bearing*engine_speed.^(0.6)*dia_bearing^3*len_bearing/disp_engine; % bearings pressure
p_pr=piston_rings*speed_piston_mean.^(0.5)/(b^2); %ringpack pressure
p_piston=p_pb+p_pr; 

This code depicts the calculation for the valvetrain effective pressure

% valvetrain

p_cam=cam_bearing*num_bearing*engine_speed.^(0.6)/disp_engine; % bearings
p_vh=cam_hydro*total_valve*val_lift^(1.5)*engine_speed.^(0.5)/disp_engine; % oscill hydro
p_vm=cam_omix*(2+10./(5+dyna_visc.*engine_speed))*val_lift*total_valve/(cylinder_count*s);
p_vs=cam_seals; % seals

This code depicts the calculation for the cam follower effective pressure. For this eengine assembly we have chosen a flat cam follower.

% cam followers - flat cam follower

p_ff=cam_flat*(2+10./(5+dyna_visc.*engine_speed))*total_valve/(cylinder_count*s); % flat cam follower
p_valve=p_cam+p_vh+p_vm+p_vs+p_ff;

This code depicts the calculation for the Auxillaries and pumps effective pressure. This code fragment also gives the total effective pressure inside an engine.

% auxiliary pressure variants 

p_oil= c_1o + c_2o*engine_speed + c_3o*engine_speed.^2; % oil pump
p_wat= c_1w + c_2w*engine_speed + c_3w*engine_speed.^2; % water pump
p_fuel= c_1f + c_2f*engine_speed + c_3f*engine_speed.^2; % fuel pump
p_aux=p_oil+p_wat+p_fuel;

% pumping

dpis= atm_pa-p_intake;
dpiv=pressure_iv*(p_intake/atm_pa.*speed_piston_mean/1000*b^2/n_iv/dia_iv^2).^2;
dpev=pressure_ev*(p_intake/atm_pa.*speed_piston_mean/1000*b^2/n_ev/dia_ev^2).^2;
dpes=pressure_exhaust*(p_intake/atm_pa.*speed_piston_mean/1000).^2;
p_pump=dpis+dpiv+dpev+dpes;

% Total Effective Pressure

p_tot=p_crank+p_piston+p_valve+p_aux+p_pump;

This fragment would give the plotting information of the code.

Here we have plotted the value of various paprts of effective pressure with the varying engine speeds.

figure(1)
 plot(p_tot,engine_speed,\'linewidth\',3,\'color\',\'r\')
 hold on
 title (\'Total mean effective pressure At Different Engine Speeds\')
 xlabel(\'Total Effective Pressure\');
 ylabel(\'Engine Speed\');
 grid on;
 
 figure(2)
 plot(p_crank,engine_speed,\'linewidth\',3,\'color\',\'b\')
 hold on
 title (\'Total mean effective pressure on the crankshaft At Different Engine Speeds\')
 xlabel(\'Total Effective Pressure on the crank\');
 ylabel(\'Engine Speed\');
 grid on;
 
 figure(3)
 plot(p_piston,engine_speed,\'linewidth\',3,\'color\',\'g\')
 hold on
 title (\'Total mean effective pressure on the piston At Different Engine Speeds\')
 xlabel(\'Total Effective Pressure on the piston\');
 ylabel(\'Engine Speed\');
 grid on;
 
 figure(4)
 plot(p_valve,engine_speed,\'linewidth\',3,\'color\',\'y\')
 hold on
 title (\'Total mean effective pressure during valve operations At Different Engine Speeds\')
 xlabel(\'Total Effective Pressure during valve operations\');
 ylabel(\'Engine Speed\');
 grid on;
 
 figure(5)
 plot(p_aux,engine_speed,\'linewidth\',3,\'color\',\'b\')
 hold on
 title (\'Total mean effective pressure on auxillary components At Different Engine Speeds\')
 xlabel(\'Total Effective Pressure on auxilary components\');
 ylabel(\'Engine Speed\');
 grid on;
 
 figure(6)
 plot(p_pump,engine_speed,\'linewidth\',3,\'color\',\'r\')
 hold on
 title (\'Total mean effective pressure on the pumps At Different Engine Speeds\')
 xlabel(\'Total Effective Pressure on the pumps in the vehicle\');
 ylabel(\'Engine Speed\');
 grid on;

This fragment prints the final values of the various pressures at various engine speeds.

% Printing Final Values For the Mean Effective pressures
 
fprintf(\' \\n fmep crankshaft (kPa)= %7.1f  \\n\',p_crank);
fprintf(\' \\n fmep piston (kPa)=     %7.1f  \\n\',p_piston);
fprintf(\' \\n fmep valvetrain (kPa)= %7.1f  \\n\',p_valve);
fprintf(\' \\n fmep auxiliary (kPa)=  %7.1f  \\n\',p_aux);
fprintf(\' \\n fmep pumping (kPa)=    %7.1f  \\n\',p_pump);
fprintf(\' \\n fmep total (kPa)=      %7.1f  \\n\',p_tot);

RESULTS:

The following plots were obtained from the above code

This shows the command window havinig the values for the frictional mean effective pressure acting on various components at different speeds.

NOTE: The first value is when the engine is idling.

 % Values for frictional mean effective pressure on the crankshaft at different speeds
 fmep crankshaft (kPa)=     2.9  
 
 fmep crankshaft (kPa)=    12.6  
 
 fmep crankshaft (kPa)=    17.6  
 
 fmep crankshaft (kPa)=    21.6  
 
 fmep crankshaft (kPa)=    25.1  
 
 fmep crankshaft (kPa)=    28.3  
 
 fmep crankshaft (kPa)=    31.3  
 
 fmep crankshaft (kPa)=    34.0  
 
 fmep crankshaft (kPa)=    36.6  
 
 fmep crankshaft (kPa)=    39.1  
 
 % Values for frictional mean effective pressure on the piston at different speeds
fmep piston (kPa)=         0.0  
 
 fmep piston (kPa)=         9.7  
 
 fmep piston (kPa)=        14.7  
 
 fmep piston (kPa)=        18.7  
 
 fmep piston (kPa)=        22.3  
 
 fmep piston (kPa)=        25.5  
 
 fmep piston (kPa)=        28.4  
 
 fmep piston (kPa)=        31.2  
 
 fmep piston (kPa)=        33.8  
 
 fmep piston (kPa)=        36.2  
 
% Values for frictional mean effective pressure on the valvetrain at different speeds
 fmep valvetrain (kPa)=    66.6  
 
 fmep valvetrain (kPa)=    36.2  
 
 fmep valvetrain (kPa)=    35.1  
 
 fmep valvetrain (kPa)=    34.7  
 
 fmep valvetrain (kPa)=    34.5  
 
 fmep valvetrain (kPa)=    34.4  
 
 fmep valvetrain (kPa)=    34.3  
 
 fmep valvetrain (kPa)=    34.3  
 
 fmep valvetrain (kPa)=    34.2  
 
 fmep valvetrain (kPa)=    34.2  
 
 % Values for frictional mean effective pressure on various auxillary components at different speeds
fmep auxiliary (kPa)=      3.1  
 
 fmep auxiliary (kPa)=     10.0  
 
 fmep auxiliary (kPa)=     16.5  
 
 fmep auxiliary (kPa)=     22.6  
 
 fmep auxiliary (kPa)=     28.4  
 
 fmep auxiliary (kPa)=     33.8  
 
 fmep auxiliary (kPa)=     38.8  
 
 fmep auxiliary (kPa)=     43.4  
 
 fmep auxiliary (kPa)=     47.7  
 
 fmep auxiliary (kPa)=     51.6  
 
 % Values for frictional mean effective pressure on the pumps at different speeds
fmep pumping (kPa)=       51.0  
 
 fmep pumping (kPa)=       51.2  
 
 fmep pumping (kPa)=       51.8  
 
 fmep pumping (kPa)=       52.9  
 
 fmep pumping (kPa)=       54.3  
 
 fmep pumping (kPa)=       56.2  
 
 fmep pumping (kPa)=       58.4  
 
 fmep pumping (kPa)=       61.1  
 
 fmep pumping (kPa)=       64.2  
 
 fmep pumping (kPa)=       67.7  
 
 % Values for total frictional mean effective pressure at different speeds
fmep total (kPa)=        123.7  
 
 fmep total (kPa)=        119.7  
 
 fmep total (kPa)=        135.7  
 
 fmep total (kPa)=        150.6  
 
 fmep total (kPa)=        164.6  
 
 fmep total (kPa)=        178.1  
 
 fmep total (kPa)=        191.2  
 
 fmep total (kPa)=        204.0  
 
 fmep total (kPa)=        216.5  
 
 fmep total (kPa)=        228.8  

PLOT 1

In this plot we can clearly see that the total mean effective pressure in an engine is stalling at the start. This is the condition where the engine is justr about to start and reaches the idle position. Thta is why we can also observe that the total pressure first decreases at idle and then increases uniformly throughtout the cycle.

PLOT 2

In this plot we can clearly see a uniform increase in the pressure gradient from when the engine starts to an idle position and from there it is exponentially increasing. This variation is generally seen due to the functioning of the crankshaft and its changoing values at a certain instant of time.

PLOT 3

The graph of the variation in pressure difference at the piston at various speeds can be resembled with that of the crankshaft. These graphs differentiate from each other only in terms of their values. From the graph we can clearly observe that the values of mean effective pressure of the piston are lesseer than that of the crankshaft. A reason for this could be the lubrication means for a piston and the crankshaft differ. The crankshaft mainly gets splashes of oil from the oil sump which helps it cool down but the piston gets constant lubrication from its rings and also from the inner cylindwr lining which houses a gallery for the coolent flow.

PLOT 4

The reason for the irregularity for the graph is the motion of the valvetrain. The motion of a valvetrain is determined by the valve timings diagram and the 4 strokes of an engine. The valvetrain opens and shuts at higher speeds almost faster than a blink of an eye. The average opening of an intake valve at the engine speed of 6000 RPM is about 150 times per second. Therfore the pressure value decreaases at higher rpms in a valvetrain and this results in increase in frictional loses.

PLOT 5

The graph for the auxillary components is almost linear from the start till the end.

PLOT 6

The graph for the pumping frictions are as showon below. The increase in the MEP of the water and the oil pump is not much at the start but as the engine speed increases the frictional effective pressure almost increases linearly due to the increased loads on these pumps to keep the engine cool and provide sufficient oiling at higher speeds.

FUTURE SCOPE:

With this code i hope to work on some changes that can be made in this program.

As the air goes in at different pressures inside the cylinder due to the intake, the air hits the valve at different angles and pressures which would hinder the oening and closing of the valve. This could also result in the differernce in the plots that we have obtained for the valvetrain.

Another change that we can incorporate is the accomodation of surface friction that is most certain in an engine. We can check the results aand compare them with the results we obtained and then compare the differences.

Also we can write a code for the frictional effective pressurer in the gear train of a manual and an automatic vehicle.

CONCLUTION:

In this project i tried to give out the relation between the frictional mean effective pressures of various components and their behaviour in different engine speeds.

The main result that can be drawn from the above graphs arre that all the parts that are experiencing effective pressure are inter-related to each other. We also conclude that with a certain variations in the engine these values for the effective pressure can be changed according to the need.

We also conclude that the tincrease in pressure values is almost identical in all the cases except for valvetrain and the reason for this was also tried to be given in the plots.