Challenge

Design & Motion Analysis of IC enginer piston assembly & verification of results

MMohd Azhar Merchant18 Jun 2020

MOTION ANALYSIS OF PISTON ASSEMBLY AND VERIFICATION OF RESULTS BY CODING ON MATLAB

AIM:

To create a 3D model and to perform motion analysis of piston assembly for different wrist pin offset arrangement by plotting the linear displacements, velocity and acceleration of the piston and Angular displacement and Angular velocity of the crank using SOLIDWORKS MOTION and to verify the zero offset wrist pin arrangement results by coding on MATLAB.

DESCRIPTION:

The Slider-Crank Mechanism is an arrangement of mechanical parts designed to convert straight-line motion to rotary motion, as in a reciprocating piston engine, or it is used to convert rotary motion to straight-line motion as in a reciprocating pump. Internal combustion engines are a common example of this mechanism. Multiple assemblies of the same can be combined to get continuous rotational motion since we get power only during the combustion/expansion stroke.

In the practical application, we would add Air-fuel mixture in the combustion chamber and the mixture would get ignited which in turn pushes the piston downward and this reciprocating motion of the piston gets converted into rotating motion of the crank with the help of the connecting rod.

SIGNIFICANCE OF THIS SIMULATION:

The main idea of running a motion analysis is the visualize the movement of the piston reciprocation if the crank rotates at a particular speed.

Usually, the process and calculations are another way round i.e. to the reciprocating motion of the piston determines the speed of rotation of the crankshaft. This cannot be done to the limitations of SOLIDWORKS motion

For example, if we want to Design an engine and I need to achieve a particular speed and to achieve that particular speed how much piston displacement I require to achieve that particular displacement speed, this can be studied using this simulation. Similar to reverse engineering.

APPLICATIONS OF PISTON CRANK ARRANGEMENT:

1) Reciprocating Engines/Pumps: The slider-crank mechanism which converts straight-line motion to rotary motion and vice-versa, this principle is used in reciprocating engines/pumps.

2) Combustion Engines: Slider-crank mechanism is used in piston-cylinder assembly in combustion engines and converts reciprocating motion into circular motion and vice-versa.

3) Rotary Engines: Fixing the crank in the Slider-crank mechanism it can be used to form rotary engines. Rotary engines are used in cars.

4) Oscillating cylinder Engine: Fixing the connecting rod in the Slider-crank mechanism it can be used to form oscillating cylinder engines.

5) Hand Pump: Fixing the slider in the Slider-crank mechanism it is used to form hand pumps.

OBJECTIVES:

1) To create the geometric models of all the components for all the arrangements of wrist pin / Gudgeon pin and to assemble them and to explain all the steps involved in it.

2) The motion analysis is going to be carried out for three different conditions using SOLIDWORKS MOTION ANALYSIS

Sl.No	Wrist Pin Offset `	Crank Speed (Rpm)
1	"0" mm	2000
2	10 mm Positive	2000
3	10 mm Negative	2000

Wrist Pin/ Gudgeon 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.

3) To plot the linear displacement, linear velocity, and acceleration of the piston and also angular displacement and angular velocity of the crank.

4) To verify the zero offset wrist pin arrangement results by coding and plotting on MATLAB.

5) To import the load and the motion results for determination of deformation, stress and strain results for connecting rod.

3D CAD MODELLING:

PISTON:

The piston is used to increase the pressure in the combustion chamber and initiate combustion.

A very small indentation is provided in the piston head to have clearance volume in the combustion chamber and the combustion can take place effectively.

After combustion, the high pressure is generated in the combustion chamber puts a downwards pressure on the piston which causes a reciprocating motion

This reciprocating motion is then transferred to the connecting rod

During the modeling process features used are revolution Base/Bose to get the outer cylindrical body and upper indentation, revolved cut is used to get the slots for the piston rings and the linear pattern was used to get the rest of the two slots and using extruded cut the holes were made later for the wrist in sitting the extrusion was made from offsetting from the midplane of the piston. And thin extrusion was used to get the slots for the connecting rod movement.

WRIST/ GUDGEON PIN:

The wrist pin provides a revolute joint between the piston and the connecting rod.

The revolute joint is nothing but giving an angular motion DOF to a particular component.

In this case, the revolute joint maximizes the efficiency of the force transfer from the piston to the crankshaft by constraining the motion of the connecting rod, in such a way it has only vertical motion and revolute displacement.

The wrist pin is created using extrusion and chamfer feature

CONNECTING ROD:

Connecting rod is the body that enables force transfer between the piston and the crankshaft.

The connecting rod is constrained on both the sides i.e. it is constrained at the top with the piston by the means of a wrist pin

The bottom end is fully restrained to the crankshaft, the rod does not have any DOF at the bottom with respect to the crankshaft by the means of an end cap.

The connecting rod has a combination of reciprocating and rotary motion.

First, the front sketch is made and the extrusion is done in midplane, the cylindrical extrusion is made at the bottom position and then cylindrical holes were made for bolts. Fillets are applied at most of the sharp edges of the connecting rod to prevent stress concertation.

END CAP:

The end cap helps the connecting rod by the means of the bolted joints to stay intact between the lobes of the crankshaft.

This is pretty much like a holding component so that proper motion transmission occurs.

The front sketch is made and the extrusion is done in midplane, the cylindrical extrusion is made and then cylindrical extruded cuts were made for bolts. Fillets are applied at most of the sharp edges of the connecting rod to prevent stress concertation.

CRANKSHAFT:

The crankshaft is the part in the reciprocating motion is converted into the rotary motion.

This rotary motion is then transferred to the crankshaft and the axle

The number of stokes needed to complete one full rotation is determined by the engine type, the diesel engine requires four strokes whereas the petrol engine requires only two of them.

The connecting rod and the end cap will be tightened over the shaft connecting the two lobes of the crankshaft.

The front sketch was made for one side of the lobe and then the extrusion was done, the extruded cut was used to remove the material and make the curved upper and lower edges, the circular extrusion was made on the front of the lobe extruded where we would be connecting the motor and the circular extrusion was made at back and mirror feature was used to get the other lobe.

ASSEMBLY:

1) FILE > NEW > ASSEMBLY > OK, First drag all the parts to one screen, now as we know the first part will always be fixed by default hence right-click on it and select float.

2) Enable all temporary axis.

3) For crank, the temporary center axis of the extruded part where the motor is going to be connected is constrained with the Right plane and the top plane of the assembly, and the front plane of the crank is made to coincide with the front plane of the assembly. Now when you rotate the crank it will rotate about the temporary axis.

4) The temporarily bolted axis of the connecting rod is made to coincide to that of the end cap and the faces of both are made to coincide and the bottom part of the connecting rod which has the end cap to it, its circular hole axis is made to coincide with that of the crank and a distance mate is provided between the crank and the connecting rod face so that they both move freely.

5) Now the wrist pin is made to coincide its temporary axis with that of the piston and midplanes of both are made to coincide with each other, and the wrist pin axis is made to coincide with the top position of the connecting rod. For making the piston move only in the vertical position the right plane of the assembly is made to coincide with that of the piston. Now when we rotate the crank the piston will reciprocate.

6) Different wrist pin assemblies are made by editing the sketch of the piston. And saving them.

MOTION ANALYSIS:

1) Click on the Solidworks add-in > SOLIDWORKS MOTION, Change the animation to motion analysis, and enable all the temporary axis.

2) Click on add motor and select the temporary axis of the crank on one side of the lobe and enter 2000 rpm clockwise and click ok

3) Click on settings and change the frames per sec to 12000 and enable precise contacts. Since if we have a smaller value of fps then there is a chance, we may miss the maximum and minimum values.

4) Click of the contacts and apply it between 1. crank and end cap 2. crank and connecting rod 3. connecting rod and wrist pin 4. wrist pin and piston .and choose material as steel dry for all.

5) Enable gravity and hit on calculate.

PLOTS AND RESULTS:

1) Zero offset of wrist pin:

Linear displacement of Piston V/s Time:

When a piston moves through a cylinder the resulting motion is almost sinusoidal if the crank has a small radius compared to the length of the rod. However, if the crank radius is large compared to the rod length, the curve shape is not at all sinusoidal.

The maximum displacement of the piston or the position at the top dead center is 302.499 mm

And 202.5 mm at bottom dead center hence the net displacement of the piston is 100mm

Linear velocity of Piston V/s Time:

Here the speed of the piston becomes zero when it reaches two extreme positions that is the Top dead center (TDC) and the bottom dead center (BDC) since the piston reaches its extreme position and starts going in the opposite direction at that instant it starts returning the piston linear velocity becomes zero and the linear velocity of the piston is maximum between the TDC and BDC which is 107.59E+02mm/s.

Linear acceleration of Piston V/s Time:

Here we can see that it piston has maximum linear acceleration at the TDC which is 2709170 mm/s^2, 1696557mm/s^2 at BDC and zero at the positions between the TDC and BDC.

Angular displacement of Crank V/s Time:

As seen the crank rotates complete 360 degrees and hence it goes from 180deg to 0deg and from 0deg to -180deg which is one complete rotation.

Angular velocity of Crank V/s Time:

From this, it checks out that we are providing a constant angular velocity to the crank which is 2000rpm = 12000deg/s

2) Negative 10mm position of pin:

Linear displacement of Piston V/s Time:

The maximum displacement of the piston or the position at the top dead center is 302.31mm

And 202.19mm at the bottom dead center hence the net displacement of the piston is 100mm.

Linear velocity of Piston V/s Time:

Linear acceleration of Piston V/s Time:

Here we can see that it piston has maximum linear acceleration at the TDC which is 2712749 mm/s^2, 1696557mm/s^2 at BDC and zero at the positions between the TDC and BDC

Angular displacement of Crank V/s Time:

As seen the crank rotates complete 360 degrees and hence it goes from 180deg to 0deg and from 0deg to -180deg which is one complete rotation.

Angular velocity of Crank V/s Time:

From this, it checks out that we are providing a constant angular velocity to the crank which is 2000rpm = 12000deg/s

3) Positive 10mm position of Wrist pin:

Linear displacement of Piston V/s Time:

The maximum displacement of the piston or the position at the top dead center is 302.31mm

And 202.19mm at bottom dead center hence the net displacement of the piston is 100mm

Linear velocity of Piston V/s Time:

Linear acceleration of Piston V/s Time:

Here we can see that it piston has maximum linear acceleration at the TDC which is 2711788 mm/s^2, 1696145mm/s^2 at BDC and zero at the positions between the TDC and BDC

Angular displacement of Crank V/s Time:

As seen the crank rotates complete 360 degrees and hence it goes from 180deg to 0deg and from 0deg to -180deg which is one complete rotation

Angular velocity of Crank V/s Time:

From this, it checks out that we are providing a constant angular velocity to the crank which is 2000rpm = 12000deg/s.

CODES FOR MOTION ANALYSIS ON MATLAB:

MOTION ANALYSIS OF SLIDER CRANK MECHANISM FOR 0mm OFFSET IN WRIST PIN:

There are 3 important things under the dynamic analysis of slider-crank mechanism:

Displacement of the Piston
Velocity of the piston
Acceleration of the piston.

O: Crank centre

A: Crank pin

B: piston / slider

AO: Crank

AB: Connecting Rod

Here `θ` is the angle which crank makes with the horizontal, and

`β` is the angle that connecting rod makes with horizontal.

Displacement of Piston:

`x=r*[(1-cosθ)+(n-√(n^2-sin^2 θ)]`

Where, n= length of connecting rod/ length of crank = l/r

if the connecting rod is large compared to crank, n will be large, and n^2 will be even larger.

Since the maximum value of the `(sinθ)^2` is 1, hence for large n^2,

will approach or n. the equation gets converted to:

`√(n^2-sin^2 θ)` will approach `√(n^2 )` or n. the equation gets converted to:

`x=r*(1-cosθ)`

This is the expression for an SHM. Thus the piston will execute SHM when connecting rod is large.

Velocity of the Piston:

`v= dx/dt=dx/(dθ)*(dθ)/dt`

`= rω[sinθ+(sin2θ)/(2*√(n^2-sin^2 θ))]`

If n^2 is large compared to `sin^2 θ` then

`v=rω[sinθ+(sin2θ)/(2n)]`

When `(sin2θ)/(2n)` can be neglected ( when n is very large) then

`v=rω(sinθ)`

Acceleration of Piston:

`a= (dv)/dt=(dv)/(dθ)*(dθ)/dt`

`a=d/(dθ) [rω(sinθ+(sin2θ)/(2n))]ω=rω^2 (cosθ+(cos2θ)/n)`

If n is very large `a= rω^2 (cosθ)` which is SHM

When `θ=0 deg` i.e at TDC `a=rω^2 (1+1/n)`

When `θ=180 deg` i.e at BDC `a=rω^2 (-1+1/n)`

CODE 1:

MOTION ANALYSIS OF IC ENGINE PISTON CYKINDER MECHANISM FOR ONE COMPLETE ROTATION OF CRANK:

%%Motion analsysis of IC ENGINE PISTON CRANK MECHANISM
% For one complete rotation of crank
clc
clear all
close all

%for finding the Linear displcaement and velocity of piston
%length of the crank
r= 50;                                                                     %dimesions in mm

%Angular displacement of the crank
theta = linspace(0,360,100);                                               %taking the values of theta from 0 to 360 having 100 intermediate points

%Angular velocity of crank
N = 2000;                                                                  %angular velocity of crank in rpm
omega=2*pi*N/60;                                                           %angular velocity of sider in rad/s

% length of the connecting rod in mm
l=212.5;                                                

%obliquity ratio
n=l/r;

for i=1:100                                                                %taking 100 interval values and plotting for reducing error
x(i)=-r*((1-cosd(theta(i))));                                              %displacement of the piston in mm

v(i)=abs(r*omega*(sind(theta(i))));                                        %linear velocity of slier in mm/s

a(i)=abs(r*(omega)^2*(cosd(theta(i))+cosd(2*theta(i))/n));                 %linear acceleration of piston in mm/s^2


end
figure(1)
plot(theta,x,'linewidth',3)
title('Linear displacement of Piston V/s Angular displacement of crank')
ylabel('Linear displacement of Piston (x) mm')
xlabel('Angular displacement of crank (theta) deg')

figure(2)
plot(theta,v,'linewidth',3)
title('Linear Velocity of Piston V/s Angular displacement of crank')
ylabel('Linear displacement of Piston (v) mm/s')
xlabel('Angular displacement of crank (theta) deg')


figure(3)
plot(theta,a,'linewidth',3)
title('Linear acceleration of Piston V/s Angular displacement of crank')
ylabel('Linear acceleration of Piston (a) mm/s^2')
xlabel('Angular displacement of crank (theta) deg')

RESULTS AND PLOTS FROM CODE 1 AND COMPARISON WITH SOLIDWORKS MOTION:

Linear displacement of the Piston V/s angular displacement of Crank from MATLAB:

PLOTS FROM CODE 1:

Linear displacement of Piston V/s Angular displacement of the crank:

Linear velocity of Piston V/s Angular displacement of the crank:

Linear acceleration of Piston V/s Angular displacement of the crank:

RESULTS AND PLOTS FROM SOLIDWORKS MOTION:

Linear displacement of Piston V/s Angular displacement of the crank:

Linear velocity of Piston V/s Angular displacement of the crank:

Linear acceleration of Piston V/s Angular displacement of the crank:

CODE 2:

MOTION ANALYSIS OF IC ENGINE PISTON CYLINDER MECHANISM FOR 13 ROTATIONS OF CRANK:

% For 13 rotation of Crank which is 13*360deg about 0.4sec of simulation
%%Motion analsysis of IC ENGINE PISTON CRANK MECHANISM
clc
clear all
close all

%for finding the Linear displcaement and velocity of piston
%length of the crank
r= 50;                                                                      %dimesions in mm

%Angular displacement of the crank
theta = linspace(0,360*13,1300);                                            %taking the values of theta from 0 to 360*13 having 1300 intermediate points

%Angular velocity of crank
N = 2000;                                                                   %angular velocity of crank in rpm
omega=2*pi*N/60;                                                            %angular velocity of sider in rad/s

% length of the connecting rod in mm
l=212.5;

%obliquity ratio
n=l/r;

for i=1:1300                                                                
x(i)=-r*((1-cosd(theta(i))));                                               %displacement of the piston in mm

v(i)=abs(r*omega*(sind(theta(i))));                                         %linear velocity of slier in mm/s

a(i)=abs(r*(omega)^2*(cosd(theta(i))+cosd(2*theta(i))/n));                  %linear acceleration of piston in mm/s^2


end
figure(1)
plot(theta,x,'linewidth',3)
title('Linear displacement of Piston V/s Angular displacement of crank')
ylabel('Linear displacement of Piston (x) mm')
xlabel('Angular displacement of crank (theta) deg')

figure(2)
plot(theta,v,'linewidth',3)
title('Linear Velocity of Piston V/s Angular displacement of crank')
ylabel('Linear displacement of Piston (v) mm/s')
xlabel('Angular displacement of crank (theta) deg')

figure(3)
plot(theta,a,'linewidth',3)
title('Linear acceleration of Piston V/s Angular displacement of crank')
ylabel('Linear acceleration of Piston (a) mm/s^2')
xlabel('Angular displacement of crank (theta) deg')

RESULTS AND PLOTS FROM CODE 2:

Linear displacement of Piston V/s Angular displacement of the crank:

Linear velocity of Piston V/s Angular displacement of the crank:

Linear acceleration of Piston V/s Angular displacement of the crank:

OVERLAPPING LINEAR DISPLACEMENT PLOT FOR ALL 3 CASES OF SOLIDWORKS MOTION ANALYSIS:

SIMULATION OF DEFORMATION, STRESS AND STRAIN ON CONNECTING ROD FOR ZERO OFFSET CASE:

All the loads and moments and other data was exported to SOLIDWORKS simulation where the FEA analysis was done at 0.4s of the simulation

MESH:

DEFORMATION CONTOUR:

STRESS CONTOUR:

STRAIN CONTOUR:

CONCLUSION:

1) From the motion analysis of piston crank assembly and from the overlapping Linear displacement results obtained from EXCEL, we can see that the

The expression for the linear displacement equation is for an SHM. Thus the piston will execute SHM when connecting rod is large.

In case of 0mm wrist pin offset Maximum displacement of the piston (TDC) is 302.4995 mm

In case of -ve 10mm wrist pin offset Maximum displacement of the piston (TDC) is 302.31 mm

In case of +ve 10mm wrist pin offset Maximum displacement of the piston (TDC) is 302.31mm

For this, we can see that the piston displacement is maximum in case of 0mm offset as the connecting rod is straight when it reaches the TDC in that case compared to when there is an offset the connecting rod won't be straight when it reaches the TDC.

2) Wrist pin offset is nothing but a small horizontal distance between the wrist pin and the crank center. Technically this cannot be perceived by the human eye after assembling the actual component.

This change helps in increasing the engine output by reducing the inertial friction between the cylinder liner and the piston.

It also highly improves the Noise, Vibration, and Harshness (NVH) characteristics of the vehicle due to the piston slap at TDC, reducing the abnormal noises from the component during combustion.

The combustion characteristics of the engine is also improved.

3) Offsetting the cylinder axis from the crankshaft axis, minimizes rod angularity when cylinder pressure is at its highest. Reduced angularity leads to lower piston thrust forces, hence lower frictional losses during the period of maximum cylinder pressure, especially at the beginning of the power stroke when pressure rises sharply about 12-15 degrees after TDC. Rather than revising a complete engine design, the easy way to do this is to offset the pin bore in the piston. The amount by which the cylinder axes need to be offset depends on many variables, but the main ones are the ratio of crank throw to con rod length and the angle after TDC at which maximum cylinder pressure occurs.

4) From the linear velocity graphs for all the assemblies, we can see that, the speed of the piston becomes zero when it reaches two extreme positions that is the Top dead center (TDC) and the bottom dead center (BDC) since the piston reaches its extreme position and starts going in the opposite direction at that instant it starts returning the piston linear velocity becomes zero and the linear velocity of the piston is maximum between the TDC and BDC.

5) From the linear acceleration graphs for all the assemblies we can see that, we can see that the piston has maximum linear acceleration at the TDC and zero at the positions between the TDC and BDC

6) From the Angular displacement graphs the for all the assemblies we can see that As seen the crank rotates complete 360 degrees and hence it goes from 180deg to 0deg and from 0deg to -180deg which is one complete rotation

7) From the Angular velocities graphs the for all the assemblies we can see that from this it checks out that we are providing a constant angular velocity to the crank which is 2000rpm = 12000deg/s.

8) The Results and Plots obtained from SOLIDWORKS MOTION are consistent with that obtained from MATLAB CODING and hence we can say that the simulation that we performed is correct and this verifies the results.

9) As seen from the simulation of deformation, stress, and strain for connecting rod for 0 mm offset, the maximum stress and strain occurs at the corners of the extruded cylindrical part in the right side due to clockwise rotation and this can be reduced by proving more curved edges and larger fillets.

YOUTUBE ANIMATION LINKS:

PISTON CRANK ASSEMBLY ANIMATION:

1) 0mm wrist pin offset: