c. kalavrytinos - dynamics analysis of a three cylinder engine

2011

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Analysis of a three cylinder engine

MSc Mechanical Engineering

Dynamics PG

Christos Kalavrytinos


ABSTRACT

This report aimed to analyse the operation of a three cylinder engine. A simulation

was carried out using the MSC Adams software package. Results were obtained for

different parameters such as crankshaft speed and bushing stiffness and damping

coefficients. The simulation showed that an increase of crank speed from 800rpm to

8000rpm resulted in an increase of piston vertical acceleration from 42 to 4200 G

therefore multiplying the force by 100 times.

The theoretical analysis suggested that three cylinder engines are balanced when

primary and secondary forces are concerned, but because of the distance of the

cylinders and the firing order, a rocking motion is induced by primary and secondary

couple moments which were calculated.

Research showed that modern three cylinder engines utilise counter rotating

balancing shafts to reduce these moments and vibrations.

Christos Kalavrytinos Page i


CONTENTS

ABSTRACT............................................................................................................................... I

CONTENTS.............................................................................................................................. II

1.0 INTRODUCTION................................................................................................................1

1.1 OBJECTIVES.....................................................................................................................1

2.0 BACKGROUND THEORY..................................................................................................1

2.1 INTERNAL COMBUSTION ENGINES.......................................................................................1

2.2 ENGINE DYNAMICS AND BALANCE.......................................................................................2

2.3 ROTATING BALANCE..........................................................................................................3

2.4 RECIPROCATING BALANCE.................................................................................................4

2.5 SINGLE CYLINDER ENGINE ANALYSIS..................................................................................4

2.6 THREE CYLINDER ENGINE FORCES.....................................................................................6

3.0 SOFTWARE PACKAGES..................................................................................................7

4.0 ADAMS SIMULATION........................................................................................................8

5.0 RESULTS......................................................................................................................... 10

5.1 ADAMS SIMULATION RESULTS..........................................................................................10

5.2 THEORETICAL ANALYSIS..................................................................................................15

6.0 DISCUSSION.................................................................................................................... 17

7.0 CONCLUSIONS AND RECOMMENDATIONS................................................................18

REFERENCES:...................................................................................................................... 19

APPENDIX.............................................................................................................................. 20

Christos Kalavrytinos Page ii


1.0 Introduction

This report aims to research, design and analyse a dynamic mechanical system. The

system operation will be simulated on the MSC Adams software package in order to

obtain parameter values to compare to theoretical values and ensure the system

operates within allowable levels.

For this specific assignment, the analysis of a three cylinder in-line petrol engine is

considered.

1.1 Objectives

The analysis will be carried out with the following steps:

Research on engine balance and vibrations

Creation of MCS Adams engine model

Simulation and results recording

Theoretical calculation

Result discussion

2.0 Background Theory

2.1 Internal combustion engines

Internal combustion engines have been around since the mid 1850's. The can be

found in many sizes and arrangements. The basic design comprises of a crankshaft,

a connecting rod (i.e. conrod), a gudgeon pin, a piston and the engine block.

Depending on the number of pistons and the angle between them, the engine is

given a name. The most common engine used in today's cars is the four cylinder in-

line motor, illustrated in Fig. 1. The pistons are translating in the same direction with

and the crankshaft throws are at a 90° angle. The three cylinder in-line engine

analysed in this report can be seen in Fig. 2 . This particular engine has a 180° angle

between each piston as opposed to the 120° configuration of the engine analysed in

the report.

Christos Kalavrytinos Page 1


Figure 1, In-line four engine.

Figure 2, Three cylinder in-line engine.

2.2 Engine dynamics and balance

With improved ride and handling performance of vehicles, their noise and vibration

characteristics have become progressively important. In both the developed and the

developing world the lifestyle of many revolves around the use of motor vehicles.

Furthermore, the proportion of time spent under idling conditions, or at low to

moderate travel speeds, has increased markedly with traffic congestion. As a result,



vehicle occupants as well as other road users are subject to noise sources that are

predominantly contributed by the power train system, as opposed to those that are

road induced or caused by aerodynamic effects. Recent surveys show that drivers

are more annoyed by structure borne noise and vibration than airborne noise, the

former being at a lower frequency and almost entirely induced by the power train

system. The internal combustion engine, as a power source, is inherently unbalanced

owing to the translational imbalance of the reciprocating elements (pistons and

proportion of masses of connecting rods in translational motion) and the torsional

defection behaviour of engine components. The combustion process acts as the

initiating source for the spectrum of noise and vibration in the power train system

which includes its own fundamental forcing frequency (this being half the rotational

frequency of the crankshaft for a four- stroke engine and all its multiples. The effect

of the combustion forces is firstly to introduce the imbalance inertial forces at the

engine rotational frequency (i.e. engine order) and all its whole order multiples (the

even order contributions being the most troublesome) and secondly to induce

torsional deflection response of the engine block and the crank shaft system. The

latter occurs at odd and half engine orders. (Rahnejat, 2000)

Therefore the engine vibrations are caused by two basic sources, the least important

being the irregular torque output of the engine's reciprocating components. The most

critical vibration occurs due to the inability to balance inertia forces due to piston

motion in certain types of engine configuration. There exist two sources of

mechanical imbalance; rotating and reciprocating.

2.3 Rotating balance

Rotating components can produce net rotating forces if not balanced properly. These

out of balance forces are due to asymmetrical mass distribution about the rotating

axis of the object in question. Due to the needs of reciprocating balance, certain

configurations of engine, rarely allow the achievement perfect rotating balance of the

crankshaft, single cylinder engines being an example.

(http://www.tonyfoale.com/Articles/EngineBalance/EngineBalance.pdf, 6/12/11)



2.4 Reciprocating balance

The piston in an engine moves along a straight line, defined by the axis of the

cylinder. However, its velocity is continually changing throughout a cycle, it is

stationary when at both TDC and BDC, achieving maximum velocity somewhere

around the mid-stroke. Oscillating forces must be applied to the piston to cause

these alternating accelerations. If these inertia forces are not balanced internally

within an engine. They must pass through the conrod to the crankshaft then on to

the main bearings and onto the crankcase, from the crankcase they are passed into

the frame through the engine mountings.

The motion of the piston is approximately sinusoidal, and therefore so too are the

acceleration forces. If the connecting rod was infinitely long, that motion would

actually be truly sinusoidal, but most conrods are approximately twice the crankshaft

stroke in length. This relative shortness of the rod means that, except for the TDC

and BDC positions, the rod will not remain in line with the cylinder axis through a

working cycle. The angularity of such a short conrod throughout a complete

crankshaft revolution modifies the piston motion, see figure 3. With a very long

conrod we would expect that the maximum velocity (and hence zero acceleration) of

the piston would occur at 90° of rotation from TDC. With a 2:1 conrod length to

stroke ratio, maximum velocity occurs just past 77°.In fact an infinite number of

higher order harmonics are introduced into the piston acceleration. These harmonics

complicate the balancing of an engine. Fortunately, as the harmonics increase in

order, their magnitude decreases, and so they become less important. In practice, it

is usual only to consider the first and second harmonics when doing balance

calculations. The reciprocating forces with a frequency equal to the engine RPM are

known as primary forces and the reciprocating forces from the second harmonic,

which cycle at twice engine speed, are known as secondary forces. It is interesting

and somewhat alarming if we calculate the magnitude of the reciprocating forces

produced in typical engines. This force is proportional to the square of the rpm.


2.5 Single cylinder engine analysis

Primary forces:

In order achieve a good understanding of the principles involved in engine balance is

first necessary to understand the concept of balance factor, as it applies to the

primary forces of a single cylinder engine. Figure 3 LHS shows how the piston



applies an upward force on the conrod, at top dead centre, and also how when close

to mid-stroke (RHS sketch), the piston moving at maximum velocity produces no in-

line primary force. As shown in the LHS the addition of a counterweight can be used

to cancel the force from the piston. Unfortunately, this simple idea is not the answer,

as can be seen when the piston is at mid-stroke. The counterweight will still produce

a centrifugal force, but which is no longer balanced by that from the piston. So an in-

line reciprocating force is replaced with a lateral alternating force of the same peak

magnitude. When the counterweight exactly balances the primary reciprocating

forces at TDC or BDC like this, we have 100% balance factor. If no attempt is made

to balance the piston force, that is; the crankshaft is in static balance after allowing

for the mass of the rotating part of the conrod. That there is a zero balance factor.

Factors between zero and 100% give rise to a combination of rotating force and

reciprocating force.


Figure 3,Primary force balancing.

Secondary forces:

In a single cylinder engine, the secondary forces provide us with a harder problem to

solve. The concept of balance factor is applied to the crankshaft is not relevant in

this case, because by definition, the secondary forces vibrate at twice the rate of the

crankshaft rotation. A balance shaft could be added, that rotates at twice the engine

speed but that would only replace the in-line forces with lateral ones, as in the case



of 100% balance factor with primary forces. However, if two counter-rotating balance

shafts, geared so they ran at twice the speed of the crankshaft were used, then we

could in fact, eliminate the secondary forces.


2.6 Three cylinder engine forces

The most common crankshaft layout for an in-line three cylinder engine is with each

crankpin spaced at 120°. This symmetrical layout completely balances primary and

secondary forces. However, due to the width of the crankshaft, serious primary and

secondary rocking couples are introduced. In addition to making 120° triples, the

Laverda motorcycle company also produced one with a 180° crankshaft. The outer

two cylinders had in-line crankpins, and hence the pistons moved up and down

together, but the central cylinder has its crankpin 180° away. The reasoning behind

this layout is to eliminate the rocking couple. In so doing, the otherwise perfect

primary and secondary balance of the 120° engine is lost. The overall primary forces

are equal to those from one cylinder alone, but the secondary forces of all three

pistons add together, as illustrated in Fig. 4. Two different3 cylinder crankshaft

configurations. On the left is a 120°, when one piston is at TDC then another will be

120° past TDC with the remaining one 120° before TDC. At 120° after or before TDC

the reciprocating forces are 50% of those at TDC but acting the opposite direction.

So all forces are balanced. Unfortunately, the opposing forces are offset along the

crankshaft and create a rocking couple. The 180° design on the right has no rocking

couple but only 2/3rds of the primary forces are balanced out and the secondaries

from all three cylinders sum together.




Figure 4,Two different 3-cylinder crankshaft configurations. Left at 120°, right

at 180° .

3.0 Software packages

In order to obtain certain geometry measurements, CATIA V5 was used in order to

sketch one of the pistons in a 120° angle, as shown in Fig. 5.

The MSC Adams software package, on which the dynamic analysis of the engine

was performed, is shown in the next section.

Figure 5, Catia V5



4.0 Adams simulation

In order to simulate the operation of the three cylinder engine, a new Adams

database is created. Then the components are imported from existing

stereolithography (.stl) files. These components can either be modelled in a CAD

package, or the default ones can be used from the Adams component examples.

In this case, the crankshaft of a single cylinder engine is imported from the Adams

library and then position markers are applied at the axis of rotation (0, 0, 0) and at the

crank throw (0, 0, 45mm). Since this crank throw will be the middle one, the angle of

the throw is changed to 120°. A second crank is imported and translated to a

distance of -90mm on the x axis and then rotated to an angle of 0°, as this crank

throw will be for the first piston. The third crank is then imported, translated to +90mm

(x axis) and an angle of 240° from the first crank. Therefore, each crank throw is

spaced at 120° between each another. Figure 6, shows the angle between the crank

throws.

The next step is to import the conrods, starting with the first crank throw. Markers are

added to the conrod at both the big and small end. Then the component is translated

so that the big end is coincident with the crank throw and the angle is vertical. The

second and third conrods are then imported and positioned the same way, only this

time they have an angle due to the crank throws being at a 120° angle. Their position

can also be seen in Fig. 6.

The gudgeon pins are then imported and the same process is followed with the three

pistons, with the components' position and angle being properly changed.

In order for the simulation to run, the software needs to know the joints that apply

between the components. Two rigid joints are added between the three cranks in

order to fix them as one. Then a revolute joint is added at each conrod's big end that

allows for rotation between the crank throw and the conrod. The piston is then fixed

with a rigid joint with the gudgeon pin at the small end of the conrod. A revolute joint

is the applied between the conrod's small end and the gudgeon pin. All the revolute

joints are set to allow freedom in the x axis.

A box simulating the engine block is added, and a rotational joint is applied between

the cranks and the block for the initial analysis, in order to allow for a motion to be

applied. The block is initially fixed on the ground. A motion of 800rpm (4800 deg/sec)

is applied for the first simulation.



Figure 6, Adams three cylinder engine model.

For the second simulation, a more realistic scenario is simulated. The block is not

fixed on the ground, but connected to three bushings acting as engine mounts.

Figure 7, illustrates the bushings and their characteristics, mostly set by guess. The

translational and torsional stiffness and damping coefficients can be set for each

axis. More screenshots can be found in the Appendix section.

After a simulation is performed for at least 5 seconds, the most important parameters

can be measured from the output plots.



Figure 7, Engine bushing characteristics.

5.0 Results

5.1 Adams simulation results

When obtaining the results from the plots, only the most important factors governing

the engine limits can be taken into account. Accelerations and forces on the

crankshaft mounts, crank throws, conrod small and big end, and piston and gudgeon

pins are of great importance. The reason being that the loads at these points must be

known in order to correctly design and select the material of the component as well

as the bearing specifications. All markers at the joint locations can be used to take

measurements of the forces on the components.

The following results are for a speed of 800rmp:



Crankshaft forces:

The following graph shows the forces on the centre of the crank between the first and

second throw:

Figure 8, Crankshaft forces.

Conrod big end forces:

Figure 9 shows the forces acting on the Y axis (vertical) at the three conrods' big

ends:

Figure 9, Conrod big end forces.

Piston acceleration:



The maximum acceleration experienced by the piston is on the Y axis at 420 m/s² or

42 G, as shown in Fig. 10:

Figure 10, Piston acceleration.

The motion driver speed was the increased to 8000rpm (48000 deg/sec) which is a

realistic engine revolution limit. As shown in Fig. 11, increasing the speed by 10

times leads to an increase of piston acceleration by 100 times (420G to 4200G).

Figure 11, Piston acceleration at 8000rpm

Bushing forces:



Figure 12 shows the forces acting on the bushings at the Y direction, which were the

highest.

Figure 12, Engine bushings forces

Engine block acceleration and displacement:

The acceleration magnitude acting on the centre of the mass of the engine block can

be seen in Fig. 13 to be 1G on the Y axis. Figures 14 to 16 show a displacement of

1.5mmon the Y axis (vertical), 0.12mm on the X axis (horizontal) and 0.7mm on the z

axis.

Figure 13, Engine block acceleration.



Figure 14, Engine block displacement on Y axis.

Figure 15, Engine block displacement on X axis.

Figure 16, Engine block displacement on Z axis.



5.2 Theoretical analysis

The three cylinder engine crankshaft positions and primary forces can be seen in Fig.

17. The first piston at TDC is balanced by the other two with a resulting net force of

zero. Secondary forces are also zero. Figure 18, explains how the induced rocking

motion can be calculated.

Figure 17,Primary forces.

Figure 18, Rocking couples.

Primary forces:



The vector diagram is shown in Fig. 19. The force for each piston is Fp=mω² R

cos(θ). In order to draw the vectors, a is chosen to be at zero degrees. Each vector

has a value m ω² R and adding them we see there is no resultant so there is no

resultant vertical component either and so Fp=0 and this will be true whatever the

crank angle.

(http://www.freestudy.co.uk/dynamics/balancing.pdf, 6/12/11)

Secondary forces:

The angle between each crank is 120° so doubling, vector B will be at 240° and

vector C will be at 480 ° all relative to A. Adding them there is no resultand whatever

the angle of vector A so Fs=0 at all angles and the secondary force is balanced.

(http://www.freestudy.co.uk/dynamics/balancing.pdf, 6/12/11)

Figure 19, Vector Diagram.

The mass of the pistons m was approximately 1kg at a 90mm distance between

them, the crankshaft speed ω was 8000rpm (837.8 rad/sec), the crank throw radius

was 45mm and the conrod length was 140mm.

So for the primary couple:

√3Ka=√3×m×R×ω2×α=4922,6Ν mFor the secondary couple:

√3KaRL

=√3×m×R×ω2×α× RL=1582.3Nm



6.0 Discussion

Apart from modelling the components, which can take up to 3 hours to complete, but

do not apply in this case (the stock Adams components were utilised), the initial

attempt to simulate the engine cycle required approximately 4 hours, including the

component import, joining and simulating. A second attempt was carried out as in the

initial one, the pistons were found to be clashing and therefore an increase in the

distance between the cylinders (75 to 90mm) was the solution. The second attempt

required approximately one hour, mainly due to the user being more familiar with the

software.

Since there were only 13 moving components, the simulation computation time was

so short that could not be measured and can therefore be neglected. Reasonably, an

increase in geometry complexion will increase computation time. However, the

software only calculates outputs based on component position, mass and centre of

mass. Thus, a simplified model can be derived from every system in order to be

simulated in Adams without the need to import complex component geometries. This

can result in simulation time reduction and more accurate results as well as easier

modification of the system parameters.

The simulation in MSC Adams shows that the accelerations at each joint can be

easily measured. A direct comparison between a speed of 800 and 8000rpm showed

that an increase in speed of 10 times, resulted in a vertical acceleration of the piston

from 42 to 4200 G (100 times increase) which is reasonable.

Measuring the bushing accelerations and forces is also useful in order to determine

the stiffness and damping coefficients to produce adequate settling times and ensure

that the natural resonance frequency vibration at low rpm does not damage the

vehicle or transfer to the passengers.

Appropriate settings of the torsional and translational stifnesses and damping

coefficients had different results. Adding more torsional resistance on the X axis at

bushings 1 and 2 helped reduce the rocking motion induced by the primary and

secondary couples.

The three cylinder engines used nowadays in the automotive industry, employ

counter-drive balancing shafts connected to the crankshaft that balance half of the

primary couple forces. Such a design is shown in Fig. 20, with the Skoda 1.2 litre

(http://www.ptc.com/appserver/wcms/ptcawards/entry.jsp?im_dbkey=6553, 6/12/11)



Figure 20, Skoda 1.2 litre 3 cylinder engine with balancing shaft.

7.0 Conclusions and recommendations

In order to ensure a mechanical, dynamic system operates within certain parameters,

its operation can be simulated using a software package such as MSC Adams. This

simulation can reduce calculation times, and decrease the time until the design of the

components begins. Dynamic loads are often the governing factors of a system's

performance specifications. Therefore, the dynamic analysis should always be

carried out before the static analysis and actual component 3D modelling.

In order to increase the results of this simulation the forces acting on the components

during the four strokes of the engine cycle must be applied. This can be done by

calculating these forces and then applying them using a step function. Thus,

according to the firing order of the cylinders, the forces will only be activated when

they are supposed to and the force will only act for a specific time duration. The

results will be more accurate and will help to better understand the dynamics of the

system.



References:

Rahnejat, H (2000). Multi-body dynamics: historical evolution and application.

University of Bradford

http://www.freestudy.co.uk/dynamics/balancing.pdf, Accessed on 6/12/11

http://www.tonyfoale.com/Articles/EngineBalance/EngineBalance.pdf, Accessed on

6/12/2011

http://www.ptc.com/appserver/wcms/ptcawards/entry.jsp?im_dbkey=6553, Accessed

on 6/12/11



Appendix

Adams screenshots:

Figure 21, Engine Isometric view.

Figure 22, Engine front view with bushings.



Figure 23, Engine top view with 3 bushings.

Figure 24, Wrong dimensions, piston clash and side view.


c. kalavrytinos - dynamics analysis of a three cylinder engine

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