Dynamic balancing of a inline engine PDF

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Dynamically balance a 6 cylinder inline engine with different firing orders, solved graphically...

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Student ID No: 20264853 Module: MP2784 Mechanics, Kinematics and Materials Assignment: Engine Balancing by Design

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Contents Introduction...........................................................................................................................................5 Engine Design 1.....................................................................................................................................5 Initial Conditions................................................................................................................................5 Layout Diagram..................................................................................................................................7 Primary Angular Positions Diagram...................................................................................................7 Secondary Angular Positions Diagram...............................................................................................8 Table of values...................................................................................................................................8 Primary (mr) polygons.......................................................................................................................9 Secondary (mr) Polygon.....................................................................................................................9 Primary (mrd) Polygon.....................................................................................................................10 Secondary (mrd) Polygon.................................................................................................................11 Engine Design 2...................................................................................................................................12 Initial Conditions..............................................................................................................................12 Layout Diagram................................................................................................................................12 Primary Angular Positions Diagram.................................................................................................13 Secondary Angular Positions Diagram.............................................................................................13 Table of values.................................................................................................................................14 Primary (mr) polygons.....................................................................................................................14 Secondary (mr) Polygon...................................................................................................................15 Primary (mrd) Polygon.....................................................................................................................15 Secondary (mrd) Polygon.................................................................................................................16 Design Evaluation................................................................................................................................16

Introduction To dynamically balance two alternative engine designs for a two-stroke, six-cylinder diesel engine. Both designs will be evaluated through complete analysis of forces and moments in order to demonstrate the effect of firing order in car engine balancing.

Engine Design 1

Initial Conditions Stroke Length (s) = 0.09 m Length (l) = 0.2 m Crank (r) =

s 2

=

0.09 2

= 0.045 m

Reciprocating Mass (m) = 5.0 Kg Engine Speed (ω) =

2 πRpm 60

=

2 π × 2500 60

= 262 rad/s

Cylinder Spacing = 0.15 m Angular Intervals =

No of Strokes × 180 ° No of Cyliders

=

2 ×180 ° 6

= 60°

Firing Order = 1-5-3-6-2-4 Obligatory Ratio =

l r

=

0.2 0.045

= 4.44 m

Distance (d) = Crank position from the Reference plane

Layout Diagram Figure 1 diagram illustrated the spacing of the cylinders with a defined central reference plane for the moments to be taken about.

Figure 1 Layout Diagram

Primary Angular Positions Diagram Figure 2 showed Primary crank positions at the instant when crank 1 is at top dead centre. Position of the cranks in firing order relative to the assumed clockwise direction of angular velocity.

Figure 2 Primary Crank Positions Diagram

Secondary Angular Positions Diagram Figure 3 diagram plotted for secondary crank positions in which all angles have been doubled, as these forces occur twice per every rotation of the shaft at the instant were crank 1 is at top dead centre.

Figure 3 shows secondary crank position

Table of values Table 1 below provided the initial values to be used to construct (mr) and (mrd) and mrd=m×r × d . polygons. Where mr=m× r Table 1 shows values of mr and mrd

Mass (m)

Radius (r)

Distance (d)

MR

MRD

Kg

m

m

Kg-m

1

5.000

0.045

-0.375

2

5.000

0.045

3

5.000

4

Kg-m²

θ Degree s

Degrees

0.225

-0.084375

0

0

-0.225

0.225

-0.050625

120

240

0.045

-0.075

0.225

-0.016875

240

120

5.000

0.045

0.075

0.225

0.016875

60

120

5

5.000

0.045

0.225

0.225

0.050625

300

240

6

5.000

0.045

0.375

0.225

0.084375

180

0

Crank Position

2θ

Primary (mr) polygons Primary force: mrω² cosθ The primary (mr) polygon in figure 4 was drawn at the instant were crank one is at top dead centre. Scale 3cm = 0.225 m

Figure 4 shows primary (mr) polygon

Secondary (mr) Polygon Secondary force: mrω² cos2θ/n The secondary (mr) polygon in figure 5 was drawn at the instant were crank one is at top dead centre Scale 3cm = 0.225 m

Figure 5 shows secondary (mr) polygon

Figure 4 and 5 demonstrate primary and secondary polygons to be enclosed which signifies the resultant to be 0. Therefore, primary and secondary inertia forces of the reciprocating parts are balanced.

Primary (mrd) Polygon Primary moment: mrxω2 cosθ The maximum out-of-balance couple represented in figure 6 by the dashed line. Scale 1cm = 0.75(mr)

Figure 6 shows primary couples polygon

The maximum out of balance primary couple is obtained by the closing line that is (6.93 ×0.016875)(

2 π ×2500 ) 60

² = 8015 Nm .

This occurs when crank 1 has rotated 210° or 30° from top-dead-centre.

Secondary (mrd) Polygon Secondary Moment: mrxω2 cos2θ/n Scale 1cm = 0.75(mr)

Figure 7 shows secondary (mrd) polygon

The closed polygon show no unbalanced secondary moments.

Engine Design 2 Initial Conditions Stroke Length (s) = 0.09 m Length (l) = 0.2 m Crank (r) =

s 2

=

0.09 2

= 0.045 m

Reciprocating Mass (m) = 5.0 Kg Engine Speed (ω) =

2 πRpm 60

=

2 π × 2500 60

= 262 rad/s

Cylinder Spacing = 0.15 m Angular Intervals =

No of Strokes × 180 ° No of Cyliders

=

2 ×180 ° 6

= 60°

Firing Order = 1-4-5-2-3-6 Obligatory Ratio =

l r

=

0.2 0.045

= 4.44 m

Distance (d) = Crank position from the Reference plane

Layout Diagram Figure 8 diagram illustrated the spacing of the cylinders with a defined central reference plane for the moments to be taken about.

Figure 8 Layout Diagram

Primary Angular Positions Diagram Figure 9 showed Primary crank positions at the instant when crank 1 is at top dead centre. Position of the cranks in firing order relative to the assumed clockwise direction of angular velocity.

Figure 9 primary crank positions diagram

Secondary Angular Positions Diagram Figure 10 diagram plotted for secondary crank positions in which all angles have been doubled, as these forces occur twice per every rotation of the shaft at the instant were crank 1 is at top dead centre.

Figure 10 secondary crank positions diagram

Table of values Table 2 below provided the initial values to be used to construct (mr) and (mrd) polygons. Where mr=m× r and mrd=m×r × d

Mass (Kg)

Radius (m)

Distance (m)

MR

Couples (MRD)

θ

m

Kg-m

Kg-m²

Degrees

2θ Degree s

Kg

m

1

5.000

0.045

-0.375

0.225

-0.084375

0

0

2

5.000

0.045

-0.225

0.225

-0.050625

180

0

3

5.000

0.045

-0.075

0.225

-0.016875

120

240

4

5.000

0.045

0.075

0.225

0.016875

300

240

5

5.000

0.045

0.225

0.225

0.050625

240

120

6

5.000

0.045

0.375

0.225

0.084375

60

120

Crank Position

Table 2 - shows values for mr and mrd

Primary (mr) polygons Primary force: mrω² cosθ The primary (mr) polygon in figure 11 was drawn at the instant were crank one is at top dead centre.

Figure 11 primary force polygon

Secondary (mr) Polygon Secondary force: mrω² cos2θ/n The secondary (mr) polygon in figure 12 was drawn at the instant were crank one is at top dead centre.

Figure 12 secondary force polygon

The primary and secondary force polygons close demonstrating that the primary and secondary forces are in balance.

Primary (mrd) Polygon Primary moment: mrxω2 cosθ Scale 1cm = 0.75(mr)

Figure 13 primary moment polygon

Secondary (mrd) Polygon Secondary Moment: mrxω2 cos2θ/n Scale 1cm = 0.75(mr)

Figure 14 - secondary moment polygon

The maximum out of balance secondary couple is obtained by the closing line that is (

13.8 × 0.016875 2 π ×2500 ) )( 60 4.44

² = 3609 Nm

And this occurs when crank 1 is at position 150 o, 60o, 240o or 330o, since the secondary polygon rotates at 2ω.

Design Evaluation Both engines exhibit primary balanced forces, these forces created by the reciprocating mass of the pistons occur once every rotation of the crankshaft. This demonstrates balance where the central principal axis is not displaced parallel to the rotating centreline whist the piston moves up and down, meaning the engine would not vibrate.

Similarly, both secondary forces are in balance, these forces occur twice per revolution of the crankshaft. These forces created because of the speed variation of the piston as it reaches top dead centre to bottom dead centre causing a difference in inertia, which is not present in this case. It is also clear from the table and radial diagrams that the primary and secondary forces balance at all times since the engine has equal reciprocal masses and equal crank spacing. Crank and connecting-rod dimensions are identical. However, although both engines are statically balanced there is imbalanced couples present in both engines meaning that neither are dynamically balanced. Engine one primary couple imbalance occurs during every rotation of the crankshaft with crank one at 210° and 30°. This imbalance caused by reciprocating masses at 180° separation along different planes shows crank 6 and 1 to cause the imbalance as the weight is disproportional. This would cause vibration along the shaft. Engine two secondary couple imbalance occurs twice per rotation of the crankshaft with crank 1 at 60°, 150° 240° and 330° due to crank 1 and crank 2 speed variation from top dead centre to bottom dead centre at 180° along the shaft. Both conditions of unbalance cause a central principal mass axis to intersect the rotating centreline. In dynamic engine balancing both unbalances can be solved with calibration instructing correct balancing weights....