Two-stroke turbocharged internal combustion engine having 15 cylinders in a single row.

The present invention relates to a two-stroke internal com- bustion engine having 15 cylinders in a single row and a crankshaft, which internal combustion engine has a firing sequence (nl - nl5) of the engine cylinders Cl to C15.

It has been suggested to provide a 15 cylinder engine with the firing sequence 1 8 15 11 4 2 9 13 10 6 3 7 14 12 5. The firing sequence of an engine is important for the vibrational characteristics of the engine system. The vibrations of primary relevance are external unbalanced moments, guide force moments, torsional vibrations in the shafting system and axial vibrations in the shafting system. The vibrations are to a large extent caused by the inertia forces on the moving masses and gas forces acting on the pistons when the engine is running. These forces on an individual piston vary in time during one revolution of the engine. And all pistons with associated moving parts, like piston rod, crosshead, connect- ing rod and crankshaft throw, in the engine contribute to the resulting pattern of vibrations. The individual piston has a certain location in the engine, such as cylinder No. 4 (and the cylinder is then called C4), and this location is of cause a fixed location for a given engine. However, the mutual timing of the movements of the pistons can be varied at the design stage of the engine by changing the firing sequence. The firing sequence decides for every cylinder in the engine when a given cylinder is to fire during one engine revolution.

Computer programs have been developed in order to calcu- late possible firing sequences. These computer programs are based on try-and-error calculations where the different even firing sequences are calculated one after the other, and for each firing sequence vector summations are calculated for the force contribu-

tions from all cylinders. For in-line two-stroke engines of up to 12 cylinders these programs have been able to cope with the amount of calculations to be carried out. When, however, the number of cylinders is increased, it becomes increasingly difficult to carry out the calculations.

For an engine with 15 cylinders the number of possible even firing orders is about 87.000.000.000, and even for the most powerful of current computers the full computations cannot be performed within an acceptable time span. It is consequently required that a selection is made among the vast number of possibilities.

The object of the present invention is to improve vibration conditions of the 15 cylinder in-line engine.

In view of this, the two-stroke internal combustion engine having 15 cylinders is according to a first aspect of the present in- vention characterized in that the crankshaft is built in three sections assembled in extension of one another, that a first crankshaft section of said three sections is associated with a first plurality of engine cylinders including engine cylinder Cl, a second crankshaft section of said three sections is associated with a second plurality of engine cylinders including engine cylinder C8 and a third crankshaft section of said three sections is associated with a third plurality of engine cylinders including engine cylinder C15, and that the firing sequence (nl - nl5) of the fifteen cylinders includes at least the following five groups of mutually different cylinders: 1) a first group of only two consecutively firing cylinders from said first plurality of engine cylinders,

2) a second group of only two consecutively firing cylinders from a single one of said first plurality, said second plurality or said third plurality of engine cylinders, 3) a third group of only two consecutively firing cylinders from a single one of said first plurality, said second plurality or said third plurality of engine cylinders, 4) a fourth group of either

only two consecutively firing cylinders from a single one of said first plurality, said second plurality or said third plurality of engine cylinders, or three consecutively firing cylinders of which the first and the third firing cylinder are from a single one of said first plurality, said second plurality or said third plurality of engine cylinders, and the second firing cylinder is from either the same plurality of engine cylinders as the first and third firing cylinder or from one of the other pluralities of cylinders, and 5) a fifth group of either only two consecutively firing cylinders from a single one of said first plurality, said second plurality or said third plurality of engine cylinders, or three consecutively firing cylinders of which the first and the third firing cylinder are from a single one of said first plurality, said second plurality or said third plurality of engine cylinders, and the second firing cylinder is from either the same plurality of engine cylinders as the first and third firing cylinder or from one of the other pluralities of cylinders. The division of the crankshaft into three sections has considerable impact on the vibrational behaviour of the engine because the distance between the cylinders in the engine is larger at the location of the division of the crankshaft. The larger distance is required in order to make room for assembly flanges and double main bearings between the neighbouring cylinders. The additional distance can e.g. amount to about 70% of the normal distance between cylinders. A consequence of dividing the crankshaft is the disadvantage of a larger resulting overall length of the engine. With a crankshaft divided in three, the two divisions cause an in- crease in engine length corresponding to more than one cylinder.

The firing sequences according to the first aspect of the present invention are all seen to include at least three groups of two consecutively firing cylinders and possibly one or two further

groups of at least two consecutively firing cylinders or one or two groups of three consecutively firing cylinders. From 10 to 12 out of the 15 cylinders are thus clearly grouped and only very few out of the possible even firing sequences for the 15 cylinder engine ex- hibit this grouping of cylinders. When a specific engine is to be built it is consequently possible to find acceptable firing sequences by calculation because the calculations can be performed only on the firing sequences fulfilling the mentioned grouping of cylinders. Optimum firing sequences for any specific application can thus be found.

It has surprisingly turned out that the firing sequences found by the applicant with the mentioned grouping have quite acceptable vibration levels. Some of the firing sequences do require the use of a vibration damper to counteract and/or dampen one of the vibration modes, and others do not, but all of them seem to be suitable for use in actual engines.

In an embodiment the first plurality of engine cylinders associated with the first crankshaft section consists of engine cylinders Cl to C5; the second plurality of engine cylinders associated with the second crankshaft section consists of engine cylinders C6 to

ClO; the third plurality of engine cylinders associated with the third crankshaft section consists of engine cylinders CIl to C15; and the third group of only two consecutively firing cylinders is from the second plurality of engine cylinders or from the third plu- rality of engine cylinders. In this embodiment the three sections of the crankshaft are associated with an equal number of the engine cylinders, namely five cylinders each, and up to two of the groups of consecutively firing cylinders are all from the first plurality of engine cylinders. In an alternative embodiment of the present invention the first plurality of engine cylinders associated with the first crankshaft section consists of engine cylinders Cl to C6; the second plurality of engine cylinders associated with the second crankshaft

section consists of engine cylinders C7 to CIl; the third plurality of engine cylinders associated with the third crankshaft section consists of engine cylinders C12 to C15; and the third group of two consecutively firing cylinders is from the first plurality of engine cylinders or from the third plurality of engine cylinders. With this grouping, up to three of the groups of consecutively firing cylinders are all from the first plurality of engine cylinders, and the crankshaft has been divided in unequal lengths with the longest section associated with cylinder Cl. When Cl is located at the free end of the engine (opposite the connection to the driven shaft) this brings the advantage that the least heavily loaded section of the crankshaft has the longest length, and the most heavily loaded third crankshaft section has the shortest length. This more heavily loaded third crankshaft section can thus be given larger shaft thickness etc. without being of a larger weight than the first crankshaft section.

Preferably, the second group is of two consecutively firing cylinders from the first plurality of engine cylinders or from the second plurality of engine cylinders. Out of these two pluralities it is preferred that the second group is from the first plurality of engine cylinders.

In case the crankshaft is divided in the cylinder ratio of 6-5-4 as indicated in the above, it is possible to utilize a firing sequence in which the fifth group consists of either three consecutively firing cylinders from the first plurality of engine cylinders or three consecutively firing cylinders from the second plurality of engine cylinders.

If the firing sequence has none or only a single pair of consecutively firing cylinders from the second plurality of engine cylin- ders it is preferred that the firing sequence includes a fourth group in which the first and the third firing cylinder are from the second plurality of engine cylinders and the second firing cylinder is from either the first plurality of engine cylinders or from the third plural-

ity of engine cylinders. In this manner the firing sequence is made comparatively well balanced despite the lack of the pair of consecutively firing cylinders from the second plurality of engine cylinders. In a further embodiment the fourth group is two consecutively firing cylinders from either the second plurality of engine cylinders or from the third plurality of engine cylinders. This provides the firing sequence with a rather large number of two consecutively firing cylinders from the plurality of cylinders, and the run- ning conditions of the engine are improved.

In an embodiment the fifth group has three consecutively firing cylinders of which one or two are from the second plurality of engine cylinders. This detail in the firing sequence is in particular useful when the other groups of the firing order comprise three or four pairs of consecutively firing cylinders from the first plurality of engine cylinders and from the third plurality of engine cylinders.

In order to diminish the vibration levels it is preferred that the fifth group has two consecutively firing cylinders from the third plurality of engine cylinders. With this grouping there are several groups of two cylinders from the two end crankshaft sections (first and third section). This provides a balanced distribution of the forces acting on the engine pistons.

In a preferred embodiment the first six cylinders in the firing sequence are two cylinders from the first plurality of engine cylin- ders followed by two cylinders from the third plurality of engine cylinders followed by one cylinder from the second plurality of engine cylinders followed by one cylinder from the first plurality of engine cylinders. This pattern of firings results in low vibration levels. In another preferred embodiment due to the low levels of resulting vibration, the first two cylinders in the firing sequence are two cylinders from the first plurality of engine cylinders, and the five last cylinders in the firing sequence are two cylinders from the

first plurality of engine cylinders followed by one cylinder from the second plurality of engine cylinders followed by one cylinder from the third plurality of engine cylinders followed by one cylinder from the second plurality of engine cylinders. In yet another embodiment there are at the most two of the groups that have two consecutively firing cylinders from the first plurality of engine cylinders.

In an embodiment none of the groups in the firing sequence includes three consecutively firing cylinders from a single one of said first plurality, said second plurality or said third plurality of engine cylinders.

In another aspect of the present invention the object of providing a selection that results in firing sequences providing acceptable vibration conditions for a two-stroke internal combustion en- gine having 15 cylinders in a single row and a crankshaft, has been solved by selecting the firing sequence as one of the following firing sequences: a) 1 3 12 14 7 4 5 10 15 8 2 6 9 13 11 b) 1 4 12 14 7 2 6 11 13 8 3 5 10 15 9 c) 1 4 12 15 6 2 7 10 13 8 3 5 11 14 9 d) 1 5 12 13 7 3 6 10 14 9 2 4 11 15 8 e) 1 5 12 13 7 3 6 9 14 10 2 4 11 15 8 f) 1 5 12 13 8 3 4 11 15 6 2 7 10 14 9 g) 1 5 12 13 8 3 4 11 15 7 2 6 10 14 9 h) 1 5 12 13 8 4 3 11 15 7 2 6 10 14 9 i) 1 5 12 14 6 3 7 9 13 10 2 4 11 15 8 j) 1 5 13 12 7 3 6 10 14 9 2 4 11 15 8 k) 1 5 13 12 8 4 3 11 15 7 2 6 10 14 9

I) 1 6 11 13 9 2 4 12 14 7 3 5 10 15 8, wherein said cylinder Cl can be located at either the one or the other of the two ends of the engine, cylinder C15 is located at the end of the engine opposite to cylinder Cl, the cylinders C2 to C14 are numbered consecutively along the length of the engine in

direction from cylinder Cl towards cylinder C15, and the direction of rotation of the engine can be in either the one or the other rotational direction. These firing sequences can be applied to an engine having a crankshaft built in three sections assembled in extension of one another or a crankshaft built in other manners, such as a crankshaft built in four sections or in less than three sections, e.g. two sections or only a single section. These firing sequences thus provide such very fine vibrational conditions that the crankshaft can be divided as is pleased for the actual installation. The selected firing sequences are very few out of the possible amount of firing sequences. These firing sequences have been verified to have excellent vibration characteristics by calculating the vibration response from an engine operating in test with said firing sequences. With respect to both the first and the second aspects of the present invention the firing sequence can be both an even sequence and an uneven sequence. When the firing sequence is even the turning angle of the crankshaft between the firing of any two consecutive cylinders is 360°/15. This fixed size angle applies to all cylinders in the engine when the firing sequence is even. And the even sequences are utilized when the desire is to find acceptable firing sequences. When acceptable firing sequences have been found it is possible to investigate whether even better vibration characteristics can be obtained by utilizing uneven firing se- quences. This can be considered as a fine-tuning of the vibration pattern. An uneven firing sequence is a sequence in which the turning angle of the crankshaft between the firing of at least two pairs of consecutively firing cylinders is different from 360°/15.

Examples of embodiments of the present invention are de- scribed in more detail in the following with reference to the highly schematic drawings, on which

Fig. 1 is a sectional view of a two-stroke engine with 15 cylinders according to the present invention,

Fig. 2 is a side view of the engine in Fig. 1, and Fig. 3 is an illustration of a firing sequence for the cylinders pertaining to the engine of Fig. 1.

In Fig. 1 is seen the cross-section through a large two-stroke turbocharged internal combustion engine of the crosshead type, having 15 cylinders. The engine can e.g. be of the make MAN B&W Diesel and the type MC or ME, or of the make Wartsila of the type Sulzer RT-flex or Sulzer RTA or of the make Mitsubishi Heavy Industries. The cylinders can e.g. have a bore in the range of e.g. 60 to 120 cm, preferably from 80 to 120 cm, and more preferably from 95 to 120 cm. The engine can e.g. have a power in the range of 3000 to 8500 kW per cylinder, preferably from 4000 to 8000 kW, such as at least 5.000 kW per cylinder. Each cylinder C1-C15 typically has a cylinder liner 1 with a row of scavenge air ports 2 in its lower end and a cylinder cover 3 with an exhaust valve 4 located in the top of the cylinder.

A piston 5 is mounted on a piston rod 6, and the piston rod 6 is connected with a crank pin 9 on a crankshaft 10 via a crosshead 7 and a connecting rod 8. The crankshaft journal 11 is located in a main bearing mounted in a bedplate 12.

The crosshead is supported in the transverse direction by guide shoes 13 sliding on vertically extending guide planes 22 extending in the vertical direction from the top towards the bottom of the engine frame 14. The guide planes are fixed to the engine frame 14, and the engine frame is fixed to the top of the bedplate 12. Foundation bolts 23 fix bedplate 12 to an engine foundation (not shown). The engine foundation is part of the ship hull in case the engine is a main propulsion engine in a ship, or is part of a building structure in case the engine is a stationary engine in a power plant. External forces and moments caused by vibrations in the engine are transferred to the engine foundation and possibly also to other structures, such as walls or a hull side. A cylinder section 15 is mounted on top of the engine frame.

The cylinder cover 3 is fixed to the cylinder section by cover studs 16. Tie-rods 17 extend from the cylinder section down to the bedplate and they fix the cylinder section 15 to the bedplate 12. There are typically four tie-rods 17 acting on each cylinder section, and the sum of the downward forces from the tie-rods exceeds the upward directed force on the cylinder cover caused by the maximum pressure developed by the combustion in the combustion chamber in the cylinder.

An exhaust gas duct 18 extends from the individual cylinder in the area of the exhaust valve and opens out into an exhaust gas receiver 19 that is common to a number of cylinders. The engine may have only a single exhaust gas receiver which is common to all cylinders, or it can have a plurality of exhaust gas receivers, such as two or three, located end-to-end in extension of each other and typically interconnected through gas flow passages 19'.

The exhaust gas receiver is a pressure vessel with a circular cylindrical cross-section. The exhaust gas duct 18 is extending into the exhaust receiver 19 and delivers the exhaust gas from the pertaining combustion chamber when the exhaust valve is open. In the exhaust gas receiver pressure variations caused by the exhaust gas pulses emitted from the exhaust gas ducts are equalized to a more even pressure.

A plurality of turbochargers 20 are connected to the exhaust gas receiver 19 and deliver compressed air via an air flow passage 24 and possibly an inlet air cooler 25 to a scavenge air system 26 comprising at scavenge air receiver 27 and flow passages 28 to an inlet air chamber 29 at scavenge air ports 2.

The crankshaft can be made in a single section or it can be manufactured in several sections that are joined into a complete crankshaft at the assembly of the engine. If the crankshaft is of a single section the distance I between the cylinders in the engine is constant through out the crankshaft. However, the crankshaft for an engine of the kind pertaining to the present invention is typi-

cally divided into sections that are assembled into a unified crankshaft. The division of the crankshaft into several parts can e.g. be caused by a desire to adjust the weight of the individual crankshaft section to be less than the maximum lifting capacity of the crane utilized for handling the crankshaft section. The lifting capacity of such a crane can e.g. be 250 t. The crankshaft is typically divided into three sections, but it can alternatively be divided into two sections or more than three sections. In the following examples of embodiments it is assumed that the cylinders in the engine can be associated with three crankshaft sections, whether the crankshaft is actually divided into sections or not.

In the side view illustration of the embodiment of the engine presented in Fig. 2 the crankshaft is divided between cylinders C5- C6 and ClO-CIl so that cylinders Cl, C2, C3, C4 and C5 are asso- ciated with a first crankshaft section and are considered to be a first plurality of engine cylinders a, cylinders C6, C7, C8, C9 and ClO are associated with a second crankshaft section and are considered to be a second plurality of engine cylinders b, and cylinders CIl, C12, C13, C14 and C15 are associated with a third crankshaft section and are considered to be a third plurality of engine cylinders c. The crankshaft has consequently been divided in the cylinder ratio of 5-5-5. This is called an even division. In an alternative division of the crankshaft the crankshaft is divided between cylinders C6-C7 and C11-C12 so that cylinders Cl to C6 are associated with a first crankshaft section and are considered to be a first plurality of engine cylinders a, cylinders Cl to CIl are associated with a second crankshaft section and are considered to be a second plurality of engine cylinders b, and cylinders C12 to C15 are associated with a third crankshaft section and are considered to be a third plurality of engine cylinders c. The crankshaft has consequently been divided in the cylinder ratio of 6-5-4. This is called an uneven division. Both examples of cylinder ratios are applicable to the present invention.

The ordinary distance between cylinders is L. In between the groups the distance can be the larger distance L2 illustrated in Fig. 2. The distance L2 = L + II. This is the normal distance between cylinders plus an additional length Il caused by the presence of two main bearings and an intermediate crankshaft joint, such as a flange connection where two crankshaft sections are joined by bolting or by another suitable joining method.

An important feature of the present invention is the grouping of the cylinders in the actual firing sequences. The concepts of the grouping of the cylinders according to the first aspect of the present invention are presented in the below Tables 1 and 2. Table 1 and the firing sequences mentioned thereafter relate to an embodiment of the engine in which the crankshaft has the uneven division in the cylinder ratio of 6-5-4. In Table 1 the first plurality of engine cylin- ders Cl, C2, C3, C4, C5 and C6 are labelled a, the second plurality of engine cylinders C7, C8, C9, ClO and CIl are labelled b, and the third plurality of engine cylinders C12, C13, C14 and C15 are labelled c. So if the table mentions e.g. bcb in a group that group has three consecutively firing cylinders of which the first and the third firing cylinder are from the second plurality of engine cylinders and the second firing cylinder is from the third plurality of engine cylinders.

Table 1 (Uneven division of the crankshaft sections 6-5-4)

Grouped cylinders

Group 1 aa aa aa aa aa aa aa aa aa aa aa

Group 2 aa aa aa aa aa aa aa aa aa bb bb

Group 3 aa aa aa aa aa aa aa cc CC CC CC G Grroouupp 4 4 bbbb bbbb bb bcb bcb bcb bcb aba bcb bcb bb

Group 5 CC bb bcb bcb bcb bcb bbb bcb aba aaa aaa

Group 6 CC cc cc cc cbc cc bcb

Group 7 bb

Based on these groups according to the present invention calculations have been made in order to establish actual firing sequences. An extract of the firing sequences are shown in the following listing of Sequences A, in which the "C"'s have been omitted so that the listing corresponds to the traditional manner of listing firing sequences. 1-15 in order words correspond to C1-C15.

Sequences A: 1) 1-5-12-14-6-3-7-9-13-10-2-4-11-15-8

2) 1-8-15-11-4-2-10-13-9-7-3-6-14-12-5

3) 1-6-11-14-8-2-4-12-15-5-3-7-10-13-9

4) 1-9-13-10-7-3-5-15-12-4-2-8-14-11-6

5) 1-3-13-15-5-2-8-11-12-7-4-6-9-14-10 6) 1-10-14-9-6-4-7-12-11-8-2-5-15-13-3

7) 1-4-12-14-7-2-5-13-11-8-6-3-9-15-10

8) 1-10-15-9-3-6-8-11-13-5-2-7-14-12-4

9) 1-4-12-14-7-2-5-13-11-8-6-3-10-15-9

10) 1-9-15-10-3-6-8-11-13-5-2-7-14-12-4 11) 1-4-12-14-7-2-6-11-13-8-3-5-10-15-9

12) 1-9-15-10-5-3-8-13-11-6-2-7-14-12-4

13) 1-4-12-14-7-2-6-11-13-8-5-3-10-15-9

14) 1-9-15-10-3-5-8-13-11-6-2-7-14-12-4

15) 1-4-12-15-6-2-7-10-13-8-3-5-11-14-9 16) 1-9-14-11-5-3-8-13-10-7-2-6-15-12-4

17) 1-4-13-15-5-2-7-11-12-8-3-6-10-14-9

18) 1-9-14-10-6-3-8-12-11-7-2-5-15-13-4

19) 1-5-11-15-8-2-4-12-14-6-3-7-9-13-10

20) 1-10-13-9-7-3-6-14-12-4-2-8-15-11-5 21) 1-6-11-13-9-2-4-12-14-7-3-5-10-15-1

22) 1-8-15-10-5-3-7-14-12-4-2-9-13-11-6

23) 1-5-13-12-7-3-6-10-14-9-2-4-11-15-8

24) 1-8-15-11-4-2-9-14-10-6-3-7-12-13-5

25) 1 -3-12-14-7-4-5-9-15-8-2-6-10-13-11

26) 1 -11-13-10-6-2-8-15-9-5-4-7-14-12-3

27) 1 -5-12-11-8-7-4-6-14-13-2-3-9-15-10

28) 1 -10-15-9-3-2-13-14-6-4-7-8-11-12-5

29) 1 -4-13-14-6-2-7-11-12-8-5-3-10-15-9

30) 1 -9-15-10-3-5-8-12-11-7-2-6-14-13-4

31) 1 -2-14-15-5-3-7-10-12-8-4-6-9-13-11

32) 1 -11-13-9-6-4-8-12-10-7-3-5-15-14-2

33) 1 -2-13-14-7-3-6-10-12-9-5-4-8-15-11

34) 1 ^■ 11-15-8-4-5-9-12-10-6-3-7-14-13-2

35) 1 -2-11-15-8-3-6-9-12-10-5-4-7-14-13

36) 1 -13-14-7-4-5-10-12-9-6-3-8-15-11-2

37) 1 -3-12-13-7-6-4-8-14-10-5-2-9-15-11

38) 1 -11-15-9-2-5-10-14-8-4-6-7-13-12-3

39) 1 -4-13-12-7-6-3-10-15-8-2-5-11-14-9

40) 1 -9-14-11-5-2-8-15-10-3-6-7-12-13-4

41) 1 -6-15-13-2-3-9-14-10-4-5-8-11-12-7

42) 1 -7-12-11-8-5-4-10-14-9-3-2-13-15-6

43) 1 -6-15-13-3-2-9-14-10-4-5-8-11-12-7

44) 1 -7-12-11-8-5-4-10-14-9-2-3-13-15-6

45) 1 -2-11-13-9-6-4-8-12-10-7-3-5-15-14

46) 1 -14-15-5-3-7-10-12-8-4-6-9-13-11-2

47) 1 -6-13-11-8-5-4-10-14-9-3-2-12-15-7

48) 1 -7-15-12-2-3-9-14-10-4-5-8-11-13-6

49) 1 -4-14-13-6-2-7-12-10-9-5-3-11-15-8

50) 1 -8-15-11-3-5-9-10-12-7-2-6-13-14-4

51) 1 -3-13-12-7-6-4-8-14-10-5-2-9-15-11

52) 1 -11-15-9-2-5-10-14-8-4-6-7-12-13-3

53) 1 ^■ 5-11-14-9-2-3-13-12-7-6-4-8-15-10

54) 1 ■10-15-8-4-6-7-12-13-3-2-9-14-11-5

55) 1 -4-13-12-7-5-3-11-15-8-2-6-9-14-10

56) 1 ■10-14-9-6-2-8-15-11-3-5-7-12-13-4

57) 1 -2-14-12-7-6-3-10-13-9-5-4-8-15-11

58) 1-11-15-8 ^■ 4-5-9-13-10-3-6- ^■ 7-12-14-2

59) 1-2-15-14 -5-3-7-10-12-8-4- ^• 6-9-13-11

60) 1-11-13-9 ^■ 6-4-8-12-10-7-3- ^■ 5-14-15-2

61) 1-3-11-14 ^■ 9-2-6-10-12-8-7- ^■ 4-5-15-13

62) 1-13-15-5 ^■ 4-7-8-12-10-6-2- ^■ 9-14-11-3

63) 1-5-14-11 ^■ 6-7-4-8-15-10-2- ^■ 3-12-13-9

64) 1-9-13-12 ^■ 3-2-10-15-8-4-7- ^■ 6-11-14-5

65) 1-4-12-13 ^■ 8-5-2-11-15-7-3- ^■ 6-9-14-10

66) 1-10-14-9 ^■ 6-3-7-15-11-2-5- 8-13-12-4

67) 1-6-15-13 ^■ 3-2-9-14-10-5-4- ^■ 8-11-12-7

68) 1-7-12-11 ^■ 8-4-5-10-14-9-2- ^■ 3-13-15-6

69) 1-2-13-14 ^■ 7-3-6-10-12-9-4- ^■ 5-8-15-11

70) 1-11-15-8 ^■ 5-4-9-12-10-6-3- 7-14-13-2

71) 1-2-11-14 ^■ 9-4-5-8-12-10-7- ^• 3-6-15-13

72) 1-13-15-6 ^■ 3-7-10-12-8-5-4- ^■ 9-14-11-2

73) 1-3-14-13 ^■ 7-2-6-12-11-8-5- 4-10-15-9

74) 1-9-15-10 ^■ 4-5-8-11-12-6-2- ^■ 7-13-14-3

75) 1-5-12-13 ^■ 7-3-6-10-14-9-2- ^■ 4-11-15-8

76) 1-8-15-11 -4-2-9-14-10-6-3- ^■ 7-13-12-5

77) 1-2-14-13 -7-4-5-10-12-9-6- ^■ 3-8-15-11

78) 1-11-15-8 ^■ 3-6-9-12-10-5-4- ^■ 7-13-14-2

79) 1-4-13-14 ^■ 6-2-7-12-10-9-5- ^■ 3-11-15-8

80) 1-8-15-11 ^■ 3-5-9-10-12-7-2- ^■ 6-14-13-4

81) 1-5-15-13 ^■ 3-2-9-14-10-4-6- 7-11-12-8

82) 1-8-12-11 ^■ 7-6-4-10-14-9-2- ^■ 3-13-15-5

83) 1-3-15-13 ^■ 6-2-7-12-10-8-5- ^■ 4-11-14-9

84) 1-9-14-11 ^■ 4-5-8-10-12-7-2- ^■ 6-13-15-3

85) 1-6-13-11 ^■ 8-5-4-10-14-9-2- ^■ 3-12-15-7

86) 1-7-15-12 ^■ 3-2-9-14-10-4-5- ^■ 8-11-13-6

87) 1-5-15-13 ^■ 3-4-10-8-12-9-2- ^■ 6-11-14-7

88) 1-7-14-11 ^■ 6-2-9-12-8-10-4- ^• 3-13-15-5

89) 1-4-13-14 ^■ 6-2-7-12-9-10-5- •3-11-15-8

90) 1-8-15-11 ^■ 3-5-10-9-12-7-2- ^■ 6-14-13-4

91) ^• 3-12-14-8-2- ^■ 6-10-13-9-4- 5-7-15-11 92) ^■ 11-15-7-5-4- ^■ 9-13-10-6-2- 8-14-12-3 93) ^■ 6-13-14-4-3- ^■ 8-10-12-9-2- ^• 5-11-15-7 94) ^■ 7-15-11-5-2- ^■ 9-12-10-8-3- 4-14-13-6 95) ^■ 2-14-12-7-6- ^■ 4-9-13-10-5- 3-8-15-11 96) ^■ 11-15-8-3-5- •10-13-9-4-6- 7-12-14-2 97) ^• 5-12-13-7-3- ^■ 6-9-14-10-2- 4-11-15-8 98) ^• 8-15-11-4-2- ^■ 10-14-9-6-3- 7-13-12-5 99) ^• 5-15-14-2-3- ^■ 9-12-11-6-4- 7-10-13-8

100) 1 ^■ 8-13-10-7-4- ^■ 6-11-12-9-3- 2-14-15-5

101) 1 ^• 3-12-13-7-6- •4-8-15-10-2- 5-9-14-11

102) 1 ^■ 11-14-9-5-2- ^■ 10-15-8-4-6- 7-13-12-3

103) 1 ^• 6-13-11-8-5- 4-9-14-10-3- 2-12-15-7

104) 1 ^■ 7-15-12-2-3- ^■ 10-14-9-4-5- 8-11-13-6

105) 1 ^■ 2-13-14-6-4- ^■ 7-8-12-10-5- 3-9-15-11

106) 1 ^■ 11-15-9-3-5- 10-12-8-7-4- 6-14-13-2

107) 1 ^■ 2-14-15-4-3- ^■ 8-10-12-7-5- 6-9-13-11

108) 1 11-13-9-6-5- 7-12-10-8-3- 4-15-14-2

109) 1 ^• 5-15-14-2-3- ^■ 9-12-10-7-4- 6-11-13-8

110) 1 ^• 8-13-11-6-4- 7-10-12-9-3- 2-14-15-5

111) 1 3-11-15-8-2- ^■ 6-10-13-9-5- 4-7-14-12

112) 1 ^■ 12-14-7-4-5- 9-13-10-6-2- 8-15-11-3

113) 1 2-11-13-9-4- 6-8-12-10-7- 3-5-15-14

114) 1 ^■ 14-15-5-3-7- ^■ 10-12-8-6-4- 9-13-11-2

115) 1 ^■ 4-14-13-6-2- 7-12-9-10-5- 3-11-15-8

116) 1 ^■ 8-15-11-3-5- 10-9-12-7-2- 6-13-14-4

117) 1 3-15-14-5-2- 7-13-11-6-4- 8-9-12-10

118) 1 ^■ 10-12-9-8-4- 6-11-13-7-2- 5-14-15-3

119) 1 6-9-13-11-3- 2-12-14-7-4- 5-8-15-10

120) 1 ^■ 10-15-8-5-4- 7-14-12-2-3- 11-13-9-6

121) 1 3-13-12-6-7- 4-8-14-10-5- 2-9-15-11

122) 1 11-15-9-2-5- 10-14-8-4-7- 6-12-13-3

123) 1 5-12-13-8-3- 4-11-15-7-2- 6-10-14-9

124) 1-9-14-10-6-2-7-15-11-4-3-8-13-12-5

125) 1-3-13-14-7-2-6-11-12-8-5-4-9-15-10

126) 1-10-15-9-4-5-8-12-11-6-2-7-14-13-3

127) 1-6-14-13-4-2-7-15-11-3-5-9-10-12-8 128) 1-8-12-10-9-5-3-11-15-7-2-4-13-14-6

129) 1-2-15-14-4-3-8-10-12-7-5-6-9-13-11

130) 1-11-13-9-6-5-7-12-10-8-3-4-14-15-2

131) 1-8-12-14-2-4-7-15-10-5-3-9-11-13-6

132) 1-6-13-11-9-3-5-10-15-7-4-2-14-12-8 133) 1-7-10-14-8-2-4-12-15-6-3-5-13-11-9

134) 1-9-11-13-5-3-6-15-12-4-2-8-14-10-7

135) 1-6-8-15-10-2-4-11-14-7-5-3-13-9-12

136) 1-12-9-13-3-5-7-14-11-4-2-10-15-8-6

137) 1-6-7-15-11-2-4-10-14-8-5-3-12-9-13 138) 1-13-9-12-3-5-8-14-10-4-2-11-15-7-6

139) 1-14-12-9-2-5-11-13-7-6-3-10-15-8-4

140) 1-4-8-15-10-3-6-7-13-11-5-2-9-12-14

141) 1-6-7-15-10-4-2-11-14-8-5-3-12-9-13

142) 1-13-9-12-3-5-8-14-11-2-4-10-15-7-6 143) 1-9-12-14-2-4-7-15-10-5-3-8-13-11-6

144) 1-6-11-13-8-3-5-10-15-7-4-2-14-12-9

With respect to the grouping we illustrate this in detail with the firing sequence 1 5 12 14 6 3 7 9 13 10 2 4 11 15 8. The firing num- ber is replaced with the labels a, b or c applicable to the cylinder, resulting in the following a a c c a a b b c b a a b c b. This particular firing sequence thus has the following groups aa, cc, aa, bb, aa and bcb. When these groups are compared with Table 1 it appears that these groups are listed in the third column, and that Group 1 = aa, Group 2 = aa, Group 3 = aa, Group 4 = bb, Group 5 = bcb, and

Group 6 = cc. The numbering of these groups does not indicate anything about the sequence of the groups, so cc is allocated to Group 6 even though cc appears immediately after the first group of aa.

When the actual sequence of the cylinders is taken into consideration in addition to the grouping of the cylinders it appears that the first two cylinders in the firing sequence are two cylinders from the first plurality of engine cylinders, and that the five last cylinders in the firing sequence are two cylinders from the first plurality of engine cylinders followed by one cylinder from the second plurality of engine cylinders followed by one cylinder from the third plurality of engine cylinders followed by one cylinder from the second plurality of engine cylinders. To give another example, the firing sequence listed as No. 144 is the following 1 6 11 13 8 3 5 10 15 7 4 2 14 12 9. This corresponds to a a b c b a a b c b a a c c b and to the groups aa, bcb, aa, bcb, aa, and cc. These groups are listed in the 5th column of Table 1, and thus Group 1 = aa, Group 2 = aa, Group 3 = aa, Group 4 = bcb, Group 5 = bcb, and Group 6 = cc.

The actual level of vibrations of course depends on the actual engine. Calculations have been made for an engine of the type K98ME, viz. a MAN B&W Diesel engine having a cylinder bore of 0.98 m and electronic control of exhaust valves and of fuel injection. The nominal distance between the cylinders is L = 1.750 m, and the distance between cylinders C6 and C7 and between cylinders CIl and C12 is L2 = 2.99 m. This engine has a nominal power of 93.450 kW at 100% engine load.

For a given firing sequence a so-called harmonic analysis is performed in order to obtain values for the various resulting vibration levels caused by the excitation sources in the engine. The harmonic analysis involves a summation of the individual harmonic contributions. The harmonic analysis can be performed electronically by a computer program such as PROFIR developed by MAN B&W Diesel or such as a textbook program as disclosed in "Die Verbren- nungskraftmaschine" of H. Maass/H. Klier and K. E. Hafner/H. Maass, published by Springer-Verlag, Wien, New York. The result of the harmonic analysis is a series of values indicative of the resulting vi-

bration level. The below List A shows the values calculated for the firing sequences mentioned in Sequences A. The columns refer to the following vibration values: El indicates 1 ^st order balancing; E2 indicates 2 ^nd order balancing; X4 indicates 4 ^th order X-vector sum- mation; X5 indicates 5 ^th order X-vector summation; X6 indicates 6 ^th order X-vector summation and X7 indicates 7 ^th order X-vector summation. The values found at the harmonic analysis are representative for the vibration level. For an actual engine it is possible to multiply the values found with a correlation factor and obtain an actual value of the excitation sources. This is commonplace to the skilled person, and to give an example relating to the particular engine K98ME the value El = 0.200 corresponds to a free moment of 409 kNm. The actual vibration levels are lower when the values in list A are smaller, and vice versa.

El E2 X4 X5 X6 X7

D 0.200 0.564 1.733 0.838 0.842 0.041 2) 0.200 0.564 1.733 0.838 0.842 0.041 3) 0.259 0.890 1.141 1.370 0.885 0.458 4) 0.259 0.890 1.141 1.370 0.885 0.458

5) 0.449 1.112 2.441 0.838 0.743 0.134 6) 0.449 1.112 2.441 0.838 0.743 0.134 7) 0.406 1.067 2.096 1.071 0.518 0.392 8) 0.406 1.067 2.096 1.071 0.518 0.392 9) 0.514 0.640 1.866 1.071 0.648 0.340

10) 0.514 0.640 1.866 1.071 0.648 0.340

11) 0.487 0.767 1.155 0.308 0.502 0.200

12) 0.487 0.767 1.155 0.308 0.502 0.200

13) 0.534 0.911 1.520 0.352 0.361 0.455

14) 0.534 0.911 1.520 0.352 0.361 0.455

15) 0.560 0.898 1.454 0.776 0.740 0.321

16) 0.560 0.898 1.454 0.776 0.740 0.321

17) 0.568 0.848 1.878 0.776 0.652 0.223

18) 0.568 0.848 1.878 0.776 0.652 0.223

19) 0.704 1.531 1.406 1.205 0.842 0.487

20) 0.704 1.531 1.406 1.205 0.842 0.487

21) 0.709 0.709 0.092 1.204 0.502 0.092

22) 0.709 0.709 0.092 1.204 0.502 0.092

23) 0.072 1.393 1.343 0.481 0.312 0.456

24) 0.072 1.393 1.343 0.481 0.312 0.456

25) 0.075 1.600 0.654 1.709 0.546 0.251

26) 0.075 1.600 0.654 1.709 0.546 0.251

27) 0.109 1.557 2.907 1.430 0.521 0.410

28) 0.109 1.557 2.907 1.430 0.521 0.410

29) 0.133 1.545 2.207 0.113 0.372 0.416

30) 0.133 1.545 2.207 0.113 0.372 0.416

31) 0.166 1.493 2.494 1.510 0.306 0.048

32) 0.166 1.493 2.494 1.510 0.306 0.048

33) 0.177 1.174 2.265 0.685 0.105 0.334

34) 0.177 1.174 2.265 0.685 0.105 0.334

35) 0.177 1.174 2.265 0.685 0.737 0.334

36) 0.177 1.174 2.265 0.685 0.737 0.334

37) 0.180 0.422 1.901 1.071 0.604 0.392

38) 0.180 0.422 1.901 1.071 0.604 0.392

39) 0.194 1.401 0.976 1.664 0.458 0.187

40) 0.194 1.401 0.976 1.664 0.458 0.187

41) 0.209 1.018 2.429 0.685 0.499 0.389

42) 0.209 1.018 2.429 0.685 0.499 0.389

43) 0.255 0.965 2.397 0.531 0.254 0.132

44) 0.255 0.965 2.397 0.531 0.254 0.132

45) 0.270 0.904 2.511 1.645 0.278 0.282

46) 0.270 0.904 2.511 1.645 0.278 0.282

47) 0.306 0.255 2.049 0.631 0.648 0.396

48) 0.306 0.255 2.049 0.631 0.648 0.396

49) 0.342 0.203 2.468 0.631 0.656 0.267

50) 0.342 0.203 2.468 0.631 0.656 0.267

51) 0.359 0.922 2.068 1.279 0.586 0.343

52) 0.359 0.922 2.068 1.279 0.586 0.343

53) 0.370 1.419 1.354 1.781 0.176 0.464 54) 0.370 1.419 1.354 1.781 0.176 0.464

55) 0.371 1.536 0.546 1.927 0.115 0.467

56) 0.371 1.536 0.546 1.927 0.115 0.467

57) 0.382 1.388 1.801 1.781 0.816 0.403

58) 0.382 1.388 1.801 1.781 0.816 0.403 59) 0.392 1.361 2.532 1.623 0.085 0.296

60) 0.392 1.361 2.532 1.623 0.085 0.296

61) 0.427 1.568 2.826 1.370 0.855 0.477

62) 0.427 1.568 2.826 1.370 0.855 0.477

63) 0.429 1.313 2.410 1.863 0.745 0.455 64) 0.429 1.313 2.410 1.863 0.745 0.455

65) 0.454 1.619 0.178 1.878 0.403 0.355

66) 0.454 1.619 0.178 1.878 0.403 0.355

67) 0.463 0.208 2.247 0.481 0.049 0.357

68) 0.463 0.208 2.247 0.481 0.049 0.357 69) 0.476 1.638 2.090 0.870 0.278 0.473

70) 0.476 1.638 2.090 0.870 0.278 0.473

71) 0.478 1.693 2.542 0.988 0.468 0.387

72) 0.478 1.693 2.542 0.988 0.468 0.387

73) 0.484 1.608 2.052 0.531 0.669 0.464 74) 0.484 1.608 2.052 0.531 0.669 0.464

75) 0.487 0.767 1.155 0.308 0.502 0.200

76) 0.487 0.767 1.155 0.308 0.502 0.200

77) 0.503 1.660 2.376 0.979 0.574 0.356

78) 0.503 1.660 2.376 0.979 0.574 0.356 79) 0.516 0.763 2.375 0.828 0.432 0.232

80) 0.516 0.763 2.375 0.828 0.432 0.232

81) 0.555 1.173 2.762 0.531 0.469 0.255

82) 0.555 1.173 2.762 0.531 0.469 0.255

83) 0.561 1.187 2.537 0.092 0.892 0.305

84) 0.561 1.187 2.537 0.092 0.892 0.305

85) 0.567 0.739 1.977 0.658 0.444 0.250

86) 0.567 0.739 1.977 0.658 0.444 0.250

87) 0.586 0.493 2.593 1.741 0.940 0.478

88) 0.586 0.493 2.593 1.741 0.940 0.478

89) 0.587 1.150 2.548 1.037 0.575 0.490

90) 0.587 1.150 2.548 1.037 0.575 0.490

91) 0.591 1.149 1.805 0.755 0.808 0.471

92) 0.591 1.149 1.805 0.755 0.808 0.471

93) 0.602 1.467 1.991 0.838 0.941 0.331

94) 0.602 1.467 1.991 0.838 0.941 0.331

95) 0.615 1.102 2.157 1.493 0.666 0.321

96) 0.615 1.102 2.157 1.493 0.666 0.321

97) 0.619 1.019 1.391 0.442 0.623 0.246

98) 0.619 1.019 1.391 0.442 0.623 0.246

99) 0.620 0.647 2.601 0.979 0.601 0.355

100) 0.620 0.647 2.601 0.979 0.601 0.355

101) 0.621 0.655 1.154 1.874 0.415 0.252

102) 0.621 0.655 1.154 1.874 0.415 0.252

103) 0.623 1.359 2.306 0.442 0.518 0.407

104) 0.623 1.359 2.306 0.442 0.518 0.407

105) 0.634 1.142 2.754 0.988 0.352 0.363

106) 0.634 1.142 2.754 0.988 0.352 0.363

107) 0.637 0.750 2.857 1.510 0.553 0.336

108) 0.637 0.750 2.857 1.510 0.553 0.336

109) 0.650 1.107 2.735 0.828 0.228 0.492

110) 0.650 1.107 2.735 0.828 0.228 0.492

111) 0.663 1.547 2.022 0.531 0.821 0.406

112) 0.663 1.547 2.022 0.531 0.821 0.40

113) 0.675 1.424 2.828 1.205 0.640 0.491

114) 0.675 1.424 2.828 1.205 0.640 0.491

115) 0.689 0.611 2.647 0.828 0.820 0.464

116) 0.689 0.611 2.647 0.828 0.820 0.464

117) 0.692 1.625 2.704 1.259 0.235 0.444

118) 0.692 1.625 2.704 1.259 0.235 0.444

119) 0.699 1.127 0.587 1.995 0.593 0.478 120) 0.699 1.127 0.587 1.995 0.593 0.478

121) 0.700 1.361 2.385 1.592 0.983 0.378

122) 0.700 1.361 2.385 1.592 0.983 0.378

123) 0.709 0.709 0.092 1.204 0.502 0.092

124) 0.709 0.709 0.092 1.204 0.502 0.092 125) 0.722 1.110 1.984 0.442 0.115 0.331

126) 0.722 1.110 1.984 0.442 0.115 0.331

127) 0.729 0.607 2.324 1.251 0.311 0.385

128) 0.729 0.607 2.324 1.251 0.311 0.385

129) 0.730 0.431 2.890 1.623 0.326 0.445 130) 0.730 0.431 2.890 1.623 0.326 0.445

131) 0.165 0.997 1.263 0.442 0.905 1.765

132) 0.165 0.997 1.263 0.442 0.905 1.765

133) 0.424 1.458 1.099 0.442 0.249 1.775

134) 0.424 1.458 1.099 0.442 0.249 1.775 135) 0.434 1.555 1.160 0.113 0.859 2.776

136) 0.434 1.555 1.160 0.113 0.859 2.776

137) 0.434 1.555 1.160 0.113 1.141 2.776

138) 0.434 1.555 1.160 0.113 1.141 2.776

139) 0.525 1.163 1.203 0.459 1.270 1.65 140) 0.525 1.163 1.203 0.459 1.270 1.65

141) 0.604 1.301 1.136 0.337 0.791 2.88

142) 0.604 1.301 1.136 0.337 0.791 2.88

143) 0.704 0.850 0.730 0.092 0.305 1.87

144) 0.704 0.850 0.730 0.092 0.305 1.87

The division of the crankshaft has considerable influence on the vibration pattern of the engine. It is therefore relevant for the understanding of the present invention also to look at embodiments where the

crankshaft has been divided in another manner than 6-5-4. As an example of another division of the crankshaft, there will now be considered the even division 5-5-5 where the first crankshaft section consists of engine cylinders Cl, C2, C3, 4 and C5, labelled a in Table 2, the second plural- ity of engine cylinders associated with the second crankshaft section consists of engine cylinders C6, C7, C8, C9 and ClO, labelled b in Table 2, and the third plurality of engine cylinders associated with the third crankshaft section consists of engine cylinders CIl, C12, C13, C14 and C15, labelled c in Table 2. Table 2

(Even division 5-5-5)

Grouped cylinders

Group 1 aa aa aa aa aa aa aa aa aa aa

Group 2 aa aa aa aa aa aa aa aa aa bb

Group 3 bb bb bb bb bb bb CC CC CC CC

Group 4 bb CC CC CC CC bcb bab CC bab CC

Group 5 CC CC bab bcb cbc cbc CC bab bcb aba

Group 6 CC CC CC CC CC

In the same manner as in connection with Table 1 calculations have been made in order to establish actual firing sequences based on these groups according to the present invention. An extract of the firing sequences are shown in the following listing of Sequences B.

Sequences B:

1) 1-5-11-13-9-2-4-12-14-7-3-6-8-15-10

2) 1-6-15-11-5-3-7-14-12-4-2-9-13-10-8

3) 1-8-10-13-9-2-4-12-14-7-3-5-11-15-6

4) 1-10-15-8-6-3-7-14-12-4-2-9-13-11-5 5) 1-5-12-14-6-3-7-9-13-10-2-4-11-15-8

6) 1-8-15-11-4-2-10-13-9-7-3-6-14-12-5

7) 1-3-13-12-6-7-4-8-14-10-5-2-9-15-11

8) 1-5-15-13-3-4-10-9-12-8-2-6-11-14-7

9) 7-14-11-6-2 ^■ 8-12-9-10-4-3- ^■ 13-15-5

10) 11-15-9-2-5 ^■ 10-14-8-4-7-6- ^■ 12-13-3

11) 5-12-13-8-4 -3-11-15-7-2-6- ^■ 10-14-9

12) 5-13-12-8-3 ^■ 4-11-15-7-2-6- ^■ 10-14-9

13) 9-14-10-6-2 -7-15-11-3-4-8- ^• 13-12-5

14) 9-14-10-6-2 ^■ 7-15-11-4-3-8- ^■ 12-13-5

15) 3-12-13-7-6 ^■ 4-8-14-10-5-2- 9-15-11

16) 5-15-13-4-3 ^■ 9-10-12-8-2-6- ^■ 11-14-7

17) 7-14-11-6-2 ^■ 8-12-10-9-3-4- ^■ 13-15-5

18) 11-15-9-2-5 ^■ 10-14-8-4-6-7- ^■ 13-12-3

19) 4-14-13-6-2 -7-12-10-9-5-3- ^■ 11-15-8

20) 5-13-11-7-6 ^■ 4-9-14-10-3-2- 12-15-8

21) 8-15-11-3-5' ^■ 9-10-12-7-2-6- 13-14-4

22) 8-15-12-2-3 ^■ 10-14-9-4-6-7- ^• 11-13-5

23) 5-12-13-8-3 ^■ 4-11-15-7-2-6- ^■ 10-14-9

24) 9-14-10-6-2 ^■ 7-15-11-4-3-8- ^■ 13-12-5

25) 2-13-14-7-3 ^■ 6-10-12-9-5-4- ^■ 8-15-11

26) 5-15-14-3-2 ^■ 9-13-10-6-4-7- 11-12-8

27) 8-12-11-7-4 ^■ 6-10-13-9-2-3- ^■ 14-15-5

28) 11-15-8-4-5 -9-12-10-6-3-7- ^■ 14-13-2

29) 2-11-15-8-3 ^■ 5-10-13-9-4-6- ^■ 7-12-14

30) 5-14-15-2-4' ^■ 9-10-12-7-3-6- 11-13-8

31) 1- 8-13-11-6-3 ^■ 7-12-10-9-4-2- 15-14-5

32) 14-12-7-6-4 ^■ 9-13-10-5-3-8- ^■ 15-11-2

33) 2-11-14-8-5 ^■ 4-10-12-9-7-3- ^■ 6-15-13

34) 3-15-14-5-2 -8-11-12-6-4-7- ^■ 9-13-10

35) 10-13-9-7-4 ^■ 6-12-11-8-2-5- ^■ 14-15-3

36) 13-15-6-3-7 ^■ 9-12-10-4-5-8- 14-11-2

37) 1- 2-14-12-7-6 ^■ 3-10-13-9-5-4- 8-15-11

38) 5-15-14-2-4 ^■ 9-10-13-6-3-7- ^■ 11-12-8

39) 8-12-11-7-3 ^■ 6-13-10-9-4-2- ^■ 14-15-5

40) 11-15-8-4-5' ^■ 9-13-10-3-6-7- 12-14-2

41) 5-13-12-8-4 ^• 3-11-15-7-2-6- 10-14-9

42) 9-14-10-6- 2-7-15-11-3- ^■ 4-8-12-13-5 43) 3-13-14-7- •2-6-11-12-8- ^■ 4-5-9-15-10 44) 6-15-13-3- 2-9-14-10-5- ^■ 4-8-12-11-7 45) 7-11-12-8- 4-5-10-14-9- 2-3-13-15-6 46) 10-15-9-5- 4-8-12-11-6- 2-7-14-13-3 47) 3-11-14-9- 2-5-13-10-8- ^■ 7-4-6-15-12 48) 4-15-13-5- 2-7-14-11-3- 6-8-9-12-10 49) 10-12-9-8- ^■ 6-3-11-14-7- ^• 2-5-13-15-4 50) 12-15-6-4- 7-8-10-13-5- ^■ 2-9-14-11-3

51) 1- 3-12-15-7- 2-6-10-13-9- 4-5-8-14-11

52) 4-13-15-5- 2-8-11-12-7- 3-6-10-14-9 53) 9-14-10-6- 3-7-12-11-8- ^■ 2-5-15-13-4 54) 11-14-8-5- 4-9-13-10-6- 2-7-15-12-3 55) 3-12-15-6- 2-7-10-13-8- ^■ 4-5-9-14-11 56) 4-13-15-5- 2-7-11-12-8- 3-6-9-14-10 57) 1- 10-14-9-6- 3-8-12-11-7- 2-5-15-13-4

58) 11-14-9-5- 4-8-13-10-7- 2-6-15-12-3 59) 3-13-12-7- 6-4-8-14-10- ^■ 5-2-9-15-11 60) 5-15-13-3- 4-9-10-12-8- 2-6-11-14-7 61) 7-14-11-6- 2-8-12-10-9- 4-3-13-15-5 62) 11-15-9-2- 5-10-14-8-4- 6-7-12-13-3 63) 5-13-11-6- 7-4-8-15-10- 2-3-12-14-9 64) 6-14-13-4- 2-7-15-11-3- 5-10-9-12-8 65) 8-12-9-10- 5-3-11-15-7- 2-4-13-14-6 66) 9-14-12-3- 2-10-15-8-4- 7-6-11-13-5 67) 5-12-13-8- 2-4-14-11-7- 6-3-10-15-9 68) 6-13-10-9- 5-2-12-14-8- 3-4-11-15-7 69) 7-15-11-4- 3-8-14-12-2- 5-9-10-13-6 70) 9-15-10-3- 6-7-11-14-4- 2-8-13-12-5

71) 1 5-13-11-7- 6-4-8-15-10- 2-3-12-14-9

72) 1 6-14-13-4- 2-7-15-11-3- 5-9-10-12-8

73) 1 8-12-10-9- 5-3-11-15-7- 2-4-13-14-6

74) 1 9-14-12-3- 2-10-15-8-4- 6-7-11-13-5

75) ^• 6-12-11-8-5-4-10-15-9-2-3-13-14-7 76) ^■ 7-14-13-3-2-9-15-10-4-5-8-11-12-6 77) ^• 5-12-13-8-3-4-11-15-6-2-7-10-14-9 78) ^■ 5-12-13-8-3-4-11-15-7-2-6-9-14-10 79) ^■ 9-14-10-7-2-6-15-11-4-3-8-13-12-5 80) ^• 10-14-9-6-2-7-15-11-4-3-8-13-12-5 81) ^■ 2-13-14-7-3-6-9-12-10-5-4-8-15-11 82) ^• 5-15-14-3-2-9-13-10-7-4-6-11-12-8 83) ^• 8-12-11-6-4-7-10-13-9-2-3-14-15-5 84) ^■ 11-15-8-4-5-10-12-9-6-3-7-14-13-2 85) ^■ 4-12-14-8-2-5-13-11-7-6-3-10-15-9 86) ^■ 6-13-10-9-5-3-11-14-8-2-4-12-15-7 87) ^■ 7-15-12-4-2-8-14-11-3-5-9-10-13-6 88) ^■ 9-15-10-3-6-7-11-13-5-2-8-14-12-4 89) ^• 3-12-14-7-4-5-10-15-8-2-6-9-13-11 90) ^• 6-11-12-9-2-4-13-15-5-3-7-10-14-8 91) ^■ 8-14-10-7-3-5-15-13-4-2-9-12-11-6 92) ^■ 11-13-9-6-2-8-15-10-5-4-7-14-12-3 93) ^■ 3-12-14-8-2-6-10-13-9-4-5-7-15-11 94) ^■ 5-15-13-4-2-8-14-10-6-3-7-12-11-9 95) ^■ 9-11-12-7-3-6-10-14-8-2-4-13-15-5 96) 11-15-7-5-4-9-13-10-6-2-8-14-12-3 97) 4-13-14-6-2-7-11-12-8-3-5-10-15-9 98) ^■ 6-11-13-8-4-5-9-14-10-2-3-12-15-7 99) ^• 7-15-12-3-2-10-14-9-5-4-8-13-11-6

100) 1 ^• 9-15-10-5-3-8-12-11-7-2-6-14-13-4

101) 1 ^■ 4-12-14-8-2-5-13-11-6-7-3-9-15-10

102) 1 ^• 6-15-12-4-2-8-14-11-3-5-10-9-13-7

103) 1 ^■ 7-13-9-10-5-3-11-14-8-2-4-12-15-6

104) 1 ^■ 10-15-9-3-7-6-11-13-5-2-8-14-12-4

105) 1 ^• 8-14-12-2-4-9-13-11-3-6-5-15-10-7

106) 1 7-10-15-5-6-3-11-13-9-4-2-12-14-8

107) 1 6-9-15-8-2-4-14-12-7-3-5-13-10-11

108) 1-11-10-13-5-3-7-12-14-4-2-8-15-9-6

109) 1-7-10-14-8-2-4-12-15-6-3-5-13-11-9

110) 1-9-11-13-5-3-6-15-12-4-2-8-14-10-7

111) 1-4-12-14-8-2-6-9-15-7-5-3-11-13-10 112) 1-10-13-11-3-5-7-15-9-6-2-8-14-12-4

In the same manner as for the firing sequences A harmonic analyses are performed in order to obtain values for the various resulting vibration levels caused by the excitation sources in the engine. The below List B shows the values calculated for the firing sequences mentioned in Sequences B. The columns refer to the same types of vibration values as in the list A and reference is made thereto for the meaning of El, E2 and X4 to X7.

List B:

El E2 X4 X5 X6 X7

1) 0.358 1.222 0.815 1.500 0.767 0.422

2) 0.358 1.222 0.815 1.500 0.767 0.422

3) 0.358 1.222 0.815 1.500 0.767 0.422 4) 0.358 1.222 0.815 1.500 0.767 0.422

5) 0.074 0.952 1.629 0.833 0.745 0.101

6) 0.074 0.952 1.629 0.833 0.745 0.101

7) 0.141 1.500 2.308 1.642 0.835 0.409

8) 0.141 1.500 2.308 1.642 0.835 0.409 9) 0.141 1.500 2.308 1.642 0.835 0.409

10) 0.141 1.500 2.308 1.642 0.835 0.409

11) 0.248 1.133 0.115 1.507 0.332 0.359

12) 0.248 1.133 0.115 1.507 0.332 0.359

13) 0.248 1.133 0.115 1.507 0.332 0.359 14) 0.248 1.133 0.115 1.507 0.332 0.359

15) 0.273 0.777 1.957 1.254 0.609 0.495

16) 0.273 0.777 1.957 1.254 0.609 0.495

17) 0.273 0.777 1.957 1.254 0.609 0.495

18) 0.273 0.777 1.957 1.254 0.609 0.495 19) 0.278 1.305 2.310 0.722 0.779 0.234 20) 0.278 1.305 2.310 0.722 0.779 0.234 21) 0.278 1.305 2.310 0.722 0.779 0.234 22) 0.278 1.305 2.310 0.722 0.779 0.234 23) 0.295 0.576 0.137 1.283 0.499 0.183 24) 0.295 0.576 0.137 1.283 0.499 0.183 25) 0.325 0.973 2.425 0.722 0.163 0.337 26) 0.325 0.973 2.425 0.722 0.163 0.337 27) 0.325 0.973 2.425 0.722 0.163 0.337 28) 0.325 0.973 2.425 0.722 0.163 0.337 29) 0.340 0.875 2.108 1.642 0.950 0.444 30) 0.340 0.875 2.108 1.642 0.950 0.444 31) 0.340 0.875 2.108 1.642 0.950 0.444 32) 0.340 0.875 2.108 1.642 0.950 0.444 33) 0.356 0.608 2.495 1.340 0.407 0.446 34) 0.356 0.608 2.495 1.340 0.407 0.446 35) 0.356 0.608 2.495 1.340 0.407 0.446 36) 0.356 0.608 2.495 1.340 0.407 0.446 37) 0.376 1.060 1.857 1.953 0.857 0.361 38) 0.376 1.060 1.857 1.953 0.857 0.361 39) 0.376 1.060 1.857 1.953 0.857 0.361 40) 0.376 1.060 1.857 1.953 0.857 0.361 41) 0.378 1.079 0.175 1.732 0.099 0.342 42) 0.378 1.079 0.175 1.732 0.099 0.342 43) 0.414 0.989 1.916 0.449 0.240 0.391 44) 0.414 0.989 1.916 0.449 0.240 0.391 45) 0.414 0.989 1.916 0.449 0.240 0.391 46) 0.414 0.989 1.916 0.449 0.240 0.391 47) 0.434 0.825 2.949 1.631 0.433 0.350 48) 0.434 0.825 2.949 1.631 0.433 0.350 49) 0.434 0.825 2.949 1.631 0.433 0.350 50) 0.434 0.825 2.949 1.631 0.433 0.350

51) 0.444 1.216 1.980 0.747 0.780 0.156 52) 0.444 1.216 1.980 0.747 0.780 0.156 53) 0.444 1.216 1.980 0.747 0.780 0.156 54) 0.444 1.216 1.980 0.747 0.780 0.156 55) 0.494 1.416 2.092. 0.833 0.757 0.434 56) 0.494 1.416 2.092 0.833 0.757 0.434 57) 0.494 1.416 2.092 0.833 0.757 0.434 58) 0.494 1.416 2.092 0.833 0.757 0.434 59) 0.496 0.718 2.123 1.461 0.613 0.365 60) 0.496 0.718 2.123 1.461 0.613 0.365

61) 0.496 0.718 2.123 1.461 0.613 0.365 62) 0.496 0.718 2.123 1.461 0.613 0.365 63) 0.525 1.281 2.331 1.557 0.560 0.452 64) 0.525 1.281 2.331 1.557 0.560 0.452 65) 0.525 1.281 2.331 1.557 0.560 0.452 66) 0.525 1.281 2.331 1.557 0.560 0.452 67) 0.585 1.097 1.479 1.722 0.847 0.305 68) 0.585 1.097 1.479 1.722 0.847 0.305 69) 0.585 1.097 1.479 1.722 0.847 0.305 70) 0.585 1.097 1.479 1.722 0.847 0.305 71) 0.586 0.803 2.160 1.340 0.400 0.385 72) 0.586 0.803 2.160 1.340 0.400 0.385 73) 0.586 0.803 2.160 1.340 0.400 0.385 74) 0.586 0.803 2.160 1.340 0.400 0.385 75) 0.594 0.060 1.965 0.449 0.300 0.477 76) 0.594 0.060 1.965 0.449 0.300 0.477 77) 0.601 1.418 0.377 1.507 0.629 0.206 78) 0.601 1.418 0.377 1.507 0.629 0.206 79) 0.601 1.418 0.377 1.507 0.629 0.206 80) 0.601 1.418 0.377 1.507 0.629 0.206 81) 0.603 1.147 2.461 0.747 0.311 0.382 82) 0.603 1.147 2.461 0.747 0.311 0.382 83) 0.603 1.147 2.461 0.747 0.311 0.382

84) 0.603 1.147 2.461 0.747 0.311 0.382

85) 0.650 1.460 1.749 1.308 0.687 0.251

86) 0.650 1.460 1.749 1.308 0.687 0.251

87) 0.650 1.460 1.749 1.308 0.687 0.251 88) 0.650 1.460 1.749 1.308 0.687 0.251

89) 0.692 0.728 0.864 1.846 0.641 0.147

90) 0.692 0.728 0.864 1.846 0.641 0.147

91) 0.692 0.728 0.864 1.846 0.641 0.147

92) 0.692 0.728 0.864 1.846 0.641 0.147 93) 0.700 1.114 1.971 0.766 0.923 0.447

94) 0.700 1.114 1.971 0.766 0.923 0.447

95) 0.700 1.114 1.971 0.766 0.923 0.447

96) 0.700 1.114 1.971 0.766 0.923 0.447

97) 0.709 1.682 1.741 0.225 0.426 0.304 98) 0.709 1.682 1.741 0.225 0.426 0.304

99) 0.709 1.682 1.741 0.225 0.426 0.304

100) 0.709 1.682 1.741 0.225 0.426 0.304

101) 0.717 0.780 2.135 1.557 0.712 0.465

102) 0.717 0.780 2.135 1.557 0.712 0.465 103) 0.717 0.780 2.135 1.557 0.712 0.465

104) 0.717 0.780 2.135 1.557 0.712 0.465

105) 0.117 1.470 1.342 0.225 1.114 2.190

106) 0.117 1.470 1.342 0.225 1.114 2.190

107) 0.117 1.470 1.342 0.225 1.114 2.190 108) 0.117 1.470 1.342 0.225 1.114 2.190

109) 0.554 1.498 0.953 0.420 0.300 1.63

110) 0.554 1.498 0.953 0.420 0.300 1.63

111) 0.554 1.498 0.953 0.420 0.300 1.63

112) 0.554 1.498 0.953 0.420 0.300 1.63

A preferred firing sequence 1 5 12 13 8 3 4 11 15 7 2 6 10 14

9 is illustrated in Fig. 2. The individual crank throw comprises two crank arms 34 and the crank pin 9, and the crank shaft journals 11

join the crank throws into a complete crank shaft.

The cylinders Cl to C15 fire in the mentioned sequence. A firing sequence is implemented in the engine by the making the crankshaft 10 with crank throws pointing in the angular pattern required for obtaining the firing sequence. The pattern required for the preferred firing sequence as an even firing sequence, viz. a firing sequence with a regular (even) angular interval of 360°/15 = 24° between the firings is illustrated in Fig. 3.

The respective angles between the crank throws 33 of the crankshaft appear in Fig. 3. It is also possible to use irregular firing sequences, viz. a firing sequence that is uneven in the sense that the angular interval between the firings of at least two pairs, and possibly several pairs, of consecutively firing cylinders deviates from 24°. A deviation of only a few degrees can result in a very dif- ferent vibration pattern in the engine.

The engine can be an electronically controlled engine without a camshaft for activating fuel pumps and exhaust valves, e.g. an engine of the type ME. If the engine is of a traditional type with a camshaft, the camshaft can be driven from the crankshaft via a chain drive or a gearing, which suitably can be located between the cylinders separated by the larger distance 12.

The engine according to the present invention is suitable for use as a main propulsion engine in a container ship, and especially in a container ship having a capacity of at least 12.000 TEU, such as from 12.200 to 15.000 TEU, one TEU being the equivalent of a single 20' container. TEU is the standard measure for the capacity of a container ship.

It is possible to make modifications to the embodiments described in the above. The groups can e.g. be differently composed, such as cac or aba. The engine frame can be of any suitable shape.

The cylinders need not be numbered with Cl at the forward end of the engine and C15 at the aft end. They can equally well be numbered with Cl at the aft end and C15 at the forward end. And the

engine can have a rotational direction either the one or the other direction. As an alternative to being a main engine in a ship, the engine can be utilized as a stationary engine in a power plant.

According to the second aspect of the present invention the firing sequence of the engine is one of the following firing sequences: a) 1 3 12 14 7 4 5 10 15 8 2 6 9 13 11 b) 1 4 12 14 7 2 6 11 13 8 3 5 10 15 9 c) 1 4 12 15 6 2 7 10 13 8 3 5 11 14 9 d) 1 5 12 13 7 3 6 10 14 9 2 4 11 15 8 e) 1 5 12 13 7 3 6 9 14 10 2 4 11 15 8 f) 1 5 12 13 8 3 4 11 15 6 2 7 10 14 9 g) 1 5 12 13 8 3 4 11 15 7 2 6 10 14 9 h) 1 5 12 13 8 4 3 11 15 7 2 6 10 14 9 i) 1 5 12 14 6 3 7 9 13 10 2 4 11.15 8 j) 1 -5 13 12 7 3 6 10 14 9 2 4 11 15 8 k) 1 5 13 12 8 4 3 11 15 7 2 6 10 14 9 I) 1 6 11 13 9 2 4 12 14 7 3 5 10 15 8, wherein said cylinder Cl can be located at either the one or the other of the two ends of the engine, cylinder C15 is located at the end of the engine opposite to cylinder Cl, the cylinders C2 to C14 are numbered consecutively along the length of the engine in direction from cylinder Cl towards cylinder C15, and the direction of rotation of the engine can be in either the one or the other rotational direction. Embodi- ments within the scope of the patent claim according to the second aspect have only a single crankshaft division, two or more crankshaft divisions or no crankshaft division at all. It is an advantage to avoid crankshaft divisions because the overall length of the engine is then reduced. Detail of the engine described in the above with reference to the first aspect of the invention also apply to the second aspect of the invention.