GUIDELINES ON SHAFTING ALIGNMENT phần 3 docx

PART A GUIDELINES ON SHAFTING ALIGNMENT TAKING INTO ACCOUNT VARIATION IN BEARING OFFSETS WHILE IN SERVICE RAδ -1 Δ= (4.3) This can be expressed in following detailed form: -1 139295.200 -214398.600 81956.600 -9075.900 8643.400 -6589.800 213.600 -53.400 8.900 -214398.600 342737.700 -147868.000 25863.000 -24630.400 18778.300 -608.800 152.210 -25.360 81956.600 -147868.000 86843.200 -29740.600 34253.700 -26115.100 846.700 -212.600 35.280 -9075.900 25863.000 -29740.600 25755.000 -64621.200 53184.900 -1724.400 431.110 -71.850 8643.000 -24630.400 34253.700 -64621.200 487261.800 -602809.500 204508.100 -51127.000 8521.100 -6589.800 18778.300 -26115.100 53185.900 -602809.500 895929.300 -459651.500 152728.000 -25454.600 213.660 -608.800 846.740 -1724.400 204508.100 -459651.500 451271.600 -264078.400 69223.100 -53.410 152.200 -211.680 431.110 -51127.000 152728.000 -264078.400 255095.300 -92936.000 8.900 -25.360 35.281 -72.850 8521.100 -25454.600 65223.100 -92936.000 40699.400 55204 -80000 24000 -2000 20000 -18000 500 -180 30 However, because of the characteristic of the shafting stiffness matrix, the above equation will have infinitely many sol utions. Hence, a submatrix of this matrix by omitting both the first and last rows and first and last columns is needed in order to solve this problem. This operation means that the constraints of the rigid motions do not affect the bearings, including translation and rotation of the shafting line. The operation is specifically to set both ends of the shafting line at an offset of zero. Accordingly, the solution for the No. 2 to No. 8 offsets can be obtained as follows: -1 -0.5225819432 -0.7255192463 -0.2621283778 0.1235714606 0.0892630911 0.0471291196 0.0955979752 δ2 δ3 δ4 δ5 δ6 δ7 δ8 = = 342737.700 -147868.000 25863.000 -24630.400 18778.300 -608.800 152.210 -147868.000 86843.200 -29740.600 34253.700 -26115.100 846.700 -212.600 25863.000 -29740.600 25755.000 -64621.200 53184.900 -1724.400 431.110 -24630.400 34253.700 -64621.200 487261.800 -602809.500 204508.100 -51127.000 18778.300 -26115.100 53185.900 -602809.500 895929.300 -459651.500 152728.000 -608.800 846.740 -1724.400 204508.100 -459651.500 451271.600 -264078.400 152.200 -211.680 431.110 -51127.000 152728.000 -264078.400 255095.300 -80000 24000 -2000 20000 -18000 500 -180 Therefore, the solution for all bearing offsets is as follows: 0 -0.52258194320 -0.72551924630 -0.26212837780 0.12357146060 0.08926309105 0.04712911959 0.01955979752 0 In practice, main engines are usually i n stalled in a horizontal position. This can be realized by rotating the whole shafting line by an angle equal to the slope of the engine section. The bearing offsets after rotation are 16 PART A GUIDELINES ON SHAFTING ALIGNMENT TAKING INTO ACCOUNT VARIATION IN BEARING OFFSETS WHILE IN SERVICE shown in Table 4.5 together with the respective calculated values. Fig. 4.4 is a graphical expression of the calculated target bearing offsets. Table 4.5 Calculated Target Bearing Offsets Bearing No. Bearing location Bearing offsets as calculated Bearing offsets with engine in nearly horizontal position No. 1 2830 0.0000 -0.5521 No. 2 4630 -0.5226 -1.0344 No. 3 8465 -0.7255 -1.1514 No. 4 15295 -0.2621 -0.5349 No. 5 22375 0.1236 0.0094 No. 6 23375 0.0893 -0.0025 No. 7 24875 0.0471 -0.0110 No. 8 26375 0.0196 -0.0050 No. 9 27875 0.0000 0.0091 Initail Bearing Offsets Obtained by Direct Calculation, (-) Upward Offset and (+) Downward Offset -1.50 -1.00 -0.50 0.00 0.50 1.00 1.50 0 5000 10000 15000 20000 25000 30000 Bearing location, distance from left end (mm) Offset (mm) Bearing offsets as calculated Bearing offsets with engine in nearly horizontal position Fig. 4.4 Calculated target bearing offsets. All translation or rotation of the shafting line as a whole will not af fect the reactions of bearings as described above, though small calculation errors could exist. Table 4.6 shows a comparison of the bearing reactions, while Fig. 4.5 is their graphical expression. It can be seen from these results that the target bearing reactions have been obtained. 17 PART A GUIDELINES ON SHAFTING ALIGNMENT TAKING INTO ACCOUNT VARIATION IN BEARING OFFSETS WHILE IN SERVICE Table 4.6 Comparison of Bearing Reactions between Offset Sets Shown in Table 4.5 Bearing reaction force (kgf) Bearing No. Target Offsets as calculated Offsets with engine in nearly horizontal position No. 1 -88333 -88084 -88082 No. 2 -17079 -17088 -17089 No. 3 -11917 -11913 -11914 No. 4 -23989 -23989 -23988 No. 5 -28172 -28189 -28169 No. 6 -26661 -26624 -26672 No. 7 -41726 -41761 -41709 No. 8 -51277 -51254 -51290 No. 9 -15265 -15069 -15058 Bearing Reaction Force (kgf), (-) Upward and (+) Downward -100000 -80000 -60000 -40000 -20000 0 No. 1 No. 2 No. 3 No. 4 No. 5 No. 6 No. 7 No. 8 No. 9 Bearing Number Reaction force (kgf) Offsets as calculated Offsets with engine in nearly horizontal position Fig. 4.5 Comparison of bearing reactions between offse t sets shown in Table 4.5. 18 PART A GUIDELINES ON SHAFTING ALIGNMENT TAKING INTO ACCOUNT VARIATION IN BEARING OFFSETS WHILE IN SERVICE 5. Optimization of Location of Intermediate Bearing The longitudinal placement of the intermediate bearing will have strong ef fect on the reaction of the aftmost engine bearing when bearing offsets vary due to changes in ship draught. In fact, there was one case in which damage to the aftmost engine bearing occurred shortly after the vessel was entered into service because the intermediate bearing was installed too close to the aftmost engine bearing. The location of the intermediate bearing has thus far been determined on the basis of experience, and there has not been a rigorous, scientific approach to the placem ent of bearings. It is generally effective to install the intermediate bearing as far as possible from the engine in order to reduce its effect on the aftmost engine bearings when there is a change in the bearing offsets. On the other hand, however, the influence number of the intermediate bearing itself will become greater because of the proximity of the intermediate bearing to the sterntube bearing. A balanced judgment is needed, accordingly. The effect of the location of the intermediate bearing on the influence number for each bearing was calculated in the example shown in Fig. 5.1. The result of the calculation is shown in Fig. 5.2. N o.1 N o.2 N o.3 N o.4 N o.5 N o.6 N o.7 N o.8 N o.9 Fig. 5.1 An example of a shafting arrangement used to demonstrate how to optimize the location of the intermediate bearing. 19 PART A GUIDELINES ON SHAFTING ALIGNMENT TAKING INTO ACCOUNT VARIATION IN BEARING OFFSETS WHILE IN SERVICE Fig. 5.2 Influence number of intermediate bearing with respect to the other bearings. -200000 -150000 -100000 -50000 0 50000 100000 150000 200000 5000 7000 9000 11000 13000 15000 17000 19000 21000 Intermediate Bearing Location (mm) Reaction Influence Number R41 R42 R43 R44 R45 R46 R47 R48 R49 Judging from the influence number of the intermediate bearing to i tself, R44, as shown in Fig. 5.2., it may be said that the level of sensitivity is the lowest for the current design position of the intermediate bearing, at 15,295 mm. However, if the influence on the first and second aftmost engine bearings is taken into consideration, the intermediate bearing should be placed further aftward 2,795 mm to a position of 12,500 mm. Thus, in order to consider the extent of influence on all bearings, a sensitivity index was proposed as expressed in Eq. (5.1). () number bearingteIntermedia :m ionconsiderat into taken bearings totalofNumber :N gith bearin to bearingteintermedia oft coefficien Influence :R Rindexy Sensitivit mi N 1i 2 mi ∑ = = (5.1) The result of applying Eq. (5.1) to the fore-mentioned example is shown in Fig. 5.3. The result suggests that a unique optimal location for the intermediate bearing exists, in terms of minimum sensitivity. In this example, the optimal point is 14,500 mm, moving aftward for 795 mm from the original design point. 20 PART A GUIDELINES ON SHAFTING ALIGNMENT TAKING INTO ACCOUNT VARIATION IN BEARING OFFSETS WHILE IN SERVICE 21 L IM Fig. 5.3 Optimal location of intermediate bearing obtained from sensitivity analysis. 0.00E+00 5.00E+09 1.00E+10 1.50E+10 2.00E+10 10000 11000 12000 13000 14000 15000 16000 17000 18000 Position of intermediate bearing (mm), L IM Sesitivity Index Initial design pointOptimized point 14,500 PART A GUIDELINES ON SHAFTING ALIGNMENT TAKING INTO ACCOUNT VARIATION IN BEARING OFFSETS WHILE IN SERVICE 6. Measurement of Hull Deflection 6.1 Items and Locations of Measurement 6.1.1 Locations to Be Measured When a ship changes from light draught to full draught, th e aft part of the hull and shafting are estimated to exhibit a hogging deflection as shown in Fig. 6.1. Fig. 6.1 Illustration showing hull deflection from light to full draught: (a) light draught; (b) full draught. ( b ) ( a ) In order to be able to investigate the effect of hull deflection on shafting alignm e nt, it is ideal to measure the changes that take occur in each bearing offset beneath the shafting line from the foremost engine bearing to the propeller. However, the locations that can be practically measured are limited to points on the dotted red lines shown in Fig. 6.2 due to restrictions arising from the arrangement of the hull structure, engine, and shafting line. In other words, measurements are only possible on the tank top beneath the shafting line from the aft end of the engine to the fore sterntube bearing and alongside the engine. In this regard, some discrepancy may exist between the measured results and actual changes in the bearing offsets. Consequently, careful attention should be paid when applying the measured results in determining shafting alignment, which will be detailed hereinafter. 6.1.2 Measurement Items The principal items to be measured include the relative deflection of the tank top from one draft condition to another, represented in dark and red in Fig. 6.3, with respect to a reference line connecting two ends of the measured line. Another method, depicted in blue, is to measure the relative deflection at one end of the measurement line from one draft condition to another with respect to a reference point produced by a laser beam from the other end of the measurement line. As can be seen from the figure, when the line passing through the 22 PART A GUIDELINES ON SHAFTING ALIGNMENT TAKING INTO ACCOUNT VARIATION IN BEARING OFFSETS WHILE IN SERVICE two end points of the measurement line is being taken as a reference line, highly accurate measurement is necessary because the relative displacement could be very small. However, a better understanding of the entire profile of the displacement along the whole length of the measurement line can be gained by using this method and conducting measurements at multiple points. On the other hand, although comparatively large displacements can be measured using the reference point at one end produced by a laser beam emitted from the other end of the measurement line, the measurement of middle points will be difficult. Possible measurement lines Fig. 6.2 Possible locations for measuring hull deflections. Reference lines Displacements to be measured Laser beam as reference line after deformation Fig. 6.3 Illustration showing displacements to be measured and their respective reference lines. 6.2 Method of Measurement 6.2.1 Measurement Apparatus There are several measurement methods available that can be used to measure displacement depending on how the reference line is set and how the measurement is made. The so-called 'piano-wire method' has been commonly used so far when a line passing through two end points is established as the reference line, in which a tightened piano wire connecting the two end points is used as the reference line. When the piano wire method is applied, a nearly truly straight reference line can be established because piano wire is very thin and able to withstand comparatively large tension forces. Additionally, piano wire sagging arising from its selfweight can be calculated for correction, if necessary. However, the possibly greatest disadvantage of the piano-wire 23 PART A GUIDELINES ON SHAFTING ALIGNMENT TAKING INTO ACCOUNT VARIATION IN BEARING OFFSETS WHILE IN SERVICE method is that the measurement has to be made and read off manually. Therefore, it is difficult for the personnel conducting the measurement to repeat the measurements under varying conditions and to measure the displacement at multiple points simultaneously. In addition, problems arise with the accuracy of the measurements when the displacement is small. Therefore, ClassNK Research Institute has developed a measuring apparatus using a steel strip with a very sm all cross sectional area as the reference line instead of piano wire in combination with highly precise laser type displacement sensors. This makes it possible to measure displacements at multiple points simultaneously with high precision. The system has already been successfully employed in actual measurements onboard a VLCC tanker for the first time in the world in August 2004. In addition to the above mentioned features of high precision, mu lti-point and automatic measurement, there is another merit to this approach in which possible dynamic components in displacement can be measured, as the measurement system allows continuous measurement to take place. The concept and mechanism of the measurement system is shown in Fig. 6.4. Figure 6.5. shows the apparatus that was installed onboard the above mentioned VLCC tanker. Tightened steel strip Laser displacement senso r Deflection line after change in condition (e.g. full loaded condition) Initial deflection line (e.g. ballast condition) Change in displacement between conditions Fig. 6.4 Concept of a new hull deflection measurement system. Since the tension force in the steel strip generated by weight can be regarded as being constan t, the sagging of the steel strip remains unchanged regardless of the draft or speed conditions of the vessel. Furthermore, since the purpose of the measurement system is to measure the deflection between two different conditions, once the first condition is set as the initial condition, only the change in deflection from the initial state needs to be recorded, therefore, it is unnecessary to know the actual extent of sagging of the steel strip or to make corrections for such sagging. In order to eliminate the effect of possible lateral and axial vibration of the steel strip during measurement, a low pass filter with a cut-of f frequency of 0.6 Hz was employed for each channel, after confirming that the resonant frequencies of the steel strip in these kinds of vibrations were higher than 5 Hz. The characteristic of the low pass filter is shown in Fig. 6.6. The configuration of the measurement system was very simple as shown in Fig. 6.7. The laser displacement sensors were powered by a stable DC power source, and the extent of displacement was measured as an output voltage signal directly into a digital recorder. 6.2.2 Calibration of Measurement System 24 PART A GUIDELINES ON SHAFTING ALIGNMENT TAKING INTO ACCOUNT VARIATION IN BEARING OFFSETS WHILE IN SERVICE In addition to the output characteristics of individual laser displacement sensors that were provided by the sensor manufacturer, the output calibration of the entire measurement system was also calibrated with a dial gauge as shown in Fig. 6.8. The calibration was performed by adjusting the distance between the sensor and the target steel strip with the help of the dial gauge, both incrementally and decrementally at intervals of 0.05 mm (0.025 mm in one place), and recording the output of the sensor. The results of the calibration are shown in Fig. 6.9. As can be seen in Fig. 6.9(a), even a small change in displacement of 0.025 mm can be clearly detected from the corresponding variation in output voltage. In addition, it can be recognized that the linearity between displacement and the output voltage was significantly high. Fig. 6.5 A new hull deflection measurement system installed onboard. (a) For the aft part of hull under the intermediate shaft; (b) Alongside the engine; (c) Steel strip tightened by weight; (d) Close-up of laser displacement sensor; (e) Laser beam as reference line. (a) (b ) (c) ( d ) Laser senso r Strip Laser bea m Weight Pulle y Laser senso r Stri p Laser senso r Stri p (e) Laser beam as reference line 25 . -21 439 8.600 81956.600 -9075.900 86 43. 400 -6589.800 2 13. 600 - 53. 400 8.900 -21 439 8.600 34 2 737 .700 -147868.000 258 63. 000 -24 630 .400 18778 .30 0 -608.800 152.210 -25 .36 0 81956.600 -147868.000 868 43. 200. senso r Deflection line after change in condition (e.g. full loaded condition) Initial deflection line (e.g. ballast condition) Change in displacement between conditions Fig. 6.4 Concept of a new. 0.0892 630 911 0.0471291196 0.0955979752 δ2 3 δ4 δ5 δ6 δ7 δ8 = = 34 2 737 .700 -147868.000 258 63. 000 -24 630 .400 18778 .30 0 -608.800 152.210 -147868.000 868 43. 200 -29740.600 34 2 53. 700 -26115.100