PART B AMENDMENT OF THE GUIDANCE TO THE RULES AND ITS EXPLANATORY NOTES 13 load of other bearings differ from the actual respective values for each bearing. In order to prevent such a situation from occurring, the Guidance specifies that calculation results with a negative bearing load are not acceptable. Figure 3.1 Negative bearing load. 1.3.2 Light Draught Condition (Hot Condition) -1 This calculation condition is used to examine the strength of the intermediate shaft bearings, engine bearings, and other bearings in the ship’s ballast condition when the propulsion machinery is in the hot condition. It is assumed here that the hull girder deflection is the same as that in the condition described in paragraph 1.3.1 above and that the differences in the change in bearing offsets are only attributable to differences in temperature. Temperature changes cause changes in the offsets of all bearings such as the stern tube bearings, intermediate shaft bearings, gear shaft bearings, engine bearings, and the like. However, since large offset changes are seen especially on gear shaft bearings and engine bearings, temperature changes on at least these bearings are to be considered in the calculation. The amount of the offset change is to be in accordance with the manufacturer’s instructions, as it varies depending on the manufacturer and their respective models. For main engines, an increase in temperature of from 20 to 55°C is generally considered and, as shown in Figure 3.2, the resulting change in the bearing offset becomes larger as the scale of the engine (bore of the cylinder) becomes greater. Figure 3.2 Relationship between change in bearing offset and cylinder bore. -2 Buoyancy acting on the propeller changes depending on the extent of immersion of the propeller. However, the effect of buoyancy is such a degree that the load on the aftmost stern tube bearing changes only slightly, and changes in the loads on the intermediate shaft bearings and engine bearings are negligible. Hence, the degree of propeller immersion to be considered in the Guidance is, for example, to be either full immersion for the ballast condition or half immersion for the light ballast condition, whichever is acceptable. -3 Assuming that the bearing offset changes to some extent as a result of the influence of the change in hull girder deflection that occurs before and after launching, in cases where shafts are coupled before launching, the alignment calculation for the hot condition is to be carried out considering the influence of the deflection as well as the change in temperature. However, according to the results of measurements obtained up to now, the change in engine room double bottom deflection ( + ) ( + ) ( - ) ( + ) ( + ) Unloading R 1 R2 R 3 R2’ R3’ 0.00 0.10 0.20 0.30 0.40 300 400 500 600 700 800 900 Change in bearing offset ( mm) Cylinder bore (mm) PART B AMENDMENT OF THE GUIDANCE TO THE RULES AND ITS EXPLANATORY NOTES 14 before and after launching is comparatively small. Therefore, calculations carried out assuming the hull deflection condition prior to launching may be acceptable, if consideration is given to the effects of propeller buoyancy and the extent of thermal increase. -4 Unloading of a bearing in the static condition, which means the detachment of the shaft from the bearing, indicates the possibility that, when dynamic loads act on the shaft, the bearing may be hit repeatedly by the shaft, resulting in eventual failure of the bearing. Therefore, all bearing loads are to be positive in the running condition of the engine. -5 In cases where a shafting system with reduction gear is used (see Figure 3.3), the gear teeth rather than the bearings are susceptible to misalignment of the shafting. The contact condition between the wheel and the pinion depends on the difference in the bearing loads on the fore and aft side of the gear. The manufacturer of the gear box will usually determine the allowable limit for the hot condition. The allowable limit depends on the manufacturer. Therefore, the Guidance specifies that the system is to be so designed as not to exceed the allowable limit determined by the manufacturer. Figure 3.3 Geared propulsion system. -6 As shown in Figure 2.1 of the Explanatory Notes , bending moment due to hydrodynamic propeller force (upward moment caused by eccentric thrust force) is generated while the ship is underway, resulting in a change in the load on the aftmost stern tube bearing. This bending moment has a comparatively small effect on the loads of the intermediate shaft bearings or engine bearings, which are to be examined in the calculation for light draught condition (hot condition). Although the Society’s Guidance primarily assumes a static condition, it is acceptable to take this upward moment by eccentric thrust force into account when performing calculations for the hot condition. 1.3.3 Full Draught Condition (Hot Condition) -1 Damage to engine bearings due to hull deflection have been seen in ships with large differences in draught such as oil tankers, bulk carriers, and the like. A significant feature of the damage was unloading of the second aftmost engine bearing, which was generally found to be attributable to hull deflection behind the main engine. However, investigations by the Society also found that unloading could take place at the third aftmost engine bearing as well as the second aftmost engine bearing, depending on the design of the engine bearing offsets. The Guidance specifies that the shafting alignment is to be designed so that the parameters, δ B2 and δ B3 , are not less than the allowable limit shown in Figure 1.3.3-1(a) in the Guidance . The two parameters represent the difference in the extent of relative displacement of the hull due to hull deflection that occurs between the “zero” or baseline displacement of the light draught, hot condition, and the point at which hull deflection results in the second and third aftmost engine bearings, respectively, becoming unloaded in the full draught, hot condition. This difference in extent is measured at the aftmost bulkhead of the engine room. Said another way, it is an inverse measure of the extent of displacement that must take place until unloading occurs. Hence, the greater the value (i.e., the greater the margin before displacement results in unloading), the less likelihood that unloading of the respective bearing due to deflection will occur. The value of these parameters can be obtained using approximation equations provided by the Society. The equations were developed based on the results of past structural analyses and measurements in which relative displacement, δ , behind the main engine is expressed using the following equation: Propeller shaft Intermediate shaft Thrust shaft Gear shaft PART B AMENDMENT OF THE GUIDANCE TO THE RULES AND ITS EXPLANATORY NOTES 15 (1) where, X : distance from support point of aftmost engine bearing (mm), L : distance from support point of aftmost engine bearing to aftmost bulkhead of engine room (mm), δ B : relative displacement of hull at position of aftmost bulkhead of engine room (mm). Figure 3.4 Calculation model for determining relative displacement of hull. If Equation (1) is assumed, the change in offsets of the intermediate shaft bearings and stern tube bearings can be obtained by δ B . When relative displacement δ changes, the change in the reaction of the second aftmost engine bearing, for example, can be calculated from changes in each bearing offset behind the main engine and the respective reaction influence number with respect to the second aftmost engine bearing. In cases where the second aftmost engine bearing becomes unloaded, δ can be calculated inversely from the change in load (reaction) that occurs in the second aftmost engine bearing and the reaction influence number for that bearing. δ B2 can be obtained from δ at that time using Equation (1). The approximation equations for δ B2 and δ B3 in the Guidance were derived using such a calculation process. The values of the reaction influence numbers considered in the calculations will vary somewhat depending on the type of support used for the bearings, which may either consist of rigid support (simple support) or elastic support. Therefore, the Guidance provides equations to approximate δ B2 and δ B3 for both cases (see Appendix A). Bearing damage is not necessarily generated under a static draught when the ship is fully loaded, but rather possibly generated by the influence of waves at that time. Figure 3.5 shows the values of δ B2 or δ B3 , whichever are less, calculated in a shafting system where bearing damage due to hull deflection has never occurred. The lower limit of δ B2 or δ B3 was determined as shown in Equation (2) using L ( mm ) so that the line of the lower limit would be below these calculated data. (2) When δ B2 (or δ B3 ) exceeds the lower limit, the difference between δ B2 (or δ B3 ) and the lower limit means that there is a sufficient a safety margin with respect to hull deflection up to the point of unloading of the respective engine bearing. It can be said that δ B2 (or δ B3 ) is a parameter that indicates the flexibility of the shaft to hull deflection. δ B ( X / L ) 1.5 ( X ≤ L ) δ B {1.5 ( X / L ) - 0.5} ( X ≥ L ) δ = { Relative displacement δ B δ = δ B {1.5(X/L)-0.5} δ = δ B (X/L) 1.5 L Aftmost bulkhead of E/R Aftmost engine bearing Y X 1 (mm) ( L ≤ 9000) - 8 (mm) (9,000 ≤ L ) L 1000 Lower limit of δ B2 (or δ B3 ) = PART B AMENDMENT OF THE GUIDANCE TO THE RULES AND ITS EXPLANATORY NOTES 16 Figure 3.5 Values of δ B2 or δ B3 , whichever is less. -2 In addition to the method described in sub-paragraph 1.3.3-1 above, there may be an appropriate method for evaluating the strength of the bearings based on the results of structural analysis or full-scale measurements. Therefore, if a document is submitted that includes an evaluation of the engine bearings in the full load condition, the Society will examine the document and approve it, where acceptable. -3 The criteria described in sub-paragraph 1.3.3-1 above apply for ships with a standard stern structure. If the ship has an unconventional stern structure, the approximation equation on relative displacement of the hull can not be applied for the ship. Accordingly, in cases where the stern hull structure is considered to be unconventional, a document including the results of structural analysis and other relevant data on the hull deflection may be required by the Society. The structural analysis is to be done to evaluate the relative displacement that occurs when the ship’s draught changes from the light ballast condition (or ballast condition) to the full load condition. Bulk Carrier Tanker δ B2 or δ B3 , whichever is less ( m m ) 15 6 7 8 9 10 11 12 13 14 x1000 L ( m m ) 0 5 10 15 20 22 Lower limi t PART B AMENDMENT OF THE GUIDANCE TO THE RULES AND ITS EXPLANATORY NOTES 17 1.4 Matters relating to Shaft Alignment Procedures 1.4.1 Sags and Gaps between Shaft Coupling Flanges Any sags and gaps between coupling flanges are measured from the aftmost coupling to the foremost coupling in turn to determine the positions of each bearing. The calculation sheet is to include expected values of the sags and gaps with the relevant tolerances, and is to be submitted to the site surveyor when the measurements are performed. 1.4.2 Procedure for Measuring Bearing Loads In general, bearing loads are measured using the jack-up method. The ‘jack-up method’ is a technique used to obtain the bearing load from a jack load using a hydraulic jack that is placed adjacently to the bearing to be measured. An outline of the measurement method is shown in Figure 4.1. As the oil pressure of the jack rises, the plotted point, that is the relationship between the jack load and displacement, shifts from the initial state of A to the next state, B, in which the bearing load becomes unloaded. When the oil pressure is raised further, the plotted point reaches the state C with a change in the gradient of the jack-up curve. As oil pressure decreases from this state, the plotted point returns to the state of A via states of D and E. The resulting curve of the change in jack load plotted during the process of lifting and lowering the shaft by the hydraulic jack forms a hysteresis curve, as shown in Figure 4.1. Figure 4.1 Procedure for applying jack-up method. The bearing load, R B , can be obtained by the following equation using jack load, R J . (3) C is a load correction factor which is given by (4) where, I BB : reaction influence number of bearing support itself I JB : reaction influence number of jack support with respect to bearing support. Dial gauge Hydraulic jac k Jack load Displacemen t A B C Increasing Decreasing D E C = I BB I JB R B = C R J . B (Bearing: unloaded) A (Jack: no load) C Bearing support Jack PART B AMENDMENT OF THE GUIDANCE TO THE RULES AND ITS EXPLANATORY NOTES 18 Attention should be paid to how to read R J . In the event that Equation (4) is used to determine a load correction factor, R J should be the average of jack loads R I and R D . This average can be obtained by extending two straight lines BC and DE to the position at which the displacement becomes zero (see Figure 4.2). Although the bearing load can be obtained from the jack load R J which is read without extending the lines BC and DE, it should be noted that, in this case, the definition of load correction factor is different from Equation (4). That is, (5) (6) Where, I BJ : reaction influence number of bearing support with respect to jack support = I JB I JJ : reaction influence number of jack support itself. However, a number of measurements are made using Equations (3) and (4) based on past experience. Figure 4.2 Bearing load measurement using the jack-up method. References [1] Guidelines on Shafting Alignment, Part A, “ Guidelines on Shafting Alignment Taking into Account Variation in Bearing Offsets while in Service ”, ClassNK, 2006. [2] H. Yoshii, “ Shaft Alignment ”, Journal of the JIME, Vol. 39, No. 9, p. 597, 2004. R D R J R I R J Jack load Displacemen t I JJ I ’ JJ R J = R I + R D 2 C = I BJ I JJ R B = C R J . I JJ : Reaction influence number of jack support itself (in case where the bearing to be measured is excluded). PART B AMENDMENT OF THE GUIDANCE TO THE RULES AND ITS EXPLANATORY NOTES 19 APPENDIX A DERIVATION OF δ B2 AND δ B3 1 Approximate Calculation of Relative Displacement of the Hull A slope alignment approach is generally adopted when designing the installation of a marine propulsion system in which the main engine is installed below a predetermined reference line. When hull deflection takes place due to an increase in draught in such a shafting system, the relative positions of each bearing to each other will change, as shown in Figure 1.1(a). Accurately determining these changes in position will have a direct effect on determining the most suitable alignment of the bearings and shafting. Hence, it is desirable to determine the relative difference in position or displacement that occurs from the initial state of the ship in the light ballast condition and after deflection in the fully loaded condition. The resulting relative displacement, as illustrated in Figure 1.1(b), is based on the state of the shafting prior to deflection of the supporting hull structures, assuming that the relative displacement of the engine portion of the shafting (the crankshaft) is negligible. It is useful to set the initial condition as a baseline against which to measure the relative displacement that results in the fully laden state. Hereinafter, the approximate calculation of relative displacement of the hull, δ , behind the main engine is examined using the XY -coordinate system shown in Figure 1.1(b), in which the aftmost engine bearing is defined as the origin of the coordinate system. It is assumed that the changes in each bearing offset behind the engine correspond to the relative displacement of the relevant part of the supporting hull structure. Figure 1.1 Change in bearing offsets due to hull deflection. Although relative displacement, δ , along the length of the shafting aft from the aftmost engine bearing to the aft bulkhead of the engine room can be determined by finite element analysis, it is also found to be roughly proportional to the n power of X . Use of such a relation can help simplify the process of determining the relative displacement for a given alignment. Figure 1.2 Comparison between FE analysis and several Xⁿ curves. (b) X Y Relativ e dis p lacement ( δ ) Aftmost engine bearing (a) Bas e line M/E Befor e deflection (Light ballast condition) After de f le c tion ( Full y loaded condition ) Relative displacemen t δ (mm) 0 1 2 3 4 5 6 7 8 0 5 10 15 X : Distance from the aftmost engine bearing (m) FEM n = 1.4 n = 1.5 n = 1.6 n = 2.0 n = 3.0 PART B AMENDMENT OF THE GUIDANCE TO THE RULES AND ITS EXPLANATORY NOTES 20 Figure 1.2 shows a comparison between the result of finite element analysis and several Xⁿ curves having various values of n, with respect to the relative displacement of the shafting from the aftmost engine bearing to the aftmost bulkhead of the engine room in a 300,000 DWT oil tanker. The figure indicates that an n of 1.5 gives the best approximation of the relative displacement. Similar results were also seen in other ships. Hence, it is thought that the relative displacement of the hull supporting the shafting from the aftmost engine bearing to the aftmost bulkhead of the engine room can be expressed as a rough estimate using an n of 1.5 (that is, X 1.5 ). The hull structure on the aft side of the engine room aftmost bulkhead includes a highly rigid stern frame, which makes it possible to approximate the liner change in displacement of this part of the hull. Therefore, the change in offsets of the stern tube bearings behind the aftmost bulkhead of the engine room is given by the tangent to a curve with an exponent of X 1.5 at the position of the aftmost bulkhead. Based on the approximation method mentioned above, relative displacement of the hull, δ , due to the increase in draught can be expressed by Equation (1). Figure 1.3 shows the calculation model used to determine the changes in each bearing offset behind the engine due to this relative displacement of the hull. where, X : distance from support point of aftmost engine bearing (mm), L : distance from support point of aftmost engine bearing to engine room aftmost bulkhead (mm), δ B : relative displacement at the position of engine room aftmost bulkhead (mm). Figure 1.3 Concept of relative displacement model used to calculate the changes in each bearing offset behind the aftmost engine bearing. In Equation (1) the relative displacement, δ , behind the engine is expressed with the distance, L , from the aftmost engine bearing to the aftmost bulkhead of the engine room, while δ B represents the extent of relative displacement at the position of the bulkhead. Hence, δ B can be regarded as a parameter to determine the relative displacement curve of the hull. δ B ( X / L ) 1.5 , ( X ≤ L ) δ B { 1.5 ( X / L ) – 0.5 }, ( L ≤ X ) δ = { Relative displacement δ B δ = δ B {1.5(X/L)-0.5} δ = δ B (X/L) 1.5 L Aftmost bulkhead of E/R Aftmost engine bearing Y X ( 1 ) PART B AMENDMENT OF THE GUIDANCE TO THE RULES AND ITS EXPLANATORY NOTES 21 2 Reaction Influence Numbers determined by Relative Displacement Model A coefficient known as a "reaction influence number" is commonly used in alignment calculations for marine shafting. A reaction influence number is defined as a coefficient that indicates the relative extent of change that occurs in a bearing reaction when the offset of a particular bearing changes for a given unit value. For example, when the offsets of support points Nos. 1 to 4 change in the shafting system shown in Figure 2.1(a), the amount of change in the reaction of support point No. 6 (the second aftmost engine bearing), ∆R 6 , is expressed using reaction influence number, C m, n , as follows: where, δ n : amount of change in the offset of support point n , C m, n : amount of change in the reaction of support point m when support point n is displaced downward by 1 mm (reaction influence number). Figure 2.1 Calculation of bearing reaction using reaction influence numbers. Equation (2) can be rewritten using the relative displacement model of the hull described in section 1. This is because the changes in the offsets of support points Nos. 1 to 4 are obtained by Equation (1). Consequently, Equation (2) can be rewritten as follows using δ B and X n , where X n is the distance from support point No. 5 (the aftmost engine bearing) to support point n in which: In Equation (3), ∆R 6 is expressed as the product of δ B and S 6 , whereas in Equation (2) ∆R 6 is expressed as the summation of the product of δ n and C 6, n ( n = 1 to 4). Since both δ B and δ n indicate relative displacements, S 6 also represents the same meaning as the reaction influence ∆ R 6 = C 6, 1 δ 1 + C 6, 2 δ 2 + C 6, 3 δ 3 + C 6, 4 δ 4 = C 6, n δ n . Σ n = 1 4 ( 2 ) Aftmost bulkhead of E/R Intermediate shaft Propeller shaft Change in bearing reaction = ∆R 6 Aftmost engine bearing 1 2 3 4 5 6 7 8 9 1 2 3 4 C 6, 4 C 6, 3 C 6, 2 C 6, 1 δ 1 δ 2 δ 3 δ 4 (a) Intermediate shaft Propeller shaft S 6 δ B (b) ( 1 2 3 4 5 ) (No. of engine bearing) 1 2 3 4 5 6 7 8 9 ∆ R 6 = δ B S 6 , S 6 = C 6, n {1.5 ( X n / L ) - 0.5} + C 6, n ( X n / L ) 1.5 . Σ n = 1 3 Σ n = 4 4 (3) (4) PART B AMENDMENT OF THE GUIDANCE TO THE RULES AND ITS EXPLANATORY NOTES 22 numbers, C 6, n ( n = 1 to 4). If we assume that the whole of the relative displacements of the support points, δ n , can be replaced with the relative displacement of the hull, δ B , at the position of the engine room aftmost bulkhead, as shown in Figure 2.1(b), S 6 can be regarded as an equivalent reaction influence number that reflects the total combined effect of each reaction influence number, C 6, n ( n = 1 to 4), on that point. In the following equation, this equivalent influence number is generalized in order to obtain the influence numbers for each engine bearing. Now, assuming that S i is the increase of reaction at engine bearing No. i (from aft) when the hull is displaced downward by 1 mm at the position of the engine room aftmost bulkhead, then this S i is expressed by following equation: where, n : number of support point (counted from the aft of the shafting), a : number of the nearest support point forward of the aftmost bulkhead of engine room (counted from the aft of the shafting), b : number of support point of the aftmost engine bearing (counted from the aft of the shafting), X n : distance from support point b to n , L : distance from support point b to aftmost bulkhead of engine room, C m, n : amount of increase in reaction (reaction influence number) at support point m , when support point n is displaced downward by 1 mm. In Equation (5), it should be noted that the subscript i in S i indicates the number of the bearing as counted from the aft of the engine. S 6 in Equation (4) corresponds to S 2 ( i =2) in Equation (5), where a and b are 4 and 5, respectively. Σ n = 1 a-1 Σ n = a b-1 S i = C b + i-1, n (1.5 x n - 0.5) + C b + i-1, n x n 1. 5 , (5) x n = X n / L . [1] Guidelines on Shafting Alignment, Part A, “ Guidelines on Shafting Alignment Taking into Account Variation in Bearing Offsets while in Service ”, ClassNK, 2006. [2] H. Yoshii, “ Shaft Alignment. propeller immersion to be considered in the Guidance is, for example, to be either full immersion for the ballast condition or half immersion for the light ballast condition, whichever is. account when performing calculations for the hot condition. 1.3.3 Full Draught Condition (Hot Condition) -1 Damage to engine bearings due to hull deflection have been seen in ships with large