A Solution to Robust Shaft Alignment Design

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1 A Solution to Robust Shaft Alignment Design Prepared for SNAME Propellers/Shafting Symposium, Virginia Beach- September 12-13, 2006 Davor Šverko, American Bureau of Shipping, Houston Originally presented at the 2006 SNAME Propeller/Shafting 2006 conference held in Virginia Beach, VA, USA, September 12-13, Reprinted with permission of the Society of Naval Architects and Marine Engineers (SNAME). Material originally appearing in SNAME publications cannot be reprinted without written permission from the Society. 601 Pavonia Ave., Jersey City, NJ ABSTRACT The primary problem that shafting alignment designers are faced with today is high sensitivity of the alignment to the hull girder deflections resulting from the changes in the loading condition of the vessel. Accordingly, the accuracy of the alignment procedure will depend on our ability to account for hull deflections in the alignment design. The shafting alignment optimization approach that ABS is proposing in this paper provides a solution to the problem. So far ABS collected sufficient amount of hull girder deflection data to generate initial database, and enable alignment designers to estimate hull deflections with high confidence on new designed tankers and bulk carriers. Establishing the hull deflection database is an essential part in shafting alignment optimization, as we want to ensures the robust alignment design, with sufficient margin of safety to remain satisfactory under extreme hull deflections, thermal change in bearing offsets, as well as to absorb much of the possible unpredicted disturbances. In this paper we will show how the hull deflections are utilized in the alignment design and optimization. We will indicate the advantages of undertaking this approach, and discuss concerns and constraints designer should be aware of when analyzing the alignment. Key words: shaft alignment, hull deflections, optimization, genetic algorithm INTRODUCTION The problem that shafting alignment designers are faced with today is high sensitivity of the alignment to the hull girder deflections resulting from the changes in the loading condition of the vessel. The accuracy of the alignment procedure will depend on our ability to account for hull deflections in the alignment design. Undoubtedly, hull deflections are the primary reason for troubles that are being experienced in shafting alignment, and for the lost confidence in the reliability of the shafting alignment design. ABS initiated a hull deflection investigation project with the motivation to reinstate this confidence. ABS s shaft alignment project consisted of hull deflection investigation and actual measurements on numerous ships of different types and sizes to acquire necessary information on actual hull deflections. In parallel to hull deflection measurements, ABS developed the analytical procedure to estimate the hull deflections. Information on hull deflections obtained by measurements is further utilized to calibrate the analytical procedure. The information obtained by the above process is now a very reliable estimate of the hull deflections that shafting may be expected to be exposed to. However, the shafting alignment design does not stop here. Being aware of the fact that the hull deflections obtained by the above procedure are estimates (may be quite accurate but are still estimates), ABS went a step further in the design process and developed the optimization software which essentially proposes the optimal bearing offsets which satisfy alignment criteria for expected extreme hull deflections, ballast and laden. The optimization process essentially defines the alignment design which is the least sensitive to disturbances from the hull deflections. Even if the hull deflections are not fully accurate, the designed bearing offset is such that can absorb those inaccuracies without compromising the alignment soundness. In this article, we will explain the above in more detail. First, it will be shown how the measurement procedure is conducted and how the hull deflection information is extracted from the information acquired. Next, it will be briefly discussed how the analytical method of predicting hull deflections works in combination with the measured deflections. Finally, the ABS shafting alignment optimization software will be presented, showing how the hull deflection data is utilized in optimum design of the propulsion shafting alignment. To illustrate how the hull deflection data is obtained and how the same data is utilized in an optimization procedure we have selected a VLCC example. HULL DEFLECTION MEASUREMENTS The hull deflection measurement procedure is described in the VLCC example. Basic parameters of the ship are given in Table 1, and arrangement of the shafting alignment is shown in Figure 1. A Solution to Robust Shaft Alignment Design 187

2 Hull deflections affecting the shaft alignment are not measured directly. We take advantage of the properties of the shafting, and use the same as a gauge from which we acquire measured data and utilize those data in a reverse analytical process to recalculate hull deflections. Figure 1 Shafting arrangement with the strain gauge location Displacement of the ship Length over PP Shafting length Propeller Engine 320,000 DWT 320 [m] 19.8 [m] 9.9 [m] diameter single screw 6 Cylinder MCR 30, rpm Table 1 VLCC example: basic vessel parameters Figure 2 VLCC example: Vertical offset of the bearings for several vessel conditions - obtained from measurement by reverse engineering analysis. 188 A Solution to Robust Shaft Alignment Design

The parameters measured are: - Bending moments (in this example we measured at five locations along the line shafting) Bearing Reactions Node # Measured reaction [kn] Reverse analysis reactions [kn]

Crankshaft deflections are measured in order to define the bending shape of the crankshaft, as shown in the figure below With moments and bearing reaction information handy, we are now able to

node # Measured moments [knm] Bending Moments Reverse analysis moments [knm] Error Estimate [%] Aft_ST 8 Not measured 992.587 N/A Fwd_ST 15 57.0 64.170 12.57 IntBea 28 185.5 171.981-7.28 ME8 40 171.

3 The parameters measured are: - Bending moments (in this example we measured at five locations along the line shafting) Bearing Reactions Node # Measured reaction [kn] Reverse analysis reactions [kn] Error Estimate [%] - Bearing reactions: forward stern tube bearing, intermediate shaft bearing and main engine bearings - Crankshaft deflections. Crankshaft deflections are measured in order to define the bending shape of the crankshaft, as shown in the figure below With moments and bearing reaction information handy, we are now able to conduct the reverse analysis and recalculate the actual bearing positions for the dry dock, ballast and laden vessel. node # Measured moments [knm] Bending Moments Reverse analysis moments [knm] Error Estimate [%] Aft_ST 8 Not measured N/A Fwd_ST IntBea ME ME ME ME5 48 Not measured N/A ME4 50 Not measured N/A ME3 52 Not measured N/A ME2 54 Not measured N/A ME1 56 Not measured N/A Table 3 Full load bearing reaction measurements compared with reverse analysis results The reverse analysis is a procedure for recalculating the bearing offsets from given bending moments (Table 2) and bearing reaction forces (Table 3), and crankshaft deflections. In reverse analysis we are looking for the bearing offsets that will provide bending moments, bearing reactions and crankshaft deflections that will best fit the measured values. In order to achieve the above we introduced the probability fitness function, and the best solution is sought based on closest match among calculated and measured parameters. Reverse analysis is conducted for every measured set of data (dry dock, ballast, full loaded ship). Information obtained is the actual vertical position of the bearings for each measured condition of the vessel (Table 4). It is imperative to evaluate the accuracy of the reverse analysis results. The accuracy will depend on the precision of the individual measurements. Therefore we assigned the confidence level of each particular reading (moment and bearing reaction), thus ensuring a more credible and trustworthy results. SG SG SG SG SG Table 2 Full load bending moment measurement compared with reverse analysis results Figure 3 Reverse analysis front-end A Solution to Robust Shaft Alignment Design 189

4 Knowing the actual bearing position (vertical offset) in the dry dock, the objective is to find the difference between bearing offsets in the dry dock and the desired waterborne condition (e.g. ballast and laden). This difference will indicate the extent of the dry dock bearing positions changed under the influence of hull deflections. Note: Ability to define an actual vertical position of the bearings has an additional significant application in failure investigation, where knowledge of the actual bearing location is of paramount importance for proper trouble shooting and resolution of the problem. Each set of vertical offsets of the bearings for a particular vessel condition is called a offset vector, and a matrix that contains particular offset vectors (Table 4) is called a offset vector spectrum. In this example we show the offset vectors for the dry dock, ballast and the laden ship, and the offset vector spectrum will be a matrix containing those three vectors. Bearing Location Offset Vector Dry Dock Offset Vector Spectrum [mm] Offset Vector Ballast Offset Vector Laden Figure 4 Absolute bearing position (as measured), compared with designed bearing offsets - Dry Dock S / T aft S / T fore Int. Sh. brg ME8 ME7 ME6 ME5 ME4 ME3 ME2 ME x11 1x x11 3x11 Figure 5 Absolute bearing position (as measured), compared with designed bearing offsets - Ballast Table 4 Offset vector spectrum - obtained by reverse analysis (see Figure 2) The offset vectors are obtained through the reverse engineering analysis. The ABS reverse analysis software is used to calculate the same from measured bending moments and bearing reaction forces. Figure 6 Absolute bearing position (as measured), compared with designed bearing offsets - Laden The charts in Figure 4, Figure 5, and Figure 6 compare offset-vectors for dry dock, ballast and laden vessel, with the originally designed bearing offset (the offset vectors are the same as in Table 4, only mapped in the different coordinate system as normally used by alignment designers). 190 A Solution to Robust Shaft Alignment Design

5 The results to be obtained from the hull deflection measurements is essentially information on the magnitude of the absolute-bearing-position change from the dry dock to ballast, and from the dry dock to fully loaded vessel. Figure 7 illustrates the above procedure and shows the actual shafting central-line deformation due to the effect of hull deflections. The next section explains ABS s approach to alignment design and optimization. We will illustrate how hull deflections are utilized in an alignment optimization process. Figure 7 Deflections of the shafting center line under laden (top line) and ballast (lower line) condition for VLCC ANALYTICAL HULL DEFLECTIONS ABS s approach in estimating hull deflections combines the analytical approach and the measurements. Accordingly, the shafting alignment software is so designed to predict the hull deflections analytically, and to correct those predictions using the pool of hull deflection data obtained by measurements. The correction factors are separately defined for particular ship type (e.g., tanker, bulk carrier, etc.) ALIGNMENT OPTIMIZATION Shafting alignment optimization has an advantage only when the hull deflections are taken into account. The goal of shaft alignment optimization is to find a dry dock bearing offset which will result in acceptable alignment conditions for a whole range of vessel loading conditions (from ballast to the laden). Essentially, we are looking for a single fittest solution for the dry dock offset-vector which will satisfy alignment criteria for the ballast, laden and all loading conditions in-between. Since the dry dock is not an operational condition, the alignment criteria in the dry dock need not necessarily be satisfactory. As it known, there are an infinite number of bearing offset-vector that may satisfy alignment criteria. To find the fittest and most robust offset-vector, a software which provides multiple solutions is needed, but the final selection of the optimum offset-vector has to be made by the designer who can make this decision based on the particulars of production procedures in the shipyard and the specific characteristics of the vessel. Providing multiple solutions is an inherited characteristic, and a relatively simple task for the genetic algorithm (GA) software to perform (Novkovic and Sverko (2003) [2]). This is the same reason that ABS adopted the genetic algorithm search engine for the shafting alignment optimization (Sverko (2003) [4]). The GA program optimizes among several constraint functions (as defined by hull girder deflections Figure 9). Constraints which bind the solution space are defined by hull deflection curvatures which normally represent the still water ballast and laden vessel loading condition. The shaded area in Figure 9 indicates the range of hull deflections which will be covered by the selected optimal dry dock offset-vector. The optimal offsetvector is shown as a thick line in Figure 9 and tabulated in Table 5. As stated above, the GA optimization program provides any desired number of offset-vectors which satisfy A Solution to Robust Shaft Alignment Design 191

6 given constraints (theoretically, there are an infinite number of solutions to the problem). To illustrate how GA works, we let the optimization software find one hundred solutions, and select one optimum offset vector (and two alternative ones) based on the condition that the standard deviation of each particular reaction is minimum. Figure 8 illustrates the output for selected VLCC example Figure 8 Results of the optimization analysis for given hull deflections, thermal expansion and bedplate presaging. 192 A Solution to Robust Shaft Alignment Design

The thick line represents the dry dock alignment selected as an optimal solution for the given: - hull deflections - thermal expansion of the engine and - main engine bedplate sagging Table 2 shows

7 The thick line represents the dry dock alignment selected as an optimal solution for the given: - hull deflections - thermal expansion of the engine and - main engine bedplate sagging Table 2 shows only the optimum solution extracted from the actual optimization software printout. For the selected example we searched for 100 solutions. Encircled bearing reactions in Table 1 are expected bearing load vectors in ballast and laden condition, as found by the optimization software Figure 1 Parameters considered in optimization process Table 1 Solution #6 Selected Optimum SOLUTION No.( 52) Generation: 1 String: 59 FITNESS: SUPPORT REACTIONS Total Total GA Max Hull Min Hull Thermal Engine Ry[0] delry Ry Ry Ry Offset Offset defined Deflect. Deflect. Offset Sag. Sup. Node (Max.Offs) (Min.Offs) (dy) Max. Min. dy No No [kn] [kn] [kn] [kn] [kn] [mm] [mm] [mm] [mm] [mm] [mm] [mm] < 8> < 15> < 28> < 40> < 44> < 46> < 48> < 50> < 52> < 54> < 56> A Solution to Robust Shaft Alignment Design 193

8 CONCLUSION Good static alignment is a prerequisite for acceptable dynamic behavior of a propulsion system. In order to obtain satisfactory alignment, it is necessary to be able to control the outcome of the alignment analysis and provide reliable data to the shipyard s production personnel conducting the alignment. Under ideal circumstances, when hull deflections are known and the bearing offsets optimized, the solution to the problem of alignment accuracy would be in completing the alignment procedure while the vessel is in the dry dock. This can be done only if there is confidence that the alignment design will result in an acceptable alignment condition for all operating conditions of the vessel, which would imply that hull deflections are accounted for in the design procedure. Moreover, the ship production practices need to be such to ensure the design requirements are met with sufficient accuracy; namely, the dry dock bearing offset should not deviate from the design values more than the accuracy of the sighting equipment allows. The biggest obstacle designers are facing is defining the hull girder deflections. The solution to the problem very much depends on the ability to accurately evaluate hull deflections. The approach that ABS has proposed in this paper provides a solution to the problem. The analytical hull deflection prediction, calibrated against the actual (measured) hull deflections, is the established ABS REFERENCES: [1] ABS (2004): Guidance Notes on Propulsion Shafting Alignment, Houston [2] NOVKOVIC, S. and ŠVERKO, D. (2003): A Genetic Algorithm With Self-Generated Random Parameters, Journal of Computing and Information Technology, 11,4: approach that will enable shafting alignment designers to predict the hull deflections level on new constructions with relatively high confidence. This approach will ensure that the alignment has been designed robustly enough to absorb eventual unpredicted disturbances, and still remain satisfactory. In this paper, we have illustrated on a VLCC example, an application of ABS s reverse analysis software, which is used to obtain hull deflections from measured bending moments and bearing reactions. We further showed how the ABS shafting alignment optimization software utilizes hull deflection information to design reliable and robust alignment. As is primarily the case with alignment designs today, the hull deflection data are not readily at hand, and this is exactly where the ABS approach in estimating the hull deflection can be utilized. Based on the main parameters of the ship (length over perpendiculars, breath, draught, mid section modulus), we can extrapolate hull deflections from a pool of data of similar vessel types, perform the analytical hull deflection analysis, correct the analytical hull deflections and apply it in the shafting alignment optimization procedure. Extrapolated hull deflections will not be completely accurate, however, the estimate will be conservative, thus enabling an additional safety margin in optimizing alignment. [3] ŠVERKO, D. (2003): Design Concerns in Propulsion Shafting Alignment, Proceedings of the ICMES Conference 2003, Helsinki, May 2003 [4] ŠVERKO, D. (2003): Shaft Alignment Optimization With Genetic Algorithms, SNAME Propellers and Shafting 2003 Symposium, Virginia Beach, October A Solution to Robust Shaft Alignment Design

VALIDATION METHODOLOGY FOR SIMULATION SOFTWARE OF SHIP BEHAVIOUR IN EXTREME SEAS

10 th International Conference 409 VALIDATION METHODOLOGY FOR SIMULATION SOFTWARE OF SHIP BEHAVIOUR IN EXTREME SEAS Stefan Grochowalski, Polish Register of Shipping, S.Grochowalski@prs.pl Jan Jankowski,