STUDY FURTHERS OPTIMISATION OF DOUBLE SLOPE STERN TUBE BEARINGS
Optimal geometric parameters for double slope aft stern-tube bearings have been determined to further reduce the risk of bearing failure
When shafts bend inside the aft stern tube bearing, the white metal liner also compresses, impacting the oil film between the shaft and the bearing. Double slope stern tube bearings have led to a reduction in resulting failures compared to single angle, however, further work can be accomplished if one can determine the optimal parameters for the bearings when operating under extreme conditions.
The double slope design concept involves two angles and their transition point axial location or “knuckle point.” The design increases the contact area between the shaft and the bearing bottom and can reduce the risk of some bearing failures. However, the design calculations are not simple, and a new study published in Tribology International furthers the study of optimisation algorithms.
Researcher Chris Leontopoulos Director of Engineering, Global Ship Systems Centre, ABS, explains the challenge: “Optimising the two angles and the axial location of the knuckle point is a challenging calculation largely because of the oil film modelling, including variations on viscosity, temperature, shaft deformation and white metal deformation as well.”
EEDI and stern tube bearings
The safety benefits of a double slope design have become more pressing. Vessels designed to meet the IMO's Energy Efficiency Design Index (EEDI) targets tend to have a more flexible hull, shorter shafts, high-powered slow speed engines and large diameter, heavy propellers. A larger propeller produces greater forces due to its interaction with water and therefore upsets the shaft and its angle with the bearing bottom much more readily. Environmentally acceptable lubricants are also regarded as more shaft alignment sensitive than traditional mineral oils, says Leontopoulos.
Single slope bearings have not prevented failures resulting in loss of propulsion in modern VLCCs and ULCCs. However, failure rate has decreased since 2017 after ABS pioneered the concept of the double slope bearing.
Excessive shaft load can cause oil film failure, metal-to-metal contact and eventual wiping and complete bearing failure. Analysis of recent failures has shown that in several cases single slope designs were inadequate, being too shallow under the high loading, and double slope geometry should be implemented to reduce the load on the bearing and achieve acceptable safety levels.
As the misaligned shaft is brought closer to the bearing surface, minimum lubricant film thickness decreases, and the hydrodynamic lubrication film becomes less able to support additional radial loads. The pressure distribution of the lubricant is altered and will form a distinct peak, with maximum pressure being located closer to the aft edge of the bearing and the longitudinal position of minimum film thickness. This is the main reason why single or double slope bearing designs are proposed.
There have been a number of initial discussions as to whether a “knuckle point”, the transition from the main slope to the secondary slope, could cause a stress concentration, when the shaft rests heavily on this edge. “This is not the case,” Leontopoulos explains. “The shaft material is way harder than the white metal material, and the concept is that the shaft weight smooths out this edge by slightly permanently deforming it through compression of the white metal material. This effectively, increases the contact area between the curved shaft and the 'sloped' bearing bottom. The bearing run-in procedure is a very important process so that this 'bedding-in' process between the shaft and the bearing occurs gradually and not in a forceful way. At the end of the bearing run-in procedure the knuckle point is effectively eliminated and the transition from the main slope to the secondary slope is gradual and seamless.”
Another debatable point is the axial position of the knuckle point from the aft edge of the bearing. The simulation optimisation results showed that the knuckle point should be positioned somewhere close to the middle of the bearing length. This would produce the lowest pressure and the highest contact area between the shaft and the bearing.
However, this contradicted the reality, where most of the times the aftmost bearings appeared to have failed by being wiped at an area of 1/3 to 1/4 from the aft edge. It was found that this was a result of the propeller forces consideration. If the vessel sails in a straight course, the propeller side forces when interacting with the water cause the propeller to slightly lift and sometimes to be slightly pushed downwards. While this operational scenario represents typically 90 percent of the vessel’s sailing time, it is not the so-called “worst case” scenario.
Turning to worst case scenarios
The latter typically occurs when the propeller pushes hard downwards when bending moments in the vertical directions prevail. This happens when the vessel turns starboard for a clockwise rotating propeller and can be further exacerbated when the propeller is close to the water surface or partially immersed. Other such loading scenarios may apply with twin-screw vessels producing side loads as well. These worse case scenarios where the propeller causes the shaft to further bend downwards are the culprits for disaster, says Leontopoulos. The shaft curvature increases, and the pressure is maximised towards the aft end of the bearing.
The secondary slope is then called upon to accommodate these increased pressures loads, and thus the knuckle point must exist at around 1/4 to 1/3 from the aft edge, in accordance to simulations under various loading scenarios. “We have seen sometimes in single sloped bearings that the shaft itself wants to “dig” a secondary slope in a forceful way. This is good if it is done in a controlled manner, however, most of the times this process results in bearing wiping and failure,” says Leontopoulos and adds: “If the shaft wants a second slope then the designer must prudently provide one.”
Leontopoulos, along with Professor Christos Papadopoulos and Georgios Rossopoulos of the National Technical University of Athens, calculated optimal angles and knuckle point parameters to further reduce the risk of failure. Optimal geometric parameters were determined for maximising the effective pressure area between the bearing and the propeller shaft and minimising the maximum local pressure exerted on the bearing surface.
The researchers evaluated the necessity of the double slope geometry for two highly misaligned shafts and compared optimal single and double slope designs in terms of bearing performance and safety margins. A double slope design model for a given set of system parameters, such as bearing load, bearing length/diameter and lubricant, is proposed in the study paper. The optimised designs presented increase the contact area between the shaft and the bearing bottom so that the bearing film does not collapse.
There are a number of loading scenarios for which optimisation can be performed, says Leontopoulos. Therefore, there is not a single best optimisation that mathematically covers all loading scenarios (e.g. straight ahead, turning, laden, ballast, etc.)
The modelling ensured that the single and double slope inclination of the bearing was accurate. Additionally, an extensive study was conducted to ensure the shaft was modelled as a bent beam within the bearing length. This required coupling of the shaft alignment calculations with the performance calculations.
The researchers calculated the equilibrium of pressure distribution on the unwrapped journal bearing geometry using a computational approach evolved from the solution of the Reynolds differential equation. A general-purpose optimiser was then used to calculate the optimum geometry based on two objective functions. Optimum designs for single and double slope bearings were calculated, and the performance parameters of the designs were compared for normal and extreme operational conditions: a partially immersed propeller and a starboard turn of a clockwise rotating propeller for various drafts. Each calculation phase involved a number of iteration loops until a new equilibrium and convergence was established.
When minimum lubricant film thickness and maximum longitudinal pressure are considered, a bent shaft model was critical for an accurate representation of the lubricant film thickness. The linear shaft model could not detect that the shaft was in contact to the bearing surface at the aft end of the bearing length, so it could potentially create an erroneous sense of safety.
The double slope design was mostly affected by the longitudinal position of the theoretical contact point and additional power losses rather than vertical offset of the bearing and minimisation of lubricant film thickness. This, said the researchers, is vital for the survivability of the vessel in extreme loading conditions which can take place due to bad weather or due to failure, overloading or malfunction of other components in the shafting system.
Further optimisation under even more extreme conditions than those covered in the study is possible. The researchers note that the double slope bearing is not complex to manufacture and yet may not be a panacea. “Triple sloped and multi-sloped bearings could be even better than double-sloped,” says Leontopoulos.
Ultimately, a bearing multi-slope optimisation process will be driven by the selection of the vessel’s significant operating conditions. If worst case scenarios are considered, the optimisation may be different to that for straight ahead. Future work could include experimental tests, simulations under transient and dynamic loads, thermo-elasto-hydrodynamic simulations and finite element method (FEM) calculations.
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