Experimental Study on the Effects of Controllable Parameters on the Healthy Operation of SF-2A Material Water-Lubricated Stern Bearing in Multi-Point Ultra-Long Shaft Systems of Ships

Abstract

Effective control of the health operating condition of multi-support, ultra-long shaft system water-lubricated stern bearings is crucial for supporting the intelligent maintenance and health management of ships. This study investigates the failure modes of water-lubricated stern bearings and focuses on the critical failure modes of abnormal wear and high-temperature meltdown to analyze the mechanisms and influencing factors of these failures. It discusses the conditions for healthy operation of water-lubricated stern bearings, as well as methods for controlling lubrication and temperature rise. Based on this, controllable parameters for the healthy operation of water-lubricated stern bearings were selected, an experimental rig was constructed, and experiments were conducted using SF-2A material water-lubricated bearings. The experimental results indicate that by controlling parameters such as shaft rotational speed, inlet lubrication water temperature, clear-water lubrication, sediment-laden-water lubrication, bearing specific pressure, and the surface morphology of the bearing liner, the velocity characteristics, lubrication characteristics, and temperature rise characteristics of the bearings can be effectively altered. The sensitivity of the lubrication and temperature rise characteristics of SF-2A material water-lubricated stern bearings to controllable parameters varies under different environmental conditions. The study finds that precise control of these parameters can improve the operating condition and reliability of water-lubricated bearings.

1. Introduction

The trend of large-scale, high-power, and long shaft systems in ships is accelerating rapidly. This includes specialized vessels such as surface warships, where propulsion shaft systems are increasingly lengthened, with more shaft sections and bearing supports. Some ship shaft systems reach lengths of 50 to 100 m, with a few exceeding 100 m, typically supported by 5 to 10 intermediate bearings, and occasionally more than 10. The practical application of multi-support, ultra-long shaft systems in ship power systems is increasingly common. The arrangement of the multi-support, ultra-long shaft system stern bearings on a certain ship is shown in Figure 1.

These ship multi-support, ultra-long shaft system stern bearings use water lubrication and come in three structural types: open, semi-open, and closed stern bearings. Open stern bearings, which are an open system, use the rotation of the shaft and the motion of the ship to introduce surrounding water into the working space between the shaft and the bearing, freely flowing through to form a hydrodynamic lubrication film, commonly used in stern frame bearings. Semi-open stern bearings pump filtered water to the forward end of the bearing, forcing it through the bearing gap to the aft end. This structure allows control over the lubrication water flow through the bearing by adjusting the pump, but semi-open systems are still susceptible to clogging from sediment and marine life, which can disrupt the lubrication state and lead to abnormal wear and high temperatures. Closed stern bearings feature a sealed lubrication water circulation system, with seals on both sides of the bearing or bearing unit assembly, effectively protecting the friction pair from external contamination. The closed structure allows control of the circulated water’s temperature, flow, and speed to provide a favorable working environment for the bearing. Bow and stern sealing devices can adopt forms such as face seals and lip-type rubber cup seals. When using multi-cup seals, the lubrication and cooling states of the cups can be adjusted while ensuring the sealing effect by controlling the pressure of the lubricating water or air between the cups [1].

The multi-support, ultra-long shaft systems of ships are characterized by their considerable length, numerous shaft sections, and multiple support bearings. The spatial alignment of the shaft line is complex, often comprising multiple bending sections forming a spatial curve [2]. Multi-source excitations, such as operational loads [3,4] (varying operational conditions), environmental loads [5] (wave impacts, hull deformations, etc.), and navigational movements (full rotations, S-turns, etc.), can cause changes in bearing positions and support forces [6]. These changes can lead to deviations from the designed operational form of the shaft system, resulting in increased loads on stern bearings, high temperature meltdowns, abnormal wear, and abnormal vibrations [5,7,8].

These failures typically originate from deficiencies in bearing design [9,10,11] and material [12,13,14] selection, compounded by operational environmental stresses. Despite extensive research into traditional stern bearing [15] materials such as Cylon, Teflon, and rubber [16], their performance under extreme conditions remains limited. Thus, exploring the potential applications of novel materials like SF-2A holds significant scientific importance and practical value for enhancing the durability and operational efficiency of bearings. On the other hand, severe wear and high-temperature failures observed in the stern bearings of ships’ multi-support, ultra-long shaft systems affect the stability, reliability, and safety of the ships’ power systems, reducing the vessels’ operational viability and drawing significant concern from users and managers [17,18,19]. The strategy of reactive maintenance can increase the risk of failures during the operation of these systems. Although regular maintenance strategies can prevent and reduce sudden failures, they may lead to unnecessary downtime [20]. Furthermore, due to the variable and uneven working conditions of the stern bearings in these long shaft systems, there are risks of over-maintenance or under-maintenance, especially under-maintenance, which poses risks comparable to those of reactive maintenance strategies. The application of condition-based maintenance strategies [21], whether based on empirical models, physical models, or data-driven methods [22], has somewhat mitigated these issues but introduced dependencies on expert system rules, challenges in building mechanism models, and the need for extensive multi-type state data [23].

The operational conditions of multi-point ultra-long shaft system stern bearings exhibit significant uncertainties, making it challenging to establish accurate mathematical or physical models, nor can a single method uniformly describe these models. This uncertainty primarily stems from the influence of different operational environments and control parameters such as speed, lubrication, and cooling conditions, which directly affect the performance and lifespan of the bearings. Therefore, researching and understanding the impact of these variable parameters on the behavioral model of stern bearings is crucial for their intelligent operation and health management. For instance, controlling the lubrication water temperature, adjusting the shaft speed, or changing the bearing materials can significantly affect the performance of the stern bearings. Although the mechanical properties of SF-2A material are comparable to those of Cylon and Teflon, its application in ultra-long shaft system stern bearings is not yet widespread [24]. Given the potential application value of SF-2A material in multi-point ultra-long shaft system vessels, exploring its performance in this scenario, particularly its response to speed characteristics, lubrication properties, and cooling features, is not only crucial for assessing material suitability but also provides a scientific basis for optimizing the design and maintenance strategies of stern bearings. The SF-2A material boasts advantages such as high specific pressure capacity, high linear velocity, relatively high thermal deformation temperature, good sand resistance, and ease of replacement. SF-2A material water-lubricated stern bearings are suitable for a wide range of military and civilian ships.

To ensure the healthy operation and operational state control during service of multi-point ultra-long shaft system stern bearings, this study delves into the friction wear state and cooling performance of SF-2A material water-lubricated stern bearings. A series of experiments are conducted to investigate the performance of SF-2A material water-lubricated stern bearings under various operational conditions, particularly exploring the impact of controllable parameters on their healthy operation. This research aims to provide experimental evidence to support the operational maintenance decisions for vessels using these bearings. The main contributions of this paper are outlined as follows:

(1) The study investigates the impact of controllable parameters on the healthy operation of water-lubricated stern bearings in multi-support ultra-long shaft systems of ships. It primarily focuses on analyzing the effects of shaft speed, water temperature at the bearing inlet, clean-water lubrication, sediment-laden-water lubrication, bearing pressure, and the surface morphology of the bearing liner on the velocity characteristics, lubrication properties, and temperature rise characteristics of water-lubricated stern bearings. This research serves as an essential supplement to the foundational engineering applications of intelligent operation and maintenance of water-lubricated bearings in multi-support ultra-long shaft ship systems. The findings aim to support the precise control of operating conditions in real-world applications, ensuring expected service performance and maintaining the healthy operational status of the bearings.

(2) The study discusses the velocity, lubrication, and temperature rise characteristics displayed by SF-2A material water-lubricated stern bearings under different experiment operating conditions, as well as the unique sensitivity characteristics of the lubrication and temperature rise states of SF-2A material water-lubricated stern bearings to control parameters, such as reactions to shaft rotational speed, bearing specific pressure, lubrication water temperature, and the presence of sediments. These findings highlight the unique behavior patterns of SF-2A material compared to other bearing materials, providing significant decision support for the intelligent maintenance of SF-2A material water-lubricated stern bearings.

(3) Systematic experiments on SF-2A material water-lubricated bearings under various operating conditions, especially in evaluating performance under changing environmental and operational parameters, provide key data for understanding and optimizing the engineering application of this material in ship stern bearings and for operational use by ship crews after installation. This contribution not only enhances the accuracy of predictions about the lubrication and temperature rise behaviors of SF-2A material water-lubricated stern bearings in real ship applications but also demonstrates that appropriate adjustments to operating parameters, such as shaft rotational speed and lubrication water temperature, can significantly improve the performance and reliability of the bearings. This deep understanding of the interaction between operating parameters and bearing performance allows health management practices to adapt more flexibly to different operational needs while maintaining optimal bearing performance.

The rest of this paper is organized as follows. Section 2 reviews existing studies and analyzes the influencing factors of typical failure behaviors of stern bearing abnormal wear and high-temperature meltdown. Section 3 discusses the necessary conditions for the healthy operation of stern bearings based on the above content, where lubrication and temperature rise are key. This involves selecting controllable parameters that affect the lubrication and temperature rise states of the stern bearings, constructing an experimental setup, and designing the experimental scheme. Section 4 analyzes and discusses the relationships between controllable parameters and the operational states of the stern bearings based on experimental results. Section 5 presents the conclusions of this paper.

2. Case Study and Failure Behavior Mechanism Analysis

The failure modes of marine water-lubricated bearings primarily include abnormal wear [25,26], high-temperature meltdown [27], cracking, and superficial surface spalling [28]. Compared to conventional stern bearings, ultra-long shaft system stern bearings are more sensitive to the alignment of the shaft line, which means they have higher requirements for lubrication and temperature conditions. Abnormal wear and high-temperature meltdown are the focus of failure modes, with cracking and surface spalling often occurring as concurrent failure modes. These concurrent failures were also observed in the experiments conducted in this study.

2.1. Stern Bearing Abnormal Wear

2.1.1. Case Studies

The case studies on the abnormal wear of water-lubricated stern bearings, particularly focusing on the failure characteristics of long shaft system stern bearings, are summarized in

Table 1. Case studies of abnormal wear in stern bearings.

Source	Ship/Year Built	Shaft System Type	Liner Material	Bearing Structure	Failure or Malfunction	Cause of Failure
[29]	98,000 t semi-submersible/2016	Long shaft system	Cylon	Open and closed types	Stern tube, (fore stern bearing group) stern tube seal failure; significant stern shaft settlement, excessive wear of stern bearing group.	Shaft misalignment; permanent hull deformation; special cargo conditions; marine growth.
[30]	Liyang wheel/1971	Long shaft system	Lignum vitae	Semi-open	Propeller strikes float, blades lose balance; extensive damage to lower half of stern bearing surface, bearing gap exceeds 10.00 mm.	Abnormal vibration of shaft system; changes in alignment.
[31]	159.6 m bulk carrier/2010	Long shaft system	Polymer material	Closed	Surface damage of about 3.00 mm on stern tube static ring, springs outside the dynamic ring blocked by sediment and cannot pop out automatically, severe wear on the surface of the dynamic ring; bearing gap 7.00 mm (normal value is 1.00 mm). Figure 2a,b show blockages of sediment in the middle and lower part of the flume, respectively.	Stern bearing operates under high sand concentration, high wear rate.
[32]	16,000 t bulk carrier/1976	Short shaft system	Lignum vitae	Closed	Excessive bearing wear up to 2.08 mm; overly large bearing gap, various degrees of wear on stern tube bronze sleeve.	Poor shaft alignment; stern tube seal failure.
[33]	9600 GT freighter/2002	Short shaft system	Polymer material	Open, seawater-lubricated	Front and rear stern tube bronze sleeves worn down to a depth of 3.00 mm, maximum bearing gap 6.00 mm (exceeding the limit value of 5.10 mm).	Shaft line subsidence deformation; excessive bearing gap; localized wear causing stress concentration.
[34]	Unlimited range dry cargo ship	Short shaft system	Cylon	Seawater-lubricated	Shaft centerline significantly exceeds normal range; partial uneven wear of stern tube bronze sleeve, abnormal shaft vibration.	Shaft centerline misalignment; propeller entangles ropes/nets.
[35]	Single-engine single-propeller bulk carrier	-	-	Closed	Traveling in light ballast condition in adverse sea conditions (Beaufort scale 9–11) with draft of 4.17 m at the bow and 7.80 m at the stern, leading to abnormal wear of the stern bearing.	Propeller emergence.
[36]	Electric propulsion test platform	-	Cylon	Closed	Severe wear on the stern tube bearing, stern shaft sinking; excessive vibration and noise at the stern tube. Figure 2c shows severe wear condition of the stern tube bearing.	Poor alignment, unreasonable load distribution; cavitation effect impacting water film load-bearing capacity, eroding bearing liner material.
[37]	China ship scientific research center	-	-	-	Obvious wear on the friction pair surfaces of the shaft and bearing; Figure 2d.	Poor lubrication of the stern bearing, causing friction vibration and noise.
[38]	4600 t juice transport ship	Single stern tube bearing	Rubber	Closed, freshwater-lubricated	Fishnet knife in scraping state against propeller hub, as shown in Figure 2e, with a design gap of about 5.00 mm, hence it can be inferred that the bearing has worn down about 5.00 mm. Bearing wear leads to seal damage, shown in Figure 2f–h, illustrating the wear state at the aft and fore ends of the bearing, respectively.	Hull deformation at the stern hub causing shaft line changes, poor alignment; seal failure triggers bearing wear, followed by meltdown, further exacerbating seal damage.

below. The table includes case vessel names, shaft system types, and material and structural parameters of the stern bearings. Based on these case studies, the failure or malfunction states displayed by the stern bearings are analyzed, and potential causes of failure are discussed.

The case analysis above involved states of abnormal wear failure of water-lubricated stern bearings, as shown in Figure 2.

2.1.2. Analysis of Failure Impact Factors

(1) Shaft alignment

Shaft alignment typically includes methods such as the straight line method, allowable bearing load method, and reasonable bearing load method. The reasonable bearing load alignment refers to the installation of the shaft line into a predetermined curved state, ensuring optimal load distribution among the bearings under the main engine’s hot conditions by adhering to specified limits on bearing loads, stresses, and torsion angles [39].

As ships operate, various factors such as hull deformation, cargo loading, maritime environment, and the wear state of bearings during operation can cause changes in the shaft line, leading to shaft misalignment. This misalignment can produce the following hazards:

a. The lower part of the stern frame bearing/stern tube aft bearing might experience localized overloading, leading to direct friction between the shaft journal and the bearing during operation.

b. The contact between the stern tube fore bearing and the shaft journal might decrease, or negative loads may occur, causing localized contact on the upper part of the stern tube fore bearing. This accelerates the wear between the shaft journal’s working surface and the bearing, damaging the front seal of the stern shaft.

c. Increased shaft system vibrations can, in severe cases, lead to wear of the main engine’s main bearings and the gearbox bearings, thereby directly affecting the vessel’s navigational safety.

(2) Shaft system vibration

Shaft system vibrations include torsional vibrations, longitudinal vibrations, and rotational vibrations. During the construction of ships, for different ship types and propulsion shaft systems, calculation documents for shaft torsional vibration, longitudinal vibration, and rotational vibration should be submitted for approval to the classification society. For main propulsion shaft systems, it is essential to ensure that there are no excessive amplitude rotational vibrations within the commonly used speed range, no dangerous resonance speeds are produced, and there are no excessive amplitude longitudinal vibrations throughout the entire speed range. Abnormal vibrations of the shaft system can affect the formation of the lubricating water film, exacerbating wear on the stern bearing. If the amplitude, stress, or torque of the shaft system’s vibrations exceed the permissible values for continuous operation specified by the standards, a “speed forbidden zone” should be established. Within this zone, the machinery should not operate continuously.

(3) Hull deformation and special cargo loading

In the case of a long shaft system ship transporting container ships under half-ship conditions, the overall deformation of the ship, considering the mass of the empty ship, cargo load, and external water pressure, is as depicted in Figure 3a [29]. Both port and starboard sides of the hull sink, with the port side sinking more, and the starboard side being relatively raised. Due to uneven cargo loading, the hull experiences overall torsion, leading to uneven spatial deformation of the shaft line. Deformation of the stern part of the hull causes the shaft centerline to deform in such a way that the aft stern bearing group is raised, while the middle and forward stern bearing groups sink, increasing the load on these bearings. Shaft alignment calculations indicate that the aft stern bearing group exceeds the permissible specific pressure values in cold, hot, and operational states, while the forward stern bearing group approaches permissible values in both cold and hot states. Special cargo conditions show a significant difference from the conventional full-load ballast deformation trend. Uneven loading causes uneven hull deformation, which in turn affects the deformation of the shaft line. Typically, wave loads exacerbate the unevenness in shaft line deformation.

(4) Propeller emergence and shallow water effects

When a vessel is in shallow waters, or in severe weather conditions not properly managed by the crew, the ship may tilt forward or backward and resonate with large waves, placing the propeller in a partially submerged abnormal operating condition, as shown in Figure 3b [35].

After some of the propeller blades emerge above the water, the propeller loses the reactionary force of the water above, thereby generating a torque, as illustrated in Figure 4. This clearly increases the load on the stern tube aft bearing, and the relative angle at the support points also increases. Compared to the increase in load on the stern bearing, the increase in relative angle poses a greater risk to the shaft system. When the relative angle at the stern tube aft bearing support is too large, a too-small bearing gap is unfavorable for the formation of a hydrodynamic water film, worsening the lubrication condition. A small bearing gap results in a lower flow rate of lubricating water passing through the bearing, insufficient cooling capacity, and thus making the stern bearing prone to high-temperature failure. Additionally, a sharp increase in the relative angle means that the load is more concentrated at the tail of the bearing, increasing the specific pressure at the end, leading to uneven stress on the bearing material, and forming significant edge loading.

Moreover, when the ship’s draft is deep but the water depth of the channel is relatively shallow, the distance between the ship’s bottom and the riverbed is smaller, and the water flow at the bottom is relatively faster, with relatively reduced dynamic pressure. During navigation, this can cause the phenomenon known as “squat”, which also increases the load and relative angle at the support points of the stern tube aft bearing.

Using a five-blade propeller as an example, Figure 5 displays the distribution of the wake behind the propeller disk and the shift in the centroid of thrust when part of the blades emerge from the water [35]. The eccentricity of thrust, which is the center point of action of the propeller’s thrust line, is crucial for analyzing the forces and torque distribution exerted by the propeller on the ship’s hull. This is clearly demonstrated in the polar diagram of Figure 5, where the changing center of thrust moves with angle. When one-third of the propeller blades are exposed above the water, this exposure causes significant shifts in the position of the thrust eccentricity, thereby also altering the propeller’s dynamic efficiency. Specifically, the movement of the thrust eccentricity leads to changes in the additional bending moments, which vary cyclically with the propeller’s rotation angle. As this is a five-blade propeller, there is a periodic change every 72 degrees (i.e., 360 degrees divided by five blades), showing how the distribution of thrust and corresponding bending moments reoccur after each specific angle of rotation, which is essential for understanding the effects on the propeller shaft’s deflection.

When the propeller is partially out of the water, it loses some hydrodynamic support from the water, resulting in a significant shift in the thrust eccentricity toward the water surface. This shift changes the distribution of forces on the propeller blades, thereby affecting the load distribution and deflection angle of the propeller shaft. Thus, the thrust eccentricity generated when the propeller blades are partially out of water, moving away from the center of the propeller, has a more significant impact. These positions typically correspond to the maximum eccentric distances, causing the propeller shaft to endure greater asymmetric loads and moments.

When the propeller is partially above water, compared to being fully submerged, each blade experiences a change in medium from water to air as it enters and leaves the water, increasing the risk of cavitation. This change leads to significant alterations in local hydrodynamic conditions, especially near the water surface. The closer to the water surface, the more affected it is by the interface fluctuations between air and water, potentially leading to unstable thrust and reduced efficiency. As the propeller rotates, the blades that are partially out of the water face less resistance than those fully submerged. This uneven distribution of forces may cause additional stress on the propeller shaft, affecting the stability of the entire propulsion system. Overall, the flow lines closer to the water surface have a greater impact on the propeller shaft–bearing assembly, especially in terms of causing thrust instability and potential damage to the shaft–bearing system.

Especially in situations where part of the blades are out of the water, due to the shift in thrust points, the instability of the shaft–bearing system may increase. For further studies on the modeling of propeller performance under off-design conditions and its operational mechanisms, refer to reference [41,42,43].

(5) Impact of sediment

When stern bearings operate in water containing a large amount of sand, the sand particles flowing over the bearing surface possess kinetic energy. Polymer material bearings, which have viscoelastic properties, are impacted and abraded by sand particles carrying kinetic energy, causing localized deformation of the bearing surface. Some molecular chains on the surface are forced to endure high stress, leading to an increase in covalent bond deformation and weakening of the bonds. This results in the breaking of surface molecular chains, which manifests macroscopically as rapid wear of the stern bearing surface. The presence of sand in the water medium significantly affects the wear rate of water-lubricated bearings; as sand concentration increases, the frequency of sand particle interaction with the bearing surface increases, accelerating the wear rate. When sand concentration is excessive, due to increased interference among the sand particles, the frequency of interactions with the bearing surface decreases, and the increase in wear rate tends to stabilize at a certain value, although at this point, the wear rate is relatively high.

(6) Marine biofouling

As shown in Figure 3c, marine organisms attach to open-type water-lubricated stern bearings [40]. These organisms, rotating with the shaft or falling into the gap between the shaft and bearing, create a wear effect similar to that of sand particles, accelerating the wear of the bearing. For closed-type stern bearings, when marine organisms fall off the bronze sleeve and embed onto the bearing, they can scratch the bronze sleeve, damaging the lubrication system and shaft seal device, affecting the lubrication and cooling state of the stern tube bearing. This can easily lead to high temperatures and accelerate bearing wear. For vessels that are out of operation, it is necessary to turn the shaft system weekly and ensure normal water supply from the stern tube pump to minimize the impact of marine organisms.

(7) Bearing structure

Water-lubricated stern bearing materials commonly include Lignum vitae, Cylon, and other high-polymer synthetic materials. Each material has different allowable specific pressures based on its properties, and different length requirements when installed on ships. If the bearing size does not meet the specified requirements, the bearing’s contact area becomes too small, causing the specific pressure to exceed the material’s performance capabilities, thus significantly accelerating bearing wear and reducing its lifespan. For instance, the China Classification Society stipulates that for seawater-lubricated Lignum vitae, synthetic rubber, or plastic bearings, the length should be no less than four times the calculated diameter of the propeller shaft or three times the actual diameter, whichever is greater.

For ultra-long shaft system stern bearings, subject to off-loading or other excitations, shaft inclination or elastic deformation of the shaft may occur. When the bearing length is excessive, sensitivity to shaft line conditions increases. An overly long bearing is detrimental to the flow of lubrication and cooling water, making the bearing prone to overheating.

By designing the bearing with a dual slope, the angular value of the shaft at the support point of the aft tube bearing calculated for alignment can be reduced. This effectively alleviates edge loading, facilitates the establishment of a lubricating water film, and enhances cooling capacity.

2.2. Stern Bearing High-Temperature Meltdown

2.2.1. Case Studies

The case studies on the high-temperature meltdown of stern bearings are summarized in

Table 2. Case analysis of high-temperature meltdown in stern bearings.

Source	Ship	Shaft System	Liner Material	Bearing Structure	Failure or Malfunction	Cause of Failure
[44]	A particular ship	Long shaft system	Polymer	Closed	Severe burning of the aft stern tube bearing and re-solidification of melted polymer material, with the bearing grooves blocked by the melted polymer material. Figure 6a–c show the high-temperature erosion and wear state of the stern frame bearing, aft stern tube bearing, and fore stern tube bearing, respectively.	Groove blockage prevented normal flow of cooling water, leading to bearing burn-out; misalignment of the shaft system indirectly caused bearing burn-out.
[45]	Gdansk University of Technology	Shaft diameter 350 mm	Polymer	Closed	Stern bearing overheating caused the polymer to melt; Figure 6d shows the melted polymer of the stern bearing.	Cooling system failure.
[46]	Datang 82	Long shaft system	Polymer	Closed	Cooling water gushing from the fore stern seal at nearly 100 °C with a lot of steam leakage; stern bearing burnt out.	Cooling water pipe clogged.
[46]	Weilun 216	-	Cylon	Open	Dry friction between the stern shaft and stern bearing; high temperature caused the nylon to melt and detach, sticking to the stern shaft; stern bearing burnt out.	Fishing net blocked the stern bearing cooling flume, causing cooling water to stop flowing.

, which discusses the parameters of the stern bearings on the case vessels and analyzes the failure characteristics and causes, with a particular focus on the failure characteristics of long shaft systems.

The cases of high-temperature meltdown failure in water-lubricated stern bearings involved in the case studies are illustrated in Figure 6.

2.2.2. Analysis of Failure Impact Factors

(1) Mid-bearing sinking causing shaft line deformation

When mid-bearings are unevenly loaded, wear or ablation can cause the shaft system to sink, leading to abnormal deformation of the shaft line, particularly in the last three mid-bearings of an ultra-long shaft system. After the shaft line deforms, the load on the stern bearing and the angle at the bearing support points increase, producing adverse effects. This results in increased bearing specific pressure and poor cooling, causing burn-out of the aft stern tube bearing.

(2) Deformation of stern bearing and its housing

In the design phase, if the stern tube bearing adopts an “integrated stern tube-epoxy resin casting” solution, the non-uniformity of the epoxy resin setting may cause changes in the concentricity of the integrated stern tube, thus causing the position of the stern tube bearing to deviate from the calculated alignment design values. Additionally, epoxy resin materials have relatively poor thermal conductivity, preventing effective heat transfer from the bearing during operation.

During the machining and transportation of the integrated stern tube, due to its length, deformation issues may also arise. In the construction process in the dry dock, if the structure supporting the stern is not rigid enough, it can cause the ship’s stern to deform downward. Particularly, in the process of shaft system construction, before the ship leaves the dock after alignment checks, the stern of the ship continues to deform downward without support, causing a significant deviation between the position of the stern tube bearing inside the dock and the underwater bearing position.

After the ship is launched, due to insufficient rigidity in the ship’s stern, part of the stern may tilt upwards. These factors causing abnormal deformation of the stern bearing and its housing will inevitably have a negative impact on the bearing load and the formation of the lubricating water film, potentially leading to high-temperature incidents or wear during operation under harsh conditions.

(3) Stern shaft’s deformation

In water-lubricated stern bearings for ships, the deformation of the stern shaft is a critical factor that significantly impacts the operational conditions and performance of the bearing. Deformation of the stern shaft can be caused by various factors, including uneven loading, thermal expansion, mechanical stress, and wear. The impacts of stern shaft deformation on ship water-lubricated stern bearings mainly include the following aspects.

a. Increased friction coefficient and abnormal temperature rise: Deformation of the stern shaft typically leads to uneven distribution of the contact area on the bearing surface. This unevenness can increase local contact pressure, thereby increasing the friction coefficient. An increased friction coefficient not only enhances energy consumption but may also lead to higher operational temperatures, subsequently causing abnormal temperature rises in the bearing.

b. Disruption of the lubricating water film: In water-lubricated stern bearings, maintaining a stable lubricating water film is crucial for ensuring low friction and longevity. Deformation of the stern shaft may disrupt the continuity of the lubricating film, leading to reduced lubrication effectiveness. In certain areas of the stern bearing, this may result in direct contact between the shaft sleeve and the bearing liner, thereby causing wear and scoring.

c. Imbalance of the stern bearing: Deformation of the stern shaft can also lead to imbalance in the stern bearing, which in turn causes additional vibration in the bearing, shaft system, and hull (especially at the stern). Such vibrations not only worsen the service environment of the stern bearing but also reduce the operational comfort of the ship and may affect the service state of intermediate bearings, even impacting the structural integrity and lifespan of the shaft system.

d. Impact on sealing performance: Any deformation of the stern shaft may affect the performance of the sealing systems associated with the bearing, such as lip seals in closed lubrication systems and face seals. Poor sealing can lead to insufficient lubricating water flow, contamination, and leakage, further deteriorating the lubrication conditions and overall performance of the bearing.

e. Effects on ancillary structures and shaft alignment: Deformation of the stern shaft can cause the trawler knife to scrape against the propeller hub, disrupting the lubrication environment, generating frictional vibrations, and noise. This may lead to deformation of the hull at the stern hub, causing changes in the shaft line and misalignment, further leading to shaft seal failures and bearing wear.

f. Stern bearing wear and reduced lifespan: Deformation of the stern shaft can lead to localized premature wear of the stern bearing, especially under high-load and high-speed conditions. Uneven wear typically results in a decline in the overall performance of the stern bearing, necessitating more frequent maintenance and earlier replacement.

(4) Fishing net entanglement and melting

When a ship’s polymer stern bearing becomes entangled with a fishing net, the net enters the gap between the stern bearing and the stern shaft as the shaft rotates. Inside the stern bearing, the fishing net is shredded, clogging the flume and reducing the flow of cooling water. Due to inadequate cooling, the net melts and further obstructs the outflow channels within the stern tube. High temperatures cause the polymer liner material of the stern bearing to melt and detach, sticking to the stern shaft, which in severe cases can lead to the stern shaft and bearing seizing, causing the main engine to stop abruptly. Additionally, the presence of steel wire or other hard materials entangled in the fishing net can exacerbate wear on the stern bearing; for closed stern bearings, this could severely damage their sealing device.

(5) Additional eccentric forces in the stern flow field

In vessels with multi-support ultra-long shaft systems that are large and have significant momentum, the load on the main engine and stern bearing increases when using large steering angles at high speeds, in strong winds, or rough seas. Due to the characteristics of propeller inflow and its considerable weight, an eccentric force is exerted on the aft stern tube bearing. A right-turning propeller, for example, results in greater load on the lower left side of the aft stern tube bearing and vice versa. As illustrated in Figure 7a, during a right turn, the lower right part of the stern bearing experiences an additive force [47]. Special measures adopted at the stern for energy saving could increase this effect. During ship trials or when the steering is poorly adjusted, conditions such as large steering angles, S-turns, or full revolutions could amplify this effect on the stern bearing, causing the stern shaft and bearing to have excessive relative inclination, destroying the lubrication film at the rear part of the bearing, leading to dry friction and burn-out at the bearing’s rear.

(6) Insufficient lubricating water flow

The water flowing over the bearing surface not only achieves hydrodynamic lubrication but also carries away heat generated by friction between the shaft and bearing. Since polymer materials have relatively poor thermal conductivity, under normal circumstances, most of the heat generated in the friction area is absorbed by the flowing water. The state of bearing lubrication and the flow of cooling water are critical factors in preventing overheating of the stern bearing.

If the flow of lubricating water is too low or zero, it cannot effectively lubricate or cool, affecting the formation of the lubricating water film and causing dry friction between the stern shaft and stern bearing, leading to a rapid increase in temperature. Operating in higher temperature environments, bearings with composite material liner often experience delamination. Furthermore, a malfunctioning flow meter could cause false alarms, as illustrated in Figure 7b [48], where the flow meter’s impeller becomes entangled with foreign objects, reducing the rotation speed of the impeller and thus the flow reading, failing to correctly reflect the actual flow. Potential causes of insufficient lubricating water flow include failures of the cooling water pump or the main engine seawater pump, open stern bearings clogged by fishing nets/sediment/marine organisms, failure of the seals in closed stern bearings, and internal corrosion and blockage of pipelines and valves (as shown in Figure 7c).

2.3. Abnormal Vibratory Noise and Other Failure Modes

2.3.1. Vibration and Noise

Water-lubricated bearings are prone to enter boundary lubrication or mixed lubrication states under conditions of low speed, high load, or insufficient lubrication. This may lead to severe bearing wear, stress concentration, and significant vibration and noise. Intense vibration and noise can potentially damage the shaft–bearing system and also affect the operational status of the power transmission shaft system and the health of the crew. Ref. [49] suggests that squealing is a vibration noise phenomenon caused by the stick-slip motion on the surface of rubber bearings. Ref. [50] indicates through numerical calculations that the nonlinear variation in the friction coefficient of water-lubricated stern bearing systems with speed and time leads to system instability.

Refs. [51,52,53] have found that with increasing speed, both fluid dynamic pressure and friction coefficients rise, causing vibrations to decrease from high to low before ultimately stabilizing. During this process, as friction transitions from stick–slip to sliding friction, noise diminishes from loud to soft, changing from squealing to humming. They propose that the emergence of noise is first influenced by lubrication conditions and subsequently by temperature. Based on these observations, it is possible to diagnose the malfunctions and failures of water-lubricated bearings through the characteristics of vibration and noise. Building on this, ref. [54] examined the impact of temperature on bearing vibrations. The results indicated that as temperature rises, thermal expansion increases, leading to higher friction coefficients and consequently greater friction-induced vibrations, especially at low speeds. Further, ref. [55] study on the nonlinear vibrations of water-lubricated bearings revealed that noise sources at low speeds are due to stick–slip friction, while at high speeds, they are caused by friction-induced vibrations. Ref. [56] discussed the dynamic characteristics of water-lubricated rubber bearings and explored vibrational phenomena. When the rotational speed falls below a certain threshold, it becomes difficult to form a hydrodynamic film, often leading to contact friction and increased vibrations. The rough interaction between the bearing and the shaft not only weakens the hydrodynamic lubrication effect but also exacerbates the vibrational phenomena. Refs. [57,58] investigated the coupling effects of friction vibration and lateral shaft vibrations, finding that lateral vibrations occur when the stern shaft contacts the rotating bearing housing, and these interact with friction vibrations to affect the propulsion system.

2.3.2. Crevice Corrosion in Bearing Housing

Crevice corrosion is a localized form of corrosion that occurs due to the presence of gaps between metal-to-metal or metal-to-nonmetal surfaces and corrosive agents. Tight fits are employed in assemblies such as the stern shaft and its bronze sleeve, stern shaft and propeller, stern shaft and coupling, as well as between the stern bearing housing and its liner. However, gaps can still exist, particularly at the ends, with gap sizes generally ranging from 0.025 to 0.1 mm. These dimensions are conducive for seawater entering and stagnating, facilitating simultaneous crevice and galvanic corrosion. Figure 8 illustrates minor corrosion at the gap of a bearing housing.

2.3.3. Stern Shaft Fracture Incident

A bulk carrier equipped with front and rear stern bearings made of polymer materials, lubricated and cooled directly by seawater, experienced a stern shaft fracture [59]. The stern shaft was made of 35# carbon steel. On 28 December 2020, while the vessel was traveling from Xiamen to Ningbo, the shaft fractured in the waters east of Taizhou. The fracture surface is shown in Figure 9. Fatigue cracks due to alternating stress were the direct cause of the shaft failure, while electrochemical corrosion resulting from the loss of integrity in the shaft’s protective sleeve was the underlying cause. Additionally, the high silt content in coastal waters and frequent encounters with floating fishing nets (drift nets) along the shipping route were indirect contributing factors.

2.4. Failure Modeling Methods

2.4.1. Mechanism-Based Models

The tribological performance of bearings directly influences the reliability and stability of the shaft–bearing system, and deterioration in tribological performance can lead to failure of the lubrication function at the bearing interface and a reduction in service life. Currently, mixed friction models for transmission system bearings are primarily categorized into deterministic models and statistical models. Ref. [60] analyzed the current state of research on sliding bearing wear, focusing on the classification of sliding bearing wear tests, wear testing machines, wear study methodologies, and wear prediction models. Ref. [61] utilized an established mathematical model to reveal the transient interactions between the sliding wear behavior of sliding bearings and their fluid–solid–thermal (FST) characteristics, validating the calculated temperature distribution through comparison with experimental results from the literature. Wear tests on lubricated sliding bearings validated the predicted wear rates. Ref. [62] investigated the oil film characteristics of sliding bearings through theoretical analysis, proposed a bearing wear fault diagnosis model, and validated this model in practical production settings. Ref. [63] studied the frictional wear performance of sliding bearings under different operating conditions, measuring the friction coefficients and wear rates of sliding bearings under various conditions using a bearing test bench. The wear surfaces were examined using scanning electron microscopy and laser 3D imaging profilometry to investigate their tribological behavior and wear mechanisms.

Ref. [64] analyzed the multibody dynamics theory and simulation models of the crankshaft system, sliding bearing tribology, and the computational methods for frictional wear pairs, summarizing the simulation models applicable to the dynamics and tribology of sliding bearings and offering perspectives on the optimization of sliding bearing wear calculation methods. Ref. [65], based on a tribological system approach, established a friction wear dynamics model upon analyzing the internal friction systems and processes of sliding bearing tribological systems, studying the friction wear characteristics of sliding bearings. This research was further extended to examine the relationship between internal temperature rise and heat generation within bearings based on dynamics model simulations. Ref. [66] developed a dynamics model for a bearing wear test bench using the substructure method, that couples friction characteristics, calculating the bearing’s frictional power consumption and shaft trajectory for comparison with actual measurements. This model laid the foundation for coupled analyses of main bearing tribology and dynamics and established a dynamics model for a bearing fatigue test bench incorporating elastohydrodynamic (EHD) characteristics, which was validated with experimental data. Based on this model, the impacts of load, oil supply temperature, oil pressure, and bearing clearance on the tribological and dynamic characteristics were investigated.

2.4.2. Based on Reliability Assessment Methods

Reliability assessment methods primarily involve developing a wear life reliability model for stern bearings based on wear data. Ref. [67] conducted experimental studies on the abrasive wear characteristics of polyurethane, styrene-butadiene rubber, nylon-6, and polytetrafluoroethylene. Based on the experimental data, formulas were derived to calculate the mass wear rate of polymer materials as a function of flow rate, abrasive particle size, and concentration. Ref. [68] fitted experimental data to derive a relationship between the wear amount of neoprene rubber and mechanical parameters, load, and rotational speed. Ref. [69] fitted experimental data based on the friction work wear theory, obtaining an empirical formula for the volumetric wear of nitrile rubber, and further proposed a reliability life assessment model for water-lubricated stern bearings.

2.4.3. Based on Statistical Analysis Methods

Degradation prediction using statistical methods commonly employs techniques such as principal component analysis (PCA) and partial least squares (PLS) to process degradation data of equipment, establish statistical measures, and assess the health status of equipment. Degradation distribution models assume that performance degradation measurements of a class of equipment over different times follow the same distribution family, with parameters that are functions of time. Common degradation distribution models include the Wiener degradation model, the Weibull distribution model, and the exponential distribution model. These methods primarily use bearing wear data to fit and derive predictive formulas for bearing wear life. Ref. [69] established a wear life model based on the relationship between wear rate and the maximum allowable clearance of the bearing. Ref. [70] employed experimental data on wear amount, using a two-parameter Weibull distribution to assess the wear life of water-lubricated stern bearings.

2.4.4. Data-Driven Intelligent Methods

Methods based on machine learning or deep learning leverage advances in artificial intelligence, and diverse and practical intelligent approaches have promoted research development in equipment degradation state and remaining useful life (RUL) prediction. Predictive methodologies utilizing machine learning or deep learning have seen fruitful outcomes and rapid development, as detailed in review articles such as [71,72]. To effectively predict the degradation processes and RUL of marine power systems, methodologies capable of understanding and analyzing the complexity and time-varying nature of degradation processes are necessary. Thus, predictive models based on deep learning, with their robust nonlinear system modeling capabilities and uncertainty handling, become powerful tools to meet these challenges. However, due to a lack of comprehensive monitoring parameters for marine power systems and sparse data on running-to-failure states, research on degradation processes and RUL prediction remains limited [73]. Current research on machine learning and deep learning methods for bearing health state identification and degradation primarily focuses on predicting wear under start–stop conditions [74], identifying lubrication states [75], predicting the maximum temperature in sliding bearings [76], dynamic temperature identification and prediction [77], predicting the contact temperature and cooling states in water-lubricated bearings [78], and forecasting changes in friction torque and friction coefficients [79]. These studies provide health thresholds and data support for the maintenance and operation of stern bearings.

3. Controllable Parameters for Healthy Operational Behavior and Experimental Design

3.1. Conditions for Healthy Operation

In a healthy operational state, there is an appropriate bearing gap between the stern shaft and stern bearing, filled with lubricating water. When the stern shaft rotates at high speeds, the water in the bearing gap is compressed, generating a reaction force. Due to the viscosity of the water, a water film forms between the stern shaft and the stern bearing [80,81]. The water film, when compressed, generates heat, which can be conducted away through the shaft neck, bearing liner, and end leakage, maintaining the bearing temperature within a relatively stable range. When the bearing is in a state of poor lubrication or dry friction, an effective water film does not form to ensure lubrication, leading to higher frictional heating and insufficient cooling, which intensifies wear and may cause high-temperature meltdown.

Successfully establishing a water film is key to controlling abnormal wear and high-temperature meltdown of the stern shaft. The successful formation of a water film between the stern shaft and stern bearing primarily depends on the following factors.

a. Bearing gap between the stern shaft and stern bearing: A reasonable bearing gap helps form an appropriate wedge-shaped space between the stern shaft and the bearing. When the wedge-shaped space is too large, due to the viscosity, the gravitational force of the water may exceed its adhesive force, causing the water film to fail to adhere to the surface of the shaft diameter, leading to the failure of water film formation. Conversely, if the wedge-shaped space is too narrow, there is insufficient lubricant available to form a water film, and the cooling capacity is also lacking [45,82].

b. Pressure per unit area on the stern bearing: While ensuring normal bearing clearance, the stern shaft can usually rotate floating on the water film. However, excessive downward or off-center forces may cause the water film to be unable to withstand the pressure, leading to direct friction between the stern shaft and bearing. When the local load at the rear end of the bearing exceeds the bearing’s load-bearing limit, it accelerates bearing wear and failure, shortening the bearing’s lifespan. This is especially true for vessels with ultra-long shaft systems, where the stern bearing is more sensitive to the condition of the shaft line [83].

3.2. Controllable Parameters for Healthy Operation

3.2.1. Lubrication State Control

When the stern shaft rotates within a water-lubricated stern bearing, the friction coefficient of the stern bearing varies under different rotational speed conditions, reflecting different lubrication states, as illustrated in Figure 10. During startup and shutdown processes, due to the weight of the stern shaft and the load from the propeller, the stern bearing is in a state of dry friction. Under low-speed, high-load conditions, the hydrodynamic effect formed is insufficient to support the stern shaft, usually resulting in boundary lubrication or mixed lubrication. Conversely, under high-speed, light-load conditions, the thickness of the hydrodynamic lubrication water film formed within the bearing clearance continuously increases, gradually enhancing the film’s load-bearing capacity and progressively separating the inner surface of the stern bearing from the stern shaft, with fluid dynamic lubrication becoming predominant. Due to the propeller’s weight, complex operating conditions, and the large length-to-diameter ratio of the stern bearings in ultra-long shaft systems, it is challenging to distinctly categorize the lubrication state of the stern bearings, which may fluctuate between various states.

Based on the working principles of water-lubricated stern bearings, the variables that can be controlled to adjust the lubrication state of the stern bearing include the shaft rotational speed, lubricating water temperature at the bearing inlet, lubricating water flow rate, and the presence of sediment particles in the lubricating water [84,85].

3.2.2. Temperature Rise Control

During a ship’s voyage, part of the heat source in the stern bearing originates internally, such as the frictional heat between the stern shaft sleeve and the stern bearing liner; another part of the heat source comes from external factors, like the temperature of the lubricating water at the bearing inlet. Compared to external heat sources, internal heat sources (frictional heat) contribute more to the temperature rise of the stern bearing. In this study, the term “temperature rise (ΔT)” refers to the difference in the temperature of the lubricating water at the bearing outlet compared to the temperature at the bearing inlet, reflecting the bearing’s cooling and heat dissipation performance. The characteristic of temperature rise represents the bearing’s capacity for temperature increase; a lower characteristic can effectively reduce the occurrence of high-temperature meltdown failures.

Stern bearings with a water-lubricated liner often consist of polymer materials, which have poor thermal conductivity. If excessive heat is generated due to abnormal friction between the stern shaft sleeve and the stern bearing liner and if the cooling water is severely insufficient, this can easily lead to high-temperature meltdown failures in the stern bearing, causing the stern shaft to bond with the stern bearing. Additionally, thermal deformation of the stern bearing and its housing can lead to issues such as thermal seizure, changes in shaft alignment, affecting the normal performance and lifespan of the stern shaft and stern bearing.

The heat generated in the stern bearing is closely related to the friction coefficient of the bearing liner, friction torque, shaft rotational speed, and stern bearing load. The spatial structure of the water film also impacts heating and cooling, such as changes in the internal space structure of the flume caused by blockages like sediment, or changes in the bearing clearance due to bearing wear. These factors all influence the temperature rise state of the bearing [86,87].

3.3. Selection of Controllable Parameters and Experimental Design

Proper lubrication and cooling conditions are fundamental to ensuring the healthy operation of stern bearings, which necessitates the effective establishment of a lubricating water film. During the service life of stern bearings, the formation of the lubricating water film is influenced by various parameters such as bearing structural features, surface morphology of the bearing liner, shaft rotational speed, shaft specific pressure, effectiveness of stern tube device sealing, lubricating water temperature at the bearing inlet, and sediment content in the lubricating water. Among these parameters, shaft rotational speed and lubricating water temperature at the bearing inlet are directly controllable parameters; by adjusting these, the operational state of the stern bearing can be changed. Shaft specific pressure and the surface morphology of the bearing liner are intermediate parameters that affect the operation state of the stern bearing and can be indirectly controlled to some extent. For instance, proper running-in and clean lubricating water can help maintain the smoothness of the bearing liner surface; cargo loading conditions and proper steering can alleviate shaft specific pressure.

In this study, the selected controllable parameters include the following.

a. Directly controllable parameters: Lubricating water temperature at the bearing inlet, shaft rotational speed, and clean versus sediment-containing lubricating water (reflecting the cleanliness of the lubricating water).

b. Indirectly controllable parameters: Shaft specific pressure and the surface morphology of the bearing liner.

3.4. Experimental Rig and Bearing

In response to the research needs outlined above, a water-lubricated stern bearing experimental rig has been designed and constructed, as shown in Figure 11. The experimental rig is installed at the Yujiatou Campus of Wuhan University of Technology. The core apparatus includes a drive motor, torque meter, support bearings, universal joints, fore loading device, experimental bearing (closed structure), stern loading devic, water tank, water tank stirring motor, water supply device, control cabinet, industrial computer, and software system.

The drive motor (rated power of 132 kW, maximum speed of 1488 rpm, rated torque of 847 N·m) enables precise control of the rotational speed. The load loading system consists of a fore loading device, stern loading device, hydraulic pump station, and oil pipelines, with the test loads applied using a vertical loading method (the loading device can apply a maximum vertical load of 10 t). The lubrication and cooling water supply system consists of a water tank, water pump, and lubricating water pipelines, providing water supply, return, and cooling to the water-lubricated bearing. The water tank is equipped with a temperature control device and stirrer, capable of accommodating clear water, sediment-laden water, and varying water temperatures for experiments. The testing system is composed of torque and speed sensors, a torque meter, load sensors, a flow meter, thermometers, and pressure gauges. The parameters that can be monitored and measured are as shown in

Table 3. Monitoring and measurement parameters.

No.	Monitoring Parameter Name	Unit
1	Torque	N·m
2	Rotational speed	r/min
3	Power	kW
4	Load force at front and rear ends	t
5	Lubricating water temperature at bearing inlet	°C
6	Lubricating water temperature at bearing outlet	°C
7	Water tank temperature	°C
8	Water tank liquid level height	mm
9	Lubricating water flow rate	L/min
10	Lubricating water pipeline pressure	MPa
11	Bearing friction coefficient (f)	-

. The experimental rig features support bearings to provide isolation, which helps protect the motor and experimental bearing.

The shaft is made of 34CrMo1 carbon steel, equipped with a ZCuSn10Zn2 bronze sleeve on the shaft neck. The stern bearing liner is made of SF-2A material. The clearance between the shaft and the bearing is 1.2 mm. The geometric structure and appearance of the experimental bearing are shown in Figure 12, with the bearing inner diameter D = 130.5 mm, bearing length L = 444.0 mm, groove width W = 4.8 mm, groove depth H = 8.6 mm, strip thickness is 16.0 mm, and the number of grooves is 23. The SF-2A material of the stern bearing liner is anisotropic, and the orientation of the bearing strips during installation is indicated in the diagram to describe the working surfaces of each bearing strip. In Figure 12, the yoz plane represents the friction contact surface between the shaft and bearing, the xoz plane is the bearing groove surface, and the xoy plane is the end face of the bearing strip.

Per- and polyfluoroalkyl substances (PFASs) are referred to as “forever chemicals” due to their extremely slow degradation in the environment, allowing them to persist in water and soil for extended periods. PFASs readily accumulates in biological organisms and may lead to higher concentrations as they move up the food chain. Long-term or high-concentration exposure to PFASs is associated with a variety of health issues, including cancer, immune system effects, and reproductive problems.

SF-2A utilizes laminated fiber cloth-reinforced composites, incorporating graphite and reinforcing fibers into the base material. It was developed to meet the high-reliability demands of water-lubricated bearings under harsh conditions such as high load, high temperature, and sediment. The physical properties of SF-2A material water-lubricated stern bearings are presented in

Table 4. Material parameters of shaft sleeve and bearing liner.

Components and Parts	Material	Poisson’s Ratio	Elasticity Modulus (MPa)	Density (kg/m3)
		Circumference: 0.28	Circumference: 1080
Bearing liner	SF-2A	Radial direction: 0.28	Radial direction: 1510	1370
		Axial direction: 0.28	Axial direction: 4020
Shaft copper sleeve	ZCuSn10Zn2	0.35	1.00 × 105	8500
Shaft	34CrMo1	0.25	2.07 × 105	7800

. Due to confidentiality and other reasons, the bearing supplier has not disclosed the chemical composition of SF-2A material but has stated that it poses no impact on environmental and human health. Meanwhile, the China Classification Society (CCS) has recognized SF-1 material from the SF series and has issued a certification [88].

Considering that ship water-lubricated stern bearings may use a closed structure for lubrication and cooling, the bearing material and its wear particles can be treated at the lubrication water tank rather than being directly discharged into natural water bodies, meaning there is no impact on the water environment during navigation.

In the shipbuilding industry, common polymer-bearing materials include ultra-high-molecular-weight polyethylene (UHMW-PE), polyether ether ketone (PEEK), phenolic resin (PF), polyoxymethylene (POM), and polyimide (PI). UHMW-PE is renowned for its extreme wear resistance and impact strength, and is often used to manufacture wear-resistant parts and sliding components. The manufacturing process and chemical structure of UHMW-PE are unrelated to PFASs. PEEK, a high-performance engineering plastic, exhibits excellent mechanical and chemical stability and does not contain fluorine elements in its structure, and so is typically unrelated to PFASs. Phenolic resin (PF) is a thermosetting plastic used in electrical insulation materials, furniture, and building materials, and its chemical structure does not relate to PFASs, nor are PFAS compounds generally involved in its production or application. POM, an engineering plastic with high strength and rigidity, is used to manufacture precision components and does not contain fluorine in its chemical structure, making it unrelated to PFASs. Polyimide (PI) is a high-performance plastic used in high-tech areas such as aerospace due to its heat resistance and chemical corrosion resistance, and its primary components do not include perfluorinated or polyfluorinated alkyl substances.

In addressing PFAS concerns, materials such as UHMW-PE, PEEK, POM, and PI, which do not contain fluorine in their chemical structures, are unrelated to PFAS issues. However, polytetrafluoroethylene (PTFE) is known for its extremely low friction coefficient and high chemical stability. PTFE, composed of polymerized tetrafluoroethylene, is part of the PFAS family. Nevertheless, this material is rarely or rarely used in extra-long shaft water-lubricated stern bearings. Additional attention may be needed when these materials are combined with PTFE.

3.5. Experimental Plan

Based on the selected controllable parameters, the plan consists of multiple experiments, as outlined in

Table 5. Experimental design setup.

No.	n (r/min)	p (MPa)	Lr	Q (L/min)	T (°C)	Sc (kg/m3)	Sps (mm)	t (h)
1	-	-	-	-	-	-	-	>72.0
2	50/80/100/200/300/400/500/600	0.50	4:6	30	20.0	0	0	-
3	50/80/100/200/300/400/500/600	0.50	4:6	30	20.0	0	0	1.5
4	600/500/400/300/200/100/80/50	0.50	4:6	30	20.0	0	0	1.5
5	50/100/220/350/420/550/680/800/920/1050	0.50	4:6	30	20.0	0	0	-
6	50/60/80/100/150/200/300/350/400/450/500/600	0.20/0.30/0.40/0.50	4:6	30	20.0/32.0/39.0	0	0	-
7	314/597/691/880/1068	0.50	4:6	30	20.0	0	0	-
8	314/597/691/880/1068	0.50	4:6	30	20.0/24.0/28.0	0	0	-
9	50/60/80/100/150/200/300/400/500	0.20/0.30/0.40/0.50	4:6	30	20.0	0	0	-
10	314/597/691/880/1068	0.50	4:6	30	20.0	0.25	<0.05	-
11	48/72/120/300/480	0.50	4:6	30	20.0/23.0/26.0	0.25	<0.05	-
12	48/72/120/300/480	0.50/0.80/1.00/1.50	4:6	30	20.0	0.25	<0.05	-
13	Condition 1: Speeds of 314, 597, 691, 880, and 1068 r/min; durations of 2.5, 5, 10, 5, and 2.5 h; two cycles; 50 h; parameters as in Experiment 7.
14	Condition 2: Speeds of 314, 597, 691, 880, and 1068 r/min; durations of 2.5, 5, 10, 5, and 2.5 h; four cycles; 100 h; parameters as in Experiment 10.
15	Condition 3: Speeds of 48, 72, 120, 300, and 480 r/min; pressures of 0.8, 1.0, and 1.5 MPa; durations of 3 h each; for a total of two cycles, amounting to 90 h; parameters as in Experiment 10.

. The conditions set for the experimental plan include the following: shaft speed n (r/min), bearing specific pressure p (MPa), bow-stern load ratio Lr, lubrication water flow Q (L/min), lubrication water inlet temperature T (°C), sand content in lubrication water Sc (kg/m³), sediment particle size Sps (mm), and the operating time t (h) for a single condition.

In the experimental condition parameters, the calculations of specific pressure and friction coefficient refer to [24,89]. The specific pressure p = (F/(D × L)), where the load F is the vertical load applied at the front and rear ends of the bearing. The friction coefficient f is derived from the torque M measured by a rotational speed torque meter, using the formula f = M/(pDL).

Stern bearings are prone to uneven end forces during actual ship operation, especially water-lubricated stern bearings at the stern end affected by the propeller. This leads to shaft misalignment and deviation from the design centerline, misalignment of the shaft at the center points of the bearing ends, and a discrepancy between the bearing’s effective support point and the geometric midpoint, as illustrated in Figure 13. To simulate the actual conditions of ship-used water-lubricated stern bearings, the load F is applied in an offset manner, with vertical loads at the bow and stern ends in a 4:6 ratio.

Bearing lubrication utilizes both clear water and sediment-laden water. For water-lubricated bearings, it is crucial to pay attention to the density and viscosity of the lubricating water. The physical properties of the utilized clear-water lubricant are shown in Figure 14. Sediment-laden lubricating water is created by adding sediment particles with a diameter of less than 0.05 mm to clear water, maintaining a sediment content of 0.25 kg/m³ in the lubricating water, which is different from simulated seawater as it does not include salt components. When substantial differences in the supply water temperature of the bearing lubrication can lead to viscosity changes exceeding 80%, resulting in lubricating water with differing physical properties.

As illustrated in Figure 15, the measurement points for assessing the wear between the stern bearing and stern shaft are strategically positioned. Measurements are conducted in the vertical position of the stern bearing on the experimental rig, considered the positive direction. Along the length of the bearing, measurements are taken at three cross-sections: the propeller end, the intermediate, and the engine end. These sections serve as the primary basis for evaluating the extent of wear.

During measurement, the positive direction serves as the reference, and at each of the three cross-sections (propeller end, intermediate, and engine end), measurements are taken at four points: directly in the positive direction, at 25 degrees to the left and right, and at 90 degrees. The arithmetic mean of the actual measurements at these four points on each section is used to determine the internal and external diameter values. The changes in these diameter values before and after the experiment are used as an indicator of the amount of wear.

4. Results and Discussion

4.1. Experimental Results Compared with Published Literature

To validate the correctness of the experimental results, this study’s findings were compared with the results of studies on polymer water-lubricated stern bearings conducted in [27,89,90]. Considering the differences in bearing structural parameters and operating conditions, the comparisons were uniformly made using linear velocity and specific pressure after appropriate conversions. The comparison results are shown in Figure 16, Figure 17, Figure 18, Figure 19. It is evident that under different rotational speeds, specific pressures, and lubricant inlet temperatures, the magnitudes of the bearing friction coefficients are similar, and the trends in their influence on the friction coefficient are consistent. This demonstrates the accuracy of the experimental results of this study and confirms that the experimental rig constructed meets the research requirements.

4.2. Influence of Surface Morphology on Speed Characteristics

4.2.1. Changes in Surface Morphology of Strips Due to Water Swelling and Break-In Treatments

Figure 20 illustrates the changes in the surface morphology of the bearing liner after water swelling (Experiment 1) and break-in treatments (Experiments 2 and 3). Figure 20a,d show the morphology of the strips in their original state after manufacturing. The surfaces are rough, with many sharp burrs along the edges of the bearings. Figure 20b,e depict the state of the morphology after Experiment 1, where the strip material swells and rounds off due to water absorption, eliminating sharp burrs. Figure 20c,f display the morphology after the completion of Experiments 3 and 4, showing the shaft and bearing break-in process.

During the break-in process of Experiments 3 and 4, extremely bright reflective traces appear at the highest load positions of the bearing, which are evident across the entire bottom range of the bearing. The micro-protrusions and surface profiles within the highest-load area (or localized high-stress areas) are polished, and the main load-bearing areas of the bearing strips undergo adaptive wear, which is a normal wear condition. The transition from the unbroken-in areas to the trace-broken-in areas is quite gradual.

Figure 21 shows the changes in the surface morphology of the strip material in the yoz plane (bearing friction contact surface; Figure 21a–c) and the xoy plane (bearing end face; Figure 21d–f) through the processes of water swelling and break-in treatments. In the yoz plane (bearing friction contact surface), the strip material has a mesh weave structure. Before water swelling, the fiber mesh is obscured by the accumulation of composites, making the surface uneven, as shown in Figure 21a. With water absorption and expansion, the rectangular features of the mesh weave structure become more apparent, forming rectangular micro-cavities within the fiber mesh, increasing in volume and arranged uniformly, and incorporating brass-colored flake materials, as seen in Figure 21b. After the break-in treatment, the edges of the mesh weave are clear, with no rough edges. The resulting clear and complete rectangular water cavity space structure and the substances filled between the layers of the composite provide good lubrication and cooling conditions during the friction process between the stern shaft and the stern bearing, as shown in Figure 21c.

The strip material is made of multiple layers of fiber mesh weaves, which in the xoy plane (bearing end face) present a layered structure. After water absorption, the end face morphology of the bearing changes, as shown in Figure 21d,e. Figure 21f is the end face morphology after the break-in. The network woven layers of material swell with water absorption, increasing in volume, which macroscopically appears as a reduction in the inner diameter of the bearing. Figure 22 shows the change in the inner diameter of the bearing during the water swelling process. Over the first 8 days, the amount of water swelling continuously increased; after 8 days, the change in the inner diameter of the bearing was very slight, with swelling within 0.010 mm, indicating that the water swelling of the bearing strips had reached saturation. Due to the water absorption and expansion properties of the strip material, the inner diameter of the bearing decreased, which should be considered when setting the initial clearance during bearing installation.

4.2.2. Velocity Characteristics of Rough Surface States

The results of Experiment 2 are shown in Figure 23. Before break-in treatments, the bearing surface was relatively rough, resulting in significant fluctuations in the friction coefficient and unstable velocity characteristics. The friction coefficient exhibited upward fluctuations at certain speeds as the speed increased. However, the overall trend generally followed the characteristics of hydrodynamic lubrication of sliding bearings, as shown in Figure 10.

4.2.3. Velocity Characteristics of Smooth Surface States

The results of Experiment 5 are shown in Figure 24. After the break-in treatment, the bearing surface became smooth, stabilizing the velocity characteristics. The friction coefficient of the bearing decreased with increasing speed. At low speeds, the lubrication film formed by the bearing was thin and provided poor lubrication, resulting in a higher friction coefficient. As the speed increased, an excellent hydrodynamic lubrication film was formed, decreasing the friction coefficient of the bearing. The friction coefficient remained essentially stable after the speed increased to 800 r/min.

4.2.4. Impact of Surface Morphology Changes on Lubrication Characteristics and Temperature Rise

During Experiments 3 and 4, the bearing surface gradually transitioned from rough (as seen in Figure 20b and Figure 21b) to smooth (as seen in Figure 20c and Figure 21c). Throughout the experiments, the bearings operated stably with consistent output torque. Experiment process data, as shown in Figure 25, reflects the impact of changes in bearing surface morphology on lubrication characteristics and temperature rise. At the ninth hour, the maximum temperature rise occurred, indicating the greatest temperature difference between the lubricant water temperature at the bearing outlet and the inlet. At the eleventh hour, as the speed was further increased to 600 r/min, the temperature rise actually decreased, likely due to gradual improvements in the bearing’s break-in condition and the establishment of some hydrodynamic lubrication effects at higher speeds, which reduced the contact of surface micro-protrusions, thus lowering the temperature rise. At the thirteenth hour, when the speed decreased to 500 r/min, the hydrodynamic lubrication condition changed, possibly worsening, leading to an increase in temperature rise. Over time, as the fit between the shaft and bearing improved and the bearing surface became smoother (facilitating the formation of a lubrication film), and with relatively less heat generated by friction at lower speeds, the temperature gradually decreased. By the twenty-first hour, although the shaft speed had decreased, the temperature rise remained nearly unchanged and maintained at a lower level, with the lubricant water temperatures at the bearing outlet and inlet achieving a balanced state.

Figure 26 shows the wear amounts of the bearing liner and shaft sleeve. The greatest amount of wear occurred at the propeller end section, followed by the main engine end section, with the least wear at the middle section. The wear on the shaft sleeve corresponded to these measurements. This was because the loading method on the bearing was biased towards stern loading (Lr = 4:6), causing a slight upward arch deformation of the stern shaft axis. This limited contact at the middle section between the shaft sleeve and the bearing liner. This biased loading method enabled the experimental bearing to better reflect the service behavior of ultra-long shaft stern bearings in actual ship working environments.

4.3. Influence of Controllable Parameters on Lubrication Characteristics

4.3.1. Influence of Lubricant Water Temperature at the Bearing Inlet on Lubrication Characteristics

In Experiment 6, the relationship between f, p, T, and n was measured, as shown in Figure 27. Under the same conditions of p and n, f increases with the rise in T. At lower p, T has a greater impact on f. As p increases, the influence of T on f gradually weakens, and n becomes the dominant factor. At high p, the impact of T on f is not significant.

As T increases, the viscosity of the lubricating fluid decreases. While lower viscosity can help reduce friction, excessively high temperatures may compromise the stability of the lubricating film, leading to an overly thin or discontinuous film. The effectiveness of the lubricating film’s establishment directly impacts the lubrication between the shaft and bearing, which can result in an increase in f, especially under high-load or high-speed conditions. With the rise in T, the diminished convective heat transfer efficiency of the friction pair further intensifies the increase in contact surface temperature. This temperature rise, particularly under high-load conditions, may lead to the softening and thermal expansion of surface materials, further reducing the effective lubrication clearance between the shaft and bearing, thus increasing the likelihood of adhesive friction. Additionally, under high-temperature conditions, the physical properties of the liner materials may change, such as softening or thermal decomposition, leading to a decrease in their shear resistance. Material softening and increased molecular activity enhance the adhesive forces between the contact surfaces of the shaft and bearing, thereby increasing f. Furthermore, high temperatures may accelerate material wear, increasing the generation of wear particles, which may embed further into the contact surfaces, causing abrasive wear and consequently increasing f.

4.3.2. Influence of Shaft Speed on Lubrication Characteristics

f is relatively high at low n, when a good lubricating water film has not yet been established. f decreases as n increases, which is related to the formation of the lubricating water film. Good hydrodynamic lubrication conditions reduce f. When n reaches a certain level, the changes in f with n are not significant and tend to stabilize.

The f of water-lubricated bearings decreases with increasing shaft speed, primarily due to the following factors: a. As the shaft speed increases, lubricating water is carried into the contact area between the shaft and bearing, forming a more complete and continuous lubricating film. This film effectively separates the bearing liner and shaft sleeve surfaces, reducing direct contact opportunities and lowering f. b. The hydrodynamic effect formed by the lubricating water on the bearing surface at higher speeds becomes more pronounced. Hydrodynamic lubrication is a mechanism where a self-generated lubricating film is formed as the liquid, creating a pressure gradient between moving surfaces, facilitating the formation and maintenance of the lubricating film. This lubrication state can significantly reduce friction and wear. c. Higher speeds mean faster motion, which helps disperse friction-generated heat quickly. Lower local temperatures are beneficial for maintaining the stability of the lubrication film, further reducing friction. d. Due to the effective formation of the lubricating film at high speeds, the possibility of adhesion between the shaft and bearing is reduced. Adhesion is a significant cause of increased friction, so its reduction is beneficial in lowering the overall friction coefficient. e. The shear force between the shaft and bearing decreases when the lubricating film is thick and even. This is because the presence of the liquid layer means that the contact surfaces do not need to counter each other’s movement directly, and the fluidity of the lubricating liquid alleviates the friction between them. In summary, the increase in shaft speed, the improved formation and maintenance of the lubricating film enhanced hydrodynamic effects, effective heat dispersion, and reduced adhesive forces and shear stresses collectively contribute to a lower friction coefficient in water-lubricated bearings.

4.3.3. Influence of Bearing Specific Pressure on Lubrication Characteristics

The impact of p on lubrication characteristics is shown in Figure 28. Under the same conditions of T and n, the bearing f increases with the load. This is due to the increased p of the bearing, making it difficult to form a good lubricating water film. At high bearing p, a higher n is required to effectively establish a lubrication film. At low p, a relatively lower n can establish a good lubrication state.

The f of water-lubricated bearings increases with the rise in p, primarily due to the following factors: a. In water-lubricated stern bearings, as the p increases, the pressure exerted on the lubricating water also increases, thereby increasing the viscosity of the lubricating water. The increase in viscosity leads to greater shear forces within the lubrication film, thereby increasing f. b. During operation, the lubrication state of water-lubricated bearings may transition from full fluid lubrication to partial fluid lubrication (mixed or boundary lubrication). Under full fluid lubrication, there is a complete lubricating film between the shaft and the bearing, reducing direct contact. However, as the p increases, the lubricating film may become too thin or rupture under the increased load, leading to partial contact between the bearing liner and the shaft sleeve, thus increasing f. c. With the increase in p, the heat generated by friction also increases, which may lead to a rise in bearing temperature. An increase in temperature can affect the viscosity and lubricating performance of water. Although the viscosity of water typically decreases with rising temperature, the increase in temperature may reduce the stability of the lubrication film, thereby increasing friction. d. At high specific pressures, the surfaces of the bearing and shaft may exhibit increased wear or deformation. Changes in surface morphology might lead to increased contact area or irregular contact points, thereby increasing f. The cumulative effect of these mechanisms results in an increase in f as the p of the bearing rises.

4.3.4. Influence of Lubricating Water Containing Sediments on Lubrication Characteristics

According to Experiments 7 and 10, the impact of clear lubricating water versus lubricating water containing sediments (Sc = 0.25 kg/m³, Sps < 0.05 mm) on the bearing lubrication state is shown in Figure 29. When the lubricating water contains sediments, the f is higher. Lubricating water with sediments is not conducive to the formation of a hydrodynamic water film, and the sediment particles destroy the water film and increase abrasive wear between the shaft and the bearing. The viscosity of lubricating water with sediments is related to the sediment content: as the sediment content increases, the viscosity also relatively increases. However, as the sediment content increases, the wear rate of the bearing also relatively increases.

4.4. Influence of Controllable Parameters on Temperature Rise Characteristics

4.4.1. Influence of Lubricant Water Temperature at the Bearing Inlet on Temperature Rise Characteristics

According to Experiments 8 and 11, the influence of T on ΔT is as depicted in Figure 30. In an environment with sediment-laden lubricating water, ΔT increases with the rise in T. For example, in a sediment-laden lubricating water environment, at n = 480 r/min and T = 20.0 °C, 23.0 °C, and 26.0 °C, ΔT increased by 3.57 °C, 3.92 °C, and 4.31 °C, respectively. In a clear-water lubricating environment, ΔT also increases with the rise in T. At n = 691 r/min, with T = 20.0 °C, 24.0 °C, and 28.0 °C, ΔT increased by 1.90 °C, 2.19 °C, and 2.59 °C, respectively. However, at higher n, the increase in ΔT was more significantly influenced by T. For example, at n = 1068 r/min, ΔT increased by 2.34 °C, 2.71 °C, and 3.32 °C.

The ambient temperature in the laboratory during the experiments was between 8 °C and 12 °C, which is lower than T. The relationship between ΔT and T is not linear and is influenced by various factors. Under the current experimental conditions, it is observed that in both sediment-laden and clear-water lubricating environments, ΔT increases with increases in T, with higher increases in the sediment-laden environment compared to the clear-water environment.

The trend in ΔT can be attributed to the thermophysical properties of the lubricating water (whether sediment-laden or clear) and its temperature’s impact on bearing lubrication performance. As the temperature of the lubricating water increases, its viscosity decreases. This reduction in viscosity leads to a thinner lubricating film between the shaft and bearing surfaces. The diminished effectiveness of the lubricating film in separating the shaft and bearing can lead to contact at the frictional micro-protrusions, fluid shear in the lubricating film, and potential boundary lubrication, thus generating higher frictional heat. Moreover, the presence of sediment particles in sediment-laden lubricating water introduces additional factors, as these particles may affect the effective viscosity of the lubricating water and their contact with the bearing surfaces can cause wear. With rising temperatures and decreasing viscosities, the ability of sediment-laden lubricating water to suspend and transport sediment particles may be reduced, exacerbating bearing wear and frictional heat. The presence of sediment particles in sediment-laden lubricating water impacts the magnitude of temperature increase, but the trend in temperature rise is similar to that in a clear-water lubricating environment.

4.4.2. Influence of Bearing Speed on Temperature Rise Characteristics

As depicted in Figure 30, irrespective of whether using clear or sediment-laden lubricating water, ΔT increases with n. This is because a higher n enhances fluid shear within the lubricating film and the frictional heat generated in potential dry friction areas. Specifically, for sediment-laden water, a step-like increase in ΔT occurs at around 100 r/min, possibly due to poor lubrication conditions under these circumstances, resulting in significant frictional heat. Another point to note is that as n increases, ΔT becomes more sensitive to T. This implies that when the bearing cooling is inadequate, it can rapidly reach abnormally high temperatures, leading to bearing melt-down failures.

4.4.3. Influence of Bearing Specific Pressure on Temperature Rise Characteristics

The results of Experiments 9 and 12 reflect the impact of p on ΔT, as shown in Figure 31. At the same n, ΔT increases with an increase in p. This is because the higher p is during shaft rotation, the greater the heat generated from friction.

In a clear-water lubricating environment, at the same n, the increase in ΔT with an increase in p is not significant and shows a relatively stable trend. For instance, ΔT caused by increasing from 0.20 MPa to 0.30 MPa in a clear-water environment is almost the same as that from increasing from 0.30 MPa to 0.40 MPa.

In a sediment-laden lubricating water environment, at the same n, the increase in ΔT caused by the same increase in p shows a relatively stable trend. For instance, the increase in ΔT from increasing the bearing pressure from 0.50 MPa to 1.00 MPa is nearly the same as that from 1.00 MPa to 1.50 MPa.

4.4.4. Influence of Sediment in Lubricating Water on Temperature Rise Characteristics

According to Figure 31, at n less than 100 rpm, the ΔT in environments using clear lubricating water and sediment-laden lubricating water are similar. This is primarily because neither environment has established a good lubricating water film at such low speeds, and the frictional temperature rises are comparably close. The dominant factor for ΔT at these speeds is the presence of dry friction or boundary lubrication at the friction pairs rather than the presence of sediments in the water. The frictional heat generated at these lower speeds is relatively minor, and the ample supply of lubricating water (Q = 30 L/min) results in similarly low and close ΔT in both environments.

However, as n increases, ΔT in sediment-laden lubricating water environments becomes significantly higher than in clear-water environments. The frictional environment in sediment-laden lubricating water is harsher and accompanied by abrasive wear, while the lubrication conditions in clear-water environments are better. ΔT in clear-water environments increases more gradually, whereas in sediment-laden-water environments, the increase is relatively steeper.

4.5. The Impact of Lubrication and Temperature Rise on Service Performance and Surface Morphology

4.5.1. The Effects of Abnormal Lubrication and Temperature Rise on Bearing Wear Characteristics and Surface Morphology

The stern bearings operated in environments of clear lubricating water (Experiments 2 to 9, and 13) and sediment-laden lubricating water (Experiments 10 to 12, and 14 to 15), resulting in the surface conditions of the shaft sleeve and bearing strips as shown in Figure 32 and Figure 33.

Figure 32a shows the appearance of the shaft sleeve after wear in clear-water lubrication, while Figure 32c,d are magnified views of Figure 32a, showing a bright shaft sleeve surface with uniformly mild scratches. There was no significant color change at the friction face and edges of the shaft sleeve, and no oxidation occurred. Figure 32b depicts the exterior of the bearing liner, and Figure 32d is a magnified view of the bearing bottom, where the bearing strip material surface in clear-water lubrication had no noticeable scratches and maintained its structural shape. There were no abrasive particles adhered to the axial edges of the bearing flume, and no apparent wear at the end faces. The alignment lines of the bearing liner were clear, and there was no slippage of the liner position.

Figure 33a shows the appearance of the shaft sleeve after wear in a sediment-laden lubricating water environment, while Figure 33c,d are magnified views of this. Figure 33b displays the surface appearance of the bearing liner, with Figure 33e–g providing magnified views of the liner. In the sediment-laden lubrication environment, the sleeve surface exhibited noticeably uneven scratches. The colors at the edges of the sleeve darkened, and the overall color of the friction face was significantly darker than in clear-water lubrication, showing signs of high-temperature friction oxidation. Figure 33c reveals deeper wear grooves at the propeller end of the sleeve due to higher load, with material deformation causing a bright appearance. Figure 33d shows that in addition to circumferential scratches, there were distinct radial scratches on the sleeve surface, possibly due to the flow of sediment water or axial vibrations of the shaft. The sleeve scratches also embedded material from the bearing liner. Figure 33e displays prominent burrs on the edges of the flume, with obvious circumferential scratches due not only to the sediment in the lubricating water but also to torsional and gyroscopic vibrations of the shaft. The load at the propeller end of the bearing strip was high, resulting in severe wear at the end faces. Figure 33f shows surface peeling on the bearing strip material, with evident surface tearing in the sediment-laden lubrication environment, related to the fiber mesh structure of the liner material. Figure 33g depicts the state of the bearing flume before cleaning, filled with a large amount of sediment and abrasive particles. The accumulation in the flume altered the internal structure of the bearing liner, reduced the lubricating water flow, and impacted the cooling and heat dissipation performance of the bearing.

4.5.2. Analysis of Wear Value and Wear Rate of Bearing Liner and Shaft Sleeve

The distributions of wear value and wear rate for the bearing liner and shaft sleeve under condition 1 (Experiment 13; clear-water lubrication conditions; wear time = 50 h), condition 2 (Experiment 14; medium–high speed, light-load conditions; wear time = 100 h), and condition 3 (Experiment 15; low-speed, heavy-load conditions; wear time = 90 h) are illustrated in Figure 34. The wear rate is calculated using the formula: Wear rate = Wear value/Wear time.

In the environment of clear-water lubrication, the wear rate for bearing liners is relatively low. However, in sediment-laden lubricating water environment, the wear rate exceeds twice that of clear-water conditions. In such sediment-laden-water environments, solid particles intervene in the contact surfaces between the shaft and bearing, leading to abrasive wear. Particularly under conditions of low speed and heavy load, these particles intensify the compression and cutting forces on the surface of the bearing liner material, accelerating material removal. For the shaft sleeve, the wear rate in the sediment-laden lubricating water environment is also higher than in the clear-water environment, but there is no significant difference in wear rates between different conditions (low-speed, heavy load; and medium–high speed, light load). The material of the shaft sleeve exhibits considerable resistance to sediment-laden water, maintaining stable performance under various speeds and loads. The wear value of the bearing liner is significantly influenced by the presence of sediment in the lubricating water, the shaft speed, and the specific pressure. The wear value of the shaft sleeve is more affected by the presence of sediment in the lubricating water than by shaft speed or specific pressure.

4.6. Statistical Analysis of Stern Bearing Operational State Monitoring Parameters

4.6.1. Basic Statistical Analysis

Descriptive statistics applied to experimental data enable the analysis of the effects of shaft rotational speed on f of stern bearings under different T and p conditions. The results of the statistical analysis are presented in Figure 35, illustrating the mean, standard deviation, minimum, maximum values, and quartiles of f under various conditions.

The mean value indicates the average level of f under different T and p conditions. The standard deviation (std) measures the dispersion of f values, with a larger standard deviation indicating greater variability. The minimum (min) and maximum (max) values represent the lowest and highest recorded friction coefficients, respectively. The quartiles (25%, 50%, 75%) provide more detail about the distribution of f; 25% is the lower quartile, 50% is the median, and 75% is the upper quartile. As p increases (from 0.20 MPa to 0.50 MPa), both the mean and maximum values of f generally rise under each T condition, indicating that an increase in p leads to an increase in f. An increase in T (from 20.0 °C to 39.0 °C) also causes an increase in f, particularly under high p conditions. At higher shaft speeds (e.g., 500 rpm and 600 rpm), f significantly decreases, indicating a negative correlation between shaft speed and f.

4.6.2. Correlation Analysis of n/T/p/f

The correlation analysis between n, T, p, and f was conducted to explore the influence of these factors on the variation of f. The analysis employed the Pearson correlation coefficient, Spearman’s rank correlation coefficient, and Kendall’s tau correlation coefficient, with the correlation matrices presented in Figure 36, Figure 37, Figure 38.

(1) Correlation betweennandf

There is a significant negative correlation between n and f. The Pearson correlation coefficient is −0.804327, indicating that an increase in n significantly decreases f. This result is further confirmed by the Spearman (−0.887814) and Kendall (−0.731729) rank correlation coefficients, both showing strong negative correlations. This finding may be attributed to enhanced lubrication effects at higher speeds, which reduce the friction between contact surfaces.

(2) Correlation betweenTandf

Compared to rotational speed, the impact of T on f is minor. The Pearson correlation coefficient is 0.108282, with Spearman at 0.099482, and Kendall at 0.076868, all indicating a very weak positive correlation. This suggests that within the examined temperature range, the increase in T has a limited effect on increasing f. This may be due to the minimal impact of temperature variations within the observed range on lubrication conditions or material properties.

(3) Correlation betweenpandf

The correlation between p and f is significant, with a Pearson correlation coefficient of 0.385286, Spearman at 0.410617, and Kendall at 0.315504, all indicating a moderate positive correlation. This means that as p increases, f correspondingly increases. This result could be related to increased p causing closer contact between the surfaces and disruption of the lubrication film, thus increasing friction.

Under the same conditions, n is the primary factor affecting f, followed by p, while the impact of T is relatively minor. These findings are crucial for understanding and optimizing the operating conditions of shaft–bearing systems, especially in applications where precise control of friction and wear is required. Properly adjusting n and p can effectively enhance the efficiency and extend the service life of water-lubricated stern bearings.

4.6.3. Sensitivity Analysis of Controllable Parameters in Friction and Wear Behavior

Figure 39 illustrates the density distribution of f for water-lubricated stern bearings under different operating conditions. As T increases (from 20 °C to 39 °C), the peak of the f distribution shifts to the right, indicating that at higher T, the general level of f increases, implying that f rises with increasing T. Additionally, the distribution of f is more dispersed under high-temperature conditions, suggesting that f is more sensitive to n and p when T is higher.

An increase in p (from 0.20 MPa to 0.50 MPa) also results in a rightward shift of the peak in f. Under high-p conditions, the variability and dispersion of f’s distribution increase, indicating that p is a significant factor affecting the variability of f. This behavior is similar to that observed under high-temperature lubricating water conditions, where the bearing exhibits higher sensitivity to T and n.

T and p are sensitive parameters affecting f. T appears to have a more direct impact on increasing f, while an increase in p affects the variability and breadth of its distribution.

Under conditions of low p and restricted n, lowering T can improve the lubrication state, allowing for optimization of f by adjusting T without changing n. Under high-p conditions, increasing n is the primary method to enhance the lubrication state, as reducing p has limited benefits in these scenarios. Additionally, attention must be paid to the cleanliness and temperature control of the lubricating water, especially in closed lubrication systems. Impurities such as sediment and wear particles in the lubricating water need to be cleaned promptly to prevent them from causing wear on the bearings. For systems using seawater as lubricating water, it is important to be mindful of fluctuations in lubricating water temperature, especially when navigating in different waters, as changes in environmental temperature can significantly affect lubrication effectiveness.

4.6.4. Sensitivity Analysis of Controllable Parameters in Temperature Rise Behavior

Figure 40 illustrates the density distribution of temperature rises in water-lubricated stern bearings under various operating conditions. Each curve represents the density distribution of temperature rise under specific p and lubricating medium (clear-water or sediment-laden water) conditions. The temperature rise curves under clear-water conditions are sharper and centered at lower temperature values, indicating that the temperature variation in bearings is relatively small and stable in clear-water environments. In contrast, curves under sediment-laden water conditions are flatter and more dispersed, indicating a wider and more unstable range of bearing temperature rises. Regardless of whether the lubricating water is clear or contains sediment, as p increases, the peak in the temperature rise density shifts rightward, indicating an increase in bearing temperature rise. Particularly, under high p (e.g., 1.50 MPa), there is a significant increase in temperature rise.

The behavior of temperature rise is influenced by several factors: a. Medium impact: sediment-laden water causes a higher temperature rise than clear water under the same p, likely due to sand particles increasing friction and wear. b. p impact: At higher specific pressures, whether in clear or sediment-laden water, the temperature of the bearings increases significantly. This indicates that p is a crucial factor affecting temperature rise. c. Shaft speed impact: Under various shaft speeds, combining different lubricating water mediums and p conditions, it is evident that higher shaft speeds result in more significant temperature increases. d. Additionally, the temperature rise in water-lubricated bearings increases with the rise in lubricating water temperature at the bearing inlet, whether in sediment-laden or clear water. This is attributed to the decrease in water viscosity with increasing temperature, leading to a reduction in lubricant film thickness, increased frictional heat, and reduced cooling effectiveness of the lubricating water.

The behavior of bearing temperature rise is highly dependent on the lubricating fluid medium, lubricating fluid temperature, bearing specific pressure, and shaft rotational speed. Variations in these factors can significantly affect the thermal state of the bearings, thereby impacting their performance and lifespan. When designing and operating bearing systems, the effects of these parameters should be carefully considered to optimize the operating conditions of the bearings and extend their service life.

5. Conclusions

Based on the investigation and analysis of failure behavior in multi-point ultra-long shaft system water-lubricated stern bearings on ships, an experiment rig was constructed for experimental studies using SF-2A-lined water-lubricated stern bearings. Variables such as shaft speed, lubricating water temperature at the bearing inlet, clear and sediment-laden lubricating waters, bearing specific pressure, and surface morphology of the bearing liner were selected as controllable parameters. Through experimental research, the effects of these parameters on the lubrication characteristics (representing the bearing’s lubrication capacity, which helps prevent abnormal wear and failure) and the temperature rise characteristics (representing the bearing’s cooling and heat dissipation capacity, which helps prevent high-temperature melting failure) of the bearing were investigated.

The main conclusions of the study are as follows.

(1) As the surface smoothness of the stern bearing liner increases (roughness decreases), the friction coefficient tends to stabilize, exhibiting favorable velocity characteristics. Smooth surfaces on the stern bearing liner facilitate the establishment of a good lubricating water film between the stern shaft and the stern bearing, resulting in stable and relatively low temperature rises and excellent cooling and heat dissipation capabilities.

(2) When the lubricating water meets the design requirements (Q = 30 L/min), the friction coefficient of the stern bearing decreases with increasing shaft speed. When the speed reaches a certain level (800 r/min), the change in friction coefficient becomes negligible and stabilizes. The temperature rise of the stern bearing increases with the shaft speed. As the stern shaft speed increases, the temperature rise of the stern bearing becomes more sensitive to factors such as the lubricating water temperature at the inlet, specific pressure, and the presence of sediment in the lubricating water.

(3) Under the design requirement of the lubricating water (Q = 30 L/min), a relatively low shaft speed can establish a good lubrication state at low bearing specific pressures; whereas at high bearing specific pressures, higher speeds are required to effectively establish a lubricating water film. The temperature rise of the stern bearing shows an increasing trend with the bearing specific pressure. Under clear-water lubrication, the temperature rise is less affected by bearing specific pressure. Under sediment-laden lubrication, the effect of bearing specific pressure is not significant at speeds below 100 r/min. However, when the speed exceeds 100 r/min, the bearing temperature increases progressively with the rising bearing pressure. Overall, the temperature rise in sediment-laden lubrication environments is higher than in clear water.

(4) With the same bearing specific pressure and shaft speed, the friction coefficient of the stern bearing increases with the rise in lubricating water temperature at the inlet, and so does the temperature rise. Under clear-water lubrication, the sensitivity of the friction coefficient to the lubricating water temperature at the inlet decreases with increasing specific pressure. In both sediment-laden- and clear-water-lubrication environments, as the stern shaft speed increases, the temperature rise of the stern bearing tends to be more influenced by the lubricating water temperature at the inlet. Lowering the lubricating water temperature at the inlet helps establish a good lubrication state for the stern bearing and slows down the temperature rise.

(5) The presence of sediment particles in sediment-laden lubricating water introduces additional factors, affecting the viscosity and specific heat capacity of the lubricating water, reducing the lubrication and cooling performance of the stern bearing, and making it easier for wear to occur due to contact with the stern bearing surface. The presence of sediment particles (Sc = 0.25 kg/m³, Sps < 0.05 mm) increases the friction coefficient and temperature rise of the stern bearing, but the overall trend is similar to that in clear-water environments.

(6) Stern bearings operating in sediment-laden lubricating water environments exhibit deteriorated lubrication conditions, increased wear of the strips, and rougher surface morphology, along with higher temperature rises in the bearing.

(7) When the shaft speed is low and the bearing operates under high specific pressure in sediment-laden lubricating water, the bearing functions in more severe operating conditions, unable to establish proper lubrication. Under such conditions, the surface of the bearing liner material exhibits slight oxidation, which intensifies with increased specific pressure.

(8) As the specific pressure borne by the bearing increases, severe wear at the edges near the propeller end of the bearing liner material, along with tearing and delamination of the middle section surface material, becomes more pronounced. Additionally, there is evidence of surface delamination of the bearing strip material at the edges near the propeller end.

Future research can be pursued from the following aspects. Based on the study of the influence of controllable parameters on the healthy operation of water-lubricated stern bearings, it is feasible to construct causal relationship machine learning models or digital twin models. These models could enable evolvable predictions for the service process of ship water-lubricated stern bearings, supporting operational control and maintenance decisions. By monitoring the operational status parameters of stern bearings, identification and prediction of health status can be conducted, followed by adjustments and simulations of operational parameters on the machine learning or twin models, selecting optimal decisions for controlling the operation of stern shafts and stern bearings. Moreover, condition monitoring can be expanded to include dynamic measurements of water film pressure and thickness, as well as the measurement of vibration and noise conditions. Additionally, further studies could investigate the potential environmental impact of SF-2A materials and the wear particles they generate.