Experimental and theoretical analysis on the nonlinear rotor-dynamic performances and vibration characteristics of a novel bearing-rotor system

https://doi.org/10.1016/j.ymssp.2023.110416Get rights and content

Highlights

  • The revised lubrication model and the bearing-rotor coupled dynamic model under different lubrication states are established.

  • The influences of multi-coupling parameters on the static and dynamic characteristics of the bearings are analyzed.

  • The variation laws of shaft vibration response under different operating conditions are revealed.

  • The correctness and rationality of the model is verified by experiment.

Abstract

The abnormal vibration of the rotating shaft in propulsion system during the startup stage seriously reduces the concealment and safety of the ship navigation. This paper clarifies the rotor-dynamic and vibration performances of a new bearings-rotor coupled system. The rotor-dynamic model and the bearing-rotor coupled dynamic model under different lubrication states are established. The influences of rotating speed, external load, length-diameter ratio and other parameters on the lubrication performances and supporting behaviors of the bearings are analyzed. The variation laws of shaft vibration response under various working modules are revealed. Results of the test and theoretical have good consistency. Results enrich the theoretical system on the analysis and optimum design for such rotating systems.

Graphical abstract

The lubrication performances, dynamic behaviors and vibration characteristics of a novel water-lubricated bearing-rotor coupling system under different lubrication state are investigated. The effects of operation parameters on static performances, dynamic properties and response analysis of such strong coupling system are revealed. The water-lubricated bearing-rotor test bench is designed and constructed. Tested water-lubricated bearings with different structures and geometries are manufactured. The tribo-dynamics and vibration analysis of the bearing are carried out. The experimental results are in good agreement with the theoretical analysis.

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Introduction

The ship propulsion shaft is the crucial element of ship power system. As the key supporting component of the propulsion shaft, the bearing plays an extremely critical role[1]. Traditionally, oil is used as the lubricating medium for the supporting parts of marine propulsion shaft. With the updating and iteration of marine equipment and the environmental protection issues, oil lubrication cannot meet the requirements of high-performance offshore work equipment in current era due to the expensive operation mode and the potential crisis of leakage pollution at any time[2], [3]. The natural advantages of wide water sources and environmental protection can make up for the defects of traditional lubrication methods. Water-lubricated bearings(WLBs) have been broadly exploited in high-tech ship, propellers[4], power plants[5] and other important production occasions. In terms of theoretical research, the research on lubrication performance[6], friction effect[7] and hydrodynamic property[8] of such bearings has achieved relatively mature research results. The coupling dynamic between WLBs and shaft system is also a hot pot in the fluid field. Meanwhile, the coupling behaviors of WLBs and shaft is complicated. Specific coupling behaviors have completely different actions on the dynamic properties of the bearing and affiliated equipment. That behaviors lead to the unclear study on regime of shaft vibration response of the bearings from startup to shutdown stage. Therefore, the rotor-dynamic effects of WLBs and the vibration response process are not yet fully realized. It is critical to clarify the complete vibration response of WLB-rotor. The mechanisms can supplement theoretical analysis for relevant research.

Sliding bearings have are good reliability and large load capacity[9]. It is widespread used in rotating machinery. Many scholars deeply studied the lubrication performance, fluid behavior, vibration response and multi coupled field friction mechanism of sliding bearings. When the sliding bearing acts on the shaft, the coupling behaviors are shown by the equivalent dynamic characteristics. The supporting properties of WLBs are the dynamic characteristics of the water film force and the lining in series. The lining material of water-lubricated bearing is generally non-metallic composite material. Its dynamic characteristics have obvious regularity. The supporting properties of the water film will be linearized into eight dynamic coefficients. The dynamic coefficients directly affect vibration response of the system[10]. However, the coefficients of water film are strong time-varying. The small disturbance also causes large changes in the supporting coefficient of liquid film under complex operation. In order to obtain complete supporting properties of sliding bearings and the overall performance of rotating machinery system, it is important to seek stiffness and damping coefficients.

Accurate estimations of supporting characteristics coefficients of bearings are of great significance for analyzing the dynamic characteristics of rotating machinery. Scholars at home and abroad deeply explored the solution of dynamic coefficients of sliding bearings. Mature research results were achieved in numerical analysis and experimental measurement[11]. Yang et al[12] designed a model updating method based on rotor disk. This method had high reliability in identifying model dynamic coefficients. Yang[13] put forward the estimation technique to realize time-varying performance of the dynamic coefficients. Experimental methods are validated under different noise measurement levels. The results established a high precision method for evaluating the overall performance of rotating machinery. Xie et al[14] carried out the study of the misaligned degree on the dynamic coefficients under different speeds and loads. The simulation results illustrated that the supporting characteristics coefficients increase with the misaligned angle. Feng[15] solved dynamic coefficients on misaligned bearing through using perturbation equation. 32 dynamic coefficients such as translation, tilt and coupling translation tilt of the bearings were obtained. Influences of operating conditions and inclination angle on supporting properties were analyzed. Kim et al[16] put forwarded a measure to calculate the translation and tilt dynamic performances of shaft coupling system. The dynamic coefficients with this method were compared with the numerical differentiation method of the load on the minor displacement and speed of equilibrium point. It is verified that the method has higher accuracy. Similarly, Liu et al[17] discussed the influence of the biaxial shaft tilt effect on the static and dynamic properties. A number of transient disturbance fluid structure coupling dynamic models were established. The variation laws of the supporting properties under shaft inclination were obtained. The research results provided reference for the optimum design and properties analysis of misaligned journal bearings. Zhang et al[17] put forwarded a method to solve the stiffness coefficients of WLBs. The perturbation model of WLBs was constructed in polar coordinates. The variation laws of bearing stiffness coefficients with load at different speed, relative clearance and length-diameter ratio were analyzed. Chen et al[18] studied on the dynamic characteristics of WLBs. A transient WLBs fluid model was built. The time-varying laws of dynamic coefficient under different transient loads were revealed. The experimental results explored that the direct dynamic coefficient arises and the cross dynamic coefficient decreases load. Du et al[19] revealed the supporting properties of incompressible hydrodynamic bearings. A method for solving bearing dynamic coefficients based on mathematical perturbation technology was proposed. The rationality and robustness of technique are testified. The vibration stability of system supported by WLBs were judged. Muhammad et al[20] corrected the modified Sommerfeld number. Dynamic parameters of oil film were formulated. The variations of dynamic coefficients with eccentricity were solved. Zhang et al[21] solved the supporting properties of the WLBs with spiral groove using mathematical perturbation technology. The relationship between dynamic coefficient and water film thickness was analyzed. It was found that the dynamic coefficients were mainly affected by the combined action of cavitation and centrifugal force. Ren and Feng[22] carried out a stability investigation on WLB. The dynamic parameters were calculated through solving Reynolds equation. The effects of geometric parameters on the performances of WLBs was analyzed. The correctness of the method is verified.

Water-lubricated bearings are vital supporting component of the ship propulsion system. When it acts on the stern shaft, the coupling behavior with the shaft is reflected in dynamic characteristics[23]. Due to the strong time-varying dynamic performances of WLBs, bearing-rotor coupling has complex impacts on the entire propulsion system. Many mature research results are also produced in the research field of water lubricated bearing-rotor. Xie et al[24], [25] developed the hydrodynamic research on the novel fluid–solid interaction model with a new type of lubricating medium. A vertical coupling model was established. The frequency spectrum and axis trajectory of supporting components were solved. Results were meaningful for the analysis of vertical coupling rotating system. Chen et al[26] studied the tribo-dynamics of WLBs during startup phase. Dynamic model of WLB-rotor in the start-up phase was built. The transient journal trajectory was solved. The influences of imperfect shaft on tribo-dynamic of WLBs was revealed. Zhu et al[27] studied the underwater explosion shock analysis of the static performance of WLB. The dynamic model of the vibration of shaft longitudinal and bearing was established. The results showed that effects of the explosion towards static performances is transient. Xie et al[28] studied vibration response and impact response analysis of WLB-rotor system under fluid lubrication regime. The variation laws of shaft vibration response with working conditions were clarified. The vibration information of shaft system under different impact situations was clarified. Results presented reliable foundation towards optimal design of such strong coupling system at medium and high-speed situation. Rybczynski[29] carried out a study to assess the possibility of bearing misalignment defects. The axis orbits of the bearing located on the rotor were theoretically analyzed. The bearing misalignment defects was evaluated by using the properties of the axis orbits. The results showed that the axis orbits carried many important supporting behaviors of the parts of the shaft system. Chen et al[30] analyzed the nonlinear hydrodynamic effect of the system. The disturbance model of polynomial was built. The effects of the disturbance on the liquid film force were explored. The vibration responses under different conditions were solved. Xu et al[31] carried out the research on the supporting properties of the bearing. The static performances and dynamic mechanism of the system were obtained. Influences of different operation parameters on the dynamic behaviors of the shaft system were gained. The results indicated that the vibration increases with structure parameter. Wang et al[32] analyzed the changing laws of the vibration responses with the stiffness coefficients of the supporting parts. The vibration responses and coupling behaviors between supporting component and shaft were studied. Hydrodynamic effect was related to operation conditions. The results indicated that the increase of the stiffness of the bearing led to the increase of the vibration response. Huang et al[33] studied the influencing factors of friction-induced vibration. A numerical model for stick–slip friction vibration was put forward. The influence of the slip coefficient obtained from the friction coefficients was analyzed. The results of friction coefficient and velocity were solved. Kuang et al[34] analyzed the friction and torsional vibration on WLB-rotor system. Friction-induced vibration of the rotor system was analyzed. Chen et al[35] proposed a novel and effective nonlinear dynamic method for solving the dual-rotor-bearing-casing systems. The method of harmonic balance-alternating frequency/time domain was adopted. The system motion equations considering radial stiffness, variable stiffness excitation and nonlinear restoring force were calculated. It was shown that the dynamic load of the bearing was closely related to the vibration response of the rotor. Results indicated that the increase in bearing clearance made the nonlinear characteristics of the force frequency response more significant. The HB-AFT method had well practicality and accuracy in dealing with nonlinear and multi frequency excitation systems.

The existing solution of bearing dynamic coefficient focuses on the limit of bearing length-diameter ratio and formularization of dynamic coefficients solution. The vibration characteristics analysis is directly studied based on the known dynamic coefficients. However, the static properties, rotor-dynamic characteristic and vibration response of WLBs are calculated together under specific working conditions. A complete research system from static performance to dynamic performance and then to vibration response analysis is formed. Such related work is still lacking.

The work emphasizes on solution of support properties and behaviors analysis. The influence of supporting properties on vibration performance under different conditions is analyzed. The novel lubrication model and the WLBs-rotor coupling dynamic model considering different lubrication conditions are built. The influences of multi-coupling parameters (speed, external load, relative clearance, length-diameter ratio etc) on the friction attributes and supporting properties of the bearings are investigated. The changing rules of axis orbit and phase diagram with speed are revealed. The variation laws of vibration response with working conditions are obtained. The rationality is testified by experiment. Researches provide a solid basis for the vibration response analysis for such rotating systems.

Section snippets

Reynolds equations

Fig. 1 present structure of the WLB. Assuming that water is incompressible, the Reynolds equation is[36]:xh3kxμdhx+zh3kzμdhz=U2hx

As for the parameters h, μd, U, kx, kz,they can be referred in the Nomenclature.

Fig. 2 shows the relationship between Stribeck curve and the lubrication mechanism. In whole operation of shaft system, relative positions of shaft and bearing are always changing. This leads to the variations of COF of system timely. Therefore, the increase of the rotating speed

Results and discussion

The work clarified the lubrication performances and dynamic responses of the WLBs. The vibration properties of WLB-rotor system with various parameters are revealed. The working conditions and structural parameters of bearing are presented in Table 1.

Conclusion

This paper studies the supporting properties and vibration performances of a new bearing-rotor coupling system. The coupling model of WLB-rotor under different lubrication regimes is established. Influences of parameters towards the supporting properties of WLBs are revealed. The variation laws of shaft vibration response are clarified. The results have good consistency. Results provide solid theoretical support for the optimum design of such coupled rotating systems. The main conclusions are:

  • (1)

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgement

This work is supported by the National Natural Science Foundation of China (No. 52105205), the Science Center for Gas Turbine Project (P2022-B-III-003-001).

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