Prediction of nonlinear dynamic coefficients of tilting-pad journal bearings with pad perturbation

Author(s):  
Mohammad Hojjati ◽  
Seyed Younes Farzanmehr ◽  
H. M. Navaz ◽  
Hassan Haddadpour

In this paper, a modified partial derivative method is developed to predict the linear and nonlinear dynamic coefficients of tilting-pad journal bearings with journal and pad perturbation. To this end, Reynolds equation and its boundary conditions along with equilibrium equations of the pad are used. Finite difference, partial derivative method, and perturbation technique have been employed simultaneously for solving these equations. The accuracy of the results is investigated by comparing the linear dynamic coefficients of three types of tilting-pad journal bearings with those published the literature. It is shown that the nonlinear dynamic coefficients depend on Sommerfeld number, eccentricity ratio, and length to diameter ratio. Similar to the case of linear dynamic coefficients of TPJB, it is observed that the eccentricity ratio effects on nonlinear dynamic coefficients are more notable when the eccentricity ratio is higher than 0.8 or less than 0.2.

Wear ◽  
1981 ◽  
Vol 72 (1) ◽  
pp. 29-44 ◽  
Author(s):  
P.E. Allaire ◽  
J.K. Parsell ◽  
L.E. Barrett

2010 ◽  
Vol 132 (3) ◽  
Author(s):  
Andres Clarens ◽  
Amir Younan ◽  
Shibo Wang ◽  
Paul Allaire

Lubricants are necessary in tilting-pad journal bearings to ensure separation between solid surfaces and to dissipate heat. They are also responsible for much of the undesirable power losses that can occur through a bearing. Here, a novel method to reduce power losses in tilting-pad journal bearings is proposed in which the conventional lubricant is substituted by a binary mixture of synthetic lubricant and dissolved CO2. These gas-expanded lubricants (GELs) would be delivered to a reinforced bearing housing capable of withstanding modest pressures less than 10 MPa. For bearings subject to loads that are both variable and predictable, GELs could be used to adjust lubricant properties in real time. High-pressure lubricants, mostly gases, have already been explored in tilting-pad journal bearings as a means to accommodate higher shaft speeds while reducing power losses and eliminating the potential for thermal degradation of the lubricant. These gas-lubricated bearings have intrinsic limitations in terms of bearing size and load capacity. The proposed system would combine the loading capabilities of conventional lubricated bearings with the efficiency of gas-lubricated bearings. The liquid or supercritical CO2 serves as a low-viscosity and completely miscible additive to the lubricant that can be easily removed by purging the gas after releasing the pressure. In this way, the lubricant can be fully recycled, as in conventional systems, while controlling the lubricant properties dynamically by adding liquid or supercritical CO2. Lubricant properties of interest, such as viscosity, can be easily tuned by controlling the pressure inside the bearing housing. Experimental measurements of viscosity for mixtures of polyalkylene glycol (PAG)+CO2 at various compositions demonstrate that significant reductions in mixture viscosity can be achieved with relatively small additions of CO2. The measured parameters are used in a thermoelastohydrodynamic model of tilting-pad journal bearing performance to evaluate the bearing response to GELs. Model estimates of power loss, eccentricity ratio, and pad temperature suggest that bearings would respond quite favorably over a range of speed and preload conditions. Calculated power loss reductions of 20% are observed when compared with both a reference petroleum lubricant and PAG without CO2. Pad temperature is also maintained without significant increases in eccentricity ratio. Both power loss and pad temperature are directly correlated with PAG-CO2 composition, suggesting that these mixtures could be used as “smart” lubricants responsive to system operating conditions.


Author(s):  
Tian Jiale ◽  
Yu Lie ◽  
Zhou Jian

The stable working condition of high speed, heavy loaded rotating machinery depends strongly on the stability provided by the journal bearing. Tilting pad journal bearings (TPJB) are widely used under such situation due to their inherent stability performance. However, because of the complexity of the TPJB structure, obtaining a reliable prediction of the journal bearing’s dynamic characteristics has always been a challenging task. In this paper, a theoretical analysis has been done to investigate the dynamic performance of a 4 pad TPJB with ball-in-socket pivot, emphasizing on the frequency dependency due to pivot flexibility. The analytical model containing the complete set of dynamic coefficients of the TPJB is built and the pivot stiffness is calculated and used to evaluate the equivalent dynamic coefficients of the bearing. In general, at lower perturbation frequency, the equivalent stiffness and damping increase with frequency. While for higher perturbation frequency, the dynamic coefficients are nearly independent of the frequency. Moreover, the results also show the limit value of the dynamic characteristics of the TPJB when the perturbation frequency is set to 0+ and ∞.


Author(s):  
Waldemar Dmochowski ◽  
Jacek Dmochowski

The paper presents experimentally obtained TPJB response to multifrequency excitation and its comparison with theoretically obtained data. Uncertainty considerations for the results obtained using the power spectral density method are also presented. It has been concluded that inertia forces and pivot flexibility effects are behind the variations of dynamic coefficients with frequency of excitation.


Author(s):  
Rafael O. Ruiz ◽  
Sergio E. Diaz

It has been identified that small variations in the pad clearance and preload of a Tilting Pad Journal Bearing lead to important variations in their dynamic coefficients. Although this variation trend is already identified, a more robust statistical analysis is required in order to identify more general tendencies and quantify it. This work presents a framework that helps to identify the relation between the manufacturing tolerance of the bearing (reflected in the pad clearance and preload) and the expected variations on the dynamic coefficients. The procedure underlies the adoption of a surrogate model (based on Kriging interpolation) trained by any deterministic model available to predict dynamic coefficients. The pad clearance and preload are considered uncertain parameters defined by a proper probability density function. All statistical quantities are obtained using stochastic simulation, specifically adopting a Monte Carlo simulation employing the surrogate model. The framework is illustrated through the study of a five pad bearing.


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