CFD based transient analysis of hydrodynamic journal bearing

Sanjay Sharma¹, R K Awasthi²

¹Research Scholar,I.K. Gujral Punjab Technical University, Kapurthala, Punjab-144603, India, and faculty Department of Mechanical Engineering,Shri Mata Vaishno Devi University Katra-182320, India

²Department of Mechanical Engineering, Beant College of Engineering and Technology, Gurdaspur, Punjab-143521, India

*Corresponding Author Email: Sanjufrnd15@gmail.com, awasthi.rka@gmail.com

ABSTRACT:

The effect of aspect ratio on linear and non linear stability of hydrodynamic journal bearing with Newtonian lubricant is presented. The aspect ratios (L/D) 0.5, 1.0 and 1.5 and eccentricity ratio of 0.2, 0.4, 0.6 and 0.8 are considered for the analysis of purpose. The Reynolds equation governing the flow of lubricant in the clearance space of a hydrodynamic journal bearing system has been numerically solved using Galerkin’s FEM. The positive pressure zone is established using Reynolds boundary condition through iteratively. The journal centre motion trajectories are obtained by numerically integrated linear and non-linear equation of motion using fourth order Runga-Kutta method. For this a computer program in Mat lab was developed based on analysis to draw the linear and non linear motion trajectories and in order to validate the developed program, the numerically simulated results computed from the present study are compared with the already published results in literature. For analysis purpose the initial values of velocities and displacement are taken as and . The results help in predicting bearing life for smooth operation.

KEYWORDS: FEM, aspect ratio, journal bearing.

1. INTRODUCTION:

Hydrodynamic journal bearings during transient periods continuously operate above critical speed in many rotating machinery for supporting radial loads. For smooth operation of bearing, several investigators have studied transient response of circular journal bearing systems by discretized time and numerically integrated linearized and nonlinear equations of motion of journal bearing system to study solid and porous bearings having L/D ratio of 1.0 with journal bearing axes parallel as well as skewed [1]. The stability analysis and dynamic transient behavior of shaft and support motions having same L/D ratio of 0.5 for both the stable and unstable operating speeds has been studied [2].

The linearized stability threshold and nonlinear transient analysis of rigid rotors in elliptical, offset elliptical, three lobe, and four lobe bearings having same L/D ratio of 0.5 was also determined [3].The study on linear and non linear transient motion analysis of a flexible shell journal bearing having L/D ratio of 1.0 and found that non linear motion equation give higher stability than linear equation of motion [4]. The transient response of plane hydrodynamic journal bearing system having L/D ratio of 1.0 during accceleration and deaccceleration periods has also investigated [5]. The study on effects of eccentricity ratio, and the deformation coefficient on elastic bearing with L/D ratio of 1.0 for different values of the normalized journal mass and found better performance under dynamic conditions [6].The transient response study of hydrodynamic journal bearing having L/D ratio of 1.0 and lubricated with non-newtonian lubricants using cubic shear stress law has been investigated [7]. The bearing stiffness characteristics, transient vibration, and frequency response of hydrodynamic journal bearing having aspect ratio L/D of 1.57 also obtained for both linear and nonlinear bearing simulations [8]. For a particular frequency of loading, the effects of mass, amplitude of load vibration and frequency of journal speed on stability of journal bearing having L/D ratio of 0.57 has been investigated [9]. Non linear transient analysis of journal bearing stability having L/D ratio of 0.5was also studied and found that the initial conditions play an important role on the behavior of the orbit [10]. In 1995 the stability of finite journal bearing having L/D ratio of 1.0 under impact excitation, position perturbation and synchronous unbalance excitations to explain the stable, critical and unstable phenomena has been investigated [11]. The non-linear time transient analysis of non-Newtonian lubricant hydrodynamic journal bearings having different power law index and aspect ratios was also performed [12]. The dynamic parameters like, stiffness and damping coefficients, critical speed and whirl ratio are calculated for various L/D ratios and nonlinear time transient analysis for stability of hydrodynamic journal bearings under various dynamic loads [13]. The effect of fluid inertia on stability of flexibly supported oil journal bearing with L/D ratios of 0.5, 1.0 and 2.0 was studied [14]. The nonlinear dynamic analysis of a flexible rotor center and bearing center by using micropolar lubricant together with short bearing approximation having L/D < 0.25 was also studied [15]. Theoretically study on Stability of a tri-taper journal bearing with various L/D ratios which is subjected to steady, periodic and variable rotating loads was also performed [16]. The dynamic behavior of compliant cylindrical journal bearings having L/D ratio of 1.33 has been investigated by using linear and nonlinear numerical approaches [17].

A study of bearing dynamics operating under transient conditions is important for enhancing smooth bearing life. An understanding on how bearing size (aspect ratio) influences bearing performance of hydrodynamic journal bearing due to transient motion is yet to be revealed. As there appears to be a very little work obtain in the published literature taking into consideration the effect of aspect ratio on journal bearing system.

3. SOLUTION PROCEDURE:

The study of transient motion through numerical simulation has been performed using flow chart as shown in Fig. 2. The simulation is performed using following steps.

The fluid-film domain is automatically discretised into four noded quadrilateral isoparametric elements by assigning number of elements in circumferential and axial direction.
Fluid-film pressure field are initialized by assigning an input value of journal centre.
Fluid-film thickness is calculated using Eq. (4).
A two point Gauss quadrature is used for the integration in elements. Thus four Gauss points are generated in an quadrilateral isoparametric element.
Element equations are assembled using indexing to obtain global system of matrices and then boundary conditions are implemented. Cavitation boundary is established using iteration.
Computed values of nodal pressure and velocity components from Eq. (9) are used to calculate fluid film forces.
By using fourth-order Runga-Kutta method, linear and non linear motion trajectories of journal centre are obtained by integrating Eq. (18) and (19).

The simulated data for non dimensional bearing performance parameters have been generated and plotted to gain understanding. The results have been discussed in the following paragraphs.

3.1 Results and Discussion

A computer program in MAT LAB was developed based on analysis to draw the linear and non linear motion trajectories. The aspect ratios (L/D) 0.5, 1.0 and 1.5 and eccentricity ratio of 0.2, 0.4, 0.6 and 0.8 are considered for the analysis of purpose. In order to validate the developed program, the numerically simulated results for eccentricity ratio () corresponding to different values of the critical whirl ratio for L/D ratio of 1.0 are computed from the present study and compared with the already published results in literature [11] as shown in Figure.3.The results are observed to be in good agreement with the published work and thus establishes the accuracy of developed code. The transient response of hydrodynamic journal bearing with respect to same critical mass for varying L/D ratio are plotted in the form of motion trajectories (Figs. 3-10). For analysis purpose the initial values of velocities and displacement are taken as and for all aspect ratios.

Fig. 2: Overall solution process scheme

Fig.3: Critical Whirl ratio versus Eccentricity ratio (hydrodynamic journal bearing)

(c)

Fig. 4: Linear trajectories for hydrodynamic journal bearings with different aspect ratio.

Figure.4 shows linear trajectories for hydrodynamic journal bearings with different aspect ratio (0.5, 1.0 and 1.5) and eccentricity ratio of = 0.2. It is observed that the linearized equation of motion give a limiting cycle at L/D ratio of 1.0, the system is unstable at lower L/D ratio of 0.5 and system is stable at higher L/d ratio of 1.5.Figure.5 shows Non linear trajectories for hydrodynamic journal bearings with different aspect ratio (0.5, 1.0 and 1.5) and eccentricity ratio of = 0.2. It is observed that by using non linearized equation of motion the system becomes stable at higher aspect ratio (L/d =1.0 and 1.5) and the system is unstable at lower L/D ratio of 0.5.

Fig.6 shows linear trajectories for hydrodynamic journal bearings with different aspect ratio (0.5, 1.0 and 1.5) and eccentricity ratio of = 0.4. it is observed that the due to increase in eccentricity ratio the lower L/D ratio of 0.5 found unstable but journal centre trying to form more trajectories towards centre, which help for smooth operation of bearing. The system is stable at higher L/D ratio of 1.5 and makes limit cycle at L/d ratio of 1.0.

Fig.7 shows non linear trajectories for hydrodynamic journal bearings with different aspect ratio (0.5, 1.0 and 1.5) and eccentricity ratio of = 0.4. It is observed that due to increase in eccentricity ratio the system become more unstable at lower L/D ratio of 0.5 than linearized equation of motion as shown in fig.5 (a). Fig. 6 (b) shows that the system trying to form limit cycle to get stable. Fig. 6 (c) shows that the system is stable at higher L/D ratio of 1.5.

(c)

Fig. 11: Non Linear trajectories for hydrodynamic journal bearings with different aspect ratio.

4. CONCLUSION:

This study investigates the effect of aspect ratio for linear and non linearized equation of motion for hydrodynamic journal bearings under transient conditions. Based on results, following conclusions can be drawn:

1) It is observed that by using eccentricity ratio = 0.2 for linear and non linearized equation of motion the system becomes stable at higher aspect ratio (L/d =1.0 and1.5) and the system is unstable at lower L/D ratio of 0.5.

2) It is observed that due to increase in eccentricity ratio at 0.4 the system become more unstable at lower L/D ratio of 0.5 than linearized equation of motion.

3) By using eccentricity ratio = 0.6, The journal trying to form limit cycle at lower L/D ratio which is in linear case. But in case of non linear trajectories the journal is trying to make limit cycle at L/D ratio of 1.0 and the effect of other L/D ratio (0.5 and 1.5) on journal bearing system in both linear and non linear case is almost same.

4) It is also observed that by considering eccentricity ratio of 0.8 the journal centre gives limit cycle at L/D ratio of 0.5 and 1.0 in both linear and non linear case and the bearing centre becomes more stable at higher L/D ratio of 1.5.

5. REFERENCES:

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