Varnish is a kind of fouling adhered on bearing inner face near the load zone. The model to analyze its influence on bearing performance and rotor vibration was set up. Pressure and temperature distribution were solved on the basis of the Reynolds equation by the iteration method simultaneously. It is found that bearing performance is changed by the step flow effect at the leading edge of the varnish. Its influence is more obvious when the rotating speed is low. Bearing varnish results in a large decrease of minimum clearance and an increase in the oil film temperature and pressure. Loading capacity of bearing is also decreased. It is harmful to the bearing. With the varnish, the minimum oil film thickness decreases. This leads to an increase of bearing stiffness and damping coefficients. Its influence is larger in the horizontal direction than that in the vertical direction. The trend of unbalance response to rotating speed is similar. There is little influence of the varnish on the modal frequency. However, system stability is improved due to the increased bearing damping coefficients.
Journal bearings have a great influence on the safe operation of rotating machinery. Machine works reliably under the squeeze flow effect formed in the convergent gap between bearing inner face and the journal.
With the development of industry, journal surface speed becomes higher and bearing load becomes more and more heavy. Varnish problem has occurred on journal bearings [
The clearance of bearing with varnish is irregular. Research on the performance of bearing with irregular clearance is mainly focused on groove or microtexture [
From inspection results of many bearings, varnish area is larger than expected. Unlike the groove or the microtexture, varnish is a kind of protrusion on bearing inner face. It is mainly located in bearing load area, which is near the minimum gap and is the most dangerous zone of the bearing. Its influence on bearing performance may be large. Research in this field should be concerned.
In this paper, influences of varnish on bearing properties and rotor vibration are studied. Loading capacity, temperature rise, oil film thickness, and dynamic coefficients were compared. Conclusions can be applied to bearing condition monitoring.
Varnish is a kind of fouling adhered on journal bearing inner face nearby the load zone, as shown in Figure
Bearing varnish model.
Varnish location in the bearing
Varnish photographs
The simplified varnish model
For ease of analysis, varnish shape is simplified. A trapezoid distribution in the boundary and a uniform distribution in the inner face were assumed, as shown in Figure
Clearance of bearing with varnish can be expressed as [
A two-dimensional (2D) Reynolds equations were used. Taking into account the axial symmetry; the solution region was selected as the rectangular region ABCD, as shown in Figure
Lubrication equation solution model.
The dimensionless form of the Reynolds equation is [
The varnish thickness is much smaller than the thickness of the pad. It has little influence on the heat conduction along the thickness direction of the pad. The heat conduction term was thus omitted. The simplistic two-dimensional energy equation with the adiabatic boundary condition is [
Bearing load is obtained by integral in axial and circumferential directions [
The computational accuracy depends on mesh density. The load and the maximum pressure were used to test grid independence. With the increase of journal eccentricity ratio in the bearing, mesh density should be increased. Thus, the grid independence test was done at large eccentricity ratio
Table
Bearing data.
Parameter | Value |
---|---|
Radius |
300 mm |
Radial clearance |
0.45 mm |
Bearing length |
300 mm |
Bearing load |
20.0 t |
Oil density |
890 kg/m3 |
Oil viscosity |
0.025 Pa s |
Rotating speed |
314 rad/s |
Specific heat capacity |
1.944 kJ/kg K |
Variation of the load and the maximum pressure with mesh density.
Load
The maximum pressure
Oil film force at different eccentricity ratio and attitude angle was calculated in advance. The back propagation neural network is well known for its strong nonlinear mapping ability. A three-layer backpropagation neural network with 8 nodes in the hidden layer, as shown in Figure
Neural network model mapping the function between the force and journal position.
Bearing data is provided in Table
Figure
Oil film thickness distribution.
Variation of the minimum oil film thickness with varnish thickness.
Figure
Oil film pressure distribution.
Pressure distribution in the central section
The three-dimensional pressure distribution
Figure
Variation of journal eccentricity ratio with bearing load.
Variation of journal eccentricity ratio with varnish thickness.
Comparison of journal eccentricity ratio and attitude angle.
The eccentricity ratio
The attitude angle
Figure
Comparison of temperature distribution.
Variation of the maximum oil temperature with varnish thickness.
Figure
Bearing temperature trend in a year.
Figure
Variation of the minimum oil film thickness with bearing load.
Varnish in the bearing results in a large decrease of minimum clearance and an increase in the oil film temperature and the pressure. Loading capacity of bearing is decreased. It is harmful to the safe operation of bearing.
Figure
Comparison of bearing dynamic coefficients.
The direct stiffness coefficients
The cross stiffness coefficients
The direct stiffness coefficients
The cross stiffness coefficients
For stability study, bearing equivalent stiffness and critical whirl ratio can be presented using bearing coefficients. They are given as [
Bearing equivalent stiffness and critical whirl ratio.
Parameter | With varnish | Without varnish |
---|---|---|
Equivalent stiffness |
|
|
Critical whirl ratio |
|
|
The dynamic equation of rotor bearing system is given as [
The homogeneous equation corresponding to (
A low pressure rotor of a large steam turbine was used. Figure
Shaft model.
Diameter |
Length |
Additional mass |
---|---|---|
600 | 300 | 0 |
630 | 142 | 0 |
660 | 594 | 0 |
1668 | 256 | 1850 |
951 | 340 | 0 |
1720 | 156 | 900 |
1116 | 236 | 0 |
1718 | 120 | 300 |
1114 | 130 | 0 |
1718 | 65 | 280 |
1068 | 120 | 0 |
1718 | 66 | 180 |
934 | 120 | 0 |
1718 | 50 | 110 |
934 | 120 | 0 |
1718 | 50 | 100 |
915 | 175 | 0 |
Shaft model.
Three unbalance masses as shown in Table
Unbalance mass.
Node | Product of mass and radius (kg m) | Angle (°) |
---|---|---|
4 | 0.5 | 45 |
17 | 1 | 135 |
32 | 0.5 | 225 |
The influence of varnish on the vertical and the horizontal vibration during the run up process is shown in Figure
Variation of vibration with rotating speed during run-up process.
Vertical vibration
Horizontal vibration
The lowest order modes are prone to be unstable and are of great concern. In this paper, stability of the first and the second mode is analyzed.
Table
Comparison of system stability.
Mode | Parameter | With varnish | Without varnish |
---|---|---|---|
Mode 1 | Frequency/Hz | 23.48 | 23.31 |
Logarithmic decrement rate | 0.5029 | 0.4645 | |
Mode 2 | Frequency/Hz | 34.45 | 34.41 |
Logarithmic decrement rate | 0.5327 | 0.4614 |
In this paper, the influence of the varnish on bearing performance and rotor vibration is studied. The results show the following.
(1) Performance of bearing with varnish is changed by the step flow effect at the leading edge of the varnish. Compared with the squeeze flow effect in the convergent clearance zone of bearing, influence of varnish is more obvious at the low speed case.
(2) Varnish in the bearing results in a large decrease of minimum clearance and an increase in the oil film temperature and the pressure. Loading capacity of bearing is also decreased. It is harmful to the safe and reliable operation of bearing.
(3) For bearing with varnish, the minimum oil film thickness decreases. This leads to an increase of bearing stiffness and damping coefficients. Its influence is larger in the horizontal direction than that in the vertical direction.
(4) For bearing with varnish or without varnish, the trend of the response to rotating speed is similar. Its Influence on the horizontal vibration is larger than that on the vertical vibration, especially in the low speed zone. This is consistent with the influence of the varnish on bearing dynamic characteristics. There is little influence of the varnish on the modal frequency. However, system stability is improved due to the increased bearing damping coefficients.
Dimensionless bearing clearance
Dimensional bearing clearance
Dimensionless varnish thickness
Circumferential angle
Journal eccentricity ratio
Journal eccentricity
Journal attitude angle
Bearing radial gap
Bearing diameter
Bearing radius
Bearing length
Bearing axial dimensionless coordinate
Dimensionless oil pressure
Dimensional oil pressure
Perturbation oil pressure
Oil temperature
Oil density
Oil viscosity
Oil viscosity coefficient
Specific heat capacity
Journal velocity
Bearing loads in horizontal and vertical direction
Bearing stiffness coefficients
Bearing damping coefficients
Bearing equivalent stiffness
Critical whirling ratio
Rotating speed
Logarithmic decrement rate
System mass, stiffness, and gyroscopic/damping matrices
Degree of freedom vector
External force vector
System eigenvalues
System eigenvectors
Amplitude of displacement vector
Amplitude of the forces vector
Real part of variable
Imaginary part of variable.
The authors declare that there are no conflicts of interest regarding the publication of this paper.