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Study on the influence of rotational speed on the dynamic coefficients of sliding bearings 1. Introduction In rotating machinery, nonlinear excitation forces such as oil film force and sealing force exist in the roto
1. Introduction
In rotating machinery, nonlinear excitation forces such as oil film force and sealing force exist in the rotor bearing system, leading to unstable factors in the system. The parameter changes of bearings have a significant impact on the dynamic characteristics of the rotor. As bearings are the main source of damping, they control the response of the rotor. The stiffness and damping of bearings also affect the critical speed and stability of the rotor bearing system. Therefore, when conducting in-depth research on the dynamics of rotor bearing systems, it is necessary to consider the role of bearings on the system.
This article takes sliding bearings as the research object and derives the Reynolds equation of sliding bearings based on the fluid dynamic lubrication control equation. Using DyRoBeS software, the oil film pressure that determines the bearing capacity of bearings was calculated and compared. The eccentricity, Z-small oil film thickness, Z-large oil film pressure, friction power consumption, temperature rise, critical journal mass, stiffness coefficient, damping coefficient, and other important parameters affecting the oil film characteristics and dynamic behavior of sliding bearings were analyzed and calculated at different speeds.
After analyzing the three-dimensional oil film pressure, it was found that there is a critical speed, and when the speed is lower than a certain critical value, the critical speed has a significant impact on the oil film pressure in Z.
2. Oil film force model of sliding bearings
Sliding bearings consist of a journal and a bearing shell, with the journal generally having a diameter 0.1% to 0.2% smaller than the bearing shell. There is a certain gap between the journal and the bearing shell, which allows lubricating oil to enter the gap and form an oil film. Due to the dynamic pressure of the fluid, sufficient bearing capacity is generated, and the circulating lubricating oil flows through the gap to cool down, avoiding excessive temperature and ensuring the normal operation of the bearing.
Figure 1 Static equilibrium position of the journal
Figure 2 Oil film thickness and oil wedge
Figure 1 is a static equilibrium position diagram of the journal, where o is the center of the bearing shell, o1 is the center of the journal, W is the static load, Ω is the journal speed, e is the eccentricity, C is the radial clearance of the bearing, eccentricity ε=e/C, psi is the offset angle, h is the oil film thickness, and Zeta is the clockwise angle from the y-axis. The static equilibrium position is determined by the eccentricity and offset angle.
The thickness of the oil film and the oil wedge are shown in Figure 2. The thickness of the Z large oil film and the thickness of the Z small oil film in the figure are:
The thickness of the oil film at any position is:
The Reynolds equation is the fundamental equation for bearing oil film analysis:
Among them, R is the journal radius, p is the oil film pressure, η is the lubricating oil viscosity, and z is the axial coordinate of the bearing shell.
The steps of bearing analysis are generally as follows: solve the pressure distribution p (Zeta, z) of the oil film through the Reynolds equation, and then calculate the static characteristic coefficients (Z small oil film thickness, Z large oil film pressure, friction power consumption, lubricating oil flow rate, temperature rise, bearing capacity, journal motion trajectory, etc.) and dynamic characteristic coefficients of the bearing.
3. Research on the influencing factors of static and dynamic characteristic coefficients of sliding bearings
3.1 Establishment of sliding bearing model
Bearing length l=125mm, bearing radius R=125mm, journal clearance h=0.5mm, lubrication viscosity coefficient μ=47 × 10-3Pa/s, calculated speed 3000r/min~12000r/min, static load 500kg, modeled by DyRoBes BePerf as shown in Figure 3.
Figure 3 Bearing Model
3.2 Study on the Influence of Rotational Speed on the Static and Dynamic Characteristics of Sliding Bearings
Figure 4: The Influence of Rotational Speed on the Dynamic Characteristics of Bearings
Figure 4 shows the influence of rotational speed on the dynamic characteristics of bearings, including the effects of rotational speed on eccentricity, Z-small oil film thickness, Z-large oil film pressure, frictional power consumption, temperature rise, critical journal mass, stiffness coefficient, and damping coefficient.
Figure 4 (a) shows the effect of shaft neck speed on eccentricity when there is a fixed load W and the shaft neck speed increases from 1000r/min to 12000r/min. It indicates that as the speed increases, the eccentricity decreases and the shaft neck center O 'gradually tends towards the bearing shell center O. Figure 4 (b) shows the effect of speed on the thickness of the Z small oil film. As the speed increases, the thickness of the Z small oil film increases because the shaft neck center moves towards the bearing shell center, resulting in an increase in the thickness of the Z small oil film; Figure 4 (c) shows the effect of rotational speed on the Z-oil film pressure. It can be seen from the figure that as the rotational speed increases from 1000r/min to 4800r/min, the Z-oil film pressure rapidly decreases. When the rotational speed exceeds 4800r/min, the Z-oil film pressure does not change much; Figure 4 (d) shows the effect of rotational speed on friction loss. It can be seen from the figure that as the rotational speed increases, the friction loss gradually increases, and the frequency of increase also increases.
Figure 4 (e) shows the effect of rotational speed on the critical journal mass. As the rotational speed increases from 1000r/min to 4800r/min, the critical journal mass rapidly decreases. However, when the rotational speed exceeds 4800r/min, there is little change in the critical journal mass; Figure 4 (f) shows the variation of inlet temperature, operating temperature, and Z-temperature with rotational speed. It can be seen from the figure that the working temperature of the bearing increases with the increase of rotational speed; Figure 4 (g) shows the values of main stiffness and main damping at speeds ranging from 1000r/min to 12000r/min. It can be seen from the figure that the main stiffness and main damping increase significantly when the speed is less than 3000r/min, and do not change significantly when the speed is greater than 3000r/min; Figure 4 (h) shows the values of cross stiffness and cross damping at speeds ranging from 1000r/min to 12000r/min. The dashed line in the figure represents negative values, Kxy increases with increasing speed, Kyx increases negatively with increasing speed, Cxy and Cyx are equal and decrease with increasing speed.
Figure 5 Neck Movement Trajectory
Figure 5 shows the trajectory of the journal movement. It can be observed that as the rotational speed increases from 1000r/min to 12000r/min, the center of the journal moves towards the center of the bearing shell.
Figure 6 shows the two-dimensional oil film pressure distribution at different speeds. From Figures 6 (a) to 6 (l), it can be seen that the center of the shaft neck changes with the increase of speed. When the speed is 1000r/min, the thickness of the Z small oil film is 0.1832mm. When the speed increases to 5000r/min, the thickness of the Z small oil film increases to 0.4283mm. When the speed increases to 12000r/min, the thickness of the Z small oil film increases to 0.4794mm. At the same time, there are significant changes in the oil film pressure distribution and amplitude.
In order to further obtain the distribution of oil film pressure, this article calculated a total of 12 three-dimensional oil film pressure analyses from a speed of 1000r/min to a speed of 12000r/min, and obtained corresponding top and slice views of the three-dimensional oil film pressure, as shown in Figure 7.
Figure 6 Two dimensional oil film pressure distribution at different speeds
Figure 7 Three dimensional oil film pressure distribution at different rotational speeds
As shown in Figure 7 (a), when the speed is 1000r/min, the eccentricity is 0.6335 and the Z-large oil film pressure is 44.278kPa; Figure 47 (e) shows the distribution of Z-large oil film pressure at a speed of 5000r/min. At this time, the eccentricity is 0.1434, and it can be seen from the figure that the Z-large oil film pressure is 30.7145kPa; Figure 7 (h) shows the distribution of Z-large oil film pressure at a speed of 8000r/min. At this time, the eccentricity is 0.0739, and it can be seen from the figure that the Z-large oil film pressure is 30.4314kPa; Figure 7 (l) shows that at a speed of 12000, the eccentricity is 0.0413 and the Z-large oil film pressure is 30.3126 kPa.
Based on the above analysis, it can be concluded that as the rotational speed increases, the oil film pressure of Z decreases. There is a critical speed of 5000r/min. When the speed is less than 5000r/min, increasing the speed will cause significant changes in the oil film pressure of Z; When the speed is greater than 5000r/min, the eccentricity is less than 0.1. Increasing the speed further will only cause a slight decrease in eccentricity, and there will also be a slight decrease in Z oil film pressure.
The reason for the critical speed of 5000r/min for Z-large oil film pressure is that the larger the eccentricity, the greater the oil film pressure, and the larger the speed, the smaller the eccentricity. Therefore, an increase in speed will lead to a decrease in Z-large oil film pressure. For the model in this article, the eccentricity is 0.6335 when the speed is 1000r/min, but it rapidly decreases to 0.0739 when the speed increases to 5000r/min. The change in speed reduces the eccentricity by 0.5596, while when the speed increases from 5000r/min to 12000r/min, the eccentricity only decreases by 0.0326. Eccentricity is an important influencing factor of Z-large oil film pressure, and a large change in eccentricity will cause a large oil film pressure. Conversely, a small change in eccentricity will also cause a small change in Z-large oil film pressure. The analysis results are consistent with the calculation results in this article.
4. Conclusion
This article establishes a dynamic model of sliding bearings and solves it. The study investigated the influence of rotational speed on the dynamic characteristics of sliding bearings, and obtained the research on the influencing factors of rotational speed on eccentricity, Z-small oil film thickness, Z-large oil film pressure, frictional power consumption, temperature rise, critical journal mass, stiffness coefficient, damping coefficient, and two-dimensional and three-dimensional oil film pressure. When analyzing the three-dimensional oil film pressure, it was found that there is a critical value. When the speed is below a certain critical value, the critical speed has a greater impact on the Z-large oil film pressure. When the speed is above this critical value, the critical speed has little effect on the Z-large oil film pressure.
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