Introduction: Bearing Optimization Approach

Hydrodynamic plain bearings play a crucial role in the overall reliability, vibration, and performance of rotary bearing systems. High-performance rotating machines operate at high speeds and subject bearings to significant static and dynamic loads. Consequently, bearing modeling must accurately simulate physical effects. However, the increasing complexity and demanding applications of bearings pose challenges for engineers striving to develop reliable designs.

One critical aspect of bearing design is optimizing the bearing clearance to prevent metal-to-metal contact, especially under heavy loading. This optimization is closely linked to the selection of the minimum oil film thickness (MOFT), which becomes a limiting factor during the process. Another limitation to consider is the maximum allowable level of bearing loading (eccentricity).

The variable parameters that can be considered in the optimization process are as follows:

• Bearing clearance (Cb)
• Radius (R)
• Bearing length (L)
• Bearing grooves positions
• Oil supply temperature (Tin)
• Oil viscosity (Visc)
• Load factor (Load_f)

 

­Objective functions and constraints:

• Minimum Power loss (Nfr)
• Minimal allowable oil film thickness (MOFT)
• Maximum allowable level of bearing loading (E)

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Since bearings are integral to the rotor system, the next optimization step involves analyzing the rotor dynamics simulation for a rotor-bearing system. This analysis ensures that resonances are avoided, and sufficient margins are provided to separate critical speeds from the operating speed.

Analysis of Results During Bearing Calculation Optimization Procedure

In most cases, analyzing the results requires striking a balance between durability and performance. Scientifically, this means meeting the criteria and constraints while achieving the best performance from the available options. For bearings of this type, clearance has the most significant influence. Therefore, a graphical display of various parameters relative to clearance, such as the charts from Figure 2-4, is commonly used to analyze the results.

With this method of analysis, it is essential to simultaneously monitor and compare the parameters as they pass different criteria on various graphs and bring them together for a comprehensive evaluation.

When analyzing the results in the optimization process, another approach is to display all critical results simultaneously. However, a direct comparison can be challenging due to significant differences in dimensions, making it difficult to exclude results that don’t meet the criteria. To address this, a proposed approach involves normalizing the parameters relative to their maximum allowable values.

For instance, in our example, friction losses have a maximum allowable value of 200 W. Therefore, we divide all obtained values in this category by 200, resulting in acceptable values ranging from “0” to “1.” Any value above “1” indicates that the friction losses criterion is not met. Similarly, we normalize the values of eccentricity, which characterizes the bearing’s degree of loading. Taking a value of 0.8, any normalized value above “1” implies exclusion from further consideration for that particular set of variable parameters.

Figure 5 displays the results after normalization, along with the clearance value in “mm” (which cyclically varies from 0.15 to 0.35 mm in our example). To incorporate Minimum Oil Film Thickness (MOFT) into the results, we transform them by shifting the values by the minimum allowable value (40um) and dividing by the maximum value obtained. This ensures values failing the film thickness criterion are below the axis, while all valid values remain in the range from 0 to 1. Additionally, this display approach allows for qualitative comparisons, visually highlighting how each value compares to the entire range’s maximum/minimum.

By normalizing the results, we can now simultaneously analyze all controlled variables on one graph (Figure 6) and exclude cases where at least one criterion is not met. Among the results, cases 5, 6, 7, 11, 12, 13, 17, and 18 meet all the criteria. From these cases, we need to select the most optimal value for our specific scenario. Case #7 stands out with the lowest friction losses and high loading efficiency, making it a prime candidate for further testing in rotary dynamics.

Sometimes, varying different parameters may lead to approximately the same results in terms of the optimal value search criterion. However, in practice, this places the responsibility on the bearing engineer to determine which of the several possible parameter sets to utilize. Therefore, conducting a more detailed analysis of the results becomes crucial.

The entire process, starting from organizing an experiment to obtaining and analyzing results, can be efficiently carried out using the AxSTREAM ION software package. This software allows for full automation of the process, enabling control over any parameter, criterion, and limitation (see Figure 7). Furthermore, it facilitates seamless transfer and calculation in specialized calculation complexes, such as AxSTREAM Bearing or AxSTREAM Rotor Dynamics, which are tailored to specific tasks. Additionally, the project itself takes the form of a block diagram (see Figure 8), offering easy scalability and the option to supplement it. For example, the results of bearing optimization can be automatically transferred to the rotor dynamics analysis module. This integrated approach streamlines the entire engineering process and ensures comprehensive and efficient analyses.

Carrying out numerical experiments on bearing calculations can significantly enhance the design results by enabling a deeper analysis of various initial parameters. This approach sheds light on the stability of the obtained optimal results, explores alternative possibilities, and determines the performance gains resulting from changes in different parameters. By considering the problem of calculating bearings in conjunction with rotor dynamics, this method contributes to improving bearing characteristics.

Moreover, the proposed approach of normalizing and analyzing results extends beyond bearings, finding applicability in a broader context. It allows for the simultaneous analysis of multiple variables with restrictions, offering valuable insights into various engineering scenarios.

By adopting such an experimental approach and utilizing advanced tools like the AxSTREAM software platform, engineers can make informed decisions, achieve better design outcomes, and optimize the performance of complex systems involving bearings and other critical components. To learn more about the tools used in this blog, request a trial.