Rotary Machine Bearing Spring Constant Calculation
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Solution Overview
Problem
Existing finite element models of rolling bearings in rotary machines suffer from errors in spring constant calculations, leading to inaccuracies in determining natural frequency and other characteristics, and require significant computational workload.
Innovation Solution
Model the rolling element as a one-dimensional elastic body with rigid elements at contact regions, using Hertz theory to calculate spring constants, and adjust for spring constants of inner and outer ring surfaces to reduce errors and workload.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If a simple finite element model approximating the rolling element to one spring element is used, then the workload is reduced, but the spring constant accuracy deteriorates leading to errors in natural frequency and other characteristics
Solution Approach 1:
The patent introduces rigid elements as intermediary components connecting the rolling element to the inner and outer rings. These rigid elements serve as mediators that transmit forces while allowing the rolling element to be modeled as a simple spring, thus maintaining computational efficiency while improving accuracy of spring constant calculation through the specific configuration shown in the figures
Solution Approach 2:
The patent changes the modeling parameters by representing the rolling element as a spring element with specific stiffness characteristics rather than a complex 3D solid model. This parameter change simplifies the finite element model while the spring constant is carefully calibrated to reflect actual rolling element behavior, resolving the contradiction between model simplicity and accuracy
2Measurement precision
If a precise finite element model divided by fine mesh is used, then the spring constant accuracy is improved, but the computational load and workload increase significantly
Solution Approach 1:
The patent segments the bearing model into distinct components: inner ring, outer ring, rolling element, and rigid elements. The rolling element is further segmented into a spring element representation. This segmentation allows each component to be modeled at the appropriate level of detail, with the rolling element using a simplified spring model rather than fine mesh, thus reducing computational load while maintaining accuracy
Solution Approach 2:
The patent uses a simplified spring element representation for the rolling element instead of a computationally expensive fine-mesh 3D model. This 'cheap' modeling approach uses fewer computational resources while still providing accurate spring constant values, effectively trading model complexity for computational efficiency
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
Reduces errors in determining rotary machine characteristics while minimizing computational effort by simplifying the modeling of rolling elements, thus improving accuracy and efficiency in calculating natural frequency and other properties.
Implementation Method 1
calculating a first spring constant between the rolling element and the first bearing ring by using Hertz theory; calculating a second spring constant between the rolling element and the second bearing ring by using the Hertz theory
Data Source
Figure 1
Figure 2(A)~2(B)
Figure 3(A)~3(B)
AI summary
A determination method for a characteristic of a rotary machine includes: calculating a first spring constant between a rolling element (15) and a first bearing ring (IIA); calculating a second spring constant between the rolling element (15) and a second bearing ring (12A); calculating a third spring constant of a first finite element model (11M); calculating a fourth spring constant of a second finite element model (12M); calculating a spring constant of a third finite element model (15M) based on the first spring constant to the fourth spring constant; and determining a characteristic of the rotary machine by using the calculated spring constant of the third finite element model (15M).