Brake Squeal Prediction Through Multi-Mode Instability Analysis
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Solution Overview
Problem
Current methods for predicting squeal instability in brake systems, such as the CEA method, are either over- or under-predictive and fail to identify all unstable modes, and do not provide information on vibration levels and excitation frequencies, making it difficult to accurately anticipate and mitigate squealing noise in brake systems.
Innovation Solution
A method that identifies N unstable modes around a static equilibrium point, models the brake system using a linear model with linearized non-linear forces, simulates excitation by imposing displacements as a linear combination of modal shapes, calculates the evolution of complex eigenvalues over time, and identifies squeal instabilities based on these calculations, allowing for the detection of unstable modes and their participation in the dynamic regime.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of operation
If the CEA method is used to identify unstable modes, then the implementation is simple and results are easy to analyze, but the method is over- or under-predictive and fails to identify all unstable modes present in the dynamic response
Solution Approach 1:
The patent combines the CEA method with the MASA method to create a hybrid approach. The CEA method identifies initial unstable modes, while the MASA method supplements this by detecting additional unstable modes that CEA misses, particularly those arising from nonlinear interactions. This merging resolves the contradiction by maintaining the simplicity of CEA while adding the precision of MASA for comprehensive mode identification.
Solution Approach 2:
The patent introduces an intermediary criterion based on the dynamic response analysis that acts as a mediator between the CEA and MASA methods. This intermediary criterion filters and validates the unstable modes identified by both methods, eliminating false positives from CEA and confirming the relevance of modes identified by MASA, thereby improving overall accuracy without sacrificing the ease of implementation.
2Measurement precision
If the MASA method is used to provide complementary analysis, then approximation of dynamic response is obtained, but the analysis is carried out mode by mode and cannot account for couplings between different instabilities
Solution Approach 1:
The patent merges the individual mode-by-mode MASA analyses into a comprehensive multi-mode analysis framework. This framework simultaneously considers all identified unstable modes and their interactions, accounting for couplings between different instabilities that single-mode analyses miss. The unified approach maintains the precision of MASA while reducing overall complexity through systematic integration.
3Measurement precision
If a single-mode MASA approach is used, then possible unstable modes are identified, but their participation in the global dynamic response cannot be evaluated
Solution Approach 1:
The patent implements a feedback mechanism where the dynamic response analysis provides information about the actual participation and importance of each unstable mode. The results from the multi-mode MASA analysis feed back into the evaluation process, allowing the identification of which modes significantly contribute to the global squeal response and which can be neglected, providing both identification and participation evaluation.
Data Source
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AI summary
The subject of the present invention is a method for predicting squeal instabilities for a friction surface of a brake system, the method being implemented by computer and comprising: identifying (500) N unstable modes around a static equilibrium point, the unstable modes being defined respectively by N frequencies and N initial eigenvalues of N modes of the brake system; modeling (500) the brake system with a linear model in which non-linear forces are linearized with respect to displacement and speed in the degrees of freedom of the brake system; simulating (510) an excitation of the brake system by imposing a movement in said degrees of freedom, the imposed movement taking the form of a linear combination of N modal deformations, a modal deformation corresponding to an unstable mode and being defined by a variable-level modal amplitude and one frequency among the N frequencies; computing (520-570) a variation in at least one complex eigenvalue of at least one state matrix of the linear model when the level of a modal amplitude of at least one modal deformation varies.