One of the critical characteristics in a brake pad is its deformation when subjected to compressive loads. This deformation is called compressibility, which can be obtained quantitatively through compression cycles performed by a specific test bench. However, such testing is costly and long enough not to meet the demand of manufacturers of friction materials.
To overcome this difficulty, this work presents regressions for the estimation of compressibility through the natural frequencies of the pads, since they can be obtained quickly and at low cost through a simple modal analysis. The theoretical basis for the correlation between compressibility and natural frequencies includes the theory of elasticity - which defines an inverse relationship between strain and stiffness - and the theory of vibrations, which defines the natural frequencies of a mechanical system as a function of its mass matrices and stiffness. Since the dependent variable (compressibility) and explanatory variable (natural frequency) are linked to stiffness, it is theoretically plausible to direct estimative.
As additional explanatory variables, in addition to the experimental data of natural frequencies, the work uses the mass values and the temperature during the natural frequency measurement to improve the regression models.