Orthonormal Basis Function Based Transient Modeling for Boring Tool Degradation Monitoring

This paper presents the investigation of modeling the interaction between the boring tool and work-piece using orthonormal basis function method. The transient response during such interaction can be considered as step response of a higher order system with lightly damped modes. The response profile changes throughout the life span of a boring tool. Obtaining a parametric model will be the base for the model-based diagnosis and prognosis for the boring tool. Two basic orthonormal function kernels, Kautz and Laguerre, have been studied. The steepest descent method was applied to search for the pole determination. The least mean square method was used to find the optimal model coefficients. The modeling results showed that Kautz and Laguerre function kernels are viable for modeling the transient response for boring tool vibration. The obtained model can be further for applying the parametric methods of fault diagnosis and remaining-life prediction.