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Mathematical modeling of flexural behavior of rotary nickel-titanium endodontic instruments
Danny Low1, Angela W L Ho, Gary S P Cheung
1Department of Endodontics, Faculty of Dentistry, The University of Hong Kong, Pokfulam, Hong Kong. dannylow@scientist.com
Abstract:
The aim of the present study was to establish a mathematical model to characterize the flexural behavior of nickel-titanium (NiTi) rotary instruments. The bending behavior of ProFile (0.06 and 0.04 tapers), K-3 (0.06 taper), Quantec (0.04 taper) with tip size of ISO 25, was assessed by pressing the tip of the static rotary file against a smooth, freely movable, glass surface. The deflected instrument was photographed digitally, and the deflection path was digitized in software, to which data a function was fitted that best described the bending behavior of the instrument. It was found that all instruments deflected in a manner closely resembling a negative exponential function: y = A x e(-x/b). The present approach indicated that the analytical difficulties of handling the complex cross-section in tapering spirals in beam-bending theory may be circumvented by a practical and elementary curve-fitting method.
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