Stability and resonance conditions of elementary fractional transfer functions

Elementary fractional transfer functions are studied in this paper. Some basic properties of elementary transfer functions of the first kind are recalled. Then, two main results are presented regarding elementary fractional transfer functions of the second kind, written in a canonical form and characterized by a commensurate order, a pseudo-damping factor, and a natural frequency. First, stability conditions are established in terms of the pseudo-damping factor and the commensurate order, as a corollary to Matignon’s stability theorem. They extend the previous result into conditions that are simpler to check. Then, resonance conditions are established numerically in terms of the commensurate order and the pseudo-damping factor and give interesting information on the frequency behavior of fractional systems. It is shown that elementary transfer functions of the second kind might have up to two resonant frequencies. Moreover, three abaci are given allowing to determine the pseudo-damping factor and the commensurate order for, respectively, a desired normalized gain at each resonance, a desired phase at each resonance, and a desired normalized first or second resonant frequency.     

Self-bonding of PEEK for active medical implants applications

In an effort to select the best possible medical grade of polyether ether ketone (PEEK) for active medical implants application, it was necessary to inspect surface thermodynamic properties of different grades and correlate with self-bonding (autohesion) strength. Autohesion is the process of choice for encapsulating active medical implants made of PEEK. Temperature modulated DSC was used to investigate crystallinity and thermal events of range of medical grade PEEK (semi-crystalline, amorphous, semi-crystalline with amorphous surface, minerals and black masterbatch filled). Lab shear test was used to measure autohesive forces between PEEK samples pressed at moderate temperature (200 °C) and pressure. Samples with higher mobile amorphous region (MAF) and lower degree of crystallinity (W_c) resulted in higher autohesivce bonding strength. However, semi crystalline PEEK with surfaces that showed high MAF and low W_c resulted in higher autohesive bonding strength when compared with crystalline samples. The presence of fillers (minerals and black masterbatch) in the crystalline structure doubled the autohesive bonding strength values of the semi-crystalline sample. The presence of large crystalline region and a larger portion of the rigid amorphous region acted negatively on autohesion strength. Semi-crystalline PEEK with a special manufacturing procedure to produce amorphous surface produced the best choice among the PEEK grades. This grade have the desired thermodynamical properties in the bulk while exhibiting best surface adhesion strength.