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The general least squares model for milling process state term is presented. A discrete map for milling stability analysis that is based on the third-order case of the presented general least squares milling state term model is first studied and compared with its third-order counterpart that is based on the interpolation theory. Both numerical rate of convergence and chatter stability results of the two maps are compared using the single degree of freedom (1DOF) milling model. The numerical rate of convergence of the presented third-order model is also studied using the two degree of freedom (2DOF) milling process model. Comparison gave that stability results from the two maps agree closely but the presented map demonstrated reduction in number of needed calculations leading to about 30% savings in computational time (CT). It is seen in earlier works that accuracy of milling stability analysis using the full-discretization method rises from first-order theory to second-order theory and continues to rise to the third-order theory. The present work confirms this trend. In conclusion, the method presented in this work will enable fast and accurate computation of stability diagrams for use by machinists.

Surface energetics effects on the mechanical strength of fibre reinforced polymer matrix been studied employed the manual scraper mechanism in extracting fibre from plantain pseudo-stem and was treated with nine different treatments. Cylindrical shape mould was prepared for mechanical test samples with continuous and unidirectional aligned fibres. Two probe liquids; water and glycerol were used in contact angle measurement for all the treated and untreated samples. The contact angle data was used for the interfacial energetics computations using Neumann and Fowkes models and the mathematical analysis were carried out using Matlab software tools. van der Waals notion of particle-particle interaction was employed to explain the physiochemical properties such as the surface interfacial energies. The average value for the interfacial free energy of adhesion for fibre-water and fibre-glycerol are -10mJ/m2 and -16MJ/m2 respectively signifying attractive van der Waal forces. The tensile test results unveil that the average value for treated fibres is greater than the average value of 171.29N/mm2 for untreated fibre except for potassium permanganate and phosphoric acid. These results reveal that an increase in tensile strength leads to an increase in the interfacial surface energy of adhesion. The treated fibres show a significant increase in interfacial surface energy and change in free energy of adhesion which suggests a better bonding mechanism of interaction between the fibre and matrix except for phosphoric acid which reveals otherwise, it may be as a result of the chemical chopped off the fibre during the treatment. The average strain rate of about 0.003 per seconds, 0.002 per seconds and 0.005 per seconds were deduced from the treated Mercerization, Acetone and MEKP respectively which reveals the lower strain rate as compared to the untreated fibre of 0.008 per seconds. The negative strain rate for the potassium permanganate and phosphoric acid was found to be -0.002 and -0.001 respectively reveals that the treatments will debond faster than other treated fibres..

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