The theoretical model of axial ultrasonic vibration grinding force is built on the basis of a mathematical model of cutting deforming force deduced from the assumptions of thickness of the undeformed debris under Rayl...The theoretical model of axial ultrasonic vibration grinding force is built on the basis of a mathematical model of cutting deforming force deduced from the assumptions of thickness of the undeformed debris under Rayleigh distribution and a mathematical model of friction based on the theoretical analysis of relative sliding velocity of abrasive and workpiece. Then, the coefficients of the ultrasonic vibration grinding force model are calculated through analysis of nonlinear regression of the theoretical model by using MATLAB, and the law of influence of grinding depth, workpiece speed, frequency and amplitude of the mill on the grinding force is summarized after applying the model to analyze the ultrasonic grinding force. The result of the above-mentioned law shows that the grinding force decreases as frequency and amplitude increase, while increases as grinding depth and workpiece speed increase; the maximum relative error of prediction and experimental values of the normal grinding force is 11.47% and its average relative error is 5.41%; the maximum relative error of the tangential grinding force is 10.14% and its average relative error is 4.29%. The result of employing regression equation to predict ultrasonic grinding force approximates to the experimental data, therefore the accuracy and reliability of the model is verified.展开更多
In this study a mathematical model for two-dimensional pulsatile blood flow through overlapping constricted tapered vessels is presented. In order to establish resemblance to the in vivo conditions, an improved shape ...In this study a mathematical model for two-dimensional pulsatile blood flow through overlapping constricted tapered vessels is presented. In order to establish resemblance to the in vivo conditions, an improved shape of the time-variant overlapping stenosis in the elastic tapered artery subject to pulsatile pressure gradient is considered. Because it contains a suspension of all erythrocytes, the flowing blood is represented by micropolar fluid. By applying a suitable coordinate transformation, tapered cosine-shaped artery turned into non-tapered rectangular and a rigid artery. The governing nonlinear partial differential equations under the imposed realistic boundary conditions are solved using the finite difference method. The effects of vessel tapering on flow characteristics consid- ering their dependencies with time are investigated. The results show that by increasing the taper angle the axial velocity and volumetric flow rate increase and the microrota- tional velocity and resistive impedance reduce. It has been shown that the results are in agreement with similar data from the literature.展开更多
基金Project(51275530)supported by the National Natural Science Foundation of China
文摘The theoretical model of axial ultrasonic vibration grinding force is built on the basis of a mathematical model of cutting deforming force deduced from the assumptions of thickness of the undeformed debris under Rayleigh distribution and a mathematical model of friction based on the theoretical analysis of relative sliding velocity of abrasive and workpiece. Then, the coefficients of the ultrasonic vibration grinding force model are calculated through analysis of nonlinear regression of the theoretical model by using MATLAB, and the law of influence of grinding depth, workpiece speed, frequency and amplitude of the mill on the grinding force is summarized after applying the model to analyze the ultrasonic grinding force. The result of the above-mentioned law shows that the grinding force decreases as frequency and amplitude increase, while increases as grinding depth and workpiece speed increase; the maximum relative error of prediction and experimental values of the normal grinding force is 11.47% and its average relative error is 5.41%; the maximum relative error of the tangential grinding force is 10.14% and its average relative error is 4.29%. The result of employing regression equation to predict ultrasonic grinding force approximates to the experimental data, therefore the accuracy and reliability of the model is verified.
文摘In this study a mathematical model for two-dimensional pulsatile blood flow through overlapping constricted tapered vessels is presented. In order to establish resemblance to the in vivo conditions, an improved shape of the time-variant overlapping stenosis in the elastic tapered artery subject to pulsatile pressure gradient is considered. Because it contains a suspension of all erythrocytes, the flowing blood is represented by micropolar fluid. By applying a suitable coordinate transformation, tapered cosine-shaped artery turned into non-tapered rectangular and a rigid artery. The governing nonlinear partial differential equations under the imposed realistic boundary conditions are solved using the finite difference method. The effects of vessel tapering on flow characteristics consid- ering their dependencies with time are investigated. The results show that by increasing the taper angle the axial velocity and volumetric flow rate increase and the microrota- tional velocity and resistive impedance reduce. It has been shown that the results are in agreement with similar data from the literature.
