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
Polypropylene(PP)with different contents of the second generation hyperbranched polyester(HBP)is prepared by melt blending method.The non-isothermal crystallization kinetics of PP and PP/HBP blends is investigated und...Polypropylene(PP)with different contents of the second generation hyperbranched polyester(HBP)is prepared by melt blending method.The non-isothermal crystallization kinetics of PP and PP/HBP blends is investigated under differential scanning calorimetry(DSC).The Mo equation is used to analyze the DSC data.The results show that the Mo theory is suitable for crystallization kinetics of the blends.Fast cooling rate is not good for crystallizing and nucleating.The values of half crystallization time(t1/2),crystallization enthalpy(ΔHc)and temperature range(ΔT)of PP/HBP blends decrease when HBP is added.The required cooling rate of PP is higher than that of PP/HBP blends in order to reach the same relative crystallinity.Crystallization rate increases with the addition of HBP.The crystallization rate reaches a maximum when the content of HBP is 5%.In addition,the activation energies of PP and PP/HBP blends are calculated by Kissinger equation,revealing that the content of HBP has a little effect on the crystallization activation energy.展开更多
In the calculation of the collision probability between space objects, the assumption of linear relative motion is generally adopted to simplify the problem because most encounters are at high relative velocity. Never...In the calculation of the collision probability between space objects, the assumption of linear relative motion is generally adopted to simplify the problem because most encounters are at high relative velocity. Nevertheless, the assumption is no longer valid for encounters at extremely low velocities, and a new algorithm is urgently needed for computing collision probability for space objects having nonlinear relative motion. In this particular case, the direction associated with relative velocity is reintroduced for integration. The different integral limits would lead to the variations of probability and integral time. Moreover, the application scope of this new algorithm is also presented. Since the nonlinear effect is only significant in some certain situations, the new algorithm needs to be considered only in such certain situations. More specifically, when space objects in circular orbits encounter with a tiny inclined angle (the extreme situation), the new algorithm can derive much more accurate collision probability than the linear method, that is to say, the linearity assumption involved in general collision probability formulation is not adequate anymore. In addition, the deviation of the probability derived by the linear method (linear collision probability) from that derived by the nonlinear method (nonlinear collision probability) also weakly depends on the relative distance and combined covariance, and essentially depends on their ratio.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.
基金Supported by the Youths Foundation of Wuhan Institute of Technology(Q200902)the Graduate Innovative Fund of Wuhan Institute of Technology(CX201101)
文摘Polypropylene(PP)with different contents of the second generation hyperbranched polyester(HBP)is prepared by melt blending method.The non-isothermal crystallization kinetics of PP and PP/HBP blends is investigated under differential scanning calorimetry(DSC).The Mo equation is used to analyze the DSC data.The results show that the Mo theory is suitable for crystallization kinetics of the blends.Fast cooling rate is not good for crystallizing and nucleating.The values of half crystallization time(t1/2),crystallization enthalpy(ΔHc)and temperature range(ΔT)of PP/HBP blends decrease when HBP is added.The required cooling rate of PP is higher than that of PP/HBP blends in order to reach the same relative crystallinity.Crystallization rate increases with the addition of HBP.The crystallization rate reaches a maximum when the content of HBP is 5%.In addition,the activation energies of PP and PP/HBP blends are calculated by Kissinger equation,revealing that the content of HBP has a little effect on the crystallization activation energy.
基金supported by the National Natural Science Foundation of China (Grant No. 11203085)
文摘In the calculation of the collision probability between space objects, the assumption of linear relative motion is generally adopted to simplify the problem because most encounters are at high relative velocity. Nevertheless, the assumption is no longer valid for encounters at extremely low velocities, and a new algorithm is urgently needed for computing collision probability for space objects having nonlinear relative motion. In this particular case, the direction associated with relative velocity is reintroduced for integration. The different integral limits would lead to the variations of probability and integral time. Moreover, the application scope of this new algorithm is also presented. Since the nonlinear effect is only significant in some certain situations, the new algorithm needs to be considered only in such certain situations. More specifically, when space objects in circular orbits encounter with a tiny inclined angle (the extreme situation), the new algorithm can derive much more accurate collision probability than the linear method, that is to say, the linearity assumption involved in general collision probability formulation is not adequate anymore. In addition, the deviation of the probability derived by the linear method (linear collision probability) from that derived by the nonlinear method (nonlinear collision probability) also weakly depends on the relative distance and combined covariance, and essentially depends on their ratio.
