The chip flow angle(CFA)catastrophe in double-edged cutting results in a significant reduction in the cutting force,which can benefit the applications.However,established potential functions(i.e.,cutting power calcula...The chip flow angle(CFA)catastrophe in double-edged cutting results in a significant reduction in the cutting force,which can benefit the applications.However,established potential functions(i.e.,cutting power calculation functions)of mathematical models for the CFA catastrophe are presented in the form of transcendental functions with two control parameters and one state parameter,which are extremely complex.A method is proposed herein to realize the regularization of the potential functions and establish mathematical models in a standard form and with complete content for the CFA catastrophe.Using this method,the potential function of the CFA catastrophe is expanded into a k-order Taylor polynomial at each midpoint of N end-to-end equally partitioned intervals of the state parameter using the Taylor function provided in MATLAB.The potential function after piecewise Taylor expansion is transformed into the same form as the potential function of the standard cusp catastrophe model by truncating the first five terms of the Taylor polynomial and eliminating the third-order term of the state parameter with elementary transformation.Hence,the regularization of potential function is realized.Subsequently,the regularization of equilibrium surface and bifurcation set can be realized based on the conclusions of the catastrophe theory.Regularization errors of the potential function,equilibrium surface,and bifurcation set are defined to evaluate the effectiveness of this regularization method.The problem of calculating regularization errors is regarded as an optimization problem.The‘‘simulannealbnd’’function provided in MATLAB is used to solve the problem.Applying the proposed method,the regularization of a mathematical model for the CFA catastrophe established by the predecessor is completed;a mathematical model(i.e.,standard cusp catastrophe model)in a standard form and with complete content for the CFA catastrophe is established;and the corresponding regularization errors are analyzed.The regularization errors of the potential function,equilibrium surface,and bifurcation set curves are 5.4855910-4%,0.3206%,and 4.6539%,respectively.Based on the equilibrium surface and the bifurcation set curves constructed using the regularized mathematical model for the CFA catastrophe,the mechanism of the CFA catastrophe and the specific approach to render the cutting system operable in a low-energy consumption state by controlling the historical change path of the control point are analyzed.This study will promote the rational use of the CFA catastrophe.展开更多
The theoretical basis of the grinding chips thermal flow being regarded as the characteristic signal of on line identification is summarized. And on line identification of grinding burn and wheel wear based on the g...The theoretical basis of the grinding chips thermal flow being regarded as the characteristic signal of on line identification is summarized. And on line identification of grinding burn and wheel wear based on the grinding chips thermal flow is introduc展开更多
Chip-based flow-through PCR implements the PCR as a continuous process for nucleic acid analytics. The sample is transported in a winding channel through temperature zones required for denaturation, annealing and exte...Chip-based flow-through PCR implements the PCR as a continuous process for nucleic acid analytics. The sample is transported in a winding channel through temperature zones required for denaturation, annealing and extension. Main fields of application are the monitoring of continuous processes for rapid identification of contaminants and quality control as well as high throughput screening of cells or microorganisms. A modular arrangement with five heating zones for flow-through PCR is discussed and evaluated. The special heater arrangement allows the implementation of up to 40 cycles on the footprint of a microscope slide, which is placed on top ofa 5 zones heating plate. Liquid/liquid two phase flow of PCR reaction mixture and mineral oil have been applied to create a segmented flow process scheme. In that way, the developed system may provide flow-through PCR as a unit operation for the droplet based microfluidics platform. The single use of disposable devices is commonly preferred due to the sensitivity of the PCR process to contaminations. All-glass microfluidic chips and disposable chip devices, made from polycarbonate as a replication with identically geometry, have been fabricated and tested. For the first time, microchannel geometries with nearly circular profile developed by all-glass technology have been transferred to mass fabrication by injection compression molding. Both devices have been successfully applied for the detection of the tumor suppressor gene p53. Although product yield and selectivity of the amplification process do not depend on the chip material, a well defined, reliable segmented flow regime could only be realized in the all-glass chip.展开更多
基金the National Natural Science Foundation of China(Grant No.51675203).
文摘The chip flow angle(CFA)catastrophe in double-edged cutting results in a significant reduction in the cutting force,which can benefit the applications.However,established potential functions(i.e.,cutting power calculation functions)of mathematical models for the CFA catastrophe are presented in the form of transcendental functions with two control parameters and one state parameter,which are extremely complex.A method is proposed herein to realize the regularization of the potential functions and establish mathematical models in a standard form and with complete content for the CFA catastrophe.Using this method,the potential function of the CFA catastrophe is expanded into a k-order Taylor polynomial at each midpoint of N end-to-end equally partitioned intervals of the state parameter using the Taylor function provided in MATLAB.The potential function after piecewise Taylor expansion is transformed into the same form as the potential function of the standard cusp catastrophe model by truncating the first five terms of the Taylor polynomial and eliminating the third-order term of the state parameter with elementary transformation.Hence,the regularization of potential function is realized.Subsequently,the regularization of equilibrium surface and bifurcation set can be realized based on the conclusions of the catastrophe theory.Regularization errors of the potential function,equilibrium surface,and bifurcation set are defined to evaluate the effectiveness of this regularization method.The problem of calculating regularization errors is regarded as an optimization problem.The‘‘simulannealbnd’’function provided in MATLAB is used to solve the problem.Applying the proposed method,the regularization of a mathematical model for the CFA catastrophe established by the predecessor is completed;a mathematical model(i.e.,standard cusp catastrophe model)in a standard form and with complete content for the CFA catastrophe is established;and the corresponding regularization errors are analyzed.The regularization errors of the potential function,equilibrium surface,and bifurcation set curves are 5.4855910-4%,0.3206%,and 4.6539%,respectively.Based on the equilibrium surface and the bifurcation set curves constructed using the regularized mathematical model for the CFA catastrophe,the mechanism of the CFA catastrophe and the specific approach to render the cutting system operable in a low-energy consumption state by controlling the historical change path of the control point are analyzed.This study will promote the rational use of the CFA catastrophe.
文摘The theoretical basis of the grinding chips thermal flow being regarded as the characteristic signal of on line identification is summarized. And on line identification of grinding burn and wheel wear based on the grinding chips thermal flow is introduc
基金This work was funded by the German Federal Ministry of Education and Research (BMBF), reference number 16SV3529, project MINAMED.
文摘Chip-based flow-through PCR implements the PCR as a continuous process for nucleic acid analytics. The sample is transported in a winding channel through temperature zones required for denaturation, annealing and extension. Main fields of application are the monitoring of continuous processes for rapid identification of contaminants and quality control as well as high throughput screening of cells or microorganisms. A modular arrangement with five heating zones for flow-through PCR is discussed and evaluated. The special heater arrangement allows the implementation of up to 40 cycles on the footprint of a microscope slide, which is placed on top ofa 5 zones heating plate. Liquid/liquid two phase flow of PCR reaction mixture and mineral oil have been applied to create a segmented flow process scheme. In that way, the developed system may provide flow-through PCR as a unit operation for the droplet based microfluidics platform. The single use of disposable devices is commonly preferred due to the sensitivity of the PCR process to contaminations. All-glass microfluidic chips and disposable chip devices, made from polycarbonate as a replication with identically geometry, have been fabricated and tested. For the first time, microchannel geometries with nearly circular profile developed by all-glass technology have been transferred to mass fabrication by injection compression molding. Both devices have been successfully applied for the detection of the tumor suppressor gene p53. Although product yield and selectivity of the amplification process do not depend on the chip material, a well defined, reliable segmented flow regime could only be realized in the all-glass chip.
