Conformal mapping modeling of metal plastic deformation and die cavity in special-shaped extrusion

With the help of Complex Function Mapping studied results, the analysis function of Conformal Mapping is set up. Since the complicated three dimension’s deformation problems are transferred into two dimension problems, both the stream function and strain ratio field are analyzed in the metal plastic deformation. Using the upper-bound principles, the theory of metal deformation and die cavity optimized modeling is established for random special-shaped product extrusion. As a result, this enables the realization of intelligent technique target in the die cavity of CAD/CAM integration.

Automatic testing system design and data analysis of permafrost temperature in Qinghai-Tibet Railway

Aimed at the characteristics of permafrost temperature influencing the safety of Qinghai-Tibet Railway and its on-line testing system, comparing the achievement of permafrost study nationwide with those worldwide, an automatic testing system of permafrost temperature, containing a master computer and some slave computers, was designed. By choosing high-precise thermistors as temperature sensor, designing and positioning the depth and interval of testing sections, testing, keeping and sending permafrost temperature data at time over slave computers, and receiving, processing and analyzing the data of collecting permafrost temperature over master computer, the change of the permafrost temperature can be described and analyzed, which can provide information for permafrost railway engineering design. Moreover, by taking permafrost temperature testing in a certain section of Qinghai-Tibet Railway as an instance, the collected data of permafrost temperature were analyzed, and the effect of permafrost behavior was depicted under the railway, as well as, a BP model was set up to predict the permafrost characteristics. This testing system will provide information timely about the change of the permafrost to support the safety operation in Qinghai-Tibet Railway.

Conformal optimal design and processing of extruding die cavity

Aimed at the optimal analysis and processing technology of die cavity of special-shaped products extrusion, by numerical analysis of trigonometric interpolation and Conformal Mapping theory, on the non-circle cross-section of special-shaped products, the conformal mapping function can be set up to translate the cross-section region into unit dish region, over numerical finite interpolation points between even and odd. Products extrusion forming can be turned into two-dimension problem, and plastic stream function can be deduced, as well as the mathematical model of the die cavity surface is established based on deferent kinds of vertical curve. By applying Upper-bound Principle, the vertical curves and related parameters of die cavity are optimized. Combining with electrical discharge machining (EDM) process and numerical control (NC) milling machine technology, the optimal processing of die cavity can be realized. Taking ellipse-shaped products as an instance, the optimal analysis and processing of die cavity including extruding experiment are carried out.

Similar extrusion and mapping optimization of die cavity modeling for special-shaped products

Aimed at the modeling issues in design and quick processing of extruding die for special-shaped products, with the help of Conformal Mapping theory, Conformal Mapping function is determined by the given method of numerical trigonometric interpolation. Three-dimensional forming problems are transformed into two-dimensional problems, and mathematical model of die cavity surface is established based on different kinds of vertical curve, as well as the mathematical model of plastic flow in extruding deformation of special-shaped products gets completed. By upper bound method, both vertical curves of die cavity and its parameters are optimized. Combining the optimized model with the latest NC technology, NC Program of die cavity and its CAM can be realized. Taking the similar extrusion of square-shaped products with arc radius as instance, both metal plastic similar extrusion and die cavity optimization are carried out.

Surface quality of extruding metal special-shape products and frictional behavior in optimized die cavity

With the help of Complex Function Mapping theory, the complicated three-dimensional deformation problems are transferred into two-dimensional problems, and the function of strain ratio field is analyzed in the metal plastic extruding deformation. Taking the strain-hardening effect of metal deformation into account, the relationship between friction behavior and optimized mathematical model is analyzed by the numerical analysis friction energy dissipation function. As a result, the method of lowering the material hardening and decreasing the reduction ratio over multi-procedures can be used to improve the surface quality of metal special-shape extrusion products.

Conformal analysis of fundamental frequency of vibration of simple-supported elastic ellipse-plates with concentrated substance

Aimed at calculating the fundamental frequency of vibration of special-shaped, simple-supported elastic plates, Conformal Mapping theory is applied, and the mathematical method of trigonometric interpolation with interpolation points mutual iterative between odd and even sequences in boundary region is provided, as well as the conformal mapping function which can be described by real number region between complicated region and unit dish region is carried out. Furthermore, in the in-plane state of constant stress, vibrating function is completed by unit dish region method for simple-supported elastic plates with concentrated substance of complicated vibrating region, and the coefficient of fundamental frequency of the plate is analyzed. Meanwhile, taking simple-supported elastic ellipse-plates as an example, the effects on fundamental frequency caused by eccentric ratio, the coefficient of constant in-plane stress, as well as the concentrated substance mass and positions are analyzed respectively.

Mapping analysis of vibrating fundamental frequency for simple-supported elastic rectangle-plates with concentrated mass

By conformal mapping theory, a trigonometric interpolation method between odd and even sequences in rectangle boundary region was provided, and the conformal mapping function of rectangle-plate with arc radius between complicated region and unite dish region was carried out. Aiming at calculating the vibrating fundamental frequency of special-shaped, elastic simple-supported rectangle-plates, in the in-plane state of constant stress, the vibration function of this complicated plate was depicted by unit dish region. The coefficient of fundamental frequency was calculated. Whilst, taking simple-supported elastic rectangle-plates with arc radius as an example, the effects on fundamental frequency caused by the concentrated mass and position, the ratio of the length to width of rectangle, as well as the coefficient of constant in-plane stress were analyzed respectively.