Stream Surface Strip Element Method and Simulation of Three-Dimensional Deformation of Continuous Hot Rolled Strip

A new method,the stream surface strip element method,for simulating the three-dimensional deformation of plate and strip rolling process was proposed.The rolling deformation zone was divided into a number of stream surface(curved surface)strip elements along metal flow traces,and the stream surface strip elements were mapped into the corresponding plane strip elements for analysis and computation.The longitudinal distributions of the lateral displacement and the altitudinal displacement of metal were respectively constructed to be a quartic curve and a quadratic curve,of which the lateral distributions were expressed as the third-power spline function,and the altitudinal distributions were fitted in the quadratic curve.From the flow theory of plastic mechanics,the mathematical models of the three-dimensional deformations and stresses of the deformation zone were constructed.Compared with the streamline strip element method proposed by the first author of this paper,the stream surface strip element method takes into account the uneven distributions of stresses and deformations along altitudinal direction,and realizes the precise three-dimensional analysis and computation.The simulation example of continuous hot rolled strip indicates that the method and the model accord with facts and provide a new reliable engineering-computation method for the three-dimensional mechanics simulation of plate and strip rolling process.

Tubular limiting stream surface: “tornado” in three-dimensional vortical flow

A new physical structure of vortical flow, i.e., tubular limiting stream surface(TLSS), is reported. It is defined as a general mathematical structure for the physical flow field in the neighborhood of a singularity, and has a close relationship with limit cycles.The TLSS is a tornado-like structure, which separates a vortex into two regions, i.e., the inner region near the vortex axis and the outer region further away from the vortex axis.The flow particles in these two regions can approach to(or leave) the TLSS, but never could reach it.

Importance guided stream surface generation and feature exploration

Exploring flow features and patterns hidden behind the data has received extensive academic attention in flow visualization.In this paper,we introduce an importance-guided surface generation and exploration scheme to explore the features and their connections.The features are expressed as an importance field,which can either be derived from a scalar field or be specified as a flow pattern.Guided by the importance field,we sample a pool of seeding curves along the binormal direction and construct stream surfaces to fit the regions of high-importance values.Our scheme evaluates candidate seeding curves by collecting importance scores from the curve and corresponding streamlines.The candidate seeding curves are refined using the high-score segments to identify the optimal surfaces.Comparative visualization among different kinds of flow features across time steps can be easily derived for flow structure analysis.In order to reduce the visual complexity,we leverage SurfRiver to achieve clearer observation by flattening and aligning the surface.Finally,we apply our surface generation scheme guided by flow patterns and scalar fields to evaluate the effectiveness of the proposed tool.

Collisionless tool orientation smoothing above blade stream surface using NURBS envelope

In five-axis machining,tool orientation above a blade stream surface may lead to tool collision and a decrease in workpiece rigidity.Hence,collisionless tool orientation smoothing(TOS)becomes an important issue.On the basis of a constant scallop height tool path,the triangular facets in the faces,vertices format are constructed from cutter contact(CC)using the Voronoi incremental algorithm.The cutter location(CL)points candidate set is represented by an oblique elliptic cone whose vertex lies at CC using NURBS envelope.Whether the CL point is above its CC is judged by the dot product between the normal vector and the point on triangulation nearest to the CL point.The curvatures at CC are obtained by fitting a moving least square(MLS) quadratic patch to the local neighborhood of a vertex and calculating eigenvectors and eigenvalues of the Hessian matrix.Triangular surface elastic energy is employed as the weight in selection from the NURBS envelope.The collision is judged by NURBS surface intersection.TOS can then be expressed by selecting a CL point for each CC point and converted into a numerical control(NC)code automatically according to the postprocessor type of the machine center.The proposed method is verified by finishing of a cryogenic turboexpander impeller of air separation equipment.

Shape Control Simulation on 4-High CVC Mill

The computation model of shape and crown on 4-high CVC mill was established by combining the stream surface strip element method for analyzing three-dimensional plastic deformation of strip and the influence coefficient method for elastic deformation of rolls, and the simulation of the shape and crown control on 4-high CVC hot strip mill was conducted. The simulated results indicate that the influence of the shifting of CVC work roll on shape and crown is very large, and the shifting of work roll can be used to preset shape and crown. The influence of the bending force of work roll on shape and crown is smaller, and it is suitable to use the bending force of work roll for shape and crown adjustment on line. With the increase of strip width, the exit crown of strip increases firstly and decreases then, and the roll gap becomes smoother increasingly. Meanwhile, the transverse difference of front tension stress decreases firstly and increases then.

Complete Mill Simulation of the Rolling Process of 1660 mm Hot Strip Continuous Mills

The three-dimensional plastic deformations of strip are analyzed using the stream surface strip element method, the elastic deformations of rolls are analyzed using the influence coefficient method, the analyzing and computing model of shape and crown of 4-high mill was established by combining them, and the rolling process of 1660 mm hot strip continuous mills was simulated. The simulated results tally well with the experimental results. The modei and the method for simulation of shape analysis and control of hot strip mills were provided.

Hodograph method of flow on two-dimensional manifold

For some special flows, especially the potential flow in a plane, using the hodograph method has obvious advantages. Realistic flows have a stream surface, namely, a two-dimensional manifold, on which the velocity vector of the flow lies on its tangent space. By introducing a stream function and a potential function, we establish the hodo- graph method for potential flows on a surface using the tensor analysis. For the derived hodograph equation, we obtain a characteristic equation and its characteristic roots, from which we can classify the type of the second-order hodograph equation. Moreover, we give some examples for special surfaces.

Stratospheric Precursor of Non-Uniform Variation in Early Spring Surface Temperature over Eurasia

The stratospheric influences on the non-uniform variation in early spring（March–April,MA）surface temperature over Eurasia is investigated based on the ERA-Interim,NCEP-1,and NCEP-2 reanalysis data for the period1980–2016.A lead–lag correlation is found between preceding winter（December–February,DJF）stratospheric polar vortex displacements（SPVD）and the MA west–east seesaw pattern in surface temperature over Eurasia.Further analysis reveals that the East Asian jet stream may act as a bridge linking DJF SPVD and MA surface temperature over Eurasia.A positive change in SPVD is associated with a decelerated polar jet stream and an accelerated East Asian jet stream in the troposphere in DJF.The East Asian jet stream signal can persist into MA.As a result,anomalous southerly/northerly winds prevail over western/eastern Eurasia,accounting for the west–east surface temperature seesaw over Eurasia.

Using a pressure controlled vortex design method to control secondary flow losses in a turbine stage

A turbine design method based on pressure controlled vortex design （PCVD） is presented to design a small-size turbine stage. Contrary to the conventional controlled vortex design （CVD） method, the main objective of PCVD is to control the axial velocity and radial pressure in the sta- tor rotor gap. Through controlling axial velocity, the PCVD establishes a direct tie to meridional stream surface. Thus stream surface variation is induced, resulting in a large secondary flow vortex covering the full blade passage in the respective stator and rotor. This secondary flow vortex could be dedicated to control the secondary flow mitigation and migration. Through radial pressure, the PCVD is also associated with the macroscopic driving force of fluid motion. So the better benefit of CVD can be achieved. The core concept behind PCVD is to mainly control the spanwise pressure gradient by altering profile loading at various spanwise locations. Therefore not only the local pro- file lift is affected, but also the resulting throat widths, stage reaction degree, and massflow rate are altered or redistributed respectively. With the PCVD method, the global stage efficiency is increased successfully while the mass flow rate keeps constant. Additionally there is no endwall shape optimization, stacking optimization, or pitch/chord variations, concentrating solely on varying blade profile deflections and stagger.