On the Parametric Modeling of Turbine Blade Section Curve

Geometric parameters of the turbine blade are classified according to their destined functions, and the mathematical definition of those parameters in the section curve is introduced in detail. Some parts of the section curve shape can be adjusted freely, offering more flexibility to designers.

Four Conic Section Curves

Mathematicians are constantly constructing and exploring the properties of abstract objects only because they find them beautiful and interesting. Later, sometimes centuries later, the objects may turn out to be e-normously useful when they are applied to the physical world. There are no more elegant examples of this than the work done in ancient Greece on the four conic-section curve. If a right circular cone is sliced by a plane parallel to its base, the cross section is a circle. Tip the

Microstructure and mechanical properties of curved AZ31 magnesium alloy profiles produced by differential velocity sideways extrusion

Lightweight curved profiles are widely utilised in the transportation industry considering the increasing need for improving aerodynamic efficiency,aesthetics and cutting emissions.In this paper,curved AZ31 Mg alloy profiles were manufactured in one operation by a novel process,differential velocity sideways extrusion(DVSE),in which two opposed rams were used.Effects of extrusion temperature and velocity(strain rate) on curvature,microstructure,and mechanical properties of the formed profiles were examined.Profile curvature was found to be more readily controlled by the velocity ratio of the bottom ram v2to the top ram v1,whereas extrusion temperature(T=250,300,350℃)and extrusion velocity(v_(1)=0.1,1 mm/s) slightly affect curvature for a given velocity ratio.A homogeneous microstructure with equiaxed grains(~4.5 μm) resulted from dynamic recrystallisation(DRX),was observed after DVSE(v_(2)/v_(1)=1/2) at 300 ℃ and v_(1)=0.1 mm/s,where the initial billet had an average grain size of ~25 um.Increasing extrusion temperature leads to grain growth(~5 μm) at 350 ℃ and v_(1)=0.1 mm/s.DRX is incomplete at the relatively low temperature of 250℃(v_(1)=0.1 mm/s),and higher strain rate with v1=1mm/s(T=300℃),resulting in inhomogeneous bi-modal necklace pattern grains ranging in size around 1-25 μm for the former and 2-20μm for the latter.Grain refinement is attributed to DRX during the severe plastic deformation(SPD) arising in DVSE,and initiates at the prior boundaries of coarse grains in a necklace-like manner.Compared with the billet,micro-hardness and ultimate tensile strength of the profiles have been enhanced,which is compatible with grain refinement.Also,an obvious increase in tensile ductility was found.However,yield strength slightly decreases except for the complete DRXed case(300℃,v_(1)=0.1 mm/s),where a slightly higher value was found,indicating strengthening by grain refinement is greater than softening caused by texture modification.The initial billet had a strong basal texture wherein the {0002} basal plane is oriented parallel to the extrusion direction(’hard’ orientation),while DVSE results in the profiles having weak basal textures and the {0002} basal plane oriented ~5-10° to the extrusion direction(i.e.towards the orientation for easier slip).This significantly modified texture contributes to the softening of the profiles in the extrusion direction,in which tensile tests were performed,and the related elongation improvement.

A defect recognition model for cross-section profile of hot-rolled strip based on deep learning

The cross-section profile is a key signal for evaluating hot-rolled strip quality,and ignoring its defects can easily lead to a final failure.The characteristics of complex curve,significant irregular fluctuation and imperfect sample data make it a challenge of recognizing cross-section defects,and current industrial judgment methods rely excessively on human decision making.A novel stacked denoising autoencoders(SDAE)model optimized with support vector machine(SVM)theory was proposed for the recognition of cross-section defects.Firstly,interpolation filtering and principal component analysis were employed to linearly reduce the data dimensionality of the profile curve.Secondly,the deep learning algorithm SDAE was used layer by layer for greedy unsupervised feature learning,and its final layer of back-propagation neural network was replaced by SVM for supervised learning of the final features,and the final model SDAE_SVM was obtained by further optimizing the entire network parameters via error back-propagation.Finally,the curve mirroring and combination stitching methods were used as data augmentation for the training set,which dealt with the problem of sample imbalance in the original data set,and the accuracy of cross-section defect prediction was further improved.The approach was applied in a 1780-mm hot rolling line of a steel mill to achieve the automatic diagnosis and classification of defects in cross-section profile of hot-rolled strip,which helps to reduce flatness quality concerns in downstream processes.