Allowance Extraction Considering of Inner and Outer Contour and Experimental Research on Belt Grinding of Hollow Blade

Aero-engine fan blades of ten use a cavity structure to improve the thrust-to-weight ratio of the aircraft.However,the use of the cavity structure brings a series of difficulties to the manufacturing and processing of the blades.Due to the limitation of blade manufacturing technology,it is difficult for the internal cavity structure to achieve the designed contour shape,so the blade has uneven wall thickness and poor consistency,which affects the fatigue performance and airflow dynamic performance of the blade.In order to reduce the influence of uneven wall thickness,this paper proposes a grinding allowance extraction method considering the double dimension constraints(DDC)of the inner and outer contours of the hollow blade.Constrain the two dimensions of the inner and outer contours of the hollow blade.On the premise of satisfying the outer contour constraints,the machining model of the blade is modified according to the distribution of the inwall contour to obtain a more reasonable distribution of the grinding allowance.On the premise of satisfying the contour constraints,according to the distribution of the inwall contour,the machining model of the blade is modified to obtain a more reasonable distribution of the grinding allowance.Through the grinding experiment of the hollow blade,the surface roughness is below Ra0.4μm,and the contour accuracy is between-0.05~0.14 mm,which meets the processing requirements.Compared with the allowance extraction method that only considers the contour,the problem of poor wall thickness consistency can be effectively improved.It can be used to extract the allowance of aero-engine blades with hollow features,which lays a foundation for the study of hollow blade grinding methods with high service performance.

Minimal Doubly Resolving Sets of Certain Families of Toeplitz Graph

The doubly resolving sets are a natural tool to identify where diffusion occurs in a complicated network.Many realworld phenomena,such as rumour spreading on social networks,the spread of infectious diseases,and the spread of the virus on the internet,may be modelled using information diffusion in networks.It is obviously impractical to monitor every node due to cost and overhead limits because there are too many nodes in the network,some of which may be unable or unwilling to send information about their state.As a result,the source localization problem is to find the number of nodes in the network that best explains the observed diffusion.This problem can be successfully solved by using its relationship with the well-studied related minimal doubly resolving set problem,which minimizes the number of observers required for accurate detection.This paper aims to investigate the minimal doubly resolving set for certain families of Toeplitz graph Tn(1,t),for t≥2 and n≥t+2.We come to the conclusion that for Tn(1,2),the metric and double metric dimensions are equal and for Tn(1,4),the double metric dimension is exactly one more than the metric dimension.Also,the double metric dimension for Tn(1,3)is equal to the metric dimension for n=5,6,7 and one greater than the metric dimension for n≥8.