For a graph G, let b(G)=max﹛|D|: Dis an edge cut of G﹜ . For graphs G and H, a map Ψ: V(G)→V(H) is a graph homomorphism if for each e=uv∈E(G), Ψ(u)Ψ(v)∈E(H). In 1979, Erd?s proved by probabilistic methods that...For a graph G, let b(G)=max﹛|D|: Dis an edge cut of G﹜ . For graphs G and H, a map Ψ: V(G)→V(H) is a graph homomorphism if for each e=uv∈E(G), Ψ(u)Ψ(v)∈E(H). In 1979, Erd?s proved by probabilistic methods that for p ≥ 2 with if there is a graph homomorphism from G onto Kp then b(G)≥f(p)|E(G)| In this paper, we obtained the best possible lower bounds of b(G) for graphs G with a graph homomorphism onto a Kneser graph or a circulant graph and we characterized the graphs G reaching the lower bounds when G is an edge maximal graph with a graph homomorphism onto a complete graph, or onto an odd cycle.展开更多
In order to analyze the influences of the different tool’s shape and surface conditions (such as different coated and material) and their interaction on the cutting temperature, a coupled thermo-mechanical finite ele...In order to analyze the influences of the different tool’s shape and surface conditions (such as different coated and material) and their interaction on the cutting temperature, a coupled thermo-mechanical finite element analysis (FEA) model of plane-strain orthogonal metal cutting process is constructed, and 16 simulation cases with 16 different types of tools, which cover 4 rake angles, -10°, 0°, 10°, 20°, and 4 friction coefficient values, 0, 0.1, 0.2, 0.3 in the same cutting condition (cutting depth and cutting speed) have been performed. Finally the simulation results are analyzed according to the variance analysis method (VAM) of orthogonal array designs (OADs), the relationships between the rake angle, tool-workpiece interface’s friction coefficient and their interact effect to the maximum temperature value and the temperature field of the chip are obtained. This result has some instructive meaning to analyze the causes of the cutting temperature and to control the maximum temperature value and the overall temperature field in the metal cutting process.展开更多
ith the three criteria for cutting variables proposed by W.W.Gilbert and K.Hitomi,this paper analyzes the reasonable selection of cutting variables,and furth...ith the three criteria for cutting variables proposed by W.W.Gilbert and K.Hitomi,this paper analyzes the reasonable selection of cutting variables,and further states the relations among maximum profit oriented cutting speed,minimum cost oriented cutting speed and maximum productivity oriented cutting speed.It puts forward a mathematical model for the optimization of cutting variables in machining.展开更多
文摘For a graph G, let b(G)=max﹛|D|: Dis an edge cut of G﹜ . For graphs G and H, a map Ψ: V(G)→V(H) is a graph homomorphism if for each e=uv∈E(G), Ψ(u)Ψ(v)∈E(H). In 1979, Erd?s proved by probabilistic methods that for p ≥ 2 with if there is a graph homomorphism from G onto Kp then b(G)≥f(p)|E(G)| In this paper, we obtained the best possible lower bounds of b(G) for graphs G with a graph homomorphism onto a Kneser graph or a circulant graph and we characterized the graphs G reaching the lower bounds when G is an edge maximal graph with a graph homomorphism onto a complete graph, or onto an odd cycle.
文摘In order to analyze the influences of the different tool’s shape and surface conditions (such as different coated and material) and their interaction on the cutting temperature, a coupled thermo-mechanical finite element analysis (FEA) model of plane-strain orthogonal metal cutting process is constructed, and 16 simulation cases with 16 different types of tools, which cover 4 rake angles, -10°, 0°, 10°, 20°, and 4 friction coefficient values, 0, 0.1, 0.2, 0.3 in the same cutting condition (cutting depth and cutting speed) have been performed. Finally the simulation results are analyzed according to the variance analysis method (VAM) of orthogonal array designs (OADs), the relationships between the rake angle, tool-workpiece interface’s friction coefficient and their interact effect to the maximum temperature value and the temperature field of the chip are obtained. This result has some instructive meaning to analyze the causes of the cutting temperature and to control the maximum temperature value and the overall temperature field in the metal cutting process.
文摘ith the three criteria for cutting variables proposed by W.W.Gilbert and K.Hitomi,this paper analyzes the reasonable selection of cutting variables,and further states the relations among maximum profit oriented cutting speed,minimum cost oriented cutting speed and maximum productivity oriented cutting speed.It puts forward a mathematical model for the optimization of cutting variables in machining.
基金partially supported by the Fundamental Research Funds for the Central Universities,Nankai Universitypartially supported by NSFC(Nos.12161141006,12111540249)+2 种基金the Natural Science Foundation of Tianjin(No.20JCJQJC00090)the Fundamental Research Funds for the Central Universities,Nankai Universitypartially supported by grant DFF-7014-00037B of Independent Research Fund Denmark。
