A more universal and flexible method of constructing the streamlined die surfaces is presented. The streamlined die surfaces are interpolated by the arbitrarily cross sectional shapes of the die entrance and exit. Th...A more universal and flexible method of constructing the streamlined die surfaces is presented. The streamlined die surfaces are interpolated by the arbitrarily cross sectional shapes of the die entrance and exit. The boundaries of the die entrance and exit are represented by Ferguson curves with tension parameters. By adjusting the tension parameter, the cross sectional shapes of the die entrance and exit with line segments can be accurately constructed. The upper bound method is used to analyze the procedure of extrusion, the pseudo independent parameters in kinematically admissible velocity and die surface are computed by minimizing the extrusion load, so the optimum die surface is obtained. The effects of frictional condition, die length, area reduction and product shaped complexity are discussed in relation to the extrusion load.展开更多
Let G（V, E） be a unicyclic graph, Cm be a cycle of length m and Cm G, and ui ∈ V（Cm）. The G - E（Cm） are m trees, denoted by Ti, i = 1, 2,..., m. For i = 1, 2,..., m, let eui be the excentricity of ui in Ti an...Let G（V, E） be a unicyclic graph, Cm be a cycle of length m and Cm G, and ui ∈ V（Cm）. The G - E（Cm） are m trees, denoted by Ti, i = 1, 2,..., m. For i = 1, 2,..., m, let eui be the excentricity of ui in Ti and ec = max{eui ： i = 1, 2 , m}. Let κ = ec＋1. Forj = 1,2,...,k- 1, let δij = max{dv ： dist（v, ui） = j,v ∈ Ti}, δj = max{δij ： i = 1, 2,..., m}, δ0 = max{dui ： ui ∈ V（Cm）}. Then λ1（G）≤max{max 2≤j≤k-2 （√δj-1-1＋√δj-1）,2＋√δ0-2,√δ0-2＋√δ1-1}. If G ≌ Cn, then the equality holds, where λ1 （G） is the largest eigenvalue of the adjacency matrix of G.展开更多
文摘A more universal and flexible method of constructing the streamlined die surfaces is presented. The streamlined die surfaces are interpolated by the arbitrarily cross sectional shapes of the die entrance and exit. The boundaries of the die entrance and exit are represented by Ferguson curves with tension parameters. By adjusting the tension parameter, the cross sectional shapes of the die entrance and exit with line segments can be accurately constructed. The upper bound method is used to analyze the procedure of extrusion, the pseudo independent parameters in kinematically admissible velocity and die surface are computed by minimizing the extrusion load, so the optimum die surface is obtained. The effects of frictional condition, die length, area reduction and product shaped complexity are discussed in relation to the extrusion load.
基金Foundation item： the National Natural Science Foundation of China （No. 10861009）.
文摘Let G（V, E） be a unicyclic graph, Cm be a cycle of length m and Cm G, and ui ∈ V（Cm）. The G - E（Cm） are m trees, denoted by Ti, i = 1, 2,..., m. For i = 1, 2,..., m, let eui be the excentricity of ui in Ti and ec = max{eui ： i = 1, 2 , m}. Let κ = ec＋1. Forj = 1,2,...,k- 1, let δij = max{dv ： dist（v, ui） = j,v ∈ Ti}, δj = max{δij ： i = 1, 2,..., m}, δ0 = max{dui ： ui ∈ V（Cm）}. Then λ1（G）≤max{max 2≤j≤k-2 （√δj-1-1＋√δj-1）,2＋√δ0-2,√δ0-2＋√δ1-1}. If G ≌ Cn, then the equality holds, where λ1 （G） is the largest eigenvalue of the adjacency matrix of G.
