A new milling methodology with the equivalent normal curvature milling model machining freeform surfaces is proposed based on the normal curvature theorems on differential geometry. Moreover, a specialized whirlwind m...A new milling methodology with the equivalent normal curvature milling model machining freeform surfaces is proposed based on the normal curvature theorems on differential geometry. Moreover, a specialized whirlwind milling tool and a 5-axis CNC horizontal milling machine are introduced. This new milling model can efficiently enlarge the material removal volume at the tip of the whirlwind milling tool and improve the producing capacity. The machining strategy of this model is to regulate the orientation of the whirlwind milling tool relatively to the principal directions of the workpiece surface at the point of contact, so as to create a full match with collision avoidance between the workpiece surface and the symmetric rotational surface of the milling tool. The practical results show that this new milling model is an effective method in machining complex three- dimensional surfaces. This model has a good improvement on finishing machining time and scallop height in machining the freeform surfaces over other milling processes. Some actual examples for manufacturing the freeform surfaces with this new model are given.展开更多
Let 5 be an orthodox semigroup and γ the least inverse congruence on 5. C(S) denotes the set of all congruences on S. In this paper we introduce the concept of admissible triples for S, where admissible triples are c...Let 5 be an orthodox semigroup and γ the least inverse congruence on 5. C(S) denotes the set of all congruences on S. In this paper we introduce the concept of admissible triples for S, where admissible triples are constructed by the congruences on S/γ , the equivalences on E(S)/L and E(S)/R. The notation Ca(S) denotes the set of all admissible triple for S. We prove that every congruence ρ on S can be uniquely determined by the admissible triple induced by ρ, and there exists a lattice isomomorphism between C(S) and Ca(S).展开更多
In this paper, we introduce the concept of VT-congruence triples on a regular semigroup S and show how such triples can be constructed by nsing the equivalences on S/L, S/R and the special congruences on S. Also, such...In this paper, we introduce the concept of VT-congruence triples on a regular semigroup S and show how such triples can be constructed by nsing the equivalences on S/L, S/R and the special congruences on S. Also, such congruence triples are characterized so that an associated congruence can be uniquely determined by a given congruence triple. Moreover, we also consider the VH-congruence pairs on an orthocryptogroup.展开更多
基金China Postdoctoral Science Foundation(No.2005037348)Science and Technology Research Program of Hubei Province,Ministry of Education,China(No.D200612003)
文摘A new milling methodology with the equivalent normal curvature milling model machining freeform surfaces is proposed based on the normal curvature theorems on differential geometry. Moreover, a specialized whirlwind milling tool and a 5-axis CNC horizontal milling machine are introduced. This new milling model can efficiently enlarge the material removal volume at the tip of the whirlwind milling tool and improve the producing capacity. The machining strategy of this model is to regulate the orientation of the whirlwind milling tool relatively to the principal directions of the workpiece surface at the point of contact, so as to create a full match with collision avoidance between the workpiece surface and the symmetric rotational surface of the milling tool. The practical results show that this new milling model is an effective method in machining complex three- dimensional surfaces. This model has a good improvement on finishing machining time and scallop height in machining the freeform surfaces over other milling processes. Some actual examples for manufacturing the freeform surfaces with this new model are given.
基金The NNSF (19970128) of China and the NSF ((011438), (021073), (Z02017)) of Guangdong Province.
文摘Let 5 be an orthodox semigroup and γ the least inverse congruence on 5. C(S) denotes the set of all congruences on S. In this paper we introduce the concept of admissible triples for S, where admissible triples are constructed by the congruences on S/γ , the equivalences on E(S)/L and E(S)/R. The notation Ca(S) denotes the set of all admissible triple for S. We prove that every congruence ρ on S can be uniquely determined by the admissible triple induced by ρ, and there exists a lattice isomomorphism between C(S) and Ca(S).
基金Supported by National Natural Science Foundation of China （Grant No. 10571061）
文摘In this paper, we introduce the concept of VT-congruence triples on a regular semigroup S and show how such triples can be constructed by nsing the equivalences on S/L, S/R and the special congruences on S. Also, such congruence triples are characterized so that an associated congruence can be uniquely determined by a given congruence triple. Moreover, we also consider the VH-congruence pairs on an orthocryptogroup.
