To meet the demands for highly advanced components with ultra precise contour accuracy and optical surface quality arising in the fields of photonics and optics, automotive, medical applications and biotechnology, con...To meet the demands for highly advanced components with ultra precise contour accuracy and optical surface quality arising in the fields of photonics and optics, automotive, medical applications and biotechnology, consumer electronics and renewable energy, more advanced production machines and processes have to be developed. As the complexity of machine tools rises steadily, the automation of manufacture increases rapidly, processes become more integrated and cycle times have to be reduced significantly, challenges of engineering efficient machine tools with respect to these demands expand every day. Especially the manufacture of freeform geometries with non-continuous and asymmetric surfaces requires advanced diamond machining strategies involving highly dynamic axes movements with a high bandwidth and position accuracy. Ultra precision lathes additionally equipped with Slow Tool and Fast Tool systems can be regarded as state-of-the-art machines achieving the objectives of high quality optical components. The mechanical design of such ultra precision machine tools as well as the mechanical integration of additional highly dynamic axes are very well understood today. In contrast to that, neither advanced control strategies for ultra precision machining nor the control integration of additional Fast Tool systems have been sufficiently developed yet. Considering a complex machine setup as a mechatronic system, it becomes obvious that enhancements to further increase the achievable form accuracy and surface quality and at the same time decrease cycle times and error sensitivity can only be accomplished by innovative, integrated control systems. At the Fraunhofer Institute for Production Technology IPT a novel, fully integrated control approach has been developed to overcome the drawbacks of state-of-the-art machine controls for ultra precision processes. Current control systems are often realized as decentralized solutions consisting of various computational hardware components for setpoint generation, machine control, HMI （human machine interface）, Slow Tool control and Fast Tool control. While implementing such a distributed control strategy, many disadvantages arise in terms of complex communication interfaces, discontinuous safety structures, synchronization of cycle times and the machining accuracy as a whole. The novel control approach has been developed as a fully integrated machine control including standard CNC （computer numerical control） and PLC （programmable logic controller） functionality, advanced setpoint generation methods, an extended HMI as well as an FPGA （field programmable gate array）-based controller for a voice coil driven Slow Tool and a piezo driven Fast Tool axis. As the new control system has been implemented as a fully integrated platform using digital communication via EtherCAT, a continuous safety strategy could be realized, the error sensitivity and EMC susceptibility could be significantly decreased and the overall process accuracy from setpoint generation over path interpolation to axes movements could be enhanced. The novel control at the same time offers additional possibilities of automation, process integration, online data acquisition and evaluation as well as error compensation methods.展开更多
We have introduced the total domination polynomial for any simple non isolated graph G in [7] and is defined by Dt（G, x） = ∑in=yt（G） dr（G, i） x＇, where dr（G, i） is the cardinality of total dominating sets of...We have introduced the total domination polynomial for any simple non isolated graph G in [7] and is defined by Dt（G, x） = ∑in=yt（G） dr（G, i） x＇, where dr（G, i） is the cardinality of total dominating sets of G of size i, and yt（G） is the total domination number of G. In [7] We have obtained some properties of Dt（G, x） and its coefficients. Also, we have calculated the total domination polynomials of complete graph, complete bipartite graph, join of two graphs and a graph consisting of disjoint components. In this paper, we presented for any two isomorphic graphs the total domination polynomials are same, but the converse is not true. Also, we proved that for any n vertex transitive graph of order n and for any v ∈ V（G）, dt（G, i） = 7 dt（V）（G, i）, 1 〈 i 〈 n. And, for any k-regular graph of order n, dr（G, i） = （7）, i 〉 n-k and d,（G, n-k） = （kn） - n. We have calculated the total domination polynomial of Petersen graph D,（P, x） = 10X4 ＋ 72x5 ＋ 140x6 ＋ 110x7 ＋ 45x8 ＋ [ 0x9 ＋ x10. Also, for any two vertices u and v of a k-regular graph Hwith N（u） ≠ N（v） and if Dr（G, x） = Dt（ H, x ）, then G is also a k-regular graph.展开更多
文摘To meet the demands for highly advanced components with ultra precise contour accuracy and optical surface quality arising in the fields of photonics and optics, automotive, medical applications and biotechnology, consumer electronics and renewable energy, more advanced production machines and processes have to be developed. As the complexity of machine tools rises steadily, the automation of manufacture increases rapidly, processes become more integrated and cycle times have to be reduced significantly, challenges of engineering efficient machine tools with respect to these demands expand every day. Especially the manufacture of freeform geometries with non-continuous and asymmetric surfaces requires advanced diamond machining strategies involving highly dynamic axes movements with a high bandwidth and position accuracy. Ultra precision lathes additionally equipped with Slow Tool and Fast Tool systems can be regarded as state-of-the-art machines achieving the objectives of high quality optical components. The mechanical design of such ultra precision machine tools as well as the mechanical integration of additional highly dynamic axes are very well understood today. In contrast to that, neither advanced control strategies for ultra precision machining nor the control integration of additional Fast Tool systems have been sufficiently developed yet. Considering a complex machine setup as a mechatronic system, it becomes obvious that enhancements to further increase the achievable form accuracy and surface quality and at the same time decrease cycle times and error sensitivity can only be accomplished by innovative, integrated control systems. At the Fraunhofer Institute for Production Technology IPT a novel, fully integrated control approach has been developed to overcome the drawbacks of state-of-the-art machine controls for ultra precision processes. Current control systems are often realized as decentralized solutions consisting of various computational hardware components for setpoint generation, machine control, HMI （human machine interface）, Slow Tool control and Fast Tool control. While implementing such a distributed control strategy, many disadvantages arise in terms of complex communication interfaces, discontinuous safety structures, synchronization of cycle times and the machining accuracy as a whole. The novel control approach has been developed as a fully integrated machine control including standard CNC （computer numerical control） and PLC （programmable logic controller） functionality, advanced setpoint generation methods, an extended HMI as well as an FPGA （field programmable gate array）-based controller for a voice coil driven Slow Tool and a piezo driven Fast Tool axis. As the new control system has been implemented as a fully integrated platform using digital communication via EtherCAT, a continuous safety strategy could be realized, the error sensitivity and EMC susceptibility could be significantly decreased and the overall process accuracy from setpoint generation over path interpolation to axes movements could be enhanced. The novel control at the same time offers additional possibilities of automation, process integration, online data acquisition and evaluation as well as error compensation methods.
文摘We have introduced the total domination polynomial for any simple non isolated graph G in [7] and is defined by Dt（G, x） = ∑in=yt（G） dr（G, i） x＇, where dr（G, i） is the cardinality of total dominating sets of G of size i, and yt（G） is the total domination number of G. In [7] We have obtained some properties of Dt（G, x） and its coefficients. Also, we have calculated the total domination polynomials of complete graph, complete bipartite graph, join of two graphs and a graph consisting of disjoint components. In this paper, we presented for any two isomorphic graphs the total domination polynomials are same, but the converse is not true. Also, we proved that for any n vertex transitive graph of order n and for any v ∈ V（G）, dt（G, i） = 7 dt（V）（G, i）, 1 〈 i 〈 n. And, for any k-regular graph of order n, dr（G, i） = （7）, i 〉 n-k and d,（G, n-k） = （kn） - n. We have calculated the total domination polynomial of Petersen graph D,（P, x） = 10X4 ＋ 72x5 ＋ 140x6 ＋ 110x7 ＋ 45x8 ＋ [ 0x9 ＋ x10. Also, for any two vertices u and v of a k-regular graph Hwith N（u） ≠ N（v） and if Dr（G, x） = Dt（ H, x ）, then G is also a k-regular graph.
