A Decomposition of a Complete Graph with a Hole

In the field of design theory, the most well-known design is a Steiner Triple System. In general, a G-design on H is an edge-disjoint decomposition of H into isomorphic copies of G. In a Steiner Triple system, a complete graph is decomposed into triangles. In this paper we let H be a complete graph with a hole and G be a complete graph on four vertices minus one edge, also referred to as a . A complete graph with a hole, , consists of a complete graph on d vertices, , and a set of independent vertices of size v, V, where each vertex in V is adjacent to each vertex in . When d is even, we give two constructions for the decomposition of a complete graph with a hole into copies of : the Alpha-Delta Construction, and the Alpha-Beta-Delta Construction. By restricting d and v so that , we are able to resolve both of these cases for a subset of using difference methods and 1-factors.

Stage identification and process optimization for fast drilling EDM of film cooling holes using KBSI method

Fast drilling electrical discharge machining(EDM)is widely used in the manufacture of film cooling holes of turbine blades.However,due to the various hole orientations and severe electrode wear,it is relatively intricate to accurately and timely identify the critical moments such as breakout,hole completion in the drilling process,and adjust the machining strategy properly.Existing breakout detection and hole completion determination methods are not suitable for the high-efficiency and fully automatic production of film cooling holes,for they almost all depend on preset thresholds or training data and become less appropriate when machining condition changes.As the breakout and hole completion detection problems can be abstracted to an online stage identification problem,in this paper,a kurtosis-based stage identification(KBSI)method,which uses a novel normalized kurtosis to denote the recent changing trends of gap voltage signals,is developed for online stage identification.The identification accuracy and generalization ability of the KBSI method have been verified in various machining conditions.To improve the overall machining efficiency,the influence of servo control parameters on machining efficiency of each machining stage was analyzed experimentally,and a new stage-wise adaptive control strategy was then proposed to dynamically adjust the servo control parameters according to the online identification results.The performance of the new strategy is evaluated by drilling film cooling holes at different hole orientations.Experimental results show that with the new control strategy,machining efficiency and the machining quality can be significantly improved.