摘要或動機

磁粉探傷過程包含兩個重要的物理現象，其一是磁力線於工作瑕疵處的漏磁現象而形成邊緣磁場，其二是鐵粉顆粒受邊緣磁場的影響而向工作瑕疵處附近聚集現象分別反應出磁場在通過不同介質時所遵循的折射原哩，以及磁場分佈對鐵粉顆粒產生的磁力原理。本研究以電磁通電產生靜磁場，並利用兩電磁鐵間的氣隙來模擬工件瑕疵，因電磁鐵的磁導係數遠大於空氣之磁導係數而造成漏磁場方向機與漏磁面垂直，形成一單純的邊界條件使得邊緣磁通密度的解析解可直接利用馬克斯威爾方程式求得。我們亦導出空氣中的磁通分佈對微小的鐵粉顆粒所產生的磁力公式，發現鐵粉顆粒受靜磁力的大小與該顆粒的體積、磁通密度與磁通密度之梯度成正比，而其方向則與磁通密度之梯度一致，此結論與磁粉探傷過程中，鐵粉向工件瑕疵處聚集的現象吻合。實驗設計採用螢光粉混合鐵粉以獲致明顯的鐵粉顆粒運動軌跡，用數位錄影機紀錄後再擷取影像圖檔判讀其位置與時間之關係，進而反算鐵粉顆粒之位置與所受之靜磁力的關係，以定量的方式證實所推導的邊緣磁場分佈公式以及磁力公式。Two important physical phenomena are observed in the practice of magnetic particle inspection (MPI). The first one is that leakage flux is present in the defect area of the work-piece under inspection. The second one is that magnetic particles aggregate in the vicinity of the defect. These phenomena manifest the theory of flux refraction, which occurs in the intersection area of two different magnetic materials, and the theory of magneto-static force, which is experienced by the iron powder in a magnetic field distribution. Two electromagnets, made of cast steel, are aligned together such that the leakage flux in the air gap forms a fringing field distribution. It is this magnetic field distribution that simulates a defect area in a magnetized magnetic work-piece. Since the permeability of cast steel is far larger than that of air, the direction of the fringing field at the surface of the electromagnets is almost perpendicular to the surface. Such a simple geometry renders an analytical solution to the Maxwell’s equations. The magnetic force of the magneto-static field exerting on the magnetic particle, an iron powder in this case, can be derived by using the principle of virtual displacement. We obtain a formula of magnetic force, whose direction coincides with the gradient of the magnetic flux density and whose magnitude is proportional to the magnitude of the particle volume, the magnetic flux density and its gradient. This formula also agrees with the observation in MPI that the magnetic particles aggregate in the vicinity of the defect.