Method and apparatus for estimating depth of molten pool during printing process, and 3D printing system

A method of estimating a depth of a molten pool formed during a 3D printing process, comprising:

• measuring a surface temperature of the molten pool by taking a thermal image of an area of a laminated printing object including the molten pool of a base material formed on the laminated printing object during the 3D printing process with a thermal imaging camera;
• comparing the measured surface temperature of the laminated printing object with a melting point (Tm) of the base material to determine a boundary of a region exceeding the melting point as a surface boundary of the molten pool;
• determining maximum lengths in x-axis and y-axis directions of a surface region of the molten pool defined by the surface boundary of the molten pool as a length (a) and a width (b) of the surface of the molten pool, respectively;
• and
• estimating a maximum depth (d) in the z-axis direction of the molten pool in real time based on the length (a) and the width (b) of the surface region of the molten pool,
• wherein the estimated maximum depth (d) of the molten pool is determined by a z-axis coordinate value (Zmax) at a point (Xmax, 0, Zmax) where a derivative in length direction of a temperature relation, Φ=T(x, y=0, z)−Tm, of the molten pool is 0, where T(x, y=0, z) is a temperature of the molten pool when assuming that the maximum depth (d) point of the molten pool is located at a center(y=0) in a width direction (y-axis direction) of the molten pool.