## 1 Introduction  
At present, Fe-based [1; 2; 3], Ni-based [4; 5], and Co-based [6; 7] self-fluxing alloy powders are widely used to repair and strengthen the surface performance in laser cladding. The mechanical properties of coatings are analyzed through microhardness, wear resistance and microstructure properties, and the results shows that coatings can be equal to, or even superior to those of the alloys fabricated by die-casting or forging [8; 9]. The repair and recycle industries are therefore greatly enhanced by the advances in laser cladding technology, and have widespread applications in many fields, such as petroleum, chemical, and military [10; 11; 12]. Curved parts, such as blades, gears and moulds, are usually key components of equipment and have a high repair and surface strengthening value, but the complex curvature of these parts can lead to variations in the distance or incidence angle of the laser, which affects the final quality of the coating. Many scholars have undertaken relevant research to obtain good cladding layers on complex surfaces. [PERSON] et al. [13] proposed an adaptive laser cladding method that considered the geometry of the workpiece, and studied the mathematical relationship between the process parameters and the width of the cladding layer. In the experiment, a changeable cladding width from 0.45 mm to 1.85 mm was obtained by changing the laser power. [PERSON] et al. [14] used the Taguchi method to obtain the optimised laser cladding parameters of a sprocket and then repairedthe damaged sprocket. The results of microstructure analysis indicated that the maximum error was 2.973 mm and that the quality of the cladding layer was good. [PERSON] et al. [15] found that laser power density would suddenly decrease with the tangential angle of the cladding outline at the bottom of overlapping zone, and pointed out that the width-to-height ratio of the single track was the key factor in pore formation. They also found that a higher power density and lower thermal conductivity could restrain the generation of pores. [PERSON] et al. [16] studied the influencing rules of the substrate incline angles on the section sizes of cladding layers, and made their robot achieve a variation in angles between 0\({}^{\circ}\) and 150\({}^{\circ}\), finally it was used on the hollow parts successfully. [PERSON] et al. [17] used the Taguchi method to obtain the optimal laser power, scanning speed, and powder flow rate. They also calculated the optimal overlapping degree by building a mathematical model, and proposed statistical algorithms to evaluate high-density samples.  
However, these studies do not consider the variation of spot size during the process of complex parts laser cladding, which is an important process parameter. Therefore, a method of controlling spot size during the laser cladding process is proposed, through the establishment of a mathematical model, in which the spot size is simplified as the area of a cylinder intersecting with a sphere, and then the interpolation points are obtained through the threshold of the spot size. Finally, the method is realized on an ellipsoidal mould and the result is analysed using microstructure, microhardness, adhesion property and wear resistance.