###### Abstract  
The warm-forging technology of the spiral bevel gear (873 K-1073 K) was studied. Based on the rigid-plastic finite element method, a numerical simulation was carried out by using DEFORM V11.0 software to explore the influence of different process parameters on gear-forming quality and forming force in the process of warm forging. Taking into account the complexity of the geometry of spiral bevel gears and the diversity of the influence factors in the forging process, as determined through nine groups of numerical simulation experiments, this paper systematically analyzed the influence law of different forging speeds, die preheating temperatures, friction factors and workpiece heating temperatures on the effective stress and strain of spiral bevel gears. The best combination of process parameters with minimum forging force was obtained via the orthogonal experiment, which provides a theoretical basis for the optimization design of the precision forging process of spiral bevel gears and also provides a new idea for studying the precision-forging-forming process of other complex parts. spiral bevel gear; warm forging; numerical simulation; process parameter; orthogonal experiment +
Footnote †: journal: Applied sciences  
0000-0002-4307-389X/00/0000-0000-0000-0000-0000-0000-0000-0000-0000-0000-00000-00000-00000-00000-0000-00000-00000-00000-00000-00000-00000-00000-00000-00  
metal flow law on each section of the spiral bevel gear in the process of plastic forming, and put forward their own views on the deformation process of the spiral bevel gear in forging [3]. [PERSON] et al. believe that although the gear forging process is very complex and there are many variables, with the development of science and technology, especially the in-depth application of computer simulation technology, the accuracy of forgings can be greatly improved [4]. In regard to improving the quality of forging and forming, based on the plastic finite element analysis software DEFORM-3D, [PERSON] et al. carried out a numerical simulation on the precision forming process of spiral bevel gear. According to the structural characteristics of spiral bevel gear, the relevant parameters of preformed blank are formulated to reduce the forming force and improve the forming quality [5]. On the basis of the shunt forging process, [PERSON] et al. proposed the closed pre-forging-porthole finish forging process for the complexity of the tooth surface structure of the spiral bevel gear and carried out a numerical simulation analysis. The results show that the process is conducive to tooth filling, reduces the forming load, and has the characteristics of a small stress value and uniform temperature distribution [6]. [PERSON] et al. used the method of combining control variables and numerical simulation to change the diameter of the cutter head to trim the tooth surface of the forging die. This method improves the fluidity of the metal, and improves the forging defects of the tooth tip of the spiral bevel gear, such as unfilled filling, cracks and the like [7]. [PERSON] et al. proposed an advanced hot forging method for spiral bevel gears which was helpful to improve the defects of insufficient filling of the gear tooth top, large forming load and low service life of die in traditional forging method [8]. [PERSON] et al. analyzed the impact of the hot-forging preform shape on forging quality, proposed an optimization design method for preform shape and conducted experimental verification [9]. [PERSON] et al. used DEFORM-3D software to numerically simulate the forging and forming process of the driven wheel of the spiral bevel gear, and through the analysis of the simulation results, the flow law of the metal material inside the gear was elaborated, and the changes in the parameters and the distribution of the stresses in the forming process were also explained [10]. In the aspect of spiral bevel gear-forging die design, based on the three-dimensional finite element analysis method, [PERSON] et al.