## 1 Introduction  
Lots of metal products are manufactured using plastic forming techniques such as forging and extrusion. Forging involves the pressure processing of metal parts with the aim of obtaining a certain shape, size, and mechanical properties. Upsetting is one of the forging methods, which is highlighted by its high efficiency in compacting [1]. Especially in hot forging, upsetting is able to eliminate internal pores at the billet's center [2, 3]. Currently, upsetting is widely used in metalworking to improve the mechanical performance of metal parts. Although upsetting has shown its advantage in metal forming, several obstacles should be handled in practice. Due to uneven metal flow in upsetting, bulging is formed around the billet's center. In addition, cracks are peculiarly prone to generating on the bulged billet surface [4, 5]. Restraint bulging is always a hot topic in the study of upsetting, especially for billets with a large height-to-diameter ratio (LHDR), which is defined by an LHDR value above 2 in this article. The mechanism of bulging formation is largely related to the friction behavior between the billet end and the anvil. During the upsetting process, the flow of metal around the end of the billet is restricted by friction, resulting in the formation of a rigid deformation zone in this area. The friction effect seriously affects the forming uniformity [6, 7, 8], and lots of efforts have been made to explore the friction behaviors between the anvil and billet end. [PERSON] [9] studied the effect of frictional conditions on the cold upsetting of square annealed aluminum billets and deduced the friction factors for different lubricantsand bulge parameters. Moreover, [PERSON] [10] investigated the variation of the friction coefficient during the upsetting process by means of an inverse algorithm and verified it by the measured load in an upsetting experiment. By means of response surface methodology and a three-level full-factorial design of experiments, [PERSON] [11] performed a general regression model involving both frictional isotropy and anisotropy to predict the plastic deformation of materials after upsetting. [PERSON] [12] also proposed a new friction testing method, the T-shape upsetting-extruding process employing a rectangular blank, for evaluating the friction conditions during the rib-web part-forming process. [PERSON] [13] proposed a dynamic friction model in which friction depends on both the time rate of strain and normal pressure to predict contact stresses in cylinder upsetting. In addition to these, many investigations have proceeded to explore other aspects [14; 15; 16; 17; 18]. The height-to-diameter ratio of the billet is another factor that largely affects bulging formation. [PERSON] [19] proposed a thermo-mechanically coupled model to study deformation characteristics in the upsetting of LHDR disk-shaped forgings and the formation mechanism of the laminated crack defect. Additionally, [PERSON] [20] simulated upsetting billets with three different height-to-diameter ratios by means of the Simufact Forming software 10.0v. Moreover, through cylindrical upsetting experiments of pure copper, [PERSON] [21] examined the influence of specimen size on dry friction in the meso/micro-forming process. [PERSON] [17] also studied the effect of height-to-diameter ratio on the formability of AA2014 cast alloy and optimized process parameters with [PERSON]'s optimization technology. In addition to the investigations discussed above, the phenomenon of surface crack generation in upsetting has also been investigated in terms of billet size [22; 23; 24]. Although the mechanism of bulging has been studied deeply with the efforts of many scholars, a new, revised upsetting method should be proposed technically in terms of manufacturing. Fortunately, several novel upsetting technologies have been invented from the point of view of restraining bulging.