## 1 Introduction  
The traditional method for tube nosing involves passing a circular metal tube through conical dies [1, 2]. However, it can buckle and fail if the tube wall experiences too much compressive stress during this process. To ensure success, a delicate balance of factors, such as tube geometry, material properties, die geometry, friction at the tube/die interface, and axial feed at the tube ends must be carefully managed. Accurately predicting and controlling buckling is crucial for a successful outcome. A comprehensive understanding of the interaction between the various elements of the tube-nosing process and their boundaries is necessary to create defect-free components. The ultimate goal of tube nosing is to improve part quality while avoiding instability. Maintaining tight control over deformation, rather than simply avoiding excessive die penetration, is one effective method for preventing fracture during tube nosing. FE simulation is a widely respected technique used in the metal forming industry for designing dies and processes [3, 4]. Preventing defects like splitting, buckling, or wrinkling in metal-forming products requires a comprehensive process simulation and verification of metal flow. Process parameters can be examined by conducting FE simulations, and forming loads and failure modes, such as necking, rupture, wrinkling, and excessive springback, can be accurately predicted. Unfortunately, the design of forming tools, material selection, lubricants, and other factors is still based on trial and error, which can be costly. This is highly undesirable in today's competitive environment due to the need for shorter production and turnaround times. Therefore, it is essential to identify the variables present in the metal-forming operation. FE simulation is the most feasible method for identifying the effect of process variables and predicting defects before the actual forming operation takes place [3]. Numerous research studies have analyzed the impact of material properties and process parameters on tube nosing. One of these studies suggested a method to determine the original shell based on the final shape [5], while another created a computer program that uses the same approach to design procedures [6]. Elastic-plastic and rigid-plastic FE simulation techniques have also examined the nosing process [7]. Researchers have used different simulation techniques to analyze the nosing process at room temperature and elevated temperatures [8]. Some have introduced a backward tracing method to determine the optimal preform for shell nosing [9], while others have proposed a preform design method for shell nosing by forward-deformation FE simulation and geometrical modification of the initial shape [10; 11; 12; 13]. Different studies have explored the temporary impacts of quasi-static and dynamic internal inversion and nosing in metal tubes [14; 15], as well as the non-axisymmetric buckling behavior of circular tubes when subjected to nosing operations using a frictionless conically shaped die [16]. FE simulation has been employed to investigate the cold eccentric tube nosing process of metal tubes utilizing an eccentric conical die [17]. An approximate theory was developed that combines the volume incompressible condition and the Levy-Mises equation to calculate preform shape, nosing ratio, and loading rate in the tube nosing process by spherical die [18]. Lastly, finite element method analysis was used for the tapered die eccentric necking process to investigate the effects of process parameters, such as the initial tube wall thickness, semi-die angle, and friction coefficient [19; 20]. The process of double-nosing in tubes was scrutinized. The findings indicated that the experimental and simulation results were congruous. The study disclosed that middle buckling can be curtailed by minimizing the friction coefficient, whereas extending the profile length from 50 to 100 mm can elevate middle buckling while shortening the workpiece length.