# Profile Design of the Grooved Die and Rolling Force Prediction in the Cold Pilger Rolling Process
## 1 Introduction  
The cold pilger rolling process is an incremental method for manufacturing metal tubes with uniform cross-sections using initial tubes, such as semi-seamless and seamless pipes. This pilger rolling process is called roto-rolling and in which a pipe is passed between the rocking set of the outer die and the hardened mandrel on the inside of the pipe. Accordingly, the tube cross-section is reduced while the length and strength are increased. In this respect, this process is similar to the drawing technique. The cold pilger rolling process can produce pipes with good surface quality, precise dimensional tolerance, and satisfactory mechanical properties owing to the involved high compressive stress. In addition, the process increases the elongation of the workpiece material due to the compressive stress applied by the axial force and forming being incremental. A very high cross-sectional reduction rate can be achieved in a single process step without causing a fracture in the material. Compared to manufacturing the same hollow-type product by a cold drawing process, the cold pilger rolling process can achieve a cross-sectional reduction of approximately 90% in a single working cycle. The advantages of this process include a short working time, increased material utilization efficiency by reduced material use, and the rationalized spatial layout of the equipment [1,2]. With the recent trend of industrial development, the number of products in which welded pipes cannot be used has also gradually increased. Thus, applications of the cold pilger rolling process to produce seamless pipe products have proliferated. Table 1 presents various fields in which the cold pilger rolling process is applied for each material. As shown in Figure 1, this process is mainly used to manufacture fittings for high-pressure vessels in various industries in which high pressure, high/low temperature and corrosionresistance are required. Some examples of these industries include special piping, power plant, chemical, shipbuilding, and nuclear power industries. However, to date, considerable time and costs are required for the cold pilger rolling process since a systematic design method of pilger rolling process has not been established. Currently, the process is mainly based on the experience and subjective judgment of experienced technicians. Moreover, most pilgering companies are small- or medium-sized and thus tend to have limitations in terms of systematic research and development of pilger rolling process, knowledgebase construction, and related areas. To overcome the above problem, the development of a pilgering die groove shape design method, which is the core design technology of the cold pilger rolling process, is required. In addition, a Q factor evaluation method for the final product, as well as a rolling force prediction method according to the die shape, are needed [3; 4; 5]. The Q factor represents the ratio of wall thickness reduction to diameter reduction. This factor should always be above 1.0 to prevent any pilgering defects and obtain the necessary tubing properties. The die shape of the cold pilger rolling process is mainly designed to reduce the pipe diameter at a constant rate from the initial stage of forming. Owing to the nature of the mandrel shape, the forming inlet can exhibit large cross-section reduction. However, if the cross-section reduction rate is large at the forming outlet, the risk exists that the mandrel will break and wear [6]. The groove shape in the cold pilger rolling process has been designed in several ways and can be classified into three categories [7; 8].