# The Study of Multi-Stage Cold Forming Process for the Manufacture of Relief Valve Regulating Nuts
###### Abstract  
Cold forging is widely used in many industries. Multi-stage cold forming is usually utilized in forging fasteners. In this study, numerical simulation and experimental investigations were carried out on a five-stage cold-forming process for the manufacturing of low-carbon steel AISI 1010 relief valve regulating nuts. The forming process through five stages included preparation and centering for backward extrusion, backward extrusion over die pin, upset, backward extrusion over moving punch, and piercing. The formability of the workpiece was studied, such as the effects on forming force response, maximum forming force, effective stress and effective strain distributions, metal flow patterns, and strength. A comparison of the forming forces obtained in the forming experiment with the numerical simulation results of the five-stage cold forming showed a good agreement with the trend of the forming force growth. For the maximum forming force and forming energy, the fourth stage of backward extrusion over the moving punch at the upper face was the largest among the five stages. The total maximum forming forces from the first to the fifth stages were numerically 440.9 kN and experimentally 449.4 kN, meaning the FE simulation and experimental results were in good agreement. The numerically simulated effective strain distributions were consistent with the experimentally tested hardness distributions. Highly compacted grain flow lines also resulted in higher hardness. The overall hardness of the workpiece formed by five-stage cold forming increased by 31% compared to the initial billet. The hardness of the workpiece increased with the forming stages, and the strain-hardening effect was obvious. The strength of the workpiece was significantly increased by five-stage cold forming. multi-stage cold forming; formability; forming force; effective stress; effective strain; hardness 20231320231  
There are many studies and analyses on cold forming. Many applications used numerical simulation for the forming design prediction and the simulation parameter settings. By using the 2D finite element method, [PERSON] and [PERSON] [5] studied suck-in type extrusion defects, level gear forging, stress analysis of forging tools, and multi-stage cold forging operation design. [PERSON] and [PERSON] [6] proposed a three-stage cold forging process for forming the spline shape at the head of the aerospace fasteners. A combination of extrusion (forward and backward) and forging very complex spline geometries is a complicated process. Insights into the operation are gained through numerical simulations of strain, damage, and flow patterns in all three stages. A multi-stage upsetting method to form a thick and wide flange at the pipe end was developed by [PERSON] and [PERSON] [7]. They analyzed the numerical simulation results and discussed the method of determining the step length. [PERSON] et al. [8] numerically studied the process design of the forward and backward extruded axisymmetric parts for cold forging operations. The forming of numerical simulations agreed with the experimental results. To analyze the formability of a multi-stage forging process, [PERSON] et al. [9] applied the FE method to construct a systematic process analysis method for the multi-stage forging of the outer race of constant velocity joints. [PERSON] et al. [10] used the numerical code of DEFORM_2D to investigate the cold-forming mechanism of a five-stage extrusion process of shaft parts that were used in gearboxes. The results illustrated that the cold extrusion of the five-stage process was feasible and the forming rules were obtained. [PERSON] et al. [11] developed a process to cold forge high-strength M8 bolts in 1600 MPa grade, which was based on the softening behavior of fully pearlitic materials with an ultimate tensile strength of 1410 MPa. The manufactured bolts were experimentally confirmed as having a tensile strength of 1600 MPa and a delayed fracture strength.