Research of effects of bar geometric parameters on initial external force in precision cropping

In precise cropping of the metal bars with different geometrical parameters, it is very important to obtain the reasonable initial external forces required by the bars rapidly and accurately. Stress concentration factor and stress intensity factor are proposed to calculate the initial external force accurately in this paper according to geometrical sizes of metal bars. By means of numerical simulation and linear fitting method, the correctional expressions of stress concentration factor and stress intensity factor of V-shaped notch tip, which include the geometric parameters of the bar, are obtained respectively and the error analyses are also performed. The ratio of the depth of V-shaped notch to the diameter of the bar is presented to be a condition parameter. The numerical analytical results show that the method of stress concentration factor can be used to calculate the initial external force accurately when the ratio of the depth of V-shaped notch to the diameter of the bar is more than 0.05, and the method of the stress intensity factor can be used when the ratio is less than 0.05. The calculating formulas of reasonable initial external forces for the bars with different geometrical parameters are also given. The cropping experimental results have confirmed that it is feasible that the reasonable initial external forces required by the bars with different geometrical parameters are calculated effectively by using the stress concentration factor or the stress intensity factor in precision cropping.