Evaluation of Friction Coefficient by Simulation in Bulk Metal Forming Process
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IN metal forming, the friction forces developed between the workpiece and the forming tools play an important role. It is usually assumed that the friction coefficient is constant over the interface between the workpiece and the tools. Frederiksen and Wanheim[1] used friction-testing methods based on the geometrical changes of the workpiece in order to adjust the frictional conditions in a simulation to the conditions of the real process. Bay[2] studied the application of the friction model for the analyses of the bulk metal forming process. On the basis of these and other results,[3–7] Ebrahimi and Najafizadeh developed an upper-bound theory to determine the average Tresca friction coefficient by conducting a barrel compression test.[8,9] According to this theory, the average Tresca friction coefficient m for a cylindrical sample can be determined by measuring the degree of barreling sample and using the following equation: m¼
Rth H b p4ffiffi 2b pffiffi 3 3 3
½1
Here, m is the average Tresca friction coefficient for a hot working process: its value ranges from 0 (perfect sliding) to 1 (sticking friction). The terms Rth and H are the radius of the sample in the absence of bulging (or condition without friction) and the final height of
Y.P. LI, Assistant Professor, E. ONODERA, Researcher, and A. CHIBA, Professor, are with the Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan. Contact e-mail: [email protected] Manuscript submitted March 4, 2009. Article published online October 29, 2009 224—VOLUME 41A, JANUARY 2010
the sample, respectively. The barreling factor, b is given by the following equation: b¼4
DR H Rth DH
½2
where DR is the difference between the maximum radius (Rm) and the radius of the originally flat end surface after expansion (Rt) of the cylindrical sample after compression, and DH is the reduction in the height of the cylindrical sample after compression. As mentioned in previous research,[10–12] at low strains levels, the contact surface (radius with Rc) of cylindrical IHS38MSV samples with the anvil surface after compression at 1000 C were found to be formed mainly by the original flat end surfaces of samples with groove profiles (radius with Rt) (Figure 1(a)). However, at higher strain levels, the contact surfaces were observed to be formed by both the originally flat end surface after expansion in the middle area and the external lateral surface of the sample (Figures 1(b) and (c)) due to barreling and its further contact with the anvil (Rc Rt). In this case, Rt could be identified from the profiles of the grooves clearly, as shown in Figure 1(c). It should be noted that Eq. [1] was proposed on the basis of the upper-bound theory, and from this theory, the contact surface should be completely generated from the originally flat end surface of the sample after expansion.[8] Therefore, this equation is not applicable at high strain levels according to the aforementioned analysis. In recent years, the relation between Rt and the friction coefficient m has received some intere
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