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156 Friction and Friction Models
40 µ =
file:///C:/DOCUME%7E1/Italy/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image001.gif30
20
µ = 0
0.10
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|
0.15
0.08
0.06
0.05
0.03
−30
0 10 20 30 40
Height reduction (%)
file:///C:/DOCUME%7E1/Italy/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image004.gif(c) Discuss the results you obtain. Try to explain the characteristic trends in the friction behavior.
Alloy
| Lubrication
| ID after Reduction compression (mm) of ID (%)
| µ m
|
Al-alloy
| Dry friction
| 30.8
| |
| Graphite–oil
| 38.1
| |
| Teflon foil
| 37.7
| |
Cu
| Dry friction
| 33.0
| |
| Graphite–oil
| 37.2
| |
| Teflon foil
| 38.5
| |
Soft steel
| Dry friction
| 33.9
| |
| Graphite–oil
| 38.4
| |
| Teflon foil
| 39.4
| |
10.2 Consider measurement of contact stresses by means of pins extending into the die–workpiece interface during a metal forming application: (a) Apply the two eqs. 10-13 and 10-14 to determine the contact stresses, as well as the Coulomb coefficient of friction, at the location where the mea- surement is done. (The solution is eqs. 10-11 and 10-12.) (b) At a specific location on the surface of a die, the contact stresses were mea- sured to be σ = 40 MPa and τ = 18 MPa. Determine the friction coefficient at this location. 10.3 A cylinder of soft steel was compressed down to an average strain of ε¯ = 1. A thin layer of aluminum foil was used as solid lubricant between the cylinder and the die. Determine the friction factor in the compression process, under the assumption Notes 157 that cylinder and foil are subjected to the same deformation. The flow stress rela- tionships at the actual temperature of compression for the steel specimen and the aluminum foil, respectively, are given as
σ¯ = Kε¯ n = 715.7 MPa · ε¯ 0.22
σ¯ = Kε¯ n = 119.3 MPa · ε¯ 0.297
10.4 In the two graphs presented here, contact stress data from pin measurements performed over the workpiece interface in ring compression are given. The data refer to different locations at the end faces of cylinders of pure Al, compressed down to a height reduction of 10%, for which the shear flow stress was determined to be k = 8 kpsi. Three different conditions of lubrication were investigated: dry friction, condition A; condition B, where a mixture of oleic acid in mineral oil was used as lubricant; and, finally, condition C, where Pb foil was used as a solid lubricant.
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(Reprinted from Int. J. Mech. Sci., Vol. 1, van Rooyen, G. T., and Backofen, W. A., “A study of the interface friction in plastic compression,” pp. 1–27, 1960 with permission from Elsevier.) (a) Specify the general expressions for shear stress in the cases of (i) Coulomb and (ii) Tresca friction, and define the symbols used. (b) Use the contact stress data in the figure to determine which of the two fric- tion models will describe measured data best for each of the lubricant con- ditions A, B, and C. (c) Calculate the friction factor for lubricant conditions A and B for points at distances r = 0.3 in. and 1.0 in. from the center of the cylinder. NOTES
1. Wanheim, T., and Bay, N.: “A model for friction in metal forming processes,” Ann.
CIRP, Vol. 27, No. 1, 1976, pp. 189–193.
2. Schey, J. A.: “Tribology in Metalworking: Friction, Lubrication and Wear,” ASM Int., Metals Park, Ohio, 1983, pp. 78–79.
3. Godfrey, D. in Ku, P. M. (Ed.): “Interdisciplinary approach to friction and wear,” NASA Sp-181, Washington, 1968.
158 Friction and Friction Models
4. Suthcliffe, M. P. F., Lee, H. R., and Farrugia, D.: “Simulation of transfer layer formation in strip drawing of stainless steel,” Wear, Vol. 254, 2003, pp. 523–531. 5. Male, T., and Cockcroft, M. G.: “A method of the determination of the coefficient of friction of metals under conditions of bulk plastic deformation,” J. Inst. Metals, Vol. 93,
1964–65, pp. 38–46.
6. Siebel, E., and Lueg, W.: Mitt. Kaiser Wilhelm Inst. Eisenforschung, Vol. 15, 1933, p. 1.
7. van Rooyen, G. T., and Backofen, W. A.: “A study of the interface friction in plastic compression,” Int. J. Mechanical Sciences, 1960, Vol. 1, pp. 1–27. 8. Hansen, A. W., Welo, T., and Valberg, H.: “A technique for measuring stresses on the tool surface,” Proc. 4th Int. Conf. on Technology of Plasticity, Beijing, China, 1993, Vol. 1, pp. 303–308.
REFERENCES
Bay, N.: “Modelling and testing of friction in forging,” in “New Developments in Forging
Technology,” Mat-Info Werkstoff-Informationsgesellschaft, Frankfurt, 2007, pp. 233–252. Lenard, J. G. (Ed.): “Metal Forming Science and Practice,” Elsevier, 2002.
Mang, T.: “Die Schmierung in der Metallbearbeitung,” Vogel-Buchverlag, 1983.
Schey, J. A.: “Tribology in Metalworking: Friction, Lubrication and Wear,” ASM Int., Metals
Park, Ohio, 1983.
file:///C:/DOCUME%7E1/Italy/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image007.gif11 Thermal Effects The energy consumed in a metal forming operation, as, for instance, in a forging stroke, is mainly transformed into heat, which leads to temperature rise in the die and the workpiece. In heavy metal forming equipment, a lot of energy is supplied to the workpiece this way, and there can be substantial global and local heating effects in the workpiece material. In many metal forming applications, there are limits on how high the tempera- ture of the workpiece can rise before one experiences problems such as reduced or unacceptable product quality. This is, for instance, the case in aluminum extrusion, where the maximum temperature of the metal near the outlet from the die should not exceed a certain critical temperature. In this process, material defects, such as surface cracking due to hot tearing of the material, start to appear when this critical temperature is exceeded, and a usable profile can no longer be manufactured. This phenomenon is explained and discussed in this chapter. In addition, it is shown how one can quantify different thermal effects in a metal forming process, such as heating due to plastic deformation inside the workpiece, and heating due to friction over its surface. When the workpiece has higher temperature than the dies, there is cooling against the dies, and the physics required to calculate the cooling is shown for a simple two-dimensional case. It is also explained how the temperature inside the tooling and on the surface of the workpiece can be measured by use of thermocouples. Use of pyrometry to measure the surface temperature on a body is also discussed. Finally, characteris- tic thermal conditions in some typical nonstationary and stationary metal forming processes are described by examples. 11.1 Thermal Effects in Metal Deformation Processes When it comes to thermal effects, heat radiation is in many cases neglected in metal forming applications. But, for instance, hot forming of steels is performed at temper- atures as high as 1000–1200◦C. At these temperatures, loss of heat due to radiation becomes significant and must be included if an accurate thermal analysis is to be done. Al and Al alloys, however, are seldom formed at higher temperature than
160 Thermal Effects
Figure 11.1. Energy consumption during deformation of ideal rigid–
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|
plastic material with constant flow stress.
550◦C, and radiation effects are less significant at these low temperatures. They can therefore be neglected without much error.
If radiation effects and cooling to the surrounding air are neglected, the follow- ing equation1 ,2 can be used to estimate the temperature in a workpiece during a
metal forming operation:
T1 = T0 + TD + TF − TT (11-1) Here, the following symbols are used:
T0 is the initial temperature of the workpiece.
TD is the temperature increase in the workpiece due to dissipated deformation energy during forming.
TF is the temperature increase due to friction in the interface between die and workpiece.
TT is the temperature decrease in the workpiece because of cooling by colder dies.
11.1.1 Effects Due to Dissipated Deformation Energy
Consider an ideal rigid–plastic workpiece without strain hardening, i.e., a workpiece of an ideal material with constant flow stress σ¯ .
The energy added to this workpiece by deformation up to an average strain of
ε¯(see Fig. 11.1), can be expressed as
WD = σ¯ε¯V (11-2) Correspondingly, the amount of heat required to give the workpiece the tempera-
ture rise TD is given by
QD = cm TD (11-3) In this equation, symbols are
c (J kg−1K−1), the heat capacity of the workpiece material;
m, the mass of the workpiece (V is the volume).