Effects of the friction coefficient on cold extrusion process of axial symmetry parts

Shao-qing WANG, Li-hua YUAN， Sen LIANG

(School of Mechanical Engineering, Qingdao Technological University, Qingdao 266000, China)

Abstract: The cold extrusion has a high strength and a good rigidity. It has been widely used in the equipment manufacturing and hydraulic systems. The cold extrusion process of axisymmetric parts were analyzed using ANSYS software. The axial, radial and circumferential stress maps of different friction coefficients are obtained. The simulation results of the compressive stress are fitted and analyzed, and the function is approximated by the least squares method. The results show that the values of axial tensile stress, radial tensile stress and circumferential tensile stress are distributed in a straight line, and the value increases with the increase of friction coefficient. Axial compressive stress, radial compressive stress and circumferential compressive stress are approximately distributed on a quadratic curve. It has an important theoretical significance for production.

Key words： Cold extrusion, ANSYS, Least square method, Axisymmetric

1 Introduction

Cold extrusion[1-4] is the machining process which place the blank in the mold cavity at room temperature. The metal extrusion from the cavity is forced to obtain a certain shape, size and mechanical properties of parts in a strong pressure and a certain speed under the action. During the cold extrusion process, the material is in a three-way stress state. The material is tightly organized and the fibers are distributed along the contours of the parts. So the parts strength and stiffness are better. The fatigue strength of the material is improved. The cold-work hardening after the extrusion can increase its surface hardness, corrosion resistance, wear resistance and fatigue strength. It has been widely used in industrial production.

M Bakhshi-Jooybari[5] developed the friction model in the extrusion process and it is shown that the model works very well for cold extrusion of aluminium in dry condition, but it does not model hot extrusion of lubricated steel adequately. P. Tiernan,et al[6] investigated the influence of die angle, reduction ratio and die land on the extrusion force during the extrusion process. A finite element analysis (FEA) of the cold extrusion process was undertaken in parallel with the experimental program. The FEA simulation was carried out using ELFEN, FEA software, specifically produced for metal forming simulation. M. S. Joun, et al[7] compared the two laws of friction. It was shown that considerable differences exist between the two friction laws, especially in friction-sensitive metal forming processes. Liliang Wang, et al[8] studied the friction test technology of aluminum extrusion process. The recent development of the friction testing techniques for aluminium extrusion processes was summed up and detailed comparisons of these techniques are presented.

In the paper the contact model of blank and mold is established in ANSYS[9-11]. The cold extrusion process of axisymmetric part is analyzed, and the stress cloud of mold and workpiece is obtained. The influences of friction coefficient on extrusion process are analyzed. The least squares method[12-15] has been applied to the stress simulation values produced during the extrusion process, and the research methods and results have an important theoretical significance for the optimization of the extrusion process.

2 Theoretical formula

The geometries, constraints and the loads are symmetrical to a fixed axis, so the stress, strain and displacement are also symmetrical to the axis under the action of the load.

The geometric equation of the axisymmetric problem is shown in Eq.1.

(1)

The physical equation of the axisymmetric problem is shown in Eq.2.

(2)

The above equation is rewritten as a form of the stress component expressed by the strain component..

(3)

Dis the elastic matrix of the axisymmetric problem.

(4)

3 Establishment of a finite elementmodel

Mold structure is shown in Fig.1. The relationship between the stress and strain of the blank is shown in Fig.2. The friction coefficient between the mold and the blank is 0.1. The elastic modulus of blank is 69 GPa and poisson ratio of blank is 0.26. The elastic modulus of die material is 69Gpa and poisson ratio of die material is 0.26. The problem is a nonlinear large deformation contact problem. According to axis symmetry of the billet in the extrusion process, the extrusion sample and the longitudinal section of the mold 1/2 is selected to establish the geometric model. The blank and die finite element grid is divided in the finite element software as shown in Fig.3.

Fig.1 Blank and die structure

Fig.2 Stress-strain curve of blank

Fig.3 Finite element grid of blank and die

4 Simulation analysis

Fig.4 and Fig.5 show the results of axial stress after extrusion deformation. The negative value indicates the compressive stress, and the positive value represents the tensile stress. The maximum axial tensile stress is 471 MPa and the maximum axial compressive stress is 801 MPa. It can be seen from Fig.4 that the axial stress on the contact surface between the mold and the blank gradually changes from negative to positive, that is, from compressive stress to tensile stress. As the blank diameter becomes smaller and elongated, there is a significant tensile stress region between the extruded inlet and the outlet along the axial stress of the blank centerline. Fig.6 for the right end of the stress along the path of the curve, the figure shows the right end of the stress along the path changes. Fig.6 shows the stress of the right end surface along the path of the curve.

It can be seen from Fig.7 and Fig.8 that the maximum radial tensile stress between the mold and the blank is 614 MPa, the maximum radial compressive stress is 1 100 MPa, the maximum circumferential tensile stress is 619 MPa and the maximum axial compressive stress is 1 250 MPa.

Fig.4 Axial stress distribution

Fig.5 Axial stress distribution of blank

Fig.6 Stress along the path change curve

Fig.7 Radial stress distribution

Fig.8 Circumferential stress distribution

5 Influences of friction coefficient on cold extrusion process

Respectively, take the friction coefficient of 0.05, 0.08, 0.1, 0.12 and 0.15. Cold extrusion simulation data sheet was obtained according to the axial, radial and circumferential stress with different coefficient of friction as shown in Table 1.

The cold extrusion simulation data in Table 1 are fitted to obtain the curves shown in Fig.9-11.

Table 1 Cold Extrusion Simulation Data Sheet

frictioncoefficientσtymax/MPaσcymax/MPaσtxmax/MPaσcxmax/MPaσtzmax/MPaσczmax/MPa0.05418-766597-980602-1 1200.08443-736613-1 060617-1 2000.1471-801614-1 100619-1 2500.12473-844619-1 140623-1 3000.15492-922634-1 290646-1 510

Fig.9 Effect of friction coefficient on axial stress of extrusion

It can be seen from Fig.9 that the value of the axial stress increases with the increase of the friction coefficient. The axial tensile stress is linearly distributed. The formula is solved by the least squares method. In order to obtain the ideal polynomial, the least squares method is used to solve the primary polynomial, as shown in Eq.5.

(5)

The collected array is substituted into Eq.5.

y=741.38x+385.26

(6)

It can be seen from Fig.9 that the axial compressive stress at different friction coefficients is approximately distributed on a quadratic curve. The least squares method is used to solve the quadratic polynomial, as shown in Eq. 7.

(7)

The collected array is substituted into Eq.7.

y=-21 661x2+2 615x-834

(8)

Fig.10 Effect of friction coefficient on radial stress of extrusion

It can be seen from Fig.10 that the influences of the friction coefficient on the radial stress and the axial stress are basically the same. The polynomials are solved by the least squares method. The analytical formulas of the radial tensile stress and the radial compressive stress are shown in (9) and (10), respectively.

y=339.7x+581.4

(9)

y=-15 397x2+131x-955

(10)

Fig.11 Effect of friction coefficient on compressive circumferential stress

It can be seen from Fig.11 that the circumferential stress increases with the increase of the friction coefficient. The quadratic polynomial is solved by the least squares method. The analytical formulas of the circumferential tensile stress and the circumferential compressive stress are shown in (9) and (10), respectively.

y=400x+581.4

(9)

y=-28 595x2+2 012x-1 158

(10)

6 Conclusions

The blank and mold contact model was established in ANSYS. The influences of the friction coefficient on the extrusion process was analyzed by using the finite element software. The simulation results of the compressive stress are fitted. The results show that the values of axial tensile stress, radial tensile stress and circumferential tensile stress are distributed in a straight line, and the value increases with the increase of friction coefficient. Axial compressive stress, radial compressive stress and circumferential compressive stress are approximately distributed on a quadratic curve. The function is approximated by using the least squares method and the influences are analyzed. The results have an important guiding significance for production.

Acknowledgement

The work was financially supported by the. National Natural Science Foundation of China(No.51375248).