Some researches upon the tool-piece contact geometry in the rolling process.

Lupescu, Octavian ; Popa, Ramona ; Popa, Ionut 等

1. PROBLEM STATEMENT

The superficial cold plastic deformation (SPD) is a mechanical treatment method of the metallic materials that allows us to obtain the mechanic characteristics improvement (Lupescu et al., 2004), the expensive materials changeover with any other cheaper, hardened using SPD process, as well as the thermo and thermo-chemical secondary treatments changeover because of their amount prices.

This technical paper shows also a surface geometry determination of the deformation focus, in case of the rolling hardening with disk rolls (Lupescu et al., 2001).

2. APPLICATION AREA

The researches objective was to determine the tool-piece surface contact projection on the tangent plan, in their initial contact point.

The literature (Lupescu, 1999) shows that process is able to be applied to cylindrical pieces, especially to big diameters (>100 mm), for individual series and also mass production series. The degree hardness resulted on superficial layer (until 1 -1, 5 mm) exceed in many cases with 10% (Lupescu & Baciu, 2002) the obtained results of the thermo-chemical treatments.

3. METHOD USED

First of all, there were established the curved radius taking into account the elastic deformation which affect the rolls. For the second step, the deformation focus surface results taking into consideration the plastic and elastic deformations aboard the working piece (figure 1).

Using the general relation to establish a surface curved radius elastic deformed (Lupescu et al., 2005):

1/[R.sup.*.sub.1,2] = 1/2 (1/[R.sub.I,1(2)] - 1/[R.sub.II,1(2)] (1)

the authors suggest for the curved radius of the roll attack surface in the case of his elastic deformation, the following relations:

1/[R.sup.*.sub.1] = 1/2 (1/[R.sub.I,1] - 1/[R.sub.II,1]) = 1/2 x 1/[R.sub.I,1]; [R.sup.*.sub.1] = 2[R.sub.II] (2)

1/[R.sup.*.sub.2] = 1/2 (1/[R.sub.I,2] - 1/[R.sub.II,2]) = 1/2 x 1/[R.sub.I,1]; [R.sup.*.sub.2] = 2[R.sub.12][R.sub.22]/[R.sub.22] - [R.sub.12] (3)

[FIGURE 1 OMITTED]

Working in a Cartesian system OXYZ because of the elastic roll deformations under the F force action, his initial radius [R.sub.11] and [R.sub.12] belonging to the principal two plans will be modified to [R.sup.*.sub.1] and [R.sup.*.sub.2] with their centers displacement from [O.sub.1] to [O.sup.*.sub.1] and from [O.sub.2] to [O.sup.*.sub.2]. Using the next notation, the total contact deformation will be:

[bar.CD] = [delta] = [[delta].sub.el] + [[delta].sub.pl], thus: (4)

[[DELTA].sup.*] = [R.sup.*.sub.2] + [R.sub.22] - [delta], so: (5)

[O.sup.*.sub.1]A = [square root of [R.sup.*2.sub.1] - [[bar.AB].sup.2]] = [square root of [R.sup.*2.sub.1] - [x.sup.2]], and: (6)

[O.sup.*.sub.1] [O.sup.*.sub.2] = [R.sup.*.sub.2] - [R.sup.*.sub.1], and: (7)

[[bar.BB].sup.*] = [([R.sup.*.sub.2] - [R.sup.*.sub.1]) + ([square root of [R.sup.*2.sub.1] - [x.sup.2]])] (8)

The deformation surface equation, belonging to the [O.sup.*.sub.2][X.sup.*.sub.2][Y.sup.*.sub.2][Z.sup.*.sub.2] system is:

[y.sup.*2.sub.2] + [z.sup.*2.sub.2] - [[bar.BB].sup.*2] = 0 and so: (9)

[y.sup.2.sub.2] + [(z - [[DELTA].sup.*]).sup.2] - [[([R.sup.*.sub.2] - [R.sup.*.sub.1]) + [square root of [R.sup.*2.sub.1] - [x.sup.2]]].sup.2] = 0 (10)

In these conditions, the contact surface curve can be determined with the system equations:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (11)

The outline intersection of two bodies (tool-piece) projected on the tangent plan in the initial contact point is an ellipse whose expression was obtained from (11):

[y.sup.2] + [[R.sup.2.sub.22] + [[DELTA].sup.2] - [[([R.sup.*.sub.2] - [R.sup.*.sub.1]) + [square root of [R.sup.*2.sub.1] - [x.sup.2]]].sup.2]]/2[[DELTA].sup.*]] - [R.sup.2.sub.22] = 0 (12)

The equation of the real contact surface in the elastic-plastic deformation process was solved using the overlap effects principle.

4. RESULTS

Thus, on the first step, it was admitted only the static contact of the elements. The ellipse from the tangent plan results like projection of the determination focus surface (figure 2) with (a) and (b) semi-axis established by (12); the small semi-axis (b) is the y value from this equation, when x = 0 and the big one (a) is the limit value of x when the above equation ensure the real values for y.

On the second step it was simulated the axis movement of the contact ellipse along the longitudinal speed direction of the deforming roll.

On the left side, the roll came into contact with the working piece, on the existing surface from the last step. On the right side the roll remain in contact with the piece on a reduce surface, because of his plastic deformation.

Thus, on the right side, the intersection outline is an elliptic contour having ([a.sub.I]) semi-axis, taking into account the elastic contact only. The semi-axis (b) is unchangeable. So:

[a.sub.I] = [a.sup.*] [cube root of 3F/E [summation] [zeta]], where: [a.sup.*] = [[2k[xi](e)/[pi]].sup.1/3] (13)

On the third step, one simulates the tool rotation either, along side OY axis. The new surface contour is represented in figure 3. In this case also, behind the roll, it remains a reduced contact surface, resulted only due to the plastic piece deformation.

Thus, during the rolling process, the real contact between tool-piece is produced on a contact surface having the following curved sectors:

* AB, remained from the initial unmodified ellipse, whose equation is done after relation 12;

* BC, ellipse arc which has a semi-axis (b) and the other semi-axis ([a.sub.I]) resulting from relation 13. The analytically expression of these outline is:

[(x/[a.sub.I]).sup.2] + [(y/b).sup.2] - 1 = 0 (14)

* CD, ellipse arc having ([a.sub.I]) and respectively ([b.sub.II]) semi-axis, calculated from the elastic pure contact conditions:

[b.sub.II] = b [cube root of 3F/E [summation] [rho]], where: [b.sup.*] = [[2[xi](e)/[pi]k].sup.1/3] (15)

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

The contact expression outline on this sector becomes:

[(x/[a.sub.I]).sup.2] + [(y/[b.sub.II]).sup.2] - 1 = 0 (16)

* DA, ellipse arc with (a) semi-axis and the other equal with ([b.sub.II]), when the analytically contour expression becomes:

[(x/[a.sub.II]).sup.2] + [(y/[b.sub.II]).sup.2] - 1 = 0 (17)

In these conditions, the mathematic expression became:

z = [[DELTA].sup.*] - [square root of [[R.sup.*.sub.2] - [R.sup.*.sub.1]] + [square root of [R.sup.*2.sub.1] - [x.sup.2] - [y.sup.2]]] (18)

with X and Y values being throughout the outline delimited by the ellipse arcs AB, BC, CD and DA, anterior defined.

5. FURTHER RESEARCHES

The determined focus surface afterwards will allow: the contact surface pressure establishment, the slides speeds between the couple elements, the power friction consumed during the process and friction parameters establishment using the lubricant film calculus.

6. REFERENCES

Lupescu, O., (1999), Surfaces polishing through plastic deformation and steels cold hardening proces (Netezirea suprafetelor prin deformare plastica si durificare la rece a otelurilor), Junimea, ISBN 973-37-0471-7, Iasi

Lupescu, O., et al., (2001), The device choosing for rolling the exterior cylindrical surface using the utilities theory, Proceedings of Modern Techniques, Quality, Reorganization, vol. 1, pg. 229-232, Chisinau

Lupescu, O., Baciu, M., (2002), The characterization of mechanical treatment at SPD at cold through rolling as a tribological process, Proceedings of Meridian Engineering, 12 (3), pg. 29-32, Chisinau

Lupescu, O., et al., (2004), Structural modification of the Ol 25 Steel in the Cold SPD Process Through Rolling, Academic Journal of Manufacturing Engineering, 2(4), pg.43-47, Timisoara

Lupescu, O., et al., (2005), About the establishment of surface geometry for the SPD process by rolling, Proceedings of Machine--Building and Technosphere of the XXI Century, Tom. 4, 12-17 September., 255-260, Sevastopol