Rigidity analysis of vibrorolled surfaces.

Polojintef Corbu, Nicolae ; Pater, Sorin ; Hule, Voichita 等

Abstract: Estimating rigidity only on the bases of theoretical methods, is difficult and the results obtained do not suit reality if not correlated with experimental attempts to analyze the rigidity of vibrorolled surface depending on the manufacturing parameters experimental measurements have been made using equipment based on the device for measuring rigidity HV 10. Results analysis made in numeric form with the help of "diag_tehno" program made in MATLAB, using the "polyfit" and "polyval" functions.

Key words: vibro-rolling, tension, "diag_tehno", harshness.

1. INTRODUCTION

Similar to the rolling procedures, in the case of vibro-rolling as well, it is estimated that the surfaces obtained shall have a higher harshness after processing, fact which represents an improvement of the mechanic properties, of scuffing and ruggedness of the surfaces. (Keesen, 1975)

The study of the deformations of the surfaces processed by rolling was approached in several papers in which there were specified the phenomena taking place as well as their effect upon the properties of the obtained surfaces. According to these papers, by the superficial plastic deformation a hammerhardening (cold-rolling) of the micro-structure are achieved, stretching and compression tensions being induced between the strata near the surface. Due to the mechanic tensions created, the hardness of the materials increases in the superficial strata.

The present paper deals with the aspects related to the plastic deformation, specific to vibro-rolling.

2. DEFINING THE PROBLEM

If the trajectory of the ball on the surface of the machine part is analyzed, one can notice that different deformation zones are created, in relation to this trajectory there resulting areas subject to tensions of a different nature (Figure 1). Thus in the area around point A, the tensions are due to the flow of the material pushed towards the ball in the area of point B, and in the area of point B the tensions are due first of all to the compression of the material under the pressing effect of the ball. (Lee, & Tarng, 2001)

The state of remanent tensions can be analysed with the help of the experimental and theoretical methods.

[FIGURE 1 OMITTED]

Among the theoretical methods, the most often used is the method of the finite element. For the study of the evolution of the state of tension there was chosen a program with finite elements on bi-dimensional geography, named Femlab version 2.2.0.125 of the Comsol firm, which can analyze the state of tension in the field of elastic-plastic and plastic deformations.

Because of the application limits of the program, the model was performed according to the following simplifying hypotheses:

--two separate analysis fields are considered (figure 1):

--the field in the vicinity of point A, of the deformation channel;

--the field in the vicinity of point B, of the edge of the deformation channel;

--the ball is regarded as being only in translation motion, being neglected the rotation motion of the ball;

--the friction forces are neglected, being taken into consideration only the forces:

--of pressing (along the Oz axis in figure 1), for the domain A; --of pushing (along the Ox axis in figure 1), for the domain B;

For the domain A, the schematic representations of the loadings and the border conditions are represented in figure. The distributed force "F" is applied on the surface "S", whereas the surfaces a,b and c are considered to be fixed. The loading is regarded as being distributed on the area of the virtual surface (in the case of the problems solved in 2D, the surface becomes an edge), defined by "S". For a loading of the ball with a concentrated force of 50 daN, using a ball with the radius of 3 mm, there is experimentally obtained a penetration of the ball of approximately 0.1 mm, these dimensions being used for the defining of the model as well.

In this case the size of the surface "S" is calculated with the following relationship (using the notations in figure 2): rad R

"S" = 2R[(arccoss h/R).sub.rad] (1)

The value "S" calculated with the help of the relationship (1) is of 1.55 [mm.sup.2] (virtual area), consequently their value of the distributed force, specified as a data of entry into the program of analysis shall be of 50x10 7 N/[m.sup.2].

[FIGURE 2 OMITTED]

3. PARAMETERS OF THE MODELING

The parameters of the modeling, set in the Femlab program are as follows:

--The type of analysis: static, nonlinear;

--The plane state of tensions;

--The triangular elements with three knots;

--The treatment of constraints: the method of -Lagrange multipliers;

--The number of elements: 9040;

--The number of the degrees of liberty 9262;

--The number of knots 4631;

--The non-linear tolerance: 0.0001;

--The maximum number of iterations: 16;

Figure 3 presents the network of finite elements generated by the program of analysis. For the material properties there have been chosen the usual values for the carbon steel OLC45.

For the programs of analysis in the field of plastic deformations, specifying a variation curve of the force according to time is need. Generally, a loading is achieved, which starts from the 0 value of the force, it rises up to a certain maximum value, after which it decreases again in 0. The diagram of the distribution of tensions for the last step of the loading cycle represents the distribution of the plastic deformation tension, which remain even after the action of the force ceases..

[FIGURE 3 OMITTED]

4. THE RESULTS OF THE SIMULATION

The diagrams of the states of tension resulted following the program are presented in figure 5. The figure shows the corresponding diagrams to the loading steps 0,1,2,3, and 6, the steps 4 and 5 being similar to the steps 2 and 3.

For the domain B the modeling was achieved according to the scheme presented in figure 4.

[FIGURE 4 OMITTED]

[FIGURE 5 OMITTED]

Both the conditions of modeling and the values of the parameters are similar to those presented for the case of domain A. The diagrams of the states of tension for domain B are presented in figure 6.

5. CONCLUSIONS:

Analyzing the diagrams of the states of tension for the last step of the soliciting cycle (figures 5.e and 6.e), there can be observed that the remnant tensions are higher for the case of domain B, which means that on the margins of the ball traces, the probability of obtaining higher harshness is higher. The smaller surface contact of the ball with the material, in the case of domain B leads to the achieving of higher contact pressures and thus to higher remnant tensions

 This fact can constitute an advantage in the case in which
 it is aimed that the vibro-rolled part be more resistant to
 tear and wear, as the portions of surface in field B (where
 harshness is higher) shall be in direct contact with the
 surfaces of other spare parts. However, having in mind the
 simplifying hypotheses enunciated up to defining the
 model, the results obtained offer only the possibility of a
 qualitative analysis and could be taken into account with
 precaution only. (Wahl, 1987)

[FIGURE 6 OMITTED]

6. REFERENCES

B.Y. Lee, Y.S. Tarng (2001). Surface roughness inspection by computer vision in turning operations, International Journal of Machine Tools & Manufacture, 41 1251-1263;

Deacu L., Pavel Gh.--Vibratii la masinile--unelte, Editura Dacia, Cluj-Napoca, 1977;

Keesen G.--An in Depth Look at Roller Burnishing, Cutting Tool Engineering, May, june, 1975;

Klocke F., Liermann J.,--Roller burnishing of hard turned surfaces, Surface Conference, Goteborg, Sweeden, 1996;

Wahl, F. M.--Digital Image Signal Processing, Artech House, Boston, 1987