Studies regarding influence of the process parameters on the surface roughness at manufacturing by grinding.

Buzatu, Constantin ; Lepadatescu, Badea ; Dumitrascu, Adela Eliza 等

Abstract: The paper presents a detailed approach of mathematical modeling for surface roughness at machining by grinding taking into account the tool constructive and process parameters and as an original element the influence of grinding fluid and friction coefficient between grain and workpiece surface.

Starting from the assumption of considering a model of abrasive grain with spherical tip, is calculated the equation of roughness parameter [R.sub.y] according to the process parameters, tool constructive parameters and the friction coefficient [mu] between tool and workpiece on the influence of grinding fluid.

Key words: grinding, surface, modeling, fluid.

1. INTRODUCTION

The final machining of part's surfaces, especially grinding and smoothing, has known an increasing importance because of greater demands regarding quality and reliability of the products.

Due to of many factors which are involved in achievement of part's surface finish a decision regarding the optimization of the machining process is necessary to take.

Together with the process parameters and tool characteristics, an important factor that influences the surface roughness, and less used in the literature is the nature and characteristics of cutting fluid. The friction coefficient variation between the tool and workpiece can conduct in time to modification of the machining surface. The roughness of part's surface is lowering if is used during machining cutting fluid that are applied as a stream or as mist (Buzatu, 1981; Buzatu, 1988).

In the paper (Diacenko & Iacobson, 1954), based on the test results were obtained corrective coefficients [a.sup.*], to modify the surface roughness in machining without cutting fluid according with the cutting speed ([a.sup.*] = 0.7-1).

In grinding and superfinish machining is necessary to use cutting fluid because of the high temperature which appears at part tool contact. In the literature are a few studies regarding the influence of friction coefficient between tool and workpiece in accordance with the nature and characteristics of cutting fluid on the surface finish (Lepadatescu et al., 2004).

In the paper is shown the theoretical modeling of surface roughness taking into account the influence of cutting fluid by the friction coefficient [mu].

2. INFORMATION

To make the mathematical modeling of the surface roughness at grinding manufacturing is used the model of grain with spherical tip, Figure 1, which is accepted in the researches of abrasive tools (superfinishing, honing, lapping, magnetic field assisted polishing).

The abrasive grain with the conical angle [beta], is considered to have height [h.sub.g], base width b, tip radius r (obtained by wearing in machining process), e distance between the grains, [gamma] and a the rake and relief angle.

According with the spherical model from Fig.1, and taking the tip radius r = 0, is obtained the equation:

b = 4[s.sub.g] tg [beta].sub.2] [square root of t/D], (1)

where, [s.sub.g] is the feed of abrasive grain, t is depth of cut, D is the grinding wheel diameter.

Considering that the b parameter is the angular pitch of the abrasive grains and assimilate grinding with face milling the paper (Diacenko & Iacobson, 1954) proposes an equation of maximum roughness h = [R.sub.y], that is obtained in grinding:

h = [s.sup.2.sub.l][delta] / 4 [Dv.sub.s] = [R.sub.y]. (2)

where, h is height of irregularities, [delta] is the angular pitch [rad], [s.sub.1] is circular part' feed [mm/sec], [v.sub.s] is angular speed of tool [m/min].

Based on the Fig.1 is obtained the next equation of irregularities height at grinding:

h = t x [s.sub.g]tg[beta]/2 / [v.sub.s] x D [square root of D], (3)

If is taking into account the next dependences at grinding (Secara et al,, 1989):

[S.sub.g] = [S.sub.l] / [N.sub.g], (4)

where [s.sub.1] is longitudinal feed, [N.sub.g] is number of grains which work in a abrasive wheel rotation equal with (Fig.1):

[N.sub.g] = [pi]D/e [k.sub.1], (5)

where, [k.sub.1] is a coefficient taking into account that a small number of grain is in working.

From the equations (3)-(5) results:

h = t x [s.sub.l]e x tg [beta]/2 / [pi] x [k.sub.1][D.sup.2] [square root of D x [v.sub.s], (6)

The condition of abrasive grain traveling without sliding on the part' surface is (Buzatu, 1988):

[alpha] [less than or equal to] a arctmu, (7)

where, [alpha] is the relief angle of the abrasive grain. Taking into account that (Fig.1):

[gamma] + [beta]/2 + 2[alpha] = [pi], (8)

results that:

tg [beta]/n = ctg ([gamma] + 2[alpha]), (9)

Developing equation (9) and with the limit condition:

tg[alpha] = [mu] (10)

Taking into account equation (6) results the final equation:

[FIGURE 1 OMITTED]

The value of optimal friction coefficient that makes the minimum height of irregularities is obtained by solving the derivative of equation (11) according with [mu]:

[partial derivative]h / [partial derivative][mu] = 0, (12)

that become :

[[mu].sup.4]ctg[delta]-[[mu].sup.3](ctg[gamma]-[ctg.sup.2] [gamma])-[[mu].sup.2](6[ctg.sup.2][gamma] + 3ctg[gamma]-2)--3[mu]ctg[gamma] + ctg[gamma] = 0, (13)

If is taking into account the values of that are very small (hundredths), and without the terms of 3 and 4 order the equation become:

(6[ctg.sup.2][gamma] + 3ctg[gamma]-2)[[mu].sup.2] + -3[mu]ctg[gamma] + ctg[gamma] = 0, (14)

whose solution is:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (15)

With a good approximation it can considered that:

e [congruent to] [G.sub.med], (16)

where, [G.sub.med] is the average dimension of abrasive grains according with the values from Table 1, (Loscutov, 1950).

When is taking into consideration the influence of abrasive grain tip radius on the angular pitch b, results (Figure 1.):

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (17)

and equation (2) become:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (18)

If is desired to carry out equation (7) in machining process, is possible to make in the same way the calculations and taking into account equation (10) is obtained an equation according with values of coefficient [mu].

It is obtained the final equation:

h = [s.sub.l]/2[Dv.sub.s][[G.sub.mead]/2 a + r ([square root of 1 + [A.sup.2]] - A)]. (19)

In this case A represents:

A = [[mu].sup.2] + 2[mu]tg[gamma]-1 / [[mu].sup.2]tg[gamma] - 2[mu] - tg[gamma] (20)

To introduce in the equation the influence of abrasive granulation it is considered that the abrasive grain is fixed in bond at level of maximum section of average dimensions (Table 1):

[h.sub.g] [congruent to] [G.med]/2, (21)

which ensure the maximum stability in the bond.

3. CONCLUSIONS

Based on above presented the next conclusions appear:

1. Mathematical modeling of surface roughness after grinding based on the spherical model is a delicate problem when it is wanted to take into account the influence of process parameters and grinding fluid.

2. The equations for height of irregularities at grinding using the model shown above (equations 11 and 14), confirm the conclusions from the literature.

3. The influence of grinding fluid on the surface finish taking into account friction coefficient i is parabolic type which impose determination of optimum value to minimize height of irregularities by verification in experimental testing

4. REFERENCES

Buzatu, C. (1981). Contributii la studiul factorilor care afecteaza cre[degrees]terea preciziei pieselor prelucrate prin strunjire si rectificare exterioara, (Contributions referring to the factors study witch affect increasing of the accuracy of the part obtained by turning and external grinding). Doctoral Thesis, "Transilvania" University of Brasov.

Buzatu, C. (1988). Automatizarea si robotizarea proceselor tehnologice, (Automation of the machining processes). Ed. "Transilvania" University of Brasov.

Buzatu, C. & Simon, A.-E. (2006). Data Base For High-Speed Steel Rp2 Tool Wear At Turning. In Proceedings of 6th International Conference--"Research and Development in Mechanical Industry"--RaDMI 2006, ISSN 86-83803-21-X, September 13 - 17, Budva, Montenegro.

Diacenko, P.E. & Iacobson, M.O. (1954). Calitatea suprafetelor la prelucrarea metalelor prin aschiere,(Quality of the surface at the machining by cutting). Ed. Tehnica, Bucuresti.

Lepadatescu, B.; Simon, A.-E. & Mares, Gh. (2004). Surface Technology. Ed. "Transilvania" University of Brasov, ISBN 973-635-390-7, Brasov.

Loscutov, V.V. (1950). Rectificarea. Masini si unelte de rectificat, (Grinding. Machine tools for grinding). Ed. Tehnica, Bucuresti.

Secara, Gh.; Rosca, D.; Mares, G.; Ditu, V.; Lupulescu, N. & Diaconu, V. (1989). Basis of cutting and surfaces generation. Ed. "Transilvania" University of Brasov.

Table 1. Abrasive grains characteristics

Granulation Number of Dimension
group granulation limits [m[micro]]

Grinding grain 8 1680-2330
 10 1190-2000
 12 840-1680
 16 710-1190
 20 840-500
 24 710-350
 36 500-250
 46 350-177
 60 250-149
 80 177-129
 100 149-105