Methodology for experimental determination of static rigidity for normal lathes.

Tonoiu, Sergiu ; Catana, Madalin

1. INTRODUCTION

For experimental determination of static rigidity for one system's element, this element will be submitted to a progressive increasing load, whose value is measured at each level. The corresponding deformation is measured with an adequate instrument, as shown by: Tonoiu et al., 1997a; Tonoiu et al., 1997b; Weck et al., 1989.

In order to determine the element's rigidity, there must be stated some things regarding: its structure, references, loading, strains. Measuring of loading and deformation is performed according to certain loading--measuring schemes. For loading measuring there is used a dynamometric device, which provides 3D forces. For the case of MSA of normal lathes, the forces are usually applied onto a rigid shaft assembled with the spindle. The shaft materializes the application points for force, AF, and deformation, Au (see Tonoiu, 1999 and Tonoiu & Iliescu, 2002).

2. LOADING--MEASURING SCHEMES

A loading scheme provides characteristics such as: loading type, direction, application point, sense, size (see Tonoiu, 1999).

The loading--measuring scheme also refers to the materialization of application points for force, AF, and deformation, [A.sub.U].

It is necessary that the loading scheme, and therefore the loading device, to allow the variation of loading force, F, with respect of two axes of the geometric reference, such as the variation of angular coordinates [[phi].sub.y] and [[phi].sub.z] (see fig. 1, a).

The scheme and the corresponding measuring instruments of a deformation, u, have to allow the measuring of deformation components, X, Y, and Z, with respect to geometric reference (see fig. 1, b). In the case of an angular deformation, these components have to be obtained for at least two points (see fig. 1, c).

For example, for the case of MSA of normal lathes, the measuring scheme can be without pieces attached to main spindle (see fig. 2, a), with shaft 1 (see fig. 2, b), or with chuck 2 and shaft 1 (see fig. 2, c). Application points of force, AF, and deformation, [A.sub.U], can be different (see fig. 2) or identical (see fig. 3), and may be considered in different positions.

Two rigid shafts that may be used for MSA loading are shown in fig. 3. The rigid shafts are composed of two assembled parts: body, 1, and spherical part, 2. Body 1 has a spherical surface, a, for deformation measuring, and part 2 has a spherical surface, b, for applying the loading force. 3 holes, c, in part 2 permit the access of the gauges used for deformation measuring. Surfaces d and e are used for assembling the two parts.

A loading-measuring scheme for MSA is shown in fig. 4.

[FIGURE 1 OMITTED]

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

[FIGURE 4 OMITTED]

The scheme in fig. 4 includes the MSA 1 and a rigid shaft composed of body 2 and the spherical element 3. MSA can be loaded on different directions. The deformation is measured for the force's application point ([A.sub.F] = [A.sub.U]) because of the spherical head of the body that transmits its deformation to three inductive gauges 4. The inductive gauges are fixed upon the normal lathe's bed with the magnetic holders 5. The loading force is realized by a dynamometric device that includes a prismatic part 6 and a rotating part 10. Part 6 is fixed to the cutting tool's support 8 of the lathe. In order to have a correct position on y-axis for the dynamometric device, there is used an adjusting screw 7. The rotating part 10 supports the force detecting element 9. The loading of MSA can be realized at different axial positions, [l.sub.1]. RPR and RGR are relative physical reference and relative geometrical reference associated to the normal lathe. RPR is the lathe's bed and RGR is placed on the lathe's bed.

3. EXPERIMENTAL DATA

The experimental conditions are as follows:

--Normal lathe: SNA500;

--System's state: repose;

--Main spindle's assembly is equipped with the right hand side shaft in fig. 3 ([A.sub.F] = [A.sub.U]);

--RPR: lathe's bed;

--RGR: O'x'y'z';

--Axial position: [l.sub.1] = 65 mm;

--F = [F.sub.st]: [F.sub.x], [F.sub.y], [F.sub.xy], [F.sub.xyz] [daN];

--U = [U.sub.st]: X, Y [[micro]m].

Experimental data are presented in tables 1, 2, and 3.

In table 1, [F.sub.st] = [F.sub.x] and [F.sub.st] = [F.sub.y], respectively. In table 2, [F.sub.st] = [F.sub.xy] and [[phi].sub.y] = 30[degrees]. In table 3, [F.sub.st] = [F.sub.xyz], [[phi].sub.y] = 30[degrees], and [[phi].sub.z] = 75[degrees].

Using the data in table 1, MSP rigidities in daN/mm are as follows:

[K.sub.xx] = [F.sub.x]/X = 400/0,0521 = 7678; [K.sub.yy] = [F.sub.y]/Y = 400/0,0363 = 11019 (1)

Using the data in table 2, MSP rigidities in daN/mm result as follows:

[K.sub.x30] = [F.sub.xy]/X = 400/0,0424 = 9434; [K.sub.y30] = [F.sub.xy]/Y = 400/0,0572 = 6933 (2)

Using the data in table 3, MSP rigidities in daN/mm are:

[K.sub.Sx] = [F.sub.xyz]/X = 400/0,0623 = 6420; [K.sub.Sy] = [F.sub.xyz]/Y = 400/0,0669 = 5979 (3)

[K.sub.Sz] = [F.sub.xyz]/Z = 400/0,0091 = 43956; (4)

where S stands for the direction of spatial force [F.sub.xyz].

4. CONCLUSION

Determination of the rigidity of normal lathes and of the main spindle's assembly (MSA) of lathes claims for a particular work environment, which refers to the structure of technological manufacturing systems, references, states, loading, and strains.

The paper presents loading--measuring schemes for main spindle's assembly of normal lathes and some research devices. So, a dynamometric device for 3D loading has been realized, and is described in the paper. In order to materialize the application points of forces and deformations, two rigid shafts with spherical heads were also realized and presented in the paper.

The paper presents a unitary methodology for experimental determination of static rigidity for main spindle's assembly of normal lathes. The methodology can be extended to other components of normal lathes or to other technological manufacturing systems.

5. REFERENCES

Tonoiu, S. & Iliescu, M. (2002). Determination of static rigidity for main spindle's assembly of normal lathe, Proceedings of the 4th workshop "Human Factor and Environmentalist", Katalinic, B. (Ed.), pp. 105-106, ISBN 3-901509-37-2, Kosice-Slovakia, December2002, DAAAM International, Vienna

Tonoiu, S. (1999). Contributions on the study of machining technological systems rigidity, Ph.D. Thesis, POLITEHNICA University of Bucharest, 1999, Romania (in Romanian)

Tonoiu, S.; Dulgheru, L.; Catana, M. & Purcarea, M. (1997a). Methods for experimental determination of static rigidity for machining technological systems, Proceedings of the 9th international Conference on Machine Tools, pp. 501-508, ISBN 973-31-1139-2, Bucharest-Romania, 1997, Ed. Tehnica, Bucharest (in Romanian)

Tonoiu, S.; Purcarea, M. & Catana, M. (1997b). Considerations on contact rigidity and dumping in machining technological systems, Proceedings of the 9th international Conference on Machine Tools, pp. 509-516, ISBN 973-31-1139-2, Bucharest-Romania, 1997, Ed. Tehnica, Bucharest (in Romanian)

Weck, M; Eckstein, R & Schafer, W. (1989). Methods for determination of machine tool static rigidity, Mechanik, No. 4, 1989, pp. 125-129 (in Polish)

Tab. 1. [F.sub.x] and [F.sub.y] loadings.

[F.sub.x] X [[micro]m] [F.sub.y] Y [[micro]m]
 [daN] incr. decr. [daN] incr. decr.

 0 0 0.9 0 0 2.3
 50 10.5 11.1 50 10 15.5
 100 19.2 20.1 100 19.5 24.7
 150 25.8 27.1 150 24 28.6
 200 33.2 33.7 200 26.9 31.7
 250 38.1 39.4 250 29.9 34.1
 300 45.1 45.9 300 33 36.2
 350 49.9 50.5 350 34.3 36.3
 400 52.1 52.1 400 36.3 36.3

Tab. 2. [F.sub.xy] loading ([[phi].sub.y] = 30).

 X [[micro]m] Y [[micro]m]
[F.sub.x]
 [daN] incr. decr. incr. decr.

 0 0 2 0 2.7
 50 7.4 10 11.1 11.6
 100 15.3 20.1 20.5 28.6
 150 22.7 28.4 29.1 37
 200 30.6 34.1 38.7 44.9
 250 37.2 38.5 47.5 50.2
 300 40.5 41.1 53.2 55
 350 41.3 42 55.4 57
 400 42.4 42.4 57.2 57.2

Tab. 3. [F.sub.xyz] loading ([[phi].sub.y] = 30[degrees]
and [[phi].sub.z] = 75[degrees]]).

[F.sub.xyz] X [[micro]n] Y [[micro]m] Z [[micro]m]
 [daN]
 incr. decr. incr. decr. incr. decr.

 0 0 0.9 0 2.7 0 1.7
 50 6.9 7.8 6.6 11.9 0.5 3.6
 100 16.4 18.4 14.3 21.6 2.1 5.3
 150 24 27.1 23.5 31.7 3.6 7.2
 200 32.8 36.5 33 41.1 4.5 7.8
 250 40.9 45.9 42 50.6 5.8 8.2
 300 48.1 53.4 50.2 58.4 6.8 8.7
 350 55.1 60 58.1 65.1 7.8 9
 400 62.3 62.3 70 70 9.1 9.1