Considerations upon the circular section circlips/retaining rings axial load-carrying capacity.

Argesanu, Veronica ; Luchin, Milenco ; Jula, Mihaela 等

1. INTRODUCTION

Circlips / retaining rings are designed to position and secure component in bores and houses. Simultaneously they provide rigid end--play take--up in the assembly to compensate for manufacturing tolerances or wear in the retained parts. For the technical designer, who uses standardized and/or in a list manufactured rings on shafts or in housings with nominal diameter, a computation is not necessary. It is of crucial importance however with special applications of the normal rings and particularly with the construction of special rings.

The reasoning for the fundamentals of the bending calculus is presented in detail (Mesaros-Anghel et al., 2006) for circlips with rectangular section, and FEM analysis has been done. The authors propose to analyze circular section circlips. The conclusions of the paper can be directly applied in technical design. In the future, if experimental research results are added, also the reconsideration of the present standards regarding shape, dimensions, and materials can be made

2. FUNDAMENTALS

The strength calculation is based on the consideration that a circlip -for the shaft or for the housing--is a curved bended bar.(Argesanu, 1999); (***. 1973); (Voinea, 1989) The ideal solution is a curved bar of same firmness (Hubener, 1970).

The circular section is particularized in fig. 1 and the following equations:

1/r = [M.sub.b]/EI (1)

If a bar with a neutral radius of curvature r, already curved, is deformed on a radius [rho], the equation is:

1/r - 1/[rho] = [+ or -] [M.sub.b]/EI (2)

Using the names for the neutral diameters, usual with circlips

r = 1/2 x [D.sub.3] ; [rho] = 1/2 x D1 ; 2/[D.sub.3] - 2[D.sub.1] = [+ or -] [M.sub.b]/EI (3)

1/[D.sub.1] - 1/[D.sub.3] = - [[sigma].sub.b]/E x [d.sub.c] 1/[D.sub.3] - 1/[D.sub.1] = - [[sigma].sub.b]/E x [d.sub.c] (4)

[[sigma].sub.b] = ([D.sub.1] - [D.sub.3]) x E x [d.sub.c]/[D.sub.1] x [D.sub.3] [[sigma].sub.b] = ([D.sub.3] - [D.sub.1]) x E x [d.sub.c]/[D.sub.1] x [D.sub.3] (5)

[[sigma].sub.b] = 1,15 ([d.sub.1] - [d.sub.3]) x E x [d.sub.c]/([d.sub.1] + [d.sub.c])([d.sub.3] + [d.sub.c]) [[sigma].sub.b] = 1,15 ([d.sub.3] - [d.sub.1]) x E x [d.sub.c]/([d.sub.1] - [d.sub.c])([d.sub.3] - [d.sub.c]) (6)

[[sigma].sub.b] = [M.sub.b]/W = P x I x 6/[d.sup.2.sub.c] x s becomes P = [[sigma].sub.b] x [d.sup.2.sub.c] x s/6 x I (7)

[FIGURE 1 OMITTED]

[FIGURE 2 OMITTED]

3. COMPUTATION OF THE CIRCLIP

For the special cases mentioned above it is of interest the axial loading behavior (and axial load-carrying capacity) of the ring as well as its stability in the reserved groove (in the shift or housing)

Fig.2 presents the situation in which a machine part presses a circlip with an axial force. At first sight, shearing seems to condition for the drawing out of use of the ring, so that, at the beginning of the use of these machine elements it was very much insisted on this kind of calculation. It was observed that, because of the relationship between the depth of the groove and the thickness of the ring, the shear never takes place because at loadings under the maximum stress there takes place a loss of stability by deformation (as in fig.3a,b,c)

It is said that the ring is "inverted" The deformation is determined by the occurrence of a lever arm that modifies by a bending moment the shape of the ring that becomes conical. For a better understanding of the situation, the deformation (the characteristic angle [psi]) is exaggeratedly enlarged. As to be seen, between the chamfer g and the level of the elastic deformation i of the groove edge, there appear the lever arm. It results in a displacement of the machine element adjacent on the distance f.

Similarly, the phenomenon appears in the case of rounded edges at adjacent machine elements. For sharp edges, plastic deformation of the groove edge (together with elastic deformation) contributes also to the apparition of the lever arm. For loads that determine a too high value of the angle v|/ there appear permanent conical deformations or even the failure of the ring.

If the ring is considered an axial elastically element, the formula (8) is applied

[P.sub.R] = C x f (8)

[pi] x E x [d.sub.c.sup.3]/6 ln (1 + 2 x [d.sub.mc]/[d.sub.2]) = K (9)

C = K/[h.sup.2] (10)

[psi] = f/[h.sup.2] (11)

[P.sub.R] = [psi] x K/h x S (12)

[K.sup.I] = K x [E.sup.I]/21000 (13)

4. FEM RESULTS

The analyze was made for a ring of 3.4 mm(***STAS 8436-69). The applied load was scaled in 10 steps from 15 to 1500 N. In figures . 4, 5 and 6. is presented the displacement of the ring for 150 and 300 N

[FIGURE 3 OMITTED]

[FIGURE 4 OMITTED]

[FIGURE 5 OMITTED]

[FIGURE 6 OMITTED]

5. CONCLUSIONS

For the reaching of high load-carrying capacities it is to be thus always aimed at that the effective lever arm is as small as possible h.

The conclusions of the paper can be directly applied in technical design and in the future if experimental research results are added, the reconsideration of the present standards regarding shape, dimensions, and materials can be made.

6. REFERENCES

Argesanu, V., s.a. (1999). Element of mechanical engineering, Ed. Eurostampa, Timisoara.

Hubener R.. (1970). Seeger rings. A manual for the Constructor, Seeger-Orbis Gmbh, Schneidhain/ Taunus.

Mesaros-Anghel, V., Argesanu, V., Madaras, L., Cuc, A. (2006). Rectangular section circlips/retaining ringsaxial load-carrying capacity considerations, COMEFIM'8 The 8-th International Conference on Mechatronics and Precision Engineering, in Acta Technica Napocensis, series: Applied Mathematics and Mecahanics, 49 vol. IV, pp.843-850, ISSN 1221-5872, Technical University of Cluj-Napoca.

Voinea, R., s.a. (1989). Introduction in solid's mechanics with aplications in engineering, Ed. Academiei Romane, Bucuresti.

***. (1973) Mechanical engineer's Manual, Materials, Material's Strength, Elastically Stability, Ed. Tehnica, Bucuresti.

***STAS 8436 -69 Wire Retaining Snap Rings for shafts and hole