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