**Paper: Effects of operating conditions and friction on the
entrapment of spherical debris particles in elliptical contacts.**

**Authors:
****George
K. Nikas**

** Published
in: **Proceedings of the
Institution of Mechanical Engineers, Part J: Journal of Engineering
Tribology, 2007, 221(6), 727-741

**Abstract**

Based on a mechanistic model of entrapment and rejection of spherical debris particles in elliptical contacts of various machine elements, which has been recently published by the present author, a parametric study has been conducted to analyse the effects of the contact load and speed, lubricant viscosity (in the case of lubricated contacts) and particle-contact-counterface friction coefficients on the critical particle size for entrapment, rejection and intermediate states. The simulation involved a conforming as well as a non-conforming elliptical contact. The parameters were varied in unequal steps as follows: the contact load from 5 to 500 N, the contact speed (average speed of the two counterfaces) from 0.005 to 5.500 m/s, the lubricant dynamic viscosity from 0.001 to 1.000 Pa·s, and the friction coefficient between a particle and a contact counterface from 0.02 to 0.20 (with, generally, different coefficients used for the two counterfaces). The results are in the form of two- and three- dimensional graphs and contour maps, showing the zones of particle entrapment, rejection, “weak rejection”, etc, in the contact inlet, the critical particle sizes for entrapment and rejection, as well as graphs showing most of these parameters and effects together for quick assessment. The model has proved an efficient mathematical tool in predicting the risks of contact damage from debris particles by offering both clear quantitative as well as qualitative answers, and can assist in the selection of proper filtration or sealing systems, or simply be used as a supplementary tool in life-expectancy calculations of concentrated contacts in machine-element applications.

**Some
figures from this work**

Figure 1 shows a spherical particle of centre K in contact with the counterfaces (surfaces 1 and 2) of an elliptical contact at points A and B.

**Fig. 1.** Debris
particle contacting the counterfaces of an elliptical contact.

The calculation of the contact geometry, the location of particle contact points A and B, the calculation of the particle-counterface normal and frictional contact forces, as well as the calculation of the fluid force on the particle from the lubricant used in the contact, are all described in a previous publication of the author and briefly summarized in the present paper. Based on the force resolution on the particle, suitable criteria for entrapment, "unconditional rejection", "weak rejection", etc, are applied, as postulated in the related previous publication of the author and summarized in the present paper.

Figure 2 shows one of the many
maps presented in the paper, depicting part of the contact inlet, where *x*
is along the line of motion and point (*x* = 0, *y *= 0) is
the contact centre.

**Fig. 2.** Force
vectors (*F*_{x}, *F _{y}*) (shown
with distributed arrows) and
contour map of particle diameters with labels 40, 80…560 for
particle diameter in micrometres.

The map shows the fluid film
contour lines (the labels are in micrometres). A spherical particle in
geometrical contact with both counterfaces at a position (*x*, *y*)
has diameter approximately equal to the film thickness at that position,
thus the contour lines also depict the particle diameter for a particle to
be in geometrical (that is undeformed) contact with the counterfaces. The
map also shows the projection on the *xy*-plane (tangent plane of
the elliptical contact) of the total force on particles in contact with
the counterfaces by means of distributed arrows. Looking at the angles of
the arrows, it is easy to establish where a particle is dragged towards
the contact and where it is pushed away. Also on the map, the zones of
particle entrapment, unconditional rejection, weak rejection, etc, are
clearly shown and quantitatively defined. For the example shown in Fig. 2,
the maximum particle diameter for entrapment at the centreline of the
contact (*y* = 0), *D*_{e},
and the minimum particle diameter for unconditional rejection, *D*_{r},
are calculated equal to 11.3 and
332.8 microns, respectively. Maps like that are presented in the paper
for various lubricant viscosities, contact loads and speeds.

Another form of mapping discussed in the paper concerns the effect of
the Coulomb friction coefficients, *m*_{1} and *m*_{2}, between a particle and the contact
counterfaces. Figure 3 shows such an example for a conforming contact,
where it is clear that the effect of the friction coefficients on the minimum
particle diameter for unconditional rejection, *D*_{r},
is significant. Figure 3 shows both a surface and the corresponding
contour map overlaid for best visualization.

**Fig. 3.** Example of
the effect of the counterface friction coefficients.

The paper ultimately presents figures showing the effects of contact load, contact speed, and lubricant dynamic viscosity on the critical particle diameters for entrapment and unconditional rejection, following a parametric study. Such results are presented in Fig. 4 for a conforming elliptical contact.

**Fig. 4.** Effects
of the lubricant dynamic viscosity, contact speed and load.

It is thus easy to quickly evaluate the risks involved in a particular elliptical contact under specific operating conditions in terms of debris particle contamination...