Using mathematical formulations to plot the graphs of the contact preload versus the Hertzian load, calculations of unit loading of the preloaded brushes on slip rings can be made. This optimizes the design of contact brushes and miniature slip rings

Albright, F. G.

Domerest, K. E.

Horton, J. C.

English

NASA Technical Reports Server

April 1965
	 Brief 65-10098 
NASA TECH 
NASA Tech Briefs are issued by the Technology Utilization Division to summarize specific 
technical innovations derived from the space program. Copies are available to the public from 
the Clearinghouse for Federal Scientific and Technical information, Springfield, Virginia, 22151. 
Contact Stresses Calculated For Miniature Slip Rings 
Preload (L) 
The problem: In order to optimize the design of 
contact brushes and miniature slip rings, the stresses 
on the contact brush and ring must be known for 
various configurations and preloads applied to the 
brushes. In general the contact area between the brush 
and ring must be as large as possible to reduce the 
contact stresses which tend to roughen the surfaces, 
causing arcing and shortening the life of the assembly. 
The maximum contact area is governed by the 
amount of friction-caused mechanical constraint that 
can be tolerated. 
The solution: Using the mathematical formulations 
given below, one can plot the graphs of the contact 
preload versus the Hertzian load. With these graphs 
the ideal configuration for the particular application 
can be obtained. 
How it's done: The calculation of the unit loading 
of the preloaded brushes on slip rings assumes 
Hertzian stresses similar to those found in bearings.
The mathematical analysis is based on the assumption 
that the brush and ring are of the same material. The 
Hertzian stress P for this application is given by 
P = L'/A 
where L' = L cos 0 
A - Area of Contact = irg2 
The area of contact A is dependent on the Hertzian 
function g which is given by 
3 73L' (I—i 2) R+Rh 
g=/
E(R'a + Rb) 
where E is Young's modulus, J is Poisson's ratio, and 
R b and R'aare radii of the objects in contact. 
From these equations, curves may be plotted vary-
ing the parameters of design, such as brush diameter, 
brush preload, groove angle (0), slip ring diameter 
( Ra), and material. An analysis of these curves will 
then help to obtain the optimum design.
conLunueu overleut) 
This document was prepared under the sponsorship of the National 
Aeronautics and Space Administration. Neither the United States Govern-
ment, nor NASA, nor any person acting on behalf of NASA: A. Makes 
any warranty or representation, express or implied, with respect to the 
accuracy, completeness, or usefulness of the information contained in
this document, or that the use of any information, apparatus, method, 
or process disclosed in this document may not infringe privately-owned 
rights; or B. Assumes any liabilities with respect to the use of, or for 
damages resulting from the use of, any information, apparatus, method, 
or process disclosed in this document.
https://ntrs.nasa.gov/search.jsp?R=19650000097 2020-03-11T17:22:01+00:00Z
A set of curves using Hertzian load versus brush 
preload have been plotted for gold while varying the 
groove angle from 600 to 900, brush diameter from 
0.007 inch to 0.010 inch, and ring diameter from 0.14 
inch to 0.35 inch. Contact stresses were found to be 
between 50,000 to 120,000 psi, with preloads varying 
between 2 and 16 grams. From the curves it was noted 
that contact stress varies exponentially with brush 
preload and the exponent is less than one. An increase 
in preload from 4 grams to 8 grams gives an increase 
in contact stress from only 72,000 psi to 90,000 psi. 
Also, small increases in brush diameter from 0.007 
inch to 0.010 inch and a decrease in groove angle 
from 900 to 60° may result in as much as 30% re-
duction in contact stresses. 
The contact area was found to be approximately 
5 x 10-8 square inch, which may not give a stable
contact with a surface finish of 5 x 1 0_6 inch 
(RMS) and the above configurations. It was also 
found that the change in ring diameter within 0.14 to 
0.35 inch had little effect on the contact area. 
Note: Inquiries concerning this innovation may be 
directed to:
Technical Utilization Officer 
Marshall Space Flight Center 
Huntsville, Alabama, 35812 
Reference: B65-10098 
Patent status: NASA encourages commercial use 
of this innovation. No patent action is contemplated. 
Source: K. E. Domerest, F. G. Albright,

and J. C. Horton
(M -FS-280) 
Brief 65-10098	 Category No. 05


Contact stresses calculated for miniature slip rings

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