# Shape Optimization of contact contacts for reduced wear and reduced insertion force

Shape Optimization of Connector Contacts for Reduced Wear and Reduced Insertion Force
Jochen Horn Bernhard Egenolf AMP Deutschland GmbH

ABSTRACT
Concept and formulas are presented for predicting optimized shapes of pin and socket spring at the entry portion of a connector. The results are reduced insertion force and wear caused by friction during mating. A particular advantage of the method is that changes of existing designs require minor shape modifications only of the regions where pin and socket slide against each other during insertion.

and the finite value of the force acting normal to the contacting surfaces, wear occurs at these surfaces. Two Cartesian systems of coordinates {Xs,Ys} and {Xf,Yf] where the first is fixed to the pin, the second to the socket are introduced. Both move relative to an external system fixed in space in which the insertion distances is measured. The schematics shown in Figures 1 and 2 offer the means to optimize the set of geometric parameters Ys(Xs) and Yf(Xf) for pin and socket springs. The subscripts s and f indicate pin (Stift) and spring (Feder), respectively. A comparison of the force components yields for the insertion force Fs as function of the insertion distance s

INTRODUCTION
Reducing insertion force and wear are among the goals of optimization of pin and socket connectors with a contact spring. Previous efforts concentrated almost entirely on development of improved coatings applied to the contact surfaces. Departing from the conventional approaches, this paper concentrates on the effect of the pin and socket’s shape on insertion force and wear. Of particular importance in this regard are special geometries of the pin tip and the socket entry.

with Ff = Ff(x)= spring force; x(s) = spring deflection; s = insertion distance; m = coefficiant of dynamic friction; a = a (s) = angle between connector axis and tangent to surface of socket and spring at point of contact; b 0 = angle between spring element and connector axis before insertion; bb= bb(s) = angle between connector axis and the line formed by connecting and actual contact point to the fixed point of the spring;

GENERAL APPROACH
To accomplish smooth and easy formation of the contact, the pin is pointed and enters funnel-shaped socket springs. During insertion, the pin and socket slide along each other, whereby a force component essentially normal to the direction of insertion evolves. This force loads the springs. The deflected springs then produce the contact force required for the electrical connection. Because of the sliding motion

? Copyright 1992 by AMP Incorporated. All rights reserved. Abstracting is permitted with credit to the source. Copying in printed form for private use is permitted providing that each reproduction is done without alteration and the Journal reference and copyright notice are included on the first page. Permission to republish any portion of this paper must be obtained from the Editor.

42

J. Horn and B. Egenolf

AMP Journal of Technology Vol. 2 November, 1992

The angle a (S) is strongly determined by the shape of pin and socket. It depends also on the first derivatives d(Y s)/ d(Xs) and d(Yf)/d(X f), which are functions of the coordinates Xs and Xf, respectively. The general behavior of the insertion force Fs(s) is shown

in Figure 2. As shown in detail in reference 1, variation of Ff(x(s)) and a(s) in equation (1) caused by variations of Y,(Xs) and Yf(Xf) indicates that the shape of the curve and its maximum depend critically on the geometry of the two contacts. This effect is used to design for reduced insertion force. Contact pressure is a measure for stress causing wear in sliding friction between solids. 2-4 Wear increases with increasing contact pressure. The glide or sliding path of the connector contacts within the entry regions of spring and pin is, in either case, characterized by the contact pressure

Figure 1. Schematic of contact model. H = width of socket, 2 · B, = width (diameter) of pin, 2. P s = width (diameter) of tip of pin, L s = length of pin taper, So = distance of spring before insertion.

The two radii of curvature Rs(s) and Rf(s) depend on the derivatives d(Ys)/d(X s), d2(Y s)/d(X s) 2, and d(Yf)/d(X f), d2(Yf)/d(X f)2, respectively. These derivatives are functions of Xs and Xf, which, in turn, are determined by the original geometry of pin and socket. Therefore, the pressure p(s) in equation (2), including its peak value, depends also on geometric parameters of pin and socket at the entry region. Since the wear is determined by the pressure p(s) it can also be controlled by proper geometric design. During insertion the position of the contact point at socket X f and pin Xs is a function of the insertion distances:

Figure 2. a) Illustration of force components during insertion, b) qualitative graphic representation of insertion force Fs as function of insertion distances. Section I would correspend to the load phase; section II to the wipe phase during insertion.

so that the pressure at the surface of socket and pin is also

a function of Xf and Xs:

AMP Journal of Technology Vol. 2 November, 1992

J. Horn and B. Egenolf 4 3

P(X s) = K · Pc(X s), and is determined by equations (1) to (7).

(9)

A computer program permits numerical evaluation of equations (1) to (9) for various combinations of geometric parameters and functions Ys(Xs) and Yf(Xf). The most desirable set of them is then selected to meet the following requirements:
?

top geometry of the pin contributes most to the insertionforce reduction. Optimizing the spring shape only reduces (Fs)max by 11%, that of the pin only by 19%. A similar performance improvement is shown for the pressure p(X s) and p(X f) in Figure 6. Introducing the new entry shapes for pin and spring reduces by 70% the stress component responsible for sliding wear and flattens the entire p(X) -curve to a more uniform one. Again, the change of the pin shape contributes most to the improvement. The validity of the optimization concept and the specific approach described here was tested experimentally. Figure 7 shows three different pin shapes used in this evaluation. Figure 8 shows the results by plotting the measured insertion force against the displacement distance s for the three different pins. The measurements confirm the theoretical predictions.

Low level of insertion force,
?

Low maximum pressure and uniform pressure distribution.

Not directly derived from the equations, a third requirement is introduced: Measured on the socket surface, the difference between the position where maximum pressure occurs and that of establishing the electrical contact should be large. This requirement results in reduced creep and also a reduction of displacement of particles generated by wear and the presence of corrosion products.

A

EXAMPLE
Without changing the main dimensions of pin and socket, a given connector was optimized regarding insertion force and pressure by modifying the shape of the two connector elements in the entry region. The original shapes are shown for the spring and the pin in Figures 3 and 4, respectively, as curves (l). To illustrate the changes, the contours of the mathematically derived optimum shapes are shown as curves (2) in the same figures.

BS

L,
v

Figure 4. Contours of pin shape at entry portion: (1) original shape, (2) theoretically predicted optimized shape. For definition of Ls, Ps and Bs see Figure 1.

g

120

1

2

J
Figure 3. Contours of spring shape at entry portion: (1) original shape, (2) theoretically predicted optimized shape. For definition of Lf and Bf see Figure 1.
o

7.3

7.3. 7.1 7.0 6.9 6.8 6.7 6.6 6.6 6.4 6.3 6.2

Insertion Distance s (mm)

*

Introducing the geometric parameters of the original design and the optimized pin-socket combination in equation (1) and plotting F s(s) versus sin Figure 5, shows that the insertion force maximum is reduced by 30% relative to that of the original combination. A comparison of the four curves in the graph illustrates also that the change in the

Figure 5. Computed insertion force Fs(s) for different combinations of shapes of pin and spring: (1) original system, (2) optimized system, (3) original spring/optimized pin, (4) original pin/optimized spring.

44

J. Horn and B. Egenolf

AMP Journal of Technology Vol. 2 November, 1992

One advantage of the concept of connector optimization by optimizing contact geometry at the entry region is that the optimized contacts can be used in the original system because the optimization does not require major dimensional changes of the connector parts. The minor changes made to correct the surface within a rather narrow range leaves the improved version compatible with the original one.

90 — i? 80 — ~ IL” a) : g ~ .Y ~ 70 — 60 — 50 — 40 30 f V u - 3

0

0

0.5

LO

1.5

2.0

2.5

Insertion Distance s (mm)

Figure 8. Measured insertion force Fs(s) for pins of Figure 7: (1) optimized pin, (2) and (3) original, wedge-shaped pin.

-- 0.1

0.2

0.3

0.4

0.5

CONCLUSIONS
X, (mm)

x f (mm)

Figure 6. Computed value P (proportional to contact presC sure) as function of a) Xf coordinate of the spring, b) Xs coordinate of the pin. In both, (1) is the original system and (2) is the optimized system.

The mathematical procedure for reducing insertion force and wear through optimization of the pin and socket spring shapes at the entry range offers a valuable design tool. The theory was confirmed experimentally and proven in manufacturing. In one actual case the insertion force of the connector with wedge-shaped pins was about 50 N. The new pin shape with optimized geometry at the top reduced the insertion force to about 20 N.

a

b

c

Figure 7. Illustration of shapes of pins: a) optimized pin, b) and c) original, wedge-shaped pin.

AMP Journal of Technology Vol. 2 November, 1992

J. Horn and B. Egenolf 45

REFERENCES
1. J. Horn, Mechanische Eigenschaften von Kontaktsystemen und Kontaktoberjlachen. Dissertation B, Technische Universit?t Chemnitz, 1985. 2. I.W. Kragelski, Reibung und Verschleiff (Verlag Technik, Berlin, 1971), p. 170. 3. J.F. Archard, J. Appl. Physics 24,981 (1953). 4. R. Helm, Electric Contacts: Theory and Applications, Fourth Ed. (Springer Verlag, Berlin, 1967).

Jochen Horn is in the Engineering Department at AMP

Deutschland GmbH in Langen, Germany.

Dr. Horn holds a diploma in physics from Technische Unuversit?t Dresden, a Dr. rer. nat. in 1976 and a Dr. sc. nat. in 1985 from Technische Universit?t Chemnitz. During 1966–88 he worked at the Technische Universit?t Chemnitz on physics of thin films. He authored or co-authored more than 40 articles. Since joining AMP in 1989, he has worked in the areas of contact physics, the characteristics and use of new finishes as well as base materials. He is a member of the Metal Finishing Working Group.
Bernhard Egenolf is Project Engineer in Automotive Product Engineering at AMP Deutschland GmbH, Langen, Germany.

B. Egenolf is Diplom-Ingenieur für Precision Engineering (1964) from Ingenieurschule (now named Fachhochschule) Frankfurt am Main. He worked at VDO, Frankfurt am Main, with thermo- and fuel sensors and at Honeywell, D?rnigheim, with electronic packaging. From Braun, Kronberg, he possesses patents for home appliances. He joined AMP in 1972 and was responsible for design and introduction of MT-Interconnectionsystem, MT-Edge and Timer-Connectors for washing-machines. Since 1984 he developed the well known Junior-, Standard- and Maxi-Power-Timer contacts.

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J. Horn and B. Egenolf

AMP Journal of Technology Vol. 2 November, 1992

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