By Robert S. Mroczkowski, Sc.D.
The purpose of this discussion is to build a bridge between contact force and connector electrical resistance, both magnitude and stability.
Over nearly 20 years of consulting on connector design issues, the most common question I have faced is some variant on, "What is the minimum contact normal force for a connector?" The second most common question is, "How much plating do I need?" Unfortunately, neither of these questions has an answer because both are application-dependent. This article addresses the issues relevant to defining a "minimum" contact normal force.
First, a general answer to the contact force question: The minimum normal force required in a given connector application is the force necessary to ensure the mechanical stability of the contact interface in the application operating environment.
Contact Normal Force Question
The "contact normal force question" is often asked with the expectation that an absolute minimum, independent of the contact finish and the application requirements, exists. This, as stated, is not the situation. There was, and possibly still is, a general idea that 100 grams is a good guideline. This is certainly not the case because demanding qualification requirements, and field history, indicate contact force in the range of 50 grams is satisfactory in some applications. The 100 gram value, as best I can determine, was first stated in 1970 by Robert van Horn of Bell Laboratories. That value was stated with many qualifications, which, of course, have fallen by the wayside over the years with only the 100 grams remaining.
 Figure 1. Contact resistance vs. contact normal force. The a-spot structure of the contact interface as a function of contact force is schematically illustrated. |
Another, even more fundamental, definition of connector performance requirements is offered in my article, "Getting Back to the Basics," in Connector Specifier May 2000: "A connector can be defined as an electromechanical system that provides a separable connection between two electronic systems without an unacceptable impact on signal transmission or power loss."
Three important components are in this definition. First, a connector is intended to provide a separable connection. There are many reasons why separability may be required, but it is a given or a connector would not be used. Second, a connector is an electromechanical system — it has an electrical function but that function is provided by mechanical means (this is where contact force comes into the picture). Finally, the last phrase, "unacceptable impact on signal transmission or power loss," can be simplified into an acceptable and stable value of connector electrical resistance.
Bridge Between Force and Resistance
The purpose of this discussion is to build a bridge between contact force and connector electrical resistance, both magnitude and stability. The important point for this article is that the contact force causes the deformation of the contact surfaces, which creates the initial contact interface. In particular, the contact force determines the magnitude of the contact area created. The contact area, in turn, determines the resistance of the contact interface. A simple formula relating contact force to contact resistance can be derived. First, Ragnar Holm, the founder of contact physics, shows that the resistance of a single contact spot, Rc, between two pieces of the same material is given by:
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where p is the resistivity of the materials in contact and d is the diameter of the contact spot (assumed circular). The diameter of the contact spot can be derived from consideration of the material hardness, H:
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where F is the applied force and A is the contact area generated by that force. For a circular contact area:
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Substitution gives the final relationship:
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For these purposes, it is sufficient to note that for a given material, the resistance of a contact between two surfaces is inversely proportional to the contact force. Increasing contact force always reduces contact resistance.
A-spots
"But," you may say, "in 'Getting Back to the Basics,' it states that a typical contact interface consists of a number of a-spots in parallel and this equation is for a single spot." Figure 1 suggests why a single-spot model is, in fact, appropriate. At low force, there is a small number of a-spots, but the number increases with the applied force. These a-spots act like resistors in parallel. After sufficient force is applied, the multiple a-spot interface behaves like a single spot of some "average" area. The current flow is constricted to the distributional area of the a-spots rather than being dominated by the individual a-spots. Trust me on this. Remember also that this argument applies to metallic contact interfaces, surfaces free of films (noble metal finishes) or surfaces that have had any films displaced by mechanical action (tin finishes).
Increasing contact force always reduces contact resistance. Figure 1 indicates that the contact resistance at a few tens of grams contact force is a few milliohms. (The asymptotic behavior is a bit daunting, but it is not as dramatic as the figure suggests.) Except for power applications, a few milliohms is an acceptable value of contact resistance so a few tens of grams contact force should be sufficient. Yes, sufficient to create the contact interface, but remember that the stability of the contact interface is also a performance requirement for a connector. What value of contact force is necessary to maintain the stability of the contact interface?
Stability, as used here, refers to mechanical stability. A mechanically stable contact interface is one that does not move under the various driving forces of the application environment. (A mechanically stable contact interface, however, is also an electrically stable contact interface.) Driving forces for motion include mechanical, such as vibration and shock, and thermal due to thermal expansion mismatches. A stable contact interface must be able to resist such forces and the required resistance arises from friction forces due to the contact force. The friction forces generated by the contact force arise from creation of areas of metallic contact (i.e., the same interfaces that create conductivity across the contact interface and reduce contact resistance). The magnitude of the friction force, Ff, which stabilizes the contact interface is given by:
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where m is the coefficient of friction and Fn is the contact force. The coefficient of friction is a function of the material, the surface roughness and the contact force. For these purposes, the most important variation is with force. The coefficient of friction can change dramatically with contact force. A typical coefficient of friction for connector materials is in the range of 0.3 to 0.7 for contact force around 100 grams, but it can rise to over 1.0 for forces in the range of several hundred grams.
Increasing contact force, therefore, benefits contact resistance in two ways. First, it reduces the magnitude of contact resistance by creating larger contact areas. Second, it increases mechanical stability by increasing the friction forces that maintain the stability of the contact interface. With respect to contact resistance, the more contact force the better. Unfortunately, there are other considerations. Engineering is a consideration of tradeoffs, and, in the best cases, optimization of conflicting requirements. Connector design exemplifies this experience. A connector is used because of a requirement for separability. High contact forces, in general, have a negative effect on separability requirements, such as mating force and wear durability. These considerations will be addressed in my next article, as the search for the elusive "minimum contact force" continues.
ROBERT S. MROCZKOWSKI, Sc.D., a Connector Specifier Advisory Board Member, is Founder, connNtext associates, 38 Cider Press Rd., Mannheim, PA 17445; (717) 664-2246; Fax: (717) 664-1666; E-mail: connNtext@earthlink.net.
