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Author: Yeh-Liang Hsu, Yuan-Chan Hsu, Ming-Sho Hsu (2000-08-04)modified: Yeh-Liang Hsu (2003-02-07); recommended: Yeh-Liang Hsu (2000-08-04).
Note: This paper is published in Transactions of the ASME, Journal of Electronic Packaging, Vol. 124, No. 3, September, 2002, p. 178~183.

Shape optimal design of contact springs of electronic connectors

Abstract

An electronic connector provides a separable interface between two subsystems of an electronic system. The contact spring is probably the most critical component in an electronic connector. Mechanically, the contact spring provides the contact normal force, which establishes the contact interface as the connector is mated. However, connector manufacturers have a basic struggle between the need for high normal contact forces and low insertion forces. Designing connectors with large numbers of pins that are used with today’s integrated circuits and printed circuit boards often results in an associated rise in connector insertion force. It is possible to lower the insertion force of a connector by redesigning the geometry of the contact spring, but this also means a decrease in contact normal force.

In this paper, structural shape optimization techniques are used to find the optimal shape of the contact springs of an electronic connector. The process of the insertion of a PCB into the contact springs of a connector is modeled by finite element analysis. The maximum insertion force and the contact normal force are calculated. The effects of several design parameters are discussed. The geometry of the contact springs is then parameterized and optimized. The required insertion force is minimized while the normal contact force and the resulting stress are maintained within specified values. In our example, the insertion force of the final contact spring design is reduced to 68.3% of that of the original design, while the contact force and the maximum stress are maintained within specified values.

Keywords: connector; contact spring; insertion force; shape optimal design.

Introduction

A connector provides a separable interface between two subsystems of an electronic system. The main function of a connector is to carry a signal or to distribute power. There are three types of connectors: circuit board to circuit board, wire to circuit board, and wire to wire [Mroczkowski, 1994]. Note that here the term “wire” also includes cables. The contact spring is probably the most critical component in a connector. Mechanically, the contact spring provides the contact normal force, which is a very important index for connector design.

All separable electrical contacts require a force to hold together the male and female halves when mated. The contact normal force provides the force that establishes the contact interface as the connector is mated, and it maintains the stability of the contact interface against mechanical disturbances during the application life. Moreover, the contact resistance of a connector is dependent on the normal force. To reduce the constriction resistance, a high contact normal force is desired.

Normal force is also required to maintain the stability of the contact interface. Sawchyn and Sproles [1992] examined connectors with different geometry parameters. Their experimental results also showed that connectors which are designed with contact geometries that provide higher local pressures, are more effective in overcoming the interference of the dust contamination. For metal connector contacts, a normal force of 100g has been a widely accepted design guideline that provides a comfortable margin to ensure reliability in general applications.

On the other hand, designing connectors with large numbers of pins that are used with today’s integrated circuits and printed circuit boards (PCB) often results in an associated rise in connector insertion force. Too high an insertion force could not only cause problems in assembly, but also cause mechanical failure in other parts of the electronic package. Connector manufacturers have a basic struggle between the need for high normal contact forces and low insertion forces. The magnitudes of normal contact force and insertion force of a connector are closely related. It is possible to lower the insertion force of a connector by redesigning the geometry of the contact spring, but this also means a decrease in contact normal force.

Design concepts other than contact springs havealso been proposed in order to reduce the insertion force without sacrificing contact forces of an electronic connector. Zero insertion force (ZIF) connectors were widely discussed in the early ‘90 [Bertoncini, et al., 1991; Chikazawa, et al., 1990; Engel, et al., 1989] and are commonly seen in electronic systems these days. However, gold plates and contact springs are still widely used in board-to-board connectors.

Structural topology and shape optimization has been a very active research field [Hassani and Hinton, 1998; Hsu, 1995]. The idea is to combine geometrical modeling, finite element analysis, and optimization into an integrated structural design process. The purpose of structural shape optimization is to determine the optimal shape of the structure that has the best performance, while satisfying all design requirements. The shape optimization methodology can certainly be applied to the design of the geometry of the connector contact springs. Sehring [1990] has suggested using finite element analysis techniques for design optimization of electronic connectors.

In this paper, structural shape optimization techniques are used to find the optimal shape of the contact springs of an electronic connector. The process of the insertion of a PCB into the contact springs of a connector is modeled by finite element analysis. The maximum insertion force and the contact normal force are calculated. The effects of several design parameters are discussed. The geometry of the contact springs is then parameterized and optimized. The required insertion force is minimized while the normal contact force and the resulting stress are maintained within specified values. In our example, the insertion force of the final contact spring design is reduced to 68.3% of that of the original design, while the contact force and the maximum stress are maintained within specified values.

Modeling the contact springs of a connector

Figure 1 shows a pair of contact springs of a board-to-board connector made of copper alloy. The springs are fixed in a plastic housing, with pins sticking out of the housing. Note that only a portion of the interface between the springs and the housing is in interference fit. The left and right springs have different shapes. When the gold plate of a PCB is inserted between the springs, the forces applied by the springs are unsymmetrical. However, in a connector, the pairs of springs are arranged in an alternate pattern, i.e., the left and right springs switch positions in the neighboring pair. Therefore force balance is maintained for the whole connector.

Figure 1. The configuration of a pair of contact springs of a connector.

Yamada and Ueno [1990] presented an analysis of insertion force in elastic/plastic mating. They considered each instance of the insertion process as a static equilibrium of the insertion force and the contact force, including the Coulomb’s friction force. The board inserted between the springs was considered rigid relative to the springs. As shown in Figure 2, at the contact point, the contact force direction is offset from the normal direction by the friction angle . The insertion process is assumed to be quasi-static. In the example presented in Yamada and Ueno’s work, the analytical expression of insertion force vs. insertion depth matches well with experimental data, using the static coefficient of friction .

Figure 2. Analysis of insertion force.

Under similar assumptions, Ling [1998] also presented a useful analysis for mating mechanics and stubbing of separable connectors. Also referring to Figure 2, there are two force components at the contact point: the normal force  and the tangential force , and . The projection of the resultant force in the y direction can be expressed as

                                                                          (1)

where  is also the required insertion force at this contact point. The projection of the resultant force in the x direction  is

                                                                          (2)

As shown in these equations, the insertion force and normal force depend heavily on the geometry of the springs, and cannot be determined using a simple beam model. A finite element analysis model is built to calculate the insertion force and normal force of the contact springs in Figure 1. Two-dimensional plane stress elements are used. Contact elements are added at the interface between the PCB and the springs. The amount of the gap and interference is prescribed as designed.

The insertion force and normal force are calculated under similar assumptions discussed in the literature. First the contact surface of the springs during the insertion process is identified and divided into discrete contact points, as shown in Figure 3. It is assumed that there is only one contact point at a given position of PCB. The insertion process is assumed to be quasi-static, therefore the static equilibrium equations such as Eq.(1) and (2) are satisfied at a contact point.

Figure 3. Discrete contact points on the contact surface of the spring.

As shown in Figure 3, to find the value of contact normal force  at a contact point  when the PCB is inserted, first the amount of deflection of the spring in the x direction  is calculated from the thickness of the PCB and the geometry of the spring. Then a secant-type interpolation procedure is used to find the value of  that would cause this deflection  in the x direction. This process continues in an iterative manner until the values of  at all discrete contact points are obtained. Figure 4 shows “normal force versus insertion length” for the contact springs in Figure 1. The coefficient of friction is assumed to be 0.175 in this figure. Substituting into Eq.(2), Figure 5 shows “insertion force vs. insertion length” during the insertion process.

Figure 4. Normal force vs. insertion length.

Figure 5. Insertion force vs. insertion length.

Figure 5 also shows the effect of the unsymmetrical shapes of the left and right springs. There are two peaks in the curve of total insertion force. In this case, the maximum insertion force 59.8g occurs at the first peak. Because of the unsymmetrical shapes, the left spring comes into contact first and the peak insertion force of the left spring occurs earlier than that of the right spring. At this contact point, the insertion force of the right spring is still low. Therefore when the insertion force contributed by the left and right springs are added together, the total peak insertion force is only slightly higher than that of the left spring. If the shapes of both springs were identical, the peak insertion force would be twice the peak insertion force of a single spring.

Figure 6 shows the stress distribution of the left and right springs calculated by the elastic finite element model. The maximum stresses, 582MPa for the left spring and 752MPa for the right spring, occur at the root of the springs. The yield stress of copper alloy is 635MPa. The right spring is over stressed at the root of the spring.

Figure 6. Stress distribution of the left and right springs.

The effect of the coefficient of friction

Figure 7 shows insertion force versus insertion length for , 0.225, 0.300. The maximum insertion force increases from 56.0g () to 90.7g (), or almost 60%. Also note that when , the location of the maximum insertion force switches to the peak of the right spring. In the mean time, the maximum normal force does not change significantly as the coefficient of friction increases.

The important role of the coefficient of friction was noticed and utilized in designing connectors for reducing the insertion force without sacrificing the contact normal force. For example, Kartlucke, et al. [1992] suggested the application of thiol-based coatings to silver surfaces to provide good corrosion protection and a reduction of the insertion and extraction forces required for electrical connectors.

Figure 7. Insertion force versus insertion length for various coefficients of friction.

The insertion forces obtained from our analysis were compared to experimental data. Three samples of the connector were measured experimentally. The insertion force of each sample was measured 30 times. In the 90 measurements, the insertion forces of the connector samples ranged from 59.5g to 69.4g per pin, and average insertion force was 62.6g per pin. Comparing with Figure 5 and Figure 7, the coefficient of friction of our contact springs is estimated to be 0.18~0.21.

In the mechanical specifications of the connector, the maximum insertion force is 95g per pin, and the minimum normal force is 60g per pin. From our analysis, normal force at the final contact point is 118g for the left spring and 148g for the right spring for . The maximum insertion force during the insertion process is 61.8g. Both contact force and insertion force satisfy the specifications. The maximum stress at the root of the right spring is 708.2MPa, which is higher than the yield strength of the copper alloy (635MPa). The size of the spring is very small (the width of the spring is about 0.5mm). Therefore plastic deformation resulted from the high stress was not visually observable in the experiments.

Another design parameter we explored was the amount of interference at the interface between the spring roots and the housing (as shown in Figure 1), which might affect the stiffness of the springs. However, we found that varying the length and depth of interference does not have significant effect on the contact normal force and insertion force of the contact springs.

Constructing the optimization model

In the current design, the normal contact forces of both left and right springs are much higher than that required by the specification. In the mean time, the stress of the right spring is too high. We can optimize the geometry of the contact springs to further reduce the maximum insertion force, while the normal force and the maximum stress are kept within specified values. The shape optimization problem of the contact spring can be described as follows:

minimize           the maximum insertion force

subject to         the normal force has to be higher than a specified value

                        the maximum stress has to be lower than the strength of material

There are also constraints on the geometry of the contact springs required by the manufacturer. These geometry constraints are embedded in the definition and restriction of the design variables used in the shape optimization model. The design variables are the positions of the control points that describe the geometry of the contact spring. As shown in Figure 8, a total of 48 control points are used to describe the geometry of the springs. To avoid generating unreasonable shapes during the optimization process, the control points are allowed to move only in the normal direction as shown in the Figures. The amount of movement  of the 48 control points are the design variables in the optimization process.

Figure 8. The control points of the springs.

 

As shown in Figure 8, the geometry of the spring is divided into three portions: the contact surface, the bending arm, and the root area. The y coordinates of the final contact points of both springs are given as part of the specification of the springs, and have to remain fixed. Therefore, one control point is located exactly at the final contact point for each spring, as shown in Figure 8. This control point can only move in the horizontal direction, which is also its normal direction. A total of 4 control points are used to describe a smooth contact surface for the right spring, while 3 control points are used for the left spring.

As discussed earlier, the contact normal force depends mostly on the stiffness of the spring, which is decided by the geometry of the bending arm portion of the spring. 10 control points are used to describe the geometry of the bending arm of the right spring, and 12 control points are used for the left spring. The maximum stress and stress concentration may occur around the root area of the spring. Therefore the profile of the spring at the root area also has to be carefully designed. 10 control points are used to describe this profile for each spring. For installation purposes, a lower bound is imposed on the y coordinates of these control points.

Finally, this optimization problem can be written into the following mathematical form:

min. 

st.    

               

               

                                                                                           (3)

where d is the vector of design variables , i=1,…48, N is the specified minimum normal force, and S is the allowable stress of the material of the spring. In our example, N=100g and S=600MPa. Note that we demand less contact force than in original design. Function  is the total insertion force. Functions  and  are the normal contact forces of the left and right springs. These functions and the maximum stress of the springs  and  are evaluated by finite element analysis, as described in the previous sections.

Shape optimization result of the contact springs

Sequential linear programming (SLP) [Vanderplatts, 1984] is use to find the solution of Eq.(3). In this optimization algorithm, the optimization model in Eq.(3) is linearized at the initial design point  to form the following linear programming sub-problem:

       

       

       

                                                                 (4)

The sensitivities (the first derivatives) of functions , , , and  required in Eq.(4) are calculated by finite differences. This linear programming sub-problem is solved to obtain a new design point. The insertion force, normal force, and the maximum stress of new design point are calculated to see whether this new design point satisfies the termination conditions. If not, the optimization model in Eq.(4) is linearized again on this new design point. This process continues in an iterative manner until the termination conditions are satisfied.

The last constraint in Eq.(4) imposes “move limits” on the design variables. This is because the linear programming sub-problem (Eq.(4)) is a good approximation to the original non-linear optimization model (Eq.(3)) only in the neighborhood of the current design point. In our example, the move limit is 0.02mm initially, and is reduced to half if the new design point obtained from the linear programming sub-problem becomes highly infeasible.

The SLP algorithm terminates after 5 iterations. Table 1 shows the iteration history. The insertion force of the final contact spring design is reduced to 42.2g, 68.3% of that of the original design (61.8g). The maximum stress of the right spring drops from 708MPa to 564MPa. The contact normal forces of the final design are 100g for the left spring, and 113g for the right spring. The SLP algorithm terminates because the design obtained in the 5th iteration satisfies all constraints, and the improvement in objective function is less than 1% comparing with the objective value of the 4th iteration.

Table 1. The iteration history

 

original

design

1st

iteration

2nd

iteration

3rd

iteration

4th

iteration

5th

iteration

 

left

right

left

right

left

right

left

right

left

right

left

right

(MPa)

541

708

498

618

497

591

465

576

489

562

457

564

(g)

118

148

107

126

103

122

102

113

100

114

100

113

(total, g)

61.8

46.7

44.1

43.0

42.3

42.2

Figure 9 shows the final designs of the contact springs. The shapes of the springs do not have drastic change, the maximum movement of the control points is less than 9% of the width of the spring, though the performance of the springs has been significantly improved. Since the change is so small that it is difficult to see the difference if the new geometry is superimposed on the original geometry. The small arrows in the figure are used to indicate the directions of movement of the control points.

Figure 10. Final designs of the contact springs.

Conclusions and discussions

This paper describes how the insertion of a PCB into the contact springs of an electronic connector is modeled by finite element analysis. The insertion force, normal force, and maximum stress of the contact springs can be calculated, and the analysis result matches well with experimental data.

Some design guidelines can be concluded from this analysis:

(1)     The unsymmetrical shapes of the left and right springs effectively reduce the peak insertion force.

(2)     The coefficient of friction between the PCB and the contact springs has significant effect on the insertion force. Reducing the coefficient of friction can reduce the insertion force without sacrificing the contact normal force.

(3)     The amount of interference at the interface between the spring roots and the housing does not have significant effect on the contact normal force and insertion force of the contact springs.

Connector manufacturers have a basic struggle between the need for high normal contact forces and low insertion forces, both are very sensitive to the shape of the geometry of the contact springs. In this paper, the analysis procedure is further combined with structural shape optimization techniques to carefully design the shape of the contact springs. The insertion force of the connector can be further reduced while the normal contact force and the maximum stress are maintained within specified values. In our example, after shape optimization, the shapes of the springs do not have drastic change, though the performance of the springs has been significantly improved.

Acknowledgement

This research is partially supported by National Science Council, Taiwan, ROC, grant number NSC-89-2212-E-155-004. This support is gratefully acknowledged. The authors also thank Nextronics Engineering Corporation, Taiwan, especially Ms. Angela Liu, for providing valuable technical data and professional experience for this research.

Reference

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