Optimization of near-constant force springs subject to mating uncertainty

Constant force mechanisms are mechanical devices that provide a near-constant output force over a sizable and prescribed deflection range. These mechanisms have proven to be innovative solutions in a variety of applications. This paper considers a new application - the robust design optimization of constant force electrical contacts. Electrical contacts are inexpensive, small-scale, springs that carry electrical current. To produce these contacts at competitively low manufacturing costs, expensive pin-joints (a principle component of traditional kinematic mechanisms) are replaced by simple cam followers. Under certain conditions, enforced in this paper, cam followers can be used to emulate traditional pin-joints, and achieve the necessary motion. These emulated pin-joints, however, are subject to mating/assembly uncertainties that affect performance and must be considered in the design. In this paper, a numerical optimization model is used to characterize the force-deflection relationships for both an exactly mated emulated pin-joint, and for one that is subject to mating uncertainties. The numerical results show that under the exact mating conditions, a contact with 97.50% constant force can be identified (an improvement of 24.3% over previously published results), albeit sensitive to mating uncertainty. When conditions are considered uncertain, a more robust design is found with a 98.20% constant force. These surprising results are described in detail and verified with Monte Carlo simulation to confirm the results.