## Cantilever Spring

The cantilever spring (unreinforced or reinforced plastics) can be employed to provide a simple format from a design standpoint. Cantilever springs, which absorb energy by bending, may be treated as a series of beams. Their deflections and stresses are calculated as short-term individual beam-bending stresses under load.

The calculations arrived at for multiple-cantilever springs (two or more beams joined in a zigzag configuration, as in Fig. 4.31) are similar to,

: Multiple-cantilever zigzag beam spring (Courtesy of Plastics FALLO)

Load on multiple spring

: Multiple-cantilever zigzag beam spring (Courtesy of Plastics FALLO)

Load on multiple spring

but may not be as accurate as those for a single-beam spring. The top beam is loaded (F) either along its endre length or at a fixed point. This load gives rise to deflecdon y at its free end and moment M at the fixed end. The second beam load develops a moment M (upward) and load F (the effective portion of load F, as determined by the various angles) at its free end. This moment results in deflection y2 at the free end and moment M2 at the fixed end (that is, the free end of the next beam). The third beam is loaded by M2 (downward) and force F2 (the effective portion of Fj). This type action continues.

Total deflection, y, becomes the sum of the deflections of the individual beams. The bending stress, deflection, and moment at each point can be calculated by using standard engineering equations. To reduce stress concentration, all corners should be fully radiused. The relative lengths, angles, and cross-sectional areas can be varied to give the desired spring rate F/y in the available space. Thus, the total energy stored in a cantilever spring is equal to:

where F = total load in lb, y = deflection in., and E, = energy absorbed by the cantilever spring, in-lbs.

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