A Low Stiffness Suspension System for Free-Free Modal Testing

Gary C. Foss Boeing Defense & Space Group

Kent, Washington, USA

ABSTRACT

To accommodate the free-free modal testing of large, low frequency structures, a suspension system is described which uses a compound spring arrangement to lower the suspension frequency over what would be achieved using a simple spring. Test data from a working prototype is presented. Performance limitations, primarily due to friction. are discussed.

INTRODUCTION

Future space missions are likely to require large structures to be assembled or deployed on orbit. A typical structure is the NASA Space Station Freedom. consisting of a large truss used as a framework to which support modules are attached. Structures so assembled may be quite large, perhaps hundreds of feet across. To design such structures, reliable analytical models must be used to verify the dynamic service loads. The analytical model must be confirmed and refined using modal test data which accurately predicts the dynamic behavior in a gravity-free environment. Zero gravity simulation is difficult to achieve in a terrestrial laboratory, but conditions may be adequate if we can provide an off load suspension system which is well distributed across the structure, and has a very low stiffness characteristic.

As a rule of thumb, the suspension frequency for a free-free modal test should be less than l/5 of the first mode of interest. Otherwise, coupling between the suspension and test modes may contaminate the desired modal parameters. Large space structures are expected to have frequencies well below one Hertz. We have set 0.1 Hz as our target suspension frequency goal over a design load range of 250 to 500 lbs. With moderate damping, this will allow testing to 112 Hz. The effective stiffness of a

suspension to support a design load of 400 pounds suspended at 0.1 Hz is about 0.4 pounds per inch. If such a stiffness can be achieved, a heavier test article can be supported at multiple points, each with this low stiffness characteristic.

With this requirement in mind, we have looked at different methods for constructing very low stiffness springs(l). One of the concepts we explored was a mechanism using compound springs (Z), which in theory can be adjusted to provide a range of spring rates approaching zero. This concept seemed attractive because it was simple, inexpensive, didn’t require a paver source, and didn’t need a high overhead ceiling to accommodate a long vertical spring.

FABRICATION

We have built four. support stands based on the compound spring principle. The basic design has gone through several iterations. While further refinements may follow, the present configuration shows promising results.

The essential arrangement is shown in figure 1. A vertical main spring supports the load. In the case of the prototype, the test load is 400 pounds and the vertical spring rate is 50 pounds per inch. The vertical suspension frequency is about 1.1 Hz. without assistance from the horizontal spring. Attached to the vertical cable is a beam which pivots around a fulcrum as the load oscillates vertically. The effect of the horizontal spring is to provide a vertical force with a negative spring rate to counteract the positive spring rate from the vertical spring. Some leverhge is gained by attaching the horizontal spring beyond the load point. To the extent that they counteract each other, the effective spring rate as seen by the load can be made to approach zero for small displacements.

1402

To achieve this, we built the arrangement shown in the figure 2 photo. The stand was constructed out of square steel tube. The horizontal and vertical springs are identical, 50 pounds per inch, and are connected through cables to hand operated winches for height and spring rate adjustment. The beam is shown below the horizontal spring and is fabricated from aluminum. The fulcrum is a spring steel flexure stretched in tension. Four of these stands were built and used to test the truss structure shown in the photo.

Experience gained from the effort shown in figure 2 uncovered several problems. As the effective stiffness of the suspension is decreased, what were minute amounts of friction at 50 pounds per inch stiffness can be very significant and undesirable at 1 or 2 pounds per inch effective stiffness. If damping is thought of as the percentage of inertial force lost thru friction, a few pounds of friction renders the suspension useless. The damping can come from a variety of subtle sources. Multi- stranded cable, used to rig up the springs, are heavy sources of damping when flexed. The fulcrum flexure is clamped at each end, and sxne localized relative sliding is likely when flexing occurs. The connections of the cables to the beam are a potential smlrce of frictional energy loss.

The original beam was constructed without much regard for weight. This later proved to be a mistake when it was found that the beam and horizontal springs totaled about 10 percent of the 400 pound design load. It was also found that the horizontal springs and cables had “guitar string” modes around 15 Hz., right in the middle of the frequency range of interest.

When using horizontal and vertical springs of equal stiffness, as shown in figure 2, another problem became apparent. The effective low stiffness was linear wer several inches. Beyond that, however, the horizontal negative stiffness predominated, and the entire arrangement was unstable. Mechanical stops were placed to limit beam travel, but during the testing one of the stops failed, and the considerable energy stored in the horizontal springs caused the beam and flexure to self destruct. The compound spring is a delicate balance between large forces, and this incident highlighted some safety issues.

These problems are summarized graphically in figure 3, a force-displacement plot of the figure 2 configuration. This was generated by moving the load up and down several inches at a quasi- equilibrium rate. Note the excess hysteresis. Also note that moving the load too far causes the spring rate. to become negative.

IMPROVEMENTS

In an effort to improve performance and safety, scune changes have been made resulting in the configuration shown in the figure 4 photo. The beam was refabricated ta be smaller and lighter (it now weighs under 6 pounds). The flexure was eliminated in favor of a simple compressive knife edge. The relatively soft and heavy horizontal coil springs have been replaced with l/4 inch diameter steel rods (k=Zl,OOO pounds per inch).

Where the horizontal spring force was relatively constant before, it now cycles from 100% load to completely unloaded cwer a range of about 3 inches from equilibrium. The effect is to eliminate the negative spring rate region as shown in figure 5. In the center of the force displacement plot, adjustment of the rod tension makes the stiffness arbitrarily small. As movement is forced beyond this central linear range, the stiffness rapidly increases to the unassisted 50 pounds per inch. This spring characteristic tends to be self centering whereas the old characteristic was unstable beyond the linear region. Figure 6 shows the same characteristic, confined to approximately the linear range. Note in figure 5, the hysteresis between up travel and down travel is about 1 lb. This would normally be a problem if the target stiffness were on the order of a few pounds per inch. The hysteresis in figure 6 wer the linear range is below the noise floor in the force measurement. The hysteresis difference between figure 5 and 6 is apparently explained by the large changes in spring loading over the wider displacement range, which would not occur during a modal test. The spring rate in figure 6 is about 0.6 pounds per inch, resulting in a vertical suspension frequency of 0.12 Hz. A free decay time history of the same system adjusted for a spring rate of 2.4 pounds per inch is shown in figure 7.

An additional benefit of this improved configuration is the movement of the horizontal spring “guitar string” mode from 15 Hz. previously, to 106 Hz, well beyond the expected frequency range of interest for most large test articles.

CONCLUSIONS

A low stiffness suspension system for the free-free modal testing of large space structures has been built and tested. The low stiffness characteristic is achieved using a coupound spring mechanism in which the effective spring rate is the sum of a positive and negative component. The lower

1403

practical limit of stiffness depends on how well friction can be minimized. Future improvements are anticipated. A smaller diameter rod for the horizontal spring would increase the linear displacement range. Further reductions of friction are possible. A beam fabricated from graphite composite would further lower the additive mass.

REFERENCES

1. Kienholtz, Crawley, and Harvey, Verv Low Freauencv Su ension Svstems for D amic I&&Q& Proc. 30th Structures, Structural Dynamics, and Materials Conference, Mobile, AL, April 1989

2. Ikegami, Eckblad. Blackman, and Watanabe, Zero-G Grou d Test Simulation M&ho& Eleventh Aertspace Testing Seminar, IES: October, 1988

1404

/ I Z

Ftgurs 2 Original suspension design used to test space truss

1405

6 3.12

Figure 4 Modified suspension design being evaluated

1406

Figure 5 Modiied design - spring characteristic

320 , m

pounds/l0

-320 m

-426m

1

I I

396m inches

Figure 6 Linear range of figure 5

1407

320 m

inches

-320 m

0.0 SeC 64.0

Figure 7 Modiied design - free decay

1408