Modeling Cable-Harness Effects on Spacecraft Structures

This research focused on the dynamic response of spaceflight cables and their effects on space structures. Due to the high mass ratio of cables on lightweight spacecraft, the dynamic response of cabled structures must be understood and modeled for accurate spacecraft control. Models of cable behavior were reviewed and categorized into three major classes consisting of thin rod models, semi-continuous models, and beam models. A shear beam model can predict natural frequencies, frequency response, and mode shapes for a cable if effective homogenous cable parameters are used as inputs. Thus, a method for determining these parameters from straightforward cable measurements was developed. Upper and lower bounds for cable properties of area, density, bending stiffness, shear rigidity, and attachment stiffness were calculated and shown to be effective in cable models for natural frequency prediction. The parameter calculation method can be applied to any stranded cable for which the constituent material properties can be determined. In addition to determining cable parameters for homogenous cable-as-beam modeling, the effect of bakeout on spaceflight cables was investigated. Natural frequencies and damping values were experimentally identified before and after the bakeout process. After bakeout, spaceflight cables showed reduced natural frequencies and increased damping, so a bakeout correction factor is recommended for bending stiffness calculations. On the modeling front, a cable model was developed using the distributed transfer function method (DTFM) by adding shear, tension, and damping terms to existing Euler Bernoulli models. The cable model was then extended to model a cabled structure. Both the cable and cabled beam models include attachment points that can incorporate linear and rotational stiffness and damping. Cable damping mechanisms were explored and incorporated to the model. From this aspect of the research, time hysteretic damping was shown to be capable of matching multiple modes of the cable response, and was superior to both viscous and structural damping for modeling cable damping. The DTFM models are combined with the determined cable parameters and damping expressions to yield frequency ranges that agree with experimental data. The developed cabled beam model matches experimental data more closely than the currently used distributed mass model. The experimental work conducted for this research included dynamic testing of cables, cabled beams, and the connection method used for cable attachment. Cables were excited with a modal shaker and scanned with a scanning laser vibrometer to determine natural frequencies and mode shapes for a two-point and four-point fixture. Cables were then attached to an aluminum beam to provide cable mass ratios of 5 to 27%, and the same procedure was followed to determine the natural frequencies and mode shapes of the cabled structure. Solid rods were also tested in all fixtures to compare the stranded cables and show the additional complexity of the transfer functions due to the stranded nature of the cables. Additional experiments were run to characterize the stiffness property of the cable attachment method. The combination of theoretical and experimental work served to determine the effectiveness of the methods and models developed, as well as allow for detailed experimental observation and analysis of cable effects. This work extends the understanding of cable dynamics and presents methods and models to aid in the analysis of stranded cables and cabled structures. Conclusions and contributions of this work are as follows: • Developed a method to calculate cable properties that are suitable to use for modeling purposes from direct physical measurements of cables. Cable parameters of mass properties, bending stiffness, and shear rigidity were determined for typical spaceflight cables. • Created a standard run procedure for testing of cables with verification of factors that would influence cable dynamic response and showed that machine made cables did not fully eliminate variability in the dynamic response. • Produced a database of cable responses for typical spaceflight cables from over 70 trials of dynamic testing which are available for further investigation. • Determined the effect of bakeout on spaceflight cable response, identified bakeout as a source of frequency response changes, and quantified the amount of frequency shift and damping ratio changes due to bakeout. • Extended the distributed transfer function shear model to include shear effects, tension, and a variety of damping mechanisms to model cables or other damped shear beams. • Developed a distributed transfer function cabled beam model that combines the shear beam cable model with attachment point models that have the capability to include both linear and rotational stiffness and damping. • Compared the developed distributed transfer function cabled beam models to the currently used distributed mass models to show the slight improvement in frequency prediction and identification of additional modes by the new distributed transfer function cabled beam model. • Investigated the influence of the attachment points, verified that the attachment points did not act as pinned constraints, and revealed results for the attachment stiffness as a function of frequency. Although this research was focused on spaceflight cables, the methods and models developed are applicable to many types of stranded cable and thus have application outside the realm of space structure design.