Rotor-pendulum model for the Perigee Assist Module nutation anomaly

Abstract

Several years ago, anomalous motion was observed in the flight data from several upper-stage spacecraft known as the Perigee Assist Module that used the STAR 48 series of solid rocket motors. The cause of the anomaly is believed to be due to the asymmetric gas and/or liquid motions in the motor chamber. Control dynamicists have conveniently modeled the motions using an attached point mass on a rotor. In this paper, the nutational stability of a spacecraft modeled as a rotor-pendulum system is examined in the flight parameter region. We show that the simple mechanical model is capable of matching the telemetric angular rates satisfactorily by adjusting a small number of parameters. Although this result strongly supports a type of resonance interaction, a simultaneous match of both the rates and the parameter region of instability does not seem possible. For the simulation of the Perigee Assist Modules, we develop an idealized model, which retains the pertinent features of the pendulum motions, but not certain constraints which may be altered in the actual liquid sloshing. I. Introduction A BOUT 10 years ago, a series of upper-stage spacecraft known as Perigee Assist Modules (PAM) was flown. These vehicles consistently displayed a nutation anomaly toward the end phase of the solid rocket motor burn. At the burnout, for some of the spacecraft, the semicone angle grew to as large as 18 deg. The flight data are well established, but the cause of the anomalous motions is not yet fully understood. Many potential destabilizing mechanisms have been ruled out, including the slosh in the fuel tanks.1 Now it is widely believed that the instability is caused by one, or a combination of both, of the following destabilizing mechanisms: 1) a jet gain moment generated by a gas jet detached from the wall; the moment amplified under the nutation forcing near a resonance condition2'3; and 2) a liquid pool of molten slag trapped in the aft annular region of the motor chamber. The slosh motions amplify under a resonant condition and cause nutation to grow in the presence of an axial acceleration. At this point, neither of these two views has provided a conclusive explanation. The similarity of the two views, however, is that both address a type of resonance interaction that is believed to be responsible for the anomalous transition. An understanding of the nature of the instability is considered crucial for both future designs of solid rocket boosters and their attitude control systems. The jet gain theory proposed by Flandro et al.2 has received more in-depth treatment than any other theory. The mechanism that these authors proposed is theoretically viable and some experimental investigations have been carried out.4 On the other hand, the slag theory is supported by some well-established slosh resonance studies in literature. 5'6 Recently, some new evidence emerged that seems to support the slag accumulation hypothesis.7 This evidence justifies more studies in the area of spacecraft-li quid interactions. In this paper, we make no attempt to discredit either of the two views. In fact, both views become intractable when the realistic physical problem is considered. On the other hand, both views seem to suggest that the instability is a result of an asymmetric motion of the bulk fluid whose mass center motion may be regarded as, in a crude sense, a point mass attached to the spacecraft.