A time domain approach for spacecraft reanalysis

Spacecraft Reanalysis is a methodology that uses results from a previous coupled loads analysis to calculate accurate loads for a new spacecraft design. Since the method is based on the previous results, it only requires a model of the component that is changed. It does not require a model of the launch vehicle or forcing functions. Examples presented in this paper demonstrate that the method is as accurate as a full coupled loads analysis for very different spacecraft designs. The impact of the method is greatest for spacecraft design where the launch vehicle model is not available. Reanalysis allows the spacecraft designer to calculate accurate internal loads throughout the spacecraft design cycle. The traditional method for calculating dynamic launch loads for aerospace payloads is to perform a coupled loads analysis (CLA). A component mode model of the payload is coupled to a model of the launch vehicle, system modes are calculated, forcing functions are applied, and the transient response is calculated. This methodology is computer intensive and requires that a model of the launch vehicle and the forcing functions as well as a model of the spacecraft be available. The purpose of Reanalysis is to calculate the response of a payload given the response of a different payload attached to the same launch vehicle. The goal is primarily to eliminate the need for a launch vehicle model and secondarily to reduce the amount of computer time required for the analysis. Furthermore, if the forcing functions remain unchanged, these are also not needed. A common assumption used to calculate loads for a modified payload design is that the accelerations at the vehicle/payload interface do not change. In this case the interface accelerations can be applied directly to the new payload model in order to calculate response (base shake). This approach, however, is only valid for very small perturbations in the payload model since significant changes will almost certainly result in modified interface accelerations. Because of this, it is difficult to predict the accuracy of the method, and conservative load factors are usually applied to ensure a valid design. Reanalysis does not assume that the interface acceleration remains unchanged. Instead the effect of the changed payload on the interface motion is explicitly taken into account. The Jet Propulsion Laboratory (JPL) has developed a method for reanalysis that combines frequency and time domain calculations to estimate the response of the modified payload [I]. The interface accelerations in this case are not assumed to remain unchanged, improving accuracy. The JPL method uses acceleration data in the time domain from a previous analysis and converts it to the frequency domain using a Fast Fourier Transform (FFT). The modifications due to replacing the original payload with a new payload are then made in the frequency domain. Finally, the modified accelerations are converted to the time domain using an inverse FFT. While this method is well developed and used extensively at JPL, it introduces an error when transforming between the time and frequency domains. This error is due to the fact that the FFT assumes periodic data while the accelerations from the transient analysis are nonperiodic. The issue of periodicity can be addressed by padding the input data with zeros or by windowing, but it is difficult to ensure that the data is not corrupted due to the Fourier Transforms. The time domain Reanalysis approach described in this paper is similar to the method used at JPL but is carried out entirely in the time domain, eliminating errors associated with timejfrequency transformations. We will demonstrate that the methodology is very accurate for large modifications in the payload model. The methodology presented in this paper is fundamentally different from other methodologies for "reanalysis," which address model modifications [2-41. In the Reanalysis method presented here the model modification refers to the removal of a component and replacement with a different component. The differences between the two components are not necessarily small. This paper is organized as follows: First we develop the coupled differential equations describing the response of the system when the payload is changed. Next we present two realistic examples that demonstrate the applicability of the method to problems of varying complexity. The first example demonstrates the accuracy of the method for an expendable launch vehicle with a statically determinate interface (six DOF). This example is also used to demonstrate some limitations of Reanalysis with respect to the magnitude of the change that can be accurately handled. The second example demonstrates the accuracy of the method for an NSTS launch with a statically indeterminate (seven DOF) interface. Finally we conclude by discussing some of the more important aspects of the time domain Reanalysis methodology.