Dan Kammer

Daniel C. Kammer

Engineering Physics
University of Wisconsin

539 Engineering Research Building
1500 Engineering Drive
Madison, WI 53706
Voice: 608/262-5724
E-mail: kammer@engr.wisc.edu

Research Interests

Professor Kammer’s research interests focus on the areas of identification and control of aerospace structural dynamic systems. This includes modal identification, test-analysis correlation, analytical model updating, control-structure interaction, and damage detection.

Professor Kammer has conducted research on correlation of test and finite element analysis results, finite element model reduction, the use and improvement of component substructure representations, finite element model updating, sensor placement for on-orbit modal identification, selection of dynamically important mode shapes, inverse system dynamics and identification, analytical model representation using response surfaces, and damage detection.

Sensor Placement for Modal Vibration Tests

Proper pretest planning is a vital component of any successful vibration test. An extremely important part of the pretest exercise is the placement of sensors, usually in the form of accelerometers. The accelerometers must be placed such that all of the important dynamic information is obtained during the course of the test. The resulting sensor configuration must be optimal in some sense such that test resources are conserved. The state-of-the-practice is to select individual sensor location/directions from a candidate set based upon one of several available criteria

Sensor Placement Triaxial sensor placement applied to X-33 advanced technology demonstrator.

Triaxial accelerometers are then placed at the corresponding locations. In general, this results in the non-optimal placement of many of the accelerometers. This work presents a new technique, based upon Effective Independence, that places triaxial accelerometers as single units in an optimal fashion. The technique is applied and compared with standard approaches using the X-33 vehicle.

Research Details

Input Force Identification Using Inverse Systems

A new method for the estimation of structural input forces was developed. The time domain technique uses a non-causal inverse structural filter that takes as input, the structural response data, and returns, as output, an estimate the input forces. This technique allows pseudo-real-time estimation of input forces for non-collocated sensor/actuator pairs for multi-input/multi-output systems.

Docking Force Axial direction docking force estimates for Mir/Shuttle missions STS-81 through STS-91.

The formulation allows the estimation of input forces for systems that possess unstable transmission zeros and hence are non-minimum phase. Input force estimation for such systems is difficult due to the unstable nature of the non-collocated inverse system. The formulation is cast as an inverse system. The term "inverse" refers to the fact that the roles of input and output are reversed from the usual forward system structural dynamics problem. If sensors such as accelerometers are placed atthe external input locations, modal parameters corresponding to structural motion with the sensor locations fixed can be identified. One of the main advantages of this approach is that it only requires measured response data.

Research Details

Structural Identification of Mir

The goal of this work was to determine if it is feasible to use Mir/Shuttle docking data to perform Mir damage detection. A time-domain technique called a Remote Sensing System (RSS) was proposed as an approach. The method uses inverse structural dynamics to identify physical characteristics of a structure which can subsequently be used for damage detection.

The RSS method was demonstrated for a numerical simulation of Mir/Shuttle docking assuming that sensors were collocated with Mir docking location. Several fixed interface Mir modes were identified from the computed RSS pulse responses using the Eigen System Realization Algorithm and then correlated with the finite element representation. The method was then applied to the combined set of docking data from Mir/Shuttle missions STS-81, STS-89, and STS-91. Two modes were identified that correlated very well with FEM fixed interface modes.

Space Shuttle and Mir

Overall, the results produced by this work appear to indicate that Mir was in an undamaged state, at least with respect to docking excitation, at the time of STS-91. The significance of the contribution of the RSS approach is that it is not affected by the nonstationarity and nonlinearity associated with the Mir/Shuttle docking interface, and docking forces at the interface do not have to be measured.

Research Details

Propagation of Modeling Errors Using Metamodels

A new method is presented for extending metamodeling techniques to include the effects of finite element model mesh discretization errors. The method employs a rational function representation of the discretization error rather than the power series representation used by methods such as Richardson extrapolation.

Examples dealing with simple function estimation and estimation of the vibration frequency of a one dimensional bar showed that when extrapolated to the continuum, the rational function model gave more accurate estimates using fewer terms than the Richardson extrapolation technique. This is an important consideration for computational reliability assessment of high consequence systems, as small biases in solutions can significantly affect the accuracy of small magnitude probability estimates.

Response Surface

In subsequent nondeterministic analyses, the rational function based metamodel also produced more accurate estimates of failure probabilities using fewer terms than the Richardson extrapolation method under very severe extrapolation conditions. This allows the use of coarser meshes in the numerical experiments, saving a significant amount of time and effort.

Research Details

Chaos in Spacecraft Attitude Dynamics

Attitude determination and control are key problems in modern spacecraft mechanics. Analysis and simulation of large angle maneuvers, such as those occurring during attitude acquisition, have become increasingly complicated because of the departure of modern spacecraft from a truly rigid body representation. This departure can be attributed to an increase in structural flexibility and the addition of internal mechanisms such as robotic manipulators, rotors, etc. Equations of motion describing the attitude dynamics of these systems can be easily generated. However, their solution in general can only be obtained by numerical simulation.

The subject of this research is to detect chaotic motion in spacecraft attitude maneuvers. If chaos exists, the attitude motion of the satellite is unpredictable, meaning numerical simulation would be useless as a design tool. A technique called Melnikov's method is employed to analytically study chaotic dynamics in an attitude transition maneuver of a torque-free rigid body in going from minor axis to major axis spin under the influence of viscous damping and nonautonomous perturbations. Melnikov's method yields an analytical criterion for chaos in the form of an inequality that gives a sufficient condition for chaotic dynamics in terms of the system parameters. The criterion can be evaluated for its physical significance and applied to the design of satellites.

Below is a movie that illustrates the chaotic motion of 10,000 initial conditions on the momentum sphere for a damped rigid spacecraft with enforced motion of a small onboard mass. Note that mixing and folding of the trajectories. This movie was made by Professor Gary L. Gray of Penn State University. Gray was a former graduate student under Professor Kammer at Wisconsin.

Movie of Chaotic Trajectories

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