Data processing: measuring – calibrating – or testing – Measurement system in a specific environment – Mechanical measurement system
Reexamination Certificate
1999-01-29
2003-04-15
Wachsman, Hal (Department: 2857)
Data processing: measuring, calibrating, or testing
Measurement system in a specific environment
Mechanical measurement system
C702S190000, C702S197000
Reexamination Certificate
active
06549858
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to the field of modal analysis and, more particularly, to a method and apparatus for decomposing a complex multiple degree-of-freedom response of a linear dynamic system into individual component single degree-of-freedom modal responses.
2. Description of the Prior Art
Many physical devices are linear dynamic systems. The vibration, or dynamic response, of linear dynamic systems is often the cause of significant problems in many manufacturing processes and inherently limits the ability of certain machines to perform efficiently. The vibration of linear dynamic systems fundamentally limits the accuracy and resolution of sensing systems, while also causing fatigue failure in structural components and electronic assemblies.
Active monitoring and control of vibration is a solution to the aforementioned problems. While researchers have been investigating active vibration control approaches for many years, there still remains fundamental problems which have prevented the widespread deployment of this technology.
Systems which react to a disturbance input by a single-mode response are termed single degree-of-freedom (SDOF) systems. SDOF systems have just a single resonant peak in their frequency response function (FRF) plots and are much easier to control and monitor than multiple degree-of-freedom (MDOF) systems. Unfortunately SDOF systems occur only rarely and are generally achieved only in contrived laboratory experiments.
The dynamic response of a “real world” linear dynamic system is typically a superposition of the response of a plurality of individual modes of response,—i.e. a MDOF system. Real world systems typically have complex response characteristics with many SDOF modes contributing to their dynamic response and many associated modal, or resonant, peaks in their frequency response function (FRFs) as illustrated in FIG.
1
A. It has proven difficult to monitor or control systems with such complex response characteristics using prior art techniques.
The general characteristics of modal decomposition are illustrated in
FIGS. 1A-1F
. These six figures show frequency response functions (FRFs) plotting the input-output relation of a linear system as a function of frequency. A specific example of a linear dynamic system is a mechanical system such as an aircraft. The input to the system is an applied dynamic force and the output is the vibration amplitude measured at different locations on the aircraft. In
FIGS. 1A-1F
the vertical axis quantity is magnitude displayed in inches per pound force and is defined as the ratio of vibration response amplitude measured at a specific location on the aircraft to the force amplitude applied at a specific location on the aircraft. The horizontal axis quantity is frequency measured in hertz.
FIG. 1A
shows a typical FRF measured on a “real world” system comprising a plurality of superposed SDOF modes of vibration. Each peak in the plot of
FIG. 1A
is associated with a particular SDOF mode of vibration of the linear dynamic system. For example, peak
2
in
FIG. 1A
is associated with a first SDOF mode of vibration which is shown decoupled in FIG.
1
B. Likewise, peak
4
in
FIG. 1A
is associated with a second SDOF mode of vibration which is shown decoupled in FIG.
1
C.
The response of a linear dynamic system is often measured and used by a control system to modify the behavior of the linear dynamic system. As illustrated in
FIGS. 1D and 1E
, the first and second SDOF modes of vibration may be controlled such that the magnitudes of their respective peaks
2
and
4
are reduced. After implementation of the modal control, the first and second SDOF modes of vibration may be combined to define the complex MDOF response as illustrated in FIG.
1
F.
The response of the linear dynamic system may also be observed by an appropriate monitoring device in order to determine the “state” of the linear dynamic system. The monitoring device may detect damage to the linear dynamic system or other changes in operating characteristics by detecting changes in the frequency, amplitude or damping of the SDOF resonant peaks in the FRF plots. Such observation may be improved and simplified by modal filtering, a generally known technique that decomposes the complex MDOF response of a linear system into signals corresponding to the individual constitutive, SDOF modal responses. However, substantial inaccuracies or impracticalities are associated with previously known modal filtering methods. Additionally, prior art modal filtering methods require an excessive number of sensors in order to perform decomposition, cannot account for phase shifts between different sensor data channels and cannot account for different types of sensors being used in combination.
Modal filtering methods are generally well known in the art and are disclosed in numerous publications including Shelley, S. J.,
Investigation of Discrete Modal Filters for Structural Dynamics Applications,
Department of Mechanical and Industrial Engineering, University of Cincinnati, 1990. An improvement to traditional modal filtering techniques, called adaptive modal filtering, utilizes a reference model for calculating modal filter coefficients. Adaptive modal filtering is discussed in many additional publications including, Shelley, S. J., Allemang, R. J., Slater, G. L., Shultze, J. F.,
Active Vibration Control Utilizing an Adaptive Modal Filter Based Modal Control Method,
11
th
International Modal Analysis Conference, Kissimmee, Fla., Feb. 1-4, 1993. Both of these documents are incorporated herein by reference. While a significant improvement over prior modal filtering techniques, adaptive modal filtering methods still suffer from many of the disadvantages described above.
Accordingly, there is a need for an improved method and apparatus for decomposing MDOF dynamic responses into signals corresponding to the constituent SDOF modal responses of the MDOF linear dynamic system.
SUMMARY OF THE INVENTION
The present invention synthesizes signals corresponding to easily controlled and monitored single degree-of-freedom (SDOF) modal responses by using spatio-temporal filtering to uncouple complicated multiple degree-of-freedom (MDOF) responses measured on real world linear dynamic systems.
The apparatus of the present invention includes at least one sensor, each at least one sensor mounted at a location on a linear dynamic system for generating at least one response isignal representing actual dynamic response of the linear dynamic system at the location. The apparatus also consists of at least one excitation actuator to apply at least one excitation input to the linear dynamic system to generate the dynamic response, and a means for receiving at least one input signal representing at least one excitation input. A data acquisition and processing system periodically samples the response signal at different instances in time, stores a sequence of digitized samples for each sampling of the at least one response signal and associates each digitized sample of the at least one response signal with one of the instances in time. The data acquisition and processing system also periodically samples the at least one excitation input signal in conjunction with the at least one response signal, stores a sequence of digitized samples of the at least one input signal and associates each digitized sample of the at least one input signal with one of the instances in time.
A central data processing unit includes means for reading the digitized samples of the response and input signals and means for calculating therefrom a first set of spatio-temporal filter coefficients. The apparatus further comprises means for generating a first reference model having dynamic characteristics substantially similar to a first single mode of the linear dynamic system, and means for exciting the first reference model in a manner similar to the linear dynamic system thereby producing a first reference modal coordinate response at each of the instances in ti
Shelley Stuart J.
Vold Håvard I.
Bose McKinney & Evans LLP
Sheet Dynamics, Ltd.
Wachsman Hal
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