Determination Of Rigid Body Characteristics From Time Domain Modal Test Data

doi:10.1006/jsvi.1994.1414

Journal of Sound and Vibration

Volume 177, Issue 1, 13 October 1994, Pages 31-41

https://doi.org/10.1006/jsvi.1994.1414 Get rights and content

Abstract

A new method is presented to identify the characteristics of a rigid body and its supports, such as the center of gravity, the moment of inertia, and the stiffness and damping matrices, based on the measured time domain vibration data. Transformation matrices are formed using only the geometric co-ordinates relative to an arbitrarily selected origin to relate the pure translational measurement to both translation and rotation of the rigid body system, The rigid body modes and mode shapes, carefully selected from the accurately determined modes and mode shapes (rigid body and structural), are used, together with the special matrix structure, such as symmetry. The test result shows that the center of gravity and the moment of inertia are determined with good accuracy. The simple test procedure makes it an easily implementable method in practice.

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Cited by (49)

On state and inertial parameter estimation of free-falling planar rigid bodies subject to unscheduled frictional impacts
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Surveys of methods for the identification of the above-mentioned inertia properties can be found in [11] or, for the particular case of modal analysis, in [12]. When the object is relatively accessible for the process, a modal analysis can be performed, as in [13] and [14], with the use of platforms on springs. A well rooted method for inertia identification requires the use of a multifilar pendulum.
This paper addresses the problem of simultaneous state estimation and inertial and frictional parameter identification for planar rigid-bodies subject to unscheduled frictional impacts. The aim is to evaluate to what level of accuracy, given noisy captured poses of an object free-falling under gravity and impacting the surrounding environment, it is conceivable to reconstruct its states, the sequence of normal and tangential impulses and, concurrently, estimate its inertial properties along with Coulomb’s coefficient of friction at contacts.
To this aim we set up a constrained nonlinear optimization problem, where the unscheduled impacts are handled via a complementarity formulation. To assess the validity of the proposed approach we test the identification results both (i) with respect to ground truth values produced with a simulator, and (ii) with respect to real experimental data. In both cases, we are able to provide accurate/realistic estimates of the inertia-to-mass ratio and friction coefficient along with a satisfactory reconstruction of systems states and contact impulses.
Measurement of the mass properties of rigid bodies by means of multi-filar pendulums – Influence of test rig flexibility
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Mass properties (mass, centre of gravity location and inertia tensor) are commonly defined as attributes of rigid bodies. The measurement of such attributes is usually performed under the hypothesis of rigid behaviour of both the body under test and the test rig. For large or heavy bodies, the forces exchanged between the body and the testing structure may be so high that the rigid behaviour hypothesis is not satisfied. The body under test can often be considered as rigid, so the accuracy of the measurement can be affected by the deformations of the testing structure.
In this paper, the effect of the deformation of the testing structure on the measurement of relatively large or heavy bodies is investigated both numerically and experimentally. The InTenso+ Measuring System of the Politecnico di Milano, a special type of multi-filar pendulum is considered relevant as example. A flexible multi-body model of the test rig is employed for assessing the influence of test rig deformations on mass properties measurement.
Experimental tests are conducted on a series of bodies to study the uncertainty. Numerical and experimental evidences show that the deformation of the testing structure can alter considerably the results of the measurement. However, this effect can be modelled with a reasonable accuracy. A proper mathematical procedure is developed for use during the measurement to compensate the effects of the undesired test rig deformations.
The presented procedure can be effectively employed when the mass properties of very large or heavy bodies have to be measured and the construction of a sufficiently rigid testing structure is impossible in practice.
Rigid body stiffness matrix for identification of inertia properties from output-only data
2016, European Journal of Mechanics, A/Solids
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A simple and less expensive extension of the Pendulum method was proposed in (Zhi-Chao et al., 2009). Another time domain method was proposed in (Pandit and Hu, 1994) that uses transformation of the translational motion to the rotational and translational motion in order to identify the inertia properties. Pandit et al. used time domain data in six axes for identification of the inertia properties from impact data (Pandit et al., 1992).
Identification of inertia properties (mass, location of the center of mass and inertia tensor) is essential for designing of engineering structures. Using modal testing is a possibility for estimation of the inertia properties in which they can be identified using the orthogonality property of mass-normalized rigid body mode shapes. However, identification of rigid body mode shapes using modal testing is not always possible, because it is not possible to excite the structure at all degrees of freedom. In this paper, output-only modal analysis in which the structure can be excited in different directions is used to identify the rigid body modes of the structure. It is shown that all of the rigid body modes of the structure can be extracted using the data extracted from output-only modal analysis. As the obtained rigid body mode shapes from output-only modal analysis are not scaled, a new method is proposed for scaling them using rigid body stiffness matrix. The inertia properties of the structure are obtained from the scaled mode shapes. The accuracy of the proposed method is studied using a numerical case study of a steel structure as well as an experimental case study of a steel frame.
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Moreover, the modal property method is based on the rigid body modes so it is the only method that can solve for the corresponding stiffness and damping matrices from the measured vibration data. The details of this method can be found in [45–47]. As discussed in the preceding section, the rotations of the engine block (pseudo angular acceleration) were used for misfire diagnosis in this paper.
In this paper, a new advance in the application of Artificial Neural Networks (ANNs) to the automated diagnosis of misfires in Internal Combustion engines(IC engines) is detailed. The automated diagnostic system comprises three stages: fault detection, fault localization and fault severity identification. Particularly, in the severity identification stage, separate Multi-Layer Perceptron networks (MLPs) with saturating linear transfer functions were designed for individual speed conditions, so they could achieve finer classification. In order to obtain sufficient data for the network training, numerical simulation was used to simulate different ranges of misfires in the engine. The simulation models need to be updated and evaluated using experimental data, so a series of experiments were first carried out on the engine test rig to capture the vibration signals for both normal condition and with a range of misfires. Two methods were used for the misfire diagnosis: one is based on the torsional vibration signals of the crankshaft and the other on the angular acceleration signals (rotational motion) of the engine block. Following the signal processing of the experimental and simulation signals, the best features were selected as the inputs to ANN networks. The ANN systems were trained using only the simulated data and tested using real experimental cases, indicating that the simulation model can be used for a wider range of faults for which it can still be considered valid. The final results have shown that the diagnostic system based on simulation can efficiently diagnose misfire, including location and severity.
An improved pendulum method for the determination of the center of gravity and inertia tensor for irregular-shaped bodies
2011, Measurement: Journal of the International Measurement Confederation
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It is a huge task to accomplish the three-dimensional solid modeling of an irregular-shaped body with all details, so the calculation method based on the CAD model is seldom used. The methodology based on experimental modal analysis is simple in positioning postures of the body when identifying the C.G. and the inertia tensor, but with this method too many parameters need to be identified, the principle is complicate, the error analysis is difficult and the hardware requirements are expensive [8,12]. Moreover, the modal analysis method is sensitive to measurement noise, selection of response measurement points and excitation conditions [4].
An improved Trifilar Torsional Pendulum (TTP) for the experimental determination of the Center of Gravity (C.G.) and inertia tensor (the three moments of inertia and the three products of inertia) for an irregular-shaped body is proposed and developed. In the improved apparatus, a universal joint is adopted to facilitate the adjustments of the C.G. of the body in line with the pendulum axis. To enhance the precision of the measurement, a tri-coordinate measuring machine is employed to measure the coordinates of the predefined points and vectors of axes, which are then used for calculating the C.G. and inertia tensor for an irregular-shaped body. The theoretical fundaments of an improved TTP, the experimental setup, data processing procedures, and error estimation for measuring C.G. and inertia tensor are presented. With the proposed TTP and data processing procedure, the relative error in the determination of the moments of inertia can be estimated within 1%, and the deviation of the measured C.G. to the theoretical C.G. is within 1.5 mm. An example is given to demonstrate the effectiveness of the new approaches.
A method for measuring the inertia properties of rigid bodies
2011, Mechanical Systems and Signal Processing
Citation Excerpt :
By this approach, the accuracy can be high, but usually cumbersome hardware and long testing time are required to obtain all of the required rotation axes. By the second approach, the body is made to move in order to excite all of his rigid modes [16–19]. The motion can be just a vibration [16,17] or a complex non-linear motion [18–20], depending on the different implementations.
A method for the measurement of the inertia properties of rigid bodies is presented. Given a rigid body and its mass, the method allows to measure (identify) the centre of gravity location and the inertia tensor during a single test. The proposed technique is based on the analysis of the free motion of a multi-cable pendulum to which the body under consideration is connected. The motion of the pendulum and the forces acting on the system are recorded and the inertia properties are identified by means of a proper mathematical procedure based on a least square estimation. After the body is positioned on the test rig, the full identification procedure takes less than 10 min. The natural frequencies of the pendulum and the accelerations involved are quite low, making this method suitable for many practical applications. In this paper, the proposed method is described and two test rigs are presented: the first is developed for bodies up to 3500 kg and the second for bodies up to 400 kg. A validation of the measurement method is performed with satisfactory results. The test rig holds a third part quality certificate according to an ISO 9001 standard and could be scaled up to measure the inertia properties of huge bodies, such as trucks, airplanes or even ships.

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Regular ArticleDetermination Of Rigid Body Characteristics From Time Domain Modal Test Data

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Regular Article
Determination Of Rigid Body Characteristics From Time Domain Modal Test Data