Experimental Characterization of a Flexible Two-Link Manipulator Arm

Experiments were performed to verify the analytical models for a robotic manipulator with two flexible links. A finite element model (FEM) employing two-dimensional beam elements was used to model the structure. A proportional model relating input voltage to output torque was used for both hub and elbow joint motors. With some minor adjustments to the link stiffness, the FEM modal frequencies matched the experimentally extracted frequencies within 1.5%. However the voltage-torque relationship for the hub motor was found to exhibit dynamics in the frequency range of interest.

Symmetric Model Correction of Mechanical Systems

This work examines the model updating problem for simple nonconservative proportionally damped systems. Model correction, also called model updating, refers to the practice of adjusting an analytical model until the model agrees with measured modal data. The specific case examined here assumes that natural frequencies and modal damping ratios are available from vibration tests and that the measured data disagrees in part with the modal data predicted by an analytical model. Most model correction schemes tend to produce updated damping and stiffness matrices which are asymmetric. The simple method presented here focuses on retaining the desired symmetry in the updated model.

Method for Determining System Eigenvalues From FRF for Noise Contaminated Subsystems

A method for determining the eigenvalues of a synthesized system from the Frequency Response Function (FRF) for noise contaminated subsystems is presented. This method first uses matrix Auto-Regressive Moving-Average (ARMA) model in the Laplace domain to describe each subsystem. Then a modal force method by ARMA model can be established. Only the FRF at the connecting joints is needed in the analysis to form a matrix named Modal Force Matrix. From this matrix, both synthesized system modes and substructure modes can be extracted simultaneously. Since the inverse operation is not required to form Modal Force Matrix, the computation is reduced drastically. The eigensolution of the system in any frequency range can be determined independently. Numerical study suggests that good results can be achieved by this method.

Interval Analysis of Neural Net Adaptive Expert Systems for Diagnosis of Machinery Incipient Failure

Interval calculus is a tool to evaluate a mathematical expression for ranges of values of its parameters. The basic mathematical operations are defined in the interval algebra. Neural networks is an approach leading to engineering expert systems that are capable of learning, self adapting to particular engineering applications and handling fuzzy and interval input information. In traditional machine learning, symbolic representations, such as first order predicate calculus, are used to represent knowledge. The resulting algorithms are specific to the selected representation and presume an ad-hoc knowledge of the system represented. In the neural network representation, knowledge is distributed to a large number of weighted synapses that facilitates learning by experience, realized through modification of the synapses weights according to a chosen learning rule. Traditional classification systems use binary logic. This assumes a clear distinction between two and only two possible states of an event. However, key elements in the human thinking are not numbers but labels of fuzzy sets, that is, classes of objects in which the transition from non-membership to membership is gradual rather than abrupt and ranges of key parameters involved. A heteroassociative neural network is used to map the existing knowledge and acquire new knowledge in learning sessions. The inputs can be binary, fuzzy and interval variables. To process the diagnosis in a back-propagation mode, interval calculus is utilized in algebraic and matrix operations and the diagnosis results in interval output parameters, the identification scores. Interval calculus was programmed in a software package to allow for interval computations. The package includes arithmetic, function and matrix operations. Available experience for failure diagnosis in turbomachinery was utilized to initially teach the system. Additional diagnoses from the author’s experience were taught to the system and additional features and diagnoses defined. Convergence of the procedure depends on the monotonicity of the functions used. For usual networks and threshold functions, convergence is warranted.

Comparative Signature Analysis Using Needle Bearings

Many signature analysis techniques have been developed for detecting bearing damage. In this paper, a number of these techniques are evaluated and their abilities to detect the existence and progression of damage are quantitatively compared. Needle bearings are used for this evaluation because they are noisier than ball bearings, and there has been little published regarding their vibration behavior. The signature analysis techniques are evaluated using three increasing levels of outer race damage. The Evaluation criteria are based on the ability of a technique to repeatedly detect a damaged bearing and to correctly indicate the progression of damage level.

Fractal Dimensions in Elastic-Plastic Beam Dynamics

The final midpoint displacement of a two-degree-of-freedom beam model subjected to a short pulse of transverse loading may be either in the direction of the initial impulse or in the opposite (“negative”) direction, when moderately small plastic deformations occur. In the range where chaotic vibrations occur, the result depends with great sensitivity on the impulse magnitude. Considering a pulse of duration 0.5 × 10−3 sec, 100 calculations have been made for pulse forces P starting at 2500 N and increasing by increments of 2.0, 10−2, 10−4, and 10−6 N. It is found that the proportion and distribution of negative final displacements remain, on average, the same, independent of the size of the force increment. A fractal dimension representing a self-similarity property is calculated for the four choices of the force increment, and is found to be approximately 0.78 in each case. A correlation fractal dimension is also computed for undamped responses.

Correlation of the SPICE Beam Expander Structural Model With Component and System Level Modal Test Results

A full scale experimental beam expander structure is modeled and correlated with modal test results on a component and system level. Correlation of the FE models is completed using the LINK module of the Leuven Measurement Systems (LMS) software which is also used to acquire and reduce the modal test data. The correlation tools used to measure the agreement between test and analytic mode shapes are the Modal Assurance Criterion (MAC), Coordinate Modal Assurance Criterion (CoMAC), and mass cross-orthogonality. In addition to the tools used to measure agreement between test and analysis modal parameters, sensitivity and optimization algorithms are used to identity structural parameters which influence a particular mode and what the minimum change(s) must be in the parameter(s) to bring about the desired agreement. As part of a system level pre-test analysis, the theoretical mode shapes along with a normalized line-of-sight error associated with each mode are used to select the best measurement and excitation locations.

A Simple Method for Extracting Normal Modes

A simple method for extracting the normal modes of structures is developed. The frequency response function relation between the complex and the normal modes is derived and a technique is developed to calculate the normal modes from the identified (damped) complex modes. In this method, only the magnitude and phase information at resonant frequencies are needed for extracting the normal mode shapes. A numerical example is employed to illustrate the theory. The results indicate that this method is more robust than other methods when the frequency response measurements are contaminated with noise.

Crack Detection in Composite Driving Shafts by Experimental Modal Analysis

A case study is presented in which a composite driving shaft of a motor-bike was loaded with different increasing numbers of load-cycles in a pulsating testing machine to reach different stages of damage. For each number of load-cycles an experimental modal analysis was performed by an iterative, global, multi-degree-of-freedom, frequency-domain modal testing technique and the eigenfrequencies and modal damping ratios were identified. From the results it is shown that the damping increases with the number of load-cycles i.e. the state of damage. However, it turned out that a more sensitive indicator for the state of damage is the splitting and shifting of the ‘double’ eigenfrequencies of the bending modes of the driving shaft with the ‘axisymmetric’ circular ring cross section. This fact is shown on the basis of several related experimental data.

A Holographic and BEM/FEM Analysis of a Fluid-Loaded Propeller

The modal dynamic characteristics of an underwater propeller are investigated using a coupling of the Finite Element Method (FEM) to model the propeller and the Boundary Element Method (BEM) to model the fluid. Results of this numerical model are presented for a fluid-loaded propeller and are compared with experimental holographic results. The FEM is known to yield very reliable solutions in the analysis of the modal dynamic characteristics of solid structures such as a propeller and the BEM is very attractive in dealing with infinite domain problems and the radiation condition, such as the infinite fluid field. Combining the two methods exploits the best attributes of both. The fluid/structural coupling is achieved by discretizing Kirchhoff’s integral with boundary elements and isolating the effective mass of the fluid. This effective mass is in the form of a mass matrix which is coupled by the degrees of freedom of the propeller. The effective mass is then input into a finite element program in the form of user elements along with the propeller’s geometry, material properties, and boundary conditions to simulate an underwater propeller in a hub. An experiment using time averaged holographic interferometry was performed to identify the resonant modes of the propeller, identical in geometry to that used in the FEM model. In order to simulate the boundary conditions of the model the propeller was rigidly clamped in a vise at it’s root and submerged in water. Excitation of the propeller was provided by means of a mechanical shaker mounted to the vise. Both the resonant frequencies and their respective mode shapes agreed favorably with numerical predictions.