Investigation on the Vibration Response to High-Intensity Pressure Waves During a Solid Rocket Motor Operation

A new experimental modal analysis method based on double-exponential windowing and application to lightly damped bladed wheels

In experimental modal analysis, the use of characterized excitation and the choice of window functions are fundamental to the estimation of system frequency response function (FRF) data. It greatly influences the quality of the resulting FRF measurements. Discussed are combination methods of several commonly-used excitation signals with window function, which is relative to lightly damped systems. Study shows that burst random signal with Rectangular works well for lightly damped structures, and pure random with Hanning will bring about higher error. A modal testing of white car body was done. Experimental parameters analysis are given to demonstrate the study result presented above. So it poses a practicable method for improving the accuracy of frequency response function (FRF) measurements of lightly damped structure by using proper excitation signal with appropriate window function.

Experimental modal analysis (EMA) with oblique excitation (i.e. oblique impact testing) is useful in improving the long test time problem of conventional EMA with normal excitation (i.e. triaxial normal impact testing), in order to extract all the important dynamic characteristics of a 3D complex structure. In this study, a new methodology involving a vector projection method is introduced to find the driving point frequency response function (FRF) in the oblique direction, without the need for a special fixture with an obliquely oriented impedance head. Hence, this presents a low cost and practical solution for scaling the mode shape, as compared to the traditional approach. Moreover, the concurrent forces characteristic of oblique excitation are used in the development of the theoretical relationship between FRFs with oblique excitation and those with normal excitation. This is important for the validation of the oblique impact testing result, such as the FRF and modal parameter estimations. The experimental results show that oblique impact testing has reliable and effective results, as compared with the triaxial normal impact testing, in terms of the FRF correlation, natural frequency discrepancy, modal damping ratio error and modal assurance criterion of the unit modal mass mode shape.

The investigation of dynamic behavior of aerospace structures is a challenging task due to the interaction of different types of aerodynamic and structural parameters. The identification of operational loads is essential for accurate investigation of the fatigue life especially in case of composite structures. In the present work, a mixed experimental and numerical approach is used for indirect identification of operational loads for composite structures using model correlation and updating technique. In the first step, the operational modal analysis using the response of accelerometers is performed for an anisotropic spar in cantilever position by using poly reference least square complex frequency (pLSCF) algorithm. Model correlation and updating of the FE model with the operational mode shapes is performed using Modal Assurance Criteria (MAC). The updated FE model is used for extraction of system matrices using Frequency Response Functions (FRFs). The physical response of accelerometers and transfer functions in the form of FRFs from the FE are used for identification of the operational loads at different locations of the structure. Finally, the proposed approach is validated by applying the extracted loads on the FE model and comparing the response at different locations.

This paper reports experimental and numerical works devoted to the role of aluminum combustion on the stability of solid rocket motors. An experimental setup, known as the velocity-coupled T-burner, which provides measurements of the contribution of aluminum combustion to stability, has been developed and used. Experiments unambiguously show that aluminized propellants have a strong destabilizing contribution, whereas nonaluminized do not. This destabilizing behavior is found to depend much on aluminum agglomerate size distribution. In addition, two-phase numerical simulations are conducted on the setup and confirm experiments. It is found that the instability arises due to a thermoacoustic coupling between pressure waves and the heat release from aluminum combustion. Simulations also stress the role of aluminum agglomerate particle size as in experiments. This work experimentally and numerically proves that aluminum combustion represents a source of instability in solid rockets that should not be overlooked. This suggests that the widely accepted viewpoint that particle phase always damps pressure waves may not be always true for some aluminized propellants.

A comprehensive numerical model for internal ballistic simulation under dynamic flow, combustion and structural vibration conditions is used to investigate the effectiveness of grain port area transitions of a reference solid rocket motor as a means for suppression of axial combustion instability symptoms. Modification of the propellant grain geometry is one of several traditional means for suppressing symptoms in actual motors. With respect to these symptoms, individual transient simulation runs show the evolution of the axial pressure wave and associated DC shift for the given grain geometry, as initiated by a given pressure disturbance. Limit pressure wave magnitudes are collected for a number of simulation runs for different grain area transition positions, steepness and aspect ratios, and mapped on an attenuation trend chart. Effects of acceleration, through structural vibration of the propellant surface, on the combustion process are investigated, and their influence on the effectiveness of grain area transitions is examined. With or without acceleration/vibrations effects included, the numerical results produced in this study confirm the significant ability of a grain area transition to suppress combustion instability symptoms.

This paper adopts composite structure system analysis method to perform modal analysis of high-speed face milling cutter which is mounted on the machine tool through FEM modal analysis. The key problem of this method is to obtain joint surface parameters between the machine tool spindle and face milling cutter through experimental modal analysis and MATLAB software. The joint surface parameters consist of linear stiffness, linear damping, rotation stiffness and rotation damping. After getting the frequency response function (FRF) at the tool tip of the face milling system through experimental modal analysis, the contact surface parameters can be used to eliminate the influence of the machine tool to get modal parameters of the face-milling cutter itself. Based on the finite element model of face milling cutter, composite structure system analysis method can be used easily to acquire the dynamic performance of the face milling system through FEM modal analysis, greatly to improve the reliability of modal analysis, and is helpful to the dynamic design and the structure improvement of high speed face milling cutter.

As an alternative to operational modal analysis and classical experimental modal analysis (EMA), a novel method was introduced previously, namely impact-synchronous modal analysis (ISMA). The effectiveness ISMA on rotor and structural dynamic systems has been proven in previous literature. More recently, an automated impact device (AID) was introduced which utilized tachometer pulse as initiation signal and its effectiveness on ISMA was proven. An attempt to further enhance this device in term of equipment and cost is then proposed by replacing the tachometer with the in-use tri-axial accelerometer through utilizing the filtered response of cyclic load component as an initiation signal to control the impact device, which is also the primary aim for this study. Prior to modal testing, accuracy of this device is illustrated at desired phase angles of 0 deg, 90 deg, 180 deg, and 270 deg. Subsequently, frequency response function (FRF) estimations obtained for ISMA using enhanced AID has demonstrated the suppression capabilities of this device on disturbances, i.e., reduction of 93.58% at 30 Hz and 57.78% at 60 Hz, resulting in a high correlation for signature assurance criterion (SAC) and cross signature assurance criterion (CSAC). Modal parameters extracted from the EMA and ISMA using impact device are presented and compared, for the first three natural modes of the test rig. It is found that natural frequencies are deviating by less than 6%, whereas modal assurance criterion (MAC) values between the mode shapes of the two tests are found to be above 0.9.

The experimental environments for impact tests are simple to construct compared to other vibration tests in experimental modal analysis. However, given that sufficient sampling time is necessary for the response to attenuate, the following two problems arise: The first is that work efficiency is lowered. The second is that the measurement time increases, which makes it more susceptible to noise. To solve these problems, it is common to shorten the sampling time and apply an exponential window to reduce the leakage error of the frequency response function (FRF). Although studies on the influence on the FRF exist, identification accuracy for damping characteristic and the influence on the residue have not discussed. In this study, the influence on the modal properties obtained and the accuracy of the results are clarified using numerical examples based on a circle fit and method using simultaneous equations of the real and imaginary parts of the FRF. Finally, the identification results were compared and made sure that the method using simultaneous equations of the real and imaginary parts of FRF can identify modal properties with high accuracy. This method is effective for improving the working efficiency and reducing the influence of noise.

As all experimental procedures, Experimental Modal Analysis (EMA) is subject to a wide range of potential testing and processing errors. The modal identification methods are sensitive to these errors, yielding modal results which are uncertain up to certain error bounds. The question hence is what these error bounds on test data and modal parameters are. In this paper, the studied source of uncertainty is related to the variance (noise) on the Frequency Response Function (FRF) measurements. Under the H1 assumptions and in single-input cases, the FRF variances can be computed from the coherences and the FRFs. In multiple-input cases, some more measurement functions are required. Advanced system identification methods like the Maximum Likelihood Estimator (MLE) and PolyMAX Plus have the possibility to take the uncertainty on the measurement data into account and to propagate the data uncertainty to (modal) parameter uncertainty. This paper will review FRF variance estimation techniques, including some pragmatic approaches. The basic concepts of Maximum Likelihood Estimation and the calculation of confidence bounds will be discussed. Some typical structural testing and modal analysis cases will be used as illustration of the discussed concepts.

MODAL ANALYSIS OF A LIGHTWEIGHT STRUCTURE—INVESTIGATION OF THE EFFECTS OF THE SUPPORTS ON THE STRUCTURAL DYNAMICS

An alternative approach to measure similarity between two deterministic transient signals

A longitudinal bar model that includes both stinger elastic and inertia properties is used to analyse the stinger's axial dynamics as well as the mass compensation that is required to obtain accurate input forces when a stinger is installed between the excitation source, force transducer, and the structure under test. Stinger motion transmissibility and force transmissibility, axial resonance and excitation energy transfer problems are discussed in detail;Stinger mass compensation problems occur when the force transducer is mounted on the exciter end of the stinger. These problems are investigated theoretically, numerically, and experimentally. It is found that the measured Frequency Response Function (FRF) can be underestimated if mass compensation is based on the stinger exciter-end acceleration and can be overestimated if the mass compensation is based on the structure-end acceleration due to the stinger's compliance. A new mass compensation method that is based on two accelerations is introduced and is seen to improve the accuracy considerably. The effects of the force transducer's compliance on the mass compensation are also discussed;A theoretical model is developed that describes the measurement system's FRF around a test structure's resonance. This model shows that very large measurement errors occur when there is a small relative phase shift between the force and acceleration measurements. These errors can be in hundreds of percent corresponding to a phase error on the order of one or two degrees. The physical reasons for this unexpected error pattern are explained. This error is currently unknown to the experimental modal analysis community;Two sample structures consisting of a rigid mass and a double cantilever beam are used in the numerical calculations and experiments.

Application of Sherman–Morrison–Woodbury formulas in instantaneous dynamic of peripheral milling for thin-walled component

Particle damping technology is widely used in mechanical and structural systems or civil engineering to reduce vibration and suppress noise as a result of its high efficiency, simplicity and easy implementation, low cost, and energy-saving characteristic without the need for any auxiliary power equipment. Research on particle damping theory has focused on the vibration response of the particle damping structure, but the acoustic radiation of the particle damping structure is rarely investigated. Therefore, a feasible modeling method to predict the vibration response and acoustic radiation of the particle damping structure is desirable to satisfy the actual requirements in industrial practice. In this paper, a novel simulation method based on multiphase flow theory of gas particle by COMSOL multiphysics is developed to study the vibration and acoustic radiation characteristics of a cantilever rectangular plate with Particle dampers (PDs). The frequency response functions and scattered far-field sound pressure level of the plate without and with PDs under forced vibration are predicted, and the predictions agree well with the experimental results. Results demonstrate that the added PDs have a significant effect on vibration damping and noise reduction for the primary structure. The presented work in this paper shows that the theoretical work is valid, which can provide important theoretical guidance for low-noise optimization design of particle damping structure. This model also has an important reference value for the noise control of this kind of structure.