Variable Amplitude Research Articles

Capability of different multiaxial fatigue evaluation approaches on adhesively butt-bonded hollow cylinders under multiaxial loading with variable amplitudes

Currently, there is a lack of reliable approaches for the fatigue assessment of adhesively bonded joints that are subject to multiaxial stresses with variable amplitudes. To improve the current situation, investigations are made on the capability of three multiaxial evaluation approaches based on fatigue tests of adhesively butt-bonded hollow cylinders under multiaxial loading with constant phase shift and variable amplitudes.The investigated approaches are the Gough-Pollard criterion, the Findley criterion and a new method presented here, which is based on a multiaxial counting method and an invariant equivalent stress hypothesis (MCES-Method).While the Gough-Pollard criterion has a low computational effort, it does not reflect the fatigue life extending effect due to a phase shift without using a fitting parameter that is not physically based. The Findley criterion is less suitable for the investigated multiaxial stress states (with and without phase shift), although the fatigue life prediction under these load conditions is at least conservative. The MCES-Method has the highest accuracy of the methods considered. By combining research findings from published papers in the context of adhesively bonded joints, all investigated load scenarios are estimated with high prognosis quality.

Seismic geomorphology and evolution of Mid-Late Miocene deepwater channels offshore Taranaki Basin, New Zealand

Deepwater channels play a significant role in deep marine environments by transporting sediments to deep marine environments, but they are also hydrocarbon reservoirs. In contrast, traditional seismic interpretation techniques have provided insights into these features; intricate channel-fill heterogeneities present challenges in revealing small features or associated elements. This study integrates high-resolution 3D seismic data, relative time geologic models (RGT), spectral decomposition, and geobody to identify the Middle-late Miocene submarine channels, their evolution, and their associated deposition elements. The geomorphologic and stratigraphic analysis results have revealed four depositional elements in the study area. These include (1) channel complexes, (2) distributary channels, (3) frontal splay channel complexes, and (4) crevasse splays. However, the channels lack constructional levee development outside the channel banks, which is linked to the limited sediment supply to deep areas. The identified channels are characterized by a narrow to wide width (0.37 km to 1.92 km), a low to high degree of sinuosity, medium incision depths, and lateral migration. The channel fill geometries are highly variable, displaying horizontal to sub-horizontal, lateral accretion, divergent, and inclined reflection packages. Most channels originate as large and wide channels from the northeast and prograde southwest direction of the Taranaki coastline, and they have evolved differently at different development stages. The channel fills exhibit a variable basal amplitude reflection, ranging from medium to high, indicating the presence of sand-prone and mixed facies, such as sand and mudstone. The spectral decomposition maps show variable color intensity, which implies different facies associations within the channels. The channel evolution is likely to be controlled by the interplay of sediment discharge, faults, sea level changes, variable gravity flow strength, and the type of materials supplied from the shelf edge.

Classification of The Analog Informative Parameters of the Rod Deepwell Pump Dynamograph Signals

In mechanized oil production, rod deep-well pumps are widely used. They consist of surface and underground parts. The above-ground part includes pump drive and wellhead fittings. The wellhead fitting is designed to seal the well. The underground part is the pump itself. The pump consists of a plunger, rod string and tubing. The main method of diagnosing a rod deep-well pump is dynamometry. Dynamometry allows to determine the equipment defects and control the efficiency of the pump operation mode without stopping the well operation. Dynamometry is a process of measuring the loads, which are perceived by the polished rod during the operation of the well. There are theoretical and practical dynamograms. Practical dynamogram is a closed non-periodic curve with variable amplitude. There are various methods to automate the process of the dynamometry result processing. In this paper we analyze the analog informative parameters of dynamometer signals. These parameters depend on the friction forces in the underground part of the rod pump, inertial forces, tightness of valve assemblies, dynamic liquid level, etc. The results obtained can be used in the development of the pumping process. The obtained results can be also applied to develop processing algorithms of practical dynamograms.

Simulation of fatigue crack growth in aluminium alloy 7075-T7351 under spike overload and aircraft spectrum loading

The trend towards virtual testing and digital-twin assisted management means that the accurate and reliable simulation of fatigue crack propagation behaviour is more important than ever. Reliable but conservative approaches to support this are in widespread use in the aerospace industry. Nevertheless, the conservatism comes at a significant cost in terms of reduced structural life and an increased ongoing inspection requirement and, as such leads to questions about the economic burden of these approaches. Recent comparisons between blind predictions and test results revealed the extent of the issue for cracking in aluminium alloy 7075-T7351 coupons with configuration and loading representative of military transport aircraft wing skins. The current models were generally conservative by a factor of two or more in terms of crack propagation life. This suggested that there was significant scope to improve the modelling to better reflect all the complex contributing factors. The current work has investigated the issue of changes in the crack front constraint as the crack progresses from a state of high constraint (close to plane strain) to a lower constraint (approaching plane stress). This issue was investigated both experimentally and with the development of an improved analytical model. A test program was conducted on several specimens, loaded under constant-amplitude, constant-amplitude with spike-overloads and a variable amplitude spectrum. Crack-opening stress levels were measured at key points in the tests and the results were used to develop and evaluate improved modelling approaches. The improved model was generally able to predict crack growth within about ± 30 % of that demonstrated along with the correct form of the crack growth, which is a significant advance and will lead to reduced costs and increased safety.

Fatigue and Ultimate Strength Evaluation of GFRP-Reinforced, Laterally-Restrained, Full-Depth Precast Deck Panels with Developed UHPFRC-Filled Transverse Closure Strips

A depth precast deck panel (FDDP) is one element of the prefabricated bridge element and systems (PBES) that allows for quick un-shored assembly of the bridge deck on-site as part of the accelerated bridge construction (ABC) technology. This paper investigates the structural response of full-depth precast deck panels (FDDPs) constructed with new construction materials and connection details. FDDP is cast with normal strength concrete (NSC) and reinforced with high modulus (HM) glass fiber reinforced polymer (GFRP) ribbed bars. The panel-to-girder V-shape connections use the shear pockets to accommodate the clustering of the shear connectors. A novel transverse connection between panels has been developed, featuring three distinct female-to-female joint configurations, each with 175-mm projected GFRP bars extending from the FDDP into the closure strip, complemented by a female vertical shear key and filled with cementitious materials. The ultra-high performance fiber reinforced concrete (UHPFRC) was selectively used to joint-fill the 200-mm transverse joint between adjacent precast panels and the shear pockets connecting the panels to the supporting girders to ensure full shear interaction. Two actual-size FDDP specimens for each type of the three developed joints were erected to perform fatigue tests under the footprint of the Canadian Highway Bridge Design Code (CHBDC) truck wheel loading. The FDDP had a 200-mm thickness, 2500-mm width, and 2400-mm length in traffic direction; the rest was over braced steel twin girders. Two types of fatigue test were performed: incremental variable amplitude fatigue (VAF) loading and constant amplitude fatigue (CAF) loading, followed by monotonically loading the slab ultimate-to-collapse. It was observed that fatigue test results showed that the ultimate capacity of the slab under VAF loading or after 4 million cycles of CAF exceeded the factored design wheel load specified in the CHBDC. Also, the punching shear failure mode was dominant in all the tested FDDP specimens.

Modeling the service life of temporary airfield operational surfaces under multi-pass aircraft trafficking

Expeditionary Airfield (EAF) surfacing systems are designed to create temporary aircraft operating surfaces. Modeling the service life of EAF surfacing systems including the matting system, aircraft, and subgrade, has historically proven difficult, exacerbated by variability between systems and the multitude of mechanisms that can constitute failure. The study presented herein outlines the development and implementation of a performance modeling approach that includes a multi-scale scheme that accounts for local characteristics of the connection points of the EAF matting system, coupled to the global characteristics of the matting array to predict cyclic passes to failure. Finite element studies were conducted for an EAF surfacing system brickwork configuration subjected to aircraft strut loads over varying California Bearing Ratio (CBR) subgrades to calibrate a transfer function to full-scale trafficking experiments. The proposed framework is then used to predict the rate of subgrade deformation for additional lay patterns, which successfully ranked the performance of each relative to full-scale trafficking experiments. An approach is proposed to couple the rate of subgrade deformation with local finite element models to capture increasing joint damage as permanent deformation accumulates, and supplemented by a variable amplitude cycle counting and damage accumulation algorithm that yields reasonable agreement with full-scale experiments while capturing the transition in failure mechanisms at higher CBR values. The results of the study presented herein captures the propensity for end connector and subgrade failure over a range of subgrade CBRs and shows promise for a broader performance framework that can be extended to other EAF surfacing systems, aircraft types, and specific matting lay patterns.

High-temperature fretting wear behavior and microstructure stability of a laser-cladding Ti-Al-C-N composite coating meditated by variable cycle conditions

Ti-6Al-4 V titanium alloy is used for low-pressure compressor blades of aero-engine due to its high specific strength, excellent corrosion resistance and high-temperature stability. Low-pressure compressor blades are subject to fretting wear in service, which may lead to fracture failure of the blades. The preparation of wear-resistant coatings is currently an effective solution in solving the problem of fretting wear on Ti-6Al-4 V titanium alloy. However, the fretting wear resistance and microstructure stability of the coating under variable cycle fretting conditions require more attention. In this work, the fretting wear performance and microstructure stability of the Ti-Al-C-N composite coating under variable cycle fretting conditions are investigated. The results show that the parameters of variable cycle operating conditions have a notable effect on the coefficient of friction (COF). The variable frequency and variable temperature working conditions result in the alteration of the fretting operation mechanism. Whereas the variable stroke amplitude and the variable load conditions do not cause changes in the fretting operation mechanism, and both are in the gross slip region (GSR). The lowest wear rate occurs under variable stroke amplitude conditions. The wear rate is the maximum under the variable cycle temperature condition. According to the dissipated energy calculation, the difference between the two different stroke amplitudes is the biggest among all the conditions. EBSD and TEM analyses show that the subsurface of variable stroke amplitude worn scar has a more uniform strain distribution, and reveals a unique subsurface structure with a transformation from crystalline to amorphous, which contributes to improving the wear resistance. This work provides insights into coating microstructure stability and wear mechanisms under variable cycle conditions.

Experimental behaviour and fatigue life prediction of bonded joints subjected to variable amplitude fatigue

The variable amplitude fatigue behaviour of adhesive joints has not been extensively considered in literature and considerable knowledge gaps regarding its underlying mechanisms still exist, hindering accurate life prediction. This study investigates the effect of loading sequence and number of load transitions on single lap joints (SLJs) bonded with a toughened epoxy adhesive. Life prediction is also conducted using established cumulative rules: Palmgren–Miner (PM), Broutman and Sahu (BS) and, Hashin and Rotem (HR). To overcome their limitations, a modified Cortan–Dolan approach is proposed. For this, SLJs were subjected to single transition (low-to-high and high-to-low load transitions at different stages of the fatigue life and with different magnitudes) and multi-block loading spectra with different numbers of transitions.Results showed an extension of the fatigue life for high-to-low transitions. This was attributed to a combination of load interaction effects, as evidenced by an elastoplastic numerical simulation, and non-linear damage accumulation. Conversely, low-to-high transitions exhibited a damaging effect. For single transition spectra, BS and HR models were seen to improve prediction over PM by indirectly considering these effects. The proposed approach further improved this prediction. Multi-block results showed no significant influence of the number of load transitions and were satisfactorily predicted using PM.

Assessment of hybrid machine learning models for non-linear system identification of fatigue test rigs

The prediction of system responses for a given fatigue test bench drive signal is a challenging problem, since highly dynamic loads from measurement campaigns must be reproduced accurately. Linear frequency response function models are commonly used for this system identification task, but energy intensive experimental iterations are required to account for system non-linearities. Two novel hybrid modeling strategies are suggested, which augment existing approaches using non-linear Long Short-Term Memory networks. These are trained and deployed on short subsequences of measurement data and recombined using a windowing technique, which enables their application to measurement data with high sampling rates. In addition to fatigue test bench commissioning, these hybrid models can also be employed in the field of virtual sensing. The approach is tested using non-linear experimental data from a servo-hydraulic test rig and this dataset is made publicly available. A variety of metrics in time and frequency domains, as well as fatigue strength under variable amplitudes, are employed in the evaluation. It is shown, that hybrid models can successfully use frequency response function models as a linear baseline estimate, which is further improved by Long Short-Term Memory networks to enable non-linear predictions.

Anisotropy-driven magnetic phase transitions in SU(4)-symmetric Fermi gas in three-dimensional optical lattices

Abstract We study SU(4)-symmetric ultracold fermionic mixture in the cubic optical lattice with the variable tunneling amplitude along one particular crystallographic axis in the crossover region from the two- to three-dimensional spatial geometry. To theoretically analyze emerging magnetic phases and physical observables, we describe the system in the framework of the Fermi-Hubbard model and apply dynamical mean-field theory. We show that in two limiting cases of anisotropy there are two phases with different antiferromagnetic orderings in the zero temperature limit and determine a region of their coexistence. We also study the stability regions of different magnetically-ordered states and density profiles of the gas in the harmonic optical trap.

Strain amplitude dependency of cyclic hardening/softening behavior of 490 N/mm2 class steel

Existing studies on the strain amplitude dependency of cyclic softening behavior in structural steels often involve limited cycles or strain amplitudes below 2.5%, failing to provide a comprehensive understanding of stabilized cyclic behavior. This study performed uniaxial tension–compression cyclic loading tests using SN490B structural steel under three loading patterns: constant, variable, and offset constant strain amplitudes. The cyclic hardening and softening behaviors and stress–strain hysteresis loops were compared. Under variable strain amplitude loading, the specimens were subjected to increasing and decreasing strain amplitudes to investigate the strain amplitude dependency of the cyclic hardening and softening behaviors. Under offset constant strain amplitude loading, mean strains were initially introduced in either the tension or compression strain range, followed by cyclic loading with a constant strain amplitude centered around the mean strains. The test results revealed the following: (1) Under constant strain amplitude cyclic loading, the material exhibited cyclic softening and hardening behaviors at strain amplitudes smaller than and larger than 0.5%, respectively; (2) Under variable strain amplitude cyclic loading, increased and reduced strain amplitudes resulted in cyclic hardening and softening behaviors, respectively. The cyclic hardening/softening behavior strongly depended on the strain amplitude. Applying a significant number of cycles after strain amplitude reduction resulted in the stress–strain curves closely resembling those under constant strain amplitude conditions; (3) Even under offset constant strain amplitude cyclic loading conditions with nonzero mean strain, the peak stresses and shapes of the hysteresis loops approached those under constant strain amplitude conditions without mean strain.

Fatigue damage accumulation in a bolted joint subjected to the random loading

Fatigue damage in structures, which escalates with cyclic loading, is traditionally analyzed using blocks of constant amplitude. This study aims to derive the fatigue loading spectrum for the Cirrus SR20 multipurpose airplane and predict the fatigue life of its main spar connection. Using available reference loading data from acrobatic and training aircraft, the loading spectrum was established, and constant amplitude loading blocks were determined through the Rainflow cycle counting and statistical methods. Fatigue damage in the bolted joint was assessed using both linear and nonlinear Miner rules, revealing that results from nonlinear criteria tend to converge towards those from linear predictions as loading blocks increase. This approach provides a robust predictive framework for assessing the fatigue life of airplane components under variable amplitude loadings, potentially enhancing maintenance protocols and structural design durability.

Study on fatigue properties with composite waveform and variable amplitude of TC21 titanium alloy pulsed laser-arc hybrid welded joints

TC21 titanium alloy is widely used in the manufacturing of key components such as aerospace industry, its welded structure in actual service is often subjected to the cyclic loading with composite waveform and variable amplitude and leads to fatigue failure. Therefore, in this work, the composite waveform and variable amplitude fatigue properties of TC21 titanium alloy pulsed laser-arc hybrid welded joints were investigated in this paper, and the micro-deformation mechanism and crack initiation mechanism of welded joints under different initial maximum cyclic stresses were revealed. The results indicated that the micro-deformation mechanism was the competition between twinning and dislocation slip in the α′ phase at low stress. When the initial maximum cyclic stress increased, the generation and slip of dislocation dominated, and the main distribution of dislocations gradually transitioned from the α′ phase to the β phase. This caused the phase transition in the β phase to the α phase, which increased the energy at the α/β phase interface and reduced the resistance of fatigue microcrack initiation accordingly, thus promoting fatigue failure. In addition, pores were the main factor of fatigue failure for welded joints. Therefore, in this work, the influence of defect size, location and shape on the fatigue life of welded joints was considered to develop a fatigue life prediction model based on the control parameter Z-parameter and equivalent stress amplitude. The predicted composite waveform and variable amplitude fatigue life of TC21 titanium alloy welded joints was within the triple error band.

Influence of Heat Treatment on Microstructure, Mechanical Properties, and Damping Behavior of 2024 Aluminum Matrix Composites Reinforced by Carbon Nanoparticles.

Nanocarbon 2024 aluminum composites with 0.5 vol. % and 1 vol. % of graphene nanoplatelets and 1 vol. % and 2 vol. % of activated nanocarbon were manufactured through induction casting. The effect of the reinforcements and heat treatment on the performance of the composites was examined. Analysis of the microstructure of the composites before heat treatment suggested the homogeneous dispersion of reinforcements and the absence of secondary carbide or oxide phases. The presence of carbon nanoparticles had a significant impact on the microstructural characteristics of the matrix. This behavior was further enhanced after the heat treatment. The mechanical and damping properties were evaluated with the uniaxial compression test, micro Vickers hardness test, and dynamic mechanical analysis. The yield strength and ultimate strength were improved up to 28% (1 vol. % of graphene nanoplatelets) and 45% (0.5 vol. % of graphene nanoplatelets), respectively, compared to the as-cast 2024 aluminum. Similarly, compared to the heat-treated 2024 aluminum, the composites increased up to 56% (0.5 vol. % of graphene nanoplatelets) and 57% (0.5 vol. % of graphene nanoplatelets) in yield strength and ultimate strength, respectively. Likewise, the hardness of the samples was up to 33% (1 vol. % of graphene nanoplatelets) higher than that of the as-cast 2024 aluminum, and up to 31% (2 vol. % of activated nanocarbon) with respect to the heat-treated 2024 aluminum. The damping properties of the nanocarbon-aluminum composites were determined at variable temperatures and strain amplitudes. The results indicate that damping properties improved for the composites without heat treatment. As a result, it is demonstrated that using small volume fractions of nanocarbon allotropes enhanced the mechanical properties for both with- and without-heat treatment with a limited loss of plastic deformation before failure for the 2024 aluminum matrix.

Overall aerodynamic performance of the airfoils with different amplitudes via a fuzzy decision making based Taguchi methodology

In this study, the overall aerodynamic performance of the airfoils with variable amplitude geometric structure for lift-type vertical axis wind turbine has been analyzed and optimized using Fuzzy Analytic Hierarchy Process (AHP)-Fuzzy COmbinative Distance-based Assessment (CODAS) based on Taguchi Method. In the design of the experiment, leading edge (LE) tubercle airfoil models, Reynolds number, and angle of attack are utilized as the control factors. Drag, lift, and lift to drag ratio performances by comparing the airfoils according to the baseline model are calculated and the combination of these performances is considered as the overall aerodynamic performance response. The experiments are carried out according to the orthogonal matrix L18. Since the importance of each response is different on lift-type vertical axis wind turbines, the importance weights of these responses were obtained by Fuzzy AHP according to the evaluation of the decision maker. Multiple responses are converted into a single response (the overall aerodynamic performance) via Fuzzy CODAS which enables to model uncertainty in order to overcome the physical effects that may arise in experiments. Thereby, a multi objective Taguchi methodology was applied for the overall aerodynamic performance with a novel Fuzzy logic based multi criteria decision analysis approach. As a result, Model-4, having tubercle design parameters of amplitude of 0.025c and 0.0125c and wavelength of 0.5c and 0.125c, was found to have the best performance with the novel Taguchi approach, which saves time and cost. In addition, it has been determined that the airfoils, Reynolds number and angle of attack are significant and what level of contribution to the overall aerodynamic performance. At this point, the most important control factor has emerged as the angle of attack.

The Orbit and Dynamical Mass of Polaris: Observations with the CHARA Array

The 30 yr orbit of the Cepheid Polaris has been followed with observations by the Center for High Angular Resolution Astronomy (CHARA) Array from 2016 through 2021. An additional measurement has been made with speckle interferometry at the Apache Point Observatory. Detection of the companion is complicated by its comparative faintness—an extreme flux ratio. Angular diameter measurements appear to show some variation with pulsation phase. Astrometric positions of the companion were measured with a custom grid-based model-fitting procedure and confirmed with the CANDID software. These positions were combined with the extensive radial velocities (RVs) discussed by Torres to fit an orbit. Because of the imbalance of the sizes of the astrometry and RV data sets, several methods of weighting are discussed. The resulting mass of the Cepheid is 5.13 ± 0.28 M ⊙. Because of the comparatively large eccentricity of the orbit (0.63), the mass derived is sensitive to the value found for the eccentricity. The mass combined with the distance shows that the Cepheid is more luminous than predicted for this mass from evolutionary tracks. The identification of surface spots is discussed. This would give credence to the identification of a radial velocity variation with a period of approximately 120 days as a rotation period. Polaris has some unusual properties (rapid period change, a phase jump, variable amplitude, and unusual polarization). However, a pulsation scenario involving pulsation mode, orbital periastron passage, and low pulsation amplitude can explain these characteristics within the framework of pulsation seen in Cepheids.

Bandgap Calculation and Experimental Analysis of Piezoelectric Phononic Crystals Based on Partial Differential Equations.

Focusing on the bending wave characteristic of plate-shell structures, this paper derives the complex band curve of piezoelectric phononic crystal based on the equilibrium differential equation in the plane stress state using COMSOL PDE 6.2. To ascertain the computational model's accuracy, the computed complex band curve is then cross-validated against real band curves obtained through coupling simulations. Utilizing this model, this paper investigates the impact of structural and electrical parameters on the bandgap range and the attenuation coefficient in the bandgap. Results indicate that the larger surface areas of the piezoelectric sheet correspond to lower center bands in the bandgap, while increased thickness widens the attenuation coefficient range with increased peak values. Furthermore, the influence of inductance on the bandgap conforms to the variation law of the electrical LC resonance frequency, and increased resistance widens the attenuation coefficient range albeit with decreased peak values. The incorporation of negative capacitance significantly expands the low-frequency bandgap range. Visualized through vibration transfer simulations, the vibration-damping ability of the piezoelectric phononic crystal is demonstrated. Experimentally, this paper finds that two propagation modes of bending waves (symmetric and anti-symmetric) result in variable voltage amplitudes, and the average vibration of the system decreases by 4-5 dB within the range of 1710-1990 Hz. The comparison between experimental and model-generated data confirms the accuracy of the attenuation coefficient calculation model. This convergence between experimental and computational results emphasizes the validity and usefulness of the proposed model, and this paper provides theoretical support for the application of piezoelectric phononic crystals in the field of plate-shell vibration reduction.

Fatigue behavior under variable amplitude loadings in AlSi10Mg alloy components produced by laser powder bed fusion

AbstractThis study investigates the fatigue behavior of AlSi10Mg alloy manufactured via laser powder bed fusion under variable amplitude loading conditions. Two material conditions were examined: as‐built and stress relief, with the later involving a lower temperature compared to the conventional heat treatments, aimed at preventing the Al‐Si network rupture. Fatigue tests were conducted using two distinct loading spectra: block loading and random loading. While the stress relief reduced the monotonic properties of the material, it resulted in increased fatigue performance due to the homogenization of residual stress throughout the depth. Fracture surface analysis revealed initiation points on subsurface defects, with both block and random loading cases exhibiting overload markings from loading transitions. The predictive model incorporating crack initiation and propagation periods yielded good results, with the equivalent stress range approach providing higher quality estimation compared to the real stress range approach.

Fatigue failure of aluminum alloy friction stir welded joints under two-stage variable amplitude loading

Fatigue failure of aluminum alloy friction stir welded joints under two-stage variable amplitude loading

Multi-condition adaptive detail characterization model of magnetorheological dampers and experimental verification

The theoretical model for predicting the damping characteristics of magnetorheological dampers (MRDs) is significant for enhancing the design efficiency of the control algorithm. However, some existing theoretical models face limitations in characterizing MRD damping characteristics simultaneously in terms of nonlinear detail characterization and adaptability to variable working conditions. Therefore, this paper proposed the Composite Double-Boltzmann (CDB) model combining the Double-Boltzmann (DB) function widely used in the field of biology and chemistry for its strong nonlinear characterization capability. Utilizing this model to fit the sinusoidal vibration testing data of the MRD prototype under variable combination working conditions, obtaining quantitative relationships between the undetermined parameters in the CDB model and the excitation current, vibration frequency, and amplitude to enable the model to address both the nonlinear details characterization of MRDs and adaptability to variable working conditions. Subsequently, the validity of the quantitative relationships were verified by comparing the calculated parameter values using the quantitative relationships with the original accurate parameter values. In order to verify the validity of the CDB model, extensive unknown working condition vibration tests were conducted on the MRD prototype under variable excitation currents, vibration frequencies, amplitudes and random excitation working conditions, employing the CDB and Tanh models to predict the damping characteristics, to compare to demonstrate the CDB model’s capability of adapting to variable working conditions while accurately characterizing the nonlinear details of MRD damping characteristics.