Effective Vibration Attenuation Research Articles

Exploring the dynamic and thermo-mechanical behavior of Banana/Kenaf/Jute epoxy hybrid biocomposites: impact of stacking sequences

Abstract This study investigates the thermal behavior and thermo-mechanical properties of banana, jute, and kenaf fiber-reinforced epoxy composites, focusing on the impact of different layering sequences and hybrid configurations. The novelty of the work lies in the tailored stacking of natural fibers to optimize composite performance, a topic of growing significance in sustainable engineering. Thermal analysis revealed the highest endothermic peak at 72 °C in BJKKJBE hybrid composites, while jute fiber-reinforced composites exhibited a marginally higher peak at 73 °C. Dynamic mechanical analysis highlighted kenaf fiber-reinforced composites as having superior storage modulus values, reaching 152 MPa at 10 Hz, followed by the BJKKJBE hybrid, which achieved 137 MPa. Additionally, banana fiber-reinforced composites and neat epoxy recorded the highest loss modulus values (52 MPa and 51 MPa), indicating excellent energy dissipation. Neat epoxy and kenaf fiber reinforced composites displayed the highest tan delta values, with BJKKJBE hybrids also showing notable damping behavior, suggesting effective vibration attenuation. On the other hand, jute-based composites demonstrated the lowest tan delta, reflecting increased stiffness. A significant outcome is the thermal expansion behavior, where BJKKJBE composites exhibited the highest shrinkage (0.3%), while the KBJJBKE reinforcement, with kenaf as a skin layer, recorded the highest coefficient of thermal expansion (257 ppm °C−1). These findings present new opportunities for optimizing fiber-reinforced epoxy composites in applications requiring tailored thermal and thermo-mechanical performance, contributing to advancements in sustainable materials design for engineering applications.

Design and test of a contactless damper for HTS maglev systems via electromagnetic shunt dampers

High-temperature superconducting (HTS) maglev system is promising to become the future high-speed transport due to its numerous advantages. However, the low-damping dynamic characteristics of superconductors make the system vulnerable to external disturbances, which present a significant challenge to its implementation. To enhance the vibration attenuation effect of the HTS maglev system, a non-contact damper that employs electromagnetic shunt damping (EMSD) and negative resistance is incorporated into the HTS maglev system. This study elucidates the principles of EMSD and negative resistance, and establishes the governing equations to describe the behavior of the HTS maglev model equipped with EMSD. Subsequently, the EMSD coupling coefficients are analysed via the finite element method (FEM) under varying conditions. Finally, a dedicated vibration test rig is designed and fabricated to validate the effectiveness of the proposed damper. The results demonstrate that the proposed damper, in combination with negative resistance, is capable of effectively suppressing vibration in HTS maglev systems. The maximum acceleration of the test model can be reduced by 86% compared with the original system without the damper. This work may provide valuable guidance for future practical implementations.

Dynamic Characteristics of Pressure-Balanced Metal Bellows in Fluid–Structure Interaction

As a flexible component in high-pressure vessels and pipeline systems, bellows experience significant fluid–structure interaction effects under high-speed internal fluids and external vibrations. Nevertheless, their dynamic response mechanisms coupled with fluid–structure interaction mentioned below have not yet been clarified so far. In this work, a novel pressure-balanced metal bellow (PBMB) for low-stiffness and high-pressure resistance is firstly proposed. Several fluid–structure interaction models were considered to study the dynamic response characteristics of the PBMB. An experimental platform associated with fluid–structure interaction was established to validate the effectiveness of its vibration attenuation performance. The results indicate that the PBMB has an obvious vibration attenuation effect in the range of 5–90[Formula: see text]Hz, and super-harmonic and sub-harmonic resonance phenomena occur in the range of 90–200[Formula: see text]Hz. Under constant fluid conditions, fluid density, viscosity, flow velocity, and pressure are positively correlated with the response amplitude of the PBMB. The response of the PBMB oscillates at the fluid entry point due to both pulsating flow velocity and pulsating pressure. After several cycles, the response caused by pulsating flow velocity gradually decays and stabilizes. Thus, the impact of pulsating frequency on the stability of the response of bellows is insignificant during the initial cycles.

Auxetic enhancement of the shunted piezoelectric effect for vibration suppression

Shunted piezoelectric patches connected to passive electric circuits can be attached to a host structure for effective vibration attenuation. The effect of an auxetic layer to enhance the electromechanical coupling and subsequently the vibration suppression is studied here. Three different configurations are considered for the layer: a classical, a homogeneous auxetic and a layer with microstructure leading to auxetic behavior. First, is presented a modification of the “current-flowing” shunt circuit for multimode vibration control. Two finite element models have been validated, the frequency response graph of the system and the most suitable values of the electric parameters are calculated and a comparison is provided. Furthermore, it is shown that the vibration reduction of the second and third eigenmodes can be enhanced, provided that an auxetic of significant thickness is used. The results demonstrate the effect of the auxetic boosting on vibration suppression.

Low-frequency and broadband vibration absorption of a metamaterial plate with acoustic black hole resonators

Acoustic metamaterials with bandgap properties can lead to effective vibration attenuation in a targeted frequency range. In this paper, a novel locally resonant metamaterial plate is proposed, connected with acoustic black hole (ABH) resonators. The structure is shown to achieve low-frequency and broadband vibration absorption. The proposed microunit design consists of three parts: the ABH resonator, supporting beams as the connector, and the frame (FC-ABH). The modal characteristics of the microunit and the dispersion relation of the infinite periodic FC-ABH structure are calculated by both Gaussian expansion method and finite element method. By the effects of flexural wave absorption of ABH coupled with the local resonance mechanism, a low-frequency and broad vibration attenuation band can be generated. When the damping of materials is included, the attenuation band can be further widened, with relative bandwidth measured by the experiment up to 0.93. The results of numerical simulations and experimental tests demonstrate that the finite periodic FC-ABH can act as an effective vibration absorber and isolator. The proposed structure may provide new ideas for the design and application of broadband vibration mitigation metadevices.

Investigations of Sustainable Biodegradable Oil and Magnetic Particle‐Based Magnetorheological Fluid Dampers for Vibration Attenuation of a Rotor Dynamic System

This article aims to study the physical characterization and performance of a material‐based magnetorheological fluid (MRF) dampers for vibration attenuation of a high‐speed rotor–motor system near resonance. Four samples are synthesized by combining electrolytic iron and carbonyl iron (CI) with Castor and Karanja oil and experimentally investigated for their contribution to vibration attenuation. The results demonstrate effective vibration attenuation of the biodegradable oil‐based MRF damper than the nonbiodegradable oil‐based MRF damper. The best vibration attenuation is observed in the case of moderately viscous MRF. CI‐based samples exhibit a lower sedimentation rate, hence recommended for MRF. The vibration amplitude is maximum for the Castor oil‐based MRF damper, however, is minimum for the Karanja oil‐based MRF damper. The steady and transient results of vibration amplitudes are obtained and analyzed for different currents supplied to the MRF damper. The range of unstable speed near resonance is also obtained. The prepared samples show higher attenuation of 6–25% than Sample 5. The vibration amplitude attenuation of Sample 4 and Sample 5 are 47% and 22%, respectively. The findings of this study carry significant implications for controlling the vibration of the dynamic system using an eco‐friendly damping system.

Synchronization characteristics of two induction motors on a floating raft system

The synchronization characteristics of two exciters driven by induction motors independently on a typical double-layer vibration isolation system, that is, the floating raft system are studied in the paper to enhance its vibration attenuation effect. Firstly, a new dynamical model for a floating raft system driven by two exciters is established by the Lagrange equation under considering the coupling effect among floating raft system and exciters. Then, the vibration responses in all directions are obtained by the Laplace transform. Secondly, the synchronization and stability solution are obtained by using the average small parameter method. Thirdly, the results of the theoretical analysis are verified by simulations. Finally, the parameter scope of a floating raft system to enhance its vibration attenuation effect is given. Moreover, compared with the traditional model, the proposed model considering the coupling effect among floating raft system and exciters is more feasible. Additionally, the effects of the mass ratio of the eccentric block, the symmetrical installation distance, parameter differences of two motors, and other dynamic parameters such as system mass and stiffness on their synchronization and the system vibration are discussed. This paper can provide a theoretical reference for the design, modeling, and application of such double-layer vibration isolation systems including the floating raft systems to enhance its vibration attenuation effect.

Low-frequency vibration attenuation of metamaterial sandwich plate with lever-type inertial amplified resonators

The utilization of sandwich plate structures is widespread across diverse engineering fields owing to their advantageous high stiffness-to-weight ratio properties. However, these lightweight and thin-walled structures commonly encounter challenges related to inadequate vibration performance in the low-frequency range, imposing significant limitations on their applications. This paper thereby presents a design for a metamaterial sandwich plate that incorporates lever-type inertial amplified resonators (IA-MSP) to achieve a low-frequency bandgap and effective vibration attenuation capability. The bandgap characteristics and vibration behavior of the IA-MSP are comprehensively studied through an integrated approach involving theoretical analysis, numerical simulations, and experimental studies. The dynamic model of the IA-MSP is mathematically formulated, theoretically elucidating the underlying inertial amplification mechanism within the proposed metamaterial sandwich plates. The investigation on vibration transmission is conducted to analyze the vibration attenuation performance of the IA-MSP, utilizing both numerical simulations and experimental methods. The findings reveal that lever-type resonators amplify the mass motion, thereby enhancing the effective mass of the system and leading to a reduction in the frequency associated with the coupled mode of the bandgap. This amplification facilitates the attainment of a low-frequency bandgap without the need for utilizing the inclusion of additional centralized mass or heavy local resonators. By altering the lever ratio R of the lever-type inertial amplified resonators, precise fine-tuning and optimization of the low-frequency bandgaps are achievable. Compared with traditional metamaterial sandwich plates with local resonators (LR-MSP) featuring identical geometrical and material characteristics, the proposed IA-MSP characterized by an R-value of 2 exhibits boundary frequencies that are half of those observed in the LR-MSP. With an increase in the lever ratio R of the IA-MSP, a noticeable trend emerges a decrease in the lower boundary frequency, accompanied by a corresponding shift of the bandgap towards lower frequencies. The present study's outcomes are anticipated to hold significant promise in the realm of sandwich plate design, with a specific focus on furnishing vibration attenuation capabilities at lower frequencies.

An analytical vibration model of a one-dimensional two-stage periodic isolation system for the broadband vibration suppression of an underwater glider

Periodic isolation system is effectively applied in broadband vibration control. To further enhance the broadband vibration attenuation effect, the paper proposes a two-stage periodic isolation system for an underwater glider. The analytical model of the one-dimensional two-stage periodic isolation system is developed through the multi-degree of freedom spring mass model method. For illustrating the superiority of the proposed two-stage periodic isolator, the force transmission ratio and the wave propagation constant of the SDOF isolator, the single-stage periodic isolator, and the two-stage periodic isolator are calculated and compared. In order to obtain the dynamic parameter influences on the vibration isolation performances as the design guidelines of the two-stage periodic isolator, the parametrical study is carried out based on the analytical model. Furthermore, a two-stage periodic isolator is designed for an underwater glider. The application effect of the two-stage periodic isolator is investigated through analytical modeling and finite element method, comparing to the single-stage periodic isolator. The research results from the analytical models show the proposed two-stage periodic isolator could strength the broadband vibration suppression. The parametrical study results demonstrate the vibration attenuation bandgap and attenuation amount are greatly influenced by the designed dynamic parameters, such as the mass unit and the spring unit of the periodic isolator, the intermediate mass of the two-stage isolator, and the number of the periodic cells. In application study of an underwater glider, the finite element results verify that the two-stage periodic isolator has more vibration attenuation effect than the single-stage periodic isolator. The vibration isolation assessment according to the proposed analytical model gives good predictive performance before the finite element model verification.

Metamaterial-based vibration control for offshore wind turbines operating under multiple hazard excitation forces

Wind energy holds growing investment perspectives due to its renewable and sustainable energy production potential. The harvesting capability of wind turbines is directly related to their size. Therefore, those wind energy generators still encounter challenges related to excessive vibrations aggravated by environmental factors, compromising energy generation and resulting in fatigue damage and downtime. Various vibration control strategies have been explored to address these issues, with passive control emerging as a preferred choice due to its ease of manufacture, cost-effectiveness, and simple installation. Nevertheless, the limitations of these controls lie in their substantial size and weight associated with optimal installation positions for achieving a good performance. Recently, mechanical metamaterials have demonstrated tremendous advancements in efficiency regarding band isolation and vibration mitigation, coupled with enhanced manufacturing possibilities. Hence, this paper proposes a novel approach to control the vibration of wind turbines employing mechanical metamaterials in their design. A spectral approach is used to model the metamaterial turbine and its interaction with external excitations, such as wind, waves, and blade rotation. The numerical results show the efficiency of the metamaterial turbine by its tunable stopband features and vibration amplitude reduction under multiple hazard excitations, emphasising its superior suppressing vibrations compared to conventional tuned mass damper. Thus, the proposed wind turbine metastructures offer a compelling combination of effective vibration attenuation while reducing dynamic resonators’ overall stiffness, mass, and size. The outcome advances wind turbine design and energy technology for reliable wind energy production.

Explosion Behaviors of Scaled Shallow-Buried Concrete–Rubber-Laminated Annular Metastructures: Evaluation of Shock Wave Attenuation

The attenuation of impact inducer vibration is critical to the safety of underground protection structure, equipment and personnel. Metamaterials and metastructures show great potential in terms of sound and impact attenuation. To effectively attenuate ground shock-induced vibration of underground protective structures, scaled shallow-buried annular metastructures with concrete–rubber layered structures were proposed and constructed. Underground explosion experiments were performed to investigate the vibration attenuation effect of annular metastructures with different layered structures. It is clear in this research only annular metastructures with concrete–rubber–concrete structures like annular metastructure model B6 have the most excellent wave attenuation performances, whose rubber layer thickness must be over 6[Formula: see text]mm and hardness is 20[Formula: see text]HA. Other layered structures with rubber layer thickness of 0.3[Formula: see text]cm or with more layers cannot effectively attenuate the shock wave in this research.

Vibration attenuation band tuning by active stiffness control of local resonators of metamaterials

This paper presents a design of metamaterials with a broader bandgap by active stiffness control of local resonators. A series of cantilever beams are connected to the host structure, serving as local resonators to open the bandgap for vibration attenuation. The piezoelectric transducers bonded on the cantilever beams are shunted to a negative capacitance-negative inductance series circuit (NCNL). The variation of the effective modulus of the piezoelectric sample when connected to NCNL is discussed. In addition, the effect of the NC circuit and negative capacitance in series with positive inductance (NC-L) circuit on the effective modulus of shunted piezoelectric transducers is also analyzed for comparison. By tuning the NCNL circuit, the elastic modulus of the beam-type resonator exhibits frequency-dependent, which will achieve active stiffness tuning. Subsequently, the transmittance analysis of a metamaterial beam with active stiffness resonators is conducted using finite element method. The finite element results show that a broader attenuation band can be achieved by properly selecting the parameters of NC-NL circuits. This work provides a promising method for effective vibration attenuation using metamaterials.

Load-adaptive quasi-zero stiffness vibration isolation via dual electromagnetic stiffness regulation

Conventional quasi-zero stiffness (QZS) isolators are sensitive to load variation, especially the load mismatch can severely degrade low-frequency vibration isolation performance. Herein, a load-adaptative electromagnetic QZS vibration isolator (LEQVI) is proposed. The stiffness nonlinearization for QZS characteristic is achieved by exploiting a nonlinear positive stiffness structure (a cylindrical coil and a magnet in the face-to-face configuration) to modulate a negative stiffness structure (a conical coil and a magnet in the nested configuration). Static modeling and tests reveal that the rated load of the LEQVI can be flexibly and linearly adjusted by regulating the excitation current. Dynamic modeling found that the load mismatch can narrow the vibration isolation bandwidth and deteriorate the vibration attenuation effect. A sliding mode control law considering input saturation is developed to adapt to unknown loads. Simulations and dynamic experiments are conducted to evaluate the vibration isolation performance and verify the effectiveness of the load-adaptive controller. The results demonstrate that the LEQVI can realize a wide vibration isolation band and effective vibration attenuation under various loads via dual electromagnetic stiffness regulation. The proposed LEQVI provides a novel perspective for designing load-insensitive QZS isolators and holds great promise in facilitating future engineering applications of QZS isolators.

Low frequency elastic waves and vibration control mechanism of innovative phononic crystal thin plates

In order to realize the metamaterials that can control low-frequency vibration and be applied to practical engineering, an innovative phononic crystal thin plate is proposed in this paper. The band gap of the thin plate is systematically analyzed according to the existing wave theory and finite element method. According to the design characteristics of thin plate structure, the influence of the thickness and material of the upper and lower plates and intermediate layers of thin plate on the band gap is explored. Then, the energy propagation behavior of the wave in the structure is briefly discussed. Finally, the control effect of thin plate structure on vibration is verified by numerical simulation. The results show that the phononic crystal plate constructed by us is not only simple in structure design and easy to implement, but also has good band gap tuning and vibration attenuation effect.

Tetrahedron structure with nonlinear stiffness and inertia modulation for enhanced low frequency vibration isolation

A novel magnetically modulated tetrahedron structure with nonlinear inertia (MMTS-NI) is proposed and systematically investigated for broadband vibration isolation. The MMTS-NI consists of the tetrahedron structure, a pair of repulsive magnets, and the attached masses. Static analysis reveals that quasi-zero stiffness (QZS) can be realized by utilizing the harden stiffness of the magnets to modulate the negative stiffness of the tetrahedron structure. And the QZS can be obtained under different loads by setting appropriate initial angles of rods and matching initial magnet spacing. Considering the achieved QZS and the inertia of the attached masses, the dynamic model of the MMTS-NI is developed to evaluate its isolation performance when subject to base excitation. By using harmonic balance method (HBM), dynamic equation is solved and the displacement transmissibility is derived. The effects of QZS and the nonlinear inertia are clarified through parametric analysis and comparative discussions. The realization of QZS is beneficial to reduce the resonance frequency and broaden the isolation band. The introduce of nonlinear inertia can considerably suppress the hardening behavior of the transmissibility curve and further reduce the starting isolation frequency. And the inertia induced anti-resonance enhances the vibration attenuation effect in the low frequency band. The experimental prototype is manufactured and thoroughly tested under sweep, periodic and random excitation. The experimental results show that the MMTS-NI can effectively isolate the frequency components above 4 Hz. And the vibration attenuation effect can be significantly enhanced in the range of 4–10 Hz by increasing the attached masses. The results provide a novel and significant methods of improving low frequency vibration isolation performance using nonlinear stiffness and inertia modulation.

Damping vibration in three-dimensional helically tapered rod with power-law thickness

Tapered structure with power-law thickness has been regarded as an efficient approach for passive vibration control. In this paper, a three-dimensional (3D) helically tapered structure with power-law feature is proposed to reduce the vibration in rod structure. Compared with the traditional one-dimensional tapered rod, this novel helix type can compress the length of tapered region by the coiling configuration and transform the flexural wave modes into various complex modes. Drawing on its folded characteristic, the helix structure can generate highly efficient space utilization and achieve a superior vibration attenuation effect in the low frequency band. Numerical investigations on the dynamics and reflection coefficient analyses of different rod types are conducted and the reduction mechanism of 3D helically tapered rod is revealed. It is found that the larger helical radius can contribute to the reduction in low-frequency vibration, but it deteriorates the vibration performance in broadband. To overcome this “sudden collapse” phenomenon in the damping performance caused by the low stiffness, the novel step helically tapered rod is presented. According to the introduced multimodal and multidirectional mode-coupling effects, this step 3D helix structure not only makes up for the shortcoming of vibration control in low frequency range, but also further improves the innate advantage of reduction effect in the high frequency band. Meanwhile, parametric studies of step 3D helically tapered rod are performed and the effect of different constituent materials is discussed to expand the utility. To validate these analyses, experimental tests are also conducted. The results demonstrate its remarkable vibration reduction in broadband frequency.

Towards Broadband High-Frequency Vibration Attenuation Using Notched Cross-Shaped Metamaterial

This paper reports a plate-type metamaterial designed by arranging unit cells with variable notched cross-sections in a periodical array for broadband high-frequency vibration attenuation in the range of 20 kHz~100 kHz. The dispersion relation and displacement field of the unit cell were calculated by simulation analysis, and the causes of the bandgap were analyzed. By studying the influence of critical structural parameters on the energy band structure, the corresponding structural parameters of a relatively wide bandgap were obtained. Finally, the plate-type metamaterial was designed by arranging unit cells with variable notched cross-sections in the periodical array, and the simulation results show that the vibration attenuation amplitude of the metamaterial can reach 99% in the frequency range of 20 kHz~100 kHz. After fabricating the designed plate-type metamaterial by 3D printing techniques, the characterization of plate-type metamaterial was investigated and the experiment results indicated that an 80% amplitude attenuation can be obtained for the suppression of vibration with the frequency of 20 kHz~100 kHz. The experimental results demonstrate that the periodic arrangement of multi-size cell structures can effectively widen the bandgap and have a vibration attenuation effect in the bandgap range, and the proposed plate-type metamaterial is promising for the vibration attenuation of highly precise equipment.

Vibration attenuation of rotating disks via acoustic black holes

Acoustic black holes (ABHs) have been found to exhibit desirable damping characteristics for vibration attenuation of thin-walled structures. However, up until now, no research has been carried out on evaluating ABH effects on vibrations of rotating structures, of which vibration attenuation issues are usually critical. To fill this knowledge gap, this work proposes a unified modeling approach for rotating thin disks with ABH indentations. The equations of motion of the system are formulated using the Rayleigh-Ritz method together with the Kirchhoff plate theory. The modified Fourier series are employed to form the displacement admissible functions. Finite element analysis is conducted to validate the proposed model. Damping performance of the ABH disk is then investigated under both non-rotating and rotating states. Finally, experiments are carried out to study the vibration attenuation effect of the ABH on non-rotating and rotating disks. The natural frequencies of the ABH disk with viscoelactic layers at different rotating speeds obtained from experiments and numerical calculations are compared to further verify the modeling approach. With all the simulation and experimental results, it is found that ABHs are capable of realizing vibration reduction for rotating structures, where the effectiveness is influenced by rotating speeds and excitation types.

Research on dynamic vibration absorber with negative stiffness for controlling longitudinal vibration of propulsion shafting system

This paper presents a dynamic vibration absorber with negative stiffness (DVANS) in controlling the first longitudinal mode of the propulsion shafting system. The dynamic modeling of the propulsion shafting system with DVANS considering longitudinal vibration is developed and theoretically studied. The vibration attenuation effect of the DVANS is compared with the traditional DVA, and the influence of the nonlinear characteristics of the negative stiffness element, as well as the flexible foundation on the vibration transmission is studied. A prototype of the DVANS embedded in thrust bearing is designed. The designed DVANS is composed of an iron block, an elastic rubber, a disc spring and an adjusting screw. The vibration transmission experiment of the propulsion shafting system is performed in order to validate the vibration absorption capacity of the DVANS. Compared with the traditional DVA, the DVANS used in this paper is more efficient in suppressing the longitudinal vibration transmission. The experimental results show that the designed DVANS embedded in the thrust bearing has an advanced vibration attenuation performance in a broad frequency range under different operating conditions, demonstrating the enormous potential in controlling the longitudinal vibration of the propulsion shafting system.

Vibration Characteristics Analysis of O-Shaped Damping Ring to Balance Damping Gear Transmission System for Three-Cylinder Engine

Balance shafts are often used to improve the engine vibration characteristics of three-cylinder engines. The balance damping gear with a damping ring is an important part connecting the crankshaft and the balance shaft transmission. The stiffness characteristics of the damping ring and the unbalance of the gear have an important influence on its vibration suppression performance, but the coupled influence of the stiffness characteristics of the damping ring and the unbalanced characteristics of the vibration damping gear is unknown. In this paper, a multi-body dynamic bending–torsional coupling model of the transmission system of a three-cylinder engine with a balance damping gear is constructed considering the equivalent stiffness of the balance shaft support. Based on the fourth-order Runge–Kutta method, the influence laws of different rotational speeds, load torques, gear unbalance, radial stiffness and torsional stiffness of the damping ring on the vibration characteristics of the transmission system are obtained. The results show that the vibration amplitude increases linearly with the increase in the rotational speed and the amount of unbalance. As the load torque increases, the noise radiation of the system increases. The change in the equivalent torsional stiffness of the damping ring has little effect on the radial vibration suppression effect of the gear. As the equivalent radial stiffness of the damping ring increases, the vibration suppression rate decreases linearly. Combined with the calculation formula of damping ring stiffness, when the inner and outer diameters of the damping ring are relatively large, the vibration suppression performance decreases sharply with the increase in the thickness of the damping ring. Therefore, in order to achieve a better vibration attenuation effect, the inner to outer diameter ratio of the damping ring should be given priority in the design of the damping gear. Thus, the thickness of the design can meet the requirements of the vibration attenuation performance and a vibration attenuation of more than 90% of the radial vibration can be achieved. The model of the damping ring size and the vibration suppression effect established based on the method presented in this paper can be used to guide the design of balance damping gears.