Spring Damper Research Articles

Solution of Damped Spring Vibration Model of Motor Vehicles with MATLAB Application

This study analyzes the application of the Runge Kutte 4 method, Runge Kute Gill, and Milne Method in two- wheeled motor vehicles. The study results show that: (1) Performance of the Milne Method: The Milne method is effective for solving damped oscillatory systems with small time steps and provides good results, although with a slight increase in error compared to the Runge Kutte 4 method. (2) Advantages The Milne method shows more efficiency in the number of function evaluations per step. It is suitable for applications requiring more significant time steps without requiring accuracy as high as the Runge Kutte 4 method. (3) Disadvantages The Milne method has lower accuracy than the Runge Kutte 4 method, especially for small time steps and requires an initial step using another method, adding to the complexity of the Implementation.

Rope on Rope: Reducing Residual Vibrations in Rope-Based Anchoring System and Rope-Driven Façade Operation Robot

Maintenance of the exteriors of buildings with convex façades, such as skyscrapers, is in high demand in urban centers. However, manual maintenance is inherently dangerous due to the possibility of accidental falls. Therefore, research has been conducted on cleaning robots as a replacement for human workers, e.g., the dual ascension robot (DAR), which is an underactuated rope-driven robot, and the rope-riding mobile anchor (RMA), which is a rope-riding robot. These robots are equipped with a convex-façade-cleaning system. The DAR and RMA are connected to each other by a rope that enables vibration transmission between them. It also increases the instability of the residual vibration that occurs during the operation of the DAR. This study focused on reducing the residual vibrations of a DAR to improve the stability of the overall system. Because it is a rope-on-rope (ROR) system, we assumed it to be a simplified serial spring–damper system and analyzed its kinematics and dynamics. An input-shaping technique was applied to control the residual vibrations in the DAR. We also applied a disturbance observer to mitigate factors contributing to the system uncertainty, such as rope deformation, slip, and external forces. We experimentally validated the system and assessed the effectiveness of the control method, which consisted of the input shaper and disturbance observer. Consequently, the residual vibrations were reduced.

Observation and Analysis of Metallic Interface Bridging and Self-Healing Under Electromagnetic Shocking Treatment

While self-healing of metals and alloys facilitated by electromagnetic pulse (EMP) energy introduced by electropulsing has been widely reported, the in-depth mechanism is still ambiguous. Here, an approximate in-situ observation was designed to explore the effect of EMP energy induced by electropulsing on the alloy interface self-healing. Electromagnetic shocking treatment (EST) utilizing EMP energy was demonstrated to promote metallic interface bridging and self-healing. At local regions, flat surfaces turn into wavy ones, especially, while local interface bridging and self-healing are commonly observed, indicating a nonlinear surface pre-melting. Based on the assumed mass–spring–damping system of the pre-melted interfaces, the mechanisms of local interface bridging and self-healing under the EST are explored. This work provides new understanding about the interface self-healing mechanism by electropulsing, as well as new insights about the effect of pulse energy (such as EMP) on metallic interface complexion.

A study on the effect of inerters in the motor elastic suspension on the stability of bogies in high-speed trains

Inerters are widely used in structural vibration systems, but there is little research on their use in the elastic-suspension of motors in high-speed train bogies. The type of the motor suspension significantly influences its vibration characteristics. To fill this gap, this paper proposes the use of the frequency-variable characteristics of the inertia spring damping (ISD) structure. The motor elastic-suspension bogie dynamic model with the inerter was established, and the effect of the motor suspension parameters on the stability of the bogie system was studied. Finally, the inertia-suspension parameters were optimized by the Non-dominated Sorting Genetic Algorithm-Ⅱ (NSGA-Ⅱ) multi-objective optimization algorithm. The results showed that the ISD structure has frequency-varying characteristics, and the maximum equivalent stiffness and damping exist in the low frequency range (approximately 10 Hz). As the equivalent conicity increases, the optimal lateral frequency and damping ratio of the motor increase, which makes the inerter suspension bogie to meet this characteristic. The optimized motor suspension parameters showed that the linear critical speeds of the bogie with inerter suspension are improved, and the stability of the bogie is higher within the equivalent conicity of 0.1-0.4. This study can provide a reference for the stability design of the bogie structure in future.

Optimization design and vibration reduction performance analysis of vehicle suspension structure

To improve the vibration reduction performance of vehicle suspension, two kinds of suspension structures (Inerter spring damper, ISD) consisting of inerter, spring and damper are proposed based on electromechanical similarity theory. A single-wheel vehicle system model with I1 and I2 ISD suspension structures is established. Through numerical simulation of single-wheel vehicle system model, the vibration responses of ISD suspension structures I1 and I2 and traditional suspension structures in single-wheel vehicle system are analyzed, and the influence of inertia-capacitance coupling between main and auxiliary parts in ISD suspension structure on vibration reduction performance is discussed. The results show that compared with the traditional suspension structure, the vibration reduction performance of the I1 and I2 ISD suspension structures are improved to a great extent, and the I1 ISD suspension structure is better than the I2 ISD suspension structure. To comprehensively consider the vibration reduction performance of the ISD suspension structure, a compromise optimization method is adopted to determine the inertia-capacitance coupling value.

Robust fuzzy output feedback control for a magnetorheological semi-active air suspension system with time-delay and actuator saturation

Magnetorheological fluid (MRF) dampers have been utilized in semi-active air suspension (SAAS) due to their attractive advantages. This paper investigates a novel robust fuzzy output feedback controller for semi-active air suspension with MRF damper (SAAS-MRFD), considering time delay and actuator saturation. An aero-thermodynamics theory is first utilized to describe the nonlinear air spring. The damping force of the MRF damper is represented by a hyperbolic tangent model. The interval type-2 (IT-2) Takagi–Sugeno (T-S) fuzzy method is second employed to capture those nonlinearities of the air spring and MRF damper. Considering the difficulty to measure all states, a novel dynamic output feedback (DOF) controller is developed by an appropriate Lyapunov–Krasovskii function and the reciprocally convex technique with consideration of time delay, actuator saturation, and output constraints. The effectiveness of the proposed controller is validated by both simulation and a quarter-car test rig (QCTR). The results indicate that the proposed controller has better performance in vibration reduction than the recent similar controllers in the literature.

Determination of the parameters of the damper device of the milling furrow opener of the sod seeder

The working process of soil cultivation by disc cutters of furrow openers of sod seeders was analyzed and the main disadvantages were identified: unevenness of the torque transmitted by them due to impact loads and high-energy consumption. An original design of a damper-safety device is proposed, allowing to eliminate them. A 3D model of the output shaft of a furrow opener with two disk cutters equipped with L-shaped knives, each of which is equipped with a damper device, is developed. Computer modeling of the milling process was performed in the ANSYS Rigid Dynamics program, during which the parameters and operating modes of the damper device were determined, in which its operation is most effective. To reduce the magnitude and unevenness of the torque, it is necessary that the sequence of the disk cutter knife entering the soil is performed at the moment when the force on the knife of the second cutter, finishing the cutting process, is 5 ... 15% of the maximum. Damping devices reduce the maximum torque consumed by cutters relative to the load torque by 49.4% with an amplitude of oscillations of the spring compression value of 1.2...1.6 mm in the case of a damper spring stiffness of 50...70 kN/m, a rotation frequency of 400...500 min-1 and a number of knives of 2...3 pcs.

Evaluation of Dynamic Compaction Load Conversion Methods and Vibration Reduction Treatments

This study aims to evaluate the accuracy of different dynamic compaction (DC) load equivalent conversion methods in DC vibration calculations. It also investigates the effect of vibration isolation treatments on the vibration reduction performance of loess foundations, with the goal of optimizing vibration control during DC construction. Five classical methods were used to convert the DC loads into time-dependent surface loads, which were subsequently fed into Plaxis’s dynamic multiplier table for the numerical implementation of DC tests. By comparing the numerical simulation results with in situ monitoring data from a loess site, the accuracy of the five DC load equivalent conversion methods was evaluated. The momentum theorem method was identified as the most precise for both vibration velocity and settlement. Subsequently, the momentum theorem method was utilized to investigate the influence of depth and distance of vibration isolation trench, as well as the properties of vibration isolation materials on vibration reduction effect. It is indicated that the optimal depth for the vibration isolation trench of the loess site is 2 m, beyond which the improvement in vibration reduction effects is not notable. The excavation distance of the vibration isolation trench should be set as close as possible to the boundary of the construction site to achieve the best vibration reduction effect. As for the properties of vibration isolation materials, it is shown that the unit weight and damping ratio of the filling material have a significant effect on the vibration reduction effect, while the influence of the shear strength of the filling material is negligible. Besides the vibrating reduction influence of filling materials, utilizing spring dampers has a better vibration reduction effect. Increasing the stiffness of the spring dampers and reducing their spacing can significantly enhance the vibration reduction effect. In practical engineering applications, it is essential to consider both the effects and economic costs to select the optimal vibration reduction treatment and its parameters. This study provides a scientific basis for vibration control during DC construction, contributing to ensuring construction safety and efficiency while minimizing the impact on the surrounding environment.

Development of a prototype of a torsional vibration spring damper using reverse engineering technology

The article discusses the issues of developing a prototype of a spring damper for torsional vibrations using reverse engineering technology (reverse engineering). A spring damper with spring plates of the Austrian company Geislinger model D90/37 was chosen as the object of research. This model of dampers is widely used as part of modern marine diesel engines MAK 8M25. The issue of creating a domestic model of a spring damper is caused by a number of problems, including the complete cessation of supplies of this type of device to Russia. Spring dampers are responsible elements of machine-propulsion systems, on the efficiency of which depends, among other things, the safety of navigation of ships. On the basis of the Federal State Educational Institution of Higher Education "Astrakhan State Technical University", using a Range Vision Spectrum 3D-scanner approved by the Federal Agency for Technical Regulation and Metrology, CAT models of the components of the spring damper were obtained: an intermediate insert and a bronze spring plate. The principle of operation of the scanner is based on structured illumination and optical triangulation. Using data from the manual geometry of a real damper, as well as using the COMPASS software product, a drawing of a general view of a model spring damper of torsional vibrations was developed. Modeling (physically and using modern software products) of torsional vibration spring dampers will allow you to accumulate theoretical knowledge and practical groundwork, which will serve as the first step to strengthen Russia's technological sovereignty in the field of their design, manufacture and repair. The result of the great work done by the scientific school dealing with the dynamics of the machine-propulsion complex, under the leadership of the Honored Worker of the fisheries of the Russian Federation, Doctor of Engineering Sciences, Professor M.N. Pokusaev, will be the first domestic prototype of a spring damper of torsional vibrations. В статье рассматриваются вопросы по разработке прототипа пружинного демпфера крутильных колебаний с применением технологии реверс-инжиниринга (обратного проектирования). В качестве объекта исследования был выбран пружинный демпфер с рессорными пластинами австрийской фирмы Geislinger модели D90/37. Данная модель демпферов получила широкое распространение в составе современных судовых дизелей МАК 8М25. Вопрос создания отечественной модели пружинного демпфера обусловлен рядом проблем, в том числе полным прекращением поставок в Россию подобного типа устройств. Пружинные демпферы являются ответственными элементами машинно-движительных комплексов, от эффективности работы которых зависит в том числе безопасность мореплавания судов. На базе ФГБОУ ВО «АГТУ» при помощи 3D-сканера Range Vision Spectrum, одобренного Федеральным агентством по техническому регулированию и метрологии, были получены CAT-модели составных элементов пружинного демпфера: промежуточная вставка и бронзовая межпружинная пластина. Принцип работы сканера основан на структурированном подсвете и оптической триангуляции. При помощи данных ручной геометрии реального демпфера, а также использования программного продукта КОМПАС был разработан чертеж общего вида модельного пружинного демпфера крутильных колебаний. Моделирование (физического и с применением современных программных продуктов) пружинных демпферов крутильных колебаний позволит накопить теоретические знания и практический задел, что послужит первой ступенью для укрепления технологического суверенитета России в области их проектирования, изготовления и ремонта. Итогом большой проделанной работы научной школы, занимающейся вопросами динамики машинно-движительного комплекса, под руководством заслуженного работника рыбного хозяйства РФ, д.т.н., профессора Покусаева М.Н. будет являться первый отечественный прототип пружинного демпфера крутильных колебаний.

Application of rigid flexible coupling technology in vibration response analysis of washing machine

The dynamic response of the box and suspension system is one of the most important factors affecting the vibration and noise of the washing machine. To ensure the accuracy of dynamic analysis, a rigid-flexible coupling model was put forward and established, enabling the acquisition of the load responses of flexible box and the dynamic characteristics of suspension system. The free vibrations of the washing machine box were analyzed, and the effective natural frequencies and modes were obtained. The modal neutral file was imported into ADAMS, where the rigid elements were replaced and spring and damping constraints were set. The dynamic responses of the center of mass displacement and load of the suspension system under different spring stiffness and damping system conditions were analyzed, which can provide important basis for optimizing the vibration isolation performance. The results show that the first-order natural frequency of the box exceeds the maximum excitation frequency, and the maximum stress is mainly distributed in the joints of the sheet metal.

In situ torque transmissibility frequency response function measurements of a centrifugal pendulum vibration absorber in a torque converter clutch damper

This investigation details torsional testing and characterization of torque converter clutch (TCC) damper variants containing centrifugal pendulum absorbers (CPAs) utilized in light duty production vehicles. Data collected on a torque converter dynamometer test stand was used to correlate a nonlinear model of the combination TCC damper and CPA when locked with zero relative slip speed. The range of test torques and speeds are related to when driveline, chassis and body noise and vibration concerns are high and the damper-CPA combination are required to provide maximum isolation. To facilitate model correlation efforts, modified configurations of the same torque converter design were procured, enabling separation of damping effects from the CPA and damper springs. Under load, the locked TCC was torsionally excited to acquire torque transmissibility frequency response functions (TTFRFs). The anti-resonance of the CPA was measured, and the viscous damping coefficient estimated. A manual tuning and modified half-power bandwidth method were used to estimate the equivalent viscous damping of the CPA. Additional test cases included torsional excitation amplitude and oil temperature to ascertain differences in CPA response and tuning order. The objective of the investigation is to demonstrate the influence of damper spring and CPA integration, extraction of CPA damping from actual hardware and the utility of including representative damping in model-based design of future damper-CPA assemblies.

Система подачи рабочей жидкости в модельный пружинный демпфер крутильных колебаний

The development of a system for supplying working fluid (engine oil) to ensure the similarity of operating conditions of a model of a spring damper for torsional vibrations of a marine diesel engine during experiments at the laboratory stand of the Marine Technology Service testing center of the Astrakhan State Technical University is considered. Currently, spring (mechanical) torsional vibration dampers of marine diesel engines are produced only by foreign companies. A lot of scientific work is required for their design, manufacture and operation, including physical modeling of the design and operating conditions of laboratory versions of dampers. The application of the physical modeling method makes it possible to reduce the cost of testing real spring dampers of torsional vibrations of marine diesel engines, determine the main dependencies of damping parameters on various operating conditions, develop basic criteria for non-selective diagnostics to assess its technical condition and predict the development of emergency situations. The modernization of the laboratory stand is necessary for the operation of model spring dampers with a developed system for supplying working fluid. The spread of spring dampers is justified by the design features of such devices, which allows the use of both elastic and hydraulic damping. For the development of the working fluid supply system, calculations were made of the stiffness and thermal power of the model spring damper, taking into account the design of the laboratory stand.

Dynamic Modeling of Suspension with Air Spring

The present work aims to model a ¼ vehicle semi-active suspension, using a combination of air spring and magneto-rheological damper. The modeling of the magneto-rheological damper will be based on the Wang model, which will be calibrated through experimental tests. The air spring model will be employed to compare performance between discrete mechanical models and the thermodynamic model. Various semi-active control strategies, such as bang-bang type skyhook/groundhook and PID, will be explored for comparison with existing selective passive systems on the market. The study of the air suspension with magneto-rheological damper will be evaluated from the perspective of comfort and drivability, following standardized parameters (ISO 2631:1978).

Stability and bifurcation analysis of a 2DOF dynamical system with piezoelectric device and feedback control

This study aims to demonstrate the behaviors of a two degree-of-freedom (DOF) dynamical system consisting of attached mass to a nonlinear damped harmonic spring pendulum with a piezoelectric device. Such a system is influenced by a parametric excitation force on the direction of the spring’s elongation and an operating moment at the supported point. A negative-velocity-feedback (NVF) controller is inserted into the main system to reduce the undesired vibrations that affect the system’s efficiency, especially at the resonance state. The equations of motion (EOM) are derived by using Lagrangian equations. Through the use of the multiple-scales-strategy (MSS), approximate solutions (AS) are investigated up to the third order. The accuracy of the AS is verified by comparing them to the obtained numerical solutions (NS) through the fourth-order Runge-Kutta Method (RK-4). The study delves into resonance cases and solvability conditions to provide the modulation equations (ME). Graphical representations showing the time histories of the obtained solutions and frequency responses are presented utilizing Wolfram Mathematica 13.2 in addition to MATLAB software. Additionally, discusses the bifurcation diagrams, Poincaré maps, and Lyapunov exponent spectrums to show the various behavior patterns of the system. To convert vibrating motion into electrical power, a piezoelectric sensor is connected to the dynamical model, which is just one of the energy harvesting (EH) technologies with extensive applications in the commercial, industrial, aerospace, automotive, and medical industries. Moreover, the time histories of the obtained solutions with and without control are analyzed graphically. Finally, resonance curves are used to discuss stability analysis and steady-state solutions.

Soft material characterization through surface wave elastography using a laser Doppler vibrometer

Soft material characterization through surface wave elastography using a laser Doppler vibrometer

Dynamic characteristics analysis of shock absorber based on fluid simulation

Pneumatic spring dampers are extensively utilized within hydraulic systems, and the flow characteristics of the internal oil play a crucial role in determining noise and vibration levels. To validate the mechanical structure's reliability, the shock absorber was simplified and the fluid domain was extracted using a CFD method. The velocity field and pressure field under different conditions were then simulated and analyzed. A finite element model of the flow field was established, and its accuracy was verified by comparing simulation results of gas side pressure with experimental results. According to the working principle of the oil-gas spring, dynamic active surfaces in contact with the main piston and dynamic driven surfaces in contact with the floating piston were defined, determining moving conditions for dynamic grids. The results indicate that as the diameter of flow channels increases, there is a decrease in average pressure drop within the oil chamber (i.e., pressure loss within the flow field). Additionally, as bend angle increases, average pressure drop decreases. However, optimization effects become less significant beyond a certain bend angle.

Exploring submergence impact on flow-induced motion energy-harvesting with circular-triangular prisms

Recent advancements in energy-harvesting have utilized Flow-Induced Motion (FIM) as a renewable source, diverging from past efforts aimed at minimizing FIM's adverse effects. This study introduces kinetic energy converters using alternating lift technology (ALT), employing a prism with a Circular-Triangular (Cir-Tria) shape, coupled with a spring and damper, to generate energy. Utilizing computational fluid dynamics in OpenFOAM for Reynolds numbers between 2 × 103 and 13 × 103 and varying submergence depth ratio from 0.98 to 5.91, this research employs a moving computational grid, two-dimensional incompressible Navier–Stokes equations, the k-omega Shear Stress Transport (SST) turbulence model, the Volume of Fluid, VOF, two-phase model, and the cylinder mass–spring–damper equation. Findings show that approaching the flow surface negatively impacts the FIM response due to the interaction of vortices from the flow surface and the prism’s upper shear layer. This interaction weakens and neutralizes the upper vortices, altering the flow structure around the prism and the governing FIM phenomena. Proximity to the free surface significantly affects FIM responses, with a notable decrease in vibration amplitude and energy conversion as the submergence depth ratio increases from 0.98 to 5.91. Maximum system efficiency of 1.4% is observed in the VIV initial branch at infinite submergence (single-phase flow). Beyond a submergence depth ratio of 5.91, FIM amplitude and energy conversion flatten, indicating negligible free surface effects.

Design of Integrated Dual Spiral Spring and Rotary Hydraulic Damper System for Torsional Vibration Damping in Pesticide Sprayer Gearbox

Design of Integrated Dual Spiral Spring and Rotary Hydraulic Damper System for Torsional Vibration Damping in Pesticide Sprayer Gearbox

Demonstrating wave and vibrational behavior in spatiotemporally modulated systems

Elastic materials with time and space varying properties are interesting candidates to control bulk and guided waves in unprecedented ways which include nonreciprocal transmission, unidirectional mode conversion, mode coupling, and frequency conversion. Previous work on elastic waves in spatiotemporally modulated (STM) media have focused on nonreciprocal vibrations of finite domains with modulated stiffness. Less attention has been given to the modulation of impedance boundary conditions of finite structures or at interfaces between domains. This work investigates elastic wave behavior at boundaries with modulated impedances. The boundary impedance is represented using a lumped parameter mass spring damper system with a spring having a temporally modulated stiffness. The effective input impedance is modeled using direct numerical simulation and a semi-analytical Fourier series expansion model. The models are compared to experiments on a base-excited cantilevered Euler-Bernoulli beam with modulated effective stiffness via piezoelectric patches with temporally varying electric shunting circuits. [Work supported by the ARL:UT Chester M. McKinney Graduate Fellowship in Acoustics and by the Office of Naval Research under Award N00014-23-1-2660.]

Trajectory-based breakup modelling for dense bubbly flows

A new model to predict the breakup of gaseous bubbles in a continuous liquid phase is developed. In the model each bubble is modelled as a spring–damper system, namely a Kelvin–Voigt element, while the outer force is derived by a Lagrangian analysis determining the largest stretching rate of the flow field below. The developed model is based on physical principles and no further arbitrary parameters have to be adjusted. Each bubble is observed on its way through the bubbly flow individually, taking into account its history along its respective path. With the implemented model numerical simulations in a wide range of scales are conducted, ranging from the laboratory scale of a vessel of 3L to the large industrial scale of 15m3. The simplicity of the model allows for a good cost to benefit ratio. In the present work, the achieved results are compared to experimental data obtained from optical measurements in a replica of a 200L aerated stirred tank reactor for various stirrer frequencies.