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Due to their small size and light mass, small precision cylindrical rollers present challenges in dynamic unbalance detection, including difficulties in measurement and the risk of surface damage. This paper proposes a non-destructive detection device for assessing the dynamic unbalance of small precision cylindrical rollers. The device utilizes an air flotation support method combined with resonance amplification to indirectly measure the dynamic unbalance. A dynamic model of the air flotation tooling-cylindrical roller vibration system was developed to explore the relationship between the vibration parameters of the air flotation tooling and the dynamic unbalance of the cylindrical roller. Modal analysis and harmonic response analysis were performed, revealing that the amplitude of the vibration system at resonance could be detected using the sensor. Additionally, modal testing was conducted to determine the natural frequency of the system. A non-destructive detection platform was constructed for testing the dynamic unbalance of cylindrical rollers. Microscopic observation of the roller surface before and after testing confirmed that the device successfully performs non-destructive detection of dynamic unbalance. [ABSTRACT FROM AUTHOR]

The two-mass nonlinear vocal cord vibration system (VCVS) serves as a mechanical representation of the fundamental vocalization process. Traditional models of the VCVS, which are based on integer-order dynamics, often overlook the impact of memory effects. To address this limitation and enhance the accuracy of simulations, this study incorporates the memory effects of vocal cord vibrations by integrating the Grunwald-Letnikov fractional derivative into the two-mass nonlinear VCVS framework. Initially, a highprecision computational scheme is formulated for the two-mass nonlinear fractional-order VCVS. Subsequently, the model undergoes a comprehensive series of numerical simulations to investigate its dynamic characteristics. The findings reveal that the dynamics of the fractional-order VCVS exhibit a significantly higher complexity compared to the conventional integer-order models, with the emergence of novel chaotic behaviors that were previously unobserved. [ABSTRACT FROM AUTHOR]

This paper focus on synchronization of four eccentric rotors (ERs) with parallel and coplanar rotational axis in a single mass vibration system, distinct from planar systems. Utilizing the average method of small parameters, the coupling motion relation are established by introducing phase differences of four ERs. The synchronous condition is determined by estimating the differences in loading torque of four ERs. The coupling dynamic characteristics are discussed numerically from coupling torque and synchronous ability. Two synchronous motion states are identified theoretically and experimentally. The results indicate that four ERs approach to in-phase when the vibration system operates in the frequency region before resonance, causing the body to move in a straight line. Conversely, when four ERs approaches to anti-phase in frequency region after resonance, the mass center of the vibration system remains nearly stationary. These conclusions play a guiding role in the design of vibratory machinery. [ABSTRACT FROM AUTHOR]

The two-mass nonlinear vocal cord vibration system (VCVS) serves as a mechanical representation of the fundamental vocalization process. Traditional models of the VCVS, which are based on integer-order dynamics, often overlook the impact of memory effects. To address this limitation and enhance the accuracy of simulations, this study incorporates the memory effects of vocal cord vibrations by integrating the Grunwald–Letnikov fractional derivative into the two-mass nonlinear VCVS framework. Initially, a high-precision computational scheme is formulated for the two-mass nonlinear fractional-order VCVS. Subsequently, the model undergoes a comprehensive series of numerical simulations to investigate its dynamic characteristics. The findings reveal that the dynamics of the fractional-order VCVS exhibit a significantly higher complexity compared to the conventional integer-order models, with the emergence of novel chaotic behaviors that were previously unobserved.

Abstract To enhance the vibration system characteristic distortion and pressure loss, we propose a novel rotary valve control vibration system. The paper presents the designed structural composition and generation mechanism of the rotary valve control vibration system. It also derives the mathematical model for the rotary valve distribution process and the overall system. The flow field inside the rotary valve is dynamically simulated using the multiple reference frame model, allowing for the determination of the change rule of the rotary valve’s output characteristics. An AMESim model was developed to analyze the vibration characteristics of the rotary valve control system. The effects of parameters such as inlet pressure, motor speed, and oil supply pump displacement were investigated. A rotary valve control vibration system experimental bench was constructed to experimentally verify the output characteristics of the rotary valve and the vibration characteristics of the system. The results indicate that the characteristic curve of the designed vibration system closely resembles a sinusoidal wave. Additionally, the rotary valve exhibits low pressure loss, making it more suitable for vibration stress relief applications. By appropriately increasing the inlet pressure and decreasing the motor speed, the vibration characteristics of the system can be improved.

To enhance the vibration system characteristic distortion and pressure loss, we propose a novel rotary valve control vibration system. The paper presents the designed structural composition and generation mechanism of the rotary valve control vibration system. It also derives the mathematical model for the rotary valve distribution process and the overall system. The flow field inside the rotary valve is dynamically simulated using the multiple reference frame model, allowing for the determination of the change rule of the rotary valve’s output characteristics. An AMESim model was developed to analyze the vibration characteristics of the rotary valve control system. The effects of parameters such as inlet pressure, motor speed, and oil supply pump displacement were investigated. A rotary valve control vibration system experimental bench was constructed to experimentally verify the output characteristics of the rotary valve and the vibration characteristics of the system. The results indicate that the characteristic curve of the designed vibration system closely resembles a sinusoidal wave. Additionally, the rotary valve exhibits low pressure loss, making it more suitable for vibration stress relief applications. By appropriately increasing the inlet pressure and decreasing the motor speed, the vibration characteristics of the system can be improved. [ABSTRACT FROM AUTHOR]

Shaker is the key facility of the vibration test system. The wide frequency band of the vibration signal poses a challenge on the shaker controller design, therefore a hardware in loop (HIL) test is desired to verify the controller performance before it is deployed in the real device. The test accuracy depends on the accurate model of the shaker simulated in the HIL simulator, which must be discretized as required by the HIL solver. In this paper, we are going to show that a high resonance peak of the shaker above 1500Hz, which is associated with both the electrical modes and the mechanical modes, can be greatly affected by the step of the discretized model. To overcome the impact of discretization effects on controller validation, this paper utilizes an equivalent model of the shaker derived from the electro-mechanical analogy method, which allows the shaker to be accurately modeled and discretized at a $1\mu $ s step in the electrical domain of the HIL402. This provides a solution for the HIL validation of mechatronic systems with high-frequency characteristics, improving the difficulties in modeling such systems in HIL. The effectiveness of the proposed method is verified in both frequency domain test and time domain test under the Typhoon 402 HIL environment.

Due to their small size and light mass, small precision cylindrical rollers present challenges in dynamic unbalance detection, including difficulties in measurement and the risk of surface damage. This paper proposes a non-destructive detection device for assessing the dynamic unbalance of small precision cylindrical rollers. The device utilizes an air flotation support method combined with resonance amplification to indirectly measure the dynamic unbalance. A dynamic model of the air flotation tooling-cylindrical roller vibration system was developed to explore the relationship between the vibration parameters of the air flotation tooling and the dynamic unbalance of the cylindrical roller. Modal analysis and harmonic response analysis were performed, revealing that the amplitude of the vibration system at resonance could be detected using the sensor. Additionally, modal testing was conducted to determine the natural frequency of the system. A non-destructive detection platform was constructed for testing the dynamic unbalance of cylindrical rollers. Microscopic observation of the roller surface before and after testing confirmed that the device successfully performs non-destructive detection of dynamic unbalance.

The four-axis variable trajectory equal-thickness screen (FAVTETS) achieves equal-thickness screening by appropriate excitation force generated by four eccentric rotors in synchronized motion. The forced synchronization exciter is characterized by an unsatisfactory synchronization effect due to the wear of transmission parts. Hence, in this paper, the four-axis controlled synchronization of FAVTETS is investigated, and an intelligent control system is proposed. Firstly, research is conducted on the variable trajectory characteristics of FAVTETS. Next, the sliding mode, fuzzy, and PID controllers are designed and compared to obtain an ideal control effect. Moreover, the influence of torsional stiffness of flexible coupling on control accuracy is considered. The results show that the sliding mode controller has a good control effect. Based on the aforementioned, the simulation model of a four-axis controlled synchronization structure is established via MATLAB/Simulink. Finally, Labview is employed to design the four-axis controlled synchronization software system. Then, the physical experiment is carried out. The four-axis controlled synchronization and vibration trajectory measurement results verify the effectiveness and robustness of the intelligent control system. [ABSTRACT FROM AUTHOR]

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This study investigates the frequency capture characteristic of four unbalanced rotors in multi-frequency ranges. First, using the average method, the synchronous condition of four unbalanced rotors in a vibration system is derived. Then, the stability condition of the vibration system is deduced, which meets the Routh-Hurwitz criterion. On the basis of the theoretical analysis, the phase difference in steady states and the resultant force on the rigid body at different excitation frequency regions are discussed numerically. Five sets of experiments are done to investigate synchronization and the Sommerfeld effect. The results prove that the vibration system has three motion states according to the excitation frequency in different frequency regions. Two stable states appear in the near-resonance region of the system. This study concludes that the synchronization of unbalanced rotors formed before and after the natural frequency is crucial for the occurrence of the Sommerfeld effect. This work can provide theoretical and experimental reference for the design of new vibration equipment in engineering. [ABSTRACT FROM AUTHOR]

In this paper, to obtain ideal dynamic behavior of vibration screen, control synchronization of three eccentric rotors (ERs) driven by motors in space vibration system is investigated by employing the adaptive fuzzy sliding mode control (AFSMC) algorithm. First, the dynamic model of the vibration system is established, and the motion equation of the electromechanical coupling system is derived via Lagrange equation. Then, the synchronization controllers of three ERs are systematically designed with the combination of AFSMC algorithm and master–slave control (MSC) structure, and the stability of the control system is verified by Lyapunov theory. Additionally, in comparison with the conventional sliding mode control (SMC) algorithm, the superiority and feasibility of the proposed AFSMC strategy are confirmed through numerical simulation in MATLAB/Simulink. Moreover, the robustness of the control system is demonstrated in the simulation via changing the motor velocities and structure parameters. The research result shows that the proposed adaptive strategy can effectively control the ERs to implement the desired in-phase synchronization motion, and the control method possesses commendable efficacy in reducing chattering, enhancing control accuracy, eliminating overshoot, and resisting parameter perturbation. [ABSTRACT FROM AUTHOR]

Aiming at the influence of gear body and unbalance on noise, a reducer was taken as the research object, the relevant structural analysis and calculation were carried out, and noise test of different scheme were carried out for comparison. Firstly, modal analysis was carried out by finite element method, and two kinds of gear body of first stage driven gear was determined. Then, the noise performance was analyzed by MASTA software, smaller peak to peak of transmission error and smaller dynamic meshing force was obtained, then the optimized gear body was determined. The dynamic model of rotor shaft-gear was established by considering the difference of unbalance of special-shaped gear body. The inertia force and excitation were analyzed, and the response of different unbalance was obtained. Finally, the bench test was carried out for verify design. The results indicate that the noise of the special-shaped gear body is more than 5 dB lower than that of the traditional structure when reducer works above 8 000 r/min. When the unbalance is less than 9.29 g, the statistical result of noise test is that the P value is greater than 0.05, this indicating that the unbalance has no significant influence on the reducer’s noise within this range. [ABSTRACT FROM AUTHOR]

Structural health monitoring (SHM) systems are designed to continually monitor the health of structures (e.g., civil, aeronautic) by using the information collected through a distributed sensor network. However, performing tests on real structures, such as wind turbines, implies high logistic and operational costs. Therefore, there is a need for a vibration test system to evaluate designs at smaller scales in a laboratory setting in order to collect data and devise predictive maintenance strategies. In this work, the proposed vibration test system is based on a lab-scale wind turbine jacket foundation related primarily to an offshore environment. The test system comprises a scaled wave generator channel, a desktop application (WTtest) to control the channel simulations, and a data acquisition system (DAQ) to collect the information from the sensors connected to the structure. Various equipment such as accelerometers, electrodynamic shaker, and DAQ device are selected as per the design methodology. Regarding the mechanical part, each component of the channel is designed to be like the wave absorber, the mechanical multiplier, the piston-type wavemaker, and the wave generator channel. For this purpose, the finite element method is used in static and fatigue analysis to evaluate the stresses and deformations; this helps determine whether the system will work safely. Moreover, the vibration test system applies to other jacket structures as well, giving it greater utility and applicability in different research fields. In sum, the proposed system is compact and has three well-defined components that work synchronously to develop the experimental simulations. [ABSTRACT FROM AUTHOR]

In a vibrating screen machinery, two eccentric rotors (ERs) are actuated by swung and fixed motors. When the working efficiency of vibrating screens is the highest, the motion trajectory of the vibrating body is an ellipse. However, to implement elliptical trajectory, the ideal synchronization between the two ERs must be needed. Hence, the self-synchronous theory and synchronous control method for the vibrating screen machinery are explored. First, the mathematic model of the vibration system is deduced based on Lagrange equation; then, the synchronous condition and stability criterion are inferred from averaged small parameter method. In addition, the synchronization controllers, related to speed and phase of the ERs, are designed by with sliding mode control (SMC), and the master–slave control strategy is applied to design the control structure. Meanwhile, the stability performance of the controllers is demonstrated by Lyapunov theory and Hurwitz condition. Finally, computer simulations are implemented to validate the theoretical reliability of self-synchronization and synchronous control. The simulation results show that the system can be self-synchronized, but the ideal synchronization is difficult to achieve when the two ERs are self-synchronously rotated, which leads to non-ideal dynamic characteristics; nevertheless, the ideal synchronization can be implemented by the proposed synchronous control method. [ABSTRACT FROM AUTHOR]

In petroleum drilling engineering, self-synchronous vibration screen with single-frequency actuation is difficult to implement the scheduled synchronous behavior caused by its invariance and instability of dynamic characteristics, which usually leads to reduction of the production efficiency. Hence, to solve the problem mentioned above, a dual-frequency counter-rotating synchronization control method among three exciters is presented by combining adjacent cross-coupling control (ACCC) structure with global sliding mode control (GSMC) theory. Firstly, motion differential equation of the vibration system in each direction is derived according to mathematical model of the tri-rotor vibration machine. Secondly, considering exponential reaching law and adaptive control algorithm, the adjacent cross-coupling controller and the vector controller of each induction motor are investigated to achieve the stable zero phase difference synchronization between double-frequency rotors. Subsequently, Runge-Kutta method is introduced to establish the electromechanical coupling control model and prove validity of the control theory. Meanwhile, it is also discussed that the rotors cannot obtain an ideal self-synchronization state since velocity of high-frequency motor is not strictly equal to twice that of low-frequency motor. Finally, based on the experimental test scheme, an experimental prototype related to controlled multi-rotor synchronization vibration system is designed independently, which further verifies the validity of theory and computer simulation. Research shows that the desirable synchronous state of the vibration system can be accurately controlled via the designed control strategy, and the control system can implement diversity of the dynamical characteristics, due to the existence of strong robustness. [ABSTRACT FROM AUTHOR]

The partial eigenstructure assignment problem is to replace a small number of eigenvalues and eigenvectors of system while the remaining eigenvalues and corresponding eigenvectors are kept unchanged. The paper studies partial eigenstructure assignment problem for vibration system via acceleration–velocity feedback control. Two new orthogonality relations are established to construct a feedback control law which can solve the proposed partial eigenstructure assignment problem. The solvability condition and parametric expressions of feedback gains are derived for solving this problem. The minimum norm partial eigenstructure assignment problem is further considered by using gradient‐based optimization method. An optimization algorithm is proposed for solving the minimum norm partial eigenstructure assignment problem. Numerical examples are provided to show the effectiveness of the algorithm. [ABSTRACT FROM AUTHOR]

In this paper, the synchronous control method for multi-motor coupled with pendulum in a vibration system is introduced. The dynamic model of three eccentric rotors (ERs) driven by three motors rotating in the same direction in the system is firstly established. However, to obtain elliptical trajectory, the ideal synchronization motion (zero-phase difference) of the three ERs should be satisfied. Therefore, the synchronous control strategy for the proposed system is described. Then, the exponential reaching law sliding mode control (ERL-SMC) with adjacent cross-coupling control structure is applied to design the controllers of rotational velocity error and synchronization error. Meanwhile, the stability performance of the controllers is demonstrated by Lyapunov theory and Hurwitz condition. Furthermore, the adaptive method is applied to the ERL-SMC to improve the control accuracy of the system. Finally, computer simulation based on Matlab/Simulink is implemented to validate the effectiveness of the control system; besides, the impact of parameter perturbations in the control system are considered to verification the robustness of controllers related to the velocity and synchronization.

The existing research of vibration synchronization among multiple rotors is mainly concentrated on plane vibration system. In this paper, the synchronization mechanism of the spatial vibration system actuated with tri-motor rotating in identical direction is studied. Firstly, the dynamic model is established, and the motion differential equations are deduced via Lagrange formulation. Then, small parameter average method is applied to explore the synchronization condition; Lyapunov equation and Routh-Hurwitz criterion are introduced to analyze the synchronization stability. Finally, the influence of the system parameter on synchronization is discussed by numerical calculation, and the electromechanical coupling simulation based on Matlab/Simulink is given to confirm the reliability of the theoretical analysis. The research result indicates that the vibration synchronization is affected by the horizontal distance between two coaxial motors, the installation height and the masses of three eccentric rotors (ERs), but the influence of the horizontal distance between coaxial motor and noncoaxial motor on synchronization is small. [ABSTRACT FROM AUTHOR]

Structural health monitoring (SHM) systems are designed to continually monitor the health of structures (e.g., civil, aeronautic) by using the information collected through a distributed sensor network. However, performing tests on real structures, such as wind turbines, implies high logistic and operational costs. Therefore, there is a need for a vibration test system to evaluate designs at smaller scales in a laboratory setting in order to collect data and devise predictive maintenance strategies. In this work, the proposed vibration test system is based on a lab-scale wind turbine jacket foundation related primarily to an offshore environment. The test system comprises a scaled wave generator channel, a desktop application (WTtest) to control the channel simulations, and a data acquisition system (DAQ) to collect the information from the sensors connected to the structure. Various equipment such as accelerometers, electrodynamic shaker, and DAQ device are selected as per the design methodology. Regarding the mechanical part, each component of the channel is designed to be like the wave absorber, the mechanical multiplier, the piston-type wavemaker, and the wave generator channel. For this purpose, the finite element method is used in static and fatigue analysis to evaluate the stresses and deformations; this helps determine whether the system will work safely. Moreover, the vibration test system applies to other jacket structures as well, giving it greater utility and applicability in different research fields. In sum, the proposed system is compact and has three well-defined components that work synchronously to develop the experimental simulations.

To solve the limitation of vibration synchronization, this paper investigates the dynamics of a vibration system driven by three homodromy eccentric rotors (ERs) using control synchronization. According to the synchronous condition and the stability condition, the changes of the phase differences of the three-ERs system and the two-third ERs system are obtained. Based on the electromechanical mathematic model of the vibration system and the master-slave control strategy, the synchronous target that three ERs achieve the same phase motion is converted into velocity and phase tracking of ERs. Considering the coupling characteristic of the self-adjusting of the system in the state of vibration synchronization, the velocity and phase controllers are designed by employing discrete-time sliding mode control. An experimental system for control synchronization is designed, including hardware composition and software programming. For the feedback signal used to match control targets, a method of calculating velocity and the phase difference is proposed from engineering. Recording the rotational velocities, phase differences, and system response, three group experiments with different control schemes are achieved. According to the experimental data, the coupling characteristic of the vibration system adopting control synchronization is analyzed, which can provide the basis for designing vibration machines using control synchronization. [ABSTRACT FROM AUTHOR]

In this study, we propose the use of a distribute manipulator for repositioning and alignment process of cable connectors to obtain the accurate pose of the connector. The accurate pose is critical for a successful mating process in wiring harness assembly tasks. Conventional actuators such as robotics grippers rely on active manipulations; for example, they uses belts and, rollers for the repositioning of the cables, and others such as parallel grippers used directly to grasping the connector. However, all these systems need a lot of many pieces and mechanisms to manipulate the cables or high accuracy control process for grasping the connector in a certain position, thus increasing the difficulty when the cables and connectors are smaller. Therefore, we present a vibrating plate to perform in-hand manipulation to reposition the cable and align the connector. We modeled and analyzed the relationship between the vibration frequency and the velocity of the cable. Furthermore, we experimentally show that the moving velocity of the cable is proportional to the vibration system frequency, and the proposed vibrating plate can reliably move the connector to the desired pose. [ABSTRACT FROM AUTHOR]

In this paper, a newly composite synchronization scheme is proposed to ensure the straight line vibration form of a linear vibration system driven by four exciters. Composite synchronization is a combination of self-synchronization and controlled synchronization. Firstly, controlled synchronization of two pairs of homodromous coupling exciters with zero phase differences is implemented by using the master–slave control structure and the adaptive sliding mode control algorithm. On basis of controlled synchronization, self-synchronization of two coupling exciters rotating in the opposite directions is studied. Based on the perturbation method, the synchronization and stability conditions of composite synchronization are obtained. The theoretical results indicate that composite synchronization of four exciters with zero phase differences can be implemented with different supply frequencies and the straight line vibration form of the linear vibration system also can be obtained. Some simulations are conducted to verify the feasibility of the proposed composite synchronization scheme. The effects of some structural parameters on composite synchronization of four exciters are discussed. Finally, some experiments are operated to validate the effectiveness of the proposed composite synchronization scheme. [ABSTRACT FROM AUTHOR]

In order to verify that the vibration system driven by multi-eccentric rotors has multiple synchronous states, a model of three eccentric rotors horizontal installation of plane motion is established to study the coupling dynamic characteristics. Based on the average method of modified small parameters, the frequency capture equation is constructed to obtain the conditions of synchronous motion and vibration synchronization transmission. According to the synchronous conditions, the stability state of achieving synchronous motion is converted into the solution of balance equation of the synchronous torque. There are multiple solutions to the torque equation because of the non-linear characteristics of the vibration system driven by multi-eccentric rotors. Then the stability condition is used to estimate which of the solutions is stable. After substituting the parameters of the experimental machine into the above method, the curves of the phase difference and its stability coefficients of three eccentric rotors system are obtained numerically. Two experiments show that the selected synchronous state depends on the initial condition and external disturbance, and if the vibration synchronization transmission conditions are satisfied, three eccentric rotors can not only achieve vibration synchronization transmission of one motor with switching off the power but also that of two motors with switching off the power. [ABSTRACT FROM AUTHOR]

To solve the limitation of vibration synchronization, this paper investigates the dynamics of a vibration system driven by three homodromy eccentric rotors (ERs) using control synchronization. According to the synchronous condition and the stability condition, the changes of the phase differences of the three-ERs system and the two-third ERs system are obtained. Based on the electromechanical mathematic model of the vibration system and the master-slave control strategy, the synchronous target that three ERs achieve the same phase motion is converted into velocity and phase tracking of ERs. Considering the coupling characteristic of the self-adjusting of the system in the state of vibration synchronization, the velocity and phase controllers are designed by employing discrete-time sliding mode control. An experimental system for control synchronization is designed, including hardware composition and software programming. For the feedback signal used to match control targets, a method of calculating velocity and the phase difference is proposed from engineering. Recording the rotational velocities, phase differences, and system response, three group experiments with different control schemes are achieved. According to the experimental data, the coupling characteristic of the vibration system adopting control synchronization is analyzed, which can provide the basis for designing vibration machines using control synchronization.

• A theoretical model of the vibration system under load was first developed. • A experiment was conducted to explore the influence of thermo-mechanical load on vibration system. • An ultrasonic vibration drilling test was performed to verify the theoretical analysis and the experimental results. The vibrational characteristics of ultrasonic vibration system play an important role in the stability and processing effect in ultrasonic machining. In this study, a theoretical analysis and experimental verification were employed to investigate the effect of the thermo-mechanical load on the vibrational characteristics of ultrasonic vibration system. Initially, a dynamic model was designed to analyze the influence of the thermo-mechanical load on the vibration characteristics. Based on the model, the single variable method was adopted to explore the effect of different mechanical loading and the rigidity coefficient of the tool on the vibrational characteristics. Then the experiment was conducted by imposing variable loads on the tool end face, and the amplitude, current, frequency and temperature of ultrasonic system were measured. Finally, the ultrasonic vibration drilling test was conducted to verify the experimental results. It was observed that the ultrasonic amplitude initially increased and later decreased with the increase in static load. In addition, with the increase in static load, the thermal effect was significant and the ultrasonic frequency presented a similar tendency, as the ultrasonic amplitude. Meanwhile, the variation of ultrasonic frequency was not significant under the thermo-mechanical load. The results of this study could provide a favorable reference in the design of an ultrasonic vibration system and selection the different tools in ultrasonic machining. [ABSTRACT FROM AUTHOR]

A nonlinear vibration system arises in physics. Besides its mathematical model, it is of great importance to have an accurate and reliable solution to the system. Though there are many analytical methods, such as the variational iteration method and the homotopy perturbation method, numerical approaches are rare. This paper suggests the barycentric interpolation collocation method to solve nonlinear oscillators. The Duffing equation is adopted as an example to elucidate the solution process. Some numerical examples are studied to demonstrate the accuracy of the present method. Results obtained by the method indicate the method is simple and effective. [ABSTRACT FROM AUTHOR]

A nonlinear vibration system behaviors always periodically; however, sometimes a vibrating structure, e.g. an empty oil tank, will be collapsed suddenly. This can be explained as a kind of rogue waves. This paper gives a general approach to search for rational breather waves to nonlinear equations including nonlinear vibration systems and dispersive wave systems. A breather type of rogue wave solution which contains two peaks whose amplitudes are two to three times higher than its surrounding waves and generally forms in a short time is constructed. Moreover, by using three-wave method, new breather-type multisolitary coherent structures are presented, the fusion interactions of localized structures are discussed and graphically investigated, showing some novel features and interesting behaviors. [ABSTRACT FROM AUTHOR]

In ultrasonic vibration machining, the cutting force and cutting heat are significantly reduced, the tool wear is reduced, and the machining efficiency is improved. The ultrasonic vibration machining process is widely used for machining the difficult-to-machine materials, such as hard and brittle materials. In order to avoid the influence of tool load on the resonant frequency, the local resonance theory is used to divide the vibration system into two subsystems. The frequency equation of complex acoustic system is derived from the total input impedance equal to zero at the junction of the subsystems, and the size of vibration system is calculated. Calculated results show that the modal analysis results and the actual measured results are less than 3% deviation from the theoretical values, which meets the design requirements and verifies the correctness of the theoretical design of local resonance. The acoustic system designed by this method is not affected by the tool load, the fluctuation of force during processing is small, and the stability of the system is improved to some extent, indicating that the local resonance system has a good processing effect. [ABSTRACT FROM AUTHOR]

• The dynamic model of the frequency-multiplying synchronization vibration system was established. • A combined control strategy was proposed aiming at frequency-multiplying synchronization. • The stability of the frequency-multiplying controller was proved by Lyapunov theorem. • The effectiveness of the frequency-multiplying controller was verified by comparative analysis. • Frequency-multiplying vibration system will be used to develop new screening equipment. Frequency-multiplying synchronization vibration system is beneficial to diverse the material screening and improve the screening efficiency. In order to solve the problems of insufficient frequency-multiplying synchronous theory and low synchronization precision of the multiple exciters in vibration systems, the dynamic model of the frequency-multiplying synchronous vibration system with multi-vibration exciters is first established. A combined control strategy including the master-slave control and the adjacent cross-coupling control strategy is then proposed, together with the adaptive sliding mode algorithm to realize the frequency-multiplying synchronous control for the multiple exciters in vibration system. The stability of the proposed multiple exciters under frequency-multiplying synchronous control is proved by Lyapunov theorem and Barbalat Lemma. The performance of the proposed controller of frequency-multiplying synchronization is illustrated by comparing the simulation analysis with the vibration synchronization method at double frequency. The results show that the proposed controller of frequency-multiplying synchronization can effectively control the multiple exciters in vibration system to achieve the frequency-multiplying synchronous motion with improved control precision. The influence of different parameters on the performance of the frequency-multiplying synchronization is discussed, which shows that the controller of frequency-multiplying synchronization has good robustness against the system parameter disturbance. On this basis, the synchronization performance of the multiple exciters under different multiplied frequencies are analyzed and explained. The proposed combined control strategy can control the frequency-multiplying synchronization of the multiple exciters in the vibration system to achieve the required stable vibration trajectory. [ABSTRACT FROM AUTHOR]

The formulae of the dynamic response related to the excitation and dynamic parameters for a multiple-degree-of-freedom linear vibration system were deduced by virtue of the Houbolt integration and backward difference methods. Then a new method for load identification of unconditional stability was proposed. Taking a linear elastic cantilever beam as an example， the exciting loads were identified using the simulation results of the single inputs of single frequency and dual frequencies， and the dual inputs of dual frequencies. Compared with the conventional state space method， the relative errors and frequency spectrum of the loads identified by the proposed method were smaller in both time and frequency domains， and there was no frequency increasing. This proposed method has improved identification accuracy and has a good anti-noise performance. [ABSTRACT FROM AUTHOR]

This paper aims to analyze the effect of vibrations from the industrial environment on the contact resistance of electrical equipment, such as relays and contactors. The vibratory movements of such equipment have been simulated in the laboratory, following their influence on contact resistance. The results were processed, obtaining a series of diagrams. [ABSTRACT FROM AUTHOR]

In grinding, regenerative vibration and forced vibration due to grinding wheel eccentric rotation are main excited-vibration sources that interact with grinding material removal mechanism. In the paper, instantaneous undeformed chip thickness in down-grinding cutting phase may consist of two components, i.e. linear kinetic thickness and nonlinear dynamic thickness. Considering abrasive grit-workpiece interaction in the grinding contact zone, the grinding vibration system is presented by a new set of differential equations of two degrees of freedom (DOF) with a close-loop feedback control system models. Conventional grinding control parameters, including wheel spindle speed, work-speed in feed direction and radial cutting depth, are often regarded as linear constants in many existing simplified models. When considering time delay, they can be transferred to nonlinear variables, so the capability of prediction and the accuracy of solution of the grit-workpiece dynamic performance are improved. Based on quantitative comparison of force and vibration magnitudes, the influence of the eccentric rotation of abrasive wheel and the negative rake angle of working grit cutting edges on grinding performance are demonstrated in the paper. [ABSTRACT FROM AUTHOR]

In the robust control of systems with dynamic uncertainty, there are mainly two methodologies: one based on the gain bound of uncertainty and the other based on the phase bound. The well-known small-gain approach belongs to the former and is able to conduct nonconservative robust performance design by using $\mu$-synthesis. Meanwhile, the study on the latter case is still under way, and only a positive-real method was proposed by the authors recently to handle the robust performance synthesis. This paper aims at improving the positive-real method. The key idea is to model a passive uncertainty not only by its phase bound but also utilizing its largest gain. This is achieved by applying the notion of output strict passivity well known in nonlinear control. Furthermore, the negative-imaginary uncertainty can be treated in this framework more naturally. A case study on a vibration system validates the advantage of the present method. [ABSTRACT FROM PUBLISHER]

[Display omitted] • A polishing end-effector with magnetorheological fluid-based damper and magnetic spring mechanism is designed, the damping and stiffness model are built, the vibration dynamic model is established and the vibration characteristics are analyzed theoretically. • Multi-objective optimization is carried out to minimize the maximum frequency response value of polishing system. • A disturbance observer is designed to estimate the nonlinear cutting force and the stability is proved. A vibration controller based on polishing force with gravity compensation is proposed to maintain the normal contact force and suppress vibration of polishing tool. • Polishing experiments are carried out to verify the feasibility of proposed strategy. Results show that the proposed method can suppress the fluctuation of the polishing force and reduce spindle vibration, maximum vibration amplitude reduced by 45%, the surface roughness is improved up 57.9%. The instability of the polishing force in the robot polishing process causes vibration of the polishing tool and degrades surface quality. Controlling vibration is essential for enhancing machining quality during high-precision polishing. This paper presents a magnetorheological (MR)-based polishing tool and vibration control method for improving the stability and reducing the vibration during machining. Firstly, a polishing end-effector with MR-based damper and magnetic spring mechanism is designed, the damping and stiffness model are built, the vibration dynamic model is established, and the vibration characteristics are theoretically analyzed. Multi-objective optimization is carried out to minimize the maximum frequency response value of polishing system. Then, a disturbance observer is designed to estimate the nonlinear cutting force and the stability is proved. To maintain normal contact force and reduce polishing tool vibration, a vibration controller based on polishing force with gravity compensation is proposed. The measured vibration amplitude and estimated cutting force are used as feedback in the controller to maintain the desired contact force. Finally, the polishing experiments are carried out to verify the feasibility of proposed strategy. The results show that the proposed method suppress the fluctuation of the polishing force and reduce vibration, the maximum vibration amplitude is reduced by 45% and the surface roughness is improved up 57.9%. [ABSTRACT FROM AUTHOR]

Membranes used in separation processes are subjected to fouling which decreases the efficiency of the process and the membrane's lifespan. To reduce this fouling, vibrating membranes made from piezoelectrics, have recently been proposed. In this study we propose an innovative and flexible design where a conventional alumina membrane vibrates under the influence of electrically driven lead zirconate titanate (PZT) piezoelectrics, which are integrated outside the filtering area. This design makes it possible to isolate the piezoelectric and electrical interconnections from the fluid during the operation. The vibration system was analysed using “hard” and “soft” PZT compositions. Both the numerical model and the measurements of the membrane vibrations in air confirmed higher vibration amplitudes in the case of the “soft” PZT. We demonstrate that the vibration system with “soft” PZT actuators also resonates under water pressure, but at amplitudes lower than those measured in air. Filtration tests with humid acid showed that when the membrane is subjected to piezoelectric vibration, the decline in the flux was reduced by 59%, compared to the situation without the piezoelectric effect, suggesting that the novel vibration system with a built-in piezoelectric can be used in fluid-separation systems to minimise the fouling of ceramic membranes. [ABSTRACT FROM AUTHOR]

Gas-solid fluidized beds are widely used for their excellent characteristics of heat and mass transfer. An active pulsating air flow is introduced into a dense gas-solid fluidized bed, forming a dense gas-vibro fluidized bed (DGVFB), to modify the fluidization quality. Interaction between the bubbles and particles in the DGVFB was investigated based on the results of numerical simulations and experiments. Micro-bubbles in the DGVFB were regarded as springs, and therefore, the interaction between the bubbles and particles was considered to be equivalent to a linear vibration system with n degrees of freedom. A dynamic model for the vibration system was developed, and modal analysis was conducted. Results of this theoretical analysis showed that the dominant frequency of pressure fluctuations in the DGVFB was equal to the frequency of active pulsating air flow. The dynamic model described the interaction between the bubbles and particles effectively in the DGVFB at low gas pulsating frequency, and shallow fluidized beds. [ABSTRACT FROM AUTHOR]

The self-synchronous process of a vibration system driven by two exciters rotating oppositely was investigated by simulation and experiment. The rotational velocities of the two motors and phase differences between the two exciters were chosen as indexes to represent for the self-synchronous process. By comparing the changes of the phase difference, the most important influence factor of the phase difference is motor, and the second is exciter, while the last one is the vibration rigid. The simulation and experimental results show that the initial phase difference between the two exciters and the initial velocities of the two motors have no effect on the self-synchronization. When the synchronous condition is satisfied, the two motors can achieve synchronous motion with different power supply frequencies. When change the masses of the two exciters, the phase of the bigger mass lags behind the smaller one. When the distances between the rotary centers of the two exciters and the mass center of the vibration rigid body are different, the phase of the bigger distance lags behind the smaller one. The phase difference can be reduced by adjusting the power supply frequency, which are caused by motor parameters, the mass of exciters, and the motor installation position and so on. [ABSTRACT FROM AUTHOR]

This paper is focused on synchronization of a dynamic model with three rigid frames (RFs) driven by two reverse rotating eccentric rotors (ERs) distributed on different RFs. The differential equations of motion are established based on Lagrange equation. Applying the average method of small parameters, the condition is derived for the vibration system to meet synchronous motion. The stability condition of the vibration system is obtained by using Lyapunov indirect method. To investigate the selected motion characteristic on synchronous state in various frequency regions, theoretical results are discussed with frequency ratio numerically. Coupled motion of the vibration system, phase difference between two ERs, motion phase between RFs, and amplitude–frequency characteristics of RFs are discussed qualitatively to reveal the selected motion characteristic. A series of experiments are done to further illustrate the selected motion characteristic in sub-resonant state and super-resonant state of the vibration system with vertical direction. Finally, the experimental results validate the predication of the theoretical method. • Synchronization of system with eccentric rotors distributed on different rigid frames. • Conditions of synchronization and stability of the system are obtained. • Explained the relationship between phase difference and motion of rigid frames. • In different frequency regions, selected motion characteristic is further revealed. [ABSTRACT FROM AUTHOR]

A comprehensive dashpot model with hysteresis damping factors that can provide a convenient calculation approach for the elastoplastic impact behavior in multibody systems is studied in this paper. At the beginning of contact, the nonlinear hysteresis damping factor in the elastic phase is derived by approximately solving a nonlinear vibration system. When impact happens at a relatively high speed with a large load, elastoplastic deformation is inevitable, and Hertz contact stiffness cannot represent the actual contact stiffness. In order to describe the contact stiffness in the elastoplastic or plastic phase correctly, a static elastoplastic contact model is adopted to calculate the contact stiffness by approximately linearizing the relationship between load and deformation. When the contact comes into the elastoplastic phase, the impact behavior can be treated as a linear vibration system, and the linear hysteresis damping factor can be obtained from this linear system. The energy dissipation in different contact phases can be described by a nonlinear and a linear hysteresis damping factors. Such a nonlinear hysteresis damping factor can make up for the deficiency of the static elastoplastic contact model when describing the energy dissipation in the elastic contact phase. Simulation results show that the proposed dashpot model is more harmonious with the static elastoplastic contact model compared to the existing dashpot models. A slider-crank mechanism with a clearance joint and a Hopkinson incident bar are exemplified in the present work by using experimental data to validate the effectiveness of the proposed dashpot model. [ABSTRACT FROM AUTHOR]

Simple adaptive control (SAC) is a control method that maintains control performance despite perturbations of a plant. However, there is a problem in that the vibratory output occurs in the transient response when SAC is applied to a vibration system which includes anti-resonance modes. The occurrence of the output depends on the structure of SAC and the output is caused by the vibratory input corresponding to the anti-resonance frequency. In order to overcome the problem, a method using an appropriate parallel feedforward compensator (PFC) is proposed. In the proposed method, an effective PFC is designed such that the gain of an augmented system is matched to that of a desired model under the ASPR condition of the augmented system. A design problem is described by LMI/BMI conditions. The problem using LMI/BMI conditions is solved by an iterative procedure. However, the leading coefficient of the PFC must be given a priori in order to guarantee the ASPR property, which provides some restrictions for applications of the proposed method. In the present paper, an improved method to overcome the abovementioned restrictions is proposed using the stability theorem of the descriptor system. The effectiveness of the proposed method is verified through numerical simulations and experiments.

This paper proposed a method based on GNAR model to identify the essential characteristics of linear and weak nonlinear vibration systems. Firstly, it proved the relationship between GNAR model and weak nonlinear system according to perturbation method of solving nonlinear differential equation and deduced the analytic expressions between GNAR model coefficients and the system frequency. Then it extracted the identification method based on GNAR model coefficients and its structure to determine whether there was a linear or nonlinear system, and to identify the system frequency and the basic characteristics of nonlinear term. Finally it analyzed single freedom degree linear vibration systems and undamped Duffing vibration systems to lest the effectiveness and accuracy of the identification method. The experimental results show that the proposed method has high accuracy and efficiency, and can be used to estimate the system dynamic characteristics. [ABSTRACT FROM AUTHOR]

The measuring tube is the core sensitive unit of the Coriolis mass flow sensor. Its design parameters directly influence natural frequency and sensitivity, such as shape and structure dimensions. In this study, we obtained under concentrated force the equivalent elastic coefficient of the measuring tube by adopting static analysis and calculating static deflection curves, including the respective U-shape, slightly curved, and straight tubes. We then obtained the resonant frequency from the second-order vibration equation. Additionally, the maximum sensitivity and position coordinates were obtained by calculating the torsional displacement curve of the measuring tube under the distribution of Coriolis force during a rated flow. Sensor models with different measuring tube shapes were designed by applying this theoretical analysis. Calibration tests for sensors were performed using a static gravimetric method. Theoretical analysis and test results show that the resonant frequency and sensitivity of the sensors calculated by applying static mechanical analysis and Coriolis distributing force align with the experimental results, thereby proving the validity of the theoretical method. Furthermore, the proposed method simultaneously obtained the relation curve of the measuring tube structure dimensions and natural frequency and sensitivity. It therefore provides theoretical evidence for the sensor design and detector installation position. [ABSTRACT FROM AUTHOR]

[Display omitted] • Cationic CNCs could achieve > 90% microalgae flocculation without pH-adjustment. • 0.34-PYR-CNC showed the best performance for both fresh and marine microalgae. • A record-low energy consumption of only 6.7 Wh/m3 was achieved. • Surface patterning can significantly enhance flux, while reducing energy input. • Increasing particle radius can mitigate fouling on the vibrating membrane surface. High energy consumption during harvesting is one of the main bottlenecks for sustainable microalgae production. Membranes can efficiently separate microalgae from liquids with low energy consumption, but membrane fouling remains an important issue. Flocculation prior to membrane filtration can increase membrane fluxes and decrease fouling, thus offering a low-cost and efficient solution to harvest microalgae. Biobased cationic cellulose nanocrystals were successfully used as flocculants for microalgae and were effective over a wide pH-range and for both freshwater and marine microalgae. Such flocculation was for the first time combined with vibration-assisted filtration using a charged, surface patterned membrane, enabling operation at very high flux (95 L/m2 h) using a vibration frequency of only 1 Hz, and even under sub-optimal flocculation conditions. Intermittent vibration decreased energy consumption further while keeping excellent filtration performance to finally achieve a record-low energy consumption for the membrane filtration of only 6.7 Wh/m3, which is >25-times lower than that of normal membrane filtration. Interaction forces revealed that increasing particle size through flocculation prior to membrane filtration can significantly prevent microalgae attachment on the vibrating membrane surface. This work opens a new direction for sustainable microalgae harvesting with an ultra-low energy consumption, combined with a very high microalgae recovery, reduced use of chemicals, and lower membrane investment cost. [ABSTRACT FROM AUTHOR]

Concept of the system design is very important in industrial world. In contrast, lecture programs or practices for the system design are not sufficiently much provided in universities. In the present paper, an educational program for the system design using a torsional vibration experimental system is proposed. The program requires to students integration of control theory, material mechanics, and mechanical dynamics which are lectured in individual situations. And the students learn the general outline of the system design in the program. The program is effective for education of the system design which is a blind side of the educational program in universities.

The complex impulse environment of the artillery firing process brings very tough vibration attenuation requirement of the artillery-mounted equipment. The experiment is designed to decrease an artillery mounted instrument container's vibration. However, after being equipped with a certain rubber shock absorber, the vibration of this instrument container wasn't being controlled. Thus, based on the theoretical analysis and dynamic simulation, we summarized that this phenomenon was caused by the rigid collision between two parts of the rubber shock absorber while reaching elastic limit. The result provides the necessary theory of choosing the appropriate artillery shock absorber. By using the Genetic Algorithm optimization design method, we found the best independent variable H. [ABSTRACT FROM AUTHOR]

This paper studies self-synchronization and stability of a dual-motor driven vibration system with a two-stage vibration isolation frame. Oscillation amplitude of the material box large enough can be ensured on the vibration system in order to screen materials. Reduction of the dynamic load transmitted to the foundation can also be achieved for the vibration system. A Lagrange equation is used to set up the motion differential equations of the system, and a dimensionless coupled equation of the eccentric rotors is obtained using a method of modified average small parameter. According to the existence condition of zero solution in the dimensionless coupled equation of the eccentric rotors, the precondition for commencing self-synchronization motion is achieved. The stability condition of self-synchronization is obtained based on the Routh-Hurwitz criterion. The theoretical analysis is validated by simulations and experiments. [ABSTRACT FROM AUTHOR]

The structure and working principle of a two-cylinder four-stroke single-piston hydraulic free piston engine (HFPE) were introduced. The basic vibration equation of free piston assembly (FPA) was established based upon the energy conversion between the injected fuel and the friction together with the load. Both the theoretical and numerical results show that the vibration system of FPA is a nonlinear conservative autonomous system in one cycle. The FPA vibration is symmetric with constant amplitude when FPA is only driven by the compression pressure in the compression accumulator and that in the combustion chamber. When considering the friction and load, FPA could still achieve a stable vibration after a few cycles' adjustment whether the input energy is equal to the consumed energy or not. The vibration characteristics are different when FPA vibrates in the compression stroke and the expansion stroke, which is the unique feature of the single-piston HFPE. [ABSTRACT FROM AUTHOR]

In this study, the dynamical model of the vibration of the wind power system was established according to the Lagrange's principle for investigating the phenomenon of frequency capture. The system response of the vibration of wind power device in the horizontal and vertical directions of tower was analyzed by numerical simulation. At the same time, the paper analyzed the characteristics of the vibration model comparing with the traditional model. Then the conditions of frequency capture were studied through the analysis of mathematical model. In particular, the effects that five key parameters had on the frequency capture characteristics were analyzed. Finally, the research reveal that reducing the eccentric mass and eccentricity of the blade, increasing the support stiffness and displacement damping coefficient, and increasing the torque of the input shaft can reduce vibration and avoid the phenomenon of frequency capture. The simulation results provide the theory basis for the design and installation of wind power device. [ABSTRACT FROM AUTHOR]

A single mass nonlinear vibration machine driven by two counter-rotating motors was taken as a research object. Based on the mechanic-electric coupling dynamic equation of the vibration machine and the electromagnetic torque model of motor, the simulation model was established. By using the actual parameters of the vibration machine, the numerical simulation of a single-mass nonlinear vibration system under three typical working states was performed. When two motors were working under the ideal state, or when the overlap angle of two eccentric blocks were different, or when the supply frequency of one motor was changed, the two motors can achieve steadily synchronous motion if parameters of the vibration system are in specific range. Finally, the self-synchronization experiment was carried out under the three working states. A comparison of experimental results with simulation results shows that the numerical simulation is accurate. [ABSTRACT FROM AUTHOR]