Vibration is a common phenomenon of a mechanical system [1
] that possesses properties which partly affect the stability and safety of equipment and machine operation. Examples of these mechanical systems include vehicles [2
], motors [4
], elevators, robots [5
], construction machinery [6
], wind power systems [7
], flywheel systems, rail transportation, and many other mechanisms in other fields [8
]. Excessive or unwanted vibration may also have a negative effect on the mechanism. For mitigating vibrations of mechanisms, Xu et al. [9
] proposed a new vibration isolation and mitigation device which is used to restrain platform vibration under a wide frequency excitation. Le et al. [10
] proposed a vibration isolation system which improves the vibration isolation validity of a driver seat. Wu et al. [11
] presented a magnetic levitation (maglev) vibration isolation system, and verified the nonlinear dynamic model and the isolation performance, which was proven to be highly effective. Moradi et al. [12
] proposed a tunable vibration absorber to suppress regenerative chatter in the milling of cantilever plates, based on the mode summation approach. Rosbi et al. [13
] proposed an optimally designed dynamic absorber, using the suppression method of the nonlinear vibration to suppress the occurrence of subharmonic vibration in the natural frequency and the damping ratio. Stelzer et al. [14
] developed a semi-active magnetorheological isolator with a low cost that can be used to mount components that generate vibrations. The isolator is applicable for automobiles, engine mounts, pumps, and the isolation of aviation and naval components. Yang et al. [15
] studied the vibration power flow and force transmission characteristics of a 2-degree of freedom (DOF) nonlinear system to test the performance of a nonlinear isolator. Wang et al. [16
] proposed a two-stage quasi-zero stiffness vibration isolation system, with a low roll-off rate in the effective frequency range of vibration isolation. Therefore, vibration is one of the important factors in machining accuracy, machine operation, and machine life, where reducing vibrations is beneficial with regards to improving machining accuracy and reducing the risk of hidden dangers.
In addition to changing the mechanical structure to alleviate vibrations, vibrations can also be reduced by designing control and theoretical methods that are suitable for the vibration system. Zhang et al. [17
] proposed a hybrid error criterion-based frequency-domain least mean square (LMS) control method, for suppressing the vibrations of milling processes using piezoelectric actuators and sensors, which is an effective and reliable way to suppress vibrations and improve the machining quality, based on the simulation and experimental results. Lou et al. [18
] proposed a novel optimal trajectory planning approach applied to a flexible piezoelectric manipulator system, which is a combination of this approach and the feedback control of piezoelectric actuators. Zhou et al. [19
] proposed an adaptive vibration control method using a pair of mirror finite impulse response filters, to reduce the amplitude of the rear gap vibration and improve the stability and ride comfort of a maglev train. Kotake et al. [20
] proposed a vibration manipulation function, applied in a one-dimensional overhead traveling crane to remove the residual vibrations of a hoisted load, and validated the abilities of the proposed function in the crane operation by simulations and experiments. Shao et al. [21
] proposed a fault-tolerant fuzzy H∞ control design approach for the presence of sprung mass variations, actuator faults, and control input constraints, to suppress the vibrations of the active suspension of in-wheel motor-driven electric vehicles.
The other fundamental flaw associated with mechanisms is that they expel undesired kinetic energy as heat, meanwhile, energy loss generated by vibrations is also a hot topic of current research. Ze et al. [22
] proposed a new capacitive energy recycling converter to improve the power generation performance of a doubly salient permanent magnet generator. Warner et al. [23
] proposed three actuator models considered for energy regeneration potential of the knee joint. Manna et al. [24
] designed a novel energy-harvesting device, using magnetic levitation to produce an oscillator with a tunable resonance, and investigated the energy-harvesting potential of this prototypical nonlinear system. Elvin et al. [25
] presented an experimentally validated electromagnetic energy harvester, the results of which show a normalized power density of 1.7 mW/[(m/s2
] when operating at a resonance frequency of 112.25 Hz. Glynne-Jones et al. [26
] described miniaturized generators for converting ambient vibration energy into electrical energy, as applied in powering intelligent sensors. These generators have been tested with a vehicle engine and have produced a peak power of 3.9 mW with an average power of 157 W. Xu et al. [27
] put forward a braking system using only electric motors/generators as the actuators, the generated energy of which can be fed back to the onboard energy storage system as much as possible. Zhang et al. [28
] proposed an energy-efficient torque allocation scheme to increase traction efficiency and brake energy-recovery. Yan et al. [29
] put forward an energy regeneration implementation scheme to achieve an energy-saving goal of active suspension with self-power supply potential in a practical application.
To obtain energy from vibrations, energy regenerating mechanisms have been generally divided into three main categories, namely, rotation energy regeneration mechanisms, linear energy regeneration mechanisms, and energy regeneration mechanisms based on energy regenerating materials [30
]. Rotation energy regeneration mechanisms convert reciprocating linear vibrations into bidirectional rotary motion to produce electricity [31
]. Liu et al. [32
] proposed an energy-harvesting shock absorber based on a mechanical motion rectifier, which is able to harvest an average power of 13.3 W for a representative period of 8 s on a paved road at 40 mph. Linear energy regeneration mechanisms adopt a coil, or multiple coils, to cut the magnetic flux to generate electric energy and produce a back electromotive force [33
]. Buren et al. [35
] presented a prototype linear electromagnetic generator that supplied power to body-worn sensor nodes with an output power of 2–25 W while walking. Arroyo et al. [36
] presented and optimized a new electromagnetic harvester with a nonlinear energy extraction circuit (the synchronized magnetic flux extraction technique), the experimental results of which show that a rectified power of 1.6 mW is harvested at 1g excitation acceleration at 100 Hz frequency over a 10 Hz bandwidth. Tang et al. [37
] presented a tubular linear electromagnetic transducer, applied in large-scale vibration energy-harvesting from vehicle suspensions, tall buildings, or long-span bridges. The experiment results show that the prototype (63.5 mm outer diameter, 305 mm compressed length) can harvest 2.8 W of power under a 0.11 m/s relative velocity, with a damping coefficient of 940 N·s/m. Sapiński [38
] proposed an energy-harvesting linear magnetorheological (EH-LMR) damper to obtain energy from external excitations, using an electromagnetic energy extractor with self-powered and self-sensing capabilities. The energy regenerating mechanism uses the characteristics of energy regenerating materials to regenerate energy [39
]. Liu et al. [40
] designed, microfabricated, and characterized a piezoelectric microelectromechanical systems (MEMS) energy-harvester which has a wideband and steadily increased power from 19.4 nW to 51.3 nW within the operating frequency bandwidth of 30–47 Hz at gravity acceleration of 1.0 g. Liu et al. [41
] studied a cantilevered energy-harvesting device, with a root mean square (RMS) harvesting power up to 13.3 mW and a RMS power density of up to 3.7 mW/cm3
/g, based on an iron–gallium alloy magnetostrictive material for low frequencies, verifying the electricity-generating capability of the harvester prototype. The energy generated by vibrations can be collected by the energy regenerating mechanisms mentioned above, and stored in a battery through a series of energy regenerating circuits. Because the linear energy regeneration mechanism has the advantages of high efficiency, non-contact, no lubrication, and being non-pollutive, this scheme was adopted for energy regeneration in this study.
This paper presents a novel electromagnetic actuator, that has been designed to produce energy via vibrations while suppressing said vibrations, which can be installed in many kinds of mechanisms to improve machining accuracy and reduce energy loss. Firstly, the electromagnetic actuator is proposed, and the vibration suppression function and energy regeneration function are explained in detail. Then, the proposed electromagnetic actuator is designed based on the static magnetic field simulation with finite element method (FEM) analysis, and its prototype is fabricated. Based on this prototype, characteristics of the electromagnetic actuator are explored via measuring experiments. Furthermore, a control algorithm with a position controller and an acceleration controller is applied to the proposed actuator. Finally, an experimental control system is built, and experiments of the impulse and sinusoidal excitation responses are carried out to verify the feasibility and effect of the electromagnetic actuator.
This paper has proposed a new type of electromagnetic actuator that may be applied in mechanisms with low vibration and a low frequency, such as in transportation machinery, mining machinery, construction machinery, and other areas. The proposed actuator has two working functions, namely, a vibration suppression function and an energy regeneration function. These functions can relieve vibrations generated by a vibrating component and collect a part of the energy dissipated by the vibrating component. The structure of the electromagnetic actuator was designed by the static magnetic field simulation of FEM analysis, and the prototype of the actuator was fabricated. On this basis, the characteristics of the electromagnetic actuator were explored, finding an output force–current coefficient of 39.49 N/A. Moreover, the control system of the experiments was constructed by a position controller and an acceleration controller. Impulse excitation response and sinusoidal excitation response analyses were carried out. The experimental results show that the vibration acceleration of the controlled object can be suppressed from 114.26 m/s2 to 3.14 m/s2, which is within 2.75% under the impulse excitation response. For the sinusoidal excitation response, the input signal under a 3 mm amplitude and 5 Hz frequency was set as the input of the excitation object, where the peak value of the displacement of the controlled object was 0.045 mm, accounting for 1.46% of that of the excitation object. The peak value of the regenerated EMF was 1.97 V, where the efficiency for regenerating energy is 11.59%. Under multiple frequencies and amplitudes, the amplitude ratio of the controlled object and excitation object was within 5.5%, and ratio of the EMF to the input amplitude was 0.13, which can predict the trend of the regenerated energy.
This electromagnetic actuator has great potential to be adopted as a viable development for occasions with millimeter-sized vibrations. The next step is to conduct a thorough study of the amplitude ratio of the controlled object to excitation object, and the ratio of the EMF to the input amplitude, to improve the control effect at high frequencies in the active control function. In the energy regeneration function, the efficiency of the proposed electromagnetic actuator will be verified by experiments, and this efficiency needs to be further improved.