Electromechanical Coupling Model Research Articles

A hybrid piezoelectric–electromagnetic body energy harvester: design and experiment validation

Abstract The rapid advancement of electronic devices and wireless sensors has heightened the demand for energy sustainability and portable power solutions. Traditional human energy harvesters have limitations in harvesting energy from ultra-low-frequency human motion due to issues related to unstable energy output and wearing comfort. To address this challenge, a piezoelectric–electromagnetic hybrid energy harvesting (HP-EEH) structure designed for the hip joint area. This innovative design employs magnetically coupled frequency boosting alongside electromagnetic energy capture to achieve high output power. Firstly, the structure and principle of the energy capture device are introduced, and the electromechanical coupling model of the energy harvester is derived using Hamilton’s principle. Furthermore, the system is numerically simulated, and the voltage output characteristics of the piezoelectric unit and the electromagnetic unit are analyzed by using the finite element analysis software. Finally, the experimental setup of the (HP-EEH) is constructed, and the voltage output characteristics are tested for different swinging angles and positions. The results show that two parts of energy can be captured simultaneously under ultra-low-frequency motion conditions. At a swing angle of 50 degrees, the piezoelectric and electromagnetic units achieved maximum output power values of 14.96 µW at 0.8 Hz and 10.4 µW at 1.2 Hz, respectively. Incorporating the output power of the electromagnetic unit aims to address the power consumption requirements of low-power devices better.

Expansion force signal based rapid detection of early thermal runaway for pouch batteries

With the extensive application of lithium-ion batteries in electric vehicles and energy storage stations, thermal safety issues have increasingly become the focus of public attention. To alleviate the safety concerns, a qualified battery management system (BMS) must be able to detect and warn of thermal abuse before it develops into a thermal runaway (TR). For the first time, the expansion force characteristics of the pouch battery module during the early heating stage of TR under typical working conditions are analyzed, which proves that the expansion force signal can reflect the internal abnormal heating earlier than the terminal voltage and the surface temperature, and has better noise resistance. Furthermore, the electromechanical coupling model (EmCM) is improved for more accurate open-loop expansion force estimation. On this basis, an expansion force based early TR rapid detection framework is proposed with less 3 min expend in tests, in which the Kalman filter ensures the stability and convergence/divergence of the observer estimation error, and the reliability of fault judgment is ensured by the adaptive threshold designed by the model structure.

Research on operating characteristics of V-shaped ultrasonic motor based on improved electromechanical coupling model

Abstract As a complex electromechanical coupling system, evaluating the motion characteristics of an ultrasonic motor via an accurate theoretical model is challenging due to the strong coupling between its electrical and mechanical properties. To address this issue, the paper first establishes a complete dynamic model of the V-shaped ultrasonic motor (VUSM). In contrast to the traditional dynamic model, the proposed model incorporates the centroid vibration of the stator and applies the weighted residual method to reduce the computational complexity by simplifying the dynamic model from infinite-dimensional degrees of freedom to two degrees of freedom. Subsequently, the finite element method is employed to determine the vibration mode of the stator structure and derive the two-phase operational mode of the motor. Using these two-phase working modes, the model is then solved to predict the motor's output characteristics under any operational condition. Furthermore, an electrical model accounting for preload nonlinearity was developed based on the dynamic model and compared with the model without considering preload nonlinearity, supported by experimental verification. The findings demonstrate that the established dynamic model and electrical model can accurately simulate the changing laws of the input and output characteristics of the motor, which provides assistance for the subsequent operation status evaluation of the motor and fault diagnosis during operation.

Electromechanical coupling modeling and fractional-order control of the seeker stabilization platform

To address the electromechanical coupling and multi-source disturbance problems of the seeker stabilized platform, this paper constructs an electromechanical coupling model of the seeker stabilized platform based on the Lagrange-Maxwell equation. To mitigate the influence of electromechanical coupling on the control performance of the seeker, a super-twisting controller based on a fractional-order terminal sliding mode surface (FOSTSMC) is proposed. Additionally, to handle various disturbances in the system, this paper introduces a method that combines the extended state observer (ESO) with the proposed controller to enhance the system’s stability and anti-disturbance performance. The Lyapunov function is designed to prove that the proposed controller can reach a convergence state within finite time. Finally, the proposed control method is compared with PID control, fuzzy PID control, linear sliding mode control, and super spiral control combined with a disturbance observer (DOB). Multiple simulation experiments demonstrate that, under the influence of electromechanical coupling and multi-source disturbance, the FOSTSMC-ESO significantly improves the stability and anti-disturbance performance of the seeker stabilization platform.

Parameter effects on performance of piezoelectric wind energy harvesters based on the interaction between vortex-induced vibration and galloping

Our previous research experimentally validated that the interaction between vortex-induced vibration and galloping is an effective method for enhancing the performance of piezoelectric wind energy harvesters under low wind speed conditions. We proposed a distributed-parameter electromechanical coupling model as well. This study aims to investigate the effects of various parameters and optimize the performance of VIV-galloping interactive piezoelectric wind energy harvesters. Initially, we assessed the applicability of the model under different circuit and aerodynamic force conditions and discussed boundary and convergence conditions by replicating previous results. Further, simulations were performed to analyze the effects of the structural parameters of the bluff body and piezoelectric beam. The width or depth of the bluff body significantly influenced the low critical wind speed, interactive occurrence, and electrical output. To achieve a balance between material cost and electrical benefit, we recommend positioning the electrode length from the fixed end with a coverage ratio of at least 60%. Additionally, the output power is highly sensitive to the piezoelectric beam length, but reducing it results in a higher natural frequency and critical wind speed. We fabricated and tested four prototypes, which have demonstrated significantly higher power densities compared with previously reported values at the same wind speed.

Modelling and dynamic characteristics of wind turbine drivetrain based on the variable coefficient sliding mode controller

Vibration is inevitable in operation of mechanical equipment, but severe vibrations will cause serious harm to wind turbines (WTs). This paper takes the drivetrain of 8 MW WT as the object, established a multi-body electromechanical coupling model of WT and verified the accuracy of the established model through the WT drivetrain in the laboratory. Subsequently, based on this model, time-frequency domain analysis was conducted on the vibration response of the WT drivetrain under different control strategies of the generator, and the influence of the generator control strategy on the vibration of the drivetrain was studied. The result shows that the generator control strategy has a significant impact on the vibration response amplitude of the drivetrain, but has a relatively small impact on the frequency component. Meanwhile, the sliding mode controller designed in this paper has good anti-interference ability, which can make the system quickly reach dynamic stability, and effectively suppress the vibration of the main components in the drivetrain. Under the new controller’s control, the transverse vibration displacement of some parts of the WT drivetrain can be reduced by up to nearly 60 %. This paper provides new ideas and new methods for the active vibration reduction control of WT drivetrain.

Electric–Mechanical coupling analysis of two-dimensional piezoelectric heterogeneous materials in flexible electric devices with extended multiscale isogeometric analysis

Piezoelectric heterogeneous materials are widely used in flexible electronic device design, enhancing sensitivity to external stimuli like pressure and acceleration. Despite their usefulness, analyzing these inherently periodic structures poses significant computational challenges. In response, this paper presents a multiscale isogeometric analysis approach tailored for simulating piezoelectric materials. We introduce an electric–mechanical coupling model using isogeometric analysis (IGA) for two-dimensional piezoelectric membrane structures, assuming the plane stress hypothesis. Our proposed algorithm enables precise calculation of both displacement and electric potential solutions, demonstrating superior convergence properties compared to traditional finite element methods. Furthermore, we extend this approach to multiscale isogeometric analysis for computing numerical solutions in porous structures and heterogeneous composite piezoelectric materials under tensile and bending conditions. Through rigorous numerical testing, we evaluate the proposed extended multiscale isogeometric analysis method, showcasing its efficacy in achieving a balance between computational efficiency and simulation accuracy. This IGA-based electro-mechanical coupling model and numerical algorithm pave the way for more streamlined and precise simulations of piezoelectric materials within the context of flexible electronic devices.

Phase field study on the grain size dependent electrical resistivity-strain response in superelastic nanocrystalline NiTi alloys

The superelastic NiTi alloy's electrical resistivity exhibits significant variations in response to deformation, making it a highly attractive material for sensing applications. However, there exists a lack of comprehensive knowledge of the effects of grain size (GS) on the electrical properties of NiTi alloy. To address this gap, a novel electro-mechanical coupled phase field simulation model is developed, with crucial parameters determined through experimental investigations. The results demonstrate a notable change in the relationship between electrical resistivity and strain, transitioning from a quasi-linear pattern to a piecewise nonlinear one as the GS increases. The observed modification is found to be primarily influenced by the martensitic transformation, characterized by a transition from a uniform mode to a localized mode. As the GS increases, there is an initial drop in the total change of electrical resistivity at peak strain, followed by a subsequent stabilization. This is because the GS, through the stress and the degree of phase transformation, exerts two opposing effects on the variation of electrical resistivity. Furthermore, the combined influence of hysteresis and hysteresis in the martensite fraction contributes to a consistent decrease in resistivity hysteresis as the GS diminishes. This study improves the understanding of how GS affects NiTi alloy's electrical resistivity-strain response and lays the foundation for future sensing performance regulation, expanding its multi-functionality as an intelligent material.

A novel compartmental approach for modeling stomach motility and gastric emptying

The stomach, a central organ in the Gastrointestinal (GI) tract, regulates the processing of ingested food through gastric motility and emptying. Understanding the stomach function is crucial for treating gastric disorders. Experimental studies in this field often face difficulties due to limitations and invasiveness of available techniques and ethical concerns. To counter this, researchers resort to computational and numerical methods. However, existing computational studies often isolate one aspect of the stomach function while neglecting the rest and employ computationally expensive methods. This paper proposes a novel cost-efficient multi-compartmental model, offering a comprehensive insight into gastric function at an organ level, thus presenting a promising alternative.The proposed approach divides the spatial geometry of the stomach into four compartments: Proximal/Middle/Terminal antrum and Pyloric sphincter. Each compartment is characterized by a set of ordinary differential equations (ODEs) with respect to time to characterize the stomach function. Electrophysiology is represented by simplified equations reflecting the “slow wave behavior” of Interstitial Cells of Cajal (ICC) and Smooth Muscle Cells (SMC) in the stomach wall. An electro-mechanical coupling model translates SMC “slow waves” into smooth muscle contractions. Muscle contractions induce peristalsis, affecting gastric fluid flow velocity and subsequent emptying when the pyloric sphincter is open. Contraction of the pyloric sphincter initiates a retrograde flow jet at the terminal antrum, modeled by a circular liquid jet flow equation.The results from the proposed model for a healthy human stomach were compared with experimental and computational studies on electrophysiology, muscle tissue mechanics, and fluid behavior during gastric emptying. These findings revealed that each “ICC” slow wave corresponded to a muscle contraction due to electro-mechanical coupling behavior. The rate of gastric emptying and mixing efficiency decreased with increasing viscosity of gastric liquid but remained relatively unchanged with gastric liquid density variations. Utilizing different ODE solvers in MATLAB, the model was solved, with ode15s demonstrating the fastest computation time, simulating 180 s of real-time stomach response in just 2.7 s. This multi-compartmental model signifies a promising advancement in understanding gastric function, providing a cost-effective and comprehensive approach to study complex interactions within the stomach and test innovative therapies like neuromodulation for treating gastric disorders.

Piezoelectric Hinged Beam with Arc Mass Stopper for Vibration and Human Motion Energy Harvesting.

Compact reliable structure and strong electromechanical coupling are hot pursuits in piezoelectric vibration energy harvester (PVEH) design. PVEH with a static arc stopper makes piezoelectric stress uniformly distributed and widens the frequency band by collision but wastes space. This Article proposes a hinged PVEH with two arc mass stoppers (AS-H-PVEH). Two arc stoppers as movable masses increase the vibration energy and the effective electromechanical coupling coefficient to achieve strong electromechanical coupling. AS-H-PVEH generates a 4.1 mW power output at 11.6-12.0 Hz and 0.2 g. AS-H-PVEH sustains 4 g acceleration vibration for 10 min without attenuation. To offset the resonance frequency increase caused by arc contact, we discuss the magnetic coupling, and axial force effects are discussed. The design of the arc stopper radius, nonlinear electromechanical coupling model, and system parameter identification method are presented. The displacement varied mechanical quality factor and effective electromechanical coupling coefficient are considered in the modified model for the first time. The model obtained good agreement under experiments. The power generation and driven wireless sensor performance of AS-H-PVEH was verified. This research has important theoretical and application value for the performance optimization of PVEH with an arc stopper.

Hybrid vibration isolator based on piezoelectric actuator and metal rubber and its adaptive control method

To achieve vibration isolation across the entire working frequency range, this paper proposes a novel hybrid vibration isolator combining metal rubber and piezoelectric actuators, along with an adaptive active control algorithm. The passive isolation system allows for manual adjustment of stiffness and damping based on the preload, overcoming the issue of fixed stiffness and damping in traditional passive isolation units. For the active isolation system, an improved Filtered-x Normalized Least Mean Squares with adaptive step size active control algorithm is proposed, overcoming the problem of narrow frequency range applicability in traditional active control algorithms. A hybrid model of electromechanical coupling and hysteresis for the piezoelectric actuator is developed for the secondary path in the algorithm. Experimental results confirm that the hybrid isolator possesses vibration isolation capabilities within the 5–500 Hz working frequency range, with vibration suppression at the first and second resonance frequencies improved by 98.9% and 92.2%, respectively, compared to the passive system. Additionally, the hybrid isolator effectively suppresses complex multifrequency signals and demonstrates robustness and adaptability. This research provides advanced technological means to address complex vibration problems, and establishes both theoretical and practical foundations for multi-degree-of-freedom vibration isolation.

Active vibration control of rotating carbon nanotube reinforced composite cylindrical shells via piezoelectric patches

This paper addresses the active vibration control of rotating carbon nanotube reinforced composite (CNTRC) cylindrical shells via piezoelectric actuator and sensor pairs. Considering circumferential initial stresses and Coriolis forces induced by rotation, an electromechanical coupling model of a simply supported CNTRC cylindrical shell, covered with surface-bonded piezoelectric sensors/actuators is established using the Lagrange equations and the model validation is carried out through a comparative analysis with existing literature. To suppress vibrations of rotating CNTRC cylindrical shells over a range of speeds, an LQR (Linear Quadratic Regulator) closed-loop controller is designed and its effectiveness is analyzed and evaluated through dynamic response analysis. Furthermore, the optimization of piezoelectric patch layout is performed by analyzing the performance of the controller for rotating CNTRC shells with typical piezoelectric sensors/actuators distributions. This paper presents and validates a strategy for vibration control of rotating CNTRC cylindrical shells using piezoelectric patches. The findings derived can offer guidance for vibration suppression of rotating thin-walled structures in practical engineering applications.

Jellyfish-inspired bistable piezoelectric-triboelectric hybrid generator for low-frequency vibration energy harvesting

In pursuit of enhancing the output power of energy harvesters, this paper introduces a novel jellyfish-inspired bistable piezoelectric-triboelectric hybrid generator (JIB-PTHG) with low potential energy barrier characteristics and low-frequency, broadband energy harvesting capabilities. The JIB-PTHG comprises two flexible beams, and two rigid links, connected via a spring. Utilizing the harmonic balance method and Runge-Kutta fourth-order algorithm, a comprehensive analysis of the mechanical properties of the low-barrier bistable structure is conducted. Static equilibrium bifurcation and dynamic response analysis are performed. Subsequently, an electromechanical coupling model incorporating piezoelectricity and triboelectricity is developed to theoretically predict the output voltage of the two modules, revealing a positive correlation between displacement and output voltage. Experiment validation demonstrated that adjusting the length of the rigid links can effectively increase the deformation of the piezoelectric beam and the relative displacement of the triboelectric layers, thus improving the generator's output performance. Specifically, the TENG module exhibited exceptional energy harvesting performance within the frequency range of 3.5–6.5 Hz, achieving a voltage of 1050 V, a power of 1.84 mW, and the ability to illuminate 70 LED lights under an excitation amplitude of 17.5 mm and a frequency of 5.5 Hz. The PEG module, displayed high output performance within the frequency range of 4-7 Hz, reaching a voltage of 6.2 Vs and a power of 12.8 μW at an excitation frequency of 7 Hz and an amplitude of 17.5 mm. Both theoretical and experimental findings indicate that the JIB-PTHG has achieved improved output power within the frequency range of 3.5–6.5 Hz. Furthermore, the JIB-PTHG has the potential to harness bridge vibration energy and convert it into useful electrical energy for powering wireless sensor nodes in bridge health monitoring systems.

Dynamic investigation of the electromechanical coupling system in a permanent magnet direct-drive locomotive under rotor eccentricity faults

In the traction system of a direct-drive locomotive, the gearbox design is eliminated, enabling the direct transmission of output torque from the traction motor to the wheelset. Due to this unique structure, rotor eccentricity, which is a common fault in traction motors, can have a direct impact on the dynamic performance of key components such as the motor, bogie, and wheelset in locomotives. In order to investigate the dynamic response of the direct drive locomotive under rotor eccentricity faults, a comprehensive electromechanical coupling model that considers the dynamic motion of the rotor is established in this paper. The coupling effect between the mechanical system and the electrical system, as well as the dynamic forces induced by rotor eccentricity, are taken into account in the model. The simulation results reveal that ripple torque has an obvious effect on rotor dynamics behaviour, while rotor air-gap eccentricity and mass eccentricity exhibit varying degrees of influence on the dynamic performance of the vehicle system. Furthermore, the influence laws of rotor eccentric distance on the vibration responses of critical locomotive components are revealed. These findings provide valuable theoretical guidance for the operational maintenance and fault diagnosis of traction motors in direct-drive locomotives.

Electrical-feed-through elimination in micro-hemisphere resonator measurement based on mixed-frequency-excitation of different harmonic signals

To eliminate the electric feed-through introduced into the measurement of the micro-resonator by the electrical scheme, an improved mixed-frequency-excitation (MFE) method is proposed in this paper. Based on the electromechanical coupling and electric feed-through model of the micro-hemispherical resonator (MHR), the mechanism of suppressing the effect of electric feed-through on the resonant signal by the MFE method of different harmonic signals is analyzed theoretically. The MFE method can be divided into two kinds according to the frequency range. The feasibility of the method is verified by the actual measurement, and the multiplexing of the same oscillator can realize the MFE for the resonator. The measured results show that the resonant response of the micro-resonator can be measured by scanning frequency, and the signal-to-noise ratio can reach more than 10dBV. The resonant frequency of the resonator can be determined according to the position of the resonant peak. The characteristics and application range of the MFE methods of two different harmonic signals are deeply analyzed. It is revealed that the reason why the MFE in the high-frequency range causes the resonance peak deviation is due to the electrostatic negative stiffness introduced by the electric feed-through. The method and research content presented in this paper have a certain application prospect in the measurement of micro-capacitive resonators.

Crack propagation effects on the critical temperature degradation of superconducting Nb3Sn single crystal

The irreversible degradation of Nb3Sn critical performance caused by the crack propagation brings challenges to the reliability of Nb3Sn service equipment. In this paper, the crack propagation behavior of Nb3Sn single crystal was studied by molecular dynamics method. The results show that amorphous transformation occur in Nb3Sn samples with cracks under the applied loading conditions. On the basis of these results, the electronic structures of different regions in the cracked sample are studied by first principles method. The critical temperature response in this process is analyzed in combination with our proposed trans-scale electromechanical coupling model. The physical mechanism behind the critical temperature degradation caused by the transition between the cracked surface and the amorphous zone at the crack tip is discussed. Amorphous states and the crack surface destroy the special kind of bonding in the atom chain direction, inducing the electronic band structure distortions. The density of states curve of Nb3Sn no longer exhibits the characteristic peaks near the Fermi surface observed in cubic crystalline Nb3Sn. The intrinsic relationship between the crack propagation, the electronic structure evolution driven by the local atomic rearrangements, and the irreversible critical temperature degradation of cracked Nb3Sn is revealed by the given model. The results deepen the understanding of the electromechanical coupling behavior of Nb3Sn under complex deformation.

Direct torque control for PMSM based on the RBFNN surrogate model of electromagnetic torque and stator flux linkage

Direct Torque Control (DTC) is widely used in motion control of motors. Classical DTC utilizes the Park transformation(dq-model) or observer to estimate the stator fluxlinkage and electromagnetic torque. However, the dq-model and observer lack descriptions of the cogging torque and magnetic saturation in permanent magnet synchronous motors (PMSM). This paper proposes a novel method based on the surrogate model to estimate stator fluxlinkage and torque for PMSM DTC. First, a finite element model (FEM) was established based on the parameters of PMSM. Using the FEM and Latin hypercube sampling (LHS), a surrogate model for estimating the stator fluxlinkage and torque of PMSM was constructed. The stator fluxlinkage and torque surrogate model, active flux observer, and dq current model under different control methods are constructed, respectively. The servo control parameters were tuned using the extended symmetric optimum algorithm, and simulation and experiments were conducted. Finally, electromechanical coupling models with a ball screw feed system were built based on various control and feedback methods. Simulation and experiment results indicate that the surrogate model reduces torque ripple, stator fluxlinkage offset, and feed system tracking error.

Design and test of liquid sloshing piezoelectric energy harvester

The energy harvester based on the piezoelectric effect can convert the vibration energy in the environment into electricity to power the network nodes. In order to broaden the effective frequency bandwidth of the piezoelectric energy harvester and reduce the resonant frequency of the system, a liquid slosh-type piezoelectric energy harvester is proposed in this paper. Based on the theory of the piezoelectric effect, the mechanical model and electromechanical coupling model of the piezoelectric energy harvester were established, and the dynamic characteristics of the liquid slosh piezoelectric energy harvester were analyzed. Based on theoretical model and experimental test, the liquid slosh piezoelectric energy harvester is studied. By making a prototype and building a vibration experiment platform, the energy capture characteristics of the piezoelectric energy harvester were tested experimentally. The experimental results show that when the external excitation frequency is close to the first resonant frequency, the maximum output power of the liquid sloshing piezoelectric energy harvester is 0.068 mW, and the optimal matched impedance is 440 kΩ. When the external excitation frequency is close to the second resonant frequency, the maximum output power of the liquid sloshing piezoelectric energy harvester is 0.178 mW, and the optimal matching load resistance is 600 kΩ. Compared with the traditional cantilever beam piezoelectric energy harvester, the liquid slosh piezoelectric energy harvester has a lower resonant frequency and achieves two resonant peaks in the range of 1–20 Hz, which greatly widens the effective frequency bandwidth and improves the energy capture efficiency of the piezoelectric energy harvester.

The Impact of Wheel Flat on Traction Drive System of Electric Locomotives

Wheel flat can seriously affect the wheel–rail contact performance and cause impact vibrations, which significantly threaten the safe operation of railway vehicles. It is crucial to accurately assess the effects of wheel flats on the wheel–rail contact performance and the vibration impact on the traction drive system. However, studies related to wheel flats have focused on the mechanical part and have yet to fully consider the electrical and mechanical parts of the entire traction drive system. Therefore, this paper first builds an electromechanical coupling model based on the electric traction drive system and the locomotive-track coupling dynamics model. Then, based on this model, the impact of the wheel flat on the electrical and mechanical parts of the traction drive system under different flat lengths, different flat depths, and different vehicle speeds was analyzed. The results indicate that with the increasing depth of the flat spot, the wheel–rail dynamic response, motor rotor speed, and motor torque exhibit more significant fluctuations. Additionally, as the locomotive speed increases, the impact of the flat on the wheel–rail contact performance intensifies. Wheel flats can excite the 1st bending mode of the wheelset, resulting in vibration shocks at 90 Hz.

Research on the Dynamic Characteristics of a Dual Linear-Motor Differential-Drive Micro-Feed Servo System

(1) Objectives: This article presents a dual linear-motor differential drive micro-feed servo system, mainly through the optimization design of the transmission mechanism. Owing to the differential synthesis of the micro feed from the upper and under linear motors, the impact of friction nonlinearity during the ultra-low velocity micro feed is avoided, endowing the system with a lower stable feed speed to achieve precise micro-feed control. (2) Methods: Transmission components of the dual linear-motor differential-drive system are analyzed using the lumped parameter method, and a dynamic model of electromechanical coupling is created, which takes into account nonlinear friction. The motion relationship of the dual linear-motor differential-drive servo feed system is characterized using a transfer function block diagram. (3) Discussions: Through simulation, the differences in response between the linear-motor single-drive system and the dual linear-motor differential-drive system are examined under fixed or variable feeding velocities as well as the impact of varying velocity combinations of dual linear motors on the output speed of the differential drive system. (4) Results: Nonlinear friction factors exert an impact on the feed velocity of both linear-motor single-drive and dual linear-motor differential-drive systems during low-velocity micro feed. However, regardless of the constant or variable speed conditions, the dual linear-motor differential-drive servo system significantly outperforms the linear-motor single-drive system regarding low-velocity micro feed. Our simulation results are basically consistent with engineering practice, thus validating the rationality of the created system models, which paves the ground for the micro-feed control algorithms.